National Academies Press: OpenBook

NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report (1997)

Chapter:3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials

« Previous: 2 Resilient Modulus Testing of Asphalt Concrete
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page97
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page98
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page99
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page100
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page101
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page102
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page103
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page104
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page105
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page106
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page107
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page108
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page109
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page110
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page111
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page112
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page113
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page114
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page115
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page116
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page117
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page118
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page119
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page120
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page121
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page122
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page123
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page124
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page125
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page126
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page127
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page128
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page129
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page130
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page131
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page132
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page133
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page134
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page135
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page136
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page137
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page138
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page139
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page140
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page141
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page142
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page143
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page144
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page145
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page146
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page147
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page148
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page149
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page150
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page151
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page152
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page153
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page154
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page155
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page156
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page157
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page158
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page159
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page160
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page161
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page162
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page163
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page164
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page165
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page166
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page167
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page168
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page169
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page170
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page171
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page172
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page173
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page174
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page175
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page176
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page177
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page178
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page179
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page180
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page181
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page182
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page183
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page184
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page185
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page186
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page187
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page188
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page189
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page190
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page191
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page192
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page193
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page194
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page195
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page196
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page197
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page198
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page199
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page200
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page201
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page202
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page203
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page204
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page205
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page206
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page207
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page208
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page209
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page210
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page211
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page212
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page213
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page214
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page215
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page216
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page217
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page218
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page219
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page220
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page221
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page222
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page223
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page224
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page225
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page226
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page227
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page228
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page229
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page230
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page231
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page232
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page233
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page234
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page235
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page236
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page237
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page238
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page239
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page240
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page241
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page242
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page243
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page244
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page245
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page246
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page247
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page248
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page249
Suggested Citation:"3 Resilient Modulus Evaluation of Aggregate Base and Subgrade Materials." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
×
Page250

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

CHAPTER 3 RESILIENT MODULUS EVALUATION OF AGGREGATE BASE AND SIJBGRADE MATERIALS INTRODUCTION Resilient modulus, when used In a layer system analysis, is a very important variable in predicting the resilient (i.e., recoverables stress, strains and deflections in a flexible pavement. In an unstabilized layer, the stress or strain can be related to permanent deformation provided the permanent deformation properties of the material are known. Resilient moduli are also now used in the AASHTO design method even though it is statistically based rather than based on mechanistic design principles. By the year 2002 a mechanistic based AASHTO design memos should be available. The widespread use of resilient moduli in pavement thickness design indicates the importance of obtaining reliable values of this design variable. A primary objective of this study is to develop laboratory resilient modulus testing procedures suitable for use by a state transportation agency. To help achieve this goal, the emphasis of the study was placed on evaluating the effects on resilient modulus of laboratory testing details such as equipment calibration and testing conditions. A limited amount of effort was also devoted to the permanent deformation characterization of base and subgrade materials. Permanent deformation characterization of all layers is as important, or even more important, than resilient modulus characterization. Permanent deformation can be measured as an extension of the resilient modulus test with little extra effort. Based on a Borough review of the literature, He repeated load, biaxial test was selected to characterize in this study the resilient modulus of unstabilized base and subgrade soils. RESILIENT MODULUS CONCEPI The resilient modulus is equal to the peak applied axial repeated stress (Figure 3a) divided by He recoverable axial strain occurring within the specimen. The resilient axial strain is equal to the recoverable deformation (bounce) which the specimen undergoes when subjected to one pulse, divided by the axial distance over which the bounce is measured. The resilient modulus (MR) IS calculated as MR ((~1 ~ 031/~Ir (5) where: MR = (] 1-~3 ~_ 'or resilient modulus maximum repeated axial stress (deviator stress) maximum resilient axial strain 97

In addition to being called MR, the resilient modulus is also sometimes called Er or just the modulus of elasticity (E). In the repeated load test, and also other dynamic tests, the applied peak stress occurs before the peak strain develops and hence stress and strain are said to be out of phase with each other. Because stress and strain are out of phase with each other, the resilient modulus concept is an approximation. The resilient Poisson's ratio (ur) is determined by _e ~2 -fir ~r where: v. = ~_ Or ~1 resilient Poisson's ratio resilient radial strain resilient axial strain (6, Once the resilient modulus and resilient Poisson's ratio have been evaluated, other dependent elastic constants can be calculated. For example, resilient bulk modulus (K) and resilient shear modulus (G) can, if desired, be calculated using the following equations: MR G = 2(1 +V ) MR K - 3( 1 -2vr) The above equations assume linear elastic response. RESILIENT MODULUS LABORATORY TESTING METHODS (7) (8, The resilient modulus of pavement materials can be evaluated in the laboratory using the following different types of repeated load and cyclic laboratory testing equipment: (~) biaxial cell, (2) simple shear device, (3) resonant column/torsional apparatus, (4) hollow cylinder, and (5) true biaxial cell. These tests all have potential, under certain conditions, for characterizing both stabilized and unstabilized pavement materials. A brief general discussion of this equipment is therefore presented including advantages and disadvantages with regard to resilient modulus testing. Triaxial Cell Advantages. The biaxial test offers three very important advantages in resilient modulus testing: 98

2 Stress State. In the biaxial test known principal stresses a, and 03 are applied to the specimen In known directions as illustrated in Figure 46. As a result, the stress conditions within the specimen on any plane are also defined throughout the test. The stress conditions applied are, in fact, those which occur when an isolated wheel loading is applied to the pavement directly above We element of material simulated in the test. Spec~mea;;)rainage, Use of Me biaxial test allows relatively simple, controlled drainage of the specimen in He axial and/or radial directions. If desired, lateral drainage occurring in, for example, a granular base can be simulated reasonably easy in the biaxial test. Pore pressures can also be easily measured at the ends of the specimen or, with more difficulty, within the specimen. Strain Measurement. Axial, radial and volumetric strains can all be measured relatively easily in the biaxial test. In addition to the above advantages, undisturbed tube samples of the subgrade obtained from the field can be extruded and tested with a minimum amount of specimen preparation. Finally, the biaxial cell used for the repeated load biaxial test can also be employed in static testing. Disadvantages. The most important disadvantage of the biaxial cell is its limited ability to handle (~) rotation of the principal stress axes and (2) shear stress reversal. Only a fixed orthogonal rotation of principal stress axes are possible in this test. Both of these limitations of the test come into play when a wheel load moves across the pavement. Also, the intermediate principal stress applied to a specimen cannot be controlled in the biaxial test. Careful equipment calibration is required, which is especially critical when applied strain is measured outside the cell. Use. The repeated load biaxial compression test has for about the last 35 years been used as the basic testing apparatus to evaluate the resilient modulus of cohesive and granular materials for pavement design applications [361. Early repeated load tests on stabilized materials were also conducted using the biaxial test [37, 381. The repeated load biaxial compression test is relatively straightforward to perform compared to most other alternatives, and it reasonably closely simulates the conditions encountered in the field. Triaxial Cell Design. Conventional Cell -- The conventional biaxial cell, which has external tie rods to hold the cell together, has traditionally been used in resilient modulus testing. In this type cell the tie rods are located on the outside of the biaxial chamber (Figure 471. To form a seal in the conventional cell, circular flat gaskets or rubber "0" rings are located between the chamber and the top and bottom of the biaxial cell. If flat gaskets are used, the nuts on the tie rods should be tightened evenly using a torque wrench. Uniform tensioning of the rods insures Me load remains properly aligned. If "0" rings are used the seal should be designed to allow the top and bosom plates to contact the chamber. Triaxial Cell wig Internal Tie Bars -- An alternative to the conventional biaxial cell design has the tie bars located on He inside of the chamber. In a cell having internal tie bars, the top of the cell is supported by the tie bars through machined, steel to steed contact. Both the conventional and internal tie bar type cells require careful machine work to insure accurate alignment. No big advantage appears to exist for either cell. Bishop-Wesley Type Cell - The Bishop-Wesley type biaxial cell, developed for static stress path testing, is completely self~ontained and does not require a separate load frame [39]. This biaxial cell uses 99

Total Axial Stress, cr' (major principle stress) a' - Al = Repeated (Cyclic) Deviator Stress Shear Stresses ~ = 0 tS3= Confining Pressure (minor principle stress) - Note: () = a1 + Cr2 + o3 = C7d + 3<s3 Figure 46. Stresses Applied to a Triaxial Specimen VERNAL L~ LL ~ _ it_ COP COUNTED LV9T TEST SPECIlI£N SPEOM£N ~£MBRANE - E=E~ SENECA _= 5 ~ = 3 ~ , ~ RUBBER GASKET // COW ~ ~O" Rid SEAL LVDT AND LOAD , ~w~- 1 _ ~ _ - ~ ~SUREhIENT REFERENT (~D ~ Ala ~' -_ _ THOMPSON BEAR aonoN siennas _ RU8SER ~ _ LO" ~1 DONNA _ LOAD to ~ -_ nE ROD _ LVDT CAMBER _ ALU - ~ - ~ - BRONZE POROUS So - ~ AWE ~ Figure 47 . Triaxial Cell Used to Test Base Materials 100

external tie bars, acne load is applied to the specimen hydraulically through the base of the cell. The toadying ram is guided by a linear bearing. Two rolling diaphragm seals separate the hydraulic loading fluid from the chamber fluid. ---on - - or --- cow - - r ~ ~ - - -- - --a ~o In the Bishop-Wesley type cell, the axial stress (ok and confining pressure (~3) are controlled ind~ernend~ently of each over. Independent control in the conventional triaxiad cell can also be accomplished by making the load rain diameter He saline as the specimen and using a rolling diaphragm to form the seam. Self~ontainment, together with the ability to nan stress paw tests, appear to be ache advantages of this type cell for routine resilient modulus testing. This cell has not been used for rapid cyclic loading, and some problems have been encountered in slow loading due to the diaphragm pulling out. Torsional Shear/Resonant Column Test Torsional Shear. The torsional shear test subjects a cylindrical specimen of material to a cyclic torsional shear loading (Figure 48~. The bottom of Me specimen is considered fixed while the top of the specimen is connected to a drive system that generates torsional motion. In the torsional shear test, the frequency of loading is generally less than 10 Hz. The modulus is determined from the shear stress-shear strain hysteresis loop. The torsional shear test can be used to determine moduli at shear strains up to about 10-3 in/in. For moderately thick pavement sections and/or weak materials, the shear strains developed under typical heavy wheel loadings can be greater than the capability of the test apparatus. The torsional shear apparatus is, however, relatively easy to calibrate, and the test straightforward to perform. The drainage condition of the specimen is not as well defined as in the biaxial test. The applied strain level beneath a pavement is smaller in the subgrade than the base. Hence, the test is most attractive for testing subgrade soils. Furler consideration of adapting this test for subgrade testing appears to be desirable. Resonant Column. The resonant column test [401, which is somewhat similar to the torsional shear test, subjects the specimen to cyclic axial strains considerably smaller than applied by heavy wheel loadings near the surface. Hence the resonant column test is not suitable for testing highway materials unless empirical corrections for strain level are applied to the measured moduli. Simple Shear In the simple shear test, shear stress is applied to the top and bottom of either a square block or disk shaped specimen as shown in Figure 49. In the repeated load simple shear test, shear stress is applied alternately in each direction. This loading condition results In a fixed O to 90° principal stress axis rotation and accompanying reversal of shear stress. Since shear stress reversal occurs in the field, the simple shear test is more realistic than the repeated load test with regard to permanent deformation. The stress paths occurring in the field due to application of a moving wheel load, however, are not faithfully reproduced in He simple shear test. The general effects of principal stress axis rotation and shear stress reversal can be studied using the simple shear test [4l, 421. Resilient shear moduli determined on sand using the simple shear apparatus and the repeated load biaxial compression test have been found to be similar at comparable stress levels [411. In ache simple shear test, however, permanent strain continued to logarithmically accumulate for 100,000 repetitions. 101

Torsion ~ cy3 ~3 . ~ ~17~ - l - c73= Confining Pressure Figure 48 . Stresses Applied in a Cyclic Torsional Shear Test \^ is ~ ~ ~ ~1~" ~ ~ /~ (a) Shear to leD = Applied normal stress ~ = Applied shear stress y = Shearing strain Shear ModulUsG=7ly 'a r OTT -r 7 -' ~ ~ ~ '. ~ ~ ~ ~ ~ ~ ~ ~ Speclmen' ~ ~ ~ ~ \\r\- (b) Shear to nght Figure 49. Stress Applied in Cyclic Simple Shear Test 102

Very little change In permanent strain occurred in the repeated load biaxial test after 10,000 to 20,000 load repetitions which is not true in a pavement. Thus, the permanent strain when stress reversal occurs is greater, and the behavior quite different than In the repeated load biaxial compression test. This difference in permanent strain behavior is explained by stress-rotation induced "anisotropy". Arther, et al. [43] have developed a "directional shear cell" for studying stress induced anisotropy. The directional shear cell, which is more complex, apparently overcomes the limitation of the conventional simple shear apparatus , , ~ , , , which applies only a fixed rotation to the specimen. Conceptually, He simple shear test is easy to perform. In practice, however, applying a uniform shear stress distribution to the top of the specimen and Inducing uniform deformation has frequently caused problems [421. Also, the complex stress state to which the specimen is subjected is not easy to evaluate [411. The simple shear test has been used on a limited basis for a long time, but because of these disadvantages has not become well accepted for either static, cyclic or repeated load testing. The simple shear test does offer an attractive alternative for evaluating permanent deformation under more realistic stress reversal conditions than the repeated load biaxial test. The test, however, is not considered to be suitable for routine resilient modulus testing of pavement materials. Hollow Cylinder Test The hollow cylinder test can more closely simulate the complex stress conditions, including principal stress axis rotation, to which pavement materials are subjected than either He biaxial test or the simple shear test [441. In this test a moderately ~ick-walled, hollow cylindrical specimen is used as shown in Figure 50. Because of the limited wall Sickness, material particle size is limited to about a coarse sand size. Both the inside and outside of the specimen is enclosed by a membrane. In addition to being able to vary the axial and torsional stress, the pressure on the inside of He hollow cylinder can be varied relative to He outside cell pressure, thus changing the tangential stress within the specimen. The hollow cylinder test, because of its great flexibility In applying different stress paths, offers a valuable tool for advanced research into pavement material characterization. The hollow cylinder apparatus appears particularly suited to investigate permanent deformation under stress states simulating moving wheel loads. Because of the complicated test apparatus required, extensive instrumentation and complicated specimen preparation, the hollow cylinder is not suitable for routine resilient modulus testing. True (Cubical) Triaxial Device The true biaxial device tests a cube-shaped specimen and is capable of independent control of each of the three orthogonal normal stresses applied to the specimen. Only two of the normal stresses are controlled in tests using standard biaxial, simple shear, and plane strain devices. True biaxial apparatuses have been built wig either rigid platens or flexible membrane boundaries and have been used on both sand and clay materials. The cubical device can be used to investigate the influence of intermediate principal stress, initial stress anisotropy, strength anisotropy, and stress invariants [451. Because of its complexity, however, the true triaixal device is not suitable for routine repeated load biaxial testing. 103

Hydraulic Pressure Supply l r ~ ~ By ~ _ L A -AL _ _ LiT I 1 1-=__ ~1 . .... ll l - : ~ ~ . . . ~ . I.D. _ _ O.D. _f 500 mm (19.7 in.) Steel- Frame Serv - Controlled Hydraulic Actuator Slip Coupling - Smoothing Bush Load Cell Top Plate Top Platen (toothed) Hollow Cylinder Specimen Bottom Platen (toothed) I. De = Intemal Diameter 224 mm (8.8 in.) O. D. = Outer Diameter 280 mm (! I.0 in.) Figure 50. Stresses and apparatus used for hollow cylinder test (after Reference 44) 104

GRANULAR MATERIAL RESILIENT MODULUS MODELS The resilient modulus of unstabilized granular base and subgrade soils is highly dependent upon the stress state to which the material is subjected within the pavement in addition to other variables. As a result, constitutive models must be used to present laboratory resilient modulus test results, including the effect of stress state, in a form suitable for use in pavement design. This section summarizes resilient modulus models presently used for granular materials. The accuracy of selected granular material resilient modulus models is examined later in this chapter. K-O Mode} The K-8 model, summarized in Table I8, in the past has been overwhelmingly the most popular nonlinear resilient modulus model. This mode! expresses resilient modulus as a function of He bulk stress (~) to which the specimen is subjected. The bulk stress (~) equals Be sum of the principal stresses (~+~2+~) acting on Be specimen. Me experimentally determined relationship between resilient modulus (MR) and ~ is a straight line on a log-Iog plot. As a result, the constants K, and K2 used in Be K-O mode] can be readily obtained using a linear regression analysis of the log MR ~ log ~ data. May and Witczak [46] and later Uzan [4] have pointed out the most serious drawback of the K-O mode! is neglecting He important effects of shear stress (Figure 51a). Other modifications of the K-8 mode} have used the minor principal stress (~3) rather than ~ and also a stress ratio term to consider behavior at stress levels above the static failure stress [41. Simple Models that Consider Shear Stress Effects Uzan Model. Uzan [41 developed a mode] that considers both bulk stress (~) and He deviator stress (od)- The deviator stress is directly related to He maximum shear stress (Im) applied to the specimen (i.e., Tm = O`' /2~. The Uzan mode} (Table ~ 8) therefore overcomes the most serious deficiency of the K-0 model: not considering shear stress effect. The Tree material constants K3, K4 and Ks given in Table IS must be evaluated by multiple regression analysis from a sequence of repeated load resilient modulus tests. The stress sequences specified in either the AASHTO T292, AASHTO T294, or SHRP P46 test methods can, for example, be used to evaluate the constants in the K-O and Uzan models. The relatively good agreement between laboratory resilient moduli and the Uzan mode! is shown in Figure Sib. The Uzan mode} also exhibits quite good agreement with the considerably more complicated contour mode} of Brown and Pappin [481. Octahedral Shear Stress. Witczak and Uzan [491 modified the original Uzan mode! by replacing the deviator stress wig octahedral shear stress which is a more fundamental parameter. The bulk stress and shear stress were also normalized using atmospheric pressure. Since deviator stress and octahedral shear stress are proportional, the two models should have the same accuracy. UT-Austin Model. The University of Texas-Austin mode} [50] uses confining pressure instead of the bulk stress employed in He Uzan mode] (Table Age. Me K-D mode! is not statistically sound since the resilient modulus is related to the deviator stress (oaf) which is hidden in the prediction variable bulk stress (O = O] +~2+~3 = O~ +3CT31. The UT-Austin mode! overcomes this problem by using as response the axial strain (ea) instead of the resilient modulus, and by using as independent predictors the deviator stress (~: and the confining pressure (~3~. 105

Table IS. Resilient modulus models used in the experimental data analysis MODEL | MODEL | LINEAR REGRESSION MODEL PLOT EXPRESSION USED K-8 I M,` = KI8K2 I Log Me= LogK, + K:Log' Log MR VS . UZAN Ml = K3yc4(a~)K ~Log MR= L~gK3 + K.Log~ ~ K5Logo ~Log MR VS M,,- N6a~N7a3N' Log M,' VS N. = K6 = 10. Log al UT-AUSllN N1 = 1- K? LogC. = a + K] Legal + K,LO8~3 Or N. = -K, Log M,, VS {TrEP M' = K' SKIS, Kll LOB Me = l~gK' + KloLog' ~* Log M,` vs l | K.' Log`, Log' l 106

6 O ' ·_ C - :' - o ._ - ._ Cat Is 3 2 1 O . ., - lt .tl~ll - . ''tt't' 620pt~>- if/ lo--. 7-~ $; ,~C, 10 5-- -~ 7.5 I - C~a,~ Legend · · Test Results ~ ~ ~ K-D Equation ~ ~ tatted ~ ~ ~ ~ Al -. 1o-s 10 ~ 10-3 Axial Vertical Strain (a) K-8 mode} B _ STATE ~ T L l · 1~ DGA-LS-2~) ~ ~ 5 ~ \: ~ P: ~3p~' I__ 2 - Legend . . Experimental Results ~ - - ~ Uzan's Equation 1 I , ~ t · ~ l ~ ~ t"'J o-s 10 ~10-3 Axial Vertical Strain (b) Uzan model Figure 51. Test results and predicted behavior using K-8 and Uzan models for a dense-graded aggregate (af ter ref erence 4) 10/

The SHRP P46 test (June, 1996) procedure uses a (! - o3) term rather than the CJ3 term shown for the UT-Austin method. This slight modification should not have any practical effect on the calculated resilient modulus. Either the UT-Austin or the SHRP P46 (1996) approach give good results. UTEP Model. The University of Texas-E} Paso (UTEP) mode} [50] uses bulk stress and axial strain as He predictor variables (Table I8~. Since resilient modulus equals the repeated deviator stress (~- O3) divided by axial resilient strain, in reality strain in ache UTEP mode! is present on both sides of the equation. From a statisticians viewpoint, the UTEP mode! is therefore not as sound of a formulation statistically as the UT-Austin model. The statistical accuracy of these models is examined later using experimental results. Four Parameter Model. Itani [511 modified the original Uzan model by adding in the effect of confining pressure (03) and changing the bulk stress to mean stress. Only very slight improvement was observed compared to the original Uzan equation which has 3 constants. Advanced Models A number of advanced resilient modulus models have been proposed for granular material. Most of these models require special instrumentation and/or tests, and the material constant evaluation is usually complicated although a better resilient modulus characterization is obtained. As result, they are not in general considered practice! for routine use but offer excellent research tools. Therefore, only a brief review is given of these models. K-G Model. Boyce [521 proposed a nonlinear K-G mode! based upon the secant bulk modulus (K) and the secant shear modulus (G), which are both functions of the stress state. When corrected to conform to Maxwell's reciprocal theorem, reasonably good results were obtained compared with measured resilient moduli. To simplify the Boyce model, louve, et al., [53] used different relationships for the bulk modulus (K) and shear modulus (G) and neglected dilatancy (i.e., volume change effects). Contour Model. The contour model, developed by Brown and Pappin [48], extended the earlier work of Boyce [52] to show that the length of stress paw followed influences the resilient modulus in addition to He mean normal stress and the shear stress. The application of the stress path concept requires a special biaxial testing apparatus Hat permits simultaneously varying He axial and confining pressure in a predetermined manner. The contour mode] relates He starting point and the end point of a stress path to the shear and bulk moduli. A good representation of observed resilient response is obtained using the contour mode' which fits nicely observed shear and volumetric strains, but resilient modulus testing is complicated. Thom [541 extended the work of Brown and Pappin [481, once again separating the response into resilient shear and volumetric strain components. Thom, however, used principal stresses and shear stress to develop a new model. This mode} shows quite good agreement with the resilient behavior of granular materials, but has the serious practical drawback of requiring the evaluation of 8 material constants. Crockford, et al. Model. Crockford, et al. [55] proposed a four constant model expressing the resilient modulus as a function of volumetric water content, soil suction stress, previously discussed octahedral shear stress, material unit weight, and bulk stress. No verification or basis of model development was presented. The model does simplify to the octahedral shear stress mode! upon neglecting suction stress, water content and material weight effects. 108

COHESIVE SUBGRADE SOIL RESILIENT MODULUS MODELS The resilient modulus of cohesive subgrade soils (i.e., fine "rained materials which exhibit plasticity) is dependent upon the deviator stress and moisture content as illustrated in Figure 52. Figure 52 gives the resilient modulus as a function of the number of load repetitions at different stress levels for compaction moisture contents above and below the optimum value. The axial stress level (SL), which is proportional to deviator stress, is given as a percent of the static failure stress of He specimen. For the same stress level, the resilient modulus decreases with increasing moisture content but remains nearly constant with increasing number of load repetitions. The influence of confining pressure on plastic subgrade soils is reasonably small but becomes increasingly important as He plasticity approaches zero (i.e., a granular material). Bilinear Mode! For many slightly cohesive and cohesive fine-grained soils, the resilient moduli obtained from the repeated load biaxial test can be modeled as a bilinear function of the applied deviator stress. Confining pressure is held constant in this model. The bilinear behavior, which is illustrated in Figure 53, can be expressed as follows: MR = K12 + K14 (KI3 (~d) when o~ < K13 MR = K12 SKIS (~-Kl3) when o~ > Kl3 (9a) (9b) where Kl2, Kl3, Kl4, and Kls are material constants obtained from laboratory repeated load tests. As indicated by Thompson and Elliot [561, the value of the resilient modulus at the breakpoint in the bilinear curve (as = K12 in Figure 53) can be used to classify fine-grained soils as being either soft, medium or stiff. The bilinear mode! has been in the past very popular for modeling low to moderate plasticity soils. This model works quite well when presenting resilient modulus results for a test performed at a single confining pressure. The important disadvantage of the mode! is Hat confining pressure cannot be considered, except by using a different bilinear mode! for each confining pressure. A simplification of this type leads to problems in using the models in a nonlinear analysis. Power Mode! A simple power mode! characterizing the resilient characteristics of cohesive soils relates the resilient modulus (MR) to the deviator stress (~: as follows 1571: MR KI6 O~ where Kit and K,7 are material constants. This mode} does not consider the effect of confining pressure and yields a stress softening effect (i.e., the resilient modulus decreases with increasing deviator stress ~- 109

20 15 10 o · SL-25% · SL-75% ~ SL=85% a. . 1 - 1 10 100 Number of Cycles, N (a) Dry of Optimum - 1 000 1 0000 20 15 10 - . . · SL=25% · SL-50% · SL=60% . ~ _ ......................................... 1 1 0 1 00 1 000 1 0000 (b) Wet of Optimum Number of Cycles, N Figure 52. Resilient Modulus of Compacted A 6 Cohesive Soil 110

is - - o A: · _1 - · c~ \ L K14 Kl3 · l _ Kl2 Kls Deviator Stress, Od Figure 53 . General relationship between resilient modulus and deviator stress for fine-grained, cohesive soils 111

Brown and Loach Models Brown [58] proposed a nonlinear resilient modulus mode} for the subgrade which considers bow deviator stress and the effective mean confining pressure. This mode! was later improved by Brown, et al. [591 and is as follows: ME = Keg o~ (P°~9 `~' ad where: a, = deviator stress caused by the-wheel loading p'O = effective mean confining stress caused by the overburden, P 0= ((it + o2 + 031/3 K,~ and Kit = material constants evaluated from the repeated load test Both models take into account in a realistic way the effect of mean normal stress caused by the pressure of the overlying materials and also by the wheel loading. This approach minimizes We problem of increasing deviator stress (ad = ol-03) and mean confining pressure ~tO) in a deep subgrade layer due to the increase in overburden stress. The improved mode} is well suited for use in a nonlinear analysis since both deviator stress and confining pressure are considered. Thompson and Robnett [601 have also proposed a mode! of this type which shows stiffening at higher deviator stress levels. Soil Suction Soil suction causes an increase in effective stress in a subgrade or base as the material dries out. The increase in effective stress can cause a significant increase In resilient modulus. Soil suction decreases as the degree of saturation increases and is not present when the soil is saturated. To mode] soil suction correctly, He soil has to be compacted at higher water content than desired and Den allowed to dry out. REPEATED LOAD TRIAMAL TEST General Test Description The repeated load biaxial test offers one of the best ways of evaluating in ache laboratory the resilient modulus of highway base, subbase and subgrade materials. The repeated load test was therefore used in this study. In the repeated load biaxial test, a cylindrical shaped solid specimen of material is subjected to repeated axial compressive stresses having a short rest period between stress pulses (Figure 3a). This type loading approximately simulates stresses caused by multiple wheels moving over the pavement. To simplify Be test, Be specimen is usually subjected to a constant all-around confining pressure (~3) simulating Be lateral stress caused by Be overburden pressure and applied wheel loadings. Me cylindrical specimen is placed inside a biaxial cell on top of a rigid base Figure 47~. A rigid platen 112

containing a porous stone is then placed on top, and the specimen is enclosed by a rubber membrane. Cohesionless materials are usually compacted directly on top of the base inside a mold. A cylindrical Plexiglas chamber is then placed around the specimen, and the specimen is subjected to repeated loading. Triaxial Compression Stress State. In the biaxial test, the top and sides of the specimen are assumed not to be subjected to shear stress (Figure 46~. Since these planes do not have shear stresses, by definition, they are principal planes. As a result, the total axial compressive stress applied to the specimen, which is larger Man the condoning stress, is called the major principal stress (ok) since it is larger than We confining stress in Me conventional test. A constant cell pressure usually remains on the specimen in the axial direction throughout the test. The repeated stress is applied in the axial direction in addition to the constant confining pressure (~3) and weight of the top platen. Therefore the repeated axial stress is called the deviator stress (o, - o3 or oh, and is numerically equal to the difference between ache maximum applied axial stress (o,) and the constant axial stress which consists of He confining pressure (03) and the weight of the top platen. Lateral specimen support is provided by the confining pressure (as) which acts in both He radial and axial directions (refer to Figure 461. The stress inside the specimen acting at right angles to the radial direction is called the tangential stress which is He Intermediate principal stress (02~. The tangential stress Ale) is usually assumed to be equal to the confining pressure (~3~. Ibis assumption is actually true only along the axis through the center of the specimen. The bulk stress Aid, also called the first stress invariant, is equal to o~ + o2 + O3. For the biaxial test the bulk stress (~) then becomes ~ = a, + 2~3. Variable Confining Pressure The lateral pressure applied to an element of material beneath the pavement gradually increases as a vehicle approaches and Hen decreases as the vehicle moves away. Resilient modulus tests simulating this condition by using a variable confining pressure have been performed on granular base and sands [6, 71-731. The theory of elasticity equations for calculating resilient moduli when a variable confining pressure is used have been given by Brown and Hyde [611. Brown and Hyde [61] concluded for granular materials that using the mean value of confining pressure (~3) in a repeated load test with constant 03 adequately simulates variable confinement for measuring resilient modulus. Poisson's ratio, however, cannot for granular materials be reliably estimated using the mean constant confining pressure to approximate variable confinement. Vacuum Triaxial Test The vacuum biaxial test, used by Sweere [64] for aggregate base, is an interesting variation of the drained repeated load biaxial test memos. In He vacuum test a cylindrical sample having top and bottom end platens is enclosed by a rubber membrane, and rests on a base plate of a loading frame. Rather than using a conventional biaxial chamber, however, the confining pressure is applied by reducing the pressure on the inside of He specimen by applying a vacuum of known magnitude. The important advantage of the vacuum biaxial test is that a cylindrical pressure chamber is not placed around the specimen, and the ram of the loading system applies load directly to the specimen through the top platen. Also, easy, 113

unobstructed access to the specimen is possible which is not true when the specimen is enclosed by We conventional biaxial chamber. The disadvantage of the vacuum biaxial test are: I. The maximum confining pressure is limited to about 10 to 12 psi (less then atmospheric pressure which is about 14.7 psi). For base and subgrade materials the applied confining pressure in the field is less than this value and hence this is not a disadvantage. Specimens cannot be tested in a saturated condition, and problems of moisture migration could occur particularly at high degrees of saturation and high vacuum levels. These problems with moisture are an important disadvantage if We effect of moisture variation on Mr is desired. Nevertheless, the vacuum trivial test offers an attractive alternative to the conventional repeated load tripodal test. This Is particularly true if optical methods of axial deformation measurement are used which are discussed in the next section. . Justification. The vacuum biaxial test should be performed at (or near) the optimum moisture content where the moisture within the specimen is continuous. The effective moisture radii of curvature of the meniscus widen the specimen is a function of the moisture content and soil structure (effective pore size, void ratio, etc.~. The soil structure for a similar specimen prepared for Be conventional drained biaxial test and the vacuum biaxial shear test is virtually Me same for stiff base materials. To maintain equilibrium across the meniscus, the pressure difference is inversely proportional to the effective meniscus radius. The pressure difference is not influenced by the pressure on the inside of the specimen. Therefore, for similar specimens and hence similar moisture contents and meniscus radii, the pressure difference across the meniscus should be the same for the conventional and vacuum shear tests. As a result, the effective confining stress applied to the specimen in each test is virtually the same. The effective confining pressure is equal to the applied vacuum (or externally applied 03) plUS the developed capillary stress. GRANULAR BASE EXPERIMENTAL STUDY AND FINDINGS This section evaluates various factors affecting the laboratory measurement of the resilient modulus of aggregate bases using Me repeated load biaxial test. These results are also applicable to cohesiontess (sand) subgrade materials. This study includes evaluating the effect on resilient modulus of measuring axial displacement at different locations on Me specimen, specimen preparation and saturation, preconditioning, stress pulse shape, oversize aggregate, quasi-static testing, and permanent deformation characterization . Resilient Modulus Testing Apparatus Repeated load testing to evaluate the resilient modulus in this study was performed using 6 in. diameter by 12 in. high specimens However, a limited number of tests were performed using 12 in. diameter by 24 in. high specimens to assist in determining the influence of scalping and replacing large top size aggregate. The 15 stress states used in resilient modulus testing are shown in Table 19. The resilient deformation was measured and averaged for the last 5 load pulses for each stress state. A 0. ~ sec. 114

duration haversine load pulse was applied with a rest period between pulses of 0.9 sec. The testing procedure used, except as noted, was similar to that given by SHRP P 46, November, 1989 [65]. A conventional large biaxial cell was used for the 6 in. diameter specimens which has a Plexiglas chamber wig a 14 in. inside diameter (Figure 471. A 5000 lb. capacity flat load cell, non-fatigue rated and mounted inside the biaxial cell on top of the load piston, was used in the electrohydraulic feed-back of the MTS loading system to monitor the actual load applied to the sample. This load cell has an output of 3-mV/V and a resistance of 350 Ohms; it was never loaded to more than 50% of its rated capacity to avoid fatigue. A storage oscilloscope was used to set the gain on the closed-Ioop testing system to obtain the correct load pulse shape. Specimen confinement was provided by air pressure which was measured using a pressure gage having 0.2 psi divisions. Data Acquisition System. A 12-bit data acquisition system (a/d board and 16 channel back plane) was used to measure load and displacement. Maximum permissible excitation voltages were used or slightly exceeded to give maximum sensitivity of the transducers. Proprietary software was used to control data acquisition and store the digital data in a 486 PC. For most of this study, 4096 data points from each channel were collected at a rate of one data point each I.5 ms. Thus, 666 data points were collected during the application of a ~ sec. load pulse. Sample Preparation Equipment Compaction Mold. A three piece split steel compaction mold was used In preparing the aggregate base specimens. The mold was assembled directly on top of the base plate, a 0.025 in. thick latex membrane was placed inside the mold, and the specimen was then formed directly on the base. A vacuum suction was used to hold the membrane to the wall of the mold during compaction. A biaxial membrane stretcher was used to place a second latex membrane on the compacted specimen when the first one was punctured during compaction. Vibrating Hammer. A heavy-duty ISamp electric-vibrating hammer applying 2000 blows per minute was used to vibro-compact the granular material in the mold. A 5.75 in. diameter steel plate was placed inside the compaction mold on top of each loose compaction lift. Each layer was compacted until the required density was obtained as indicated by measuring the distance from the top of the mold to He top of the layer at 4 equally spaced locations. A small spirit level was placed on top of He compaction plate to insure each lift was parallel. The smooth surface on top of each lift was lightly scratched to achieve good bonding wig the next lift. The surface of the final lift was made at right angles to the axis of the specimen by compacting it using a specially machined "T" shaped plate which bottoms out on top of the mold at the required specimen height. A platform mounted on 4 wheels, which moves up and down by hydraulic jacks, was used to transport the specimen from where compaction was performed to the loading frame without causing specimen disturbance. The platform was then raised, and the biaxial cell was carefully slid onto the loading frame. 115

Table 19. Standard stress conditions used in resilient modulus test TEST ON FIN IN G DEVIATOR N O. BULK SEQUENCE PRESSURE STRESS LOAD STRESS NO. as (PSI) at - ~3 NISI) APPLICATIONS e use iS 15 _ 1 3 3 100 12 2 3 ~1W 15 3 3 ~1 - 18 4 5 100 20 10 1 - 2S 15 1 - to 10 100 8 10 20 100 tiO ~10 ~1 - ~ 10 15 10 100 55 11 1S 15 100 60 12 15 30 100 75 13 20 100 7S 14 20 20 100 80 15 100 100 Table 20. EVDT displacement transducer characteristics ID l LVDT | Type | Linearity | Linear | Se ~ibvi~ _ ExrERNAL i 0.20% full range i 0.0042 Max 2.0 mV/V in. (2.5 Khz) (F.R.: i 0. lOin.p) - i 0.0320 MA /0.001 in. 2a ~ 0.2sa6 full range i 0.020 Max 1.3 mVlv in. INTERNAL (2.5 Khz)( ~(F.R.: i 0.25 in.) i 0.073 Mm /0.001 in. fib TOP-BO11OM ~ 0.1096 Fill range i 0.00074 Max 4.1 mV/V in. (2.5 Khz)~° (F.R.: ~ 0.05 in.) i 0.0056 Min /0.001 iN. 38 1 I I i 0.2596 filll r tge 1 i 0.0071 Max 1 2.1 ~ V/V ill. INTERNAL (10 Khz)( ~BIER.: ~ P.25 m.) ~ 0.052 Min 10.001 m. 3b CLAMPS j: 0.20% filll range ~ 0.00049 Max 2.8 mV/v in. _ ~(10 Kh7~)t5, (F.R.: :t 0.1 m.) ~ 0.00363 Min /0.001 in. Note: 1. Maximum gain in the Analog Devices 3B17~1 module. 2. Minimum gain in the Analog Devices 3B1701 module. 3. F.R.= Nominal linear All range of the LVDT. 4. LVDT's used with Origmal Testing Setup Synthetic, SHRP, and GT BASES (1, 2, 3, 4) Speciemn Tests. 5. LVDT's used with Improved Testing Send GT BASE (100, 200, 300) & Stabaliz~ BASE (1 and 4~. 116

. Equipment Calibration EVDT Calibration. All of the EVDTs used in the experiments CTable 20) were calibrated periodically using a calibration stand having I/1000 in. divisions and a ~ in. displacement calibration range. The LVDTs were calibrated at maximum, intermediate, and minimum levels of output signal gain to allow testing specimens with different stiffness by only changing the gain. Load Cell Calibration. The 5,000 Ib. flat load cell used in testing the 6 in. diameter specimens and the closed-Ioop range card were calibrated together in a calibration laboratory for all four load ranges available on the testing system. This calibration was periodically verified using a 4500 Ib. reference proving ring as a standard. Testing System Alignment and Compliance. Equipment compliance errors (i.e., unwanted movement in Me system) and also alignment errors significantly affect the measured values of resilient modulus. Great caution was therefore taken to identify and minimize these errors. The recommended procedures given in Appendix D were followed for minimizing compliance and aligning and calibrating Me system. Axial Displacement Measurement As previously shown in Figure 47, axial displacement in most of Me resilient modulus tests was measured simultaneously by (~) a pair of EVDT transducers mounted outside the cell, (2) a pair of EVDTs placed between clamps attached to the specimen and (3) either two or three EVDTs attached between the top platen and the base platen of the cell (these transducers are called top-bottom EVDTs). The characteristics of the three types of EVDT displacement transducers used are described in Table 20. The purpose of measuring axial displacement using the three different techniques was to evaluate the variability and reliability of the resilient modulus obtained using each method. External EVDT Transducers. Two pneumatically actuated, precision EVDTs were placed outside the cell on opposite sides of the loading piston. The external EVDTs measure the total displacement of the loading ram including any extraneous deformation in the system such as displacements in the porous stone and at all interfaces as, for example, between the loading platen and the specimen. To minimize the ejects of extraneous displacement, a 6 in. diameter by 12 in. high aluminum cylinder was used to calibrate the extraneous deformation in the system as described in Appendix D. Internal Top to Bottom EVDTs. Three EVDTs were placed between the top platen and the base of the cell to reduce the amount of extraneous axial deformation measured compared to external EVDTs (Figure 47~. Two of the Free top to bottom EVDTs were located on opposite sides of the specimen along a projected specimen diameter. The third transducer was located at a right angle to the first two transducers along another specimen diameter. This arrangement of transducers permits defining He plane of the top platen which is always slightly inclined due to the presence of a small amount of eccentricity in the loading. During Be later part of the study, when top to bottom EVDTs were reintroduced into the study, two more sensitive top to bottom EVDTs were used as indicated in Table 20. LVDTs on Internal Clamps. Two aluminum clamps which fit around Be specimen supported a pair of EVDTs and their cores between quarter points of the specimen (Figure 47~. The clamps were placed between the 1/4 points, rather than the middle I/3 points, since the magnitude of the very small displacement which occurs at small load levels is slightly greater and hence is measured more accurately. 117

The clamps were hinged on one side and spring loaded on the other side. The clamps each weigh 0.54 Ibs. and exert an average force of lO.O Ibs. on the 6 in. diameter specimen. During specimen loading, the inertia force exerted on a clamp is equal to the mass of the clamp multiplied by the acceleration to which it is subjected. To minimize this inertia force, which can cause slippage if it becomes sufficiently large, as many holes as practical were drilled through the O. 125 in. thick aluminum plate from which the clamps were machined. Effect of Compaction Method on Aggregate Breakage and Structure Laboratory specimens of granular materials are presently prepared using both impact and static compaction methods. Relatively little is known, however, concerning the influence of specimen preparation memos on the resulting aggregate structure and particle breakage compared to what is actually developed in the field. Resilient and permanent deformation behavior, however, is influenced by both particle breakage and aggregate structure. The aggregate compaction experiment involves comparing aggregate orientation and particle breakage of specimens prepared in the laboratory with the structure resulting from compacting a crushed stone base material in the field using a heavy vibratory roller. Material and Test Procedure. Bases i, 3 and 4, used in this and many subsequent experiments, are described in Table 21 and the gradation curves are given in Figure 54. Laboratory compaction of specimens was performed in 6 in. diameter Proctor molds using both (~) modified Proctor impact compaction (modified AASHTO Test Method TRIPOD) and (2) vibratory compaction using the previously described electric vibrator. Each layer was compacted until the required density was achieved which took approximately 40 seconds of vibration. Aggregate Structure. To permit investigating the structure of the unstabilized base, a portion of the fines in each base was replaced with Portland cement. After wetting and curing for 7 or more days, Be cylindrically shaped test specimens were cut across a diameter using a rock saw. The structure of the compacted specimens was then analyzed by examining the number and type of crushed aggregate particles and the orientation of the major axis of the aggregate larger than about ]/2 in. in diameter. Specimens of crushed stone compacted in the field were prepared as follows: First, an area of existing aggregate base about lO ft. by lO ft. in plan was thoroughly scarified using the blade of a motor grader. The material within an area 3 ft. by 3 ft. in plan and ~ in. deep, equal to the thickness of the base, was then removed by hand. Base ~ material, with about 4% by total weight of fines replaced by cement, was placed in the excavated space. The loose base, including the newly placed material, was then subjected to 6 to 7 passes of a ~ ton vibratory roller in each of two perpendicular directions. The base was covered with straw, soaked with water, and allowed to cure for 17 days. Four 6 in. diameter cores were taken from the hardened base. Results. Table 22 compares particle orientation and particle breakage caused by conventional modified Proctor impact hammer compaction with laboratory vibration for Bases I, 3 and 5. For Base I, Be results from field compaction using the heavy vibratory roller are also included to establish actual field behavior. Less particle breakage was caused by laboratory vibration than by either laboratory impact compaction, which caused the most breakage, or by field rolling. Resulting particle orientation was also different for each method. 118

Table 2 I. Physical description of bases I, 2, 3 and 4 Material No. Desc~lptlon WE Waded, Tic, 1.5 m. rn~mum size, subangular to angular crushed stone. 4 percent fines. Speciemen compacted GT-BASE 1 to: 100 % T-180 density; dry density = 143.0 pot at 5.0 % water content. Well graded, nonplastic, 2.5 in. maximum see, subangular to angular cn~l stone. 4 percent fin - . Speciemen compacted GT-BASE 1 to: 100 % T-180 density; dry density = 143.0 pcf at 5.0 % (MODIFIED) water content. ~ Well graded, nonplastic, 1.25 in. maximum size, subangular to GT-BASE 2 angular crushed storm. 10 percent fines. Speciemen compacted to: 100 % T-180 density; dry density = 141.3 pet at 5.1 % water canted Well graded, 1.25 in. maximum ~e, soil-aggregate blood GT-13ASE 3 20 perch friable soil. S - imeD ~tcJ ~ 95% T-l80 deposit; dry Minsky = 141.1 pcf at 7.~% User code - . Well grad - , 314 in main ske gram, PI ~ 5. GT-BASE 4 Specimens compacted to ss % T-1~; dry density = 142.2 at 4.1 % water content - C, 80 z 0 0 dL go at ~ ~0 J o lo.'- _. ,_ ~ O .001 . 1~ . --' 1- 1~ . 33E1 - 1 1 1 1 1 1 1 64 1 1 1 1 1 1 1 61 1 1 1 1 1 1111 ~ 1 ~D~ " ll. t I I I :J .~R : ~IS F7~Di r~rlr, t r ll9~frPr · illll I I ·~u I 1 1lll1- 1 1 t~.11~' 1 ~J.~1J ~J-~1aL~1JA _ ~. I 11141 1 1' I tl~i i I ~ I 148 ~ ~ I I I 1~11 i ~i I I I ~ ~il I I 41 ~ I I 101 1 ^~ I I .~11 i ·-- --i---~--~-~------~---~-~-~^, ~--,-~,~,~,,,~, I II I Itl.. I I I I 11111 ~ I ~815' 1 I I~ I I i'lli I I I I I 1111 ^~^ I 1, 1 ll11 1 I II I ~ ill. I I I I I 1811 ~I yl 1 1811 1 ,~,,- ~,l- ~---~--~-~;~ ~-f -~-~-~- 1 ~1 1 11181 ~1 ~ 1 t.' 1 1~. ~ 1661. 1 1 1 1 1 1 1 811 1 1 1 1 1~141 1 ~ ~ 1 1 1 I81 1 I I till ~I I 1~6116 1 ,. ~ I I 1111 1 ~r ~t ~ ~r~r~ ~r ~ v~r I I ~ ~ I i~lll I ~ ~ ~ itll ~ ~ ~ I I llil I l I I I 1111 1^m I I ilel ~I I I I 1111 I ~ ~ t 1 161. i~Y I ~ I tilt ~ I I i t 11111 i I ~ t~r~r~lr ~·~-t-~Yl~ 6111. D 1 ~ 1 16111' 1 ~. 1 1 1 8161 ^~. 1 ~ ~ ~ ~ l' 1 ...... ~r ~.~.~!,. ~, ~' ~s~2 , I l~ _~l I · I"l I o 0 B"ES -~.~llL - .- ~I.ll~lJl. ~. 4_& ~ ~.. 1 ~ t~' 1 1 ~ ~ ~ 1188 1 ~1 1118 1 1 ~ 1 ~ 1118 1 ~ ~ ~ ~ tl1' 1 ~ 1 ~ ~ 1881 . ~. ~ . ~ . . . . . . _, , ,w,=_ . , 1 1 1 1 ~ ~ Illl ~1 ~ 1 ~ ~ tIt1 1 1 1 ~. . ~ ..~e . .01 .1 8lEVE 81E;ZE OPENING) (It4.) Figure 54. Grain s~ze distribution curves and T-180 densinr test results for bases 1,2,3 and 4 119

Table 22. Effect of compaction method~n particle fracturing and orientation COMPACTION t~ETEtOD NO. OF CUMULATIVE I RUBBER Of DIFFEREHCEl1,l PARTICLE COHMEN" AND SAMPLES AREA Of | FRACTURESnn.2 1~) | INCLtHTlON ~08SERYAtlONS ale'`' USED ~ WE | (DEGREES) SHED ST-£ __ ,' 64 0.~. . 36.. _ _ _ 8,.75 17 ·~.2 ~ ~0.66 ~- 1 1 2 ~ E ASK 3 - SOIL AGG NEGATE BLEND Wll 1 1.5 In., lIAXIII UM AGGREGATE 48 PRIMARY BR""G£; PR~HIN0t ~ SHA~R SHE AGGR£GA~ - 42 PRJ~IARY BRE4ICAG£, BREAKAGE IN URGE ~ SEAM SUE AGGR£GAUS 14 PRI`tARY BP`EAKAGE; 22 SECONDAFlY 8REA"GE l PREDOlilNA~ let StldALE SIZE AGGREGATES. FIELD Yl8RATION LAB lilPACT 2 LAB VIBRATION LAB IMPACT 2 - S. 0.41 ' . 42 . - O.S3 . 37 BASE ~ - 314 IN. GRAVEL WITH SLIGHTLY PLASTIC FINES. - 16 PRJ~ARY 8R£AKAGE; SECONDARY BREAKAGE; PREDOMINANT IN SHALL SIZE AGGREGATES LAB VIBRATION LAB IMPACT LAB VIBRATION 2 12 PRIMARY BREAKAGE; 2 SECONDARY BREAKAGE; SeE AGGREGATES _ C4 1 0.22 ~ ~. 42 0.1S . 120 ~2 PRIMARY BREAKAGE, SECONDARY BREAKAGE; PREDOMINANT IN SMALL SHE AGGREGATES ~ PRIMARY BREAKAGE; 2 SECONDARY BREAKAGE; PREDOMINANT ~ SHALL SHE AGGREGATES

particle Breakage. Two kinds of aggregate breakage were observed to take place in both the laboratory and field. The first, called primary breakage, involves the breakage of an aggregate that has no other apparent aggregates situated either directly above or below it. The second form of breakage, termed secondary breakage, occurs when one aggregate is located directly on top of another one. During compaction, the upper aggregate is pressed against the lower one which helps to cause particle breakage. Laboratory vibratory compaction of a well graded I.S in. maximum size crushed granite gneiss base caused ~ ~ % less particle breakage than compaction in the field with a ~ ton vibratory roller (Table 22~. Laboratory impact compaction caused 17% more particle breakage than field compaction. Compaction using a laboratory vibrator causes more breakage of smaller particles compared to impact compaction, which is also true for the field vibratory roller. The impact hammer, in contrast, causes breakage of both large and small particles. Particle Orientation. Field vibratory roller compaction causes the least orientation of the long axis of particles with the average particle inclination being 36.5° from the horizontal Table 22~. Both the impact and vibratory hammers caused more particle orientation (i.e., particles were more horizontally aligned) than caused by the ~ ton vibratory roller with their average inclinations being 30.2° and 28.0°, respectively. Effect of Fines. Particle breakage due to laboratory compaction of bases having 10% fines (Bases 3 and 4, Table 21 and 22) was found to be 50 to 70% less than one with only 4% fines (Base I). All bases consisted of a I.S in. maximum size crushed granite gneiss. The reason for Me significantly greater particle breakage in Base ~ is primarily because it had only 4% fines compared to 10% fines for Bases 3 and 4. Fines are defined as material passing the No. 200 sieve. The presence of more fines help to separate the larger particles and to act as a cushion. Less particle orientation also occurred in the laboratory compacted specimens having 10% fines compared to the base with 4% fines. Recommendations. Neither the laboratory impact hammer nor the vibratory hammer exactly duplicate the aggregate breakage process nor give the same orientation of aggregate particles which occur due to vibratory rolling in the field. Laboratory vibratory compaction, which results in fewer broken particles, is slightly more desirable than impact compaction and hence is recommended. Laboratory vibration causes breakage of smaller particles which is also true for We field vibratory roller. Nevertheless, the impact hammer could still be used at the present time as an alternative to the vibratory hammer. Trnpact compaction is more applicable where specimens are prepared having ~ to 10% or more fines causing total particle breakage to be low. Effect of Compaction Mold Size on Maximum Dry Density Introduction. Resilient modulus tests must frequently be performed on base materials having a maximum aggregate size of I.5 in. or more. To obtain results representative of field conditions, the tests should be performed on specimens prepared using the complete gradation without removing any of the large top size material. Density tests. usually performed in the laboratory, must be first run to establish _ . ., . ., . .. , , ~ · . - ~ ~ · ~ ~ ~ . · · ~ , . · ~ ~ ~ ~ ~ ~ ^1~ ~ L target densities before specimens can be prepared for trlaxlal testing. l he maximum size of aggregate ular can be compacted in a mold of a given diameter is an important practical consideration when large aggregate base materials are used having maximum particle sizes greater than 3/4 in. A compaction experiment was therefore conducted to determine the effect of compaction mold size on the resulting maximum dry density. 121

Materials arid Test Procedures. The base materials used in this experiment are described in Table 21. The testing plan and compaction test specifications are summarized in Table 23. The effect of mold size on the maximum dry density of the compacted aggregate specimens was determined by compacting each base in a different size mold using the AASHTO TWO compaction energy as shown in Table 23. The full gradation of the aggregate was used in performing the compaction tests using each size mold. Results. The maximum dry densities and optimum water contents determined for each base and mold size are summarized in Table 24. Figure 55 shows for a I.5 in. maximum top size aggregate base 03ase I) the typical variation between moisture content and dry density obtained using 4 in., 6 in., and 12 in. diameter compaction molds. Tests were also performed on three other base materials. Using the same size compaction mold, the maximum acceptable range of two density test results, expressed as a percentage of the mean value, should not exceed I.9% according to an early version of ASTM D-1557. For Bases ~ through 3, the maximum difference between the mean maximum dry density and the extreme value for any two mold sizes used was ~ %, 0.5%, 0.9%, and 0.9% of the mean maximum dry density. These results, even though for different mold sizes (i.e., 4 in., 6 in., and 12 in.), are all one-half or less of the allowable I.9% deviation from the mean density once permitted by ASTM D-1557. Recommendation. The use of a 6 in. diameter compaction mold is adequate, without replacement, for establishing maximum dry densities for materials having up to a I.5 in. maximum aggregate size. For 3/4 in. diameter maximum size material, either the 4 in. or 6 in. diameter mold can be used. The 6 in. diameter mold, however, is in general, preferable to smaller ones. Location of Axial Deformation Measurement Device The purpose of the synthetic specimen experiment was to statistically evaluate the variability and reliability of the previously described three different displacement measuring techniques for determining resilient modulus: (~) two externally mounted EVDTs, (2) two or three EVDTs from the top platen to bottom platen and (3) EVDTs located on clamps at I/4 points. Resilient modulus tests were performed on two 6 in. diameter by 12 in. high synthetic elastomer specimens, one having a relatively low resilient modulus (7880 psi) and the other having a moderately high value (50,500 psi). Use of synthetic specimens tested at the same temperature eliminates the effects of variability associated with specimen preparation and natural material variation. Two 0.5 in. diameter aluminum plugs 0.75 in. long were epoxy glued opposite each other into each synthetic specimen at the I/4 points. By rigidly attaching EVDTs between Me two pairs of plugs in each specimen, all system compliance deformation is eliminated as well as He potential for slip and vibration associated with clamps (Figure 56~. Later in the study, steel plates 0.25 in. thick were epoxy glued to He ends of He specimen and then machined. Steel end plates eliminate serious cupping of He ends which occurred on SHRP synthetic specimens during extensive usage. Test Procedures. Tests were carried out at a stabilized temperature of 25°C + I°F. Clamp mounted EVDTs and EVDTs mounted on the plugs glued in He specimens could not be used at the same time. Therefore, one test series was conducted on each specimen using the plug mounted EVDTs, and a second series was performed using the clamp mounted EVDTs. The tests were conducted using quick setting grout between the top and bottom loading platens and the sample. Both a confining pressure of O and 10 psi was used with the load sequence consisting of 122

Table 23. Test conditions for laboratory compaction experiment TEST PARAMETER h1( LD DIAMI TER ~ 4 In.(1-)-- 6 in.t') BASE IdIIMBER i,2,3,4 1 ,2,3,4 HAMMER WEIGHT (Ibs) - 1 0 1 0 DROP WEIGHT (in) 1 8 1 8 MOLD HEIGHT (in) 4.58 4.58 -NO. OF LAYERS 5 5 BLOWS PER LAYER 2 5 5 6 COMPACTION EFFORT 56,250 56,250 (Ibs.-ft-/cu.tt.) 12 In. 1~2 11.5 24 ~2 s 384 56~250 Table 24. Summary of moisture-density test results for 4, 6 and 12 in. compaction molds I COMPACTION MOLD SIZE (IN) BASE 4 IN. DIAMETER 6 IN. ~ IAMETER 112 IN. I DIAMETER Opt(%) Ymax (pcf) c~opt(°/O) ~ j~ ~- 3.7 141.5 5.0 -- 143.0 6.5 141.0 2 4 .8 1 4 0. 1 5.1 ~ 4 ~ .3 4.9 ~ 4 3. 8 3 7.0 1 43.7 7.4 ~ 41.1 . 4 4.0 1 45.9 4.1 1 42.2 . ~. Tmax (pcf) 123

Ad - - ~ 1" let he 140 {3 139 138 137 1 1~ -1~ 6 IN. DIAMETER MOLD _ _ V 73i / L ~ , ~ IN. DIAMETER MOLD _ _ .-. _ = _ . LIZ 12 IN. DIAMETER MOLD- O 1 2 ~ ~ S 6 WATER CONTENT, w (#) 7 8 9 Figure 55. Moisture~ensity relationships for 4 in., 6 in. and 12 in. compaction molds 124 . i/

-A - - - - ~. - ~ - ~ t Figure 56. Synthetic polymer specimen wtih axial deformation measurement system rigidly attached to specimen 125

~ AN ~- A deviator stresses (~-~3) of 3, 6, 10 and 37 psi. All test conditions were considered together in the statistical analyses. Previous studies have shown confining pressure and stress level have a negligible effect on resilient modulus. Test Results. The statistical summary of the resilient modulus test results for the synthetic specimens is given in Table 25. This table gives for each specimen- and measurement method the mean resilient modulus, standard deviation and coefficient of variation. These statistics are based on approximately 40 measurements. Upper and lower 95% confidence intervals for resilient moduli for each test series and memos are also included in He table. Figure 57 and 58 illustrates He variation in observed resilient moduli with displacement measurement memos for the soft and stiff synthetic specimens, respectively. Discussion. Use of synthetic specimens eliminates variability associated wig specimen preparation. However, important experimental errors still remain which contribute to variability of measured moduli. The small resilient displacements which occur at low stress levels are hard to measure and contribute to variability. Problems wig alignment of both the load and He specimen are also present. Finally, strain is not uniform over the height of the specimen due to end effects. Statistical Analysis -- Both Anova and Duncan's multiple range test reveal that statistical differences at He 95% confidence level exist between the mean resilient modulus obtained from each one of the measurement methods. Similarly, Hardley's Fmax test indicates that the variances in the resilient moduli obtained using each measurement memos are not the same at the 95% confidence level. These findings indicate that the resilient moduli are statistically different at the 95% confidence level when displacements are measured at different locations in the testing apparatus. The test shows at the 95% confidence level that the resilient moduli measured using EVDTs rigidly mounted to plugs are statistically different than the value obtained using clamps mounted on the specimen at the same locations. This finding is true for both the low and high modulus synthetic specimens. Relative MR Values -- The mean value of resilient moduli determined from measurements made using EVDTs mounted on the plugs were used as reference values. They should be the most reliable since extraneous displacements and potential slip was eliminated. On this basis, the clamps gave better average resilient modulus values compared to those obtained for the externally mounted EVDTs for the stiffer synthetic specimen (~% error for He clamps compared with -14% for the external EVDTs). In contrast, the external EVDTs gave the best average results for He low stiffness specimen (~2.5% error for the external EVDTs compared wig hi% for the clamps). Low stiffness specimens undergo a large amount of deformation for a given stress level compared to a stat- specimen. l herelore, extraneous deformations included in the external EVDT measurements, such as deflection in He load cell and porous stones, become less important in measuring resilient moduli of low stiffness specimens compared to the large deformation occurring in He specimen. On the other hand, a stiff specimen has important extraneous deformations associated with externally mounted EVDTs which can be on the order of magnitude of the small deformations occurring in the stiff specimen. As a result, the externally mounted EVDTs did poorly with the high stiffness specimen. 126

Table 25. Statistical summary of resilient modulus from synthetic specimen experiment i ' ~ ~ SP ECIMEN STATISTIC E=E RNAL(1 ) CLA HPSt2) P LUG 5(2} TOP.BO=OM TOP'S OT TON AV~ A~ AV~ AVO .-~(~) AVO.-2(~) SE' IES 1 ~ INTE, PAL HEASU lEMENT ~ PL JOS TU ~ . . - 40 40 40 MEAN 807 7 . 7078 B'11 ~1155 . 273 430 CV 14.4 . s.5 ..1 LOWER Cl(~) 7t06 . 7701 .~7 _ UPPER Cl(5) ~ ~ ~ 1 . 7 ~ ~ ~7 0 ~ 6 SERIES 2- tNTERNAL H"SUREME~ USING COPS ~0 ?085 s.0 5.1 sl78 210 TU 900 - N ~ ~ HEAN 8226 742. ~1058 00 CV 1 2.9 1.2 LOWER Cl(6) 7881 7308 UPPER Cl(5) ~ ~ ~ ~7 ~ ~ ~ sl7e 284 4 a. 682 6723 ·870 167 2.4 681 ~ ·024 SERIES 3 - INTERNAL MEASUREMENT ON PLUGS _ 40 45,81 1 lle ~ -. 4S,286 41,354 . ~N - ~ 0 IdEAN 4S,388 TV 960 ~4,721 N 10.. LOWER Cl(t) ~ 1, ~ 7 UPPER Cl(5) ~ 4, 9 0 0 . SERIES ~ I=ERN" M"SUREME~ USING C"MPS 40 40 50,641 41,1 l' t,824 2 1 08 11.. 4.e 4e,l76 4s,480 52,408 41,.30 40 40 ', - ~74 41,500 t,251 4730 1 1.. 1 0.3 42,.~4 44,.~. 4l,'68 4e,034 TU sl0 O ~ I ~EAN 42,237 47,410 ~4057 3728 1 CV 11.? 7.. 1 LOWER C't) 40,160 41,21. | UPPER Cl(6) ~ 3 . · 2 6 ~ ., ~ 0 ~I NOTES: 1. ~R CALCU"TED USIN¢ AVERAGE ~R 2 ~ER - L L=Te. 2. EITHER L"~e B~EEN PL=S OR L~e ~ ~" ~RE USED. MR CALCU"UD FROM AVERAGE FOR ~O LVDTe. 3. MR CALCU"=D U~NG ~E AVERAGE FOR 3 L"~e " - ~P CAP TO BASE. 4. HR CALCU""D USING ~E AVERAGE FOR ~O ~ICALLY OPPOSED L"Ts FROM TOP CAP TO BAS~ S. UPPER AND LOWER ~S PERCE~ ~N~DENCE ~RVAL (C0. ~R VALU" ARE GIV - . 127

9000 8000 7000 6000 SOOO 4000 3000 20 1000 ~. . , EX[. IOP-BOTI. CLAMPS PWGS MEASUREh1:ENT DE VICE Figure 57 . Resilient moduli using external, top to bottom, clamp and plug mounted EVDTs:, soft synthetic specimen U. A_ 60 5 R ~ F By 3 R U. Ez3 4 20 EXT. TOP-BOTI. CI^MPS 'L GS MEASURE1\IENT DEVICE Figure 58. Measured resilient moduli using external, top ~ bottom, clamp and plug mounted LVDTs: stiff synthetic specimen 128

. Use of clamps mounted directly on the specimen completely eliminates from resilient modulus calculations the extraneous deformations occurring outside the specimen. Some slippage and/or rotation of the clamp, however, might have occurred for the low stiffness synthetic specimen which had a hard, smooth surface. Slip would be considerably less likely on a soil specimen which permits the clamp to penetrate a small distance into the specimen. Further, the driving force acting on the clamp that tends to cause slippage is equal to the mass of the clamp and EVDTs times the acceleration applied during loading. The clamps are subjected to the greatest acceleration and hence force as a soft specimen undergoes large displacements. For these reasons the clamps performed best with the stiff specimen. Identifying Peak Load and Displacement Using a Data Acquisition System The number of measurements collected by an analog to `digital data acquisition system potentially has an important effect on the peek value observed for load and displacement. To investigate this effect, 102, 205 and 666 transducer output readings were collected for each of the 5 one second pulses used to obtain an average load cell or EVDT output reading. The previously described 12-bit resolution data acquisition system and associated software were used in this experiment. The 5 Lip flat load cell, and the following EVDT transducers were also used: external EVDTs, EVDT i; Top to bottom, 2b; clamps, 3b (refer to Table 20~. The tests were performed on 4 different specimens of Me same Base 4 material and the results are summarized in Table 26. Findings. The findings, which are somewhat surprising, show that the use of 205 measurements over a ~ sec. interval gives more accurate results, as defined by the coefficient of variation (CV), Can for either 102 or 666 readingslsec. The overall average value of the coefficient of variation for load and resilient modulus, which have similar values of CV, is 0.62% for 205 readings/sec. compared to 1.06% for 666 readings and 1.61% for 102 readings. For 666 readings/sec., very similar results were also obtained for 20 other tests on a range of materials. Average resilient moduli values, based on clamp measurements, were nearly the same. Specimen Conditioning Conditioning a specimen consists of applying typically between about 200 and 1000 or more stress pulses to the specimen to prepare it for the resilient modulus test. One purpose of conditioning is to simulate the stress history to which an element is subjected during construction. Another more frequently mentioned purpose is to reduce the detrimental effects of specimen defects and bedding errors caused by irregular contacts between the specimen and the top and bottom platens [52, 66, 671. Bedding errors are small for granular materials but can be as large as 20% of MR for cohesive soils. Another frequently mentioned purpose of specimen conditioning is to reduce the subsequent variation of resilient modulus wig load repetitions. Cohesive Soil Bedding Errors. Small irregularities exist between the top and bottom of the specimen and the rigid end platens. As a result, unwanted deformation occurs in the vicinity of We end caps [68, 69, 70, 711. Bedding errors are particularly significant at low deviator stress levels [701. In the past bedding errors in repeated load testing have been assumed to be minimized by the application of repeated load cycles during the conditioning phase. Pezo, et al. 1772, 731 have found for cohesive soils important seating and be~ing errors to still be present Alter conditioning. Good contact between Me 129

c) c. u, {'5 o - - A, to ~ 11 o ~ o 'v I) - ~ ·e ~ c A: ~ Hi J o a) :: ~ o :: ~ o ~ 8 I _ ~ . Cal D - g~ - ~ ,1 _ ~ a, a_ ~ t. a_ _ ¢ g~ LIZ ~ #~ o ~ ~ _ ~ I; g~ _ -_. .- :] ooo moo as Z o o o o o o 0 ~ ~ _ ~ ~ - __ - ~ - .~. - ~. 3_ ~Z O - d; _ ~ ~ _~ ~ ~ · · ·@ · ~ oo ~_o_ "o ~ · · - ~o _ ., 0 ~o _ ~ ~ _ ~o 0 ~ ~o 0 0 0 . . . uJ ~ 0 0 0 · · - ~ 0 0 0 0 0 · · ~ 0 0 0 e. 0 0 0 0 0 0 · · ~ 0 0 0 - .o- ~. omo _.o · · ·· · ~ oo__o" 0 _ 0 _ ~ ~ · · ~ 0 0 0 0 0 0 . . . W 0 ~ ~ · · ~ ~ ~ 0 0 ~ ~ .~. o^, - ~ ~ 0 e · ~ ~ · ~ · · · · · ~ · O · ~ UJ X e "o 0 "oo "oo .~_ .~_ 130 ~ o o C)8 2 ; g! ~ a, ~ ~ Z ~ 8 oz z o 0 C! ~ C) ~ ~ ~ ~ C! @ ~Z Z o ~: O Z `, ~ '- 'S a: OO I,L DI J o ~ m! Z O Ee iT 88 =e ~W O~ ° 0 ~ ~ o 2 , ~ ~ ~ 0 Z ,. IL Z" =¢ Z W Z D~ o~ ;5 ~e a3 ~= cn=O ~ 0 EE Z z ° i!! a ~ `' ~ · e a, z

specimen and top and bottom caps is necessary particularly when deformations is not measured on the specimen. Pezo, et al. [721 used hydrostone, a quick setting grout, between the cohesive test specimen and the end caps which provided uniform contact thus reducing the required number of conditioning load repetitions. SHRP Conditioning Procedure. 1989), and also an alternative method were both used in the experiment. The SHRP conditioning procedure requires the application of 200 load repetitions. Note that the June 1996 version of SHRP P46 requires 500 to 1000 repetitions. A confining pressure (as) and a deviator stress (a,-a3), each having a magnitude of 15 psi, are applied following the SHRP procedure. This conditioning stress combination results in a relatively low principal stress ratio a~/a3 = 2.0. The SHRP conditioning method, specified in P 46 (November, Alternate Conditioning Stress State. During construction the base is usually compacted using a heavy vibratory roller operating directly on each lift. After compaction, heavy construction traffic moves over the base causing additional high states of stress. As a result, during construction the base is generally subjected to a more severe loading condition than any other time during the life of the pavement. Placement of the asphalt concrete surfacing provides protection to the base resulting, in general, to a less severe stress condition. Base Construction -- The characteristics of a typical vibratory roller was used to theoretically mode} the base compaction process. The vibratory roller selected causes a maximum dynamic force of 44,775 Ibs. The roller has a drum 60 in. in diameter and is 84 in. long. Assuming during compaction this roller presses into the base 0. ~ in., He average dynamic pressure exerted on the surface is about 35 psi. The contact pressure increases to 53 psi if during the final stages of compaction He drum presses into the surface of the base 0.05 in. which is realistic based upon field observations. Stress States -- Stress states in the aggregate base were predicted for total aggregate base thicknesses of 6 in., 12 in.' and IS in. (Figure 591. The loading used was that caused by the vibratory roller. The ratio of elastic moduli between successive layers for the conditions analyzed determine the state of stress developed due to vibratory compaction. Therefore, the stresses calculated are correct for different subgrade stiffnesses as long as the ratio of adjacent elastic moduli stay the same. Field observations indicates this assumption is reasonable. Calculated stress states at the center of a 6 in. and 12 in. thick aggregate base caused by the vibratory roller are shown in Figure 60. A 0.5 psi residual stress was used for the lower 6 in. thick lift and 3 psi was used for the upper lifts. These are the residual stress levels measured in the field as a part of this study. The effect of material weight is included in determining the stresses shown. Averaging the stresses for these two conditions gives a confining pressure of about 12 psi and a principal stress ratio 0~/03 = 3.~. To insure ~ adequate level of conditioning is applied to the specimen, a confining pressure of 15 psi and a principal stress ratio of 3.5 was used in the experiment as the alternate conditioning stress state. When weak bases are tested use of a higher principal stress ratio could cause failure of the specimen. Discussion -- Stress states caused by vibratory compaction, construction traffic, and even traffic on the completed roadway, can result in principal stress ratios greater Han the Oi/~3 = 2 used in the SHRP (November, 1989) procedure. The use of an alternate stress ratio of Ot/03 = 3.5 applies a greater repeated shear stress to the specimen during conditioning which potentially could affect both the elastic and even more likely He permanent deformation response of the specimen. 131

q - 35 PSI Elf ~ 1.5 E.1 1 - = ~ In. 6 In. . ~ ~ . , ~ , ~. /~/ ~/ -///-X ~'/ E. ~ 5,000 PSI At. ~ 0.4 Em ~ 15,000 PSI 0.3 E.' ~ 10, - 0 PS! 0.36 Em ~ 2 Es Figure 59 . Elastic layered system used in compaction stress analysis-rectangular loading ' e 30.8 PS' , .e / ~ ~ Us ~ 5.5 PSI ~3= 5.5 PSI ~1 / O-s ~ 5.6 (a) 12 in. EASE / ~1 e 34.8 PSI .e . . ... : ~ j<.'. ~ . 1 art / O-e ~ 2.0 fib) 6 A. BASE ~3 ~ 17.8 PSI Figure 60. Approximate average stress state at the center of two aggregate bases due to compaction with a lO-ton vibratory roller 132

Materials and Test Methods. The conditioning experiment was conducted using Base ~ and Base 4 which was previously described in Table 21. Two replicate tests were performed for each material and for both the SHRP and alternate conditioning method. After specimen preparation by vibratory compaction, the top platen was placed on the specimen and vibrated for about 10 sec. Conditioning Sequence. The conditioning sequence used in this experiment for both the SHRP and alternate procedure is shown in Figure 61. The initial test sequence, which is the same as the SHRP (November, 1989) procedure, consists of first applying 200 conditioning load repetitions. The specimen is then subjected to the 15 stress levels previously given in Table 19. Two additional conditioning phases were applied to each specimen consisting of 1000 load repetitions using the same stress state as in the initial 200 load repetitions. A full resilient modulus test sequence was performed following each conditioning phase. Results. The resilient moduli measured during the conditioning experiment for the SHRP and alternate stress state are summarized in Table 27. Regression analyses were performed on the resilient moduli measured for each condition to determine a K-D resilient modulus model. Then, using the analysis of variance on the regression coefficients, the K-O models for each pair of replicates were compared to determine if the two regression lines were statistically the same as an indication of the test repeatability. The F-test, for a 95% confidence level, was used to evaluate the repeatability of the test. All replicate samples had statistically similar variance using the regression analysis on each pair of results and also between similar replicates. Therefore, each set of replicate test data was combined into a single regression model. K-D models were developed for Base ~ and Base 4 after each conditioning sequence. These regression models were then compared using the analysis of variance to determine He effect on resilient modulus of the SHRP and alternate conditioning stress states and ache number of conditioning load pulses applied. Two regression models were compared at a time using the F-test for a 95% confidence level. The results of these statistical comparisons are summarized in Table 28. Practical Findings For either conditioning method, the measured resilient moduli generally decreased gradually wig increasing number of conditioning pulses as illustrated in Figure 62. The crushed stone base, which did not have plastic fines and was compacted to 100% TWO density, underwent an average of 4% reduction in the initial resilient modulus after 5200 repetitions. The grave! base, with plastic fines and compacted to 95% of TWO density, underwent an average resilient modulus reduction of 8%. These findings indicate that bedding errors were not present since the resilient moduli decreased wig increasing number of load repetitions. The small 4% decrease in resilient modulus over 5200 load repetitions is considered to be negligible especially considering some of He decrease could have been caused by electrical drift in the closed-Ioop testing system. The two different conditioning stress states used in the experiment gave resilient moduli for He materials tested that were on the average within 2.5% which is a negligible difference. For He evaluation of permanent deformation, conditioning using He principal stress ratio of 3.5 would more accurately depict the actual stress state and hence rive a more reliable indication of notentin1 permanent ~leformatinn behavior. ~, ~.. I, _ , .._~. .. _. ~a. e~, w _.,,_, ~_. ~,, ~ Thompson and Smith [741 found that stress repetitions cause a significant strengthening and stiffening eject before bedding errors are minimize. The level of strengthening and stiffening was found to be related to the position on the curve relating permanent deformation with load repetitions, with a sudden decrease in permanent deformation usually occurring between 100 and 1000 repetitions. 133

~- CONDITIONING ]1st PREC. No. Repititions = - Test Mr 200 1,500 2nd PREC. Test ~Test Mr ~ 3rd PREC. ~Mr = - 1 JOOO 1,500 1 JOOO CONDITIONING SINCE STRESS STATE: GT : ~1 = 52.5 ff3 SHRP: ~1 = 30.0 ~3 = 15 PSI Figure 61 . 1,500 = l5 PSI Conditioning and testing sequence used in conditioning experiment 134

Table 27 . Conditioning test results - --ado ~4 · he · ~S~cQ ~ { - · Eta -~ '- r' ~ 2" r ~lo_ - . ~ Id ~ 1. ~ old ~ ~ ~ ~ ~ A' hod ~ ~ ~ ~ar ~ ~ ~ ~ ~ ~ ~ 0~ . ~ em_ ~ ~ 0_ ___ ~ _ ~ ~&~ Lam . '~ ,,et?~ &~.6 1~.. · Id '' - ? Gus?.' 1,41~`t 1~J 1 ~o. ~.~1 o.~1 I . Qt~, o. ~o.71~ o.~ I It and .~ _ - -O.805" .~4nt Q~74 o.~71~e owlet I. Its ~.~ :~ _ . ~ off Id ~ ' ~ ' 1 Son ~ f~T ~ bat 1~ Icon ~ 21~ ~001 ~it_ SAL _ bar AL ~ooml E~ am a. ~ ~ . ~1.~ ~e ~e ~2 . I I .~4e outgo. of. o.~ I. of. _ Cam _~1 . ~ ~_~ £~ ~ teas 3,~., 0~?5~ Qume 0.~ 0."S21 Bee 1S~ ._ ~ . &~.. ~e .~ 0.~1 on 1 ·. ~ _ ~ _ . -~ 1~L~ I U~2~d.~o~d I ~-~ ~ ~L~ 1 ~2,dr~c~d I ~ ~ 1 o~ ~I ~ I ~ ~ ~ I ~ -r-~-1- I~ I ~ ~ - ar --! _ -_ ~ I c_p. I _I I a~ I ~ I a~. I ~- I a~ I ~ I ~_1 E_ . P. ~ - 4 . . . . . . .00 te.~.3 I 1~.~.3 1 ·7.8100 1 '.,294.. 1 ·~.=s.e ~ ·e,ss3.s ~ ·~4~.1 1 1~.~5 1 1~.e 1 lJ.~O 1 _ ~t~ I ".ot~ lo lo ~o.oo so,~o~.e I -,~.e I -,~ t I ee,oQ~.e I -.~.e 1 - .~.o l as,ma~ l 21, - 0.e l _ ~ ~i2 1 - ,elzil ~s.~ ~ 1 2s,~1 - 10 ~o ~- ~-~32 s 1 - ~0 2 1 31' - ' ~= ~ - ~1-~ ~ ~ l ~ ~la2 ~ ~ 857~' 1 ~ 574 ~ r =~.~. 1 n.~2s.e 1 a5 200.2 1 L I I 1 1 e~ff~ T^~.e-1S" la-1ffE~ 7~-37~= 1S ~1 1 1 1 ! ~1~ I ~P~ I ~d.~-~d ~-2r~-~- - 1 A_~ 1 1C~1 t~ 1 ~ 1 ~ 1 ~ 1 ~ 1- - - 1--~ 1 ~-1 ~ 1 ~ 1 - - 1 ~ 1 ~ 1 ~ 1 1~1 ~ 1 ~ 1 ~ 1 ~ 1 ~ 1 ~ 1 ~ 1 ~ I ~ 1 ~ 1 ~ 1 ~ 1 ~ 1 ~ 1 1 · I · ' 28 00 1 21,100 1 1 ~ 5411 0 1 i. ~' r 23,.17 ~ 1 10~ .~ 1 _24,124 S 1 - ", -2 1 ~ ~- ~ ~ . 1-=~71 2 1 ",~ 1 r ~o~ ~o __ I ~ ao * 1 - .SO1 ~ ~ -,~ ~ 1 =-a. 1 - - .-o.. 1 ="s.S ~ "~ 5 1 -- 1~1 ·~sT.? r -.~-S 1 a. ~. l ".~. 1-",.1~51 L 10 1 ~I .0-~1 "'11641 "~Sl ^~51 Bl~I U,1~41 - ~121 "~1 "~41 - ~21 - ~61 - ~51 - ~] _ ~ ~ ~_ _ t~t _ 0.~40 _ 0.~2 1 1 a_p. 1 1 ~ 1 .60513 1 _ I ( - · ] ~20 1 ~1 ~ 4~?1 ~1 Q~1 0 ~..,q~ Table 28. Conditioning test statistical comparisons 1 1 . . - · - - -- . SAMPLE 1 1eSVe. 2nd ~ 1~Ve3rd 1 1stVe. 2nd 1 1dVe3rd _~ 1 ~ 1 D ff~- BASE 1 1 F · 1.SZ2 1 f -1.758 1 F - 1.594 1 F ~ 3.001 1 f · ~108 1 f - 3~554 1 F ~ 0~213 - 1 ~ 1 S~ 1 s~ BASE4 1 F-0.408 1 F-0.001 1 F-0.259 1 f-0.039 1 F-0.79 1 F-1.4Z3 1 F-0~42 4~" 1 ~ 7~001 1 ~ 4.g4 1 < 7~001 1 ~ 4.94 1 c 7.~1 1 ~ 4~" "MPlE BAS~ ~ BASE 4 1st SItRP V~ 1et GT ~ffCf~ I Sb/p. Sa`T. I Same F-1.~ 1 F, 0.078 ~ 4." 1 c 7.001 . . . . ~_ . . ~ ~ T same F-1.545 1 F-~017 < 4." 1 c ,.m, |2nd SHRP V~ 2nd G1. 1 h~er~ 1 r 3une-- I f ~ ~046 1 C4." 1 . . ~ . 1 ~ I I f ~ 4.532 1 1 <~." 1 135 13rd SHAP V~ 3rd GT 1 , I ~eroapt 1 1 - ~ - 1 F.6.196 1 I_ 1 ssn. 1 1 F-1~1 1 1 <~" 1 Sbpe Samo f ~ 0.103 S-no s o,~ 7.001 , Slope F-0.884 < 7.001 FS0.019 c 7.001 1 Sbp. 1 1 D~e( - i 1 F - 10.192 I > 7.001 I s~ 1 I f ~ 0 225 1 <~.oo

10 - - ~ 6 a e: . . ; . ~-10 - 8 1 ~/~=2 A 2 f7~ ~ W. . ~ 1 . ~ . O 1000 2000 3000 4000 5000 6000 Conditioning Repeddons . . ~ VEL~PLAS ~ (~%T-l~ = -D SIDNE B} NOVELS SIlC (100°/. TIC HE T-lSO) · I · 1 Figure 62. Decrease In initial resilient modulus win Increasing number of conditioning repetitions - clamp data 136

600 500 '~ 400 JO - ~_ 300 lo 200 100 fin ItN o .... .... .... 0.15 0.2 0.25 0.3 0.35 TIME (see) it -AVERSE t, ~ BITT o o HALFS~ -MUIR Figure 63. Load pulse shapes used in load pulse experiment 137

Test Results, Representative test results are presented in Tables 29 and 30 which give the values of resilient moduli at bulk stresses (~) of 12, 60, and 100 psi calculated from the K-O regression model. To statistically analyze the resilient modulus test results, the K-8 mode! Table IS) was assumed to give a good fit of the test data. Also, assume for now the null hypothesis that Me regression lines for the 4 pulse shapes are the same. An analysis of variance was performed on each data set to reject or accept the null hypothesis. An analysis of variance showed that for externally measured axial displacements, the resilient modulus for all pulse shapes was statistically the same at the 99% confidence level. A large standard deviation in resilient modulus, which was typically twice as large as for the internal measurements, resulted in an overlap of confidence intervals which explains why the resilient moduli were the same. For clamp mounted EVDTs, the results indicate the regression lines for all the pulses are statistically Be same for Base ~ (except one test) and 4, but are different for Base 2 which had 10% fines (Table 31~. A direct statistical comparison between the pneumatic pulse and Be haversine pulse results in a similar conclusion. Base 2, which showed the largest effect of pulse shape, exhibited similar moduli for the pneumatic, sinusoidal and triangular pulses (Figure 64~. The difference in moduli, when compared with the havers~ne pulse, were typically less than about 5% but the error was as large as 25% for very low bulk stress levels. The resilient moduli obtained using the haversine pulse was assumed to be He correct one for this comparison. Recommendations. Previous research has indicated the effect of load pulse shape on the resilient modulus of granular materials is not significant [36, 381. As a result of these early findings, pulses having a variety of shapes have been used for resilient modulus testing. This study, however, indicates Hat for some materials the shape of the load pulse does not have an effect upon the resilient moduli, particularly at low stress levels as defined by a small value of bulk stress. The haversine load pulse probably best approximates the loading to which a small element of base material is subjected due to traffic. A pulse of this shape should be used. If a pneumatic system is employed, adjustable constrictions should be placed in the main air line going to the valve used to control the pulse and In the exhaust port of the valve so Hat He pulse shape can be adjusted. For any shape pulses the area under the load-time pulse curve should be made equal to He haversine pulse for the best approximation; this was not done in the present experiment. Scalp and Replacement Effects on Resilient Moduli Introduction. To achieve high production rates, use of as small a sample as practical is desirable for resilient modulus evaluation. However, incorrect values of resilient modulus and permanent deformation results are obtained if the maximum size of He aggregate used in He test is too large compared to the diameter of the specimen. The Corps of Engineer's Laboratory and Testing Manual CEM Ill0-2-1906 requires that the diameter of He specimen be at least 6 times He size of the maximum aggregate. A practical alternative to using maximum aggregate size in determining required specimen size is to use the maximum nominal size. Maximum nominal size is He first standard size sieve, used in establishing the grading, on which material is retained. Relatively little research, however, has been carried out on the effect of aggregate gradings having top sizes greater Han 3/4 in. because of He large size of the biaxial cell necessary to provide a reasonable 138

Table 29 . Effect of pulse shape on resilient modulus calculated from K-D model: base ~ results FULL GRADATION REPLACED GRADATION PULSE 13EXTERNAL CLA,JIPSEXTERNAL CLANIP' , (P6~) B1 BFS1 El1 BFS2 B1 BF9t | B1 BFS2 B1 BRS1 B1 BRS2 E31 BRS1 . . . 12- i 7,054 20,134 19,271 25,039 1 5,080 1 4,4Q1 18,057 Havereln. 60 50,687 58,227 50,048 55,20t 42,~;2 40,152 43,458 100 71,6" 77,894 67,756 70,944 59,896 55,597 57,429 1 2 - 1 5 , 8 ~ ; 8 1 6 , 3 6 8 1 8 , 2 7 2 ~1 9 , ~1 4 , ~ 5 4 1 3 , 1 6 4 1 6 , 4 3 Trlangular 60 52,236 54,31 0 50,1 47 52,91 8 42,91 3 41 ,285 44,1 39 _ 100 76,243 79,470 69,090 ~72,071 59,966 59,341 60,395 12 15,933 16,958 17,289 19,440 1 G,267 1 1,794 16,050 Slaousoldal 60 52,433 54,135 50,556 52,704 45,928 44,36S 46,086 100 76,524 78,249 71,069 72,330 63,847 67,557 64,413 . . . 12 15,632 17,377 18, ~=,"5 15,352 13,427 15,972 Pneumatlc 60 50,695 55,160 49,452 52,870 45,877 46,210 45,497 100 73,643 79,588 68,077 71,645 64,937 68,405 63,426 Elt BRS2 - 17,154- 42,628 5s, - 8 14,488 42,71 4 _60,201 14,823 45~264 64,51 0 14,526 45,1 28 64,668 Note (1). Notabon: 81 = Bass 1; B2 = Base2; B3 = B - s3; B. = B.sse4 F = Full gradation; R = particles greater than 1 m. were scalped and replaced w~ 3I4 in. to 1 in. particles; S (followed by a numbers = The specimen number w~hin ~e test series. Table 30 · Effect of pulse shape on resilient moduli calculated from K4 model: base 2 results FULL GR ADATION REPIACED GRAC ATION PULSE B EXTERNAL CLAMPS EXTERNAL CLAMPS (P81) ~ 2FS1 1 B2FS2 1 E 2FS1 1 B2FS2 1 B iRS1 1 B2RS2 1 B RS1 12 18,725 19,700 23,100 28,498 21,080 20,438 27,801 Haverelne60 5 1,086 53,203 53,198 58,768 5B,829 49,794 62,556 100 70,250 72,927 69,323 73,945 77,852 66,058 80,920 12 20,256 17,887 19,157 ~ 19,194 18,m 18,885 23,242 Trlang ular60 49,676 49,066 50,487 50,739 53,588 50,333 S9,503 1 00 66 040 67 590 68,669 69 078 74,753 68,704 80,t 90 . . , ~ 12 19,041 17,761 18,899 21,887 1 9,78S 16,679 22,869 Slnousoldsl60 48,897 52,382 S1,462 57,488 S3,329 50,989 58,861 _100 65,961 73,836 70,724 78,104 73,054 72,695 79,458 12 ~ 17,934 21,071 17,900 22,391 20,131 22,398 Pneumatic60 48,927 50,387 50,141 55,m 53,507 5t,144 57,993 100 67 282 66,450 69 530 74 519 72 973 73 102 78 436 . , . . , . ' Note (1). Notabon: B1 = Base 1; B2 = Base 2; B3 - Base 3; B4 = Sase 4 F = Full gradation; R = partcles greater than 1 in. were scalped and replaced w;~ 3/4 in. to 1 in. particles; S ffotlo Hed by a num~r) = The specimen num"r ~~in ~e test sen - . 139 ~ B2RS2 1 ~ 28,11 2 57.377 1 71 959 ~' 21,809 54~459 72~814 21,585 1 55,154 1 1 74. 1 21,760 54.451 72,851

;- v ·. v, - I" v] i] lo: v) Ed vO o As · - - ~ I c Ed En a: ~ ~ ~ o ~ i ~ ., ~ ~ E _ tB! 1 1 h b Ld . , I I 11 1 81 W l | ~ l ol ILL Ill F| ~ | ol ~ l I j : tt:~41 ~1 it; ·! _l _ _ I8 t No l ~ - £ ~ ~ ~ ! ~ ~L ~ ~ ~ ~ o j ~ ~ ~ £ t' ~ dL ~ ~ . ! ~ I 1 9 I] lit li,lml s 1, o _ ei m ~ l ~ v ~ v 0 0 140 i ~ 1t _ d ~ . .

30 ~ 25 20 - 15 10 a _5 _~ Tnangula~ Load Pulse \ \ \ \\ - . \ ~ Pa' T -. ~~ _ - I Sinusoidal~ 1. . 1 ,_1 Pulse 1 i i I En or: "+" - Smaller Menus I 0 20 40 60 80 100 120 BuLk Stress, (a) (psi) Figure 64. Difference in resilient moduli for haversine pulse compared with pneumatic, sinusoid and triangular pulses 141

specunen diameter to maximum aggregate size ratio [51, 75]. To avoid using a large diameter specimen in resilient modulus testing, He large material is frequently removed (i.e., scalped) and replaced by an equal amount of finer material. In the scalp and replace experiment carried out in this study, the scalped material was replaced by an equal amount of aggregate having the largest acceptable size range. Testing Procedures and Materials. The SHRP P46 (November, 1989) testing procedure was followed, except as noted, for both the full and scalped gradation specimens. Resilient moduli were determined from displacement measurements made using both external EVDTs and internal EVDTs mounted on clamps attached to the specimen. Bases I, 2 and Base IM, previously described in Table 2), were all tested in He scalp and replace experiment. Statistical Analysis. To statistically analyze the scalp and replace test results, the K-8 mode! was . . . . . . . ~ . . ~ · . - . · ~ used. An analysis of variance was performed using separate K-U models tor each replicate specimen for each base and gradation tested. The resulting moduli from replicate specimens were found to be statistically He same at He 99% confidence level. Hence, a single K-D model was fitted to the combined data for both replicates. A statistical comparison of He resilient moduli was performed between the full gradation and He scalped and replaced gradation using moduli calculated from the K-0 model. To compare the regression lines by the analysis of variance, He variance of the two lines must be similar. Application of the F test allows a direct comparison between He scalp and replace resilient moduli and those obtained from the full gradation. Test Results. Table 32 gives calculated resilient moduli obtained using the K-O model. The analysis ot~varlance is summarized in ladle ;;. For both me external and internal LVL)1 measurements, Base I and Base 2 filll gradation specimens give a regression mode} having He same slope but a different intercept as the scalped and replaced gradation model. Resilient moduli obtained using the internal LVDT measurements, for the full gradation, are on the average I8% and 24% higher in Base ~ and Base 2, respectively, than for the scalp and replace gradation for a range of bulk stresses (~) between 12 psi and 100 psi. A reasonably similar comparison is true for external EVDT displacement measurements. The two regression lines for Base 2 have the same slope, but the filet gradation specimens have an intercept that on the average is IS% higher than the scalp and replace gradation. The Base l and Base 2 mean square error (MSE) for external EVDT measurements is on the average higher Can the mean square error of the internal clamp EVDT measurements by 22% and 350%, respectively, for both Fill gradation and scalp and replace regression models. The data obtained from the internal EVDT measurements therefore fits He regression line better and gives a statistically more reliable mode! since the confidence intervals are not as large as for the external measurements. The statistical analysis shows that for external EVDT measurements, the full gradation specimens have statistically He same regression model as the scalp and replace gradations Table 33~. The standard deviation of the external measurements for He Base 2 full gradation specimens is considerably larger Han for internal EVDTs, producing a much wider confidence interval that prevents distinguishing between the two gradations. In contrast, He internal measurements performed on clamps, which have a much smaller variance Han the external measurements, indicate that the two regression models have the same slope but different intercept. The two regression lines based on clamp measurements can be assumed to be parallel with the full gradation mode] having resilient moduli on the average 23% higher Man for the scalp and replace gradation. 142

Table 32. Resilient moduli calculated from K-8 mode} based on two replicate specimens - scalp and replace study . - ~tEUUEN'T EXODUS ~ - - ~Ep' Mono ~ ~ _ . . ~) I. . ~' RJU ~L -~ ~' In .. ~t ~UCED-TE-UL 17~U ~0 ~ ~ ~ {s, . ~"~ _ PULL CAL ~0 ~1 ' "PLACED EXrE-AL 14, ~41~. ~ ~ (~) ~~ =0 - 2 DUE MTBWL = ~18 non ~2 AID ~7 - UL r1~1 ~ ~ ~ (S) ",3 "~ - ; _ ___ ~2 ,IJI1 E(~L -;tl~ " - . "SE2 ID Fm~ YM' Ytl/l 5 ~ (2) ?.4 the ~ ~ (X) "~ 226 Nat _ Ate ear cart _ 711 .0 _ ~1 "~ ~ ~ ~2L~. I - - _~ - l~_~ (.'-1 42~) Table 33 . Comparison of K-8 regression mode! for full and replaced gradations . _ _ ~ ~0 ~LVDt In RKU~ MEL ~"~4s~i OF ~S. ' ~noN ~o, rs ~ ~MT - UL IDS 0~) · 3.7S~ ~ 0~41820~) ~. ~= ~ ~ . . ~ <~- ~ ·. 1-d 1 L-ooQq. l"+05557t - ·1 1 he 1 LOO ~ · 553 4 0~57D8~) ~1 ~1 "a .1 ~EMIL UNDO ~ 3.~7d ~ .&~7LO3(~) "1 00~ # 1 ~ 1 uloo - a .88740.48423U~) ~lo.0o1-l 7.ttl ~U. L . . . ~ad M!E~L ~ ~ ~ 3~' ~ 0~N "4 ~ # 1 ~1~L 1 ,£0~O.,~,,40~2DSO=~) ~ 1~1 ~7 ~. .,L # 1 R ~1 us pan · ~e' 4 0584551l=~) 87J I 0~ I 1 1 . . __ ~ore: 1. "E ~ ~t~d - - d ~ - "_d~ 143

SCUD Ad ReDIace R~endations. Based on the above findings and past experience, Me size specimen required should be no less than 6 times the maximum nominal aggregate size. The nominal aggregate size is the first sieve used in establishing Me gradation smaller than the sieve size for which all ~ ~ ~ - ~ · . ~ ~ · · · ,. · · . · ~ . . . . · . - material passes. anus, a 1.5 in. maximum size aggregate (l in. nominal size) can be tested using a ~ in. diameter specimen without scalping and replacement. A statistical analysis of the findings indicate that a scalped and replaced gradation of the type employed in this study under-predicts the resilient modulus and should therefore not be used if sufficiently large specimens can be tested. If large test specimens are not practical, a scalped and replaced gradation can be conservatively employed. If the K-8 mode! is used, the following adjustment to scalp and replace results can be employed. Increase the intercept K! in the K-8 mode! by a constant factor which depends upon the material type and the amount and size of material scalped and replaced. Laboratory tests performM on large specimens should be performed to establish the magnitude of this constant. For this study an Increase was found In K! of about 20%. The slope K2 of the mode! does not significantly change wig scalping of We large size material and replacement. Specimen Saturation Base and subgrades in the field are subjected to a wide range of moisture conditions during natural environmental cycles. A particularly critical condition occurs when pavement materials reach a saturated or nearly saturated condition. This experiment was conducted to define appropriate test procedures for saturating granular materials. For all materials having stiff skeletal structures, such as aggregate bases and granular subgrades, full saturation can be achieved at values of Skempton's B pore pressure parameter considerably less than I.0. The actual degree of saturation achieved for B < ~ was estimated using relationships developed from the equations of Black and Lee [761. These relationships are given later in the moisture sensitivity section of this chapter. Preparation and Saturation Procedure. Specimens of Base ~ and 2 Table 21) were prepared to 100% of TWO maximum dry density using vibratory compaction at the optimum moisture content. Base 4 was compacted using vibration to 95% of the T-] 80 maximum dry density. A total of 9 saturation tests were performed on Bases I, 2 and 4 which are stiff aggregate and soil-aggregate bases. These bases have, for the confining pressure of 10 psi used in the tests, average resilient moduli of about 34,000 psi. After preparation, the 6 in. diameter specimens were placed in a biaxial cell and subjected to a confining pressure of 10 psi. To saturate the specimen, desired water was introduced at the bottom of the specimen under a small hydrostatic head difference of 2.5 to 3 ft. of water. The reasonably small head difference was chosen to minimize piping of fines and allow gradual specimen saturation. At selected time increments, the degree of saturation was estimated using Skempton's B pore pressure parameter. The B pore pressure parameter was monitored for a minimum length of time of about 24 hours, or until no significant change occurred in the value of B for two consecutive readings. Bacl~ressure was then applied to increase the degree of saturation of samples that did not achieve a sufficiently high degree of saturation during the flushing phase. All three bases required backpressure to reach full saturation. The effective confining pressure ((73') was kept constant throughout this phase by increasing the backpressure and the confining pressure by the same increment. Backpressure was 144

increased simultaneously with the confining pressure until no additional changes occurred in the value of B for two consecutive readings. Saturation Test Results. Flushing -- The saturation test results indicate that for the clean, relatively low fines content base materials (Bases ~ and 2), a B pore pressure value of approximately 0.2 was achieved after about 24 furs. of flushing. The results for Base ~ are summarized in Table 34. For stiff, low compressibility aggregate base materials, A B-value of 0.2 corresponds to a degree of saturation of about 98%. Flushing for 24 furs. appears to be a desirable flushing time for typical base materials. A small increase In the degree of saturation, at a decreasing rate, does frequently continue to occur after 24 hours. Base 4, which had a small quantity of plastic fines, achieved B pore pressure parameter values of 0.10 and 0.14 after 24 hours of flushing CTable 351. This B-value corresponds to a degree of saturation of about 97%. Backpressure -- Test results indicate in a carefully performed test a backpressure of 10 to 20 psi should be adequate to achieve a degree of saturation of 99% or more for commonly used base materials (refer to Tables 34 and 35~. When a lower level of care is exercised, higher levels of backpressure may be required. Resilient Modulus Variability - Type ~ SHRP Base Materials The purpose of this study was to statistically evaluate, using acutal base materials, the same three displacement measurement techniques employed in the synthetic specimen study: (~) external EVDTs, (2) top to bottom EVDTs and (3) EVDTs on clamps. This experiment, however, includes variability due to specimen preparation as well as material variation occurring between replicate specimens. Test Procedure. Materials and Results. Eight different base materials (Table 36) furnished by SHRP for the round-robin resilient modulus study were tested following the SHRP P46 Protocol (November, 1989) for resilient modulus. The order in which the X materials were tested were randomly selected, and two specimens (in one case three specimens), of each were prepared and resilient modulus measured. The K-O resilient modulus mode]was used for this and several other studies sinceit was specified in the SHRP P46 Protocol (November 1989~. Table 37 summarizes the K-O mode' constants K, and K2 and associated statistics obtained from this experiment for the three displacement measurement techniques. Statistical Analysis. The procedures given in ASTM E691-92 [77] were used to analyze the K-8 model constants K, and K2. The "K-value" method was used to examine the precision of each measurement technique and the "H-value" method to examine the consistency of He test results for the three different methods used for measuring displacement. Since all samples were tested in the same laboratory, by the same operators and in the same environment, the major sources of variability are due to (~) specimen variability and (2) the fact that the displacements were determined at different points on He specimens by different sets of LVDTs. This latter error may, for analysis purposes, be visualized as determinations performed by different laboratories. 145

Table 34 Samradon test result far base 1 B V^LuE(" . . S~ uH^TlON [ELL CON~NiNG B^CK B^SE PH^SE PnESSunE PRESSunE s I 1 f P s . 4 1. 4 fLUSHlNG 11.4 1.4 11.4 1.4 1 1 11.4 1.4 _ --·L63F- 6.4 B^CK PRESSURE 21.4 11.4 26.6 1G.4 10.8 - lO]B- fLuSHING 10.8 0.8 10.8 0.8 1 2 10.8 0.8 _ 13.8 6.8 B^CK PnESSunE 20.8 10.8 26.8 13.8 30.8 20.8 11.2 1.2 fLuSHlNG 11.2 1.2 11.2 1.2 1-3 11.2 1.2 16.2 6.2 B^CK PRESSunE 21.2 11.2 26.2 16.2 31.2 21.2 ~ S(2) { ~ ) T1~E(3) EL^PSE0 (HRS] 0.14 0.18 0.24 0.22 0.74 0.84 o.es O . 1 0 0.16 0.20 0.22 0.44 0,72 0.88 2.88 0.10 0.14 D.16 0.20 ''0 T] 0.60 0.82 0.98 0.OO4 0.OO3 O.6 l2 24 3 ~ 3G 33 36.62 ee e" ~ ~ . ~ ~ .~ 2 1 6 23 - 23.2 2~ 3 ~. 23.4 23 5 ~ nea ~ . ~ e ~ 0.B84 0.!01 0.DO4 0.084 0.98g o.ses o.sb7 o.' 1 ~ 20 ~6 36.2S 36.40 36. 66 36.70 1.000 NOTES: 1. SKE~PTON~ PORE pnEssunE P^R^~ETEn(B) ~ C^LCUL^TED BY ~V1D~G THE CH^NGE ~ THE PORE PRESSURE BY THE ~CRE^SE ~ THE CELL CONF~ING PnESSuRE ~ PSIIN TH~ T^BLEt DEGnEE Of S^TUR^TION ~)c^LcuL^TED US~G THEORETIC^L EOU^T1ON ^ND ~E^SURED SPECI~EN . EL^PSED ~E FRO~ THE BEG1NNiNG Of THE s^TuR^TIoN TEST. 146

Table 35. Saturation Test Results for Base 4 SATU RATION Cam ARM - 8 A" 8 ( 2 ) BASE PHASE PRESSURE PRESSURE 8 YALUE(~) ( {PSI) (PSI) .. 11.4 1.4 . PLU5HlHa ~ LEAK WAS DETECTED AT THE TOP 1 1. ~1. ~0. t 0.9 8 3 11 .. 1 .. 0.1 0.983 . 1 ~16.. 6.. 0.32 0.991 21.4 11 .. 0.~. . BACK DEMURE 2 ~ . ~1 ~ . ~0 . ~ S 0.9 9 6 3 1. ~2 1. ~0.6 ~ . 3B.. 26.4 0.7S 0.999 1 1.3 1 .3 0.0 ~ 0.0 8 0 FLUSHING 1 1 . ~1 . 3 0. 1 0.9 8 . . 16.3 6.3 0.26 0.993 21.' 11.3 0.42 26.' 16.3 0.50 . 4- 2 BACK "E"URE 31.3 21.3 0.~. 0.99S 36.3 26.J 0.72 41.3 S1.3 0.~4 46.3 S6.3 0.92 . ~ 1.3 ~ 1.3 0.0 ~ 1.0 0 0 ~_ ~ 1.3 1.3 0.12 0-.-9 S7 FLUSHING 1 1 . 3 t . ~O .1 ~ O . 9 S 9 16.3 6.3 0.32 0.995 21.S 11.3 0.~. 0.995 ~ 6. ~1 6. ~0. ~ 2 . 31 .S 21.' 0.~' 0.998 · 3 BACK PRE"URE 3 ~ . ~2 l. ~0.7 ~ . 41.S 31.S 0.~. 0.999 46.3 36.3 0.04 . 51 .S 41.3 0.0J t.000 TIhIE(~) ELAPSED (HR8) 0.75 0.75 48 49.1 49.' 60.1 50.e 0.~. __28 28.6 28.. 29.t 29.' 29.' 30.2 30.e 31.1 -0.~' 24 24.. 24.7 25.2 25.. 26 26.' 26.' 21 NOTES: 1. SKEMPTON'S PORE PRESSURE PARAMETER (B) IS CALCULATED BY DIVIDING WE CHANGE IN WE PORE PRESSURE BY THE INCREASE IN THE CELL CONFINING PRESSURE (5 PSI IN THIS TABLE). 2. DEGREE OF SA~RA~ON (S) CALCULATED USING THEORETICAL EQUATION AND MEASURED SPECIMEN STIFFNESS. 3. ELAPSED TIME FROM WE BEGINNING OF WE SA=RA~ON TEST. 147

Table36 · Summary of SHRP Type ~ Base Materials Material No. | Descriptlon Well graded, r~astic,~.5 ~ maximum I, ~bangubrto unbar Id Cow. Coat agg~s ~ bat k, ~ 26 w~h~.S~" to: 100 % T 180 deadly; dry derby ~ 138.6 pet ~ 6.0 % Mere - - Well grated, nonplastic, 1.S h n~wrn-0, sir to Angus arched stom. Coarse aggrieve 18 brown to may 51 w th some embedded I. ~ aide 18 Rely Aimed by finer meal. Spewer chipped to: 100 % _ _ T-180demly;dty dens ty~138.6 peat 6.0% ~erconter~ WeN Misdo, nor~astk, 1.5 h maximum laze su~ularto 148 angular crushed ~one. Coame aQgr~e vases h mbrtrorn #ah to dark gray. Speclm~ compacted to: 100 % T-180 dens ty; dry dens ty ~ 138.6 pa. ~ 6.0 % who corisr~ - - Well graded, nonplastic, 1.5 in ma dmum laze singular to 173 angu ar ~ ~one. Coarse aggregate hi ~ whys me ash erred black panicles. SO Id to: 100 % __ _ T-180 density; dry density = 133.6 pc! ~ 8.0 % wstsr capers ~ I_ > n _ ~ m - -em 178 Rule Bushed Cone. Coarse averse ~ its web embedded small black pi. Sped Red to: 100% T-180;drydensly=133.6 =~ 8.0% w~ercadenL Well graded, nonpoetic, 1.5 h maximum laze subar~ar to 1 96 abut cut To - . Coat pet ~ 1= may with clerk Kidded pant. Spy card to: 100 % T-180 density; dry dens ty ~ 138.6 pd at 6.0 % tier content . _ WeN graded, n0astJc, 1.75 h rnexJmum ^e Carte t 97 Angie Bushed stab. Coal" par&lee am lit Cay wth dark Added pane-. Sp~r~ cued to: 100 % T-180 dirty; dry densely ~ 133.6 pd at 8.0 % Her corms Poorly graded, nonplastic, 1.S ~ mum - e su~ to 202 =gular crushed stone. High~ssoor4~ Coarse what wth ~ Cry carom. Speclmens compacted to: 100 % T 180; dry densky ~ 133.6 pot ~ 8.0 % Oar coning 148

Table37. Summary of SHRRP resilient modulus test results: K-8 mode} SPECIMEN EXTERNAL | TOP-BO;0 1CLAMPS rat K1 | K2 | rat | K1K2 rat 1 K1 0~22s7 ~,02t.040~S2710.9~71 ~,10S. ~0.60929 o.ms8 a,~25.0~ 0.~6e s^7.n0~3o.st t 1 0 ~7e 0~0303 o.sez, / ~,9382. 0.9~1 22 ~,378 ss0.5121 00.9281 6 s=3.~3 0~27~0 0.96~79 6,668.~2 0.~3282 ~982 .70~6161 S0.91880 Saws." o~7 0~1. .,9, 0.62 o . 0 0 m ~ 7 ~ 1 10 . 0 2 8 3 s0 4 0 7 0 ~ 3 5 . ~ 7 0 ~ s 0 . 0 0 7 8 9 1 0 ~ 0 t 0 ~05~0.8 9.. ~0 ~14 0.90416 :~.920.682040.89898 ~9~01 ~9 0.71 "9 o.~s 5,t 9421 0.90134 3,358."0.599820.89570 3~." 0.61 ~0.~2 4,1 ".80 0.90275 30;.840.6~930.89734 3,0093 0.6661 2 0.95488 ---4,6~.01 0.00 1 At ".930.~1110.~1 " 19 1 = 0.~7" 0.~7 ~.20 02 1.St.402 62 72 0.9 10.7 . ._ 0.94;3S8 4~.19O."t ~0.918" 5,1~47 O.tt =2 0.9~9 7,~.02 0.9236S 4,4~.=0~0.9~17 4,"7.8S O.tl 319 0.~" 6,~9 0.93862 4,=9~10.61~0.91~7 4,7~.16 0.61 t75 0.~128 6,7~.71 0.014" 1~.320.017"0.~ - m31 0.~1 " 0.~9 ~= 1.6 3.12~80.8 7.8 02 0eS 10.8 0.849= 7~7240.~0.~42 6,~." 0~919 0.~8 8,~." 0.869" 6,771.110.561270.82352 6,901.02 O S7471 0.91 ~8,6~.42 0.85943 7,139.1 8OSS7640.83797 6,917.69 Oft 95 0.91112 8,"6.93 0.01013 ~.070.~0.01 ~16.67 0.00724 0.~4 121.49 1~2 . 520.71.7 02 12 0 ~1.4 _ _ 0.79373 4,~."0.618=O.~t 7 4,~." 0.~7 0. ~6,~t .49 0.84696 4,~ ~0.59~0.~8 4,~." 0.61 ~o. - m 5,"7." O . 8 2 0 3 5 ~ , ~ . UO . 6 ~ 7 6O . ~ 7 3 ~ , S ~ 3 . ~O. . 6 1 1 ~O. . 9 1 6 ~ , ~ . ~ 0.02661 48.210.012560.01258 239S2 0.00203 0.00910 ~.93 3~2 1.02.11.5 52 03 1.0 7.7 015665~3 7,S26.180.468380.88315 6,69228 050826 0.94681 10,321.76 0.61894 1~916=0.3n"0.~4 12,"137 0.3 ~0.7~18 11,~." 0.7~3 10,221220.~130.77~9 9,6~." 0.~81 0~9 10,"1.1 3 O.t 2400 2695.04O.O~S0.0 ~.5S 0.0 ~0.~1 "937 16.7 "..10.711.7 - .6 1~0 9.S S.0 0.815138 9,87S."0.~10.78 ~10,589.94 0.~10 0.9 ~13,9~24 0.83083 6,714."0.~90. ~7,~^ 0.48711 0.78218 1 t ,~." 0112509 B~.9SO S14=0. ~9,10837 0.47 ~0.~" 1~7 0.00S73 1~;80.400.0~90.08202 1481 = 0.01~1 0.07024 1~37 0.7 19.19~9 ~16.3 SeS ~2 _ lOn 0.87602 7,S~0.640.48504O.UO4O s~.12 0.47 ~0 ~6,~." O.m10 5,7~.490.~9790.7 ~6,~.19 0.~1 0. ~7~21.92 0~82406 6,~.070.5174 10, ~7~11 .1 6 0~ 1672 0. ~6,629. 0.05196 1~7."0.0~70.017" 1374.97 0. ~0. ~69~" _ 6.S 15.9 6.3 ~19.1 3.. 0.3 10.4 0~85576 0.~9 0.91111 K2 2" 2BC 2BD ~E" 8T~ND. DEV CV{%) 0.~915 0.45453 0.48671 0.46346 0.01659 3.6 518 51C HEAN ST - D. CY(%) 0~532 0S4247 0~389 0.00142 0~ 1 1488 ~EA~ ST - D. CY - ) 0.47~ 0 S2467 0. 0.02521 5.0 173A 1738 ~EAN 8TAND. DEV CV(%) o-~ 0.47~ 0.48289 0~00636 13 178A 1788 ~"N Br - D. CV^) 0 50753 0.53962 0~52358 0.01 604 3.1 194A 196B M 87 - D. CV~) 197A 197B 8TAND. DEV CVt%) 202 B 2=C MEAN 87 - D. CV0C) AVG r~ 0~9261 0.40527 O~98" 0-00633 1.6 0.37880 0.405Z! O~9203 0.01323 3.4 0~3972 0.47~ 0.50890 0.03482 6.1 NOT£: 1. AN A\JERAGE VALUE OF Ti1E D1RE£ LVDT DISPLACEME~ R"DINCS WERE USED. 149

Results of Statistical Analvses. The one-way analysis of variance used was carried out separately for each material both within and between measurement methods [771. Figures 65 and 66 present plots of the k statistics for the K, and K2 constants, respectively, used in the K-O resilient modulus model. Analysis of Plots using Seraph - An analysis of the k-graph for Kit (Figure 65) and K2 (Figure 663 do not reveal any significant imprecision for any of the three types- of measurements. This means, for example, that although there are differences between Kit values for the Tree methods, this difference is apparently due to Me fact that the measurement methods are different. For We K-O model, K, determined using clamps has a poorer measurement consistency than both the external and top-to-bottom methods. Nevertheless, all three methods of measurement are acceptable based on the consistency of results defined by the maximum permissible k statistic (Figures 65 and 66~. Discussion -- The results from this study indicate that the K-O mode! constants K, and K2 have reasonable accuracy In regard to variability for the 3 measurement melons used and the ~ materials tested. Plots of the h statistic reveal, however, that for the K-8 mode} the clamp readings give higher variability compared to the external and top-to-bottom methods which have similar variability. To have random error in each measurement method, the h statistic should exhibit about an equal number of positive and negative values. For the K, constant, the three measurement methods have random errors (Figure 67~. However, the error in the K2 constant, which is related to stress state, is systematic and not random for the 3 methods (Figure 68~. The type of error in the clamp measurements appears to be different than both the external and top to bottom methods since the sign of the h statistic is different. The resilient moduli determined from readings performed on clamps give a different K-D mode} than obtained from external or top to bottom cap displacement measurements. In general, Kit is higher and K2 smaller for clamps than for He other methods. Repeatability of Resilient Modulus Measurements Introduction. To investigate the variation in resilient moduli predicted from measurements, values of resilient moduli for bulk stresses of ~ = 20, 35 and 50 psi were analyzed using the results from tests on 26 different specimens (13 replicate pairs) and 4 different materials. These results were developed using a data acquisition rate of 666 data pointsIsec. The use of 200 data points/sec., the optimum for He specific system used in this study, should slightly reduce the overall resilient modulus variability. The use of improved resilient modulus models, discussed in the next section, would also reduce the variability a small amount compared to the K-O model used. Analysis of Repeatability. The mean value, standard deviation and coefficient of variation for each test are summarized In Table 38 for bulk stresses of ~ = 20, 30 and 50 psi. The standard deviation and coefficient of variation was determined for each pair of replicate tests at each value of bulk stress. The standard deviation (~) and coefficient of variation (CV) for the population was then estimated by averaging the individual values for each of the 13 replicate pairs. These results show that the coefficient of variation (CV) is on the average ~ ~ % higher for clamps when compared to external measurements. At a bulk stress of 50 psi (resilient modulus of about 50,000 psi), however, the coefficient of variation was 10% less for clamps. This improvement in performance at a higher specimen stiffness of clamps relative to external EVDTs is caused by the great importance of extraneous deformations as material stiffness becomes large. 150

1.8 1.6 ~ 1.4 en 1.2 1.0 0.8 z 0.6 8 oe4 ~ 0.2 0.0 1 1.6 1 12 1.0 0.6 0~4 Q2 ~0 . _ . , . . . . . _ EMUS PENIS SIBS k ~ 1.~ _ _ _ _ _ _ _ L t 2ti 51 148 173 178 196 197 202 MATERIAL Figure 65 . Variability of Kit constant as indicated by the k statistic: SHRP materials . -cam-PERM=81-E ~ · 1.~ ! ~ _1- ~ _ __ _ ~ __ _ _ H HEmOD T-S CEP __ tar 25 51 149 173 i79195 ~_ 26 51 148 173 1781S,B 1" 21J2 MATERIAL Figure66. Variability of the K2 constant as indicated by the k statistic: SHRP base materials 151

1. o, 1.0 0.5 Z 0.0 -1.0 -1.52 1 .5 1.0 0.6 o.o ~.5 -1.0 -1.5~ . _~ ~ ~ ~ 3 ~; MAXIMUM PERMISSIBLE h-1.15 ~ - ~ . .~ . | MlNiMUM PERMISSIBLE h =-1.15 | ' 1 - ~-I I u"509~ r r -z . . T-B ~3 CLP 26 51 148 173 178 196 197 202 MATERIAL Figure 67 . Variability of the Kit constant as indicated by the h statistic: SHRP materials i l=---l_ NtAXIIJIVt~l P - MISSIRLF h . 1.15 j ~1 | MINIMUM PERMISS118LE h --t.15 | . i . 26 51 148 173 178 196 197 202 MATERIAL Figure 6& . Variability of the K2 constant as indicated by the h statistic: SHRP base materials 152 MEASURMENT MOOD EXT T-S CLP

Table 38. Average statistical results for 13 tests using replicate pairs _e . . ~ LYDT TEST HEAN e · ~ PS' HE" e · ,~ PSI HE" e · ~ pew t.OSlilON ~ERIE8~13 HR ~HR o . OR _ (P81) (P81) ( % ) (P8l) lPSI) ( ~ ) (PS1) (~81) ( % ) EXTERNAL G! 24818 t 007 4.06 34936 t llS 4.~' <belt 2258 1.28 GT Q 28137 1440 1.13 30848 1309 3.St 50638 2648 S.23 A ~26478 1 228 4.~S S7390 1532 4.10 47046 2454 S.22 _ _ . CLANP' 29283 2081 7.11 1.014 2528 6.47 48880 2833 ·.04 G! Q 29459 1321 4.~. 40306 1452 3.60 8001 ~ 746 l.~. 1 Am 1 ·361 117°' 1 1.71 1 llll0 ~ 108 1 i.O2 1 48441 1 1200 1 4-73 ~ FORTIES: 1. GT INDICATES RESU' TS FROM ME GENERAL GEORGIA "CH MAT SERIES FOR HAVERSINE LOADING. GT~ INDICATES RESULTS FROM ~E GEORGIA TECH GUASkSTA~C TEST SERIES FOR ~ HAVERSINE LOADING. ,. NoTAnoN: e · BULK STRE"; ~ · StANDARD DE~DON; C' ~ COEFFICI£= OF VARIATION. - 153

Variability of Model Constants vs. MR. For actual design applications, the overall reliability of the resilient modulus test is indicated by the variability of the resilient modulus. As shown in Figure 69, the values of K, and/or K2 used in the K-O model for calculating resilient modulus vary from one test to another, even for Me same material and testing conditions. The variations in K, and K2 usually appear to be more significant than the actual variation in resilient modulus calculated using these constants in the K-8 equation for ranges of the bulk stress (~) of usual interest. The above discussion is also true for other type resilient modulus models and was found to be valid throughout the study. Repeatability Models The laboratory repeatability of the resilient modulus values are given in Table 39. Results are presented in terms of Me coefficient of variation (CV) as a function of the number of replicate laboratory tests performed. The results of each replicate pair of tests were combined to develop the resilient modulus K-8 model. The coefficient of variation (CV), as a function of the number of replicate tests performed, is determined using Me relationship CV 2~/(n MeanM (12) where ~ is the population standard deviation, n is the number of replicate tests to be used, and mean MR is the mean calculated resilient modulus at a particular value of bulk stress. The average coefficient of variation of resilient modulus given in Table 39 for one specimen is 9.3% using external EVDT measurements and Il.~% for cIamp-mounted EVDT measurements. By using two replicate specimens, the average coefficient of variation for the resilient modulus drops significantly to 6.6% and 7.~% for external and clamp measurements, respectively. These coefficients of variation are valid for typical unstabilized aggregate bases and the K-6 model. As shown In the table, if more than two replicate specimens are used, the return, in terms of rate of decrease in the coefficient of variation, becomes rapidly less. These coefficient of variation findings indicate that the number of replicates used in a testing program may have, under ideal conditions, more potential impact on the required pavement thickness than does the location of the axial displacement transducers on the specimens. This finding only applies when careful system calibration has been carried out after minimizing extraneous system deformations. Accuracy of Resilient Modulus Models The K-D model, previously given In Table ~X, is widely used for predicting an appropriate resilient modulus for design. This model, for example, is used in the 1986 AASHTO Guide. A statistical analysis was carried out using resilient modulus test data from the latter part of the study to compare the accuracy of the K-D mode! with the Uzan, UT-Austin and UTEP models Table Ala. This section explores the accuracy of these models using the tests data on granular materials developed as a part of this study. Study Methodology. Base I, 2 and 4 materials (fable 21) were used in this study. Gradations used with these methods included the conventional gradation (BIBF, B2F, and BE test series) and the scalped and replaced gradation (B2BR and B2R test series). A total of six different combinations of gradations and materials were used to identify the optimum resilient modulus model. Two replicate 154

70,000 60,000 Cry 50,000 - C]: :~ 40,000 CO - C' 30,000 o Z 20,000 - cn lJJ a: 10,000 ' _ 10 20 30 . , . . . . . . . 1. . . . ..... 40 50 60 70 80 100 . . . . . . . . ,,,, I o'er LEGEND ·-4 ~(FIT) EXT (UL) EXT (LL) CL(F~) CL (UL) - CL (LL) K ~ MODEL 99% CONFIDENCE Kt =4,653 K K,- 2,995 K2 -.6505 NTERVAL _ ~ ~ lll.~1111111~1111011~' Ilililil~6rilarl~ll ~ nib I_ ~10000 20 30 40 50 60 70 80 100 70,000 60,000 50,000 40,000 30,000 20,000 8(PSI) Figure 69 . Variation of resilient moduli for external and clamp based K-8 models: 99 percent confidence interval 155

Table 39. Resilient modulus coefficient of earl on for selected bulk stresses: K-O model METHOD NO. OF OF SAMPLES BULK STRESS, MEASURE ~ N ) 2 0 | 3 5 1 9.3 8.2 EXTERNAL 2 6.5 5 .8 S 5.3 4.7 4.6 4.1 1 12.8 10.8 CLAMP 2 9 . 1 7.5 ~7.4 6.1 , ~6.4 s.3 s 0 AVON 0.4 7.. 8.0 S.2 9.3 6.6 5.4 ~ .6 9.7 6.9 4.9 1 1.1 7.8 8.4 Table 40. Comparison of statistics for K-D, Uzan and UTEP models: single and pair of specimens No.of ~ Mcasuremel: ~ K~Mode! ~Uzan Model ~ UTEP Model Specimens ~Method ~ ray%) ~ a(%) ~ MSE rot%) ~ a(%) ~ Ex:te~1 90.1 4.7 0.00386 97 2.0 0.0122 96.3 1.2 . Clamps 96.9 2.1 0.0085 98.8 0.6 0.00033 99.1 0.6 External 94.6 2.0 0.0013 7 96.4 1 .9 0.00091 97.2 1 .6 Clamps 1 89.3 1 3.4 10.003891 96.1 1 2.2 0.01461 97.8 1-3 L Notation: 1. r2 = Square of correlation coefficient 2. c' = Standard deviation 3. MSE = Mean squared error 156 MSE 0.00068 0.00026 0.00071 0.00082

specimens were tested for each material/gradation combination giving a total of 12 complete resilient modulus tests. A statistical analysis showed the validity of combining the data for the replicate specimens. Results. A summary of the statistics for the K-8, Uzan and UTEP resilient modulus models are shown in Table 40 for both externally mounted EVDTs and EVDTs located on clamps. As shown in these tables, both the Uzan and UTEP models give a much better fit of the data with smaller standard deviations (~) and mean square errors (MSE), and larger r2 values than the K-D model. K-D Mode! - The popular K4 mode! only uses the bulk stress ~ = a, + o2 + O3. As a result, applied shear stress and strain are not considered in the model. These variables, however, have been known for some time to have an important effect on the resilient modulus of granular materials. As a result, a near perfect fit of experimental data is not usually possible using the K-D model, regardless of how accurate the tests are performed. Based on experience using more advanced models, near perfect fit of the data is indicated for a single specimen by an r2 value consistently greater than about 0.97 and a small mean square error less than about 0.001. For a K-8 mode! fitted to data obtained from a single specimen, the test results tabulated in Table 41 give an average rid value of 0.90 for externally mounted EVDTs and 0.97 for internal clamps. Average mean square errors (MSE) for externally mounted EVDTs are 0.004 and for cIamp-mounted EVDTs are 0.0009 (l able 41~. When two replicate specimens are used in the mode! fit, the average r2 values for the external measurements increases to 0.95 while it decreases to 0.89 for internal clamps. For the K-O model, these results further substantiate findings presented earlier indicating internal clamps give more consistent results for a single test, but have a higher scatter between tests than for external EVDTs. These average r2 and mean square error results can serve as a general guide for evaluating experimental K-D mode! accuracy. Uzan and UTEP Models -- Now compare Me Uzan and UTEP models Table 41) with the K-D mode! using the test data obtained by combining the results from two replicate tests performed on identical but separate specimens. The r2 and mean square error (MSE) values presented in this discussion are Me average of the external and clamp EVDT measurements. The UTEP model, which results in the best fit of the data, has an average r2 value of 0.975 while the Uzan mode! has a slightly lower value of r2 = 0.963. In contrast, the K-O mode} has an average r2 value of 0.920. An examination of the mean square error (MSE) indicates a similar ranking of Me methods with the average MSE for the UTEP model being 0.575 x 10~3, Me Uzan mode! ~ . ~ 8 x 10~3, and for the K-D mode} 2.63 x 10-3. The mean square error for Me K-O mode! is thus more than 2 times that of the other two models. On the average the unexplained error is only 2.5% for the UTEP mode} and 3.7% for Me Uzan model. In contrast, Me K4 mode! has an average unexplained error of 8%. Nonlinear Curve Fining - In He past, curve fitting has been carried out by taking the logarithm of each side ofdle equation to linearize it. This linearizing method was used, for example, to analyze the data given in Table 41. Linear regression techniques are then easily applied to determine the regression constants and associated statistics. Palmer [78] has used true nonlinear regression Mat does not require linearizing the resilient modulus mode] first. The full gradation data for Base ~ and 4 was used in Me study as well as He replaced gradation data for Base 1. 157

Table 41. Comparison of mode} fit statistics for K-O, Uzan and UTEP models: single and replicate specimens . SINGLE SPECIMEN TWO REPLICATES Model I rig I <I I MSE | ~ | r2 | ~ | MSE | __ . . . CLAMI' MEASUREMF~TS . _ _ ~ K-43 96.9 2.1 1 0.00085 0.00068 89.3 3.4 0.00389 0.00118 Uzan 98.8 0.6 1 0.00033 0.00015 96.1 2.2 0.00146 0.00073 UTEP 1 99 1 1 0.6 1 0.00026 1 0.00013 1 97.8 1 1.3 1 0.00082 1 0.00044 EXTERNAL MEASUREMENTS l , K-0 90.1 4.7 0.00386 0.00183 94.6 2 1 0.00137 Uzan 97 2 0.00122 0.00075 96.4 1.9 1 0.00091 UTEP 98.3 1.2 0.00068 0.00042 97.2 1.6 1 0.00071 0.00059 0.00048 0.00041 Notation: 1. r2 = Square of correlation coefficient 2. ~ = Standard Sedation 3. MSE = Mean squared error 158

The linear and nonlinear regression analyses were found to give very similar relationships for resilient modulus as shown in Figure 70 for the K-8 model. The linear K-O curve fitting approach, however, was found to clearly give a smaller confidence interval than the nonlinear approach CTable 421. For the UTEP model, the nonlinear regression analysis gives similar or slightly less variation (Table 42~. These findings indicate that the linear regression approach commonly used for the K-O mode} is more desirable than using true nonlinear regression. Linear regression can also be used with the other more accurate models. Mode! Confidence Intervals -- Palmer [781 also studied the confidence intervals for the resilient modulus models. As shown in Table 42, the confidence intervals for the K-O models were found to overlap significantly for Bases ~ and 4 which have a full (i.e., unscalped) grading. As a result, the K-O mode! is not capable of distinguishing the difference between these two materials even though they are different. Also, a single K-8 model, with a single set of parameters K! and K2, was statistically found to fit He combined data for Bases ~ and 4 equally well as for the individual materials. These results show that the K-O mode! does not have the highly desirable ability to always distinguish between dissimilar materials. Of great practical significance is the fact that the Uzan, UT-Austin and UTEP models are capable of distinguishing between Me two different materials as indicated in Table 42 by essentially nonoverIapping confidence intervals. Recommendations - Design Resilient Modulus Model. Since the K-0 mode! does not have the ability to distinguish between different materials, it is not suitable for resilient mode! characterization particularly for directly comparing different materials. The Uzan, UT-Austin, and UTEP models all give a better characterization of resilient modulus than the K-D mode! and have, from a practical viewpoint, sufficient accuracy. The UTEP model, in contrast to others, uses axial strain as one of the two variables required for predicting resilient modulus. The stress, as opposed to axial strain, is usually known at the beginning of the design process. Therefore, to use the UTEP method in most applications an iterative approach is required. Since the determination of a suitable design resilient modulus is not straightforward, the UTEP mode! is not the best choice for use in practice. Either the Uzan mode} or the UT-Austin mode} are suitable for use in practice. The UT-Austin mode! has the important statistical advantage of not having a variable repeated in the two terms. The Uzan model, in contrast, uses repeat variables in the two terms and hence is over parameter~zed which, statistically, is not desirable. The UT-Austin mode! does have a very slightly smaller percentage-wise spread in the confidence interval. Location of EVDT Displacement Measurements The memos usM to measure axial displacement in the resilient modulus test on granular materials potentially has a significant influence on the reliability of the results. This discussion is restricted to the three EVDT measurements used in this study: external, top to bottom, and clamps. The resilient modulus models discussed in this section were previously presented in this chapter and summarized in Table 18. Accuracy. Consider the accuracy of the three methods for granular base materials and the specific apparatus and calibration procedures employed in this study. Extreme care was exercised in removing compliance from the testing system and in calibrating the system using both aluminum and 159

C ~ arnp-measurecl - ,0 60 - :' ~ 0 ~so _ ~ 0 ._ _ ._ As ~ so - 30 - +~/ 20 - 10 Legend First Sample + Second Sample Rest ~ tend Modulus ++ ~ W __ 0 20 40 60 eo 100 Bulk Stress Figure 70. Comparison of K4 model linear and nonlinear fit of resilient modulus data: example with largest difference 160

ASK(1) Table 42 . Comparison of 95 % confidence interval and mean square error for resilient modulus regression models MEAN SQUARE ERROR | EXTERNAL CL - PS ~ o~ (x~ o8) _ CONSTANT I EXTERNAL MR I CLAMP MR |UPPER(3) | EQN(3) lLOWER(3) 1 UPPER(3)T EaN(3) |LOWER(3) _ K-e MODEL 4800 0.732 s400 0.747 ~ 6 6 0 0.~59 6890 0.804 1 1 (NL)(2J ~ (N L ) (2 ) 3 .4 . K 1 2 7 ~ 0 3 6 2 0 K2 0.S82 0.6S7 K1 2400 3620 K2 0.528 0.638 K 1 2 0 3 0 K2 0.53 K 1 1 2 5 0 K 2 0. ~ 8 8 ~ ~ ~. . _ __ _. UZAN `'ODEL ~ 6 1 0 0.55 4440 5720 7090 0.491 0.~42 0.61 1 3.1 22.0 6.9 3630 0.492 6Bt0 0.647 k 1 1900 2620 k 2 0.8 ~ 0 0.9 9 3 k 3 .0.~40 .0.3S7 k 1 1500 2060 k 2 1.0 ~ 0 1.1 ~ 9 k 3 0. 6 1 0 0. S 1 9 AUSTIN MODEL 1 3300 1.0 9 0 - 0.2 8 0 2600 1.260 .0 .43 0 42 0l, 0.540 ·0.1 ~o 3 S 0 0 ~ 1 2 0 0.760 0.617 .0.31 0 0 260 5 ~ 1 0 6 6 0 0 0.623 0.~1 0 3.2 .0.094 -0.020 4700 0.070 0.21 0 2.7 1.3 . ~ ~ 4.S 2.7 KS 73.10 8S.7S I 98.40 K6 0.93 1.01 1 1.08 K7 .0.66 .0.S9 1 .0.S2 . ~, K5 82.4 1 94~4 106.4 1 68.3 74.8 1 81~3 1 4~7 L -- K6 1.03 1.10 1 1~17 1 0.97 1 1.02 1 1.06 K7 .0.77 -0.71 1 .0.64 1 .0.60 1 .0.S6 1 0.52 UTEP MODEL (No N. LINEAR) 64.80 0.83 · 0. ~ 7 I K8 1 220 1 286 I K9 1 0.690 1 0.736 I K10 1~0.310 1.0.279 I K8 1 t 10 I ~ 33 I K. I 0.710 I 0.761 I IC10 1 0.390 I.0.3BSI K8 1 160 1 . I K9 1 0.69 1 I K10 1 .0.32 1 . 630 0.770 .0.1 90 2 1 0 0.770 · 0.3 2 O L ~ . o 0.78 .0.2< 1 840 0.5 3 0 0.200 ~o 0.6 1 0 .0.270 ~o 0.53 .o.1 7 7s.0s 0.90 ·0.41 8S.30 0.96 .O ~ 5 2009 1 41 80 0.580 1 0.640 -0.113 1 -0.030 691 , 0.6S0 -0.21 1 1 NOTES: 1. BASF 1 AND 2 ARE ~E FULL GRADING. 2. NONLINEAR (NL) CURVE FIT1-ING OF DATA WAS USED. 3. NOTATION: EQ~ - CONSTANTS OBTAINED FROM CURVE F~NG UPPER = UPPER CONFIDENCE INTERVAL CONSTANTS LOWER - LOWER CONEIDENCE I~ERVAL ~NSTANTS UNITS: (PSI) 161 9.9 , 1 2.2 890 0.670 .0.1 so 3240 0.63 .0.05 1.4 1.7 0.9 2.2

15 a: 10 e ~ a: A Zen O 111 ~ ~ ~I': Lll mc, fez O ~-1 0 tar -20 STANDARD DEVIATION (my) _,, - ... A:~D'-DEvIATIU" 20 2s 30 as 40 BULK STRESS Figure 71 . Observed error between clamp and externally measured resilient moduli 162

synthetic specimens. The high level of care required to achieve good results should be remembered in interpreting these findings. The resilient moduli calculated for the K-O mode! using externally mounted EVDTs on the average is about -5 to ~.5% less than the values obtained using clamps for bulk stresses (~) varying from 20 to 40 psi, respectively (Figure 71~. This is approximately the range in bulk stress of usual interest. The average standard deviation of the difference in the resilient modulus of the two measurement methods is 8.7% for this range of bulk stress. The difference in resilient moduli between external measurements and clamps is also quite similar for the UT-Austin model. On the average, EVDTs placed between the top and bottom platens were found to give only slightly better results than for the externally mounted EVDTs Because of extraneous deformations in the system, determining the correct axial deformation, even with careful equipment calibration, is quite hard using external L`VDTs. This is particularly true for small displacements due either to use of a small applied axial stress or a very stiff material. Relatively stiff granular bases having moduli greater than about 15,000 psi and less Man approximately 50,000 psi are typical of the bases tested in this study and used in practice. These relatively stiff materials, upon repeated loading at conventional stress levels, undergo small axial deformations. These small deformations cause small accelerations on the clamps which support the EVDTs and small inertia forces which do not cause slippage of the clamps. As previously discussed, resilient moduli measured using clamps showed relatively good agreement with values measured between plugs glued in the synthetic specimens for stiffness as in the range of typical base materials. For these reasons, resilient moduli obtained from cIamp-mounded LVDTs of the type used in this study, are more accurate than moduli obtained using either external or top to bottom LVDTs for typical stiff aggregate bases. Variability. Variability relates to the amount of scatter in measured resilient moduli both within a single test and also between tests. The observed variability of test results for Base 1 and Base 4 is illustrated in Figures 72 and 73, respectively. Each UT-Austin resilient modulus model, which was found to be the most accurate, was fitted to the combined results of two tests on each material. Figures 72 and 73 are representative of He larger observed differences in moduli for He study but not the largest variation. For Figures 72 and 73, the UT-Austin resilient modulus mode] was used to calculate resilient moduli as a function of confining pressure for values of deviator stress (~-03) Dual to two times the confining pressure (a,). For deviator stress ratios of (o,-a~)/a~ = 1 and 3 used in the testing sequence, the effect of deviator stress was small and hence its effect is not shown on the figures. Two sets of 95% confidence intervals are shown on these figures. The wider confidence intervals are based on examining the variability of the individual mode} constants. The smaller confidence intervals are based on variability of the resilient moduli calculated using the models. For both interpretations of the confidence intervals, the external EVDT regression lines fall within the 95% confidence intervals for the clamp mounted EVDT data. The difference between the two definitions of 95% confidence intervals, determined by He two different approaches, is quite large. Statisticians argue the significantly larger confidence interval based on mode] constants is the correct one. However, throughout the study the different methods of measurement, or even He same method and different specimens, have been found to give mode! constants Hat appear to be quite different. When resilient moduli are calculated, however, He actual variation in modulus is much less than expected. From a practical viewpoint, use of the end product, i.e., the resilient modulus model, is considered to be acceptable for design purposes. 163

120' - ~100-~ - `~, 80 o 60 Z 40 In 20- _ o 0 5 10 15 20 25 30 120 _ 100 cn By - En J o he - cn lo is: , . , NOTE: INSIGNI~CA~ DEVIATOR CREW EFFECT _^ _ .~. .o~ ~D IMPS: RANGE OF CLAMP DATA fO SAMPLES INTERVAL CALC. Me CLAMPS . . . _ ~ . . . . . . 7 as% CONFID - CE ' - --.~7 --ad Z'= ~-% Confides - 1 1 1 1 1 CONFINING PRESSURE, o3 (PSI) Figure 72. Observed variation in Base ~ resilient moduli using external and clamp EVDTs: UT-AUSTIN mode! . ~- ~ NOTE: INSIGNIFICANT DEVIATOR STRESS EFFECT 80 60 40 20 - ~ O 0 5 10 15 20 25 30 _ ~ A\ \ ,_ , I, - , 95% CONFIDENCE r / UdTERVAL L/ CALC. I'JIa ~ CLANIPS \ RANGE OF CLAMP DATA TWO SAMPLES CONFINING PRESSURE, 03 (PSI) Figure 73 . Observed vanationin Base 4 resilient moduli using external and internal clamp EVDTs: UT-AUSTIN mode! 154

Finally, vertical bars with horizontal lines at the top and bottom of them are also shown in Figures 72 and 73. These bars indicate the actual extreme variation in measured resilient moduli observed in the two replicate tests using clamps. This band, which has data points within it that are not shown, reflects primarily experimental variability of the raw data but also includes a small effect of deviator stress on resilient modulus. Only the Base 4 data for the external EVDTs fall outside the scatter in measured data for the clamps as illustrated in Figure 73. Although not shown on the figures, the confidence interval for moduli measured using clamps was slightly less than for the external EVDTs although for practical purposes He interval can be considered the same except at levels of bulk stress greater Man about 50 psi. Displacement Measurement Me~od. In selecting a displacement measurement method, consideration must be given to both how complicated the method is and also the variability in the resilient modulus test results. Resilient modulus variability caused by specimen preparation and testing results in a relatively large 95% confidence interval even when two replicate tests are performed. The observed difference in the present tests between resilient moduli obtained using either clamp-mounted EVDTs (or top to bottom EVDTs) and external EVDTs, based on the data presented, does not appear to justify the use of either type of inside mounted EVDTs for routine laboratory testing of aggregate bases. This difference on the average was less Man 6%. Great care am effort, however, were expended in calibrating the testing system for the use of externally mounted [VDTs. Synthetic specimens were used with EVDTs attached over the middle one-half of the specimen. Use of clamps throughout the test, in addition to externally mounted EVDTs, helped to insure that the external measurement system gave good results. The results of the multi-lab tests on granular bases given in Append H indicate significant differences in laboratory determined resilient rnoduli can exist between laboratories even when the testing system has undergone the extensive calibration described in Apperulzx D. This type calibration was not carried out in other multi-lab tests performed before this study. Even considering the large variability that occurs in resilient moduli caused by variable factors such as seasonal moisture changes, the use of inside deformation measurements, as previously discussed, is the most desirable technique. Lim+Fly Ash Stabilization A limited experiment was conducted to establish the feasibility of performing in the biaxial cell resilient modulus tests on lime-fly ash stabilized base materials. Tests were performed on the Base 2 material at two levels of stabilization: (~) 4% lime and 8% fly ash and (2) 2% lime and S% fly ash. Tests were also performed on Base 4 using 4% lime and S% fly ash. Test Procedure. Hydrated lime and Type ~ fly ash were used to stabilize the bases. The amount of lime and fly ash mixed wig each base was by percent weight of the aggregate base material. Resilient modulus results are given in Table 43 for specimens tested in the as-compacted, dry and soaked conditions. Specimens were soaked by applying to He inlet drainage line a 2.5 ft. head of water, measured at the center of the specimen, using the procedure described in the saturation section. Drying was accomplished by either placing the specimen in an oven for 24 hours at 49°C (120°F) or by placing He entire biaxial cell in a constant temperature room at 41°C (105°F). The Illinois curing procedure was used for He lime-fly ash specimens. The Illinois procedure consists of placing the specimen inside a sealed container and curing for 72 furs. at 49°C (120°F). Findings. The purpose of this experiment was to determine resilient modulus test procedures for lime stabilized materials. For curing the lime-fly ash stabilized granular materials, the Illinois method was found to be rapid and hence practical. The addition of lime-fly ash offers a practical alternative for 165

Table 43 . Summary of results for lime-fly ash stabilities base resilient modulus tests SrECIME Sr=~" M~. ~ - MOURN MOD" ~ =-~9 MoD~R"i~MC if. raw. ram RODS. ~ ~c, ~ r ~ mE I .d=S S 1 ~d=10 1 * (lo) I .3=10 DI". @3=20 1 DI". BASE 2 (4% UME 8 % FLY ASH ~ ~ In - '~ Amen ~~~~. o~r~ - 1. loo 4~ - t~ 4~ "' Q~ _ "1. ea I a" opt T ~So ~.~ t= ~ - &" 1. &~ - ·~ 4 ~" ~a - - ^ - ` - '=,1" =~1326 I'Cf .06 ~ 10860 4W" ~w ~a- ~_ 100 A~E~6 1~13104 4111821 07 ~Q00114 ~e770 &4t ~22~ ~- ~1. 1.J?~46 1.~0 .~1340 nl Qa ~_ _ ~1 106F 10~ n ~* ~Op ~1- 26130E-06 1~OC8OO 49t31 · ~1 QOI ~311;- ~s -a. a ~104 e e ~ . Ex~l ·00 &1ettE<6 1~1~7 Q - # - ~1 QO~ _ _ 80 - J eM h' 100 &1~ - 1.06Gie4 'Q ~416t QO~t U,462 ~e 1 ~_ 100 7.eff6E ~Q ~Q1~181 11~2 Q00166 1~7 E ~&~6 l.a946 'QU - 1 ". QOOO.. t1.,7= A1 Op~ 100 2~ - 1.4922t .0~2 #~2 QOO" 120, ~1.40 v'S ·&n T ~tO 4~14E" 12~S 47#1 " ~O.OOle45 ~ JR~ 8825;2 ~ -1S25 1- ~1 SoldDe -1aOt? 57.t 0~002a5 ~711- l° ~t - 5E<6 1 t.7 - 416~11 1166 Q0a2113 __ 100 S.931£.06 1.1DS8S ~ ~# ~Q000" n. -<. ~d 24 h~ 100 &04BEa0t 1.~51 4#116 9~2 0~0016' "tHS21594 . S- ~Top ~100 &~E ~1260~S ·Q- ~2 o~ooOas 7~608·1448 a ~100 ·0113E~06 1.11i ~4~01 ~Q ~Q000S7 -712·17.82 |~4906-C6 ~ 21-e ~74 ~7e Q t.Ol~E4t6 t:2S006 Q~1 87 ~Q0014 ~W" O; ~Q - 1641 ~7a0E436 t 1S1-e ~ 21 ·7~e Q-114 &1ettE<6 1.1~7 Q - # - ~1 Q0 ~ ~& ~ ~K~e ~n ~·1; t li 7.eff6E ~Q114 ~Q1~181 11~2 Q0016 s~6 l~a946 QU-1 ". Q000a. 2~ - 1.4922t 4~2 #~2 Q001= 4.~4E" 12~S ~n., s7 ~.001# 404266~06 1=t~e -1aOtie 57.t Q002a, ~6~66£~6 1. ~46~11 1166 Q0a2113 S.931£.06 1.1DS8S ~. ~#,. Q~ . ."aF~3t 1 ~S1 ^6101. 1~2 n~&t &~7E ~12110~S ·Q~141 9~2 Q00066 ~OII BE~06 1.11i ~Q~01 ~Q ~QOOOS? _ BASE 2 (e2% UME 8 % FLY AS~ A20p~ ~S ·~" ,l"7 ~o -~76 ~ -1~, ~ ~op~ ~D - 1e2163 -62 - ~1 Cud e~ le?01 1c' 24111. -~" Op~ ~ ~ eB2 ~D ~ 1263 - 0~ Q~d ~S ~ eL. - 2a61 E 06 1.~?4 1.04 - s7.0 ~oosa6 2ied0E'G6 1. ~-1.0~0 eq7.1 0.0~ s-1 E~6 1.~064s 481- 9ttS Q00064 ass2£~6 '.sc - 7 4~6 11Qt Q00340 a~6 '.15~0 ~s ~- . Q0Ot:# aa64E~6 1.156 - 45771i W:. o.0oOall 1.761£~06 1.~7= 1.1547 "O &00679 1.7S7£4 ~1.~2 -1.to60 - 6 Q004 - 2~E" 1.41 ~Q"40 9.S Q0011# 2716£-06 1.~2 ~n. "S &00110 2ac7£~06 1 ~Q5 ~90 ~800040 21878~06 1 ~4 ~844 Q00061 BASE 4 (4% LIME 8 % FLY AS~ 6~E ~1. ~4 ~".0 Q004" 6~0E" 1 ~Q'213 9~S 0~00~0 `216E" l..nt. 1.04" ". Q~ - ~ ~^ ~s tlon ~ 4-S8O 492~2 2H, - 2~512 aso l79,=7 1U ~`16 122124 12~840 &~ 266~ - Q96493 40m ". Q0000e . - X~ 1.~7S10 <?~7 s7.. ao~ 7.~ - 1.~0 47 ~". em262 a - ~£ - 1.5~s ¢~06 - 2 cool" aossE4~ 1.6~7~6 ~Q667e -2 Q00117 1249E-Ot 1.19637 Q3~- 9~1 solnl;7 1.1 te£-06 122531 43as7 9&3 QOOtoO 154509 21~ 1614 - <48 ~6 467 ·~380 144674 10~812 Q47 1~?22 Q" 67, - 2 11e,~9 67,?22 Q07 1t7,tl9 Ql3 241,076 .t17.SG1 220 S27__862 2 - ,t17 lQ l~etS 180,707 1S7, ~2tO 187.467 as2 1 ~164~ 1~2t7 1. - 1~487 2~t _ ~ 2t9~1 20~6 _ 181,94e 1~,049 D 1 S1,~ _ _ ~7 t.l~.~7B _ _ 6~ _ ~ 263,493 264~7 209 leO.S14- e0.660 627 1=las | - , ~`" 1.806E436 1.07790 4eCo 61.~ Q01022 26"E~ Q06C" Q017e 99.0 Q~no. _ B AS-K 4-(^ Ll-~E 8 % F-LY AS~) - . r1.102£-06 t.~" ·Q - 60 "4t Q00442 . 1 2~076~06 1.~0 1.~t "6 QC0312 r1.~7£01.:#740 Q5~ "2 QOOt" 1 2?~06 l.=Uo 4.6t76 - .2 Q01422 E - r~l-MEAsuREME~r USINC EX=RNAL L~5 --MEASIJREME?w USING TOr m}TOM LVD~S O.~" · h2"SURmE" USING C~,S L`qm S.7 £ - 121 ~0 ~"4 Qooo77 ·.1296 - ·.~. Q1 ~"3 QOlS18 r2~201 ~Q ~301= 2448£- 260300 Q ~965 Q0079 &314E" 1. ~Qt299 9&S QOOt" &062£ - 1.6~2 Q6902 - . QO~eS f~£" 124lnt ~18 9Q7 Q00008 1 6~£ - 1~11 4= S9 - 7 &000 - 1 2.~76416 1.t~4 47~7 864 Q00601 26~46 1.a6~ Q6622 "d QO~ S.10-06 1.S1~4 Q687t 07.t QOO=S 219~4t 12:~617 Q ~B7,. Q~1 2611E4t 1.21 - 4.4279 "t Q00117 166 ~Os. - t ~61Q147 - 454,919 21~22i 167,~ ·la" 132~2 10B,l14 ~. - lff,-e 116.623 - .17 ~2 "2292 a4e 1 - , - 20 ~&m 187,003 1~069 <1e . 11~ as,o~ ·1 1.- 77,9" 74~ 4" 77,C7J . ^~iD 2" 1 1 ~. & - 1 .49,.. 1 ·44.~0 426 1 1~484 1 1~.~= 436 1 ~4 1 ~S73 ·2, ~i931 1 2tA403 ~19 1 1 ·42~ 1 1~416 Q44 rl^4- 1 ·2 ~.,." 1 - ." "S11 .14 - ,74S 87,~0 Q99

improving marginal base/subbase materials. ~nportant improvement in the resilient modulus was observed even for stabiluM specimens tested immediately after preparation. Specimens moist cured in Me oven for 72 hours following the Illinois method, had resilient moduli on the order of 10 times greater than the unbound granular specimens. In general measured axial displacements of the cured stabilized materials were about 0.0001 to 0.001 in. which Is extremely small. As a result, system compliance and EVDT sensitivity become critical factors In the test. Fair agreement was found between the moduli obtained from clamp and top to bottom transducers. The inside transducers used should have the maximum practical sensitivity; the high 3b output transducers shown in Table 20 were used in this study. Use of a higher output transducer would have been desirable. Resilient moduli determined using external displacement transducers were found to be unreliable. The primary problem was that extraneous system deformation was larger than the specimen deformation and hence could not be readily compensated for even wig careful calibration. As a result, externally mounted transducers, with the load cell located inside We biaxial cell, should not be used to measure the resilient modulus of cured lime-fly ash stabilized granular specimens. For the lime-fly ash specimens tested, the K-0 resilient modulus mode} gave extremely variable r2 values typically In the range of 0. l to 0.5. These results show that the K- d mode! should not be used for stabilized specimens because it does not consider the effect of deviator stress which is of moderate to high unpor~nce for stabilized materials. The UT-Austin model, in contrast, gave r2 values typically in the range of 0.90 to 0.97. The r2 values were slightly lower than obtained for unbound specimens and were also less consistent with r2 for some tests being in the vicinity of 0.7 to 0.8. The reasonably low correlation coefficients observed are $ least partly due to the previously discussed problems of measuring the very small deformations Mat occur in very high moduli materials. Recommended Test Method. The resilient modulus test proposed for granular materials (refer to Appendix E) can also be used for Me-fly ash stabilized materials. Very small deformations occur when a specimen is treated with a high level of lime-fly ash and then allowed to cure for 72 furs. For those conditions axial deformation measuring devices should have a minimum a.c. transducer output of 2.5 mv/vIO.OO! in. for a 3v excitation Higher transducer output is desirable). The specimen should be 6 in. in diameter and subjected to a minimum deviator stress of 10 psi. Use either the Uzan or UT-Austin resilient modulus mode! in reducing He test data. Quasi-Static Resilient Modulus Tests - A Simple Alternative The quasi-static test consists of rapidly applying the desired stress pulse and leaving it on the specimen for a long period of time compared wig the 0. ~ sec. used in He repeated load test. The resilient modulus is then calculated using the recovered deflection which occurs when the load is removed (Figure 743. The quasi-static series of tests were performed to determine if a quasi-static test can be employed to evaluate the resilient modulus of typical aggregate base materials. This type of loading can be readily applied using a simple loading system such as a static type of pneumatic testing system. Clamp mounted EVDTs and a voltmeter, if desired, can be used to measure axial displacement. The same considerations for system compliance and calibration should be given in this test as for a resilient modulus test. 167

1 a, Load Duration l I l l l , _ 1 ~1 / / UNLOAD Strain Figure 74. Evaluation of resilient modulus from quasi-static loading-unIoading s~ess-strain curve 168

Materials and Test Me~od. Bases I, 2, 3 and 4 were used for this study (refer to Table 21 and Figure 541. These bases encompass most materials likely to be used for unstabilized aggregate base. Two replicate samples were prepared and tested for each base. ~_, The closed-Ioop testing system was used to apply the loading so that the quasi-static resilient moduli could be directly compared with moduli obtained using the conventional O. ~ sec. haversine loading. For the quasi-static tests, the time the rectangular pulse was left on the specimen was the same as the recovery period between pulses. Both 2.5 and 5.0 min. load/unload durations were used for comparison. The standard resilient modulus loading sequence and stress state, including conditioning and seating load, was also employed for the quasi-static tests. Three load and unload cycles were applied for each stress condition including conditioning. The auasi-static resilient deformation was determined unon unloading by taking the absolute value of the difference between specimen deflection just before the end of the loading period and again at the end of the recovery period. Resilient moduli were then calculated following the same approach as for the repeated load test. Test Results. Table 44 gives the K-8 mode! constants and r2 values for each condition tested in ache quasi-static test series. Resilient moduli calculated at bulk stresses of 20, 35 and 50 psi using the K-8 mode} are presented in Table 45 for Bases 3 and 4. Included in these tables are the data obtained by applying a true sinusoidal 5 and 10 hz loading to the specimen (indicated by T.S. 5 hz and T.S. 10 hz in the tables). Quite good agreement was found to exist between resilient moduli measured using a haversine pulse, continuous pulse and the quasi-static pulse. Discussion. An analysis of variance using the K-6 resilient modulus mode! was performed at the 95% confidence level to evaluate the quasi-static test. This analysis showed that statistically the 5 min. and 10 min. duration quasi-static test K4 mode] have the same slope and intercept. Also, slopes and intercepts for the K-D mode} from the quasi-static test are statistically the same as those obtained from the conventional repeated load test. Only the intercept for one replicate of Base 4 was statistically different at the 95% level; the replicate specimen had Me same intercept. The quasi-static approach works for a clean nonplastic aggregate base. Base 3 and Base 4, however, had soil mLxed with the aggregate which might help to explain why one specimen of Base 4 had a significantly different intercept but the same slope of the regression line compared to the conventional test. Thus, the 5 men. quasi-static resilient modulus test and the conventional test are statistically the same for the clean aggregate bases tested and for practical purposes the same for the other bases. The total testing time required to perform a 5 min. load duration quasi-static test is about 260 min. compared to 130 min. for the 2.5 min. test. The 2.5 min. quasi-static test can be used which reduces the testing time by one-half. Additional testing would very likely show Mat a ~ or I.5 min. quasi-static test could also be successfully used to significantly further reduce the testing time. The 2.5 min. qua~i-static resilient modulus correlates very nicely with conventionally measured values as shown in Figure 75 (Clamps: r2 = 0.993; External: r2 = 0.970~. For both the 2.5 and 5 min. tests, the quasi-static resilient moduli tend to be slightly less than the conventional values by typically 5 to 8% which has been found to adso be true for other similar tests. Use of the regression equations given in Figure 75 corrects for this difference. Over researchers have found ~'a~i-~tatic tone tests correlate well with resilient modulus [64, 79, 801. Recommendation. Expensive electronic instrumentation is not required for the quasi-static test. Load can be applied using a pneumatic cylinder and a solenoid valve. A hand-operated switch can be used 169

Table 44. Comparison of resilient modulus results for haversine quasi-tatic and 5 Hz and 10 Hz Continuous Sine Loading - Single Data SPECIMEN BlSIC BlS2C PUMICE HaversIne - SeO mla - 2.S~ Have~s~e SO my 2.S mls ME4SUREME:NT I ODNT, EXTERNAL . I ~2 I re T 3,669 T 0.6237 4,219 05912 3,891 0.6071 4695 ~5769 4,306 0.6303 S,957 05287 - 0~9349 Q9480 Oe9236 Oe961 7 Qg342 0.9366 CLAMPS 4773 4,393 3,564 6,493 7,352 0~412 0~5614 0~6089 Q4881 Q`S899 0~4696 Q9620 Oe9498 Oe9729 O.9832 Q9~/76 0.95" B2S1C B2.~2~ ~- Haversinc T.S. 10 Hz T.S.SHz 5~0 mln . 2.S min Haversine T.S. 10 Hz T~.R 5H~ s0 mID 2.S min _ Haversine T.S.lOHz B3S1C T.S. ~ Hz 5~0 min 2.S min B3S2C B4S1C B4S2C; HaversIne T.S.lOHz T.S.SHz 5.0 min 2~5 min Haverslne T.S. 10 Hz T.S.SHz 5~0 min 2~5mIn HaversIne T.S. 10 Hz T.S.SHz S.Omh 2~mln ~5 7,240 7,532 4587 s 8,S76 8,410 13,227 6,303 7,221 4,586 3,262 2,029 2,689 3,369 3,134 2,388 3,799 4,470 0.6146 o 5383 05294 0~5723 . 0~6208 0.4997 0.49 7o 03792 05827 0 5496 0~5876 QS401 0.6706 0~8269 - 0~7426 Q684C 0.7094 Q7712 0.6443 0.6077 1 __- 2,91S _ 0.7202 . 3,171 0.6911 2,970 ~0.7380 . 2,954 0.7001 2,991 Q6gl7 . ~ 2,908 0.7126 2,944 _ Q7091 3,001 0.7164 3,119 0.718S . 2,960 0.703S . Q9014 - 0.9136 0.9041 0.9049 . 0.8914 0 8804 0.9218 0-8823 O.9362 0.9451 0.9764 0.9073 0.9243 0.9272 . 0.9397 0.8907 Q8881 0.9171 0.8932 0.8591 O.9437 Q9536 0.957S Q9517 0.9450 o.ss7s o.s607 0.9632 O.9S32 . . O.966C 170 9,~ 9,921 10,770 12,062 7,566 10,889 11,03S 17,S12 ~5 9,304 4166S 6,210 3,417 2,796 ~"s 3,267 3,257 2,498 3~04 3,411 ~. 3,107 3,070 3~219 3,174 A 3,426 3,032 3,370 3~207 2,970 Q4777 - Q4746 0~4565 - 0.4167 0.5124 0~4461 Q4402 . 0.3243 0.6031 0.4973 0~5814 O.SO96 0 6564 Q7370 0.7398 09~ Q7050 0~7676 0~6467 0.6730 . , .. Q7026 l 0.6994 0.7053 l . 0~6844 Q7181 l 0~6588 l 0.7049 QC764 0.7052 0.7023 0.9511 O.9477 0.9649 0~8937 0.8301 0~9578 0~9466 0.9106 0-9699 0.9275 0~9541 . O.g4O1 0.9527 0~9343 Q9368 0.9371 0.g301 0.8507 0.9121 0.8943 0.9814 Q9876 0.9771 O.9790 0.9831 Q9857 Q9K8 Q9853 0~97S5 O.979 7

Table 45 . Comparison of K-8 Mode! Resilient Moduli for Selected Pulse Types - Bases 3 am 4 I 1 1 . TEST _SPECIMEN B3S1 C B3S2C z5 min. PUl-5~ Havemine (Peg ~ 20 35 50 RESILIENT MODULUS (peg Keg MODEL EXTERNAL 664 . 37,045 45 682 . l 28,659 38,773 47,010 24,320 35,385 44,959 24,1 60 38~77 51 ~42 24,873 37,689 49,1 19 2G,193- 38,421 49 047 . 26~45 39,~ 50~75 24,123 37,1 58 48,937 26,177 37,542 47,241 26,62-4 36,861 45,356 T9. 1D ~ 35 28,5= 38,014 45,592 T 5. s Hz 20 _ _ _ 35 50 24,41 4 35;!51 44~" 5.0 min. 20 35 50 20 35 50 ~0 35 20 35 50 20 35 50 20 35 50 25,4= 38,416 26,';29 37,260 48,51 1 25,568 37,550 Z6,918 39,938 51 .356 r 24,904 38,267 50,31 8 25,707 36,916 46 494 25,61 4 37,328 4T,456 2~5 min. Haverelne T.S. 10 HL T.S. 5 Hz 5.0 min. 35 _ 50 25,177 34,m 42,71 8 TEST SPECIMEN B4S1C B4S2C 5.0 min. 24,058 35,597 45,694 aJU 34,982 44 771 . 25,1 84 37,692 s5,581 24,632 36,630 53 682 . 25,664 38,321 5G,381 26,841 40,12S 59 104 . 1 6,858 35,798 52,304 T.S. 5 Hz 27,097 40,952 53,284 PULSE Haverelne (P60 20 35 50 20 35 50 20 35 50 20 35 50 20 35 50 20 35 60 - 20 35 60 20 35 60 20 35 60 12 35 60 EXTERNAL 25~14 37,725) 4e,~ 25,138 37,009 47,354 RESIUENT MODULUS (pe, K~ MOD L CLAMPS ~r 37,775 48,533 24,950 36,903 47~359 T.S. 10 HL 26,628 39,514 50,816 24,662 36,172 46,172 5.0 min. Heverelne 24~325 361356 46,970 24,655 35,647 50 843 25,051 37,166 54 344 . 25,5165 37,328 53 749 26,521 39,353 57,551 1 7,008 36,071 52,669 T.S. 10 H~ ' T.S. 5 i1z 5.0 min. 5.0 min. 171

100 I - cL At on c: 30 20 1~ 10 20 ~1 ~s~_~4 tin + ~ ~3 - i _, ~ t 80 7+ _ ~ BASE 1 O BASE + BE 2 31< BASE 3 PREDICTED 1 _ ~ rev ran OY-,~ _ ~ _ ~ ~ .~. 1 ~ ~ Or = 4395174~ ~r(2.5 ~ ~ i airs - j . OR' = 0.99305 i i ~ t 30 ~ O ~ QUASISTAnC (EXTERNAL Mrt25) APSE (~sands) Figure 75. Resilient modulus correlation between 2.5 min. quasi static test and repeated load haversine test 1' 1.16 ·= ·~ 1.12 3 ·~& 1.~ 1.04 1 . · ~ ' T 1 l \ \ \ ! I . I . I . I . I . I 0 20 40 60 Quasi - Static Resilient Modulus Ash 80 100 Figure 76. Correction factors for 2.5 min. quasi static test ~ 72 . .___ ___ . - 70 00 90

to actuate Me solenoid valve. If desired, a proving ring could be used to measure We applied load, and clamp mounted EVDTs read using a simple voltmeter used to measure specimen deflection. Test data can be reduced using either a computer or by hand. Neither complicated equipment nor a high level of technical skill is required to perform this test. The 2.5 min. (or an even shorter test) quasi-static test offers considerable appeal for routine testing of aggregate bases. Me quasi-stafic test is recommended for lobs that do not have closed loop testing systems as a simple replacement for the repeated load test on granular bases which have at most a small amount of plastic fines. The quasi-static test results should be corrected for dynamic effects using Figure 76. Permanent Deformation Introduction. Establishing the susceptibility of unstabilized base materials to permanent deformation, from a practical viewpoint, is often more important that evaluating by laboratory testing the resilient modulus. Permanent deformation in a thin layer (or sublayer) is equal to the average permanent strain multiplied by the thickness of the layer. The susceptibility to undergo rutting for the ~ sets of specimens included in the permanent deformation study varied by about 100% (Table 46~. In contrast, the variation of He average resilient moduli for these materials is 47% for a representative bulk stress (~) of 36 psi. Thus, the variation in the resilient modulus is usually much less than for permanent deformation. The SHRP-173 material, included in this study, exhibited unstable permanent deformation behavior and hence had the greatest permanent deformation. Surprisingly, this material had the highest resilient modulus. Overview. The proposed permanent deformation test is performed on the same specimen used for the resilient modulus test. The standard resilient modulus test is performed first. Permanent deformation is measured throughout He test by obtaining, after the specimen is set up in the biaxial cell, an initial underformed specimen deflection using either a pair of dial indicators or L`VDTs. Additional permanent deformation readings are then taken at the end of the preconditioning phase, after resilient modulus testing is complete, and at selected numbers of load repetitions until the long term test is complete. Permanent deformation measurements spaced about one log cycle of load repetitions apart are desirable but not absolutely necessary if readings fall at inconvenient times. A total of at least 10,000 load repetitions should be applied during the test; preferably 50,000 repetitions should be used. Permanent strain is He measured permanent specimen deformation divided by the specimen height over which it is measured. Test Procedure. A pavement is subjected to a large number of load repetitions compared to the 1700 repetitions required following the SHRP P 46 (November, 1989) resilient modulus test procedure. Therefore, the permanent deformation test was continued to a total of about 70,000 load repetitions. After 70,000 load repetitions, He rate of increase in permanent deformation is quite small for good quality base materials subjected to realistic repeated load biaxial stress conditions. Permanent deformation was measured using an externally mounted dial indicator graduated in 0.001 in. divisions. A dial indicator gives sufficient precision since permanent deformations are quite large compared to resilient deflections. An initial deformation reading was obtained before beginning the test. Additional readings were taken at the end of conditioning, after completing the conventional resilient modulus test and at about He end of about each log cycle of additional load applications. A closed-Ioop electro-hydraulic testing system was first used for performing the resilient modulus test. After completing He resilient modulus test, the biaxial cell was carefully transferred from the closed- loop testing system to a pneumatic system. A new initial dial reading for specimen height was taken on 173

Table 46 . Permanent Axial Stra~n Measured ~n Repeated Load Triaxial Test at 200, 1700, 5000 and 70,000 Load Repetitions TEST TOTAL ~AN~ S~ (~C~ SERIES SAMPLE 1 ~ ~. N SAM~E 2 ~ ~. N AVG. ~ ~. 200 1700 6000 70000 200 1700 6000 70000 200 1700 SHRP 173 0.0625 O.2860 0.3S68 o.460S 0.1417 O.3633 0.4487 O.6S33 0.0987 0.3092 O.4060 5 H. R= 51 0.0 683 0. 15 60 0 2 00S 0.40S3 0.04 26 0.14 92 0.19 33 0.4208 0.0 60 0 0. 1 4 92 0.1 ~ 7 SH" 196 0.0768 0.2692 0.3568 0.092 0.042S 0.2526 0.3217 0.37" 0.0426 0.2626 0.3383 B 1 BF 0.0768 0.1983 0.2S68 0.3667 0.0250 0.1908 0.2683 0.3a68 0.0600 O. l 908 0.2683 D I CR 0.0287 0.1483 0.2087 0.3083 0.0342 0.1368 0.1868 0.2e68 0.0300 o. 1426 o. l 967 5 ~0.0 l 25 0.l 608 0.2068 0.2e67 o.o l 26 O. l 460 0.021 8 2.8333 o.o l 26 0.1476 0.21 l 7 52R 0.0667 0. l 467 0. l 860 0.2460 0.0333 O. l 4 l 7 o. l 9 l 7 0.2692 0.0460 O. l 442 0. 1883 R2F 0.0342 o. l 360 0. l 826 0.0626 0.0326 o. l 26 7 °. l 760 0.2368 0.0333 0. l 308 o. l 783 70000 RANK e MR N - 70,000 (~ ) 47 0.6175 o.~" 7 33 0.~1 7 0.3668 0.287C ~2 0.27SO ~0 0.262S 0.2608 1 43 NOTE: 1. THE LONG-TE~ PE~~ - T ~O~A~ON PORTION ~ THE TEST WAS P~O~ED AT ~3-~ ~ "D 01 / O3 ~ 4. ~E PE~ S BIVEN IN THE TA"E U; CUII4ULATIVE ~ROUBHOUT THE T"T . 2. M, lS ~VEN FOR ~ -" "I WHICH CO - "PONDS TO ~E S="S STATE USED ~ THE LON~TE~ ~R~ - OF ~E T"T . 3. N" TOTAL NUMBER ~ ~UED LOAD REPETITIONS . 174

an externally mounted dial gage. The repeated load test was then continued using a confining pressure of 6 psi and principal stress ratio CIt/03 = 4. About ~ 8 hours was required to apply 70,000 load repetitions. The pneumatic open-Ioop testing system was used for the long term portion of the test since monitoring by a technician is not required, and the test is inexpensive to perform. Electrical drift of the electronic load feed-back control, which is Important for a closed-Ioop system, is not present in an open-Ioop testing system. Permanent Deformation Test Results. Measured permanent axial strains observed in the tested specimens for 1700, 5000 and 70,000 load repetitions are shown in Table 46 for ~ series of tests. Permanent strain is calculated by dividing the measured permanent axial deformation of the specimen by the specimen height. Specimen height is the axial distance over which the deformation occurs for external measurements. For each test series, permanent strain was measured for two replicate specimens. For the data shown In Table 46, the average variation at 70,000 load repetitions between the average permanent strain of We two specimens and either measured value was 5.3 %. The maximum variation for a single pair of specimens was 12.9%. Almost 25% of available pairs of data were rejected for this comparison because of excessive scatter of permanent strain between the two replicate specimens. Usually 10~000 to 50,000 load repetitions are required before a base material reaches a reasonably stable condition. A stable condition occurs when the rate of increase in permanent deformation as a function of the number of applied load repetitions becomes very small. For weak materials, an unstable condition may exist with the rate of permanent strain accumulation increasing with the number of load repetitions. Permanent strain response at 70,000 load repetitions, by which time most base materials have stabilized, was therefore selected as the reference for comparison with the permanent strain behavior at 1700, at the end of the resilient modulus test, and 5000 load repetitions. ~ion. The average permanent strain measured in two companion specimens should be used as the basis of comparison with the permanent strain observed in a high quality reference base material. The permanent strain occurring during the conditioning phase of We test should be neglected since it is frequently somewhat erratic during the first few cycles of loading due partly to seating errors. A pneumatic testing system Is ideally suited for loading the specimen to 50,000 repetitions during the permanent deformation portion of the test. Use of a pneumatic testing system permits running the permanent deformation test overnight without a technician being present. Following this approach, permanent deformation characteristics can be obtained for almost no additional cost and very little loss of time during We working day. The resilient modulus portion Of the test can he performed 1l.sin~ a cln.sed- loop, electro-hydraulic testing system. ~ rid ~ _ Bide ~ T~d ~:1:~., ~ T~1 ~ ~ ~_. ~ _~_ _, _ ~ i__ ~ . ~ \ ~ _~ __ - __ `~;lurlllarlon 1nsraulllly unstable permanent aerormallon for permanent strain' Denavlor sometimes occurs in pavement materials subjected to large numbers of load repetitions such as ache SHRP 51 material Table 46~. After about 10,000 load repetitions, permanent strain in the specimen started rapidly Increasing with Increasing numbers of repetitions (Figure 771. Figure 78 also illustrates material deformation instability. Whether We permanent strain response becomes stable with additional load repetitions depends upon several factors including (~) the stress state at which the test is performed, (2) the overall quality of Me base tested including particle shape, fines content and moisture susceptibility, (3) the degree of saturation at which the test is performed and (4) level of compaction. 175

z 0.006 ~ 0.005 Q - z 0.004- a: In 0.003 - ct 0.002 3 o.oo' z a: ~` / _~ 6~7- 06000' 1 00 1 000 1 0000 1 00000 NUMBER OF LOAD REPETITIONS, N Figure77 . Comparison of permanent deformation as a function of number of load repetitions for a stable and unstable base F. 12 He a: 1.0. - ~ 0.8 CO he 0.4 CL 0.6 A 0.2 x a: . ~ ARCED ~ so pERCENT FINES (~,~2)/03 - 6- ~ / - 10 PERCENT FINES (~1-72)las ~ 3 CRUSHED GRANlfE GNEISS 100°~ T18~D S - 75# 1 _ L i l l l o.o 0 10000 20000 30000 40000 50000 60000 1 NUMBER OF LOAD, REPETITIONS, N Figure 78 . Influence of number of load repetitions and material quality on permanent deformation 17S

AS a result of unstable behavior, the SHRP S! material ranked two positions better in Table 46 after 1700 load repetitions and 3 positions better after 5000 load repetitions than after 70,000 load repetitions. Material instability did not clearly show up until after SOOO load repetitions. Also, a comparison of the rankings for all materials after 70,000 load repetitions with those at 1700 and SOOO repetitions shows at least three important variations in rankings out of the eight sets of test data. Thus, for the stress conditions and materials used in this study, somewhat misleading indications of potential permanent deformation performance is obtained for almost one-third of the materials studied if only 1700 to SOOO load repetitions are used. ~ _~ ~_~_4 ~ ~` ~^ An., ~ ~ ~ ~` ~ ~_1 C_ ~_~_^ a_ ~_~_` ~` a_ ClllQ ~UllLOllL - - 111~ ~11~t U1 U~VldtV1 bL1~b ldLlU =1U 1111= ~11~11L U11 pO1111~1~11L Q~1Vllll~LlU11 is illustrated in Figure 78 for a granite gneiss compacted to 100% of AASHTO T-lSO density. At a fines consent of 10% and a deviator stress ratio of 3, only small changes in permanent deformation occur after 5,000 and 10,000 load repetitions. In contrast, when subjected to the same stress ratio, a specimen having 16% fines and compacted to 100% of AASHTO TWO density continues to undergo very large increases in permanent deformation up to test termination of 50,000 load repetitions. Recommendations. Marginal Aggregate Materials - - In regions where marginal materials are use, permanent deformation tests should be routinely performed. When marginal materials are employed, He test should be conducted to at least 50,000 load repetitions. After completing the resilient modulus test, the desired stress state to use in He permanent deformation portion of the test (refer to Table 47) is applied to He specimen. Continue the test until reaching the total required number of load repetitions. High Quality Base -- Unstable permanent deformation behavior may occur in poor bases when subjected to deviator stress ratios as low as about (~-~3~/~3 = 3. Instability can occur even in higher quality bases subjected to deviator stress ratios above 5 or 6. Because of the potential for unstable permanent deformation behavior, 1700 to 5000 load repetitions is not adequate to reliably define potential long term behavior for materials varying widely in quality. When only high quality aggregate base is used together with deviator stress ratios less Han about 5, 5000 load repetitions should generally be adequate to define permanent deformation behavior. A high quality base is composed of a 1.5 in. or larger maximum size crushed stone Hat is well graded, has no more than 896 nonplastic fines, and is compacted to at least 100% of AASHTO TWO density. Only a limits number of tests, performed when the material is first used, are required to define He permanent deformation characteristics. Stress State -- As shown in Figure 78, He stress state at which a permanent deformation test is performed has an important effect on the measured permanent strain. A nonlinear finite element study using the GAPPS computer program indicated the stress states summarized in Table 47 to be appropriate for permanent deformation testing of base materials [ad. SUBGRADE EXPERIMENTAL STUDY Introduction The experimental work on subgrade soils consisted of the following four phases: 177

Table 47. Suggested stress states for evaluating permanent deformation characteristics of aggregate bases Structural Strength Equivalent Full Depth AC Thickness Stress States Teq (inches) as ~Si) | ~1/~3 Teq<8 1 6 1 6 Teq < 1 1 6 4 Teq> 11 4.5 2 LIGHT MEDIUM HEAVY 1. An alternative would be to use a confining pressure of 6 psi for all pavement strengths 2. Equivalent full-depth thickness AC obtained by replacing the aggregate base by an equivalent thickness of AC. Use 1 in. of AC to replace 2 in. of aggregate base. 178

Phase I: During Phase ~ a statistical experiment was performed to determine Me critical specimen preparation and loading variables for both cohesive and cohesionIess subgrade samples and guide in the selection of the test procedure used during Phase Il. Phase B: The purpose of this testing phase was to provide data for developing generalized resilient modulus and permanent deformation models which can be readily used in design. Resilient modulus tests were also performed to determine Me benefits of using grouted specimens ends and to determine the effects of misalignment. Repeated load tests were performed on 52 clayey sand specimens in this phase. Phase IlI: Phase ITT tests were performed to validate the models developed during Phase IT by using them to predict, based upon the measured static strength, the resilient moduli for specimens of a silty sand (A-5) prepared by impact compaction. The Phase ITI tests included both static and repetitive load tests. . . Phase TV: Since all of the Phase T. IT, and ITI tests were performed on impact compacted specimens, it was Me intent during Phase IV to determine the influence of compaction method and moisture conditioning procMure upon Me measure resilient modulus in an effort to determine Me most appropriate compaction method for preparing a cohesive specimen. Both a silty sand (A-5) and clay and (A~) soil were used during Phase IV. Both static and repetitive load tests were performed to determine whether the Observed changes in static strength would reflect the changes measured in resilient modulus. - ~7 To give reproducible results, instrumentation supports were developed to properly align inside LVDT clamps and hence give more repeatable resilient modulus test results. Also, special techniques were established to minumize specimen end effects by grouting. This grouting procedure permitted determining the influence of end effects on resilient modulus. The experiments were statistically designed, and where appropriate statistics were used to evaluate test results. Basic Material Properties _, ~., During Phases I and II, repeated load tests were performed on a naturally occurring clayey sand Hat classifies as AN by the AASHTO system. The cohesionless soil tested in these phases was a naturally occurring, uniform fine to medium slightly silty sand that classifies as A-3. These soils were selected to exhibit clearly cohesive and cohesionless soil behavior. During Phases IT and IV, a cohesive silty sand (A- 5) soil was added because previous research suggested that such soils are difficult to compact and test. The North Carolina Department of Transportation selected all three test soils and obtained 1000 lb. samples of each. All soils were tested in the remolded condition. Table 48 summarizes the basic soil properties for the three soils tested. Figure 79 gives Heir grain size distributions, while Figure 80 shows the Standard Proctor (AASHTO T-99) compaction characteristics. 179

75 mm 90 80 - .= 70 ID -, 60. D 50 40 ID 0 30 20 10 ' O, No. 40 No. 200 , . . . . . . . . . . . 100 10 1 0.1 Particle Diameter, mm Figure 79 . Gram size distribution for test soils 120 a, 1 1 O i~ ._ In ID 100 .--L 0.01 O.OOt Processed , ~ A-6 50 ,_. G = 2.68 Zero Air Voids . ~ =, A-5 10 15 20 25 Molding Water Content, TO Figure 80. Standard proctor compaction curve for cohesive soils 180

Table 48. Summary of subgrade soil properties Property | Soll Grai ~=: -Nn 4 100 100 100 . --No 40 84 85 61 . -No. 200 42 48 7 Clay Fraction A= , new am_ _ An_ _. it: - - rim . D ~. ~- . Classifica ion AASHTO I AT USCS I SC 2.65 0.'7 0.42 Figure 81 compares He moisture density results for cohesive A-5 and AN specimens prepared by kneading compaction (solid symbols on the figure) to the AASHTO T-99 compaction curves~solid lines). The kneading compaction of the ~ in. high, 4 in. diameter resilient modulus specimens used 24 tamps of a 70 Ib. spring load hammer on each of 10 layers. This kneading compaction energy was selected to approximately match the AASHTO T-99 maximum dry density at the optimum moisture content. All compaction tests were performed using a standard 4 in. diameter Proctor mold. Test specimens were ~ in. high and T-99 compaction specimens were 4.58 in. high. In Figure SI, the dry density points for the kneading compacted specimens fall close to He AASHTO T-99 compaction curve. Casagrande and Hirshfeld [X2] demonstrated Hat kneading compaction requires a trial and error procedure involving varying the applied energy to fit a desired compaction curve. Previous experience gained compacting 1.4 in. diameter specimens by a similar spring loaded hammer suggests that a technician can achieve consistent moisture~ensity curves only after preparing at least five specimens. Specimen Preparation The repeated load tests were performed on specimens ~ in. high and 4 in. in diameter. The cohesive silty sand (A-5) and clayey sand (A~) specimens were prepared by both impact compaction (AASHTO T-99 type compaction) and kneading compaction using the previously described spring loaded hammer [821. The slightly silty sand specimens (A-3) were prepared by impact compaction. The specific specimen preparation procedures used, including soaking, are given in Appendix G. 181 . .

120 1 10 ._ In ~100 90 60 A-6 ~ it' \ Zero Air VoWs G = 2.68 _ , ~ Impacl Kneading A-5 10 50 ._ In 40 30 - cn 20 10 15 20 Molding Water Content, °/O 25 Figure 81. Comparison of kneading compaction characteristics of A-5 and AN sol . . CL, ~ Impact 1 _ ~ Kneading 10 15 20 Molding Water Content, % 25 Figure 82. Static strength as a function of moisture content for Me clayey sand (A~) cohesive soil 182

Static Shear Strength In the generalized models developed later in this chapter to predict resilient modulus and permanent strain of subgrade soils, the applied deviator stresses are divided by the static shear strength of the soil. Moisture content, confining stress, and aging all influence the resilient modulus. This dependence is reflected In the measured static shear strength of the soil. Static strength is expressed as the failure deviator stress (sat). Since the static shear strength occurs at relatively large strain, errors due to not grouting specimen ends are small. In addition, static shear strength tests can be performed using a standard biaxial cell and constant rate of displacement loading frame without extensive instrumentation and a data acquisition system. Figure 82 shows the static shear strength (sift of the compacted clayey sand (A~) specimens as a function of the molding moisture content. For these tests, the loading displacement rate was selected so that specimens failed in about 30 minutes. The strength of the impact compacted clayey sand (A~) specimens decreased almost linearly wig increasing moisture content and replicate tests show good agreement. The specimens compacted by kneading at optimum moisture content have both a higher density and higher static shear strength than the specimens compacted by impact. In contrast, specimens prepared by kneading compaction at densities close to those for the T-99 impact test have, for moisture contents both above and below optimum, lower static shear strengths than the impact compacted specimens. In tests performed on the clayey sand (A~) specimens for mode} development, the deviator stress levels were selected as a fraction of the static shear strength measured on impact compacted specimens. To measure the static strength of the cohesioniess soil, undrained static biaxial shear tests were performed on partially saturated sand specimens at confining stresses of 3, 7.5, and 15 psi for both Me loose and dense specimens. For the loose sand the Mohr-Coulomb strength envelope had an internal angle of friction equal to 42° and zero cohesion. The dense sand had the same friction angle as Me loose sand but the cohesion intercept, which equals I.7 psi, is much higher than for the loose sand. These tests suggest a similar tote] stress friction angle for both the partially saturated loose and dense specimens, but a larger total stress cohesion intercept for dense specimens. Capillary tension appears to account for these unexpected results. The dense sand specimens should actually have a higher effective stress friction angle (l') than the loose sand. For partially saturated specimens, this difference is reflected in different total stress cohesion intercepts. Cycling the load during resilient modulus testing may eliminate the suction caused by capillary effects. Test Procedure Triaxial Cell, EVDT Clamps and Alignment Supports. A biaxial cell capable of handling specimens up to 4.0 in. in diameter was used for resilient modulus testing (Figure 83~. Air was used as Me confining fluid during all of Me static and resilient modulus tests. Four clamps held Me two inside EVDTs to the middle half of the soil specimens. To repeatedly mount these clamps onto the soil sample, an alignment stand was developed and is described in Appendix G. The alignment stand also reduced Me risk of damaging or deforming the soil sample during clamp installation. In selected tests axial specimen displacement was measured between the top platen and base as shown in Figure 83. Soil specimens were placed in the biaxial cell and loaded by a closed-Ioop loading system. A load cell was used having a maximum capacity of 2000 Ibs. The load cell is located outside the biaxial cell and connects the biaxial piston to Me load actuator. Load is controlled by Me microprofiler program, and its 183

~- - Load" Cell Leads Loading Piston Lilt r~~ Top Cap _ LVDT Clap LVDT Coil Vacuum Inlet LO Lesde / Lead Cell Wide LOT Leads G= ~. . -1 LVrDT Rod Camer - ~ Allen H ad w~t~ Grout _ C~em~ Specimen Membrane mat Spacim ~ lye Rod '' Hydroatone Grout Pedestal '-O-R~e Sew Figure 83 . Final configuration of the biaxial cell 184 Pressure ~t

output is connected to a data acquisition system which collects load readings. Load and deformation were measured for the last 5 load pulses for each applied stress level. The two LVDT electrical leads were passed out the biaxial cell through a sealed hole in the cell base (Figure 83) and each LVDT was connected to an analog signal conditioner. An outside LVDT mounted on the actuator was connected to a Bird analog signal conditioner. The three signal conditioners were connected to a terminal board In the back of a 386 PC computer which monitored displacements and loads. The maximum range of the inside LVDTs is ~ 0.1 in. and the outside LVDT has a range of ~ 0.25 in. A pressure transducer was used to measure the confining air pressure applied to the soil sample during tests. A pressure transducer was used having a maximum range of 100 psi. The pressure transducer was connected to a signal conditioner with the output reading being monitored by a voltmeter. A similar pressure transducer was used to monitor the pore water pressure at the base of the soil specimens. Data Acquisition and Data Analysis. Proprietary software was used to acquire the data from the closed- loop testing system and the analog signal conditioners. The program used for data acquisition was written in quick basic within the data acquisition software shell. A high performance multifunction analog, digital, and timing input/output board was setup to accept instrument sensors and digitized analog signals. The input voltage range for the data acquisition board is set up to remain between i 10 V. The precision of input signals measured by the analog-to~igital converter (ADC) equals the total voltage range (20 V) divided by 2~2 which equals 4.~8 mV. The two types of EVDTs used have ~ 0. ~ in. and ~ 0.25 in. ranges, respectively, which allows measuring minimum deformations of 4.~S x lO-s in. and 1.22 x 104 in., respectively The 2000 Ib. load cartridge can detect a minimum load of 0.976 Ib. A computer program written in Pascal was developed to calculate He resilient modulus values from the data file obtained by Me data acquisition program. End Preparation and Conditioning Grouted Ends. Grouting the specimen ends with hydrostone treatment provides an even contact surface and a solid continuous connection that eliminates the need for specimen conditioning [721. While grouting causes full friction on the ends of the specimen, it does not significantly affect Be measured moduli for specimens having a height to diameter ratio of at least 2 to I. Pezo, et al. [72] performed an experiment to determine Be measured resilient modulus after different numbers of load repetitions on specimens with grouted ends. Grouted specimens subjected to 200 cycles at a deviator stress (a,) of 4 psi under a confining stress proof 6 psi have been found, based on a statistical analysis of the results, to behave the same during the first five cycles as during the last five cycles. Procedures used in this study for grouting specimen ends are given in Appendix G. Soil specimens typically are conditioned by repeated loading to give better contact between the platens and specimen ends and to also reduce the effects of ~ixotropy [831. While grouting with hydrostone eliminates Be end condition problems, it does nothing to eliminate thixotropy effects. To allow for some aging, Pezo et al. 172] recommends before testing to age cohesive soil specimens for 2 days after compaction. Allowing only 2 days for specimen aging is not adequate for cohesive soils sensitive to aging effects. Because of time restraints, specimens were tested in this study 2 furs. after preparation. Further research is needed to determine correction factors for the effects of aging including comparisons with field behavior. 185

Axial Deformation Measurement Method. The accurate measurement of axial deformation is a very important concern in repeated load testing. The SHRP P46 (November, 1989) protocol requires measuring the cyclic deformation using two externally located EVDTs on the vertical load piston, AASHTO T-274-82 recommends placing two EVDTs on clamps attached to the central half of the specimen. Fixing clamps to sonic subgrade specimens, however, can cause significant disturbance. A third alternative is to measure displacement between the specimen top cap and the base of the biaxial cell. If the top cap has been grouted to the specimen by hydrostone, a minimum amount of compliance (i.e. unwanted deformation) occurs between the cad and specimen. From tests performed on three different synthetic specimens with resilient moduli of 1670 psi, 6550 psi, and 32,300 psi, external EVDTs have been found to measure subgrade resilient moduli 15 to 50 % too low; with proper equipment calibration this error can, however, be reduced. Values measured by He top to bottom internal EVDTs accurately measure the resilient modulus provided the ends are grouted 1721. Calibration and Evaluation Tests Svn~etic SDecimen. A svn~etic specimen having a resilient modulus of 57,000 psi was obtained from eliminate the university or lexas to calibrate the experimental setup and to eliminate alignment problems. Deformations were measured by internal LVDTs held by clamps epoxied to the middle half of the 8 in. high by 3.~15 in. diameter synthetic specimen while the unconfined specimen was subjected to a repeated deviator stress of 44 psi. Because of the synthetic specimen's high resilient modulus, (MR=57 ksi), large cyclic stresses were needed to accurately measure axial deformations. Compacted Specimens. Eight clayey sand (A~) specimens, compacted at both optimum and wet of optimum moisture contents, were tested with both grouted and ungrouted ends to verify the findings of Pezo et al. The specimens compacted wet of optimum moisture content were also used to identify whether excess pore pressures, which would decrease He resilient modulus, build up during repeated loading. All eight tests were subjected to a load sequence combining the standard SHRP P46 (November, 1989) load sequence with 2000 load repetitions at a deviator stress equal to 5O~O of the static failure stress (SL=50%) and a confining stress of 3 psi. The SHRP P46 (November, 1989) load sequence requires 100 cycles each of deviator stresses equal to 2, 4, 6, 8, and 10 psi at the three confining stresses of 6, 4, and 2 psi after 200 cycles of conditioning at a cell pressure of 6 psi and deviator stress of 4 psi. In three of the four tests at each moisture content state, the SHRP load sequence preceded the SL = 50% cycling. In the fourth test for each moisture content, the constant stress level cycling preceded the SHRP load sequence. The results of these eight tests were used to qualitatively evaluate the effect of end condition and load sequence on resilient modulus. Of the four tests conducted on bow the optimum compacted specimen and wet compacted specimen, one test had grouted ends and internally mounted top to bottom EVDT clamps, while the other three tests had ungrouted ends with porous stones allowing water to drain from the base and internal EVDT clamps fixed to the middle half of the specimen. Load Sequence Phase ~ Tests. The Phase ~ testing, was performed to identify the critical test variables and then select a suitable test procedure before performing the mode! development tests proposed for Phase Il. During the Phase ~ testing, four variables were included in a statistical experiment including two specimen state variables and two loading variables. Resilient modulus tests were performed on ache clayey sand (Am) and He sand (A-3) specimens. A statistical analysis of variance performed on the measured data was used to 186

identify the important load sequence variables to help select a robust experimental procedure for resilient modulus testing. The load sequence variables studied were: Rest period between load pulses: short (0.4 sec.), standard (0.9 sec.), and long (2.9 sec.) 2. Load Level Sequence: decreasing, constant, and increasing The rest period represents We time delay between 0.~ sec. haversine load pulses. The load level sequence variable included a decreasing pattern of 50 load repetitions each of deviator stresses equal to 15, 10, 5, and 3 psi followed by 50 cycles of a deviator stress OD = 10 pSi; a constant sequence of 250 repetitions at OD = 10 pSi; and an increasing pattern of 50 cycles each of OD = 3, 5, 10 and 15 psi followed by 50 cycles of OD = to pSi. Me confining pressure (03) was maintained at a constant 3.0 psi during all Phase cohesive soil testing. For each load variable combination, resilient moduli were measured during load cycles 245 to 250 when OD = 10 pSi. The specimen states included in the experiment were: I. Moisture content: dry of optimum, optimum, and wet of optimum 2. End condition: flat ungrouted, sloped ungrouted, and flat grouted. The combination of specimen states gives 3 x 3 x 2 = IS different specimens included in the experiment. The sloping end condition had a 0. ~ in. difference between opposite sides which gives a ~ .4° slope for a 4 in. diameter specimen. The results of this split plot type of experiment was studied using the analysis of variance. The sequence of load variable combinations were randomized as well as the order that specimen states were tested. Each of the load sequence combinations were replicated 9 times under 9 different sets of specimen conditions. Therefore the dependence, if any, of the measured resilient modulus on load variable factors could be identified. Specimens were not duplicated in Me testing program. To minimize the influence of specimen variability, tests were repeated on all specimens that appeared to be in error. Table 49 shows the experimental design used for Phase ~ testing of compacted AT specimens. For each of the Phase ~ tests, the resilient modulus was determined using both a single external EVDT and two EVDTs clamped to the center half of the specimen. Cohesioniess Soil Test Results - Phase I. The Phase ~ experimental design for sand specimens is given in Table 50. Since grouting is not required for cohesionIess specimens, only regular and sloped ends were included for the loose and dense specimens used in the experiment. The sand specimens were prepared and tested at a moisture content of about 9%. The loading sequences consisted of a constant confining stress of to 7.5 psi and 50 cycles at each deviator stress level. The increasing sequence of deviator stress used in the experiment consisted of applying deviator stress of 3, 5, 10, 15, and 15 psi. The decreasing deviator stress sequence consisted of applying 50 repetitions each of deviator stress equal to 15, 10, 5, 3, and 15 psi. The level test sequence consisted of 250 repetitions of a 15 psi deviator stress. 187

Table 49. Phase ~ plan for cohesive soil End Type w/c, Rest Load % period Sequence Regular Opt SO Dec reas ing Long Level Short Decreasing Long Increasing Long Decreasing Standard Level Starboard Increasing Short Level Short Increasing Sloped Dry Long Increasing Standard Increasing Starboard Level Short Decreasing Short Increasing Short Level Long Decreasing Standard Decreasing Lone Level . Regular Wet Standard Level Long Level Short Leve! Short Increasing Standard Creasing Long Decreasing Long Lncreasing Standard Decreasing Short Decreasing Sloped Wet Standard Level Short Decreasing Long Decreasing Standard Increasing Long Increasing Short Increasing Long Level Standard Decreasing Short Level Regular Dry Short Dec reas ing Long Increasing Standard Decreasing Short Level Standard Level Short Increasing Standard Decreasing Long Increasing Long Level End Type w/c, Rest Load % period Sequence - ~. Dry song Creasing Short Level Short Decreasing Standard Level Short Increasing Long L,eve} Long Decreasing Standard Increasing Standard Decreasing Opt. Short increasing Short Decreasing Short Level L`ong Decreasing Standard Level Standard Increasing Standard Decreasing Long Level Long Increasing Wet Short Level Short Decreasing Short Increasing Standard Level Standard Increasing Long Level Long Increasing Starboard Decreasing Long Decreasing _ _ Opt. Long Level Long Increasing Long Decreasing Standard Decreasing Short Decreasing Short Level Standard Level Short Increasing Standard Increasing Grouted Grout Grouted -Sloped 188

Table SO. Phase ~ plan for cohesiontess soil End Type~ ~ ~~~ Regular Rel. Density Dense :~ SW. Long Short Long Long Std Std. Short Short . _ Decreasing Level Decreasing Increasing Decreasing Level Increasing Level Increasing Sl-oped Toose Long Sld. Ski. Short Short Short Long Std. Long Std. Long Short Short Std. Long Long Ski. Short Sld. Short Long Std. Long Short Long Std. Shon Increasing Increasing Level [Decreasing Increasing Level Decreasing Decreasing Level Level Level Level Increasing Increasing Decreasing Increasing Decreasing Decreasing Level Decreasing Decreasing Increasing Increasing Increasing Level Decreasing Level Sloped Dense Regular Loose 189

Effects Of Specimen Preparation Compaction Method. Laboratory specimens should accurately represent the field soil structure and moisture content. When evaluating in place subgrades, undisturbed sampling provides the best technique to obtain representative specimens. If resilient moduli et different moisture contents are required, then the undisturbed specimens must be soaked or drained. To simulate compacted fill, laboratory compaction of specimens is often required. Seed et al. [831 described the influence on resilient modulus of different compaction types and soaking procedures. The AASHTO T274-82 resilient modulus test compaction method is based on the work of Seed, et al. To develop practical procedures to use for production resilient modulus testing. both A-5 and AN snecimen.s were nren~rer1 hv troth impact anti l~n~Aine ~^mn~tinn ~ r------~~ ~~~ r--r~~~ an A -~^r~~~ ~~~= ~~-~~-'~^'~ . . . . . . . . and selected specimens were soaked to achieve a high degree of saturation. Soaking Specimens. Figure 84 shows measured resilient modulus as a function of deviator stress for To impact compacted specimens prepared at optimum moisture content. After preparation, the specimens were soaked from the bottom under a 10 psi back pressure. The soaked specimens were tested with porous stones at Me top and bottom of Me specimen and base drainage permitted. These results indicate excess pore pressure did not build up as a result of the grouted end. Also, the soaked specimens have about 25% lower resilient moduli Man measured on an unsoaked specimen and tested at optimum moisture content. Granular Soil Model. The resilient modulus tests on Me granular A-3 sand were performed using 6000 load repetitions at a constant stress level (SL) given in terms of static failure stress. Since the resilient modulus varies with confining pressure, Me first 2000 load repetitions were applied at each of the following 3 increasing confining pressures: 3 psi, 7.5 psi, and 15 psi. Tests at different stress levels were performed on bow dense specimens, tamped to an initial relative density of 80%, and loose specimens tamped to an initial relative density of 40%. Table 51 shows the cyclic deviator stress (od), given as a percent of the static strength reported earlier, used for testing both dense and loose sand specimens. Table 51. Target a,d for Repetitive Load Sand Tests at Different SL's a, ~ ad S~s [~ St psi) 03 (E)Si) Dr (%) ~ 3 40 ~1~ 7.5 40 I_ 15 40 ~1~ 3 80 I_ 7.5 80 15 80 75% 9.75 22.5 45 20 40 62 Failure adf ~Si) 12.7 30.4 60.5 28.9 ~1 54.5 85.2 190

20 15 - ~n :D - ~ 10 - 0 ._ ._ In a: 5 O 6.. ·~ ~Q - ~ . -it,. r Legend Optimum ~ Wet of Optimum X Soaked 0 Soaked & Drained .,,, i,.. ~ ~ . 0 5 1 0 1 5 20 25 30 Deviator Stress, psi Figure 84 . Effect of moisture conditioning on resilient moduli of A-6 cohesive soil compacted using impact method 191

COHESIVE SUBGRADE FINDINGS Moisture Conditioning During the service life of a pavement, the subgrade experiences widely varying moisture conditions. In preparing a specimen for resilient modulus testing, the appropriate critical field moisture conditions should therefore be reproduced In the laboratory so as to give realistic results. To simulate the wet season, specimens at a high degree of saturation should be tested to obtain conservative resilient moduli. One method of simulating wet subgrade conditions is to prepare a specimen at optimum moisture content and then soak it to achieve a high degree of saturation. Soaking He specimen gives a high degree of saturation which reduces capillary tension (i.e., soil suction) and thus reduces effective stress and resilient modulus. A buildup in pore pressure during loading also can reduce the resilient modulus. Specimen Soaking. Soaking the specimen to raise the moisture content is quite attractive because this method is quite simple to perform. The specimen can be compacted at the anticipated field moisture content using a procedure to obtain the proper soil structure as discussed in the next subsection. The degree of saturation can be determined by weighing the specimen to determine the increase in weight as the specimen takes on water. The results in Figures 85 and 86 show He important reduction in resilient modulus that occurs upon specimen soaking under a back pressure of 10 psi applied at the base and He corresponding increase in modulus after water is partially drained from the specimen. The more cohesive clayey sand (Figure 85) subgrade soil was clearly much more moisture susceptible than the silty sand (Figure 86) with the average retained resilient modulus upon soaking being about 40% and 75%, respectively, of the impact compacted specimens at optimum moisture. Soaking the silty sand for up to 10 days only increased the degree of saturation from 84% to 92% for the kneading compacted specimen. Achievement of a higher degree of saturation would have resulted in a larger reduction in resilient modulus. The results of this study and also one performed by Elfino and Davidson [84] show, however, soaking a specimen sufficiently long to obtain a high degree of saturation is time consuming. Elfino and Davidson found that while low plasticity A-3 soils required only hours of soaking without back pressure to reach 98% saturation, high plasticity A-2~ clayey sands took ~ week or more. Unless performed using back pressures greater than 10 psi? saturation levels more than 95% may not be achieved for plastic clays. R~m~datinn. Moisture sensitivity tests on cohesive soils should be carried out to determine He subgrade resilient modulus for each season of He year which is required following the AASHTO 1986 design procedure. For routine testing, a limited number of tests should be performed for each soil type at a moisture content 3 to 4% above the optimum value in addition to tests at optimum and, if desired, below optimum. For each soil type, generalized relationships or correction factors, such as those presented subsequently in Chapter 4, can be developed to consider He effect of moisture content on resilient modulus [851. By having standard relationships of this type, resilient modulus tests need only be performed at He optimum moisture content. Soaking cohesive soil specimens to obtain a high degree of saturation is not considered to be practical because of the long time that can be required. Also, He use of back pressure saturation is not considered practical for routine testing. A much more practical approach is to simply initially prepare the specimen at He desired moisture content. Specimens cannot be successfully prepared at moisture contents greater than 3 to 4% above optimum and achieve satisfactory dry densities. A moisture content 3 to 4% above 192

30 25 - ._ In <,, 20 0 15 I) 10 'cn a) 5 o ~1 1 1 O Optimum 0 Wet of Optimum · Soaked · Soaked & Drained Qua ~ it' .~, , , l - O. O I I I I T T l 0 5 10 15 20 25 30 Deviator Stress (psi) Figure 85 . Effect of moisture conditioning on resilient moduli of clayey sand (A-6) cohesive soil impact compacted 193

30 - 25 20 15 ~_ ·0'10 cn fir. ~ _ O- 30 25: ._ In By a, 20 _ ° 15: ~'10 ._ an 5 O- O Optimum Soaked · Soaked & Drained A\ l i 10 15 Deviator Stress (psi) (a) Compacted using impact method O Optimum · Soaked · Soaked & Drained .. ·.. ` ·.. . do-. i., .,. s~ 1 1 1 1 1 0 5 10 15 Resilient Modulus (psi) (b) Compacted using kneading method Figure 86. Effect of moisture conditioning on resilient moduli of silty sand (A-S) cohesive soil 194

optimum, however, is sufficient to show moisture sensitivity. Appropriate methods for compacting specimens at various moisture contents are discussed later. General Factors Influencing Resilient Modulus As a part of this study an experiment was performed to evaluate the importance of load sequence and selected variables describing sample conditions. An analysis of variance was performed on resilient modulus test results for the cohesive clayey sand (AASHTO AT classifications tested in this experiment. The correlation between controlled test factors and measured resilient moduli was examined using the following variables and combinations of factors: 1. 2. 3. 4. -I - Jr - ~ ~ 5. End Type and Rest Period; 6. 7. 8. 9. End type (flat & grouted, flat & ungrouted, or sloped at I.4° & ungrouted); Moisture content (dry of optimum, optimum, or wet of optimum); Rest period (short (0. 15 sec.), standard (0.9 sec.), or long (2.9 sec.; End The and Moisture Content: End type and Load sequence goad sequence increasing, constant, or decreasing); Moisture Content and Rest Period; Moisture Content and Load Sequence; Rest Period and Load Sequence. Each of nine different samples covering the combinations of end condition and moisture content were tested under nine different load patterns involving combinations of rest period and load sequence. All three load sequences had 250 cycles at a constant confining stress of 3 psi. The resilient modulus was always measured during the last five cycles when deviator stress equalled 10 psi. The increasing load sequence had 50 cycles each of 3, 5, 10, 15, and 10 psi while the decreasing load sequence had 50 cycles each of 15, 10, 5, 3, and 10 psi; the constant load sequence had 250 cycles at a deviator stress of 10 psi. For each of Me above conditions, the statistics F value describing the linear correlation was calculated as well as the probability that this F value could have been exceeded if the resilient modulus and the input variable or variablets) were independent. Input variables with F values having probabilities of being exceeded less than 5% were considered to be correlated to MR. The only variable combinations for testing of cohesive soils found to be significantly correlated to MR were end type, moisture content, and end type/moisture content. Therefore, both rest period and load sequence did not significantly influence Me resilient modulus and can be selected to most efficiently perform Me resilient modulus test. Cohesive Specimen Conditioning The number of applied load repetitions, for reasonable values of deviator stress, does not affect Me resilient modulus for either grouted or ungrouted specimen ends as illustrated in Figure 87. This finding was developed using solid end platens wig axial deformation being measured between He top load platen and base of He cell. By inference, this finding should also apply when axial deformation is measured directly between end platens. When deformation is measured outside the biaxial cell, specimen conditioning influences He measured value of resilient modulus with conditioning becoming progressively more important as He applied axial strain decreases [Figure 881. When axial deformation is measured outside the biaxial cell, He use of a seating load improves test results. 195

50000 ~3 ` ~40000 at.= 30000 20000 I I Notes: Specimen Age = 131 days Deviator Stress = 10 psi Confining Stress = 6 psi . grouted 1- ungrouted 1 ~ 0 1000 2000 Load Repetitions Figure 87 . Effect of grouted specimen end on resilient modulus: deformation measured from solid platen to biaxial base (ADer reference ~O 196

3~00 20000 - ~ 1~ 1 To TO + L'onG~ning.Pr.es,s.u,re,=6 psi o lO-s 104 Sample l t Grouted .° Grouted Stumpy 2 ~ Ungroutod ~ w/o In. ~ a ^ ~ ~ 0 ~ + ~ &+ lo-3 Axial Strain Figure 88 . Variation in resilient modulus of two compacted subgrade soils with axial strain for different end conditions (After reference 80 197 10

Using an increasing sequence of deviator stress at a constant confining pressure gives similar resilient moduli as if just the largest deviator stress is used [721. For a silty clay, conditioning Me specimen with O3 = 3 psi and ad = 3 psi, as compared to using O3 = 6 psi and ad =4 psi, did not affect the resilient moduli measured at similar stress conditions after conditioning [861. These findings, together with those from this study previously described, suggest that modest changes in conditioning stress state apparently do not have an important effect on the resilient modulus of cohesive soils. Recommendation - Use a simple conditioning sequence which is practical to perform. For the proposed unconfined compression test, 200 load repetitions are recommended for specimens without grouted ends at a deviator stress of 4 psi. Strength Gain with Time- Compacted Cohesive Soils After compaction in the laboratory, the resilient modulus of a specimen increases with time (Figures 89 and 90~. Strength gains can be as great as 25 to 40% or more in some cohesive soils after only about ~ week. As shown in Figures 89 and 90, the effect of strength gain with time becomes less with increasing strain (or stress) level applied to the specimen. An important portion of the strength loss that occurs after remolding during specimen preparation is recovered in about 6 to 30 days after specimen compaction. Early studies by Seed et al. [83] indicated that conditioning a specimen for about 2000 load repetitions eliminates the effects of strength gain with time. In contrast to these results, recent expenmen~, however, clearly show that specimen conditioning does not eliminate the effect on resilient modulus of strength gains 1721. Recommendation. Strength gain with time is quite important if a resilient modulus is to be measured in the laboratory that is representative of the field value. Contacted specimens should age for at least 2 days (preferably 7 days) after preparation before testing. To prevent moisture loss during storage, specimens should be covered wig Saran wrap, stored In a sewed container and place in a moisture room. Correction factors should be develops for each soil type to allow extrapolating the 2 day (or 7 day) resilient modulus result to a long-term design value. Axial Deformation Measurement Tn~oduction. The appropriate memos of support and location is an important concern for the devices that measure axial specimen deformations during loading. The SHRP P46 (November, 1989) protocol requires measuring the resilient deformation using two external EVDTs located on the vertical load piston while AASHTO T-274-82 recommends placing two EVDTs on clamps attached to the central half of the specimen. Fixing clamps to a soft subgrade specimen sufficiently tight to avoid slip is difficult without disturbing the specimen. Other alternatives are to measure displacement between the specimen top cap and the base of He biaxial cell or to use a type of sensor which does not contact the specimen. Non-contact type sensors allow measuring axial deformation on He specimen without the potential problems of disturbing He specimen or slip Hat may occur when clamps are used. 198

Q 45000 an - :] 40000 ._ ._ v) 35000 3000 50000 , . . . . . . . . Soil 13 Moisture Content=17.8 ~ 0.2 °/ '. D'y Density ~ 102.1 ~ 0.2 pcf Confining Stress . 6 pal 0 ° · 50 days O ~ 6 days O 0 2 days O O /~~-' -4 ' ' ' . . . . . 10 103 Axial Strain, inch/inch lo2 Figure 89 . Variation of resilient modulus with the induced resilient axial strain of companion samples of A-7-6 plastic soil tested after 2, 6 and 50 days of compaction (After reference 72) 20000 ._ cn Q - ~n o e 1 0000 c · _ · _ an a) Figure 90. lo lo O 1........... Soil 7 - wet Moisture Content = 21.1 ~ 0.5 onto Dry Density = 103.6 + 0.6 pcf Confining Stress = 4 psi 34 days ~ 6 days 0 2 days Moo , . . . . . . . . 104 10-3 Axial Strain, inch/inch 10-2 Variation of resilient modulus with induced resilient axial strain of companion samples of A-6 soil tested after 2, 6 and 34 days (After reference 72) 199

Specimen Conditioning/Grouting. In testing cohesive soils, uneven contact between the end platens and specimen result in unwanted deformation (i.e., compliance) at that interface. Uneven contact is not a problem with granular materials. Typically, cohesive soil specimens are conditioned by repeated loading for 200 to 2000 repetitions to give better contact between the platens and specimen ends and somewhat reduce other compliance problems. In recent years, placing a thin layer of quick setting grout on the ends of the specimen has been used. Grouting the specimen ends with, for example, hydrostone, provides an even contact surface and a solid, continuous connection between the platens and the specimen that eliminates the need for specimen conditioning [721. While grouting causes a roughened, fully frictional end condition, it does not significantly affect Me measured resilient moduli for specimens having a height to diameter ratio of at least 2to 1. System Calibration. Calibration of the testing system employed in this study was performed using a synthetic polymer specimen having a reference resilient modulus of 57,000 psi as determined by cyclic torsion and other tests at the University of Texas-Austin. Figure 91 shows Me measured resilient modulus of the unconfined synthetic specimen when loaded repetitively at a deviator stress of 44 psi. During early tests the two internal EVDTs positioned on opposite sides of the specimen measured very different resilient moduli values because of alignment problems at the piston to load cell junction. Modifications in the test setup led to the results shown in Figure 91. The external EVDTs measured a resilient modulus that was 15% lower than the value measured by the internal clamps. These results dearly show the unpo~tance of using synthetic specimens to calibrate the test setup. Axial Strain Measurement. The purpose of one experiment in this study was to determine if grouting the ends of cohesive specimens, which is time consuming, is necessary to obtain satisfactory resilient modulus results. Also, the effect of load sequence was studied. For specimens with ungrouted ends, axial deformation was measurM using the following two mesons: (~) an external transducer and (2) two EVDTs mounted on clamps attached directly to the specimen. Because of grouted ends, tests performed on this type specimen had no provision for drainage. Hence, the testing apparatus had solid end platens with porous stones. Axial deformation was measured on specimens with grouted ends by two methods: (~) an outside EVDT and (2) two EVDTs that measured deformation between the top platen and base of the cell. Compacted Specimens ~ Eight clayey sand (A~) specimens, compacted et both the optimum moisture content and wet of optimum, were tested wig both grouted and ungrouted ends. The specimens compacted wet of optimum moisture content were also used to identify whether excess pore pressures build up during load cycling which decreases the resilient modulus. All specimens were subjected to a load sequence combining He standard SHRP P46 (November, 1989) load sequence with cycling for 2000 load repetitions at a deviator stress equal to 5O~O of the static failure stress (i.e., SL=50%) and a confining stress of 3 psi. The SHRP P46 November, 1989) load sequence required 100 load cycles each of deviator stresses equal to 2,4,6,8 and 10 psi at the Tree confining stresses of 6,4, and 2 psi after 200 cycles of conditioning at a cell pressure of 6 psi and deviator stress of 4 psi. In Tree of He four tests at each moisture content, the SHRP load sequence preceded He SL=50% cycling. In He fours test on each moisture content state, the constant stress level cycling preceded He SHRP load sequence. 200

100 80 ~n - 3 ^^ o c ~ 40 a, ._ In 0 ~ 20 O ,- . 1 . I . ^ t W ~- ~- ~2 - ._ ... .. .. .....  ~ ~,.~ 1 . . . . . . o Outside EVDT ~ Inside EVDT . T T I I I I ~ I l 10 100 Number of Cycles (N) 1 000 Figure 91. Measured resilient moduli of synthetic specimen 201 1 0000

Test Results -- Figures 92 and 93 give Me resilient modulus for different end conditions as a function of deviator stress for tests performed on clayey sand (A~) subgrade specimens compacted at optimum moisture content and wet of optimum, respectively. The loading sequence for all specimens consisted of first the SHRP P46 (November, 1989) protocol followed by 2000 cycles at a confining stress of 3 psi and a deviator stress of 18.5 psi for optimum specimens and a deviator stress of 15 psi for 2% wet of optimum specimens. Outside EVDTs, not corrected for extraneous system deformation, gave average resilient moduli about 50% lower Wan obtained using fixed EVDTs and clamps for the ungrouted specimens. External deformation measurements made on specimens with grouted ends gave much better results than ungrouted ends with the outside measurement being on the average only 12% low at large deformations. For large axial deformations (i.e., high deviator stress), extraneous system deformation was clearly found to become much less important. Figure 94 shows the influence of conditioning method on resilient modulus at and above the optimum moisture content. These results are based on outside EVDT axial displacement measurements. Also, specimens wig ungrouted ends had porous stones and an open base drainage valve. On Figure 94 the ungrouted curve indicates the average results for two tests. Both the grouted specimen tests and ungrouted tests were performed using the SHRP P46 (November, 1989) test procedure followed by 2000 load cycles at a confining pressure of 3 psi and deviator stress that gave SL = 50% of the static failure stress. The ungrouted and conditioned specimen was subjected to the 2000 load cycles first, and then the SHRP P46 (November, 1989) test procedure. Figure 94 shows for external axial deformation measurement that the grouted end specimen has the highest resilient moduli while specimens tested with ungrouted ends and base drainage have lower resilient moduli. For He specimens compacted wet of optimum (Figure 94 (b)), conditioning by 2000 load cycles at a deviator stress of 15 psi and confining stress of 3 psi did not eliminate the difference between grouted and ungrouted MR values. In this experiment, the softer wet specimens may have been disturbed during installation of He internal EVDTs which were clamped to the specimen. Test Procedure Discussion and Recommendations Axial Straw Measurement Basics. Whether specimen conditioning is needed and effective is an important practical consideration for cohesive soil specimens. Extraneous deformations in He testing system cause He resilient modulus to be smaller than the true value. These deformations occur at all interfaces between He deflection measurement reference points. Extraneous deformation for cohesive soils can be broken down into two distinct types: (~) irregular contacts between the ends of the specimen and loading platens and (2) extraneous deformation occurring in other parts of the testing system between reference points. As previously shown in Figure 87, tests on grouted and ungrounded specimens indicate .. . . . . . clung the specimens For ZOUU or more repetitions does not always reduce the effects of irregular panicle contact with the end platens. As shown in Figure 87, He highly plastic AT soil, when tested with ungrouted ends, had a resilient modulus about 14% lower than the 35,000 psi value obtained for grouted ends. In He same series of tests, He 51,000 psi resilient modulus of a low plasticity AN soil was observed to be about 20% less when ungrouted ends were used compared to grouted ends. In He above two examples most of the error in resilient modulus was due to irregular end contact since deformation was measured between a solid top platen (no porous stones were used) and He base of He cell. 202

20 ·= 15 _' in JO <5 10 ·_ in 0 5 G 20 in 15 - cn ~ 10 ~_ ._ I_ a) 5 O- l o external EVDTs intemal clamps \ ~ ' ~3 of ~ O- , . . . , , , I 1111 . 0 5 10 15 Deviator Stress (psi) (a) Ungrouted ends Q`` - ` external LVDTs internal fixed . ~W=' ~ - I I T I .- lll 1 5 10 15 Deviator Stress (psi) (b) Grouted Ends Figure 92 . Effect of end conditions on resilient modulus of clayey sand (A-6) subgrade soil impact compacted at optimum 203

75 15 :, ~ 10 ._ - .m 0 5 o 20 - _ - ,°~ 1 5 - cn - 10 ·O - .m ~ 5 G O- o 20 . external LVDTs internal clamps \\~ ~ 1 -1 am_ 0 5 10 15 Deviator Stress (psi) (a) Ungrouted ends . - r ~ _ 5 Deviator Stress (psi) (b) Grouted Ends 3 external LVDTs - internal fixed -- 1 l ,.. ~ ~ 15 10 Figure 93. Effect of end conditions on resilient modulus of clayey sand (Am) subgrade soil impact compacted at wet of optimum 204

20 - ~ 15 y - cn 3 - o 10 ~_ ·O ·O ~ 5- ~: o 20 _` to 15 - cn - o a) ._ in a: 10 Grouted Ungrouted Grouted ~ Ungrouted Q \ · Ungrouted & Conditioned _ _ _ is_ - _ ~ 1 ~ 0 5 10 15 Deviator Stress (psi) (a) Optimum Moisture Content · Ungrouted & Conditioned ~% ~ 4- -it O- 1 1 1 1 . I I 1 1 0 5 10 15 Deviator Stress (psi) (b) 2% Wet of Optimum Moisture Content Figure 94. Influence of conditioning method on resilient modulus using external L`VDTs with impact compacted clayey sand (A-6) 205

In marked contrast to these findings, grouting He specimen ends has been found to have no measurable difference for resilient moduli less Han about 10, 000 psi as previously shown in Figure S8. These results indicate Hat extraneous deformations caused primarily by specimen end effects become negligible compared to specimen deformation when He resilient modulus is less Han about 10,000 psi. End effects and extraneous deformation from over sources, however, become progressively more important as the resilient modulus of He specimen increases (i.e., as specimen deformation decreases). External Tranducers. The use of exte~naDy mound tranducers to measure axial strain is quite desirable from a practical viewpoint. However, if extemal Reducers are used, the problems of irregular contacts at specimen ends and extraneous specimen deformation must be overcome. Experience has shown that In research laboratones extraneous system deformations can be accountM for to an acceptable degree of accuracy by very carefill system calibration as described in Appendix D and discussed in He previous section on aggregate base. The required level of calib~on to achieve satisfactory results is admittedly Odious and time consuming. Also, in practice the multi-laboratory series of tests has shown that production oriented testing laboratories have problems achieving consistent ~nterIab results due to variations In system calibration and testing technique. As a result, satisfactory results cannot be refeeds upon using externally mounfed[L~VDTs and, conversional Biaxial cells especially when the resilient moduli are greater than ahou! lO,OOO pus Recommended Test Procedure. An unconfined compression resilient modulus test is recommended for cohesive subg~e soils to give a simple, practical test procedure. These soils must be strong enough to hold together during trimming and testing and in general have a plasticity index greater than 10. The test, except as noted later, should be performed using solid end platens without porous stones to eliminate extraneous deformations caused by porous stones. The proposed undrained test represents a conservative condition of drainage and specimen confinement. The University of Illinois has successfully used for a number of years an unconfined test for measuring the resilient modulus of cohesive soils [873. The Illinois DOT uses these resilient moduli in design. The unconfined test is realistic because the confining pressure existing in He upper portion of the subgrade is small. More importantly, He effect of confining pressure on resilient modulus is small for most cohesive subgrade soils. As a result of these two factors, the unconfined test offers a quite practical, realistic simplification for routine~ng of cohesive subglade soils. Tnaxial equipment is not required, and easy access to the specimen is available for quickly installing and adjusting deformation measurement sensors. For shffto hard specimens, axial defonnation should preferably be measured directly on the specimen, Over its midge I/2 using either (~) an optical extensometer which are discussed later in this chapter, (2) non- contact sensors or (3) clamps. Measuring axial deformation on the specimen eliminates the problem of irr~ar specimen end cones. Clamps should not be used on specimens having undrained shear strength less than about 750 psfti.e., very soft, soR and some firm cohesive subgrade soils). The resilient modulus of these weak son's, if desired, can be measured using EVDTs or non-contact sensors placed between the solid top and bottom end platens. By using the unconfined compression test, a special tripodal cell is not required for making optical extensometer measurements. Use of an optical extensometer, although somewhat expensive, offers a very practical alternative to EVDTs and non-contact sensors, as previously discussed in this chapter for aggregate base materials. For soDc and very sonic subgrade soils, clamp mounted L`VDTs are not recommended because of (~) the possibility of clamp slip or rotation that may occur for a specimen having a stingless less than about 10,000 psi and (2) potential damage to a soR specimen during clamp installation. 206

Measurement of axial deformation between end platens is considerably easier and more practical Wan on He specimen using clamps or non contact sensors. The actual resilient modulus, however, can be as great as 30% larger Can the measured value due to non-uniform specimen end contacts. A reduction in MR due to non-uniform end contacts can be eliminated by grouting the specimen ends. Grouting makes top to bottom deformation measurement a possible alternative although the procedure is reasonably complicated. Specimen end grouting is not recommended for routine testing only because of Be time and the expertise required to properly prepare the grouted ends. Grouting procedures used in this study are given In Appendix G. If a grouted specimen is tested using a confining pressure, developing He fills confining stress on the specimen presents problems due to He low air permeability of the grouted ends. A prick alte~ive to group the Amens ends is to measure the amal deformation between the ens! platens play on an ungrouted specimen. Then correct the measured resilient modulus, which wall be too small because of non-uniform end contacts, using an empirical correction based on previous studies preferably for the type soils being Am. Such an empirical relationship, based on very Emoted data, is shown in Figure 95. Additional studies need to be performed to validate this relationship before it is used. Use of an empirical relationship such as Figure 95 is justified, using the 1989 AASHTO design method, since the eject on pavement thickness of small changes in subgrade resilient modulus becomes less as He resilient modulus increases. Ibis decreasing sensitivity of MR on design Sickness is particularly evident by the time the resilient modulus reaches 10,000 psi. For a furler discussion of sensitivity, refer to the reliability discussion In Chapter 4 and also in Appendix F. Since the correction is only applied for resilient moduli greater Han 7,500 psi, the effect on resulting pavement thickness should be small particularly when compared to variability of other factors such as seasonal variation in moisture content, stiffness variation along the route and increase in stiffness that occurs With time after specimen preparation. Test Details - - In the unconfined test, without end grouting the cohesive soil specimen should be subjected to 200 repetitions of a cyclic 4 psi axial stress to condition He specimen. Resilient moduti are then measured for axial stresses of 2, 4, 6, X and 10 psi (if specimen does not fail). The unconfined test should be performed only on soils Cat undergo softening (i.e., a reduction in resilient modulus) with increasing applied axial stress. If so~cen~ng does not occur or problems are encountered handling the specimen, then *e soil should be tested as a granular material. Many silty sands and sandy silts will fall in this category. A complete description of He test is given in Appendix E. Specimen Compaction Soil Structure. Both the method of compaction (static, kneading, impacts used In preparing a specimen and the moisture content at which He specimen is compacted can have an Important influence on the resulting structure of the plate-like clay particles that make up a cohesive soil. The resulting structure is often referred to as the fabric of the soil. Since the soil fabric in turn influences the resilient modulus, both the method of compaction and moisture content must be carefully selected to give results comparable to those of undisturbed samples of compacted soils obtained from the field. Consider a clay specimen compacted at a given energy level by kneading caused, for example, by a sheepsfoot roller or laboratory kneading compactor. If compacted dry of the optimum moisture content, the soil has a flocculated fabric wig the clay plates having random orientation and point to point contacts as shown in Figure 96a. If the same soil is prepared by kneading compaction wet of optimum, the clay plates have a dispersed fabric with the plates being approximately parallel to each and not touching (Figure 96b). The orientation of clay particles and presence or absence of point contacts affects the resilient modulus of He specimen. 207

1.5 ,,,,,,1..~. ~ ·e e~ e~ ~ meet eee_ee ~ear < ~ ~1 ~i ~d 1.4 ~1.3 o C) - 1.2 1.1 - 1-_ o t E beck a~e ~ e ED see ecee~ecec~ E ~e jam ea ~en '--1~' ' - ' ' -' 1 ~. - . - ~ at. , , , I , , 10000 20000 30000 ~._ - .~...... 1 '( . ~._ ~r ~_ ~_~* _.~. ! e ~eel e c ~eeee ~ee ~j ee~e ece-~ea ~e ~I ~ _ 40000 50000 Measured Resilient Modulus, MR (psi) Figure 95. Preliminary correction factors for cohesive subgrade resilient modllli using axial deformation measured between platens - ungrouted specimen ends - \ \ \ /' (a) Flocculated (b) Dispersed Figure 96. Soil fabrics after Lambe (After reference 88 and 89). 208

Influence of Compaction Memos. An increase in compaction energy decreases the optimum moisture content, specimens compared dry of the new optimum still have a more flocculated fabric than specimens compacted wet of optimum. Monismi~ [901 has suggested that a degree of saturation equal to 80°/0 approximately corresponds to the line of optimums on a standard compaction plot of specimen dry density as a fimction of compaction moisture content. Therefore, specimens compacted to a degree of saturation less than about 80% are more likely to have a flocculated soil fabric, and specimens compacted to a saturation level greater than 80°/0 are more likely to have a dispersed fabric. While soil fabric cannot be quantitatively measured, physical behavior can be used to qualitatively evaluate soil fabric. For example, an increasing level of dispersed fabric leads to a decrease in initial modulus when tested in the tripodal cell, increased shrinkage when a specimen is dried and decreased swelling upon soaking [911. losing these physical indicators of soil fabric, Seed and Chan studied the structure of clays compacted using different techniques. For samples prepared wet of optimum, kneading was found to induce significant shear strains during compaction and to cause a relatively dispersed fabric. Static compaction was found to cause much less shear strain and a more flocculated fabric. While these differences do not significantly affect behavior for specimens compacted to less Man an 80°/0 degree of saturation, they play an important role for specimens compacted to high saturation levels. At wet of optimum moisture contents the resilient moduli of specimens prepared by static compaction have been found to be consistently higher than the results of tests on undisturbed specimens [831. In contrast, the resilient moduli of laboratory specimens prepared by kneading compaction were found by Seed et al. to nicely bound Me resilient moduli measured of undisturbed samples taken from Me field. Kneading compacted specimens did have a greater variability compared to the moduli for statically prepared specimens. Specimens compac~wet of optimum by stoic compaction have similar resilient moduli as specimens compacted by kneading dry of optimum and then soaked to a wet state and tested. Specimens compacted by kneading compaction at a wet of optimum moisture content have lower resilient moduli Man soaked specimens. Test findings -- Cohesive subgrade soils are usually compacted using a sheepsfoot compactor which causes a Pleading type of soil structure. The results of this study show that specimens prepared in the laboratory at and above the optimum moisture content by impact compaction exhibit similar resilient moduli as Pose cornl)acted using laboratory kneading compaction. This important finding is valid for deviator stress greater than 4 psi which is applied to most subgrades. The important practical implication of these findings are that specimens with consistent density are harder to obtain using kneading compaction Man for impact companion. In addition, the operator can significantly influence the dry density obtained using the kneading compaction method. Since homing compaction has a relatively small influence on resilient modulus, impact compaction similar to AASHTO T-99 compaction should be used in preparing cohesive specimens at and above Me optimum moisture content to avoid potential variability problems. The findings upon which the above conclusion is based are summarized in Figures 97 and 9X for the clayey sand (A~) soil and In Figures 99 and 100 for the silty sand (A-5) soil tested In this study. Results are shown for specimens prepared at optimum and above optimum water content using both the lmeading and impact compaction methods described in the previous section. Tile solid lines represent resilient modulus results measured during the SHRP load sequence at a confining stress of 4 psi. The dashed lines and solid symbols represent resilient modulus results measured during cycling at a single deviator stress equal to a constant stress level. Recommended Compaction Procedures. From He above discussion, it is recommended to follow AASHTO T-274-X2 for preparing specimens in He laboratory to give similar soil structure and hence comparable resilient 209

30 - 25 ·~ In 20 a' ._ ._ co tar 15: 10 - O to :\ ·.\ i\ ·.V 0 Knead-SHRP ~ Impact-SHRP · Knead-Constant ~ Impact-Constant l _ ~ ..~=.g 1 1 1 1 1 · ~ , I '- f , I , , - T I I I 5 10 1 5 20 25 30 Deviator Stress (psi) Figure 9 7 . Effect of impact and kneading compaction on resilient moduli: A-6 cohesive soil compacted at optimum 30 25 .m a, 20 :, ~ 15 ~_ 3) 10 G 5 O o l | ~ ~ Knead-SHRP \ ~ Impact-Varying \ · Knead-Constant \~'"''""'~'"'''''''''' '^~': ~ l l l .~ ~ ~ ~ 1 ~ ~ r ~ I I ~ ~ 1 l~7--~ I-I 1 1 5 1 0 1 5 20 25 Deviator Stress (psi) Figure 98 . Effect of impact and kneading compaction on resilient moduli: A-6 cohesive soil compacted 2% wet of optimum 210

20 - 15 10 ~_ ._ cc 5 O 0 Impact-SHRP ~ Knead-SHRP - A., I"'. I; · Impact-Constant · Knead-Constant I. N.. - , . , i . . . .. ~, , _ 0 5 10 15 Deviator Stress (psi) Figure 99. Effect of impact and lading compaction on resilient moduli: A-S cohesive soil compacted at optimum 20 C=n 1 5 _' co - ~ 10 ·_ cn ~ 5 a: o 0 Impact-SHRP ~ Knead-SHRP · - Impact-Constant · Knead-Constant -..~; o · ~o ~ Deviator Stress (psi) 10 Figure 100. Effect of impact and hawing compaction ITS on resilient moduli: A-S cohesive soil compacted wet of optimum 211 15

moduli as for cornpac~ field specimens of cohesive subgrade soils. These recommendations, which are briefly sum~ri~ below, were apparently drawn by AASHTO T-274 from the work of Seed and Chan [91] and Seed et al. [X31; these findings are in agreement ui~ the present study. In general, kneading compaction is not recommended for routine testing because the method is too complex. I TN-PLACE CONDITIONS I Applicable Saturation at Time Post-Construction Compaction of Compac ion e-Service | (DO) ~Moisture Content ~Methods ; ~less than the moisture ~impact . ~ 80 content at time of static constru ction kneading greater Man or equal impact > SO to the moisture content kneading at time of construction greater Han the moisture <80 ~ consent et time of construction ~static STRESS SEQUENCE EFFECT AND FAILURE STRESS RATIOS - GRANULAR MATERIALS Past research has shown that for granular materials a single properly preconditioned specimen can be used to evaluate the resilient modulus over a reasonably wide range of stress levels [79, 92-951. Similar conclusions were reached by Allen and Thompson [61 for gravels having plasticity indices as high as 9. The sequencein which different stress states are applied has little effect on resilient properties. · . · . · . . · · . . . · · · - provided tile specimen has been preconditioned and the applied principal stress ratio C)~/03 iS kept less than about 6096 of the principal stress failure ratio Oi/~3. Note that this criteria is more stringent than the ratio of 6 to 7 proposed by Hicks [921. The principal stress failure ratio O~/03 for a cohesionless material is given by 01/03 1 + sine 1 - sine (13) where ~ is the dynamic angle of Internal friction of the material and the other terms have been previously defined. Assuming ~ = 50° for a I.5 in. diameter, well-graded aggregate base, equation (13) gives a failure stress ratio O!/03 = 7-5. this principal stress ratio corresponds to a safe stress ratio of about 4.5 for good base materials. In the absence of test results, Table 52 gives maximum stress ratios to use in testing as well as failure stress ratios for a range of granular base and subgrade materials. 212

Table 52. Approximate allowable and failure stress ratios Oi/~3 for twice Hangar base and subgrade mateirals Dynamic Principal Stress Material Quality ~ Ratio (C'~/~3) Base | Subgra~e (degrees) Allowable | Failure Poor ' 30 3.0 Very Poor Fair 35 2.2 3.7 Poor Good 40 2.S 4.6 Fair Excellent 45 3.5 5.S Good 50 4.5 7.5 Excellent 55 6.0 10.! 243

SYSTEM COMPLIANCE System compliance is extraneous deformation (i.e., other than that of the specimen) which occurs when load is applied to the specimen during the biaxial test. Compliance can cause Me load pulse shape and magrutude to change with stress {ever. When axial deformations are measured outside the biaxial cell, they include both the deformation of the specimen and also all other deformations between the reference points for deformation. As a result, when externally mounted EVDTs are used, compliance causes the calculated resilient moduli to be less than the true values if compliance is not accurately measured and taken into consideration in the calculation. Even when compliance is corrected, important errors may be present. . Compliance is present in the load frame and all parts of the apparatus e Compliance is particularly important in an internally mounted load cell, porous stones, filter paper, end platens, and schemes used to obtain frictioniess ends such as using silicone grease [681. Unwanted compliance seating errors occur during the test due to two surfaces of tile testing apparatus not bearing perfectly against each other. Seating errors can occur at a number of locations including (~) connection between the load ram and the top load platen, (2) between the bottom platen and Me base of the biaxial cell, and (3) between the loading platens and the porous stones. Calibration Compliance errors can be calibrated if axial deformation is measured outside the cell [68, 691. To~ calibrate compliance in the biaxial cell, a dummy aluminum or steed specimen is placed in the cell and subjected to a Fill sequence of stress levels. The theoretical deformations in the dummy specimen, which has a known modulus, can be readily calculated for a given stress level. The extraneous deformation in the testing system equals the difference between externally measured deflection of the specimen pavement material and the deflection occurring in the "dummy" specimen. System compliance calibration procedures for repeated load biaxial testing are given in Appendix D. Accuracy. To obtain reliable resilient moduli when axial deformation is measured outside the cell, very carefid calibration is required by a skilled laboratory technician after system compliance has been minimized. Many labs do not have the required capability to perform a reliable calibration. Even wig good calibration Me accuracy becomes highly suspect when the magnitude of the system compliance correction becomes an important portion of the total observed deformation [691. System compliance becomes quite important when resilient moduli become greater than about 10,000 psi to 15,000 psi [1091. With system compliance calibration, resilient moduli greater than about 60,000 psi measured with external EVDTs were found in Me present study to be unreliable. Moduli of this magnitude may be measured in granular materials at confining pressures greater Man about lO psi. Finally, We reliability of compliance calibration at deviator stresses less Man about 5 psi is also subject to important errors. Resilient moduli for lime fly ash stabilized aggregate base material measured using L`VDTs mounted outside Me cell were found to be unsatisfactory with errors as large as about 40% . The lime fly ash specimen moduli varied from about 400,000 to 600,000 psi. 214

LOAD ALIGNMENT - Good load and specimen alignment is critical to obtaining accurate resilient moduli. Misalignment errors occur due to the axis of the applied load not coinciding with the axis of the specimen (Figure 101~. Also, the ends of a cylindrical biaxial specimen must be perpendicular to its long axis. Misalignment errors cause bending which results in non-uniform distribution of strain in the specimen and an erroneous estimate of the resilient modulus. Figure 102 shows connections typically used to transfer load from the ram in the biaxial cell to the specimen so as to reduce problems at this connection. - To minuTuze misalignment errors (~) the biaxial cell must be carefully machined to be in perfect alignment, (2) He cell must be aligned relative to the external loading ram, (3) the specimen must be a right circular cylinder, and (4) the specimen must be aligned with the biaxial cell. To satisfy the above requirements, He external load ram, biaxial cell and specimen should all be vertical when He cell is placed on a horizontal surface. Alignment of the system should be checked following the procedure given in Appendix D. In the conventional biaxial cell, the top of the cell is supported by the cylindrical Plexiglas chamber. Either an O-ring or a flat gasket is placed on the ends of the chamber to form a seal. When a flat gasket is used, load alignment is influenced by the uniformity of tightness of the nuts holding the tie bars down and by the condition and type of gasket used. A thin, low compressibility gasket should be used and the nuts uniformly tightened wig a torque wrench. For a properly designed O-ring seal' alignment is not influenced since the top plate of the cell bottoms out on the chamber. Check all O-ring sealed interfaces by loading He two parts and measuring deformation to be sure the seal is correctly made. Minimizing Misalignment Even after carefid system calibration, alignment errors should be evaluated during the conditioning phase of each repeated load test. For the two EVDTs used to measure axial displacement, illustrated in Figure 103, the ratio of maximum axial L`VDT displacement (Yma,`) to the minimum reading (Ymin) should be no greater than 1.10 in accordance with the SHRP P 46 procedure (November, 1989~. Excessive eccentricity can often be reduced by stopping the test and very lightly laterally tapping the base of the biaxial cell to obtain better specimen alignment. If flat gaskets are used to seal the cell chamber, an alternate approach is to adjust the tension in the rod bolts on one side of the biaxial cell which also changes the alignment of the loading ram. The Ym,,`/Ymjn eccentricity ratio varies throughout the test. This ratio is directly proportional to He distance of the transducer from the loading piston (Figure 103~. Hence, the eccentricity ratio Ym,,,/Ymin does not consider the distance which the EVDTs are located away from the load axis. Therefore, the EVDTs should be placed as close as possible to the load piston since the I. 10 ratio criteria is quite strict. Tests on 29 different specimens (at 15 stress levels), which included four different base materials, gave an average eccentricity ratio Ym~,,/Ymin = 1.14 throughout the test for both external and clamp mounted transducers. Each external EVDT, however, was located only 2.2 in. from the load axis while each clamp was 4.0 in. away. The standard deviation of He eccentricity ratio for the external transducers was 4% compared to 8% for the clamps. Experience indicates Hat in setting up a specimen, with careful calibration of tile biaxial cell and testing system as described in Appendix D, an eccentricity ratio of about I. 10 can be initially achieved. Great care should always be taken to minimize eccentricity. 215

ele · te el,' ..~e ~ #' ~ I. 1 (a) Perfect alignment 1 ~ .'^ 1 1 ~ ' ; ~ T 1 (d) Misalignment due to specimen 1 ~ · ; ~ ,... 'lo I'. 1 _ ; (e) Misalignment due to apparatus Figure101 .Example of possible Initial misalignment with cone seating connections (after reference 7 i) 12.5 mm dia. steel ball \ ~ conical \ L~seating .. ,.b ., ,.- , ~ i.. .. . .. ...... ''at.. (a) Steel ball and coned seating Ram with hemispherical end Flat ended ram \ \ Halved \~ tJ steelball W · ~ 1 1 \ (b) (c) HaIved Steel ball Hemispherical tipped and flat ended ram ram and coned seating Figurel02 . Examples of connections typically used with biaxial cells with external tie bars (after reference 7 I) 216

1~VDT Z _. 1.. l D I D -1 1 Fl LVDT 1 you ~ f(D) YE e~OTA~ON Figure 103.Displacement measurement as a result of specimen end rotation J O. ~ .- ''''10& O ~ . . _ _~? mom _r.~ '1.` me, ~'-p it' Figurelo4 .CIamps used with 2 EVDTs to measure axial deformation on the specimen 217

External Measurement External deformation measurement is very easy to perform, but He results are in general less reliable and depend upon minimizing system compliance and careful equipment calibration. Remaining compliance effects can Men be minimized by calibration using a dummy sample of known stiffness made of steel, aluminum or Plexiglas. Displacement can also be measured within the cell between Be end platens. This approach eliminates several compliance errors but does not handle non-uniform strain distribution, compliance in Me porous stones, and bedding errors. The results of this study show satisfactory resilient moduli can be obtained when Hey are less than about 60,000 psi using externally mounted transducers. However, great care must be Wakens to (~) nunzmize system consonance am (2) calibrate the system. Most labs Will not be able to achieve good results using external measurements. System compliance and calibration are discussed subsequently. AMAL DEFORMATION MEASUREMENT Axial deformation measurements during repeated load testing have been made outside [38,96,97] and inside the biaxial cell directly on the specimen 13S,55,92,98-1001. The SHRP PA test procedure (November, 1989) measures axial deformation of the load piston outside of the biaxial cell. To avoid the effects of end friction, bedding, seating and system compliance, in recent years most researchers have measured axial deformation inside the cell particularly for granular and stabilized materials. Internal Measurement Internal axial displacement measurements have been made using spring loaded clamps, studs or vanes placed In the specimen, and blocks or targets taped or glued on the membrane to serve as reference points between which deformations are measured inside the cell on the specimen. Deflection is measured between these reference points using EVDTs, proximity gages, optical extensometers or other special instrumentation. On stabilized materials long gage length wire resistance strain gages have sometimes been placed directly on the specimen to obtain accurate results. Internal measurement techniques are much less sensitive to system compliance effects and, in general, give more valid resilient moduli than external methods even with system calibration. ~amps. The use of clamps placed around the specimen with two EVDTs between He clamps to measure axial deformation has been quite popular for many years (Figure 47 and 104~. To provide for misalignment between clamps, He rod holding the EVDT core usually has a hinged connection or is cut in half with a flexible wire between He two segments. The thin, circular aluminum or Plexiglas clamps consist of two pieces Hat are hinged on one side and have a spring loaded connection on the over (Figure 104~. Clamps are usually placed at either He I/4 points in from each end of He specimen [6, 38, 52, 93] or at He I/3 points [1001. The gage length used over the center portion of the specimen is a compromise between measuring the axial deformation as close as possible to He center of the specimen, where strain is reasonably uniform, and using a longer gage length which gives larger deformations Hat can be more accurately measured. Both clamps must be in a horizontal plane (i.e., perpendicular to He axis of He specimen) to obtain accurate readings from He clamp supported EVDTs. A jig or gage rod, temporarily placed beneath each side of He clamp, together with a spirit level can be used to achieve accurate alignment [1001. Both 218

barreling of the specimen and clamp misalignment can cause unwanted tilt of the EVDTs resulting in error in axial deformation measurements. O-Ring Clamp -- For aggregate bases, Crockford, et al., [55] fastened 3 small, individual aluminum blocks onto the top I/3 points of specimen and 3 blocks onto the bottom I/3 points. A pair of aluminum blocks, one located above the other, supported each EVDT measurement assembly. Clamping action was provided by placing a large O-ring around each level of 3 blocks. Three axial EVDTs were used to measure deformations which define the plane of the axial specimen deflection. Clamp Slip and Positive Clamp Support ~ Clamp slippage is a potential problem in measuring resilient modulus ITS, 73, 1011. The force tending to cause slip between a clamp and the membrane is equal to the acceleration acting on the clamp times its mass which includes the mass of the supported EVDTs. Thus, use of a short pulse duration time is more critical with respect to clamp slippage than for a long pulse time that gives smaller accelerations. The force resisting slip is equal to the clamping force times the coefficient of friction between Me clamp and the membrane/specimen. Using a reasonable clamping force while minimizing clamp weight reduces the tendency of the clamp to slip. For example, the clamp employed in the present study, was minimized by drilling as many holes as practical through it (Figure 104~. Each clamp wieghed 0.54 Ibs., and the spring holding We clamp together exerted a force of 10.0 Ibs. Good results using aluminum clamps were obtained during this study when placed on 6 in. diameter aggregate specimens and even for slick, stiff (MR = 50,540 psi) and soft ~ MR = 7880 psi) synthetic specimens covered with a rubber membrane. For both the stiff and soft specimens the resilient modulus measured using clamps was only 6% lower Can measured using plugs. To prevent slip between the clamps and Me membrane, Chisolm and Townsend [100] placed a small quantity of 5 minute epoxy glue on top of each of the clamp contact points with the rubber membrane. Sweere [641 used individual EVDT support blocks glued directly to Me membrane. For static tests, relative slip between the specimen and the enclosing membrane does not occur until near or after failure [701. Studs and Pins -- To eliminate possible slip, metal studs have been placed Trough the rubber membrane into granular specimens as shown in Figure 105a [101, 1021. Use of studs offers an excellent positive method for supporting EVDTs or proximity gages. To prepare a granular specimen with studs, Boyce and Brown [101] used a vibratory table to density the material. The care required to properly place the studs and prepare the specimen, however, makes this method unsuitable for routine laboratory use. Large aggregate present cause considerable variation in strain from one location to another. Boyce and Brown [101] concluded Cat measurement of at least three axial strains is necessary to provide a reliable average value. Tile results of this study, however, indicates Mat two EVDTs are sufficient to give a reliable resilient modulus, provided good alignment is achieved. Two EVDTs are more practical to use for production type testing. Pins have been pushed into sand plugs placed in the specimen to support proximity transducers as shown In Figure lOSb [1031, and small cross-shaped vanes have been pushed into a soft cohesive soil. Holes have also been drilled in asphalt concrete specimens and reference plugs glued in. 219

or I: ~ o ·~. .. ~ e .-. · ~ .. lo · ~ ·. em · ~ ::W · ~ OWL ° 9 :1 ~ ·- - e \\ 'of w. e_ '4~" (a) Studs placed in specimen to support LVDTs (after reference 101) l [HE SAND RUBBER UEIIBRANE `34=t FDCATiON AWL ALL== NEOPRENE IMBRUE l _ 200 ~ S1EL l ~ _PP~ Em; ~ TRANSDUCER ~, r (b) Pin supports for proximity gages (after reference 103) Figure 105. Selected methods used to support axial deformation measurement devices 220

Non-Contact Proximity Sensors. A number of different non-contacting sensors are available which do not contact each other including inductive, optical, ultrasonic, and pneumatic types. Ultrasonic type non~ontacting sensors have a low sensitivity while pneumatic type non-contacting sensors are large and hence are not suitable for resilient modulus measurement [1041. Both inductive proximity gages and optical extensometers offer excellent methods for measuring both axial and radial deformations. Inductive proximity gages have been successfully used by Dupas, et al. [103] and Pezo, et al. [72 ~ to measure axial strain over the middle portion of aggregate base and subgrade specimens Although proximity gages are non-contacting, lightweight blocks or pins must still be attached to the specimen similarly to L`VDT based axial measurement systems. The most reliable approach is to measure the relative displacement of two points on the specimen using two proximity gages attached to Me same reference rod Figure 106~. Thus, the measurement of average strain on each side of the specimen requires 4 proximity gages. Supporting each pair of gages on a single reference rod minimizes the effect of system compliance. Inductive proximity gages are accurate, reliable and only moderately expensive. The cost of measuring deformation on bow sides of the specimen is about $6,000 to $S,000 not including the data acquisition system. Disadvantages include having to place the 4 lightweight targets on the specimen at the correct location and Den positioning and zeroing out the proximity gages. For small displacement measurements obtaining the required gage sensitivity can be a problem. The use of blocks attached to the specimen with "0" rings, as previously described, appears to offer an excellent method of rapidly attaching He proximity gage target to the specimen. Optical Measurement Systems. Optical measurement systems to determine axial strain were first used in He 1970's [6, 105, 1061. Since then, little use has been made of this powered! technique which has technically greatly advanced in the last 30 years. To use a modern optical extensometer, two lightweight reflective targets are attached on the sides of a specimen. The optical extensometer, which is located outside the biaxial cell, optically monitors the movement of the relative displacement between the two targets as shown in Figure 107. This movement is then converted into a d.c. analog voltage output that is recorded using a data acquisition system. Advantages -- The use of a modern optical extensometer has many advantages and features including: · Speed and ease of set up of the axial displacement measuring instrumentation during an experiment. . Rapid calibration check of the measurement system. · Rapid, simple target installation - just stick two targets consisting of tape on the specimen. · Clean but small AC asocial displacement output signal. . Elimination of problems associated with positioning clamps and zeroing LVDTs or proximity gages. Variable gage lengths up to 125 mm between measurement points can be used by changing adapters. High scan rate of up to 2000 scans/sec. depending upon the digital optical system used; the system used in this study was analog based and hence had a continuous scan. 221

- Light Weight Target . . . 1 1 1 Hi. - - Specimen · I - Figure 106. Setup for noncontact proxomity gages 222 Non-contacting Sensors

MEL (a) Actual test set-up _1 _1 in_ ~1 OUTPUT | Control Unit ~ B n ~ Triaxial Ce11 20 ~ r ~rFa'Opti~l ~ ~ `` ~ 1: ~ Target ~ Specimen Video Tripod ///\\\///\\\ i///\\\ (b) Schematic layout of system Figure 107. Noncontact optical extensometer measurement system (compliments of the Cooke Corp., Tonawanda, N.Y.) 223

Disadvantages -- For diametral testing, Me optical extenso meter has Me disadvantage of a cost of $30,000 to $50,000 or more depending on the accuracy desired and options selected. For repeated load biaxial testing, a $30,000 to $40,000 system gives sufficient accuracy. An additional important disadvantage of the optical extensometer when used in biaxial testing is that the optical line of sight must pass through a flat, clear plate of preferably optical glass. To overcome this limitation, the chamber of the biaxial cell has to be redesigned to be either square or else round with a small flat window. The flat window must extend over a height slightly greater than the gage length over which relative deformation is to be measured. A 3 in. to 6 in. wide window is sufficient. An appealing practical option to constructing a special biaxial cell is to conduct a vacuum biaxial test for routine work. A vacuum biaxial test, previously discussed in this chapter, does not require a biaxial chamber surrounding the specimen. Hence, a special tnaxial chamber Is not required. Finally, a single optical extensometer with dual lenses only measures axial displacement on one side of the specimen. Optical Extensometer Experiment. The repeated load resilient moduli were evaluated for 2 cylindrical, synthetic polymer specimens using a Mode! 200X Cooke optical extensometer. The Mode} 200X camera houses two independent transducer systems with the lower image converter A and the upper image converter B in one block as shown in Figure 107. The A lens determines Me displacement range. The specimens were tested in the unconfined condition to allow evaluating the extensometer without having to construct a special biaxial cell. Equipment Setup and Calibration -- The digital extensometer camera was placed on a sturdy video tripod having both vertical and horizontal positioning capabilities for rapid, adjustable sighting ability. Two targets were placed on each specimen at a gage length of 5.67 in. Targets consist of a 0.75 in. strip of white and black electrical tape. The two strips of different colored electrical tape are placed horizontally on He specimen wig one piece of tape overlapping the other to form a high contrast, horizontal interface. The optical extensometer was positioned IS.3 in. away from the specimen which was located on the loading pedestal of a closed-Ioop test system load frame. Two small high intensity lights, placed near the specimen, were pointed on the targets to provide opimum contrast between the black and white target colors. The targets are sighted through the optics of the extenso meter and the system rapidly zeroed by adjustments on the camera. Triggering of displacmeent measurement occurs automatically as load is applied to the specimen. The resulting difference in d.c. voltage output from He A and B extensometers is recorded on an analog data acquisition system. The factory electromptical extensometer calibration was verified using a 0.001 in. micrometer calibration system put together for this test series. The micrometer was moved over a known distance with one target attached to a fixed location and the over to the adjustable end of the micrometer. The same gage length was used in calibration as used during testing. In the calibration, He known distance between the targets was related to the voltage output from the optical measurement system over the expected variation in displacement. Experiment Methodology and Results -- The resilient modulus of a soft and stiff synthetic specimen was evaluated for 5 consecutive load pulses which constituted one test. A test series consisted of repeating He S pulse test 10 times to establish repeatability accuracy. One test series was performed leaving the specimen in the load frame and not changing its position. Another test series consisted of removing and replacing the specimen about ~ to 10 times. The specimen repositioning series permitted determining the reproducibility of the resilient modulus that can be obtained by testing different, perfectly prepared specimens composed of He same material. The external data acquisition rate for most tests was 200 data points per second with a 0. ~ sec. load pulse duration. Very high scan rates used in preliminary 224

tests showed extensive high frequency specimen vibration when subjected to Me repeated load; this behavior has not been reported before. Test Results -- Reproducibility of the axial deformation measurements on the specimen were found to be excellent using the optical extensometer (Table 53~. When the synthetic specimens were left in one position (the sin" position in Table 53), the observed coefficient of variation (CV) between tests was 0.22% for the soft specimen (MR = 5667 psi) and 1.56% for the stiff specimen (MR = 53,815 psi). The relatively large CV for the stiff specimen was partly caused by the system load pulse not being in proper adjustment. The applied pulse was observed on an oscilloscope and the closed-Ioop testing system adjusted before performing the tests on the soft specimen. Upon removing and replacing the synthetic specimens (the in/out condition in Table 53), the coefficient of variation (CV) increased by a factor of about 2 for the soft specimen and 4 for the stiff specimen Table 53~. Nevertheless, Me coefficient of variation for the soft specimen was still I/3 to I/37 that of the clamps and external EVDT measurement techniques whose results are shown on Me right side of Table 53. The coefficient of variation of the stiff synthetic specimen measured using Me optical extensometer was about I/2 to I/3 that of the conventional value. Use of an accurately adjusted load pulse in the optical extensometer tests would undoubtedly have given better relative performance of the extensometer. Design Implications Making reliable axial displacement measurements is Me key to obtaining an accurate, reproducible value of resilient modulus. As a result, the presence of extraneous deformation, which is always present in a testing system, also plays an important role in repeated load biaxial testing. Table 54 gives a summary evaluation of available methods of deformation measurement. External Transducers. External transducers give satisfactory results provided the system is carefully and completely calibrated by a skilled technician or engineer. Equipment calibration includes insuring accurate load alignment, minimizing extraneous system deformations and accounting for remaking extraneous deformation by calibrating with a metal specimen of known stiffness. Equipment calibration is described in the next section and also in Appendix D. The results of this study including the round-robin tests indicate that equipment calibration is not as stra~ghtfonvard nor as easy as it might appear. The results from laboratory to laboratory are variable and not always satisfactory. Even wig good calibration, resilient moduli greater than about 60 ksi cannot be measured using externally mounted transducers. Because of the potential for inaccurate results due to calibration problems, the use of external EVDTs for deformation measurement of bases ranked last out of the 5 me~ods summarized in Table 54. For reasonably soft cohesive subgrade soils (MR ~ 103000 psi), system calibration is not as demanding as for aggregate bases. Measurements on He Specimen. The best measurement approach from both a theoretical and a practical standpoint for obtaining a consistent. reliable resilient modulus is to measure axial deformation .. . . . _ _ _ . ~ ~ directly on the specimen. By measuring relative displacement between two points on the specimen, enects are eliminated of extraneous deformations occurring past the ends of the specimen. Hence, special calibration using stiff dummy aluminum or steel specimens is not required. Problems are also avoided with nonuniform strain distribution which is present in both diametral and biaxial testing. Even when 225

Table 53. Summary of optical extensometer experiment resultstt' ~;~ Condition Optical Extensometer _ MR CV CVS 3) Temp. Asia . (°/0) (°/0) ~ ~) External ~ Clamps ~ Plugs ~ Top STIFF(2) SPECIMEN I Bottom . ~_ 53815 1.56 3.55 77.4 56584 3.03 3.42 77.4 IN IN/OUT 7 9 1 11~5 1 7.6 SOFT SPECIMEN IN IN/OUT _ 5667 0.22 0.29 78.5 5181 0.88 0.36 78.5 13.6 1 1.2 1 3.5 1 4.5 Notes. I. Air temperature was increasing slightly throughout the experiment 2. In this test senes, Me load pulse was not adjusted properly which explains the relatively high CV 3. Average CV for 5 load pulses 4. Compare with CV Dom optical extensometer tests; specimen stif~esses were similar but the same specimens were not used 1 Tabb S4. Summary of axial deformation measurement techniques for routine repeated load testing 10 0.6 Overal 1 Reproduci hi l ity, Method Accuracy CV (%) High MR T Low MR LVDTs: External Poor-Good 11 (3) ~ 1 3~3) Measurement LVDTs Top to Fa~r-G~d 8 4.5 Bottom _ LVDTs: Clamps on Good 8 5-13 Specimen Proximity Good Gage EXceJk~t _(4) _(~) Optical Extensometer Excellent 3 I Level of | Relative Complication(l) | Cost (1 - 10 Scale) | (I - 10 Scale)(2) Comments Requires elaborate calibration |of cell and testing system by |skilled technician/engineer(3) _ . IEIiniinates most calibration |problem if porous stone not fused on top ~ bottom 1 IClamp must be designed and [installed properly; more |VariabIe for IOW MR 4-5 5 3 10 Must attach 4 targets to spec. | & set up 4 transducers |Vcty rapid, easy setup and fuse Notes. 1. Level of Complication: High level of complication requiring experienced, skilled technician = 10; low level of skill requiring modest technician skill = I 2. Relative Cost: High relative cost = 10; low relative cost = I 3. Proper calibration extremely hard due to extraneous deformation; mpn~ducibility given for very good calibration - average CV is likely to be large; Not valid if MR > 60 ksi; calibration not as critical if MR < 10 - 15 ksi 4. Unknown Reproducibility 226

deformations are measured directly on the specimen, accurate load alignment must be insured and extraneous deformations minimized to obtain proper specimen loading for all stress conditions. Optical Extensometer. In contrast to other methods for measuring deformation on Me specimen, the optical extensometer is extremely easy to set up, calibrate and operate. Using this type measurement system, Me potential for error is minimized and obtaining an accurate deformation does not require a highly skilled technician. The primary disadvantage of this technique is the $30,000 to $40,000 cost of an extensometer. A special biaxial cell with a flat window is also required unless Me vacuum triaxia! shear test Is used. Axial deformation is measured on only one side of the specimen using a single optical extensometer. With proper load alignment, the resilient moduli obtained on one side should be acceptable considering the reasonably small effect modest variability of the resilient modulus has on the resulting pavement Sickness (refer to Chapter 4~. Of course two optical extensometers could be used for optimal accuracy at a cost of $60,00 to $80,000. The optical extensometer is given the best overall rating out of Me 5 methods summarized in Table 54. Non-Contact Proximity Gage. The non-contact proximity gage gives excellent results but requires considerably more effort and expertise to set up, calibrate and operate Man the optical extensometer. This drawback slows down production type testing. To slightly speed up production testing, axial strain could be measured on only one side of the specimen. Use of two deformation measurements is recommended. The overall use of proximity gages ranks second out of the 5 methods considered. It is just slightly better overall then clamps but not as practical. Clamps. Good overall results can be obtained using sensitive EVDTs supported by lightweight clamps and EVDTs carefully placed on a base or subgrade specimen. Proper zeroing of the EVDTs and placement of the clamps on the specimen requires a good technician and slows production. This method is rated third out of the S methods. For small displacement measurements such as stabilized materials and even high quality base, clamps may give better results than non-contact proximity gages. L`VDTs are available which give higher voltage output than proximity gages and hence more accurate displacement can be measured with clamps. SPECIMEN DRAINAGE Repeated load tests have been performed on pavement materials in both the drained condition [~l, 103, 1071 and Me undrained condition [55,92,93,1001. Since present pavement design procedures are based on total stress concepts, the resilient modulus should be evaluated using total stress rather than effective stress regardless of whether a drained or undrained test is performed. Following the total stress approach, stresses are not corrected for porewater pressures developed in Me specimen. Instead, the total stress approach assumes that the laboratory resilient modulus test is performed using stress states that induce pore pressures in the specimen similar to those that develop in the field due to traffic loading. The resilient modulus obtained in this way is then used in the usual layered system analysis which is based on total stress. No attempt is made to calculate pore pressures generated within Me pavement nor do they have to be measured in Me laboratory. in a drained test, the drainage lines leading to Me inside of Me specimen are kept open. Since Me drainage lines are kept open, the confining pressure placed on the specimen is equal to the cell pressure. Either a leak in He rubber membrane surrounding Be specimen or else forgetting to open Me drainage line leading to the inside of the specimen results in uncertainty as to Me actual level of specimen confinement achieved. Such tests should be repeated. 227

Recommendations Q~j3Is. An undrained condition represents He worst possible condition due to the potential for pore pressure development and hence reduction in stiffness and increase in permanent deformation. For granular teas", however, drainage will occur In Be field with increasing load repetitions and hence a drained testing condition is recommended. ~5~. For cohesive subgrade soils, drainage of water in the field will also occur but considerably more slowly than for granular materials. Either a drained or undrained test can be used for cohesive subgrade soils. If an undrained test is performed for either base or subgrade materials, the drainage line should be led open during He preconditioning phase to minimize pore pressure build up [92, 1001. MOISTURE SENSITIVITY For nest testing purposes, such as Feting He effect of Tonsure on resilient modulus at a high level of saturation, a degree of saturation of about 909G to 959` is adequate to establish trends. These levels of saturation for base materials can usually be achieved using just a flushing technique involving passing desired water through the specimen. Resilient modulus testing of a specimen which has been taken to a relatively high degree of saturation by flushing is easier to carry out Man if back-pressure saturation is used which may be necessary for fine "rained subgrade materials. Recommendations Granular Materials. Flushing of aggregate base materials was accomplished in the tests performed in this study using a static head of water at the center of the sample varying from 2.5 to 3 ft. Me static head of water is, In effect, a small backpressure. Very limited test results indicate that the 2.5 ft. of static head might be slightly more effective than a 3 ft. head which causes a larger hydraulic gradient Trough the specimen. This approach is recommendM for granular materials to evaluate moisture sensitivity of He resilient modulus. Chaney, et al., [1081 used carbon dioxide to flush air from a specimen of soil as an aid to obtaining a high degree of saturation. A trial test on a crushed stone material (Base I) using carbon dioxide as the flushing medium did not increase He degree of saturation and hence was not used. Liar. To evaluate moisture sensitivity in compacted cohesive materials, initially compact He specimen to a high degree of saturation following the compaction procedures given later in this chapter and in Appendix E. For undisturbed specimens, back pressure saturation and testing will probably be required. For routine testing, the recommendation is given to perform the test at He optunum moisture content and correct He resilient modulus using empirical correction factors such as Pose given In Chapter 4. Sedation. If an undrained, saturated resilient modulus is desired for either base or subgrade materials, a degree of saturation in excess of about 99% is probably required. This type of test is similar to a liquefaction test in earthquake engineering. It is not considered in general necessary for modeling aggregate bases or granular subgrades. The level of saturation is often defined using Skempton's B pore pressure parameter wig B = AU/&O3 where 603 is He ~plied change in Licit cell pressure "d Au is He corresponding observed change in pore water pressure 228

The B pore pressure parameter concept of Skempton assumes a large difference in stiffness exists bawem the soil and water which is not true for aggregate base and granular subgrades wig stiff skeletal structures. These stiff materials can have a relatively high degree of saturation even though the measured Skempton B pore prmsure parameter is small. This behavior, which at first may appear to disregard the basic B pore pressure parameter concept, results because a granular material can have a stiffness on the order of IlS that of water. Theory, however, assumes Me skeletal stiffness is very small compared to Nat of water. The difference between store and water stiffness is much less than for most cohesive soils usually tested ~ g~hnical laboratories. For example, at a back pressure of 40 psi, the theory indicates Tat We degree of saturation for a B pore pressure of 0.2 is 94, 97, 98 and 99% for resilient moduli of 10,000, 20,000, 30,000 and 60,000 psi, respectively (refer to Figures 108 through ~10~. ~n~t ~ For very stiff materials, a B pore pressure parameter of I.0 Is impossible to achieve even at 100% saturation regardless of Me magnitude of back pressure used. Therefore, over criterion defining saturation must be employed such as (~) using Figures 108 to ~10 to dethrone the B-value at Be descry level of saturation, or (2) increasing the back pressure and measuring B until no furler increase in B or water intake into Be specimen occurs with increasing back pressure. In practice both methods (~) and (2) should be used. Figures 108 to Il0 were developed using equations presented by Black and Lee [761. The assumptions Bade In developing these figures are as follows: (1) Be base has a porosity (n) of 0. 17 and Poisson's ratio of 0.35 and (2) Be compressibility of water is 0.3875*10-S in2/Ib. ~ A saturated specimen can be achieved using a low initial value of back procure if Be initial degree of narration is higher Man about 97 or 98%. Otherwise, large values of back pressure are required to achieve full saturation. Cohesive soils having low permeability will probably require back pressure to achieve a degree of saturation of 99% or more. Figures have been given by Black and Lee 176] from which Be required back pressure for saturation can be estimated for a given initial degree of saturation and time Be back pressure is left on the specimen. If back pressure Is used, it must be left on throughout the resilient modulus [est. ~ n ~ Achieving a saturated sample requires the use of good equipment by a meticulous laboratory technician. Water leaks in the system are an important problem when saturating a specimen. 01d Imes and valves should be replaced. Careful removal of small aggregate particles from all connations and ping e cell is assembled is absolutely essential to avoid leakage. Sharp aggregate may penetrate Be membrane during compaction. A leaking membrane must be either repaired, replaced, or a new membrane placed over it which is Be more frequent solution. SPECIMEN END FRICTION End friction, which can never be completely eliminated, results in the specimen assuming a barrel shape. Also, end friction results in a nonuniform strain distribution down the axis of Be specimen. Minunuz~ng barreling is most important in lateral strain measurements. Barreling also causes rotation of EVDTs or proximity gages clamped to the specimen which can lead to errors in axial displacement measurements. Fnctionless ends have net been commonly used for resilient modulus testing. Use of frictionless ends presents practical problems in providing specimen drainage, particularly when testing high p~meabili~ granular base materials. For granular materials having a degree of saturation less than about 229

do ~ - ui .` 0.6 e Q.,. e 02 e a CL n ~ 0.17 FIR ~ 10,000 For · do3stOPSl, B.P.~20 PSI · ace ~ S PSI, 8.P. · 20 PSI · A~s10~.P.-~~ · 03 · S PS3, B.P. ~ ~ ~ Be it, . Q. _ IS 88 91 .. 87 100 DEGREE OF SATURATION, S (PERCENT Figure 106. Degree of salvation as a finch of B pore pressure parameter: Mat = 10,000 psi 1 m e ~ 0.8 .` 0.6 e 0.4 e i,' 0.2 o .. ~1 ~ - n ~ 0.17 'R · 30~000 PSI · 6~3~10 PSI, B.P. ~20 PSI Ao3 ~ ~ PS, B.P;- 20 PSI · 6~3~10 PSl, B.P.~4OPSJ · Ao3 ~ S PSI, B.P. ~ 40 PSI o.o 1 - 1 90 92 84 86 DEGREE OF SATURATION: S (PERCENT) 88 100 Figure 109. Degree of saturate ~ ~ fiction of B pore pressure parameter: Ma = 30,000 pSi 230

1~ m a: Q8 0.6 - 0O 0.4 In tar o So - l 7! . n · 0.17 HR · ",~ "1 · 6~3~10PS,8.P.-20PSI · 6~3 ~ s PS', B.P. · 20 · 6~3 ~ 10 PSI, B.P. ~ ~0 PS · &<S3 ~ S PSJ, B.P. ~ 40 PSI . as .. 87 98 .. too DEGREE OF SATURATION, S (PERCENT) Figure 1 10. Degree of saturation as a fimction of B pore pressure parameter: MR = 60,000 psi '~) · ~ ·SPEOU~ · · . . a i//// y/' POP'OUS S7ONE _TEFLON OR f1UBSER SItE ET HlaH VACUV~I SILICONE GREAS£ DR`IN`GE L1NL Figure ~ ~ t. FrictionIess end platen used at Waterways Experiment Station (after reference 100) 231

80%, a polished solid top platen can be used with drainage provided in the base platen. This arrangement also eliminates He upper porous stone and hence its compliance. A small porous stone for drainage has also been used in the middle of the platen with friction minimized by applying silicone grease and a Teflon or rubber sheet as shown in Figure ~ ~ I. Use of a stainless steel disk cut into segments and placed between the platen and specimen was found to be quite effective in reducing barreling [52, 1011. For cohesive soils, drainage has been achieved using both strips and jack-o-lantern type filter paper strips connected to a porous drainage ring located around the sides of He end platens below the frictionIess ends. Such drainage techniques may not give full drainage for a granular base or subgrade. Recommendation - For routine resilient modulus measurement, elaborate techniques to minimize end friction are not required provided the specimen height is at least twice its diameter. Attention should be given to minimizing end friction if Poisson's ratio is measured. RESILIENT MODULUS AND PERMANENT DEFORMATION MODEIS FOR COMPACTED COHESIVE SOILS Basic Concepts Based on the experimental observations reported earlier in this chapter, generalized models are developed for He response of compacted cohesive soils under repeated loading. The key element in developing these models is in establishing appropriate normalized variables which give clearly defined relationships between resilient and permanent strain and pertinent independent variables such as stress level, moisture content, density and shakedown stress. Once these relationships are developed for a given soil type, He resilient modulus and permanent strain can be easily calculated for different soil moisture contents, densities and stress levels without performing additional resilient modulus laboratory tests. The stress-strain behavior of two soil samples subjected to different levels of repeated deviator stress are presentM in Figures 112 and 113. These figures illustrate two different general classes of deformation and stability behavior. 1. Ankle Condition. As shown on Figure 112, after a finite number of repetitionsof stress during which significant permanent deformations accumulate, the components of stress and strain form a stable hysteretic loop wig only insignificantly small permanent deformations occurring in subsequent cycles. 2. Unstable Condition. In He second class of behavior (Figure 113), He permanent deformation increases rapidly with increasing number of repeated stress cycles. For this condition, large permanent deformations accumulate and cause failure or a limiting state of serviceability. In Figure 114, He permanent strains developed per load cycle are plotted against the number of load repetitions for three compaction moisture contents. The rate of strain accumulation decreases with increasing number of load repetitions for all levels of repeated stress. A strain rate of 10-5% per load cycle is very small, and He soil at this strain rate has reached an equilibrium condition sometimes referred to as a state of "apparent shake down." The stress level (SL) separating the stable from He unstable condition is expressed as the ratio of the applied repeated deviator stress divided by the deviator stress required to cause failure in a static test. The same confining pressure is used in each test (Figure ~ 15~. 232

60 - 50 · - Ad ~ 30' · - e~ 68 20 I' 10 / ,~ ,%~ iS~-S~p n at odd)- 25 < rat A_ 0 _ 0~0 160 2~0 Low Stress Levels Stable Condition Static 1 1 4.0 5.0 6.0 3.0 Axial Strain (%) Figure 112. Stress-strain at apparent shakedown condition for compacted dry of optimum A-6 cohesive soil 60 _% SO u, u, 0 ~ - e~ ._ a 20 e;3 Hi; 10 O _ 0~0 1 1 ~ .1 Ff] stadc 1 jog Sample Failled After 3335 Cycles High Stress Level Unstable Condition i S=ss-S~ Loops at c~d=0.95 Bee 2.0 30 Axial Strain (%) Figure 113. Stress-stra~n curves at rachit~ng condition for compacted dry of optimum A-6 cohesive soil 233 4.0 S.O 6.0

~o ~ 1 OO0(l.O c~ ~ ° 1~0.0 x c~ ~ 100.0 ._ u, ~: c~ ._ x z c~ - - c~ ° ~ S~25~o I I ~ ~ ~ I ~r ~t t · t ~ c - - ~ &;3L~=~U~O ~ -- a' S~609to 10.0 t.0 O-1 ~_ I ~ I ~ I l" ~ ~ ~ 1"L , ~I ~I ~ ~ I t t ~ ~ ~ I ~ ~ 10 100 Number of Cycles, N 1 000 Figure ~14. Rate of accumulation of permanent strain in A-6 cohesive soi! compacted wet of optimum 1 0000 - ..... ......... ~ . ~ __ _ ==== _ _ - ~ 75 ~n - ~ 50 c~ c~ _. co c, ._ - ;~ 25 Unstable - A ~ , _ ,' _ 1 . O l ~ I -0.25 ~0.20 -0.15 _ ' -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 Norlllalized Water Content, [(w-wO)/wO] Figure Il5. Shake-down envelope for compacted A-6 cohesive soil under cyclic loading 234

Apparent Shake Down Envelope. For a given soil and {eve! of compaction, whether the soil is stable or unstable depends primarily on the applied level of repeated axial stress and the compaction moisture content. Figure ~ 15 presents data from a number of different repeated load tests performed on different specimens of Me same AT soil. The ratio of the repeated deviator stress to the static shear strength (SLY and the normalized water content [(w-wO )/wO )] for different tests are shown in the figure. The optimum moisture content is wO. A curve is shown on this figure which separates stable (i.e., shake down) behavior from the unstable condition (i.e., ratcheting). This curve can be used to predict the maximum repetitive stress level to which the soil can be subjectM without causing instability. Cumulative Permanent Strain. The number of load applications (N*) required to reach the apparent shake down condition depends on Me compaction moisture content and Me stress level (SL). An empirical relationship between the normalized repetitions to shake down and SL is presented in Figure ~16. The total permanent strain Eep* accumulated until the state of apparent shake down depends on the level of stress repeatedly applied and the compaction moisture content. The developed relationship between these variable is presented in Figure ~17 for the AT soils used in this study. The permanent strain Iep accumulated in N number of stress repetitions, normalized by I:sp* and N*, respectively, appears to have a unique relationship. Figure IlS presents the relationship between He normalized permanent strain ratio ~ep/~ep*) and the normalized load cycle ratio (N/N*) for all the AT soil test data. This relationship is independent of the repeated stress level and compaction moisture condition. Resilient Strain and Resilient Modulus Mode' hn this section linear relationships are developed using normalized variables that allow the estimation of resilient modulus. Figure ~ IS presents the observed linear relationship between the normalized resilient strain and the cumulative permanent (plastic) strain at the state of apparent shake down for different compaction moisture contents. The data from this study indicates: (~) a linear relationship exists between He normalized resilient strain and the logarithm of permanent strain (icy*), with cumulative permanent strain becoming greater as the resilient strain increases and (2) for the same level of developed permanent strain Q:ep*), the resilient strain decreases with increasing compaction moisture content. However, Eep* is also dependent on moisture content and hence the resilient strain increases with increasing moisture content. After determining resilient strain from Figure ~19, the desired resilient modulus (MR) can then be evaluated from the expression MR = O~ /Cr* Components of Model. The generalized permanent strain and resilient modulus models proposed for compacted cohesive soils for a known moisture content consists of the following components: I. Shake Down Envelope. The shake down envelope helps to identify He critical level of repetitive stress at which the material becomes unstable. To evaluate this critical stress level for a given soil, determine: (a) He optimum moisture content (wO) from compaction tests, (b) the as compacted moisture content (w), (c) the deviator stress at failure (ah i) from a static biaxial test and (d) repeat (b) and (c) for specimens compacted at different moisture contents. The shake down envelope, as shown In Figure ~15 for the AT soil, is a unique curve and should be valid for all test conditions. This envelope must be established using the above procedure for each soil. Permanent Strain Accumulation. The permanent strain component of the mode} can be used to estimate the total permanent strain accumulated for a desired number of load cycles and level of repeated stress. The following steps are needed: 235

;{ 20000 X 15000 z 10000 cn cc o z TO ~ 1~0.0 - _J x a. _]1 00.0 Cal _ ·co 10~0 e_ c~ - ~: ~10 E P. ~o 0.1't .30 4.20 o z O 0.00 o 0.25 I . N X [1XW-WO)/WO]2- J1784+1.79 X 103X (SL) r'=0.87 o 0650 S=ss Lev~, SL 0.75 Figure ~16. Number of cycles required to reach apparent shakedown as a function of stress level t.00 log~ot~ p/[(SL.~"S x (e)31~=~.3~2.476 x (w-wO)/wO ?~.915 1 1 1 -0.10 0.00 0.10 Normalized Water Content, lfw-wO)/wO] 0.20 0.30 Figure ~17. Cumulative permanent strain mode! for A-6 soi! used in study 236

1~50 · ~ ~ 1.2S c: ·d 16m can c: [] 0.7S 0.50 . ~ 0.25 Z . 0.00 , . . . . 0.001 l.OFO.164Iog:O(N/N) r2=0.942 . . I, 1 11 , I I ~1 11 TT~T7Tr ,, t I, ~ , ~, I ~ 1 11 ~0~_ 0~ 10.000 1 ~1 1 t~ 0.010 I I I ~ I ill t J I I l 11' 0.100 Cycle Ratio, N/N 1.000 Figure 118. Permanent strain ratio as a function of normalized number of load cycles forming a model for permanent strain accumulation for A-6 soil fir 3 0.75 By _* A c: 3 0.50 o - ·5 0.25 a: ~ 0.m ll 1 1 £ ~l-(w-wo)/wo]4 - 0.0132~.27 X ~ p r'=0.952 . ,~ - o o o 0.0 1.0 2.0 3.0 Accumulated PeImanent Strain At Shakedown, ]:£ p (%) Figure 119. Resilient strain versus permanent strain at apparent shakedown of compacted cohesive A-6 soil 237 4.0

Evaluate Me deviator stress at failure (~` i) from a static biaxial test on the soil compacted at a known moisture content (w). b. Evaluate the number of load repetitions (N*) and total cumulative permanent strain (map*) at shake down from the type plots shown in Figure ~16 and Figure ~17. These results are used to evaluate the resilient strain and resilient modulus as explained in the third component of this model. Evaluate cumulative permanent strain (mop) at the desired number of load repetitions N from a Figure IlS type relationship. Permanent strain is used to estimate permanent deformation (rutting) in the subgrade of a pavement. 3. Resilient Modulus. This component of Me mode} provides the resilient strain and hence the resilient modulus of a soil compacted at a known moisture content and subjected to a repeated loading at a given level of stress. The following steps are needed: a. Perform steps (a) and (b) of step 2 to evaluate map* b. Evaluate £r* from the or* = f (pep*) relationship (refer to Figure ~ 19~. c. Evaluate the resilient modulus Mr* by dividing the repeated deviator stress a, by the resilient strain Br*. Illustrative Example. Calculate the resilient and permanent strain for the AM soil used in this study compacted to the following conditions: (~) as compacted moisture content w = 26.2% and (2) dry unit weight ye = 97 pcf. Layered elastic theory indicates a representative deviator stress applied to the subgrade for this problem is o~ = 4.7 psi. For the AT soil used in this study, the optimum moisture content is we = 239G, Me static deviatoric strength is an = 26.6 psi and Me specific gravity of solids (G.') is 2.73. Solution. Now evaluate the basic quantities usM in the analysis: (~) stress level SL = o~ /~.f = 4.7 psi/26.6 psi = 0.~; and(2)normal~zed moisture consent, (w-wO)/wO = (26.2-23~/23 = 0.139. From basic phase relationships, the soil's void ratio e = (G5 Yw /Y~ ~ - ~ = (2.73~62.4~/97 - ~ = 0.76. Entering Figure Il5 with the normalized moisture content (w-wO )/wO = 0.139 gives a shake down stress level SL = o~ /~`f = 0.54. Then, the shake down deviator stress case = (0.54) (26.6) = 14.0. Therefore, the applied repeated loading of o~ = 4.7 psi will lead to a stable condition (i.e., (shake down) as shown by examining Figure ~ 15. Now determine the cumulative permanent strain (pep*) and the resilient modulus at Me applied deviator stress a~ = 4.7 psi which corresponds to a previously calculate stress level SL = 0. ~ 8. Entering the equation given in Figure Il6 with SLY = 0.18 gives N* (~-(w-wO) ~ wo)2 = 1438 and further manipulation of this equation gives N* = 1940. Solving Me equation given in Figure ~ 17, Eep* / [(Swill 75 x e3] = 38 and hence Eep* = (0.18)' Is . (0.76~3 . (38) = 0.83%. Inserting the value of Eep* just determined into the equation given in Figure ~ 19 gives fir* = 0.13%. Therefore, the desired resilient modulus MR* = Od / Er* = 4.7 psi /0.0013 = 3608 psi. 238

Mode] Validation Silty Sand Subgrade Soil. The generalized mode! summarized above was developed using the AT soil described in Table 48. Initial mode} verification is provided by comparing predicted resilient strain, resilient modulus and permanent strain with measured results for the silty sand (A-5) soil also described inTable48. The optimum moisture content (wO ~ must be determined from a compaction test and the failure deviator stress (~`f3 from a static biaxial test performed at the confining pressure of interest. Then use Figures I l7 and I l9 to predict the expected values of permanent and resilient strain (and hence resilient modulus.) The predicted values are compared for this example wig Me experimental results given in Table 55. Calculated and measured resilient moduli show good agreement over a wide range of stress levels. Calculated permanent strains, however, show poor agreement with measured values as a result of using the normalized relation-ships for Me AT soil rather than Me A-5 soil used in the comparison. The A-6 soil has relatively poor permanent deformation characteristics which accounts for Me predicted permanent deformations being greater than those measured. Unless proved to be valid, normalized relationships should be developed for each subgrade soil type encountered in a geologic region. Alternate Subgrade Resilient Modulus Mode' Li and Selig [57, ~10] have proposed a simple, practical memos for predicting the design resilient modulus of fine "rained subgrade soils. Although developed primarily for compacted soils, the approach is general and could be adopted for undisturbed materials. The Li and Selig resilient modulus prediction technique considers the~mportant factors influencing the modulus: (~) soil type and structure, (2) physical state (i.e., moisture content and dry density) and (3) stress level. To achieve He most accuracy using this approach, the resilient moduli should be measured for each soil type of interest. Tests, however, need only be performed at the optimum moisture content and maximum dry density. This simple approach, therefore, requires performing for each soil type only one time a limited number of resilient modulus tests at He reference state optimum moisture content and maximum dry density. The reference moisture content and dry density, in general, are He optimum values established using either He standard or modified Proctor compaction test (AASHTO T99 or TISO test method). If resilient modulus test results are not available, the power mode! constants given in Table 56 can be used as a guide for selecting realistic constants. These constants can then be used in the power equation given at the bottom of Table 56, together with the design deviator stress (od), to calculate the resilient modulus at the AASHTO T99 compaction reference state. Mode] Approach. Using He Li and Selig approach, estimation of resilient modulus is based primarily on He power mode! given at the bottom of Table 56. Using the power mode! to express resilient modulus Is a practical alternative to ~eslighUy more accurate bilinear mode} given by equations (9~. The resilient modulus at the break point of the bilinear mode! can also be estimated using this approach as will be demonstrated subsequently. The first step in calculating the resilient modulus at a desired moisture content and dry density consists of determining the reference resilient modulus MR (OP\) at the soils optimum moisture content (won,) and maximum dry density (ydmaX) reference state. 'rhis state is determined by performing either an AASHTO T-99 or AASHTO THEO compaction test or their equivalent. 239

it: ·m co c a. q At Ed · ~ - o ~ · - 4 - ~ I: - · - ~ - · o ~ v a) D Ig 1~ 1~ 1: ~ ~ ~ :~m . ~ I ~ ~ | | 0 | 0 0 | 0 0 | 0 0 . ~. ~ H~ ~ ~L 1~ T ~m : : j_~0. ~0. 7~ 1 ~ 1 10 1= ~ 1~ ~ 1- ~ Lath. W~ ~ ~ 240

- a Z 0 0 ~ Zip O ~ ~ ~ 0 no ~ ~ Cal ~0 e. 4 - C~ c: ~ ^ 0 O ~ V Cal Cd 0 ~ V ~ 0 ~ ._ 3 o ~ . En AM Y . If. }. ~-1 - 18- 1 1~-1 §~- §- ~ t ? o ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 3 3 3 3 3 3 ~ ~ 3 3 3 3 3 3 3 3 3 3 . a ~ 0 ~ ~ ~ Ifs I °l | | 2~ I ~~ ~ ILIAC ~ ~L: 1211 Lit 121 ~ ~ ~ ~ ~1 - ~ :~3~ ~ ~ ~ ~ ~ ~ ~ o _ =~ =~ ~! -~ ^~ m~ _ ~ -~ -! =! ~! =~ ~! s~ m1 ol -1 ol -1 ~ ILL I I ~ ~ 1 ~: 1i ili~ili ilili i ili 1 ~ i44~T 1 1 - 1 - - 1 ~ 1 X _ 1 -- 1 - ~ 1 1 ~ 1 1 ~ 1 1 ~ 1 1 ~ 1 ~ 1 ~ 1 ~ 1 ~ 1 ~ 1 ~ 1 ~ 1 ~ 1 ~ 1 - !1:L ~ ~ ~ ~ ~ ~ ~ ~ 1 -1 -1 ~1 ~1 =1 -1 =1 -1 -1 -1 ~ . 1 ~ ~ ~ t] ~ ~ 241 .^ a O ~ 11 0 _ ~ ~ no ~ X

Example. The Li and Selig approach can be best illustrated by the following practical example. ORen the design moisture content (w) and dry density (Yd) is different from the reference state. For example, to simulate a weak wet season subgrade condition, He resilient modulus to be usM in one portion of a pavement design might be at a moisture content above the optimum value wig the corresponding dry _ _ _ A"na;~r 1~o than V ao ;ll'~c! - q.~1; - ll;r - ~" 1~^ Tl~^ '.~ - ^~q^~;r~ ^~.~r~ ;~ ~;~^ In ~ U~ll~lt' I`;~ Ul=1 rd(malc) ~ 1ll"~"at`;U Ill rl'&Ult; 14U 111O Uppt;l ~Ulili)~LlUll SHIV\; lit (l't;Ult; l4U Was A-etemuned by performing an AASHTO T-99 compaction test. This curve establishes the reference state defined by w,,p~ and Y`' Oman' (point ~ in He figured. The resilient modulus is determined for this reference state by performing a laboratory test. Point 4 represents the point of higher moisture content and lower density at which the design resilient modulus is desired. The curve upon which point 4 lies corresponds to a compaction curve that could be obtained using a lower constant energy than for the reference upper curve. The resilient modulus must now be determined at the different physical state (i.e., different density and moisture content) than He reference value. Visualize a change in resilient modulus occurring in three increments while moving in Figure 120 from point ~ to 4 as shown on the figure. Point 4 represents the correct resilient modulus at the corresponding desired physical state. In moving along the curves, however, the following two rules must always be followed to obtain the correct end point resilient modulus: (~) movement must be along a compaction curve which represents a paw of constant compaction energy or else (2) along a horizontal line which represents a path of constant dry density. Movement must also either begin or end at He reference point (i.e., the point on the compaction curve corresponding to wape art Ya tmax') In Figure 120, the path which satisfies these requirements is from ~ to 2, then from 2 to 3 and finally from 3 to 4. To solve this problem, the resilient modulus is calculated at the end point of each increment of movement. Step I. Now apply this incremental movement approach to He problem summarized and solved in Table 57. Steps given in the table correspond to Hose given here. As the first step in determining He required resilient modulus, move down the constant energy compaction curve from ~ to 2 and calculate the resilient modulus at point 2. When movement is from the reference point down a constant energy compaction curve, He new resilient modulus is determined from He following general expression developed by Li and Selig: where MRC = [0.96 - 0.~S (W - WOP, ~ + 0.0067 (W-W0Pt ~ ~ · MR(OPL) MRC = MR (~) resilient modulus at point defined by w on a compaction curve reference resilient modulus at w<,p, and Yd~ma,`' for He compaction curve (14) The above expression is valid, as a good approximation, for all fine "rained soils and its derivation is discussed subsequently. . · ~.- ~a- - Step 2. Now move from 2 to 3 along a constant density line and calculate MR((,Pl) for the lower compaction curve from He following general expression given by Li and Selig for constant density: MR = [0.98 - 0.28 (w-w~,p) + 0.029 (w-wOp~ ~ ~ MR(OP~ 242 ~.~.~ap ~ . (1~

110~0 108.0 106.0 A; 1 04.0 - .2 ~102.0 c 100.0 98.0 9660 94.0 _ 92.0 - 1 15.0 17.0 . _ . _ (I) Initial Reference State: MR(OPt) Known (Wopt 18%, Ed = 107 pep _ (I Reference Case ~_ _ - AASI ITO T99 Compaction Curve - Lowl)ensitY \~ 3) Desired: Constant Energy Compaction Curve (W = 22C%o, ad = 97 pcf) 1 1 1 1 19.0 21.0 23.0 25.0 Water Content, w(°/O) - Figure 120. Illustrative example problem - Li and Selig resilient modulus model 243

Table 57. Numerical example problem for determining resilient modulus fine-grained subgrade: Li and Selig Method [57, Il0] Required: Determine the resilient modulus of a clayey silt at a moisture content of 22% and a dry density of 97 pcf (Point 4, Figure 120~. Solution: Perform an AASHTO T9 compaction test on the clayey silt to determine the reference compaction characteristics as shown on We upper curve in Figure 120 (We, = IS%, ym"~ = 107 pc0. The soil has a T-99 compaction reference resilient modulus of 22,000 psi at We design deviator stress. Ihe reference resilient modulus at W,~,p and York can be determined from design relationships such as equations, graphs or a catalog of soil types and corresponding reference resilient moduli. The resilient moduli selected should be based on the results of laboratory resilient modulus tests. Next, knowing the moisture content (22%) and dry density (97 pcf) at which We design resilient modulus is desired, sketch in the lower compaction curve on a scale plat. The corresponding optimum moisture content is about 19.596 for a maximum dry density of 101 pcf. In drawing in We curve remember the zero air voids curve is approximately parallel to the line of optimum moisture contents for different energy levels. Now perform Steps 1 to 3 calculations as described in the text: Step 1: Points 1 to 2 using Equation (14) Point 2: Yd = 101 pcf, w = 23%) MRC = [0.96 - 0.18 (w-w,,pt) + 0.0067 (W-W(,Pt) ] · MR(q~t) = [0.96 - 0.18 (23-18) + 0.0067 (23-18)2] . (22,000 psi) = 5,005 psi at Point 2 Step 2: Points 2 to 3 using Equation (15) (Point 3: Yd = 1Ol pcf, w = 19.5%) MR(OPt) = MR / [0~98 - 0.28 (w-w~ + 0.029 (w-w~,p~ ] 5,005 psi / [0.98~.28 (23-19.5) + 0.029 (23-19.5)2] = 14,089 psi at Point 3 Step 3: Points 3 to 4 using Equation (14) (Point 4: Ye = 97 pcf, w = 22%) MRC = [0~96~18 (w-w.,p) + 0.0067 (W-W{,PL) ] MR(opt) [0.96~.18 (22-19.5) + 0.0067 (22-19.5)2] . (14,089 psi) 7,775 PS; at Point 4, which is the required design resilient modulus 1 1 244

where MRD = Resilient modulus at moisture content w; on constant density line (point 2, Figure 120) MR(OlPl) reference resilient modulus at was and Y`yma~c, on constant density path Equation (15) is solved for MR(OPl) for the lower compaction curve (refer to Step 2 in Table 57~. Step 3. The desired resilient modulus is then calculated by moving down the lower compaction curve from point 3, the reference point for that curve, to point 4. Calculate MRC from equation (14) using the known resilient modulus MR(OP,) previously calculated in Step 2. For most design problems, the physical state at which the design resilient modulus is desired will probably lie on the AASHTO T-99 (or T-180) compaction curve. For this condition, only Step calculations are required. Equation Development. Equations (143 and (15) were developed by correlating for a wide range of cohesive soils the resilient modulus ratios MRC/MR`op`, and MR6/MR`op~with the corresponding difference in moisture content (w-w<,p~) as shown in Figures 121 and 122. Equation (14), which is for constant compactive effort has a correlation coefficient r2 = 0.83, and is based upon data from 26 repeated load tests on 10 fine-grain soils. Equation (15), which is for constant density, has a correlation coefficient r2 = 0.76 and was developed from 27 repeated load tests on ~ ~ fine-grained soils. The repeated load test data was taken from the literature from 8 different sources for each correlation. Breakpoint MR Estimation. The bilinear resilient modulus mode} for f~ne-grain~ soils has a distinct breakpoint as shown in Figure 53. The resilient modulus at the breakpoint can be estimated using the following expression developed by Thompson and LaGrow [85,1111: MA= 4.46 + 0.098 (% clay) + 0.~19 (Pl) where (16) MR((,Pt) = Breakpoint resilient modulus at optimum moisture content and 95% of AASHTO T99 maximum dry density % clay = % particles finer than the 2 micron size PI = Atterburg plasticity index Equation (16) is for cohesive soils compacted to 95% of AASHTO T99 maximum dry density at the optimum water content. Equation 16, although useful, has the important disadvantage that the resilient modulus is at only He breakpoint. The breakpoint is often, but not always, at or close to He minimum value of the resilient modulus. Thick pavement sections apply low deviator stress to the subgrade. As a result, He breakpoint resilient modulus is lilcely to be too low for strong sections resulting in unnecessary additional thickness. 245

R - ' 5 3 ~ ~ 2 . ~/M, ( - i) = 0.~ - 0.18 (W - W - i) + 0.0067 (w - we,,,) 2 ~ = 0.83 1. -6 -5 -~ -3 -2 - 1 0 1 2 3 4 5 6 (w -wqpt\%) Figure 121. Correlation of resilient modulus ratio MC~/M~,p~ with moisture content change constant compactive effort (after reference 57 and ~ 103 Ret, 5 ~3 \ ^^ dS I\ ~ _~ -6 -5-~ -~-2 - 1 0 ~ ~3 ~5 (W -Wollty%) M!~/M, ( - ,) = 0.98 - 0.~ (w - w~,) + 0.~29 (w-wept) 2 = 0.76 . I . I . I . I .A ~ 1 - Figure 122. Correlatmn of resilient modulus ratio MD,'/M~.p`) moisture content change constant density (after reference 57 and 1 10) 246

SUMMARY AND CONCLUSIONS General Conclusions - Granular and Cohesive Materials The repeated load biaxial test is proposed as the most appropriate method at this time for evaluating in the laboratory the resilient modulus of aggregate base and granular subgrade materials. An unconfined repeated load test is proposed for cohesive subgrade soils. Great caution, however? must be exercised in performing these tests. The proposed test procedures are given in Appendix E. General important findings relating to laboratory testing details are as follows: I. Testing. A large number of resilient modulus tests were performed on both aggregate base subgrade and synthetic specunens. A closed-Ioop, electro-hydraulic testing system was used to apply a 0. ~ sec. haversine shaped load pulse. The tests were performed on a very carefully calibrated testing system. Resilient moduli were determined using (~) EVDTs mounted externally to the biaxial cell and also using EVDTs located on clamps attached directly on the specimen. A limited number of tests were also performed with EVDTs mounted between the top and bottom platens. 2. System Compliance, Calibration and Specimen Misalignment. To obtain reliable, accurate results from the repeated load biaxial test, compliance in the testing system must be minimized and the system carefully calibrated, including testing synthetic specimens. Follow the procedures given in Appendix D. During testing, to insure good load alignment, the ratio of the maximum to minimum displacements obtained from two independent transducers should initially be less than 1.10. Complete system calibratiorl, carefully performed is absolutely assert if axial defonnation is measured outside the biaxial cell. With proper, tedious, equipment calibration, both clamp mounted L~VDTs and external EVDTs gave satisfactory results for resilient moduli of aggregate bases less than about 60,000 to 70,000 psi. The use of external L`VDTs should not be attempted, even under He best of conditions, when Be resilient modulus is greater than about 70,ED0 psi. The calibration procedure required when external EVDTs are used is very tedious, time-consuming and may be subject to erratic, unknown errors in He resilient modulus. Exterrud [VDTs are considered not suitable for routine laboratory testing of ei~herg~r or cohesive materials if reliable resilient moduli are required. This conclusion was supported by a limited multi-laboratory study on aggregate base material given in Appendix H. 3. ~L=. Measurement of axial dLefonnati~n and system calibrafio It are the most important factors in obtaining accurate, rehinge resilient modulus test rests. Preconditioning, pulse shape, pulse time, type testing equipment, etc. all have a relatively minor effect on resilient modulus compared to these two factors. Adequate sensor sensitivity, for specimen loading conditions giving small deformations, is also an important consideration often overlooked. Measurement of axial Spacemen outside of the triadic cell cannot be Reperked upon to give reliable values of resilient mod~di. This finding is true for most laboratories even if He calibration procedures given In Appendix D are follows including correcting measured deformations for system compliance. To obtain accede resilient modFuli, awl displacement of grander materials shard be measured Erectly on Me speezmen. Axial displacement can be measured using either an optical extensometer, clamp mounted L`VDTs or proximity gages. In general, as sensitive as possible displacement measurement gage should be used. Maximum recommended excitation voltages should be used; for small displacements even consider exceeding these voltages by 10 to perhaps 20%. 247

4. Modern Optical Extensometer. A modern optical extensometer offers at this time the most practical, reliable memos of axial displacement measurement. The optical extensometer, however, costs a minimum of about $30,000 to $40,000. Use of this measurement system requires a special biaxial cell or else a vacuum test has to be performed. Aggregate Base and Granular Subgrade Materials I. Vacuum Shear Triaxial Test. Most aggregate base and granular subgrade resilient modulus tests are performed at optimum moisture content and maximum dry density. For this condition, a repeated load can be applied to a granular specimen subjected to a vacuum inside the specimen rawer than the conventional external confining pressure. This approach eliminates the need for using a biaxial cell. As a result, axial deformation can be readily measured using a modern optical extensometer. The vacuum type biaxial test is limited to a maximum confining pressure of about 10 to 12 psi which is adequate for granular base and subgrade materials. Use of a vacuum type repeated load test with axial strain measured with an optical extensometer offers a very practical and accurate test procedure. 2. Quasi-Static Modulus Test. For some laboratories, the quasi-static modulus test offers a realistic, simple test which does not require either an electro-hydraulic testing system or a data acquisition system. The quasi-static test, in summary, consists of first conditioning Me specimen and then applying a single pulse to the specimen for a short time (2 to 5 min. was used in the tests but shorter times can be used) and then removing the load. The test, if desired, can readily be performed using an inexpensive, pneumatic loading system and simple instrumentation consisting of clamp mounted EVDTs and a voltmeter to read the output. 3. Moisture Sensitivity. The resilient modulus moisture sensitivity of a material indicates how much detrimental effect an increase in moisture has on the resilient modulus of a particular class material. Resilient modulus tests should be performed to evaluate moisture sensitivities of pavement materials. 4. I. For the good quality aggregate base materials tested in this study a reduction in resilient modulus was not observed due to bedding errors (i.e., irregular particle contact with the end platens). As a result, 200 repetitions of a conditioning loading was found to be adequate for good quality aggregate base. A realistic principal stress ratio (o,/a2) for an aggregate base is about 3.5. The experimental findings, however, indicate using a principal stress ratio of 2.0 during conditioning gives similar resilient moduli during subsequent testing. Therefore, to avoid causing excessive permanent deformations in weak specimens, a principal stress ratio of 2.0 was used in the recommended test procedure. After vibratory compaction, the top platen was placed on the specimen and vibrated for about 10 sec. To obtain good contact. 5. Repeatability of Ma. In the present study the coefficient of variation (CV) of resilient modulus measurements using one specimen was 9.3 using external transducers and ~ I. ~ % using EVDTs mounted on clamps. Using two specimens, the coeff'cientof variation decreased sign~ficandy to 6.6% and 7.~% for external and clamp measurements, respectively. The coefficient of variation of course varies wig Be equipment used, skill and experience of Be technician performing Be test and materials being tested. Nevertheless, this 30% reducfion in variation gives a great deal of justification for using a duplicate set of specimens as a routine MR test pro cedFure. Even more support is given to using duplicate specimens considering all the problems that can 248

develop during a resilient modulus test involving sample preparation, instrumentation and even human error (particularly if the test is not automated). 6. Resilient Modulus Models. The popular K-D resilient modulus, for duplicate specimens, was found to have an average r2 value of 0.89 with a mean square error of 0.00389. Improved models had average r2 values between 0.96 and 0.98 and mean square errors 409to or more smaller Han the K-D model. Perhaps more way, the K-B mode! ~ not have the required accuracy to flush one muted from another at the 95% confidence [eve!. The Uzan, U.T.-Austin, and UTEP models did have this ability. These three models are superior to the K-8 model. Either the Uzan or the U.T.-Aust~n models are considered suitable for use in practice. The Uzan, UTEP and U.T.-Austin models (also the related SHRP P46 Qune, 199~ model) all work with materials having important cohesive properties such as I'me-flyash stabilized base materials; the K-O is not applicable for such materials and should not be used. 7 Lime-Flyash Stabilization. The addition of lime-flyash to an aggregate base can increase its . resilient modulus by a factor of about 10 provided the lime-flyash specimens are permitted to cure. . ~ ~ , . . ~a ~ · , _ ~1 _ ~ ~ _ The repeated load test can still be used to measure me resilient modulus. Axial Deformations, however. are extremely small. As a result, external axial displacement measurement is unreliable . .. . . ~ ... . . . ~ , . . ~ ~ ~ A. ~ ^~ ~ ~ A _ even under the best of conditions, and deformation must be measured Erectly on the specimen. An optical extensometer, which has a very high sensitivity, is well suited for such stiff materials. If conventional EVDT or proximity transducers are used to obtain reliable results, instrumentation should be selected having as high sensitivity as available and practical. S. Cement Stabilization. Resilient modulus tests on cement stabilized specimens were not performed during this study. The high stiffness of cement stabilized specimens gives small axial displacements which require a very high precision measurement system. To accurately measure resilient moduli of cement stabilized materials (~) use an optical extensometer having high precision and (2) use cylindrical specimens either 4 in. or 6 in. in diameter depending upon the precision of the extensometer and size of aggregate present. An alternative approach would be to use the diametral test and optical extensometer. 9. Permanent Deformation. For most miseries and inserrice conditions, the measurement of pennanent defo~n is mom import than the measurement of resilient modulus. Permanent deformation repeat load biaxial tests should be performed for all classes of base/subbase materials, particularly for marginal materials. To perform this test, 50,000 or more load cycles should be applied to He specimen to evaluate their potential rutting characteristics. A pneumatic loading system can be used wig permanent deformations being measured using dial indicators. Cohesive Subgrade Soils I. Unconfined Compression Test. An unconfined resilient modulus test is proposedfor cohesive sods. The unconfined test does not require a biaxial cell, has a fewer number of stress sequences and allows the easy use of an optical extensometer to measure axial `deformation. The effect of eliminating in He test the small confining pressure present in He upper part of He subgrade is only slightly conservative for cohesive soils. The proposed unconfined resilient modulus test procedure is given in Appendix E. S`milady to aggregate base minerals, equipment calibration and the correct measurement of resilient al specimen defonnaiion are considered the most ~mpo~a~ factors in obtaining accurate resilient moduli test results. 249

2. Axial Deformation. Axial deformation of unconfined cohesive subgrade specimens should be either measured directly on We specimen or else between solid end platens. If deformation is measured between solid end platens, either the specimen ends should be grouted, or else the resilient moduli obtained should be corrected empirically for end effects. EM effects due to irregular particle contact are not eliminated by con~ionzag am become zmpoffant for resilient moduli greater than about lO,OOO psi. The solid end platens proposed for the test prevent drainage and hence give a conservative resilient modulus. 3. Moisture Sensitivity. The reduction in resilient modulus due to an increase in moisture content is an important factor that should be considered in developing a laboratory testing program and subsequently in design. 4. SDecimen Conditioning. Special conditioning has been considered in both the SHRP and AASHTO test procedure to eliminate end effects and specimen aging effects. Recent carefully conducted research, however, shows conditioning does not eliminate either of these problems which both must be considered in resilient modulus testing. 5. Strength Gain with Time. After compaction, cohesive soil specimens undergo up to 30% or more strength gain wig time. Contrary to early results obtained by Seed am his associates, conditioning compacted specimens does not hale the strength gain with time effect on the resilient Mobius. Because of this strength gain, compacted specimens should be tested at the same age (2 days is recommended). For design, the laboratory resilient moduli should preferably be empirically corrected for longterm strength gain. 6. Specimen Preparation Me~od. The resilient modulus of cohesive soils is dependent upon the method used to compact the specimen. This variation in resilient modulus caused by different compaction melons results from differences in soil structure. Therefore, laboratory compacted specimens of cohesive soils should be prepared by different compaction methods depending upon He as-compacted and anticipated future moisture content. 7. practical MR Models for Design. models were developed for compacted cohesive soils. Fundamental resilient modulus and permanent deformation To apply this approach, generalized normalized relationships are first developed for a specific AASHTO soil class using He repeated load tria~cial test. Specimens are tested at only He optimum moisture content and dry density. After once developing the generalized relationships, resilient moduli for site specific conditions can then be determined by performing a conventional static shear strength test and several over routine tests. Another fundamental resilient modulus mode! proposed by hi and Selig is also presented. Both of these models offer a practical approach for design involving the performance of a minimum number of resilient modulus tests when the approach is first developed. 250

Next: 4 Significant General Findings »
NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report Get This Book
×
MyNAP members save 10% online.
Login or Register to save!
  1. ×

    Welcome to OpenBook!

    You're looking at OpenBook, NAP.edu's online reading room since 1999. Based on feedback from you, our users, we've made some improvements that make it easier than ever to read thousands of publications on our website.

    Do you want to take a quick tour of the OpenBook's features?

    No Thanks Take a Tour »
  2. ×

    Show this book's table of contents, where you can jump to any chapter by name.

    « Back Next »
  3. ×

    ...or use these buttons to go back to the previous chapter or skip to the next one.

    « Back Next »
  4. ×

    Jump up to the previous page or down to the next one. Also, you can type in a page number and press Enter to go directly to that page in the book.

    « Back Next »
  5. ×

    To search the entire text of this book, type in your search term here and press Enter.

    « Back Next »
  6. ×

    Share a link to this book page on your preferred social network or via email.

    « Back Next »
  7. ×

    View our suggested citation for this chapter.

    « Back Next »
  8. ×

    Ready to take your reading offline? Click here to buy this book in print or download it as a free PDF, if available.

    « Back Next »
Stay Connected!