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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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Suggested Citation:"2 Resilient Modulus Testing of Asphalt Concrete." 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.
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CHAPIER 2 RESILIENT MODULUS TESTING OF ASPHALT CONCRETE INTRODUCTION This chapter evaluates resilient modulus testing methodology attest details for asphalt concrete. The measurement of He resilient properties of asphalt concrete has been the subject of considerable research. Different testing devices and techniques have been used in these studies. All of these efforts have led He American Society for Testing and Materials to standardize the resilient modulus testing method of asphalt concrete (ASTM D 4123-82~. However, as demonstrated in the "Workshop on Resilient Modulus Testing" held at Oregon State University in March 1989, there was strong consensus among pavement engineers that the ASTM D 4123 nroce`1ure is ~,nnen~nrilv fim~.-~nn~,mins' ~nr1 that the. tP..Ct results are difficult to reproduce. Recognizing the importance and existing problems of resilient modulus testing of asphalt concrete, the Strategic Highway Research Program (SHRP) has developed a resilient modulus test procedure for asphalt concrete (SHRP Protocol P07) as a part of He Long Term Pavement Performance Monitoring CUTUP) program. This testing procedure incorporates recent findings on resilient modulus testing into He existing ASTM D 4123-82. A comparison between ASTM D 4123 and the November 1992 version of SHRP Protocol P07 is summarued in Table I. An important overall 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, for example, equipment calibration and testing conditions. Detailed laboratory studies were therefore carried out using different devices to evaluate the effect of laboratory test apparatus and testing details on resilient modulus test results. Based on the findings from the present study, a number of revisions are suggested to SHRP Protocol P07 (November, 1992~. METHODS FOR DETERMINATION OF MODULUS OF ASPHALT CONCRETE The resilient modulus of asphalt concrete has in the past been determined by two approaches: (~) predict the resilient modulus using physical and mechanical properties of He mixture using available correlations, and (2) measure the resilient modulus by laboratory testing. Empirical Predictive Methods The most well-known predictive methods are the Marshall stability-flow ratio, the Shell Nomograph, and the Asphalt Institute predictive model. Nijboer [~] suggested He use of the Marshall stability-flow ratio as follows: S60°C 4 S4tC = ~ .6(stability/flow) where S is the modulus given in kilograms per square centimeter, stability in kilograms, and flow in 10

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be - - ~ in ~ ~ ·O · - · - c~ cat c ~ c) in - · · en - c~ · ~ - ~ [L, 3 ~ ~ _ t- Cal t_ en C ~ ~ S - tell O ~ ~ a_ C- ~ Cal cat E ~ ~ . _ ~ ._ ~ en ~ ~ ~ C ~ ~ ._ C) D ._ us -3 · E cat sE ~I'd ~' 8 3 ~ 4,, _ ~ I, ~ o ~ 8 ~ - ~. i~ ' ~ E j &= 5 C o ~1 = ~ ~ = ~ o , I,,, c: * * * * * G) Us O _ ._ By' ~·~ AS 13

millimeters. This relationship was recommended for use in high temperature ranges by Heukelom and Klomp 191. McLeod [101 modified this equation using He English units: Modulus = 40(stability/flow) where modulus is given in pounds per square inch, stability in pounds, and flow in inches. Shell Nomograph. The Shell Nomograph was originally developed by Van der Poel [111. He defined tile stiffness as a modulus which is a function of temperature and loading time. Later Heukelom and Klomp [91 developed a relationship between He bitumen stiffness and He mixture stiffness based on volume concentration of aggregates. After McLeod [10] modified the nomograph by changing the entry temperature criterion, finally CIaessen et al. [121 produced a pair of nomographs used in the current Shell design manual. where E* = P = ac P - opt C - 1 - C2 = P - 200 - f = V = v n(106,70) = T = Asphalt Institute Method. The Asphalt Institute resilient modulus method was originally developed by Kallas and Shook [131 using cyclic biaxial test results. Their equation was refined by Witczak [141 from an expanded data base which relates dynamic modulus of asphalt concrete with percentage passing the No. 200 sieve, loading frequency, volume of voids, viscosity of asphalt cement at 70°F, temperature, and percentage of asphalt cement by weight of mix. Since this data base was based on mixtures of crushed stone and gravel, Miller et al. [151 modified the equation for a broader range of material types. The final form of the equation by Miller et al. [15] is: logic ~ E ~ = C1 + C2 (pa pop + 4.0)0 s dynamic modulus (1Os psi) percentage of asphalt cement by weight of mix optimum asphalt content (2, 0.553833 + 0.028829(P2,,o/f° l7°33) - 0.03476Vy + 0.070377~(106,70) + (0.93 1757/f° °2774) 0.000005 T exp(1.3 + 0.498251ogl00 - 10.00189 T exp (1.3 +49825l°glof~lfl ll percentage passing the No. 200 sieve loading frequency (Hz) volume of voids viscosity of asphalt cement at 70°F (megapoises) temperature of pavement (°F) 14

The Asphalt Institute Method Laboratory Test Methods i' s available in the form of an easy-to-use computer program. In He preceding section, the modulus of asphalt concrete was presented in several different forms including dynamic modulus, stiffness, and resilient modulus. In the following sections, typical laboratory testing methods are discussed for the determination of resilient modulus for asphalt concrete. Stress State. The stiffness (modulus) characteristics of asphalt-bound materials can be considered not to be significantly influenced by stress state at moderate to low temperatures. However, at temperatures above 25°C the stress state, and therefore test configuration, have an influence on the stiffness characteristics of these materials. This influence becomes more pronounced as the binder becomes less stiff [161. Anisotropic Behavior. The determination of He resilient modulus of asphalt concrete involves using various types of repeated load tests. The most commonly used tests are as follows: Uniaxial tension test Uniaxial compression test Beam flexors (bending or rotating cantilever) test 4. Indirect diametral tension test S. Triaxial compression test A pavement layer has cross anisotropy in which radial properties are constant in all directions but are different from properties in He vertical direction. Wallace and Monismi~ [10] have claimed ~at, for an adequate description of the resilient characteristics of such a material, the following five parameters are required: 2. 3. 4. 5. Vertical strain due to an increment in vertical stress Radial strain due to an increment in vertical stress Radial strain due to an increment in radial stress Vertical strain due to an increase in radial stress Radial strain due to an increment in radial stress in a direction perpendicular to the strain They reported that the biaxial test measures the first and sometimes the second parameter whereas the diametral test measures a composite of the third and Fox parameters with roughly equal weight being given to each parameter. Due to anisotropy of asphalt concrete, the resultant discrepancy in resilient modulus between diametral testing and biaxial testing can be quite pronounced. Wallace and Monismith [171 carried out tests on an asphaltic concrete core taken from San Diego test road [id. They showed Hat as a result of placement and compaction efforts, the material was about twice as stiff in He radial direction as in the vertical direction. An asphalt layer of typical thickness is subjected to a bending action which is primarily resisted by He radial rather Man He vertical stiffness of the asphalt layer. Therefore for vertical cores taken from the pavement, the diametral test or flexural bending test should give a more relevant assessment of the 15

stiffness of the asphalt layer than tests performed in He vertical direction. Diametral test results are hence particularly attractive for evaluating radial tensile strain for a fatigue analysis. The diametral test has additional advantages since thin cores can be tested which permits more measurements over the depth of thick asphalt layers. FIexural Test. Early work to evaluate the resilient modulus of asphalt concrete was conducted by testing beam specimens under a third-point loading configuration. The flexural stiffness of beam specimens can be determined from the following equation: Pa `3L2 _4a2, where Es = 48 f ~3 Es = flexural stiffness (nisi) P = repetitive load applied on the specimen (Ib) a = ~h(L~) (in.) = reaction span length (in.) = moment of inertia of beam cross section (in.4) ~= measured deflection at the center of the beam specimen (in.) A number of different flexural test procedures have been developed to study the resilient and fatigue characteristics of asphalt concrete mixtures including: FIexure tests in which the loads are applied repeatedly or sinusoidally under center-point or third-point load Rotating cantilever beams subjected to sinusoidal loads Trapezoidal cantilever beams subjected to sinusoidal loads or deformations The advantages of the flexure test are [191: (~) it is well known, widespread in use, and readily understood; (2) The basic technique measures a fundamental property that can be used for both mixture evaluation and design; (3) Results of controlled-stress testing can be used for the design of thick asphalt pavements whereas results of controlled-strain testing can be used for the design of thin asphalt pavements. The method, however, is costly, time consuming, and requires specialized equipment [191. Also, the stress state within the pavement structure is biaxial, whereas the state of stress is essentially uniaxial in the flexure test. Triaxial Test. Numerous advantages are inherent in using the cyclic or repeated load biaxial test memos. The stress system that acts upon a specimen during the biaxial test approaches the system of stresses that are present in the upper portion of Be asphalt concrete layer of a pavement during loading. Furthermore, the strength of asphalt concrete can be determined when specimens are tested to failure under a single loading. The chief objections to the use of this method are its cost and the relative complexity of Me necessary testing equipment. In addition, the size of specimens required for testing of coarse aggregate mixtures and number of specimens needed for a test series discourage the adoption of the memos for routine testing. The analysis of biaxial data for bituminous mixtures is often complicated by a curved envelope of failure for which there is no well defined or proven application [201. One big advantage of 16

~ - biaxial testing is Mat stress levels and strains are generally much larger than for diametral testing so that greater testing accuracy can be achieved for stiff asphaltic materials. The influence in the biaxial test of secondary factors such as poor contact of deformation sensors, minor sample disturbance, etc. are less important than for the diametral test. Indirect Tensile Test. The indirect tensile test was developed simultaneously but independently in Brazil and in Japan [211. The test has been used to determine the tensile strength of Marshall-s~ze asphalt . · . . . . concrete specimens. lne testing system includes indirect tensile loading apparatus, deformation measurement devices and data recording system. The indirect tensile loading apparatus consists of upper and lower loading plates and upper and lower 0.5 in. wide loading strips having the same curvature as the specimen. Load is vertically applied to the sides of the specimen and maximum tensile stress plane develops along the vertical diameter. The indirect tension test simulates the state of stress in the lower position of the asphalt layer which is a tension zone [221. Schmidt [23] proposed the use of a repeated load indirect tension test (which is called the diametral test) to determine the resilient moduli of asphalt concrete specimens. Figure 6 shows that the values of the resilient moduli obtained from this test compare favorably with those obtained from the direct tension, biaxial compression and beam flexure tests. Baladi and Harichandran 1241 conducted a comparative study of the following test methods: 1. 2. 3. 4. 5. Triaxial test (constant and repeated cyclic loads) Cyclic flexural test Marshall test Indirect tension test (constant and variable cyclic loads) Creep test The results of this study indicated that: 1. The repeatability of test results is poor. 2. . . 3. -line material properties obtained from the dltterent tests are substantially different. The results from the indirect tension test were Me most Promising although Rev were not consistent. - r ~ ~lo, _ _ _~ The advantages of the indirect tensile test are summarized as follows [17, 2l, 22, 251: 1. 2. 3. 4. 5. 6. The test is relatively simple and expedient to conduct. The type of specimen and the equipment can be used for other testing. Failure is not seriously affected by surface conditions. Failure is initiated in a region of relatively uniform tensile stress. The variation of test results is low compared to other test methods (refer to Figure 7~. A specimen can be tested across various diameters, and the results can be used to determine whether the sample is homogeneous and undisturbed. 7. The test can provide information on Me tensile strength, Poisson's ratio, fatigue characteristics, and permanent deformation characteristics of asphalt concrete. The main disadvantage of the test is its failure to completely simulate the stress conditions encountered in practice. As previously discussed, the diametral test does reasonably well simulate the tensile stress condition existing in the bottom of the asphalt concrete layer. The American Society of 17

7GO 6m 5m - ~ c 400 ~- ~ - - ~ c) . - - ~ c ~ 3a , 200 - 1W 1~0 :E ~Assumc V Q5 - c ~ _ ~ ~ ~ 4~30 ~ . 3m ~ ._ _ ~ c ~ ._ ~. 2m a: ~ - ~ Diam~ral [ensign _ x D'r~ Compress~on 0 Dir~ Tension `,_ ~Assumev~Q5 ~,~Assume2, 0.2 . , ~ ~ ~ A, ~ Notes: 1. Diametral tensile stress shown an the atcissa is the werage value from center to edge, i. e., 4Z ~ of max. ~x ' ~P.Q710. Oirect tensile or compressive stress aionq ar~s of 8" tall 4" diamMer specimen, strain measured w~th 2''long strain qa~es. I 1 I ,,,, I I ~ 0.2 0.3 0.4 0.5 I.0 2 3 S tres s, p s i 1 t.,, . I 4 510 (a) Direct tension, compression, and diametral methods Ffe~cural 8tams - t. &. ~,. Diametrai Cores - O. ~, c,0 ~V 0 35 - --~ ~· ~Flexural Values N50tes: 1Ca ~ Assume V ~ Q 2 . 1 ~ 1 2 1. Stresses on tIexural values are maximum fiber stross. Stresses 3n diametral values are maximum throwh center. _ . ~,, ., 1 1 1 1 ! , ,,, 1 1 3 ~510 20 30 40 50 100 150 Maximum Stress. psi (b) Flexural and diametral methods Figure 6. Companson of resilient modului of AC specimens using direct tension, compression flexural, ar~d diametral methods (After Ref (22) ) 18

o - x 100. _. us P. - LO i: u, ~4 ~4 - 10. us - ~1.0 . 0 c a cut _ _ O . 1 . . . , ° C = ( F-32)ll.8/ l()5psi = 689 spa/ 1 ~z,L, ~ / / ~ ~ A r ~- LEGEND: Tes c Temperature - 40°F (23 Test Temperature ~ 70°F Test Temperature - lOO.F 0.1 1.0 10. 100. Appeal t Concrete Modules (Compression Samples Without Confinement), psi x 105 Figure 7. Comparison of test results between the unconfined compression and indirect tension tests (After Ref (23) ) 19

Testing and Materials has adopted the repetitive indirect tensile test as a standardized method of measuring _ . , the resilient modulus of asphalt concrete (ASTM D 4123-82~. Control Mode. Two basic types of loading have been used in laboratory tests: controlled-strain and controlled-stress. Repetitive load is applied to produce a constant amplitude of repeated deformation or strain. Asphalt concrete in thin pavements (surface layer thickness of less than 3 in.) is considered to be in a controlled-strain condition. In controlled-stress tests, a constant amplitude of load is applied. The controlled-stress test simulates Me asphalt concrete in thick pavements (surface layer thickness greater than 6 ink. A comparative evaluation of controlled-stress and controlled-strain tests is presented in Table 2 [191. If Me testing procedure measures a real material property, the resilient moduli from the controlled- stress mode and controll~-strain mode must be the same because the sample does not know whether it is under the controlled-stress mode or controlled-strain mode. Bow Me controlled-stress and controlled-strain modes have been used in flexural beam and uniaxial tests. Only the controlled-stress mode has been applied to the indirect tensile test. The reason why the controlled-strain mode has not been used in the indirect tensile test is because the mechanism of forcing the deformation (either horizontal or vertical) back to the original position is not available. One can glue the upper loading strip to the specimen in order to control the vertical strain. However, this mechanism will develop a plane of maximum tensile stress along Be horizontal diameter when the loading head moves upward, which violates the theory behind the indirect tensile test. DIAMETRAL RESILIENT MODULUS TESTING DEVICES AND MEASUREMENT SYSTEMS USED IN EXPERIMENT Loading Devices Based upon He previous discussion of testing methods, the diametral test was selected for use in developing a standard test procedure for resilient modulus testing of asphalt concrete. The diametral test can be performed on small field core specimens and hence is practical for routine use. Also, the indirect tension to which the specimen is subjected during loading simulates reasonably well the tensile stress condition in He bottom of the asphalt concrete layer. Because of the popularity of the diametral test method, a number of test apparatuses have been developed which have important fundamental differences in equipment design concepts. Practically no research, however, has been previously performed to evaluate these testing systems. An experiment was therefore designed to identify the most reliable and accurate diametral test apparatus available and then to develop appropriate test procedures to allow the device to be used for routine testing. A representative group of the most promising diametral testing devices were carefully selected for evaluation In He testing program. The testing devices chosen are as follows: Retsina device, MTS device, Baladi's device and the SHRP Load Guide device. A detailed description of these testing systems is given in Appendix A. The simplest comparisons between He test devices can be made with respect to Heir loading configurations and diametrical deformation measurement systems. The Retsina device has fully independently aligned upper and lower loading strips and EVDTs that are clamped on the specimen to measure deformation. The MTS system has a guide rod that semi-rigidly aligns He upper and lower loading platens and extensometers Hat clamp on to ache specimen for deformation measurements. Both the Baladi and SHRP devices have heavy guide posts Hat rigidly align the upper and lower loading strips. 20

· - 'e o - ~: · - c~ of - - o A: en v: cr. v) - - o 5~ o c) o o ~- ad - - A · - ice o - Hi At - a: · - :- - ;- · - E lo C) Cat ·s ·= U. - - 1 _ O ~ D3 Cd ~3 O O O U. U. An O _ C) .- =: _ ~Cal ·E V ~ C .S C~ ·t _ · ~ :, C~ - s ·- o ~ o .~! ._ _ o ~o C = ,~' o ·_ o E o 3 - - e~ C~ C~ C~ _ U. :, ._ _ C ._ C=~ C~ C . _ _ _ U. - n - C\5 oo C ·~ ~ 3I C~ O _ _ _ Cc ~ ._ ~ ._ 3 U. C) ~ .S ._ _ o~ _ - g ·_ ._ C) U) C~ q) ·E ~o -~m o · - oo o ·- · - o ·> - c o3 ~ C~ ~ . ·= C~ _ o os o C) ~o 0 - =2 · - C~ ;: c U) V) ~2 - Ct E _ ~ . ~ C~ - C oo ._ ·E oo ~ E _ U, C~ ~ _ · _ C C} ·_ ~ ·' ~ ,,= o CO :- g CD - C) - ._ ~: e~ - ou c~ l-, ~> o :^ c~ ~ ·~ 8 · ~ _ C~ C) 4_ o ~ o o ._ ,. .- C D o E .~ C ~ ._ t) 3 oc oo O ~ ~o O .0 C ._ E =: c: U] ~ ~Z .° _ C~ ._ U) U) ._ c o - _ o C) ._ C) CO ~Q o C ·~ m ~ 21

Both systems measure diametrical deformation by EVDTs mounted to the fixture itself, with only the EVDT cores touching the test specimen. Deformation Measurement Devices The resilient modulus Is determined by entering an elasticity equation with deformations measured during the diametral test. Since diametral test deformations are extremely small, the use of accurate deformation measurements are critical in the determination of resilient moduli. For example, errors in deformation measurement can be caused by extraneous deformation in the system, rocking of the specimen and unwanted movement of the gages. Therefore, three deformation measurement systems were evaluated as a part of the testing program. In He initial part of testing, stand-alone devices (i.e., EVDTs) and mountable devices (i.e., an extensometer mounted on the specimen) were evaluated. A ea~e-point- mounted (GPM) setup was also developed and used in the testing program. measurement devices are described here in detail. ~ ~ , These deformation EVDT Stand-Alone Devices. Different EVDTs were used during testing to measure vertical and horizontal deformations of He specimen under repeated loading. The L`VDTs were spring-Ioaded on to the center of the specimen In the horizontal diametral plane and were spr~ng-Ioaded on to the top of the upper loading plates to obtain the vertical deformation. Different configurations were used to measure the vertical deformation for different devices. The three types and makes of EVDTs used for the testing are provided below: TYPE A LVDT: Type: AC LVDT Range: 0.25 in. 2. TYPE B LVDT: Type: DC LVDT Range: 0.05\ in. TYPE C EVDT: Type: AC EVDT Range: 0.2 in. The EVDT setup for different devices is described in Table 3. For He Retsina device, a vertical EVDT could not be mounted within the limited space on the top of the upper loading strip. In the case of Baladi's device, there is just one arm to hold an EVDT at the top and so only one EVDT could be used. However, for the SHRP EG device and the MTS device, two EVDTs were used, and He average of the two readings was taken to compute He vertical deformation. For all the devices the horizontal deformation was measured by the same EVDTs. Two EVDTs were used in each device wig one on each side of He specimen at the center. The two deformations were individually calculated and arithmetically summed to get the total horizontal deformation. 22

Table 3. EVDT setup for different diametral loading devices ~I Vertical Deformation | Horizontal Deformation j || DEVICES | Number Used | Type Used | Number Used | Type Used l 1 . Retsina 2 I Baladi l 1 A | 2 SHRP LGD 2 B ~2 l MTS 2 B 2 C C C C The EVDTs present a convenient memos for measuring deformation. They are cheap and readily available. The measurement of the same deformation using two stand-alone ~VDTs permits estimation of the rocking taking place in the sample. When rocking occurs, the tip of an EVDT resting on a small irregularity on the specimen surface could slide over the irregularity thus recording a different deformation than actually occurs. The problem can be partially alleviated by placing a wide tip on the EVDT end. Over a period of time the shafts of the displacement transducer tend to develop increased friction. As a result, they may stick in varying positions giving erroneous results. This problem can be alleviated by the regular use of a lubricant applied to the shaft. The EVDT calibration should be checked at least once a month to ensure correct measurements. Care has to be taken to ensure that stand-alone EVDT devices are mounted perpendicular to their measuring surface. Improper alignment results in higher deformation values. Two (or morel EVDTs mounted on He top of He upper loading plate, one on each side of He loading ram, can detect He rotation of the upper plate. There is no way to separate the transverse (sideways) motion from the actual deformation. In spite of the simplicity of the EVDTs and their ease of use, many potential problems exist that can result in incorrect deformation values. As a result, the use of externally-mounted, stand- alone EVDT devices is not very promising. Horizontal Deformation Calculation for a Rocking Sample -- When using a stand-alone EVDT measurement device, care should be taken in interpretation of the horizontal deformation data obtained from the EVDTs if rocking is observed from the data. Two distinct cases are possible when rocking occurs: Case I: Sample movement is caused by rocking deformation due to load (see Figure Sa). As explained in Figure Sa, calculate the deformation as the difference of the two EVDT deformations. Case 2: Sample movement due to rocking is less than the deformation due to load (see Figure Ebb. As explained in Figure fib, calculate the deformation as the sum of the two EVDT deformations. 23

OR -!- ~ 4i ~ , FLY 1 L. 1_ 1-2 Compute L' and 1= as shown , - L2 = ~ R ~ Ix, ~ - ~ R -^2 ~ = ~ ^~+~2) = Actual deformation (a) Rocking exceeds deformation due to toad - ~ -. | ~ Ll it\.//,'~L2 I' g llME . _ ~ LIME . \ - This portion will vary based on the magnitude of rocking (may not be seen at all) Compute L' and L2 as shown L, ~ Lit = ~ R ~ A' ~ ~ ~ ^2- R ~ = (~+A2) = Actual deformation (b) Rocking less than deformation due to load Original position Position after rocking but before deformation Position after rocking and deformation Figure 8. Effect of rocking on horizontal defonnation measured by L,VDTs 24

Mountable Devices. A mountable deformation measurement device is mounted directly on the specimen instead of being attached to a stationary object. This type of system has been extensively used in resilient modulus testing for the measurement of horizontal deformation in the diametral test. The mountable measurement device used in this study consists of an extensometer assembly that can be spring-Ioaded on the horizontal diametral plane of the specimen. The horizontal extensometer assembly, manufactured by the MTS Systems Corporation, consists mainly of a pair of dual averaging axial extensometers (0.15 in. travel, Model 632.94B-20), gage length extenders and adapter brackets. There are two sets of adapter brackets and gage length extenders, one each for 4 in. and 6 in. diameter specimens. The adapter brackets span the thickness of the specimen at the horizontal diametral plane. They are held in place by means of springs that run parallel to the front and back faces of the specimen. The spring tension used should be sufficient to hold the extensometer assembly in place but not too strong to invalidate the theory used in calculating the resilient modulus. A theoretical calculation of the constraint imposed by the diametral device indicates that the reduction of horizontal expansion, due to the confining influence of the spring tension, is less than 0. ~ % [261. An alternative to springs is to glue the adapter brackets to the specimen which is not considered practical. Once the adapter brackets are put in place, the extenso meters, with length extenders, are mounted at the ends of the adapter brackets through knife edge points and held in place by small springs that hold Hem to the adapter brackets. Care has to be taken to ensure that the ends of the adapter brackets where the knife edges rest are smooth. Grooves at the ends cause errors resulting in smaller deformation due to slippage of the knife edge points in them. The deformations from the extensometers at the front and back of the specimen are internally summed resulting in only one source of error compared to two sources generated by use of two EVDTs. The extensometer assembly measures the maximum deformation occurring in the horizontal diametral plane. Due to the long contact area of the extensometer, local burrs and depression in the specimen do not affect He results very much. The major disadvantage associated with this system is its high initial cost. The biggest advantage of using the MTS type mountable device is it eliminates most of the extraneous deformation caused by rocking. However, this does not mean that when rocking occurs the measured deformation is the same as for no rocking. The load applied and the stress and strain pattern in the sample may change when rocking occurs. Using He MTS type mountable device, the occurrence of minute rocking, which can not be seen by the naked eye, cannot be detected. In a procedure, such as SHRP P07 (November, 1992), where alignment is achieved by comparing two independent deformation measurements, He use of a mountable MTS type system would not be allowable. Gag+Point-Mounted (GPM) Devices. An interesting approach for measuring deformation is to glue small tVDT mounting blocks directly to the sample surface. Small EVDTs are then placed between these two gage points to measure deformation. When using this type device, the potential effect on the measured resilient modulus of the following factors needs to be considered: 25

1. 2. 3. 4. 5. 6. 1. 8. Weight of the measurement devices and their mounts Alignment of these measurement devices with the axis of measurement Whether the EVDT is parallel to the surface of the specimen The size of the mount (glue points) Measurement gage length relative to aggregate size Type of glue used The surface characteristics and aggregate fabric near the glue points Sensitivity of EVDTs L`VDT mode] 099 XS-B (O.~ in. travel) manufactured by Schaevitz was used in the gage-point- mounted system. These EVDTs weigh less than 5 grams. Lightweight mounts were made for these EVDTs wig a very thin gluing surface. A non-sag epoxy was used to glue the mounts on Me surface of the specimen. A view of the GEM setup is shown in Figure 9. Accurately gluing the GPM devices to field cores is hard to accomplish if the surfaces of the specimen are not smooth. Also, He specimen deformation/stra~n/stress behavior at the surface is assumed to be representative throughout the specimen. Presence of large aggregates under or near the gage points can give highly inconsistent results if the gage length is too small. When the system is used to measure vertical deformation, it becomes very important to control rocking as much as possible. Specimen bulging also causes incorrect deformation readings. Theory indicates Mat the stresses at Me surface of Me specimen are different from Me stresses in the interior and Mat the assumption of a two~imensional analysis might not be entirely valid. The advantage of measuring between gage points for vertical deformation is that extraneous deformation is eliminated including the effects of rotation and rocking. Again, as with mountable devices, it does not ensure that the resilient modulus measured during rocking is perfect. The gage-point-mounted system is not as expensive as He extenso meter system but is not as simple to use as stand-alone systems. The GEM memos requires a significant amount of care on the part of the operator, and the procedure is somewhat cumbersome. A waiting period is required for the epoxy to dry before testing can begin. With proper care the gag~point-mounted system offers a good reference test method for resilient modulus measurement, but is too time consuming to set up for routine testing. Marking Device To align a specimen correctly, it is very important that the axes marked on the specimen are diametral axes and accurately define the vertical diametral plane. To measure the horizontal deformation accurately, it becomes important to define a horizontal diametral plane, and this plane should be perpendicular to the vertical diametral axes marked on He specimen. It is comparatively easy to mark mutually perpendicular diametral axes on one face of the specimen. But, to accurately mark diametral axes on both faces of the specimen so Hat they define diametral planes that pass through the center of the specimen and are perfectly perpendicular to each other is not an easy task. The marking device developed and used for this project was designed so that mutually perpendicular axes could be accurately marked for either 4 in. or 6 in. diameter specimens on both faces of the specimen (Figure 10~. This innovative device is described more completely in Appendix A including detailed instructions for its use. 26

-A ~ - .. : ~. l ~ ~:~;~ Figure 9. View of the GEM setup 27

MARKING EDGE- YYINDOW CAN SUDE ON OR ROTAlE ABOUT S~L ROD- S~L ROD SCAlE 1'=2' 1~ -1 ~ 1~-______ 1~________ 1~______~ 1p--_____ ~ 1 ~L 1 1 l I 1 11 1t--11 1F-~11 I 1 11 1F-- 11 1F-~11 1 11 1F--11 1FJI I 1 11 1F--41 1L-~-A1 l ~I _ _ _ =- . _ _ o ~LLc3` L r L~ - 0 5' S~ ROD Front view of the front plate MARKING EDGE~ 0.5. SlEa ROO _ SCALE 1 -=2. Bac k view 0 f the bac k p 1 ate r TRANSPAR~JT / ~lNDOW THIN UNES M~KED ON BACK OF WINDOW ~Mark ng tool ~ ~NG NUT ~- Figure 1 Oa. Schematic view of the marking device developed at NCSU 28

: ~< x%~;~;~jj~jj~jjj~j~ A-: :::::: :~:~:~ I; ~~ ~] : : . ::: ::~: :: :: : :: :: ::::::;::;:: :::~: :::::~":-::::::;~:.~. .~:~§ ~i: :: : : : ~-~-~:~. , ~\~\~\~\~ : ' : : ;::~: ~ . 1 ::4 ::b 5 : l I..',~ :- :~: ~ :~:~:~ be: ,:,:~::::::-~:; ::;:; In: An,:;;;:: :::: :- % ~;~;~,~x,~;~<~xix~xi~< Figure 1 Oh. Marking device developed at NCSU 29

This marking device, along with lines etched on the center of the loading strips, helps reduce rocking and makes He alignment of the specimen much easier. INDIRECT TENSION TEST ANALYSIS METHODS FOR DETERMINATION OF RESILIENT MODULUS Analysis Methods Different theoretical analyses, used to evaluate resilient moduli from He experimental diametral test data, are described as follows: ASTM Analysis. This analysis is adopted from the ASTM D 4123-82 procedure for the resilient modulus testing of asphalt concrete. Absolute values of all deformations are used in this analysis. The analysis method is described in more detail in Appendix A. SHRP P07 Analysis. This analysis is adopted from the SHRP P07 Protocol (November, 1992) [27] for resilient modulus testing of asphalt concrete specimens. Absolute values of all deformations are to be taken for this analysis. To improve the accuracy of the calculated values of Poisson's ratio, the SHRP PO7 (November, 1992) procedure uses a compliance factor applied to the measured vertical deformation. More details are provided in Appendix A. Rogue and Buttiar's Analysis. Roque and ButtIar [28] proposed an analysis method for the gage-point- mounted system of measurement. The approach only applies for a gage length to specimen diameter ratio of ~ :4 and when the surface mounted EVDT is 0.25 in. from the surface of the specimen. Horizontal (tensile) deformation is considered to be positive, while vertical (compressive3 deformation is considered to be negative for this analysis. A step-by-step procedure for this analysis is described in Appendix A. This method accounts for bulging and non-uniform stress distribution in a diametral specimen subject to a vertical load. Elastic Analysis. The elastic analysis method was developed during this study and is based on the assumption of linear elastic behavior of a statically loaded specimen. The final form of these equations closely resemble He corresponding equations given in ASTM D 4123-82. The development of the elastic analysis equations are given in Appendix A. Notation Used in Experiments A standard set of notations is described below which is used in presenting He diametral test experimental findings. However, a large number of variables were employed in He experiment. A notation system similar to this one was required to permit tabulations of the results in tables and databases. Additional notation employed is described where it first appears. Value of Resilient Modulus and Poisson's Ratio Notation Used pr: Variable Represented Poisson's ratio 30

mr: i: Analysis Methods. Resilient modulus This letter is used as a suffix to the resilient modulus (mr) and Poisson's ratio (pry notations given above if the value is calculated from the instantaneous values of recoverable deformation. Otherwise, the values of mr and pr were calculated from the total recoverable deformation. .rq. : denotes He use of Roque and ButtIar's analysis .sh. : denotes He use of SHRP P07 analysis tel. : denotes the use of elastic analysis .as. : denotes the use of ASTM D 4123-82 analysis Measurement System. A combination of the following letters is used to denote the measurement method used for horizontal and vertical deformation. For an exception to this rule, refer to the note given in the next section on Poisson's Ratio. The first letter in the two letter combination indicates the method employed for horizontal deformation. The second letter, when used, indicates the method employed for measuring vertical deformation. x : denotes the use of extensometer for the measurement of deformation v : denotes the use of EVDT for the measurement of deformation r : denotes the use of ram movement for the measurement of (vertical) deformation; an EVDT is placed at the end of the ram to measure its movement. m : denotes the use of a gage-point mounted EVDT for the measurement of deformation. The gage length used is identified in the test description in He relevant section. For example, .xv. denotes the use of an extensometer for measuring horizontal deformation and He use of a EVDT (or EVDTs) for measurement of vertical deformation Or. : Poisson's Ratio. denotes the use of EVDTs for the measurement of horizontal deformation and the ram movement for vertical deformation .c. : denotes the use of a calculated Poisson's ratio .a. : denotes He use of an assumed Poisson's ratio. Values of 0.2, 0.35, and 0.5 were assumed for test temperatures of 41°F, 77°F, and 104°F, respectively. 31

Note: When an assumed Poisson's ratio is used, the vertical deformation is not of significance. Ordy the horizontal deformation has to be used in the analysis. Hence, instead of using a combination of two letters for the measurement system, a single leKer is used. For example, .x. indicates that the value is based on horizontal deformation from the extensometer and .v. indicates that the value is based on the horizontal deformation from EVDTs. Use of He Notation System. Each test result is described by the combination of (type of value).(analysis method).(measurement system).(Poisson's ratio, if required). For notation that does not follow this system, descriptions will be given in the relevant sections. To illustrate the use of the system, some examples are given below. pr.el.xm: Total Poisson's ratio calculated using the Elastic analysis, horizontal deformation measured by an extensometer, and the vertical deformation measured by a gage-point mounted EVDT. Calculation is based on the total recoverable deformation. mr.as.x.a: Total resilient modulus calculated using the ASTM analysis, horizontal deformation ~ ., ~ measured by an extensometer, and Poisson's ratio is assumed. Note: There is no indication about the measurement system used for obtaining the vertical deformation as it does not have any significance in determining resilient modulus. Also, the total value of recoverable deformation is used for He calculation. mr.as.xr.c: Total resilient modulus is calculated using the ASTM analysis, horizontal deformation being measured by an extensometer, vertical deformation measured from the ram movement, and a calculated value for Poisson's ratio is used. Note: Poisson's ratio is calculated using the same ASTM analysis method, using deformation obtained from He measurement devices identified above. PRELIMINARY RESILIENT MODULUS EVALUATION WITH FIELD CORES Calibration with Synthetic Specimens The testing system calibration procedure included alignment of the top and bottom loading rams, calibration of extensometers and load cell, and adjustment of gain settings on the MTS console to check the shape and timing of the wave form. Four types of synthetic specimens were tested to verify the calibration of the system. The synthetic specimens were made from Polyacrylate Lucite), Polyethylene, Teflon, and cast synthetic rubber used for Hveem Stabilometer calibration. Alignment, specimen set-up proc~ures and operation of the system were adjusted until He resilient moduli determined for the synthetic specimens were acceptable when compared to reference values. Resilient Modulus Testing of field Cores Resilient modulus testing was conducted on the asphalt concrete cores obtained from test sections at the Penn State University and supplied by SHRP. Two sets of cores were supplied consisting of five samples each, one from a new (labeled "N") pavement and another from a five-year old (labeled "O") pavement. Two mutually perpendicular diametral lines were drawn on He sample and marked either "A" 32

or "B". The indirect tensile strengths at 77°F were 223 psi and 61 psi for "N" and "O" cores, respectively. All the samples were tested in accordance with SHRP P07 procedure (November, 1992 version), along both He axes. Each time a core was tested, direction A or B was chosen randomly for the first set of readings. Effect of Testing Axis. Results obtained from the field core testing program indicated that the MR values were slightly higher along the diametral axis that was tested first (Figures I ! and 12~. Figures I ! and 12 present the total MR values calculated from assumed and calculated Poisson's ratios, respectively. A comparison of these figures indicate that the axis dependency becomes more significant when MR values are determined from Poisson's ratios calculated from vertical and horizontal deformations than when assumed-Poisson's ratios are used. Fairhurst et al. [26] studied the change in MR values based on calculated Poisson's ratios at different specimen rotations using laboratory compacted specimens. They found that MR values at 0° specimen position were larger Han those at 90°. Since the 90° position was always tested after the initial 0° position, they suggested that the decrease in the MR values at the 90° position could be due to internal damage done to the specimen during testing in the initial position. The same data used in Fairhurst's paper were plotted, together with the field core data, in Figure 12 under the legend of "lab. specimens". The alcis dependency from the field cores was not as prominent as obtained by Fairhurst et al. [26]. This difference in behavior might be a direct consequence of the load level applied. If higher load levels were used, damage would be more severe and hence the difference in MR values would be larger. SHRP P07 (November, 1992) limits the load to 30, 15 and 5 96 of the indirect tensile strength at 77°F for testing temperatures of 4l, 77 and 104°F, respectively. The load level used in Fairhurst's paper was 20 % of the indirect tensile strength at 73°F which was allowed in ASTM D 4123. The load levels required by SHRP P07 probably yield less damage and hence less axis dependency. Effect of Rest Period. The effect of rest period on the resilient modulus of asphalt concrete has been studied by several researchers [14, 29, 301. At low temperatures and short stress durations the dependency of rest period is not significant, but it is significant for warm temperatures and long stress durations. Thus, for warm temperatures and long stress durations the viscoelastic response should be included as a factor in the material characterization. Mon~smi~ [16] suggests the ratio of He rest period (time OFF) to the time of loading (time ON) is Important because it directly affects the amount of recoverable strain Hat occurs and hence the resilient modulus. The smaller the ratio, the smaller will be the recoverable strain and hence larger values of resilient modulus will be determined. This trend is also temperature dependent with dependence decreasing with decrease in temperature. Fairhurst et al. [261 investigated the effect of rest period duration on the magnitude of resilient modulus. The results indicated that He resilient modulus increases slightly with shorter rest periods. This is not surprising, since shorter rest periods for the specimen between loading pulses results in less time for rebound strain to occur and Bus gives higher MR values. The results from the tests on field cores indicate very little effect of rest period on the values of resilient modulus as shown in Figure 13. In some cases the MR values even increased slightly with 33

3E+06 - os Q - u, ~n 2E+06 - c o c: 1 E+06 o - ce - o OE+OO ~ OE+OO .: ~, ~F ,~ ~D 1 E+06 2E+06 Total lUlr along First Axis Tested (psi) | ~ N core + O core | 3E+06 Figure 1 1. Axis dependency of total MR calculated using ASTM analysis with assumed Poisson's ratio and hor~z. Extensometer data A __2_ ~1_ _ ~, . ... . . . 6.0E+05 - - ~n - - os 0s 4.0E+05 c o Q c 2.0E+oS o - - i~ O.OE+OO O.OE+OO ~o O o/ ~* /+ + c~ 0 c~ ,' | O N core + O care ~ ~b. Speamen 2.0E+05 4.0E+ 05 Total Mr along Flrst Axis Tested (psi) l 6.0E+Os Figure 1 2. Axis dependency of total MR calculating using ASTM analysis with calc. Poisson's ratio, ram movement and hor~z. Extensometer data 34

0 5 ~ . ~ ~00 O O O O O hi) O U. O O O CM C~J ~ · Let) 0 (!Sd) NEW lessor 35

increasing rest periods. The increase was observed more often in the old specimens than in the new specimens. The apparent contradiction of these results to the findings by other researchers is explained by considering the ratio of rest period to the time of loading. First, the beneficial effect of rest period is not very significant after a rest period to loading time ratio of about ~ [161. The rest period to loading time ratios in the proficiency testing were 9, 19, and 29; therefore, very little effect of rest period would be expected. Secondly the order of testing the specimens for different rest periods tended to cause less damage. That is, the case where the worst damage was expected (0.9 sec. rest period) was tested before the case with minimum damage (2.9 sec. rest period). This order of testing might have increased the fatigue damage as Me test progressed resulting in less recoverable deformation and hence a slight increase in We MR values. These findings indicate that a rest period of 0.9 sec. used with a 0.l sec. loading time is adequate to minimize the effect of rest period. Effect of Temperature. The resilient modulus of asphalt concrete decreases significantly with increasing temperature as illustrated in Figure 14 for the SHRP core specimens. These results are in agreement with Me findings of others [28, 291. Effect of Poisson's Ratio. Figure 14 clearly demonstrates Me magnitude of difference in the resilient moduli determined using assumed compared to calculated values of Poisson's ratio. The largest discrepancy in MR occurred with Me new ("N") cores at 41°F, with He MR value using assumed Poisson's ratio values being about 5 times larger Han He MR values obtained using calculated Poisson's ratios. Also the temperature susceptibility (i.e., the slope of He MR VS. temperature curve) was considerably less when the calculated Poisson's ratio was used. The measured value of Poisson's ratio, as determined from the total vertical and horizontal deformations, was found to vary between negative values and I.5 (Figure 15), which goes out of He theoretical range of O to 0.5 for linear elastic isotropic materials. Bow Cochran [31] and Baladi and Harichandran [24] have found that using an assumed value of 0.35 for Poisson's ratio resulted in I.5 to 2 times higher values of resilient modulus than obtained using the measured Poisson's ratio calculated from measured horizontal and vertical deformations. Fairhurst et al. [26] have found that Poisson's ratio increases with an increase in temperature which contributes to a decrease in MR. They concluded that when a Poisson's ratio near 0.5 is measured, the theoretical maximum value for elastic isotropic materials, the applied load might be too high. They also observed that Poisson's ratio at the 90° position is slightly higher than at He 0° position. This could be possibly due to a redistribution of the applied load into the region outside the center, as a result of the weakened central zone, causing greater overall horizontal deformation and hence a higher Poisson's ratio. Fairhust et al. concluded Hat Poisson's ratio serves as an indicator of excessive damage to a specimen during the resilient modulus testing. Vinson [321 concluded from a theoretical finite-element study Hat an increase in Poisson's ratio from O. 15 to 0.45 did not affect the calculated resilient modulus very much. He also concluded that for a resilient modulus test performed under typical loading conditions (i.e., a steel/asphalt concrete interface) the resilient modulus obtained using an assumed Poisson's ratio is more accurate than that obtained using a calculated Poisson's ratio because of induced shear stresses in He specimen. However, he obtained better results with calculated values of Poisson's ratio when a soft modulus material was placed between the steel platen and asphalt concrete. 36

- ~ - - 60 80 Temperature (F) N. 2nd axis + Ol 1st axis l x N. 1st axis ° O. 2nd axis ~ P07recom. 100 1: >0 Figure 15. Poisson's ratio, calculated using ASTM analysis from extensometer and ram movement data, as a function of temperature 37

McGee [33], however, concluded from an experimental study that resilient modulus values obtained using an assumed value of 0.35 show more scatter than those obtained using calculated values. Poisson's ratio was also found to increase with increase in loading level, temperature, and asphalt content. Based on the resilient modulus testing of field cores in accordance with the SHRP P07 (November, 1992) procedure the following conclusions are made: I. The MR values from the axis tested second are slightly smaller than those from the His tested first. The load levels recommended by SHRP P07 (November, 1992) seemed to reduce He testing axis dependency significantly compared to high load levels apparently by minimizing He damage induced testing the first axis. 2. The eject of rest periods varying from 0.9 sec. to 2.9 sec. Is not significant for the loading history required by SHRP P07 (November, 1992) and 0. ~ sec. haversine load pulse. 3. The resilient modulus significantly decreases as temperature increases. The resilient modulus temperature dependency predicted using Equation (2), developed by Miller et al. all, indicates less temperature dependency than found during the present study for diametral tests performed on asphalt concrete cores. The equations of Miller et al. were developed from cyclic biaxial compression tests. In contrast, the diametral test subjects the specimen to indirect tension. A state of compression would be expected to be less temperature susceptible than a tensile stress state. This difference in stress state helps to explain the apparent discrepancy between the Miller et al. results and the core test findings from this study. EVALUATION OF RESILIENT MODULUS TESTING DEVICES USING SYNTHETIC SPECIMENS Testing Program To evaluate different types of loading and measurement devices, synthetic specimens were tested in accordance with SHRP P07 protocol (November 1992). The synthetic specimens were tested using the Baladi, MTS Retsina and SHRP EG devices. Test Series No. ~ The first series of resilient modulus testing included He following test variables: I. Loading Devices: 2. Measurement Devices: Extensometer, EVDT 3. Specimens: 4. Axis: 5. Preconditioning: 6. Rest Period: Baladi, MTSshort, MTSIong, Retsina, SHRP EG Lucite, Polyethylene, Teflon, and Rubber Two mutually perpendicular testing axis (A and B) ~ (15 cycles) and H (75 cycles) Three rest periods: 0.9, I.9 and 2.9 seconds 38

All testing was performed at room temperature. The specimens were stored in an environmental chamber at 77?F for at least 24 hours before testing. Every effort was made to maintain room temperature at 77°F, and the specimens were returned to the environmental chamber as soon as testing was finished. A haversine load of 0.! second loading time was applied for all testing configurations. Data for five consecutive cycles was collected after the completion of the preconditioning cycles. Test Serges No. 2 The experimental variables included in Test Series 2 are summarized as follows: Variables Methods Tested Loading Devices: Baladi; MTSIong; MTSshort; and SHRPEGD Measurement Device: Extensometer 3. Specimens: Lucite; Polyethylene; Teflon; and Rubber 4. Rest Periods: Three rest periods: 0.9, I .9, 2.9 seconds 5. Axis: Only axis A was tested to eliminate axis dependency as a variable 6. Preconditioning: Only the 75 cycles of preconditioning cycles (H level) was tested to eliminate this as a variable 7. Testing Subsets: To increase the amount of data for statistical purposes, two sets (Subset ~ and Subset 2) of testing with the above parameters were repeated on each specimen on the same axis. The specimen was realigned each time testing was performed. Data Analysis. Statistical Analysis Test Series ~ and 2 utilize a full factorial design to investigate the effect on resilient modulus of pertinent variables. The findings from the full factorial experiments and also He studies were thorou~hiY analyzed using the analysis of variance (ANOVA) test and generalized linear models. The statistical analysis procedures used are briefly summarized in this section. The ANOVA test procedure utilizes the F-value as a statistic to test the null hypothesis. For these tests, the null hypothesis is Hat there is no effect of different loading, measurement devices and other independent test variables on the results obtained from the tests. The level of significance (p-value) for the ANOVA test is the probability of having a F-value greater than the calculated F-value from a data set for the factor in question if the null hypothesis is true. A smaller value of this probability, as reflected by a smaller p-value, implies evidence for rejecting He null hypothesis (and hence, proving that some parameters do have a significant effect on the results obtained from the test). For example, a p-value of 0.001 on the resilient modulus value obtained using one variable indicates a much more unusual result (if the null hypothesis were true) Man a p-value of 0.5 on MR from another variable when the null hypothesis were true. Generally, a p-value _ ~ less than 0.05 indicates significance of a parameter on the dependent variable. 39 _ ~

A general linear model can be used for multiple regression models in which a dependent response, such as resilient modulus, is related to a set of independent variables such as rest period or testing axis. This general linear model has the following form: y = as + am + a2x2 + ... + akXk + (4) For a multiple regression model, the As can represent independent variables, independent variables raised to powers and cross-product terms involving the independent variables which represent interaction between those variables (such as interaction between axis and rest period, etc.~. Test Findings and Analysis. The test Series 2 results are summarized in Tables 4 and 5. The ANOVA analysis was performed on various dependent variables. The dependent and independent variables chosen for the study are shown in Table 6. An effort was made to strengthen the inferences from the statistical analysis by selecting the log of variables to give a better normal shaped distribution. Taking the log of the variables did not alter the p-values significantly, and the same general trends were observed. Hence, the results obtained using the log of the variables were included in Tables 4 and 5. The variability in resilient modulus was studied, rather than the resilient modulus itself, since the "true" MR values for the synthetic specimens are not known. The resilient moduli obtained from the SHRP Asphalt Concrete Core Proficiency Sample Program by averaging results from different testing labs serve only as reference values. The average resilient moduli obtained by various labs are' influenced by the type of device used and hence an average value from all labs does not have real meaning. Two kinds of variability were studied (Figures 16 and 17~. First, variances were obtained for mean MR values. Each mean MR value was obtained by averaging the resilient modulus for 5 sequential load pulses for each test configuration. Variances were calculated for 12 of these average MR values in Test Series ~ and for 6 values in He Test Series 2 for each specimen. This variance is referred to as var- A. Variances were also determined for the 5 sequential load pulses for each test configuration. Then the average of 12 variances in the Test Series ~ and 6 variances in the Test Series 2 were calculated for each specimen. This variance will be hereafter referred as'var-B. As shown in Table 7, the ANOVA analyses showed in general very little significance of the test factors considered. 'However, the type of loading device used does have a significant effect on most dependent variables of the study as indicated in Table 7. Based on He previous findings of testing devices for determining the resilient modulus of asphalt concrete, the diarnetral test was selected as the most practical device for routine use. The specific design details of a diametral testing device, however, can have an important effect on He measured resilient modulus. In tile past, very little research has been conducted to evaluate different testing systems. Therefore, an experiment was undertaken to establish He behavior characteristics of He following devices, which cover a wide range of equipment design variables: (~) Retsina device, (2) Baladi's device, (3) SHRP EG device, and (4) MTS device. Rocking The amount of rocking was studied by taking the absolute difference between the readings from the two independently supported EVDTs used for the measurement of horizontal deformation. As explained earlier, Table 7 shows the ANOVA analysis on the effect of loading device on the dependent 40

Table 4. Summary of test results for synthetic specimens (first set) Device EXT/LVDT Specimenmr.as.x.a orVAR-A ** VAR-8 *'. mr.~.v.a ~ . _ 3ALADI EXTLucite 537,001392,247,874 1,1 72,77G,304 Poly 219,8899,097,312 44,084,44S Teflon 127,308820,260 S,4 12,640 . Rubber4,921. 2,047 28,027 _ LVDT Lucite 493, 11212,062, 1 92, 128 1 ,33S,668,000 Poly 223,164155,791,511 48,204,773 Teflon 154,8271 ,782,S7G,586 28,911,584 Rubber 6,1 2S77,935 20,204 UTSLONG EXTLucite 423,8309,91 0,870,097 S0O,607,S90 Poly 1 94,8578,480,S73 32,320,77S Teflon 122,6782,4S0,902 10,61 S,588 Rubber 4,7547,880 26,443 LVOT Lucite 507,79010,931,763,837 38,882,000,000 Poly 198,723153,553,81 7 2,481,492,190 Tcflon 83,414548,299,422 17,750,820 Rubber 5,47637,082 42,386 MTSSHORT EXTLucite 484,3573S3,422,352 GS2,683,760 Poly 191,90740,900,929 1 8,46S,869 Teflon 114,6551,989,455 S,292,573 Rubber 4,5695, 102 76S LVDT Lucite **~* Poly 187,07674,S91,387 56,0S5,S62 Teflon 107,6142,229,427 3,S18,588 Rubber 8,067415,464 1,463 RETSINA EXTLucite 494,491165,81 7,96S S6G,S1 2,S26 Poly 186,89433,031,90S 24,263,829 Teflon 107, 8988,400,071 4,818,704 Rubber 4,6221,574 _ 11,478 LVDT Lucite 592,00938,709,680,726 7,457,399,000 Poly 199,53970,521,819 170,098,978 Teflon 1 15,8886,415,801 27,165,519 Rubber 5,399 9,075 __ 17,173 SHRP EXT Lucite ~ 15,891 340,900,588 796, 146,096 Poly 207,651 27,667,835 23,738,401 Tetlon 126,636 3,067,025 7,661 ,058 Rubber 5,495 1 7,24S 44,363 LVDT Lucite 448,616 171,886,970 20B,223,600 Poly 211 ,S27 41 ,243,248 25,832,908 Teflon 1 27,144 3,225,892 3,443,045 Rubber 7,383 71,400 176,184 NOTES: * rnr.as.x.a if extensometers were used; mr.as.v.a if LVDT's were used ** VAR-A: variance (refer Figure 7.1 tor details) * ** VAR-B: variance (refer Figure 7.1 for details) *~** The value tor this cell is missing as it was computed to be a negative value 41

Table 5. - Summary of test results for synthetic specimens (second set) DEVICE SPECIMEN mr.as.x.aVAR-A *VAR-B * BALADI Lucite529,31 8 448,1 75,01 2 924,770,31 8 Po iy240, 234 17 , 165, 405 57 , 770, 782 Teflon1 1 9,896 2,282,31 1 6,266,582 Rubber4,708 1 ,1 03 8,543 MTSLONG Lucite479,241 294,308,062 652,1 21 ,669 Poly190,51 1 16,170,822 23,449,693 Teflon1 06,91 6 753,423 3,1 45,697 Rubber4,490 1 ,507 1 3,798 .. MTSSHORT Lucite 503,786 654,842,448 550,323,959 Poly 189,211 6,715,688 20,823,487 Teflon 1 06,866 3,397,305 2,395,702 Rubber 4,377 1 35 789 SHRP Lucite 504,01 4 1 ,01 0,1 90,272 1 ,095,761 ,585 Poly 208,623 19,080,741 38, 170,451 Teflon 1 20,582 5,781 ,533 3,937,799 Rubber 5,378 1 0,794 33,042 _ . . . * Note: VAR-A, VAR-B: variance (refer to Figure 13 for details) 42

Table 6. ANOVA setup (testing of synthetic specimens) I SET DEPENDENT VARIABLES INDEPENDENT VARIABLES . jRST Mntmr.as.x.a) NDEV Vartmr.as.x.a) RESTP l Mn~mr.as.v.a) PREC Vartmr.as.v.a) AXIS l log(Mn mr.as.x.a) l fog(~/ar mr.as.x.a) l log(Mn mr.as.v.a) log(Var mr.as.v.a) DiffHZ NDEV DiffVT AXIS SECOND Mn~mr as x q DEVICE Varkmr.as.x.a) RESTP tog(Mn mr.as.x.a) SUBSET log(Var mr.as.x.a) DiffVT DEVICE SUBSET NOTES: Mn: Mean Var: Variance FIRST SET: NDEV: For statistical purpose, the 5 loading devices and the 2 measurement devices were combined into ~ 0 different devices. RESTP: rest period PREC: level of preconditioning cycles AXIS: Axes of testing (A or B) SECOND SET: DEVICE: the four loading devices chosen for this set SUBSET: Two subsets of tests (hence, two alignments) 43

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Table 7. ~~ Summary of ANOVA results (testing of synthetic specimens) ~ SET DEPENDENT LEVEL OF SIGNIFICANCE(P-VALUE) VARIABLE ~ ndependent Variable: DEVICE Lucite Po' Teflon Y FIRST Mn(mr.as.x.a) 0.0001 0.0001 0.0001 Var~mr.as.x.a) 0.2571 0.4595 0.0098 Mnkmr.as.v.a) 0.0016 0.0001 0.0001 Vartmr.as.v.a) 0.4210 0.0001 0.0042 log(Mn mr.as.x.a) 0.0001 0.0001 0.0001 fog(\/ar mr.as.x.a) 0.4827 0.5741 0.1455 fog(Mn mr.as.v.a) 0.0001 0.0001 0.0001 log0/ar mr.as.v.a) 0.0001 0.0001 0.0001 I DiffHZ 0.0001 0.0000 0.0000 1 DiffVT 0.0001 0.0001 0.0046 1 SECOND Mn~mr.as.x.a) 0.0283 0.0001 0.0001 Var~mr.as.x.a) 0.7507 0.11 56 0.1525 log(Mn mr.as.x.a) 0.0272 0.0001 0.0001 fog(Var mr.as.x.a) 0.8035 0.1660 0.2990 DiffVT 0.0001 0.0001 0.0001 Notations: urn: Mean Var: Variance (of type var-B) DiffHZ: Absolute difference between Horizontal EVDT's DiffVT: Absolute difference between Vertical EVDT's 46 Rubber 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 - 0.0001 0.0088 0.0001 0.0001 0.0020

variables listed in the second column of the table. As the data in Table 7 shows, the type of device has a significant effect on the amount of rocking. The SHRP EG device has the least mean absolute difference between the readings from the two EVDTs and thus the best control on rocking (Figure IS). The test procedure for the SHRP EG device requires the operator to follow an extensive alignment procedure before testing. Furthermore, it has heavy guide columns on two sides and a heavy upper plate which might play a part in controlling rocking. Baladi's device was the second best one with respect to rocking probably because of its four guide posts. An alignment procedure Is not required before testing with the Baladi device. Had an alignment procedure been followed, He Baladi device would likely have given comparable results to the SHRP EG device. Rocking was quite small for both the Baladi and SHRP EG device. The MTSIong testing device was somewhat poorer in controlling rocking than the Baladi device. The MTSIong device did control rocking better than the MTSshort device. The better performance of the MTSIong device, compared to the MTSshort and Retsina devices, may be due to the use of a heavier long ram which might prevent movement away from He loading axes. The MTS short and Retsina device had He poorest control over specimen rocking. Probably He best indicator of repeatability is He ratio of standard deviation to the mean value of the difference in horizontal deformation measured by the two EVDTs (Figure ISb). The MTSshort, Retsina, and SHRP devices all show good repeatability in the amount of rocking. However, the larger amount of rocking observed in the MTSshort and Retsina devices (Figure ISa), suggests that the good observed repeatability is due to the measurement of large amounts of rocking each time. Rotation of the Upper Plates The rotation of the upper plates was studied for He MTSshort, MTSIong and the SHRP EG testing devices for both He Test Series ~ and 2 results. Rotation of He upper plate could not be measured for the Baladi and the Retsina devices. Figures 19 and 20 show Hat the deflection values obtained for the three testing devices were similar. The very large value obtained for the Teflon specimen from the MTSIong testing device in Test Series ~ (Figure 19a) is believed to have occurred due to bad specimen alignment. The low resilient modulus in Table 5 obtained for this setup using the EVDT for horizontal deformation measurement supports this observation, The MTS testing device, which has a thin top plate, showed approx~m$ely the same rotation of the top plate as did He SHRP device with the thicker, heavier top plate. This suggests Hat rocking of the specimen in the MTS device may be at least pardy due to He flexibility of the upper loading plate of the testing device allowing movement in the lateral (translational) direction and not due to its rotation. For He SHRP device, the heavy columns restrict He translational motion of the upper plate in the horizontal plane. The heavy upper plate may not be making a significant contribution to He prevention of rocking. Deflection Measurement Device Two deflection measurement devices were studied: (~) an extensometer which mounts on the specimen and (2) externally supported (stand-alone) EVDTs. Tests in this section were performed on 4 types of synthetic specimens. Figure 21 shows that variability is reduced, and hence better repeatability is obtained, by the use of extensometers compared to LVDTs. The LVDTs failed to give reasonable MR values for some test setups although the extensometers gave good MR values during the same test. The 47

0.06 . . I 5- 0.03 Q 0.02 ~ 0.m a: 'it Salad MTSbng MTSs~rt i _ _ . _ ~ Retsna SHRP l ~ ~ i.. | ~ Ludte ~ PI ~ R~ ~ TO | Figure 1 8a. Variation of mean absolute difference between horizontal LVDTs for different devices and synthetic specimens - Test Series ~ 25 2 A ~ 1.5- C) ID 1 cn 0.5 ,~ BE MTSbng MTS short ~ , ~ Lid . ~ Retsr. SHRP L ~ Lie ~ Poly [9 Row Ei3 Tenon Figure ~ fib. Variation of standard deviation/mean absolute difference between horizontal EVDTs for different devices and synthetic specimens - Test Series 48

0.001 4 c Q0012 c' .m 0.0008 <~ Q0006 := o ~0.0004 o 0. o . ~ t: , ~ , ~ 1 MTSlong MTSshort SHRPext SHRPh~dt | ~ Lucite Poly ~ Rubber ~ Teflon Figure ~9a. Variation of mean absolute difference between vertical EVDTs for different devices and synthetic specimens - Test Series Ma 3 25 a' a' := 2 co 1.~- us 1 O5 O ~ , v~ , ~ , ~ 1 MTSlong MTSshort SHRPext SHRPI~dt ~3 Rubber ~ Teflon ~ ~ Lucite ~ Poly Figure 19b. Variation of standard deviation/mean absolute difference between vertical EVDTs for different devices and synthetic specimens - Test Series ~ 49

Q000~- G 0. OOC125; .= 0-00020 O.a301 5 0.0001 O a~s o.oowo-~ hATSshort SHRP 1 MTSlong | ED Lucite Pow ED Rubber Id Teflon Figure 20a. Variation of mean absolute difference between vertical EVDTs for different devices and synthetic specimens - Test Series 2 1 0.8 tD A a' ~ O.6 !t A: 0.4 U] 0.2 O - ~ ; MTSlong l , MTSshort SHRP | fez] Lucite Poty 2~ Rubber ~3 Teflon Figure 20b. Variation of standard deviation/mean absolute difference between vertical LVDTs for different devices and synthetic specimens - Test Series 2 I 50

as Q45 0.4 0.35 0.3 0.~- 0.2 0.1 5 O1 O.C~ - ,l~ ~52 ~ - O ~, , , . O O.Ofi 0.1 Q15 0.2 0. . . . . 0.3 Q35; 0.4 Q45 Q5 Extensometer Figure 21a. Square root of variance (var-B)/mean MR for Extensometer and LVDT measurement devices: Test Series 1 0.35 0.3 0.25 - a' Q 1 5 C] En O1 3" 0.2 3 - am ~ o 0 QOS Q1 Q15 0.2 0.25 Q3 O35 S.D.IMean ICIER, Extensometer Figure 21b. Standard deviation (from var-A)/mean MR for Extensometer and LVDT measurement device: Test Series 1 51

~e ~e A. resilient moduli obtained using the LVDTs are significantly affected by He alignment of the specimen where as Hose obtained using the extensometer are not. A minor disadvantage associated with the use of the extensometers is Hat the magnitude of rocking cannot be evaluated. However, if care is taken in specimen alignment and the testing device has a reasonable control on rocking, rocking should not be a significant problem when extensometers are used since minor misalignments appear not to have a significant effect on the results. The mean resilient moduli obtained for the different specimens (Figures 22 to 25) show that EVDTs usually give either higher or similar values as those obtained using the extensometer. When a specimen is loaded, the diameter of the specimen moves down a small amount, depending upon the stiffness of the specimen. The extensometer moves down wig He specimen diameter while He EVDTs remain at He original position. As a result, EVDTs measure smaller deformation than the extensometer which results In the higher resilient moduli than for He EVDT system. This effect is clearly seen for the very soft rubber specimen (Figure 24) as it undergoes significant vertical deformation. Resilient Modulus Variability Figure 26 shows the coefficient of variation (A variances associated with all the loading devices using the synthetic specimens. A careful examination of this figure, as well as Figures 22 to 25, shows that the observed coefficient of variation (CV) is strongly dependent upon specimen stiffness. The Lucite and Poly specimens had resilient moduli in the range typically exhibited by asphalt concrete mixes. The resilient moduli of these two materials are about 200,000 psi and 500,000 psi, respectively. For the 4 testing devices examined, use of the softer Poly specimen resulted in an average coefficient of variation of 2.4 % compared to 5.2 % for the stiffer Lucite specimen. For this comparison and the following one, both the A variance and B variance (Figure 27) were used to determine the coefficients of variation. This comparison shows relatively little differences in He coefficient of variation between devices, and any of He devices could be used based upon variability considerations. Friction and Inertia of the Testing Devices A comparison of mean resilient moduli shown in Figures 28 to 31 indicates that the use of the MTS device results in lower MR values than the Baladi or SHRP EG devices. For the MTS device, all the load is applied to the specimen. In contrast, Baladi and SHRP EG devices lose some of the load to friction In He guide posts wig He amount depending upon the alignment. Also, some inertia forces which oppose the applied load are caused by acceleration of He heavy upper plate and the counterbalance weights of He SHRP EG device. The inertia forces become greater as the vertical deformation becomes greater as was true for the rubber specimen (Figure 30~. Thus He actual load applied to the specimen by the SHRP EG device is less and hence the deformations are smaller which results in high resilient moduli. Effect of Specimen Alignment When Using Extensometers Figures 28 to 31 show the mean resilient moduli measured using an extensometer for the two subsets of Test Series 2. For each subset test the specimen was realigned. The resilient moguls are almost equal for bow He subsets, suggesting Hat alignment is not a very significant factor when the extensometers are used to measure deflection. Also, Figures 22 through 25 show the use of EVDTs result in considerably greater variability in resilient moduli than does He use of extensometers. These findings 52 ... . .. . .

66+~ - SE+~ BE+ c. U3 3E+t)5 29+0~ 1E+05 CE +00 . ~ MTS - g 1 MTSsl~rt Ressna SHRPLGI Nae: M ssng d~ata MTSshat as t was c~edto be a negarvevaLe | ~ Extensometer ~ LVDT Figure 22. Mean MR values for Lucite specimen: Test Series ~ 3E +05- . 2E +05 2E +05 1E+05 5E +04 ~+W Salad MTSbng MTSs~n '/] r/U _ ~/1 Retsna SHRPLGD | ~ Extensometer LOOT Figure 23. Mean MR values for Poly specimen: Test Series ~ 53

8000 - 7000 6000 5400 - ~3 g 4000 G 3000 2000 1 000 o lit Ba ad MTSlc~g MISshoR Relsat. SHRPLGO 1 | ~3 EXtensometer ~ LVDT Figure 24. Mean MR values for Rubber specimen: Test Series ~ 1 ~ 80000 20000 //1 BE hITSbng // MTSs~ l z] Extensometer ~ LVOT Ress~ SHRPLGD Figure 25. Mean MR values for Teflon specimen: Test Series 1 54

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BE +05 SE +05 c. 4E + 05- ~n Q G a, OE +C~ HE +05 1 E +(35 OE +00 Baladi 1 MrSIong L MISshart 1 SHRPLGO I t~ subsen subsets Figure 28. Influence of testing device on mean MR value for Lucite Specimen Test Series 2 25+ 20E +05 8 1.5E+ G c 1.0E+O5 s~ +~- QOE+O . 1 1 MTSlong MTSshort ~- / _ , '_ . . ~ SHRPLGD Baladi | ~ subsen ~ subset | Figure 29. Influence of testing device on mean MR value for Poly Specimen: Test Series 2 57

MOO- , 5000 4000 U) Ct - G 3000 2000 1 000 O Baladl MTSlong I. MTSshort r SHRPLGD 1 | ~ subsen subset Figure 30. Influence of testing device on mean MR value for Rubber Specimen: 1 .~ +0~ 1 .2E +05 8 G +04 c a, 4.0E +04 O.OE +00 1 MTSlong MTSshort SHRPLGD Baladi | ~] subset ~ subset:2 Figure 3 1. Influence of testing device on mean MR value for Teflon Specimen: 58

indicate that extensometers rather than EVDTs should be used to measure deformation in resilient modulus testing. The use of an extensometer achieves better repeatability and has less influence from misalignments as compared to EVDTs. When extensometers are used, all the loading devices appear to perform reasonably good. However, the SHRP FIG device controls rocking the best of all the devices in this study. The original SHRP EG device used during this testing, however, is bulky, heavy and is a little complicated to use. Also, He inertia from the heavy upper plates and the counterbalance weights appears to reduce the load reaching the specimen causing the resilient moduli to be high. The SHRP EG device is also slightly too large to use inside commonly available environmental chambers. The loading strips are located In line with the guiding posts, and hence it is hard to visually align the specimen in the center of the loading strips. Alignment is even harder once He device is fitted in an environmental chamber. The guide posts are probably farther apart and bulkier than required. The alignment procedure required by the SHRP EG device before the commencement of the test is very time consuming because it requires a number of adjustments to achieve accurate alignment. This rather cumbersome procedure may not be suitable for state DOT laboratories. Also, ~perfect" alignment may not be possible to achieve when using field cores. According to these tests, the mountable extensometers produce more consistent resilient modulus values when specimen rocking occurs. Based on the experience and finding; in this section, the following modifications to the original SHRP LG device should be made: 1. Reduce the weight of the upper plates using high strength, light weight materials, thus eliminating the need for counterbalances, Reduce the overall size of the device, 3. Add the capability to test 6 in. diameter samples. EVALUATION OF GAG~POINT-MOUNTED LVDT SYSTEM Testing Method In this experiment, the Gage-Point-Mounted deformation measurement results are compared with the those obtained using MTS horizontal mountable extensometers. The Gage-Point-Mounted (GPM) memos was proposed by Roque and Buttlar [28] for the accurate determination of material properties of an asphalt concrete specimen, such as Poisson's ratio, from the indirect tensile test. Poisson's ratios determined from other conventional approaches have been found not to be reasonable with the values ranging from less than zero to as high as 2. For the Gage-Point-Mounted method, two Lucas Schaevitz sub-miniature series LVDTs, Mode! XS-B 099, were attached to the surface on one face of the specimen. The SHRP LO testing device was used because it minimizes rocking. The same asphalt concrete specimen was also tested using the MTS loading device, horizontal mountable extensometers, and two EVDTs at the top of the upper loading plate (no gage-point-mounted EVDTs were used). Two different gage lengths, ~ in. and 2 in., between the gage-point-mounted EVDTs were used in the SHRP EG device setup to determine if the measured Poisson's ratio and resilient modulus would 59

be significantly affected by a change in gage length. A load slightly less than 15 % of the indirect tensile strength at 77°F was used to minimize specimen damage. The LVDT assembly was glued on the surface of the specimen after aligning it using a device developed for that purpose. The alignment device is described in detail in a later section. The EVDT body and the core were mounted in tiny lightweight aluminum blocks with a tapered end that had a gluing surface of I/16 in. x 5/16 in. The smaller dimension of the aluminum blocks were orientated in the direction of the deformation measurement to provide an accurate gage length. The aligning device maintained an accurate gage length, and also kept the height of the EVDT axes close to 0.25 in. from the surface of the specimen [281. The EVDTs were zeroed in the alignment device and locked in place at the desired gage length. A non-sag epoxy was then applied to the gluing surface of the mounting blocks, and the aligning device was aligned and centered on the sample surface. The enoxv is a 100 % solids. two-Dart eDoxv adhesive r - ~ ~ ~ ~ ~ designed to provide a non-sagging consistency. The epoxy was set under pressure from the self weight of the aligning device for a period of at least 12-16 hours to develop a good bond with the asphalt surface. After curing, the aligning assembly was carefully dismantled, and testing was performed on the sample. In general, the performance of MARK-8 epoxy was excellent. An unbiased effort was made to carefi~ly align the sample for both test setups. The two horizontal EVDTs, simultaneously used with He GEM setup in the SHRP EG device, indicated the occurrence of very small rocking although no rocking was visible during testing. Rocking was visible with the naked eye in some tests using the MTS setup. Tests were performed at 77°F. Test Notation. The different parameters/setups used in He testing are identified by the Test ID in Tables ~ through ~ I. Each character in the testing identity stands for a parameter in He test and is described below: Character No. 2 3 4 5 6 Discussion of Test Results Description Sample No. used for the test: ~ or 2 Testing axes (mutually perpendicular): A or' B Load level: L, (600 Ibs.) or H (700 Ibs.) Rest period: ~ (0.9 sec.) or H (2.9 sec.) Preconditioning cycles: ~ (75 cycles) or H (150 cycles in SHRP setup; 100 cycles for MTS setup) ~ or 2 (l in. or 2 in. gage length in the GPM setup with the SHRP EG devices or M (MTS device with mountable extensometers) The Gage-Point-Mounted (GPM) system consists of attaching small EVDTs directly to He face of the specimen. The test results obtained from the GEM deflection measurement setup are tabulated in Table 9 and for He MTS setup In Table 10. The coefficients of variation, which are the standard deviation divided by average value of the variables, are tabulated in Tables ~ ~ and 12. The coefficient of variation 60

Table 8. Average values from the GPM setup under the SHRP device: Test ~pr.rq.mm mr.as.v.amr.el.mm.c mr.eLm.amr.ellrq.m.a ~0.3241 0.4275 909676 463825895040 818253891576 lALLH10.3354 0.4384 917049 473678899606 80705 1879371 1AHLL 10.2625 0.3682 891961 524648888659 865820943406 1AHLH 10.3356 0.4391 978054 5199439~887 859820936868 l B L L L 1~ . 0 4 ~ 4 0 . 0 6 4 1 6 6 8 1 ~ 6 1 7 2 8 3 7 97 1 1 8 3 9 1 2 5 0 3 6 21 3 6 2 4 0 6 lBLLH1-0.1053 -0.0032 643819 728423695 157 14815351614294 l B H L L 10 . 0 0 6 9 0 . 1 1 2 6 7 5 2 6 ~ 4 4 4 3 6 6 87 9 3 2 5 0 1 2 4 4 9 8 71 3 5 6 5 4 9 lBHLH 10.0237 0.1299 818375 462066859668 12905791406227 1BLHH10. 1016 0.2089 931386 426950%2288 12239771333657 2ALLL12.0136 1.8260 4 177327 19367612722522 847004922903 2ALLH 12.4425 2.4349 -1499556 12765003570419 860072937142 2AHLL 11.2382 1.2385 2643774 112 1 27 12093340 896523976860 2 A E ~ H 11 . 1 1 8 4 1 . 1 2 5 8 2 3 4 9 8 8 9 1 0 3 5 0 2 21 8 4 0 6 9 8 8 4 ~ 4 5 19 1 5 7 6 3 2AE~H11.2900 1.2849 2457908 8844431944839 815219888271 2BLLL10.0783 0.1852 1 142123 10661501 185823 15954071738370 2BLLH 10.0984 0.2047 1 192633 ~1~56 ~1~5818393~ 2BHLL 10.1986 0.3051 1247324 ~1~42 13911111515767 2BHI H 10.1860 0._923 1269990 ~1~270 14437341573107 AHLH2 0.1501 21~- 502 5871 AHHH2 O. 1520 1740835377627 537345 AHLH2 0. 1823 742539365399 5020 17 AE~I2 0.1 133 72 135632 1080 500969 1BHLH2 0.1509 786156467590 677348 1 B ~H2 0.2083 769860444516 564463 1 B HLH2 0.205 7 5 2~498775 6497 Note: * Values not reported as one of the LVDls mounted on the diameter moved out of measurement range, which was kept small to get more accuracy. Table 9. Average values from the MTS setup: Test Series 2 - Test ID~ ~ pr.as~r ~ pr.as.xv mr.as.xr.c mr.as.xv.c mr.as.~a 1AHLHM ~.0653 0.1 193 358883 682625 1087474 AHHHM ~.0534 0.1392 363007 685813 1039149 ALLH}Jf ~.08~:' 0.0738 349592 639899 1154243 ALH ~-0.0729 0.1009 353872 663652 1109190 1BHLHM 0 0737 0.0945 368739 684893 1165136 1BE~M -0.0679 0.1166 377741 722372 1158769 . 108 ~0.0307 3762 14 6987 13 1440637 BHLHM ~.1088 0.0094 343500 595626 132 164 1 61 Test Series l

Table 10. Standard deviation/average values (coefficient of variation) of five consecutive test cycles from the GEM setup: Test Series ~ Test ID pr.rq.mm pr.el.mm mr.rq.mm.c mr.as.v.a mr.el.mm.c mr.el.m.a mr.el/rq.m.a 1ALLL 1 0.39580._9080.0685 0.0128 0.0477 0.1544 0.1544 1ALLH1 0.38020.28190.0859 0.0078 0.0620 0.1 198 0.1 198 1AHLL 1 0.32680.22570.1394 0.0084 0.1191 0.0436 0.0436 1AHLH1 0.28660.21 130.0436 0.0073 0.0448 0.1486 0.1486 lBLLL1 -1.41840.9~030.1174 0.0150 0.1066 0.0786 0.0786 1 B L L H 1 ~ . 3 6 5 8- 1 2 . 5 0 7 50 . 0 7 2 3 0 . 0 1 0 1 0 . 0 6 6 2 0 . 0 9 3 5 0 . 0 9 3 5 1BHLL1 9.67370.60340.0919 0.0079 0.0826 0.1280 0. 12&0 1BHLH 1 2.17260.40500.0597 0.0104 0.0525 0.1018 0.1018 1 BLAH 1 0.43790.21460.0443 0.0044 0.0378 0.0695 0.0695 2ALLL1 0.19530.15 180.3114 0.0233 0.2454 0.1975 0.1975 jALLH1 0.926 10.5549-18.9983 0.0177 0.4986 0.0835 0.0835 HALL 1 0.23830. 19720.2463 0.0157 0.1926 0.0784 0.0784 2A~H 1 0.49800.39590.5411 0.0141 0.3804 0.0971 0.0971 2AHHH 1 O. 10830.08850.0474 0.0 100 0.0287 0.0736 0.0736 2BLLL 1 0.91190.38940.1960 0.0184 0.1929 0.2219 0.2219 2 B L L H 1 1 . 2 4 4 00 . 6 0 2 30 . 1 1 9 3 * 0 . 1 3 9 2 0 . 3 6 8 8 0 3 6 8 8 2BHLL 1 0.52640.34150.0883 * 0.0888 0.2212 0.2212 2BHLH1 0.68710.43380.1381 * 0.1183 0.1868 0.1868 1AHLH2 0.4535 0.015 1 0.3612 0.4279 1AHHH2 0.19 10 0.0278 0.0534 0.0745 1AHLH2 0.7381 0.0117 0.1562 0.1495 1AHHH 2 0.5827 0.005 1 O.087 1 0.0853 BHLH2 0.4890 0.0153 0.0739 0.1685 1BHHH2 0.1495 0.0069 0.0381 0.0383 11BHLH2 0.3769 0.0 47 0.0704 0.1976 Note: * Values not reported as one of the LVDrs mounted on the diameter moved out of measurement range, which was kept small to get more accuracy. Table ~ I. Standard deviation/average values (coefficient of variation) of five consecutive test cycles from the MTS setup: Test Series 2 .. . . Test ID pr.as.xr pr.as.xvmr.as.xr.cmr.as.xv.cmr.as.~a 1AHL ~.0969 0.06730.01400.01260.029~ 1AHHHM -0.0527 0.0~80.01520.00800.0116 1ALLHM ~.061 1 0.07360.02120.00870.0111 1ALHHM ~.0500 0.04650.0 1760.02290.0 15 1 1 BH[HM ~.0396 0.06920.01260.01790.0200 I 1 B H ~ M - 0 . 0 6 1 8 0 . 0 7 7 20 . 0 2 1 0O. . O 1 2 6O. . O 1 8 0 PAHLHM ~.0132 0.11360.00760.00510.0081 ~B HLHM -0.0246 0.45600.01050.00950.0085 62

o of c) · - ~"o' ~ ~ - ~o v,c ~ -0 ~ - · 3o =~_Cal . ~ ._ ~ ~. Cal ~. ~ Cal Cal .o i_ 3 ~ Cal LO C,0 O 4_ u, cn _ Cal ~ O ._ ._ a ~ C) ~ _' . . on . 0 . . . l C~J~ . - ~9 Cal ~ F E L E l E E ~ E [ E r X ~ a, 1 ~ L J. T ]~1 ~ ~ U11~: ~1°1 I IOI O l I l N|. T~ ~1~ ~F :~R'1°1 ~ ~1 Nit ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ :~L O ~ O N ~ 0 I ~ 0 | N 1 0 1 I o l C I 0 I o l l o l o l C I o l O I I o ~ o l ~ I N o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 °1 1°~R ~ ~ ~ ~ ~ ~] o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 °1 1°1°1° = = = = = = = = = = = = = = = = iTi ~r ~ ~r ~ ~ ~ ~] ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ I ~ I I ~ I I ' I I ~ ~] P _ ~ ~ tn ~ ~ O ~-O _ _ _ _ ~-8I T~TmI -1 0 ~ | -I 1 ] I O 1 § ~ I U, I Cl I 0 I ~ I I N | ~ I ~ 1 2 1 0 1 1 ~ I U' I I N I Ll l _ _ ~___ C`l __ ~ C~J O N O O ~ _ ~ ~ _ | | ~ | ~ | ~ O O. O O O O, O O, &. O O O _ _ _ O, O O, O O o,l lololo o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 °1 1°1°1° mm o ~ ~ ~ ~ 0 ~ ~ ~ 0 ~ ~ ~ ~ ~ _= ~ _ -I T~l~l~ ~ L I L | ~ ~ L° L~ ~ ~ ~ ~ ~ ~ BL L I L I ~ ~ = = = = = = = = = = = = = = = ~, ~ ~ ~ ~ ~ ~ ~ I i#~U 63

gives a basis for comparison of the variation observed in resilient modulus and Poisson's ratio using different analysis methods and testing setups. The mr.el/rq.m.a values in Table 9 were calculated using the elastic analysis after applying correction to the measured deformation for bulging as in Roque and ButtIar's analysis. An assumed Poisson's ratio of 0.35 was used and the horizontal deformation was obtained from the mounted EVDTs for this value. Poisson's Ratio. Poisson's ratios and the resilient moduli calculated using equations ~ and 9 in Appendix A and deflections from the GPM setup were not realistic. Poisson's ratios varied from negative values to as high as 2.44. For some tests the average values were close to 0.35 (the value that is assumed at 77°F). As much as 40 % deviation occurred from the average values when Poisson's ratios were close to 0.35 Table 9 and ~I). Poisson's ratios calculated using the MTS setup and the horizontal deformation from extensometers and vertical deformations from EVDTs mounted on top of the upper plate (pr.as.xv in Table lO) were between O and 0.15 and the coefficient of variation was usually less than 10 %. Values of Poisson's ratio from the GPM test setup having a 2 in.. gage length were positive, but small (between 0. ~ to 0.2) and the coefficient of variations were large for the 5 load repetitions. For the GPM test device, Table 9 shows that for different test conditions (and hence, different alignments) all the values varied considerably, especially for the ~ in. gage length. Thus, it seems that Me alignment may play a critical role in obtaining reasonable results with this setup. Also, Me values obtained wig a ~ in. gage length for sample 2 West ID's starting with 2 in Table 9) gave bad results in the direction of axis A. A visual observation revealed that sample 2 had a large aggregate aligned perpendicular to the A axis very close to where the EVDT was glued. It seems that, depending on aggregate alignment within the sample, different results can be obtained. Overall, it is concluded Hat it is difficult to obtain good Poisson's ratios with the GPM setup with a ~ in. gage length in the diametral test. Resilient Modulus. Resilient Moduli were calculated using the Roque, ASTM and elastic methods as discussed previously. Typical values obtained for the same mix and same type of specimens at 68°F were between 1,150,000 to 1,870,000 psi in earlier studies at NCSU. Tests at 77°F would result in slightly smaller values. As can be seen from Table 10, for the MTS setup, most of the resilient moduli calculated for specimen ~ were close to I.l million psi and for specimen 2 the values were near I.4 million psi. Values for mr.el/rq.m.a CTable 9) also are close to the range given above. Therefore this range of resilient moduli were used as a basis for comparison. Resilient moduli obtained from the MTS setup wig mountable extensometers (mr.as.x.a) and those obtained from the SHRP EG device with stand alone EVDTs (mr.as.v.a) showed much smaller deviation Tables ~ ~ and 12) within 5 cycles. However, as shown in Table 9, He values of mr.as.v.a, in He GPM setup with the SHRP EG device, varied significantly with each different test condition. This finding gives furler support, using actual asphalt samples, that extensometers give much better performance than EVDTs even with rocking of the SHRP EG device. Average values (mr.el/rq.m.a) obtained by using He horizontal deformation obtained from the GPM EVDT, correcting it for bulging effects (using an assumed Poisson's ratio of 0.35 and then using the equation developed in He elastic analyses) gave reasonable results. However, the five cycle variances were very high as can be seen from Table ~ I. The values from the elastic analysis, without correction for bulging in the GPM setup (mr.el.m.a), are comparable to the mr.el/rq.m.a values. As suggested by 64

. Rogue and ButtIar [28] there exists a need to incorporate Be effect of bulging and non-uniform stress distribution in Be analysis system, especially when surface-mounted EVDTs are used. The gage length of ~ in. proposed by Roque and ButtIar [28] for the GPM setup is too small to obtain reasonable and consistent values of Poisson's ratio and resilient moduli under repetitive loading. The deflection measurements from the 2 in. gage length are less sensitive to the presence of large aggregate particles, but Be variances within 5 cycles were approximately equal for Be 1 and 2 in. gage lengths. EVALUATION OF A PROPOSED DEFORMATION MEASURING SYSTEM (EXSUM) Using an assumed value of Poisson's ratio, as is usually done at the present time, introduces an error into the calculated resilient modulus. For example, an assumption of a Poisson's ratio of 0.35 for a sample with actual Poisson's ratio of 0.3 can cause a 9 % increase in the calculated resilient moduli. Undoubtedly Poisson's ratio varies with many variables including the type of mix, temperature, and the damage level. Thus, it becomes important to cad curate the resilient modulus using an actual Poisson's ratio rawer Can an assumed value. However, wig the current equipment available at most testing laboratories, it is better to rely on an assumed value because measured Poisson's ratio values are often grossly incorrect. A new system for deformation measurement consisting of a modification of the GPM setup along wig the use of a mountable extensometer is proposed for the evaluation of Poisson's ratio and resilient modulus. Proposed Deformation Measurement System Concept As indicated by previous studies, moduli calculated from horizontal deformation (obtained with the help of an extensometer) and an assumed value of Poisson's ratio were very consistent. Also, the inconsistency and inaccuracy in measuring Poisson's ratio is a result of the measurement systems being mounted on the top of the upper loading plate. A measurement system located on the upper loading plate picks up extraneous deformation resulting mainly from rocking of the specimen. Also, local shear may occur near the loading strips which results in misleading vertical deformations. A measurement system wig ~ternally-mounted transducer for measurement of horizontal deformation and a SIIrface-Hounted transducer for measurement of vertical deformation (the EXSUM system) was developed to avoid the aforementioned problems (Figure 32~. The idea is to retain the consistency provided by He externally- mount~ extensometer measurement device for the measurement of the horizontal deformation. To obtain a correct value of He vertical deformation actually occurring in the specimen, a measurement system must be used that eliminates the extraneous deformation due to rocking. The use of a surface-mounted I,VDT aligned vertically on the face of the specimen achieves this goal. To avoid the end regions where local shear might be occurring, a gage length smaller than He diameter of He specimen was selected. A 3 in. gage length is used for a 4 in. diameter specimen, and a 4.5 in. gage length is used for a 6 in. diameter specimen. The resilient modulus and Poisson's ratio can then be calculated using Equations A-S and Am, respectively, which are given in Appendix A. The device discussed earlier was used for marking the diametral axes on the *ont and back of the specimen. A precision alignment system was designed and manufactured Figure 33~. A complete description of the device and its setup is given in Appendix A. 65

:~: ::: ::~:::: -. ~ :~ ~: I: -. - :: :: :~:: : ~ .: ~: ~ - : ~:: :::: ::::: :~:~:~:~:~:~:~:~:~:~~ :: :-:::: :: ::: ::::::::::::: :-: ::--::::: ·:~ ~:~:~:~:~:~:~: -; :: :-::.:. -: : : .: :.: ::: :::: ;::: ::: ::: :::-~;:;:::::;:::::::::;~:::::::::::: ::: ::::: :;::: : :;::;::::: :;:-:"':;::: ·: ~ `: ·: ·::::: i::::;;: ;: ; ~;~:~:~:~:~:~:~:~:~:~: ~:. : ~: ~ . . .-.-. . ~ .- ~ ~ ~ ~ .:. .-. -. i:::: Figure 32. EXSUM system mounted on a specimen 66 t; ..-.. ~ . .~ Ale. i,~;< ~ ~

:~:~:~ :::: Lila ~ ~< ~ ~: , Figure 33. Alignment and setup device for the EXSUM system 67

Testing Protocol Two series of tests were performed using the proposed measurement system. The SHRP EG device was used in the first series to minimize rocking. Since initial testing showed promise, the MTS device was used at three different temperatures for the second series of tests. Test Series I The testing variables for the first test series are as follows: Loading device: SHRP EG Device Temperature: 77° F Sample type & size: Medium gradation (see Appendix B), 4 in. diameter, 2.5 in. thick specimen Loading history: 0. ~ sec. loading time and 0.9 sec. rest period Load levels: Low load (L) of 375 Ibs. or high load (H) of 800 Ibs. which are approximately 7 % and 15 % of He indirect tensile strength at 77° F Seating load: 25 Ibs. for low load level and 50 Ibs. for high load level Loading waveform: Haversine Preconditioning: Data was collected after the completion of 70, 85, and 100 cycles. For Test Series I, resilient modulus testing was repeated four times with different alignments. The first and last tests were performed using a best effort to align the specimen. The second test was performed with a slight tilt to He left from the correct alignment and the third with a slight tilt to the right. The results are summarized in Table 12. The test ID is a combination of three letters in the following order: (alignment, test No, ~ to 4), (load level, ~ or H), and (preconditioning level, ~ (70 cycles), 2 (85 cycles), or 3 (100 cycles)~. Test Series 2 The variables included in this series of testing are summarized as follows: Loading device: MTS Device Temperature: Low ~) - 41°F, moderate (M) - 77°F, and high (H) - 104°F Sample type & size: Medium gradation (see Appendix B), 4 in. diameter, 2.5 in. Hick specimen Loading history: 0. ~ sec. loading time and 0.9 sec. rest period 68

Load levels: 41°F: Low ~) - 800 Ibs. or High (H) - 1550 Ibs. 77°F: Low (L) - 375 Ibs. or High (H) - 800 Ibs. 104°F: Low (L) - 110 Ibs. or High (H) - 210 Ibs. Seating load: 41°F: 50 Ibs. 77°F: 25 Ibs. and 50 Ibs. for load levels ~ and H. respectively 104°F: 10 Ibs. Loading waveform: Haversine Preconditioning: 41°F: 90, 100, and 110 cycles 77°F: 70, 85, and 100 cycles 104°F: 30, 40, and 50 cycles The test results are summarized in Table 13. The test ID is a combination of Tree letters in the following order: (temperature; Lo, M, and H), (Ioad levels; ~ or H), and Preconditioning level; 1, 2, or 3~. Test Results and Discussion Poisson's Ratio. The results obtained from He Test series 1 and 2 using the EXSUM deformation measurement system are quite promising. Poisson's ratio values are all positive and between 0. 18 and 0.5. The coefficient of variation is usually less than 10 %, and becomes less than 5 ~ at high load amplitudes. The proposed measurement system (EXSUM) can therefore determine Poisson's ratio values that are both consistent and reasonable. Some general findings for Poisson's ratio from the data in Table 12 and 13 are as follows: 2. 3. 4. For Test Series 1, Poisson's ratios, obtained using the EXSUM system, range from 0.2 to 0.3 (as compared to the assumed value of 0.35 at 77°F). For Test Series 2, except for the t e s t temperature of 41°F, the values of the EXSUM measured Poisson's ratios are very close to assumed Poisson's ratio values which are 0.2 at 41°F, 0.35 at 77°F, and 0.5 at 104°F Table 12~. For Test Series 2, even at 41°F, the values using the EXSUM system are all positive compared to negative values obtained using EVDTs mounted at the top of the upper loading plate. Testing at 41°F was performed after testing at 104°F, which might have caused more damage in the specimen and hence the observed higher Poisson's ratio ranging from 0.21 to 0.32. Most importantly, EXSUM measured Poisson's ratio values were all positive and within O to 0.5, He theoretical linear elastic range on which the analysis is based. Higher Poisson's ratios were measured with higher load amplitude (Figures 34a and 34b). The lower values (0.18~.28) obtained In the SHRP device (lest Series 1) at 77°F may result from the fact that less load is applied to the specimen due to friction. Also, previous testing would have caused damage and hence higher Poisson's ratio (0.28~.35) when the specimen was later tested in He MTS device. 69

a3 -.~- , - ~ Q2 ,§ 315 5 as Am' .9 a2- _ a2 / Q2 Am PC'55~-S R (a) Test Series ~ with SHRP EG device 77°F as as Q. PC~S Rem ~ =" ~ ~ 41 F · "F ~ leaf | - (b) Test Series 2 with M rS device as Figure 34. Effect of load amplitude on Poisson's ratio (pr.el.xm) obtained from the EXSUM setup using Elastic analysis 70

The coefficient of variation (CV) for the measured Poisson's ratio (pr.el.xm) is small (usually less than 10 %), except at low temperature. The coefficient of variation (CV) of Poisson's ratio decreases wig increased load amplitude (Figures 35a and 35b). Changes in alignment in Test Series ~ do not seem to have made any significant difference in the measured values of Poisson's ratio (Table 13). Resilient Modulus. Some findings for resilient modulus from Tables 13 and 14 are summarized as follows: 1. 2. 4. The resilient modulus of We asphalt specimens calculated from Poisson's ratio obtained using the data from surface-mounted EVDT and Me extensometer (mr.el.xm.c) is close to that calculated using an assumed Poisson's ratio (mr.el.x.a) as shown in Figures 36a and 36b. For Test Series 2, a slight increase in resilient modulus occurred with increased load amplitude, the increase being greater when the calculated Poisson's ratio (pr.el.xm) is used (Figures 37a, 37b, and 37c). The coefficient of variations for resilient moduli are reasonably small, being usually less than 5 % and reducing with an increase in load amplitude (Figure 3Sa and 3Sb). The coefficient of variation for the resilient modulus is not significantly affected if MR is calculated using the measured Poisson's ratio (calculated from the EXSUM deflection system) compared to those calculated from an assumed Poisson's ratio (Figure 39~. The EXSUM deformation measurement system gives reasonable, consistent and reproducible values of Poisson's ratio. The resilient moduli values obtained using the measured Poisson's ratios obtained using the EXSUM system were close to those calculated with an assumed Poisson's ratio. The coefficient of variation obtained for both resilient moduli and Poisson's ratio values were small except at low temperatures where rocking is the greatest and the deformations are very small. Also, higher load amplitudes result in a lower coefficient of variation, indicating more consistent test results. To obtain satisfactory values of Poisson's ratio at low temperatures, rocking must be minimized using an improved loading device such as SHRP EGD or its modification. However, in this study, when the EXSUM system was used at low temperatures, a continuous plot of the vertical deformation was obtained using a strip chart recorder to ensure that rocking had little effect on the vertical deformation measurements. When the ~noise" in the deflection measurement was comparable to the magnitude of the measured deformation, the test was stopped and the specimen and the test fixture was realigned. The use of the EXSUM deformation measurement system requires an increase in time for testing because of He significant time required for mounting the EVDT on the specimen. More reliable values of Poisson's ratio could be obtained if two EVDTs are mounted, one on the front and one on the back surface of the specimen. Corrections for specimen bulging as done by Roque and Buttlar [28] for the GEM setup makes the analysis of the test results more relevant. 71

Ate ~1 ac6- 02 ale 3 ~ AL , - 75 a~ o - - (a) Test Series 1 with SHRP EG device v am Q1. Co - . TV - ~,~ 77@F are - - ~ Temperamm aos al al s CO - . ~ Vim Lot ~ Alma (b) Test Series 2 with MTS device ~2 Figure 35. Effect of load amplitude on the coefficient of variation (cv) of Poisson's ratios (pr.el.xm) obtained from the EXSUM setup using Elastic analysis 72

e - ,ct v: of: _ 3 c Be ~5 0 ~i_ _ can .m ~ e _ _ ~_ ~O ~_ ~Be ~.O so c' O He A_ C1) v: c ~O a_ t c ~_ ~ _ c~ ct s~ _ c~ ct ~ _ ~: ~ _. s~ ~ O ~ a.) u, ct ct e~) v:) v _ ~ O v: ·_ ~ c~ - c~ _ ~ c~ _ ~ s~ _' ~_ c~ ~ t~_ ~e~ ~ e X E ~ . N E _ ~ == E =7 E ~ E _ i 0° ~-N E N O- _ O O C~ O o CO o o o0 - o o) 0 U~ _ a) a) CO _ CO CO CO C~ N O O U' C~ O J ~_ _ o O . CO O O O _ O O ~n O 82 . ~ . - ~ _ - N Nl O _. ~ _ a) ~ e N O _ 3 _ - CO O N O O O O O O O ~ _ ~ ~ 0 C~, Oo CO, O O O . (D _= ~0 ~0 O O O' O . _ N O N 8 ~o o o o o ~ __ CO 0 C~ =. o =, o o o . = . _ Nl Nl $ ~ O _ O N a) t_ $ ~ ~r C~ O ~ CO ~ Nl N Nl 0 2 a) CO _ o a, ~ ~ 0 _ ~ . o o o . a~ _ _ CO C~ ~ N e N _ C~ CO I' ~ IN' I~IC~! ~ I~~IC~! ~O ~ O ~ O ~ ~ 8 ~ o ~ 0 ~ ~ ~ N ~ o ~ ° ~ ~o~o~o~ ~o~o~o~ ~ ~o~o~o~ ~4 ~o~o~o~ ~o~o~o~ ~ ~o~o~o~ ~ N O N N 1010101 1010101 1 1_10101 14 1010101 1010101 1 1°1°1°1 1' 1 010 1 ° I ~ 83 1 o l P 1 1 1 N I O I O I ~ 1°101o1 1010101 1 1°1°1°1 1 1 0 1 ° 1 ~ 1 1 ~ 1 ~ 1 0 1 1 ~ o I ° I ~ I 1 ~.r~l I 1 1 ° IN ~ 1 7 10 1$ 1 1 1~ 1~1~1~1 101=ol~1 1 ~1~1~1 1 ,0, ,m, 'm~u~l~l , ~c~lml~l , 12121~1 ~ lilil°1 1°1°101 1 101°1°1 1 I N I CO ~ N I ~ ;5 1 Cl) I ~ I 1 1 ~ 1 $ 1 ~ 1 1 ] ~ TmIsI 1~1~1~1 1 Pr1U 73 ~. i ~ i ° i N °1°1° . I N I c~1 °= _ 1_ 1 _ _T010 C\1 1 ~ 1 0 °o.lo.lo ooR ~Ti ololo °1°1° 01~1,` _1cO10 °.1°.1°. 1°1°1° 1 · ~ 1~1~t 1~1colo IC~I_IN 1~1~1~ 1-1- 1-1 r~ 1~121~= I C~ I N I N I 1 - 1-1-1 t=T-Tu, I 1a)1a)1CM1 1C01C01~1 10lolo l T~ ~ 1 ~ 1 ~ °1°1° l I II I I lELd

. 1.2. . - Q9 as £+ .- . ~+~. :~+0e' I+ ~ 16+~- , a7 _ a? as as MR-, sesuned P I) I LILA - AM ~ Atom I (a) Test Series ~ with SHRP EG device / ~ 0 23 to t.t t.2 (~+~ ~m 1E+ - As+ - MR - D, a5~T ad P=~s Ram ~ ~ ~ ~ O H41 ! t,-~ Amp. l (b) Test Series 2 with MTS device Figure 36 Comparison Of MR values - mr.el.x.a (using assumed it), and mr.el.xm.c (using calculated it), obtained from the EXSUM setup using Elastic analysts 74

5~+~ ~- 4.5E +06 ° ~/ 5, 4.0E+06- ~ _ ~ 3.5E +06 / / (a) 41°F 3.0E +06- ~ 3.0E +06 3.5E +06 4.0E +06 4.5E +06 fiOE +06 m (pa, Lov, Load Arrp | ~ m.d A a 0 m.aL,anc | 9.0E +05 S.~+05 ~o 5, ROE+05 7.5E+05 7 HE +7g~ +05 7.5E +05 ME +05 8.SE +05; 9.CE +06 m ash, Lou Load ~ - 1 3E+05 _ 1.2E+05 I ~ 1.1 E+t~ ~(c) 104°F 1 .OE +1~ +05 1.1 E +05 1 .2E +05 t .3r +05 m - , Low Load Arrp lo c' - - | ~ m.eL,ca 0 m.elxmc | (b) 77°F - - - - - (c) 104°F | ~ m.euca 0 m.eLxmc 1 Figure 37. Effect of load amplitude on MR - mr.el.x.a (using assumed ,u) and mr.el.xm.c (using calculated ,u), obtained from the EXSUM setup using Elastic analysis for Test Series 2 at different temperatures 75

~ Q OS. Mao O ao.- 3: acr3 ~ Qua ~ am C] TV 0- 1 a.~; am Am a.m ~ 0.02 as, o.m 3 C: - a~ - - ~_ - a" ~ - - - ~ t~ 3.. C] . _ . Ace oC3 once ao6 ace Cce#. of Vanatan. Low Mad A,npli~de OR, assumed nu O An, c~c~a`ea nu --- 1 (a) Test Senes 1 with SHRP LO device - - - - O Q01 Ace 303 am Caste. Of Vara~On, LOW Lead Amplitude OR, assumer nu O OR, c~cu~atca nu (b) Test Series 2 with MTS device QC)5 Ace Figure 38. Effect of load amplitude on the coefficient of variation (cv) Of MR - mr.el.x.a (using assumed flu ) and mr.el.xm.c (Using calculated ,u ), obtained from the EXSUM setup using Elastic analysis 76

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INVESTIGATION OF EFFECT OF TEST VARIABLES Test Variables The MTS testing device was selected for the final phase of testing for the study of effect of various variables on the resilient modulus of asphalt concrete specimens. Earlier findings show that stand-alone measurement devices do not provide good results when used to measure horizontal deformation. Thus extensometers were selected for the final phase of testing. Specimen Related Variables. Asphalt concrete specimens with two different gradations (medium and coarse - see Append us B), were made with 4 in. and 6 in. thicknesses. The resulting thickness to diameter ratios were 5/8 and I, respectively. Instead of the ~ types of asphalt concrete specimens required for a full factorial experimental design, only 6 different specimens could be tested. A 6 in. diameter and 6 in. thick specimen could not be tested in the MTS device. The data pertaining to the 6 specimens tested are tabulated in Table 14. Table 14. Asphalt concrete specimens used in experiment . Gradation Diameter Thickness Test ID (in.) (in.) Medium 4 2.50 M! . Medium 4 4.00 M2 Medium ~6 ~3.75 r M3 Coarse 4 2.50 C! Coarse 4 4.00 C2 Coarse 1 1 3~75 1 C3 1 Earlier tests indicate a reduction in resilient moduli occurs when the specimen is tested again at a different orientation. Also, the SHRP P07 (November, 1992) test procedure requires testing along a single axis. Hence, the effect of specimen orientation was not included in this study. Stage ~ Testing Test Variables. A specimen having a medium gradation (MI) and one having a coarse gradation (C3) were tested in Stage I. These specimens represent extremes in He different types of specimens included in the experiment (refer to Table 14~. The various levels of variables studied under this stage are as follows: Temperature: Loading Period: Low (L) - 41°F, moderate (M) - 77°F, and high (H) - 104°F L (0.05 sec.) and H (0.2 sec.) 78

Rest Period: Ratios of rest period/Ioading period of 4 ~) and 24 ~ were used Load Waveform: H traversing) or S (square) Load Amplitude: Two load levels were used: SHRP P07 load levels ~ and approximately half of the SHRP P07 load levels ~3- Specific conditions are as follows: Temperature Load Level 41 °F: 77 °F: 104°F: 30% and 15% of indirect tensile strength at 77°F 15% and 7% of indirect tensile strength at 77°F 5% and 2% of indirect tensile strength at 77°F Preconditioning Cycles: Three different levels of preconditioning cycles (l, 2, and 3) were chosen at the three different temperatures Table 15~. These levels were based on experience with asphalt concrete field cores and the range of preconditioning cycles recommended by SHRP P07 (November, 1992) procedure. Table 15. Levels of preconditioning cycles, stage ~ testing SHRPP07 ~Preconditioning cycles ~ Temperature suggestions ~2 . 41 °F 50-150 25 100 77°F - 50-100 25 75 104°F 1 20-50 15 T 30 T 3 200 150 60 Test Protocol. A full factorial design of He variables ' described above was conducted on the two types of asphalt concrete specimens at three different temperatures. Data was collected at He end of the three levels of pre-conditioning cycles given in Table 15. Testing was performed prior to the development of the new EXSUM system. The MTS device was used for testing. Extensometers were used for the measurement of horizontal deformation, and two EVDTs mounted on the top of the upper loading plate were used for the measurement of the vertical deformation. Seating loads of 10 % of the final load levels were used as suggested in He SHRP P07 (November, 1992) procedure. The testing program consisted of 16 statistically designed test combinations as given in Table 16. Notation. The test results are tabulated in Appendix ~ (fables I-! to I-6~. The test ID consists of 7 characters in the following order: Specimen type - M! or C3; Temperature - I,, M, or H; Sample No.-l or 2 (2 indicates a replacement specimen was used to complete the testing program at a particular 79

Table 16. Testing Program, stage || ID, test | Load ~Load | Load ~Rest | sequence | Amplitude| Time | Waveform | Period l | Ll L | H | H | 02 l L| L | H | L 03 | L L | S H | 04 | L ~L | S | L || 05 | L| H | H I H 06 l Ll H | H | L || 07 l I H | S | H 08 | L H | S l 09 | H L | H H 10 l H L | H L 11 l H L | S H 12 l H L | S L 13 l H H | H H 14 l H | H L 15 l H H | S H 16 l H H | S L ~0 .

temperature); Test sequence IDES to 16 (refer to Table 16); Preconditioning level - 1, 2, or 3. Stage 2 Testing Test Variables. Before beginning the second stage of testing, the EXSUM system for deformation measurement was proposed and tested. Therefore, all six types of specimens were evaluated with the EXSUM deflection measurement setup using the MTS testing device. Variables whose effects were clearly defined in Stage ~ were eliminated from this stage of testing. Test Protocol. All six types of specimens (MI, M2, M3, CI, C2, and C3) were tested to study the effect of specimen sue and gradation on the resilient moduli of asphalt concrete CTable 131. Load levels of 40, 70, and 100 % of the SHRP P07 (November, 1992) recommended values were used in the tests. According to the SHRP P07 (November, 1992) procedure, He seating load is lO % of the total applied load and hence the cyclic load should be 90 % of He total applied load. Thus, the cyclic load applied was 36, 63, and 90 % of He recommended SHRP P07 (November, 1992) total load levels. These loads are tabulated in Table 17 for the three test temperatures. Table 17. Cyclic load levels used in Stage 2 tests expressed as a percentage of indirect tensile strength at 77°F Temperature P~, Public (%) (SHRP P07) ~ ~ (°F) (%) Level 1 Level 2 41 30 10.80 18.90 77 15 5.40 9.45 104 1 5 1 1.80 1 3.15 Level 3 27.00 13.50 4.50 The high seating load specified by SHRP P07 was found to cause significant damage to He specimens especially at temperatures of 77 and 104°F. At 41 °F the seating load required by the SHRP P07 (November, 1992) procedure exceeded 150 Ibs and was often as high as 300 Ibs for the asphalt concrete mixes and the specimen sizes used in the study. At 77°F and 104°F the specimens undergo important levels of creep under these seating loads. To minimize these problems a seating load equal to 5 % of the cyclic load level (E'<,,d,=) was used at 41°F and 4 % at 77 and 104°F. Even ~en, for the larger sample sizes used at 41°F, the seating load was still about 150 Ibs for the highest load level. Although quite high, this seating load does not cause damage at 41 °F. At 104°F damage appeared to be caused by seating loads above 20 Ibs. Therefore, a-maximum seating load of 20 Ibs was used at this temperature. Also for the smaller load levels, the 4% criteria resulted in some loads being less than 5 Ibs. A seating load of less than 5 Ibs could result because of load fluctuations in ache separation of loading strip from the surface of He specimen. Hence, to avoid loss of contact, a minimum seating load of 5 Ibs was used. 81

A havers~ne waveform was used with a 0.l sec. loading time and 0.9 sec. rest period. At 41 and 77°F data was recorded after 90, 100, and ~10 load repetitions. At 104°F the data was recorded after 40, 50, and 60 load repetitions. Data were collected at three preconditioning levels to increase Me amount of data. For the second stage of testing, a single sample was selected for each specimen type for testing at all temperatures. Testing began at 41°F and then at 77°F and 104°F. Finally, the specimens were retested at 77°F to ensure that excessive specimen damage had not occurred. The average values of resilient modulus and Poisson's Ratio from five consecutive load repetitions and the associated coefficients of variation are tabulated in Appendix ~ CTables ]-7 to ]-10~. In tills section test variables such as load pulse shape, rest period, load pulse duration, and number of preconditioning cycles are discussed in a qualitative manner. Detailed supporting data can be found elsewhere [341. Discussion of Results of Stage ~ Testing Load Pulse Shape. This experiment was conducted to determine if a 0. ~ sec. square shaped pulse, which has sometimes been used in diametral testing, gives the same resilient moduli as the more commonly used 0. ~ sec. haversine pulse. A decrease in resilient modulus occurs at low to moderate temperatures when a square load pulse is used when compared to a haversine load pulse. The difference in moduli values becomes greater wig increasing temperatures with the difference being as much as 2 to 3 times at 104°F. The area under the square load pulse is significantly larger than under the haversine waveform. Therefore, a greater amount of energy is applied to a specimen subjected to a square pulse. The larger applied energy causes greater horizontal deformation for the same applied load compared to the haversine wave and therefore results in a smaller resilient modulus. When a different shape pulse is used, Me area under the pulse should be made the same as the haversine pulse. Compared to a haversine pulse (Figure 40), Poisson's ratio is usually greater when a square pulse is used. Horizontal deformation increases approximately in proportion to the vertical deformation thus causing Poisson's ratio to increase. Since load is applied in the vertical direction, a time lag occurs for deformations to occur in the horizontal direction because of the viscoelastic behavior of asphalt concrete. Thus, for the haversine waveform, less time is available for the horizontal deformation to catch up with the applied load as the load starts to decrease once the peals is attained. For a square pulse the load is sustained over a time period and hence a larger horizontal deformation corresponding to the applied load is achieved. Vertical deformation is not as time~ependent as horizontal deformation, since the load is applied on the vertical diameter. Therefore, an increase in the ratio of horizontal deformation to vertical deformation would be expected for a square wave and hence a larger Poisson's ratio. The significant dependency of the resilient modulus on Me wave form makes it important to standardize He load pulse used in resilient modulus testing. Also, comparison of resilient moduli should be avoided where measured using different load pulse shapes. A haversine pulse should be used rather than a square pulse since it simulates the field loading condition better and causes less damage to the sample. Rest Period. There was little effect on resilient modulus when the ratio of rest period to loading pulse increased from 4 to 24. This finding was true for bow He medium and coarse gradation asphalt specimens . a, , . ~ _ _ ~ _ _ _ _ _ _ ~ , 82

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and temperatures from 4l0'F to 104°F. In some cases, the resilient moduli increased slightly. This increase in resilient modulus is perhaps partly due to the accumulation of a small amount of damage as the tests progressed. Also, for the last half of the test sequence during the longer rest periods, the larger seating loads may have prevented sample recuperation. The work of Monismith [16] also indicates that the beneficial effect of the longer rest period is not noticeable once the ratio of rest period to loading time exceeds 8. Load Pulse Duration. . ~.. ~, The load pulse duration in a pavement increases with increasing depth in the pavement. therefore, the erect on resilient modulus of the load pulse duration is of practical importance since it is desirable to test all asphalt specimens at the same pulse duration. Tests were performed on asphalt specimens having both medium and coarse aggregate gradations using load pulse duration times of 0.05 sec. to 0.2 sec. At 41°F, for the type M! medium gradation specimen, no trend in the effect of loading period on resilient moduli was observed. For the coarse gradation specimen (type C3), a slight reduction occurred in resilient modulus with increase in loading time for the haversine wave form and a slight increase in resilient modulus for the square load pulse. The observed differences in behavior may be due to the time dependent behavior of asphalt concrete and Me more severe condition of loading caused by Me square load pulse. The effect on resilient modulus of loading period Is not significant at 41°F. At this low temperature the specimens behave essentially like an elastic material and hence are less affected by Me changes in the loading time. At 77°F and 104°F the resilient moduli decrease considerably with increases in loading time. At these higher temperatures, larger loading times cause larger deformations with less recovery of the deformations occurring. Typically, Me coefficient of variation for resilient modulus ranges from O to 5 % wig some values as high as 10 %. Overall, the coefficient of variation in Poisson's ratio and resilient moduli is slightly smaller with increased load time (Figure 41~. Field data, collected at Me US- 421 test site in Norm Carolina, shows that a 0. ~ sec. loading pulse occurs at a depth of 2 in. under a vehicle moving at 10 mph which is in agreement with theory [2,351. Therefore, at normal traffic speeds the pulse time is much less than 0. ~ sec. Use of the conventional relatively long pulse time of 0. ~ sec., compared to the pulse time caused by normal traffic, causes more damage to the asphalt concrete and results in a lower resilient modulus than a faster pulse time. Hence the conventional 0. ~ sec. pulse is conservative. The use of a 0.05 sec. loading time is too small to achieve repeatable results even using an efficient loading system. A high speed data acquisition system is also required for a 0.05 sec. pulse. Maximum loads are also hard to achieve using asphalt concrete specimens at high temperatures using small loading times. A loading time of 0.2 sec. is too long to be representative of equivalent pulse times for even slow moving vehicles. Thus, the recommendation is made to continue to use the loading time of 0.1 sec. as specified in the SHRP P07 (November 1992) resilient modulus testing procedure for asphalt concrete. Preconditioning Cycles. At 41°F the resilient modulus (mr.el.x.a) did not significantly change with increasing number of preconditioning load cycles. However, at 77°F and 104°F He resilient moduli decreased consistently wig increasing number of preconditioning cycles. This decrease in resilient modulus probably occurred due to accumulation of specimen damage as preconditioning progressed. The purpose of preconditioning is to obtain stable deformations and hence consistent resilient moduli~roughout the test sequence. The coeff~cientof variation for resilient moduli and Poisson's ratios, 84

cM ~ is: ~ ~ ~ ~-~- ~x x it: sty Jo ~ N ~CO O _OOO [1, · ~ OOOO P°!J0d peon Jabuol 'uo!~e!Je~ Jo aeon 85

for the data collected for five consecutive load cycles, might indicate whether the deformations have become stable. At 41°F, no significant trend was observed. The second preconditioning level (100 cycles) appeared to be reasonable with regard to the variation in Poisson's ratio and resilient moduli and was chosen as Me preconditioning level for 41°F. As seen earlier, a significant trend was not evident in MR values so the choice of this level should not affect the resilient modulus value. At 77°F, the coefficient of variation of the five cycle resilient modulus data decreased as the number of preconditioning cycles increased from 25 to 75 or 150 repetitions. Also, the resilient moduli decreased suggesting more damage. For 77°F, the number of preconditioning cycles to use was selected to be between the 2nd and 3rd preconditioning levels. (i.e., between 75 and 100 preconditioning cycles). At 104°F, We 2nd and 3rd levels showed improved performance of resilient modulus values, both being almost comparable. The MR values kept decreasing with increasing number of preconditioning cycles. Also, keeping the number of preconditioning cycles small means less damage to the specimen. Thus, at 104°F a preconditioning level of 50 cycles was chosen for final testing. Calculation of Poisson's Ratio. In the first stage of testing, the values of resilient modulus and Poisson's ratio were computed in accordance with the SHRP P07(Nov. 1992) procedure as well as the elastic analysis. Poisson's ratios calculated from the SHRP P07 analysis (pr.sh.xv) were usually lower than those obtained using the elastic analysis (pr.el.xv). The difference was approximately 0.01 to 0.05 at 41°F, 0.05 to 0.15 at 77°F, and 0.05 to 0.20 at 104°F. Also, the SHRP P07 analysis with an assumed value of Poisson's ratio always gave significantly higher values of resilient moduli than those calculated from the elastic analysis with an assumed Poisson's ratio (i.e., mr.sh.x.a were always significantly higher than mr.el.x.a). Discussion of Results of Stage 2 Testing The average values of resilient modulus and Poisson's ratio from five consecutive load cycles and the associated coefficients of variation have been tabulated in Appendix ~ (rabies I-! ~ to I-14~. The test ID consists of four letters which indicate He following: (~) specimen type: MI, M2, M3, CI, C2, or C3; (2) load amplitude level: I, 2, or 3; (3) preconditioning level: I, 2, or 3. The elastic analysis was used since He over me~ods do not consider different gage lengths for measurement of vertical and horizontal deformations. Poisson's Ratio. Better Poisson's ratio results were obtained at the higher temperatures. For the first trial at 77°F (testing was done at 77°F before testing at 104°F), most of He Poisson's ratio values were between 0.2 and 0.5 with small five-cycle variances. The coefficient of variation for the Poisson's ratio values (pr.el.xm) improved (reduced) at higher load amplitudes. At the highest level of load, the coefficient of variation was less Can 5% in almost. all He cases. For the second trial at 77°F (testing done at 77°F after testing at 104°F), all He same specimens showed an increase in Poisson's ratio values, indicating that damage does increase Poisson's ratio (Figure 42~. Hence, Poisson's ratio serves as an indicator to the damage occurring in the specimen. However, for high load amplitudes Poisson's ratio values were not, comparatively, as different as Hey were for low amplitudes. This behavior could be a result of the load-history dependence of asphalt concrete. The specimen goes through different thermodynamic states and some of this process is irreversible. The thermodynamic state of He specimen changes after the largest load has been applied during the first trial. Hence, although the magnitude of 86

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loads for the smaller amplitude in the first and second trial is the same, the specimen behavior is different. However, when the largest load is applied again in the second trial, the specimen shows comparable behavior as it is very nearly at the same thermodynamic state as it was when the larger load was applied during the first trial. As before, the variation in Poisson's ratio for the second trial was small and it decreased with increasing load amplitude (Figure 43). At 77°F it appears that higher load amplitudes result in more reasonable Poisson's ratios and smaller variance in five cycle data. At 104°F, most Poisson's ratio values were between 0.4 and 0.6 with the coefficient of variation usually less than 5%. A trend of smaller coefficient of variation with increasing load amplitude was not seen. At load amplitude levels 2 and 3 the coefficients of variation were similar. For field cores, the use of a measured Poisson's ratio may lead to a higher estimation of resilient moduli values. For example, a constructed surface course has a resilient modulus of 500,000 psi and measured Poisson's ratio of 0.3. After 10 yes., the pavement needs maintenance and resilient moduli of field cores are evaluated. Because of an increase in Poisson's ratio due to damage, the measured resilient moduli after 10 yrs. might not show any significant decrease, thus resulting in an overestimation of the pavement condition. In such cases, the resilient moduli should be based on horizontal deformation and the initially measured value of Poisson's ratio of 0.3. Then, the calculated resilient moduli would represent the deterioration of the pavement. As more data becomes available, consideration should be given to the use of Poisson's ratio as a direct indicator of deterioration in an asphalt concrete pavement. Load Amplitude. Overall, at higher load amplitudes, the f~ve-cycle coefficient of variation for Poisson's ratio became lower with increased load amplitude at 41°F and 77°F. However, at 104°F, the five-cycle variance was almost equivalent for load amplitude levels 2 and 3. At 41°F there was an overall increase in resilient moduli (mr.el.x.a) with increasing load amplitude. The coefficient of variation in the resilient moduli decreases at higher load amplitudes. Also, the highest load level did not seem to cause any significant damage (based on measured vertical deformation as the tests progressed). Higher load amplitude is required to generate adequate values of deformation for measurement purposes. Thus, at 41°F, testing at the SHRP P07 (Nov. 1992) level of 30% of the indirect tensile strength at 77°F is recommended. The resilient moduli (mr.el.x.a) from the first trial at 77°F exhibited a small decrease with increasing load amplitude. However, resilient moduli values from the EXSUM setup (mr.el.xm.c) usually increased with increasing load amplitude. At the higher loads the resilient moduli (mr.el.x.a and mr.el.xm.c) agree better than at other levels. As before, the coefficient of variation reduced with increasing load amplitude. The results from the second trial at 77°F showed no trend in the mr.el.x.a values, but the coefficient of variation reduced with increases in load amplitude. A comparison of the resilient moduli values (mr.el.xm.c) at the highest load amplitude with the first trial at 77°F, revealed a good similarity except for the 4 in. diameter and 2.5 in. thick specimens (types M! and CI). The reduction in resilient moduli resulting from damage to the specimens was counteracted by the increase in Poisson's ratio due to damage. Thus it seems that once we are able to measure Poisson's ratio with confidence, the resilient moduli values should be calculated based on that value. So, if slight damage is occurring to the specimen, the decrease in resilient modulus due to the damage can be compensated by an increase in Poisson's ratio values. A comparison of resilient modulus (mr.el.x.a ~ and Poisson's ratio (pr.el.xm) values between the two trials suggest that while there was a decrease in resilient modulus values (Figure 42) of approximately 5% to 20%, there was a corresponding 5% to 25% increase in pr.el.xm values (Figure 42~. 88

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At 104°F, the overall trends indicate an increase in resilient moduli with increased amplitude for both mr.el.x.a data, from assumed Poisson's ratio and mr.el.xm.c data, from calculated Poisson's ratio. As with Poisson's ratio, the variance in the resilient moduli at the 2nd and 3rd load levels was reasonably similar although the scatter was relatively large. At 104°F, the specimen undergoes significant damage, as can be seen from a rapid increase in the permanent vertical deformation as the test progresses. Thus, to Limit the damage to minimal values, it becomes important to keep the load levels as small as possible, but large enough to maintain adequate specimen deformations and load control. Significant deformations were obtained at 104°F, even with small loads in the resilient modulus test. Hence, it is recommended that a smaller load amplitude of 3.5 to 4 % of He failure load should be used. This load should give essentially He same resilient moduli values (Appendix J. Table J-14). Recommended Seating Loads. SHRP recommended seating loads are suitable for testing at 41°F and 77°F, but at 104°F, the seating load should be reduced. The 10% seating load recommended by the SHRP P07 protocol is not necessary. Instead seating loads of 5%, 4%, and 4% of the total load to be applied at each cycle for resilient modulus testing are recommended at 41, 77 and 104°F, respectively. At 104°F, a minimum seating load of 5 Ibs. must be maintained, and the seating load should not exceed 20 Ibs. Specimen Size and Type Specimen Diameter. The effect of specimen diameter can be studied by comparing the resilient moduli and Poisson's ratios obtained for specimen types M! and M3, and C! and C3. From a comparison of resilient moduli and Poisson's ratios and their coefficients of variation, an influence of specimen diameter on specimen response is not apparent at 41°F. Tables I-~! to ]-14 (Appendix ]) show that the effect of specimen diameter on resilient modulus and Poisson's ratio seems to increase with increasing temperature. At higher temperatures the coefficient of variation reduced for the 6 in. specimen diameter. At 104°F, there was a 24% (medium gradation specimens) to 50% (coarse gradation specimens) decrease in resilient modulus (mr.el.x.a) compared to the 4 in. specimens. An assumed Poisson's ratio was used for both the gradations for the 6 in. diameter specimen (Figure 44~. However, at 77°F, only the coarse gradation specimen showed a decrease in resilient modulus with increase in diameter. Thus, it seems that at lower temperatures testing specimens of different sues is less likely to affect results than at higher temperatures. At higher temperatures specimens possess more non-homogeneity and this would cause a change in MR value with a change in diameter based on the aggregate to size ratio. Specimen Thickness. The effect of specimen thickness can be investigated by observing the difference in behavior between specimen types M! and M2, and C! and C2. Tables I-! ~ to I-14 (Appendix ]) show Hat no-significant trend was seen at any temperature in He five-cycle coefficients of variation. Also, there was no consistent trend in the resilient moduli values (mr.el.x.a). Since there is no difference in the five cycle variance, increasing the sample thickness will not help attain more repeatable results in the resilient modulus test. Specimen Gradation. The resilient moduli for coarse gradation specimens (C! & C2) were as much as 75 % higher than for the corresponding medium gradation specimens. This difference in MR increased with increasing temperature which is of significance for pavements constructed in regions having warm summer temperatures. For the 4 in. diameter specimens, the effect of gradation was smaller for the 4 in. thick specimens than for the 2.5 in. thick specimens (Figure 45~. Thus, as He specimen size, thickness, and diameter increases, He effect of gradation decreases. The coefficients of variation obtained for medium gradation specimens were less than for He coarse gradation specimens. The 90

4.0E+OS 3.SE+OS .= 3.0E+OS / /1 / 2SE+OS 20E+OS , , , 1.SE+OS 1.5E+OS 20E+OS 2SE+OS 3.0E+OS 3.SE+OS 4.0E+OS MR (psi), 4" diameter 3~ MG o CG Figure 44. Effect of specimen diameter on MR (mr.el.x.a - obtained from horiz. extensometer deformation using Elastic analysis and assumed By, for Stage 2 tests at 104°F 91

-- 3~ - ~ 2£- - ·zO~- ' 3~ 08 3~ 2£ +~ . - - 2£ . - 3.~ . - 1§ .. - - ,~ 1 ~ 4.~ o ~ x~ ~ Isis 1 1 x+ - , Ate- l E+ - 1~ - o Cc3 (b) 77°F qCE.gq~a art ~ 2~+a. I. - --,~ ~ ~ . x2 ~o ~ sol ~ USED .~ - 3£ - - , z~- Z£ + - - SEAM +- Z£~= Z£.- 3~.- ~R - , USA l ' 4'.~2~ ~ · sir ~ ~1= Figure 45. Effect of gradation on MR (mr.el.x.a - obtained from horiz. extensometer deformation using Elastic analysis and assumed it), at different temperatures and different specimen sizes for Stage 2 tests 92

differences In coefficient of variation for the two gradations were close to zero for the larger 6 in. diameter specimen that were 4.5 in. thick. Thus the medium gradation specimens can be tested using 4 in. diameter and 2;5 in. thick specimens, but the coarse gradation specimens should be tested using 6 in. diameter, 3.75 in. thick specimens to obtain good values of resilient moduli. Use of a 4 in. diameter specimen 2.5 in. thick is acceptable for testing medium gradation asphalt minces have a maximum aggregate size of about 3/4 in. However, for aggregate sizes greater than 3/4 in., a 6 in. diameter specimen 4.5 in. thick should be used to test these coarse gradation mixes. MULTI-LAB VALIDATION STUDY The details of the limited, multi-lab validation diametral resilient modulus test can be found in Appendix H. The general purpose of this study was to determine, with statistical analysis, the effects of multiple operators, retesting specimens, and assumed versus calculated Poisson's ratio on the resilient moduli determined for identical specimens. The specimens were tested at three different laboratories, using similar equipment but different equipment operators. The specific conclusions of the multi-lab validation study are: 1. The recommended testing protocol yields better estimates of Poisson's ratio, but the use of an assumed Poisson's ratio yields more consistent moduli. 2. The experience of the operator has a significant effect on the resilient modulus values during testing. The more experienced the operator, the less variation in the resilient moduli values. The difference in the resilient moduli for calculated versus assumed Poisson's ratio is also much smaller with an experienced operator. The coefficient of variation of the resilient moduli determined from calculated and assumed Poisson's ratios does, as indicated by the primary test program, increase with increasing temperature. 4. The number of times a specimen has been tested also has an effect on the resilient modulus. Structural damage to the retested specimens has a larger effect on resilient modulus than He lab-to- lab variation. The statistical analysis was performed on a very limited number of samples, making the interpretation of the statistical results somewhat less reliable. An extensive validation study is recommended to obtain better evaluations on sample-to-sample and lab-to-lab variations. COMPARISON OF LABORATORY AND BACKCALCULATED RESILIENT MODULI Resilient moduli for use in design are presently determined by both direct laboratory measurement and by backcalculation from falling weight deflectometer (FOOD) tests. Both laboratory tests and backcalculation procedures from field data have important limitations and advantages. In laboratory tests, fabrication of test specimens Hat duplicate field conditions and simulating in-situ stress states and environmental factors are difficult. In backcalculation procedures, the theory used assumes very ideal behavior of the materials (i.e., homogeneous, linear elastic, isotopic). Such materials are not found in pavements. The purpose of this study was to compare He resilient modulus determined using the proposed 93

laboratory procedure with FWD backcalculated values. A field test section on U.S. 421 in Norm Carolina was used to obtain field data and laboratory test specimens. The details of this study are given in Appendix T. however the specific conclusions of this study are: The backcalculated and laboratory AC resilient modulus values are similar if the field data is obtained on asphalt concrete layers less than 4 in. Hick. 2. There is a significant difference between the laboratory and field AC resilient moduli if the field data is obtained on sections with total asphalt concrete thicknesses of 9 in. or more. Since the data used In this study is rawer Emoted, it is not clear how much different the laboratory resilient modulus is from the FWD backcalculated modulus. Once LTPP field test data is fully collected and analyzed, a better assessment can be made on this issue. SUMMARY AND CONCLUSIONS Existing methods were reviewed for empirically predicting the resilient modulus for asphalt concrete. The Asphalt Institute Method, corrected for locally used materials and testing devices appears to offer a beginning point for developing a practical alternative to performing resilient modulus test on a routine basis. Different laboratory test methods, such as the repeated load biaxial test and the diametral test, apply different stress conditions to a specimen. As a result, the resilient moduli obtained from these different methods do not always agree. The repeated load diametral test was concluded to be the most practical, realistic method for evaluating the resilient modulus of asphalt concrete. An extensive resilient modulus testing program was, therefore, carried out using the diametral test. All tests were conducted using a 0. ~ sec., haversine shaped loading pulse using a closed loop, electro-hydraulic testing system. Experiments were performed to identify the most accurate and reliable diametral testing device. Loading equipment evaluated in the study were as follows: (~) Retina device, (2) MTS device, (3) Baladi's device and (4) SHRP Load Guide ~G) device. The following four deformation measuring devices were also studied: (~) stand along EVDTs, (2) an extensometer mounted on the specimen, (3) a gage-point-mounted (GPM) setup and (4) a special combined measurement system using a surface mounted EVDT to measure vertical deformation and externally mounted transducers to measure horizontal deformation. Diametral resilient modulus tests were performed on laboratory prepared asphalt concrete specimens having a coarse and medium gradation as well as on field cores and synthetic specimens. Temperatures of 41°F, 77°F and 104°F were used in these tests. In performing these tests, equipment calibration, including the use of synthetic specimens, was found to be a critical aspect required to obtain reliable test results. Specimen rocking was also determined to be an important consideration in selecting an appropriate loading device. A square wave load pulse produces more damage and a significantly smaller resilient modulus compared to a haversine wave. Therefore the square wave load pulse should not be used for resilient modulus testing since it is not representative of He pulse developed in the field. 94

5. The loading pulse time significantly affects He resilient modulus. A loading time of 0.2 sec. reduces Me values. and produces more damage than for a 0. ~ sec. pulse. A shorter loading time ~ , . ~ , _ ~ rat ~- ~ ~ ~ ~ ~ ~ ~ ~ ~ · . · . . ~ ~ .~ . ~ a~ -, ~ .~ of ().()5 sec. is representative ot~ high vehicle speeds, but is not practical as the repeatability of the test is poor and accurate load control at higher temperatures is hard to achieve. A loading time of 0.] sec. is therefore proposed which is in agreement with the SHRP P07 (Nov. 1992) procedure. 6. 7 8. 9. The ratio of rest period to loading period of 4 and 24 used in this StU6Y 40 not have a significant _ , - , . . ~ . . . .. . . . . . . . . . #. .. . . enect on the resilient module values. Also past research has shown that a rest perlocl/loaulng time ratio greater Han ~ provides no extra benefit. A rest period/Ioading time ratio of 9, as presently used by SHRP, is a good choice. At 77 and 104°F the resilient moduli decreased wig increasing number of preconditioning cycles. Based on a study of trends in the coefficient of variation for MR , the following preconditioning levels were Axed at the three deferent test temperatures to make resilient modulus test results more repeatable: 41° F: 77° F: 104° F: 100 cycles 100 cycles 50 cycles A significant difference between resilient moduli and Poisson's ratio is obtained using the SHRP P07 (Nov. 1992) analysis and the elastic analysis. The elastic analysis is essentially the same as the ASTM analysis except it allows the use of different deformation measurement gage distances while the ASTM analysis does not. The SHRP equations give resilient moduli values as much as 45% higher when an assumed Poisson's ratio is used. The elastic analysis with the appropriate coefficients for measurement geometry used in testing is the recommended approach. 10. ~- 12. Poisson's ratios obtained using the EXSUM system at higher temperatures are reasonable. The system can be modified with further use to make it simpler. The 4 in. diameter and 2.5 in. thick specimens may be acceptable for testing medium gradation mixes, but 6 in. diameter and 4.5 in. thick specimens should be used to test coarse gradation mixes. Grain sue distributions for the medium and coarse gradation mixes are given in Appendix B. Table Be-. SHRP recommended loads are suitable for testing at 41°F and 77°F, but at 104°F, the load should be reduced. The 10% seating load recommended by the SHRP P07 protocol is not necessary. Instead seating loads of 5, 4, and 4% of the total load to be applied at each load cycle for resilient modulus testing are recommended at Ill, 77, and 104°F, respectively. At 104°F, a minimum load of 5 Ibs. must be maintained, and the seating load should not exceed 20 Ibs. An Improved diametral test was developed to evaluate the resilient modulus of asphalt concrete. The proposed test procedure is given in Appendix C. A closed loop, electro-hydraulic testing system and also a data acquisition system is used to apply a 0. ~ sec. haversine-shaped load pulse to a disk-shaped specimen. 13. Loading Device. The SHRP EG device minimizes rocking of the specimen. The good performance is apparently due to (~) use of two guide columns, (2) a counter-balance system, (3) 95

an innovative semi-rigid connection between the upper plate and the load actuator, and (4) its sturdiness. The disadvantages are its bulkiness, complication of use, possible inertia from the counter-balance system, friction in the guide columns, and limitation of the sue of the sample that can be used. 14. 15. 16. 17. Ad. 19. Mountable Extensometer. A mountable extensometer device, compared to the stand-alone EVDT measurement device, provides less variance and hence better repeatability within the five consecutive cycles used for resilient modulus determination. However, using the SHRP EG device EVDTs gave comparable performance to the mountable extensometer. Mountable deformation measurement devices are recommended for resilient modulus testing because of the smaller variability. Poisson's Ratio Importance. Poisson's ratio is one of the most important parameters influencing the resilient modulus. The variation In MR values due to the testing axis dependency and different lengths of rest periods are almost negligible compared to the magnitude of difference in the MR values from assumed and calculated Poisson's ratios. Poisson's ratio should be evaluated using the EXSUM deformation measurement system. EXSUM Deformation Measurement Device. The proposed EXSUM deformation measurement system provides a promising measurement method for determination of consistent and reasonable Poisson's ratios. At 41°F, however, increase In variability occurs due to misalignment and rocking which become more Important for the small deformations occurring at low temperatures. Use of the SHRP EG device, or its modification, together with the EXSUM setup ensures obtaining reasonable values of Poisson's ratio even at low temperatures. The use of the EXSUM setup requires an increase in testing time compared to conventional measurement systems because of the significant time required for mounting the EVDT on the specimen. Preconditioning. Specimens were subjected to 3 different numbers of preconditioning load cycles at each temperature. No significant difference was observed in the variation of resilient moduli and Poisson's ratio for the last 5 load cycles for He largest two preconditioning cycles. However, MR values did decrease with increasing number of preconditioning cycles. For 41 °F and 77°F, 1 00 p recond itio ning cycl es are reco mmend ed wh il. e th e us e of 50 cy c I es i s r e co mm en d ed at 1 04 ° F . Calculation of MR. A significant difference exists between resilient moduli and Poisson's ratio values computed using the SHRP PO7 analysis and the elastic analysis used in this study which is similar to the ASTM analysis. The SHRP analysis gives higher values when an assumed Poisson's ratio is used as compared to the elastic analysis with an assumed Poisson's ratio. Load Amplitude. The load amplitudes recommended in SHRP protocol are suitable for testing at 41°F and 77°F, but at 104°F a smaller load should be used. Load levels corresponding to 30, 15, and 4% of the indirect tensile strength at 77°F are recommended for testing at 41°F, 77°F, and 104°F, respectively. 96

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