**Suggested Citation:**"APPENDIX C. LABORATORY EVALUATION OF INFLUENCE OF GEOSYNTHETICS ON CROSS-ANISOTROPY AND PERMANENT DEFORMATIONOF UNBOUND GRANULAR MATERIAL." National Academies of Sciences, Engineering, and Medicine. 2017.

*Quantifying the Influence of Geosynthetics on Pavement Performance*. Washington, DC: The National Academies Press. doi: 10.17226/24841.

**Suggested Citation:**"APPENDIX C. LABORATORY EVALUATION OF INFLUENCE OF GEOSYNTHETICS ON CROSS-ANISOTROPY AND PERMANENT DEFORMATIONOF UNBOUND GRANULAR MATERIAL." National Academies of Sciences, Engineering, and Medicine. 2017.

*Quantifying the Influence of Geosynthetics on Pavement Performance*. Washington, DC: The National Academies Press. doi: 10.17226/24841.

**Suggested Citation:**"APPENDIX C. LABORATORY EVALUATION OF INFLUENCE OF GEOSYNTHETICS ON CROSS-ANISOTROPY AND PERMANENT DEFORMATIONOF UNBOUND GRANULAR MATERIAL." National Academies of Sciences, Engineering, and Medicine. 2017.

*Quantifying the Influence of Geosynthetics on Pavement Performance*. Washington, DC: The National Academies Press. doi: 10.17226/24841.

**Suggested Citation:**"APPENDIX C. LABORATORY EVALUATION OF INFLUENCE OF GEOSYNTHETICS ON CROSS-ANISOTROPY AND PERMANENT DEFORMATIONOF UNBOUND GRANULAR MATERIAL." National Academies of Sciences, Engineering, and Medicine. 2017.

*Quantifying the Influence of Geosynthetics on Pavement Performance*. Washington, DC: The National Academies Press. doi: 10.17226/24841.

**Suggested Citation:**"APPENDIX C. LABORATORY EVALUATION OF INFLUENCE OF GEOSYNTHETICS ON CROSS-ANISOTROPY AND PERMANENT DEFORMATIONOF UNBOUND GRANULAR MATERIAL." National Academies of Sciences, Engineering, and Medicine. 2017.

*Quantifying the Influence of Geosynthetics on Pavement Performance*. Washington, DC: The National Academies Press. doi: 10.17226/24841.

**Suggested Citation:**"APPENDIX C. LABORATORY EVALUATION OF INFLUENCE OF GEOSYNTHETICS ON CROSS-ANISOTROPY AND PERMANENT DEFORMATIONOF UNBOUND GRANULAR MATERIAL." National Academies of Sciences, Engineering, and Medicine. 2017.

*Quantifying the Influence of Geosynthetics on Pavement Performance*. Washington, DC: The National Academies Press. doi: 10.17226/24841.

**Suggested Citation:**"APPENDIX C. LABORATORY EVALUATION OF INFLUENCE OF GEOSYNTHETICS ON CROSS-ANISOTROPY AND PERMANENT DEFORMATIONOF UNBOUND GRANULAR MATERIAL." National Academies of Sciences, Engineering, and Medicine. 2017.

*Quantifying the Influence of Geosynthetics on Pavement Performance*. Washington, DC: The National Academies Press. doi: 10.17226/24841.

**Suggested Citation:**"APPENDIX C. LABORATORY EVALUATION OF INFLUENCE OF GEOSYNTHETICS ON CROSS-ANISOTROPY AND PERMANENT DEFORMATIONOF UNBOUND GRANULAR MATERIAL." National Academies of Sciences, Engineering, and Medicine. 2017.

*Quantifying the Influence of Geosynthetics on Pavement Performance*. Washington, DC: The National Academies Press. doi: 10.17226/24841.

**Suggested Citation:**"APPENDIX C. LABORATORY EVALUATION OF INFLUENCE OF GEOSYNTHETICS ON CROSS-ANISOTROPY AND PERMANENT DEFORMATIONOF UNBOUND GRANULAR MATERIAL." National Academies of Sciences, Engineering, and Medicine. 2017.

*Quantifying the Influence of Geosynthetics on Pavement Performance*. Washington, DC: The National Academies Press. doi: 10.17226/24841.

**Suggested Citation:**"APPENDIX C. LABORATORY EVALUATION OF INFLUENCE OF GEOSYNTHETICS ON CROSS-ANISOTROPY AND PERMANENT DEFORMATIONOF UNBOUND GRANULAR MATERIAL." National Academies of Sciences, Engineering, and Medicine. 2017.

*Quantifying the Influence of Geosynthetics on Pavement Performance*. Washington, DC: The National Academies Press. doi: 10.17226/24841.

**Suggested Citation:**"APPENDIX C. LABORATORY EVALUATION OF INFLUENCE OF GEOSYNTHETICS ON CROSS-ANISOTROPY AND PERMANENT DEFORMATIONOF UNBOUND GRANULAR MATERIAL." National Academies of Sciences, Engineering, and Medicine. 2017.

*Quantifying the Influence of Geosynthetics on Pavement Performance*. Washington, DC: The National Academies Press. doi: 10.17226/24841.

**Suggested Citation:**"APPENDIX C. LABORATORY EVALUATION OF INFLUENCE OF GEOSYNTHETICS ON CROSS-ANISOTROPY AND PERMANENT DEFORMATIONOF UNBOUND GRANULAR MATERIAL." National Academies of Sciences, Engineering, and Medicine. 2017.

*Quantifying the Influence of Geosynthetics on Pavement Performance*. Washington, DC: The National Academies Press. doi: 10.17226/24841.

**Suggested Citation:**"APPENDIX C. LABORATORY EVALUATION OF INFLUENCE OF GEOSYNTHETICS ON CROSS-ANISOTROPY AND PERMANENT DEFORMATIONOF UNBOUND GRANULAR MATERIAL." National Academies of Sciences, Engineering, and Medicine. 2017.

*Quantifying the Influence of Geosynthetics on Pavement Performance*. Washington, DC: The National Academies Press. doi: 10.17226/24841.

**Suggested Citation:**"APPENDIX C. LABORATORY EVALUATION OF INFLUENCE OF GEOSYNTHETICS ON CROSS-ANISOTROPY AND PERMANENT DEFORMATIONOF UNBOUND GRANULAR MATERIAL." National Academies of Sciences, Engineering, and Medicine. 2017.

*Quantifying the Influence of Geosynthetics on Pavement Performance*. Washington, DC: The National Academies Press. doi: 10.17226/24841.

**Suggested Citation:**"APPENDIX C. LABORATORY EVALUATION OF INFLUENCE OF GEOSYNTHETICS ON CROSS-ANISOTROPY AND PERMANENT DEFORMATIONOF UNBOUND GRANULAR MATERIAL." National Academies of Sciences, Engineering, and Medicine. 2017.

*Quantifying the Influence of Geosynthetics on Pavement Performance*. Washington, DC: The National Academies Press. doi: 10.17226/24841.

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C-1 APPENDIX C. LABORATORY EVALUATION OF INFLUENCE OF GEOSYNTHETICS ON CROSS-ANISOTROPY AND PERMANENT DEFORMATION OF UNBOUND GRANULAR MATERIAL The application of geosynthetics has potential abilities to reduce the thickness of base courses, improve performance, and extend the service life of pavement structures. Accurate and efficient laboratory characterizations of geosynthetic-reinforced materials are important for including geosynthetic products in pavement design. To develop a laboratory methodology compatible with the current Pavement ME Design, it is necessary to quantify the characteristics of geosynthetic reinforcement in terms of the resilient properties and permanent deformation properties of the geosynthetic-reinforced unbound granular material (UGM). Mechanistic Models for Geogrid-Reinforced UGMs Cross-Anisotropic Properties of Reinforced UGMs UGMs exhibit cross-anisotropy characteristics. The constitutive model used to characterize the cross-anisotropic behavior is shown in Equation C-1. 1 1 xy xx x x x x x y yxy xy x x y x E E E E E E Ï Ï Ï Îµ Ï ÎµÏ Ï Ï ï© ï¹ â â ï¬ ï¼ïª ïº ï¬ ï¼ï¯ ï¯ïª ïº =ï ï½ ï ï½ïª ïº ï® ï¾ï¯ ï¯ â âïª ïº ï® ï¾ïª ïºï« ï» (C-1) where xÏ is the stress in the horizontal direction; yÏ is the stress in the vertical direction; xÎµ is the strain in the horizontal direction; yÎµ is the strain in the vertical direction; xE is the resilient modulus in the horizontal direction; yE is the resilient modulus in the vertical direction; xxÎ½ is the Poissonâs ratio in the horizontal plane; and xyÎ½ is the Poissonâs ratio in the vertical plane. xE , yE , xxÎ½ , and xyÎ½ are the cross-anisotropic properties of UGMs. Stress-Dependent Permanent Deformation Properties of Reinforced UGMs A new mechanistic-empirical rutting model is proposed to evaluate the stress-dependent permanent deformation characteristics of geogrid-reinforced and unreinforced UGMs, as shown in Equation C-2. The proposed rutting model is able to determine the accumulated permanent deformation at any specific stress state and number of load repetitions. ( ) ( )0 2 1m nNp e J I K Î²Ï Îµ Îµ Î± ï¦ ï¶ âï§ ï·ï¨ ï¸ = + (C-2) ( ) 2sin 3 3 sin Ï Î± Ï= â (C-3) ( ) 6cos 3 3 sin cK ÏÏ â = â (C-4)

C-2 where 2J is the second invariant of the deviatoric stress tensor; 1I is the first invariant of the stress tensor; 0Îµ , Ï , Î² , m , and n are model coefficients; and c and Ï are the cohesive shear strength and friction angle, respectively. In this model, the two terms, 2J and 1I KÎ± + , are incorporated into the Tseng-Lytton model (1) and used to reflect the influence of a stress state on the permanent deformation characteristics of UGMs. The concept of the proposed rutting model is illustrated in Figure C-1. The Drucker- Prager plastic yield criterion (2) was applied in this study. As shown in Figure C-1, the black dot represents the current stress state in the 1 2I Jâ plane. The term of 2J represents the softening effects of the deviatoric shear stress on the UGM, and a higher 2J yields a larger permanent deformation. Thus, the power coefficient m is always a positive number. In addition, the term 1I KÎ± + indicates the hardening effect of the hydrostatic stress on the UGM, which is highly affected by the material cohesion and internal friction angle. A higher 1I KÎ± + value results in a smaller plastic deformation, so the power coefficient n is always a negative value. Figure C-1. Illustration of the Proposed Rutting Model Based on Drucker-Prager Plastic Yield Criterion Materials and Experiment Materials Aggregate One crushed granite material was used in this study. The gradation of the selected aggregate material is shown in Table C-1. It has a maximum dry density of 2.16Ã103 kg/m3 and an optimum water content of 6.7 percent. The compacted aggregate specimen has a cohesion of 20.2 kPa and an internal friction angle of 51.3 degrees. Failure Envelope Hardening Capacity Softening Stress Current Stress State à¶¥Ü¬à¬¶ I1 à¶¥Ü¬à¬¶ = Î±Ü«à¬µ + Ü

C-3 Table C-1. Gradation of Crushed Granite Aggregate Sieve Size (mm) 25.4 19.0 12.7 9.5 4.75 2.36 1.18 0.6 0.075 Passing Percentage (%) 100 97 86 68 46 30 20 15 4.1 Geosynthetic Three types of geogrids, TX-1, TX-2, and BX-3, and one type of geotextile, GT-4, were selected to reinforce the UGMs. âTXâ denotes that the aperture shape of the geogrid is triangular. âBXâ means the aperture shape of the geogrid is rectangular. âGTâ means the geosynthetic product is a geotextile. The physical and mechanical properties of the selected geogrids and geotextiles are shown in Tables C-2 and C-3, respectively. Table C-2. Physical and Mechanical Properties of the Selected Geogrids Geogrid Type Aperture Shape Aperture Dimension (mm) Tensile Sheet Stiffnessa (kN/m) MDb XMDc TX-1 Triangle 40Ã40Ã40 225 225 TX-2 Triangle 40Ã40Ã40 300 300 BX-3 Rectangle 25Ã33 300 450 a Tensile sheet stiffness values are at 0.5% tensile strain for TX geogrid and at 2% tensile strain for BX geogrid. b MD=machine direction. c XMD=cross-machine direction. Table C-3. Material Properties of the Selected Geotextile GT-4 Material Properties Test Method Unit Minimum Average Roll Value Test Modulus @ 2% strain ASTM D4595 kN/m 1313.3 Flow Rate ASTM D4491 l/min/m2 3055.5 Permittivity ASTM D4491 sec-1 1.0 Apparent Opening Size ASTM D4791 mm 0.43 Pore Size O95 ASTM D6767 microns 3503 Pore Size O50 ASTM D6767 microns 1853 Factory Seam Strength ASTM D4884 kN/m 43.8 UV Resistance (at 500 hours) ASTM D4355 % strength retained 80 Geosynthetic-Reinforced and Unreinforced Aggregate Specimens The geosynthetic-reinforced and unreinforced aggregate specimens were fabricated as 15-cm diameter and 15-cm-high cylinders at the optimum water content using a modified compactive effort. The effect of the geogrid depends upon its location within the base course. To evaluate this effect, the geogrid was placed in the middle of the specimen, one-quarter below the middle of the specimen, and at the bottom of the specimen, as shown in Figure C-2.

C-4 Figure C-2. Geosynthetic Location in UGM Specimen Test Methods Cross-Anisotropy Test The cross-anisotropy tests were conducted on both the geogrid-reinforced and unreinforced aggregate specimens using the universal testing machine (UTM) with a rapid triaxial test (RaTT) cell. Figure C-3 shows the configuration of the cross-anisotropy test. Prior to testing, the RaTT cell was moved downward to encompass the specimen. The confining pressure was applied directly to the specimen by the RaTT cell via a pneumatic bladder. The dynamic axial load was applied to the specimen through the loading frame of the UTM. In pre- conditioning, the confining pressure was controlled at 103.4 kPa, and a 103.4 kPa deviatoric axial load was applied for 500 repetitions. Table C-4 shows the cross-anisotropy test protocol developed by Texas A&M University (3). According to the cross-anisotropic constitutive model, three stress modes were used in the loading protocol, including the compression, shear, and extension modes, which are detailed below. (a) Control specimen (b) Geosynthetic-reinforced in the middle (c) Geosynthetic-reinforced one- quarter below the middle (d) Geosynthetic-reinforced at the bottom 15 cm 15 cm 7.5 cm 15 cm 3.75 cm 15 cm 15 cm

C-5 Table C-4. RLT Test Protocol for Determining Cross-Anisotropic Properties of Geosynthetic-Reinforced and Unreinforced UGM Stress State Static Stress (kPa) Dynamic Stress (kPa) Compression Shear Extension yÏ xÏ c yÏ c xÏ s yÏ sxÏ eyÏ exÏ 1 40 25 5 0 10 -5 -5 5 2 50 25 10 0 10 -5 -10 5 3 70 40 10 0 10 -5 -10 10 4 130 60 20 0 20 -10 -10 10 5 150 70 20 0 20 -10 -10 10 6 170 100 20 0 20 -10 -20 20 7 220 120 30 0 30 -15 -20 20 8 250 140 30 0 30 -15 -20 20 9 250 120 30 0 30 -15 -20 20 10 250 105 30 0 30 -15 -20 20 Compression Mode In the compression mode, the radial stress was kept constant while the axial stress was dynamically cycled in an increment of yÏÎ , as illustrated in Equation C-5. 1 1 xy xx c x c x x x xc y c xy xy yc x x y x E E E E E E Ï Ï Ï Îµ Ï Ï Ï Îµ Ï ï© ï¹ â â ï¬ ï¼Îïª ïº ï¬ ï¼Îï¯ ï¯ ï¯ ï¯ïª ïº Î =ï ï½ ï ï½ïª ïº Îï¯ ï¯ï¯ ï¯ ï® ï¾ â â Îïª ïº ï® ï¾ïª ïºï« ï» (C-5) where cxÎµÎ is the change in the radial strain due to an infinitesimal change in the axial stress c yÏÎ ; cyÎµÎ is the change in the axial strain due to an infinitesimal change in the axial stress cyÏÎ ; and cxÏÎ is zero. Shear Mode In the shear mode, an increment of the dynamic axial stress, syÏÎ , was applied to the sample while the radial stress was reduced by a small change in the dynamic stress, sxÏÎ , such that 12 s s x yÏ ÏÎ = â Î . Equation C-6 is constructed for the shear mode. 1 1 xy xx s x s x x x xs y s xy xy ys x x y x E E E E E E Ï Ï Ï Îµ Ï Ï Ï Îµ Ï ï© ï¹ â â ï¬ ï¼Îïª ïº ï¬ ï¼Îï¯ ï¯ ï¯ ï¯ïª ïº Î =ï ï½ ï ï½ïª ïº Îï¯ ï¯ï¯ ï¯ ï® ï¾ â â Îïª ïº ï® ï¾ïª ïºï« ï» (C-6)

C-6 The change in the first stress invariant, 1IÎ , is calculated to be zero, as shown in Equation C-7: 1 12 2 02 s s s s y x y yI Ï Ï Ï ÏÎ = Î + Î = Î â Ã Î = (C-7) The incremental change of the second deviatoric stress invariant, 2sJÎ , is written as: ( ) ( ) 2 2 1 2 2 2 1 3 3 4 s s s s s s y x x x y s y J I I Ï Ï Ï Ï Ï Ï Î = Î â Î ï© ï¹ = â Î Î + Î + Î Îïª ïºï« ï» = Î (C-8) where 2IÎ is the incremental change of the second stress invariant. The change in the strain energy, sEÎ , is given in the following equation: ( ) ( )1 12 2s s s s s s s s s sx x y y x x y y xE Ï Îµ Ï Îµ Ï Îµ Ï Îµ ÎµÎ = Î Î + Î Î + Î Î = Î Î â Î (C-9) Since the total work on a deformable body is path independent due to the law of energy conservation, the work performed on the unit volume, dW , is formulated in terms of stress invariants, as shown in Equation C-10: 1 1 21 2 4 29 2 y y y xy xx y x x x xy E E EI dI dJdW E E E E G Î½ Î½ ï© ï¹ = + â â +ïª ïºï« ï»ï² ï²ï ï (C-10) Since the first stress invariant, 1IÎ , is zero, the change in the strain energy, sEÎ , is formulated in Equation C-11 based on Equation C-10: 2 2 s s xy JE G ÎÎ = (C-11) By substituting Equations C-8 and C-9 into Equation C-11, the shear modulus in the vertical plane is then determined, as shown in Equation C-12: ( ) 3 4 s y xy s s y x G Ï Îµ Îµ Î = Î â Î (C-12) Extension Mode In the extension mode, the static axial stress yÏ was reduced by a small change in the dynamic stress eyÏÎ , and the radial stress xÏ was increased by a small dynamic stress exÏÎ . Therefore, in each loading cycle, the aggregate specimen was loaded to ( ),e e e ey y x xÏ Ï Ï Ïâ Î + Î and was unloaded to ( ),e ey xÏ Ï . The constitutive equation is constructed for the extension mode in Equation C-13.

C-7 1 1 xy xx e x e x x x xe y e xy xy ye x x y x E E E E E E Ï Ï Ï Îµ Ï Ï Ï Îµ Ï ï© ï¹ â â ï¬ ï¼Îïª ïº ï¬ ï¼Îï¯ ï¯ ï¯ ï¯ïª ïº Î =ï ï½ ï ï½ïª ïº Îï¯ ï¯ï¯ ï¯ ï® ï¾ â â Îïª ïº ï® ï¾ïª ïºï« ï» (C-13) where exÎµÎ is the change in the radial strain due to exÏÎ and eyÏÎ ; and eyÎµÎ is the change in the axial strain due to exÏÎ and eyÏÎ . As seen in Table C-2, 10 stress states were associated with corresponding dynamic stresses. At each stress state, every loading cycle of the dynamic stress consisted of 1.5 seconds of loading and 1.5 seconds of unloading. The LVDTs measured the vertical and horizontal deformations of the specimen. The test data were used to calculate the anisotropic properties of geogrid-reinforced and unreinforced aggregate specimens using the system identification method. Figure C-3. Configuration of the Repeated Load Triaxial Test Permanent Deformation Test Compared to the cross-anisotropy test, the permanent deformation test used the same UTM configuration (see Figure C-3) but a different test module. The axial load follows a haversine shape with 0.1-second load period and 0.9-second rest period in every load cycle. After pre-conditioning, the specimens were subjected to 10,000 cycles of repeated load at a specified stress level. The LVDTs only measured the vertical deformations of the specimen. The test data were used to determine the permanent deformation properties of geogrid-reinforced and unreinforced aggregate specimens. To evaluate the effect of stress level on the geogrid reinforcement of UGM specimens, a new permanent deformation test protocol was developed, as shown in Table C-5. The proposed

C-8 test protocol includes seven stress states (i.e., Stress States 1â7) for model calibration and two stress states (i.e., Stress States 8 and 9) for model validation. Stress States 1, 2, 3, 4, and 9 apply the same I1 with various J2, whereas Stress States 1, 5, 6, 7, and 9 employ the same J2 but different I1. This test protocol allows quantifying the influence of the two stress terms, I1 and J2, on the permanent deformation behavior of geogrid-reinforced and unreinforced UGM specimens, individually. Table C-5. RLT Test Protocol for Determining Permanent Deformation Properties of Geosynthetic-Reinforced and Unreinforced UGMs Stress State Confining Pressure, Ï3 (kPa) Deviatoric Stress, Ïd (kPa) Bulk Stress, I1 (kPa) Second Invariant of Shear Stress Tensor, J2 (kPa2) Comments 1 27.6 192.9 275.6 12406.0 Model Calibration 2 48.2 130.9 275.6 5712.5 3 68.9 68.9 275.6 1582.4 4 91.9 0 275.6 0 5 48.2 192.9 337.6 12406.0 6 68.9 192.9 399.6 12406.0 7 89.6 192.9 461.6 12406.0 8 34.5 172.3 275.6 9890.0 Model Validation 9 103.4 192.9 503.0 12406.0 Test Results Impact of Geosynthetic on Cross-Anisotropy Characteristics of UGMs The measured vertical and horizontal resilient deformations in the cross-anisotropy test were analyzed using the system identification method to back-calculate the vertical and horizontal resilient moduli, yE and xE , respectively, based on the constitutive model presented in Equation C-1. The determined vertical and horizontal moduli and anisotropic ratio of the geosynthetic-reinforced specimens were compared to those of the unreinforced specimens (the control) by calculating the normalized modulus ratio of the geosynthetic-reinforced specimen to the unreinforced specimen, as shown in Equations C-14âC-16. x geo x control E Normalized HorizontalModulusRatio E â â = (C-14) y geo y control E Normalized Vertical Modulus Ratio E â â = (C-15) geo control AR Normalized Anisotropic Ratio AR = (C-16)

C-9 where x geoE â is the horizontal resilient modulus of the geogrid-reinforced specimen; x controlE â is the horizontal resilient modulus of the unreinforced specimen; y geoE â is the vertical resilient modulus of the geogrid-reinforced specimen; y controlE â is the vertical resilient modulus of the unreinforced specimen; geoAR is the anisotropic ratio of the geosynthetic-reinforced specimen; and controlAR is the anisotropic ratio of the unreinforced specimen. The comparison results are shown in Table C-5. Table C-6 shows that the normalized horizontal and vertical modulus ratios of all three types of geogrid-reinforced specimens are larger than 100 percent at every stress state, which indicates that the geogrid increases both the vertical and horizontal moduli of the UGM specimen since the total elastic deformation of the specimen is restricted due to the adding of the geogrid in the UGMs. However, the inclusion of the geogrid does not influence the anisotropy ratio of the UGM. Compared to the geogrid TX-1, the geogrid TX-2 provides slightly higher horizontal and vertical modulus ratios at most of the stress states, which demonstrates that the geogrid with a higher sheet stiffness is more beneficial for the reinforcement. Compared to the geogrid TX-1 and TX-2, the geogrid BX-3 provides comparable reinforcement on the horizontal and vertical resilient moduli of UGM. This indicates that the aperture shape of the geogrid does not significantly affect the resilient modulus of the UGM specimen. Different from the geogrids, the geotextile only reinforces the horizontal modulus of the UGM specimen, which results in the increase in anisotropic ratio of the UGM. Tables C-6, C-7, and C-8 also present the effect of geogrid location on the horizontal and vertical resilient moduli of the UGM. The normalized modulus ratios when the geogrid is placed in the middle or one-quarter below the middle of the specimen are larger than 100 percent at every stress state, while those of the specimen with the geogrid placed at the bottom of the specimen fluctuate around 100 percent. This indicates that placing the geogrid in the middle or one-quarter below the middle of the specimen increases the vertical and horizontal moduli, but placing the geogrid at the bottom cannot reinforce the UGM neither vertically nor horizontally. Compared to the geogrid placed in the middle of the specimen, the geogrid placed one-quarter below the middle of the specimen provides slightly smaller normalized vertical and horizontal modulus ratios at most of the stress states, which indicates that the geogrid placed in the middle of the specimen has a slightly better reinforcement effect. It must be noted that the bottom of the UGM specimen interfaces with an aluminum platen, which differs from the interface between a pavement base layer with the subgrade. Thus, placing a geogrid at the bottom of the UGM specimen and at the bottom of the base layer may introduce different effects on the UGM performance, which needs to be studied based on pavement structural analysis in the future.

C-10 Table C-6. Influence of Geosynthetic on Cross-Anisotropic Properties (Geosynthetic Location: Mid-Height) Stress State Geosynthetic Type x geo x control E E â â (%) y geo y control E E â â (%) geo control AR AR (%) 1 TX-1 115 119 97 TX-2 119 124 96 BX-3 123 120 103 GT-4 153 92 166 2 TX-1 112 120 93 TX-2 119 125 95 BX-3 117 131 89 GT-4 157 109 144 3 TX-1 107 112 96 TX-2 115 110 105 BX-3 126 120 105 GT-4 144 98 147 4 TX-1 119 119 100 TX-2 124 122 102 BX-3 118 121 98 GT-4 131 100 131 5 TX-1 120 117 103 TX-2 118 120 98 BX-3 124 116 107 GT-4 132 104 127 6 TX-1 115 118 97 TX-2 121 115 105 BX-3 122 115 106 GT-4 127 99 128 7 TX-1 108 107 101 TX-2 114 112 102 BX-3 112 111 101 GT-4 124 103 120 8 TX-1 103 102 101 TX-2 107 109 98 BX-3 111 112 99 GT-4 124 95 131 9 TX-1 108 105 103 TX-2 110 109 101 BX-3 121 109 111 GT-4 117 98 119 10 TX-1 106 103 103 TX-2 105 107 98 BX-3 110 110 100 GT-4 122 102 120

C-11 Table C-7. Influence of Geosynthetic on Cross-Anisotropic Properties (Geosynthetic Location: One-Quarter below the Middle) Stress State Geosynthetic Type x geo x control E E â â (%) y geo y control E E â â (%) geo control AR AR (%) 1 TX-1 113 112 101 TX-2 109 115 95 BX-3 121 110 110 GT-4 132 85 155 2 TX-1 108 110 98 TX-2 112 116 97 BX-3 109 122 89 GT-4 125 97 129 3 TX-1 114 113 101 TX-2 107 115 93 BX-3 112 124 90 GT-4 118 102 116 4 TX-1 107 117 91 TX-2 109 122 89 BX-3 119 120 99 GT-4 122 95 128 5 TX-1 114 110 104 TX-2 110 115 96 BX-3 108 119 91 GT-4 124 99 125 6 TX-1 108 110 98 TX-2 112 106 106 BX-3 111 115 97 GT-4 115 91 126 7 TX-1 106 105 101 TX-2 105 107 98 BX-3 113 124 91 GT-4 106 103 103 8 TX-1 109 106 103 TX-2 114 103 111 BX-3 119 108 110 GT-4 109 95 115 9 TX-1 110 105 105 TX-2 108 109 99 BX-3 115 110 105 GT-4 107 89 120 10 TX-1 105 106 99 TX-2 108 111 97 BX-3 109 108 101 GT-4 110 87 126

C-12 Table C-8. Influence of Geosynthetic on Cross-Anisotropic Properties (Geosynthetic Location: Bottom) Stress State Geosynthetic Type x geo x control E E â â (%) y geo y control E E â â (%) geo control AR AR (%) 1 TX-1 98 102 96 GT-4 104 97 107 2 TX-1 103 98 105 GT-4 104 93 112 3 TX-1 103 102 101 GT-4 108 95 114 4 TX-1 97 100 97 GT-4 94 102 92 5 TX-1 102 103 99 GT-4 107 96 111 6 TX-1 103 101 102 GT-4 116 103 113 7 TX-1 101 96 105 GT-4 104 95 109 8 TX-1 97 102 95 GT-4 106 93 114 9 TX-1 101 97 104 GT-4 102 92 111 10 TX-1 98 102 96 GT-4 97 93 104 Impact of Geosynthetic on Permanent Deformation Characteristics of UGM The proposed mechanistic-empirical rutting model was employed to quantify the permanent deformation characteristics of geogrid-reinforced and unreinforced UGMs at various stress states. The model coefficients were determined using the solver function in Microsoft Excel to fit the measured permanent strain curves from Stress States 1â7. Figures C-4 and C-5 compare the model-predicted permanent strain curves with the laboratory-measured ones at different stress states for both unreinforced and geogrid-reinforced UGMs. The root-mean-square error (RMSE) values were calculated to evaluate the goodness of the model fitting. In general, a small RMSE value indicates a high goodness of fitting (4). The figures show that all of the determined RMSE values were relatively small, which indicates that the proposed model accurately captures the influence of stress level on the permanent deformation of the geogrid- reinforced and unreinforced UGMs. Figures C-4 and C-5 also present the determined coefficients of the proposed rutting model, which were used to predict the plastic strain curves of the UGMs at Stress States 8 and 9 in this study. To examine the accuracy of the proposed rutting model, the model-predicted permanent strain curves were compared to the laboratory-measured permanent strain curves from Stress States 8 and 9, as shown in Figure C-6. The model predictions had small RMSE values for

C-13 both geogrid-reinforced and unreinforced UGMs at the two stress states, which indicates that the proposed rutting model is accurate to predict the stress-dependent permanent deformation characteristics of geogrid-reinforced and unreinforced UGMs. Table C-9 lists the determined model coefficients for the geogrid-reinforced and unreinforced UGMs tested in this study. The determined model coefficients can be used to predict the permanent deformation of UGMs at any stress levels and number of load repetitions. Figure C-4. Comparison of Lab-Measured and Proposed-Model-Predicted Permanent Deformation Curves for Unreinforced UGM 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0 2000 4000 6000 8000 10000 Ac cu mu lat ed Pl ast ic Str ain (% ) Number of Load Cycles Control S1 Control S2 Control S3 Control S4 Control S5 Control S6 Control S7 Predict S1 Predict S2 Predict S3 Predict S4 Predict S5 Predict S6 Predict S7 S1: RMSE=0.012 S2: RMSE=0.002 S3: RMSE=0.002 S4: RMSE=0.004 S5: RMSE=0.012 S6: RMSE=0.016 S7: RMSE=0.018

C-14 Figure C-5. Comparison of Lab-Measured and Proposed-Model-Predicted Permanent Deformation Curves for Geogrid-Reinforced UGM Figure C-6. Validation of Prediction Accuracy of Proposed Model for Geogrid-Reinforced and Unreinforced UGMs 0.0 0.2 0.4 0.6 0.8 1.0 0 2000 4000 6000 8000 10000 Ac cu mu lat ed Pl ast ic Str ain (% ) Number of Load Cycles TX-1-Mid S1 TX-1-Mid S2 TX-1-Mid S3 TX-1-Mid S4 TX-1-Mid S5 TX-1-Mid S6 TX-1-Mid S7 Predict S1 Predict S2 Predict S3 Predict S4 Predict S5 Predict S6 Predict S7 S1: RMSE=0.008 S2: RMSE=0.007 S3: RMSE=0.011 S4: RMSE=0.004 S5: RMSE=0.013 S6: RMSE=0.009 S7: RMSE=0.012 0 0.2 0.4 0.6 0.8 1 0 2000 4000 6000 8000 10000 Ac cu mu lat ed Pl as tic St ra in (% ) Number of Load Cycles Measured Control S8 Measured Control S9 Model Predicted Control S8 Model Predicted Control S9 Measured TX-1-Mid S8 Measured TX-1-Mid S9 Model Predicted TX-1-Mid S8 Model Predicted TX-1-Mid S9 Control: RMSE=0.031 (S8) RMSE=0.011 (S9) TX-1 Mid: RMSE=0.011 (S8) RMSE=0.020 (S9)

C-15 Table C-9. Determination of Model Coefficients for Geogrid-Reinforced and Unreinforced UGMs Material Type Permanent Deformation Model Coefficients Îµ0 Ï Î² m n Unreinforced 0.149 72.4 0.247 1.70 â2.16 TX-1 Middle 0.076 48.3 0.174 1.73 â2.12 TX-2 Middle 0.068 82.1 0.165 1.84 â2.21 BX-3 Middle 0.082 31.2 0.182 1.64 â2.01 TX-2 One-Quarter below Middle 0.093 62.5 0.159 1.62 â2.03 TX-2 Bottom 0.142 35.1 0.294 1.79 â2.26 GT-4 Middle 0.112 60.4 0.261 1.76 â2.18 References 1. Tseng, K.H., and Lytton, R.L. (1989). Prediction of Permanent Deformation in Flexible Pavements Materials: Implication of Aggregates in the Design, Construction, and Performance of Flexible Pavements. ASTM STP 1016, American Society for Testing and Materials (ASTM), West Conshohocken, Pennsylvania. 2. Drucker, D.C., and Prager, W. (1952). Soil Mechanics and Plastic Analysis for Limit Design. Quarterly of Applied Mathematics, Vol. 10, No. 2, pp. 157â165. 3. Adu-Osei, A., Little, D.N., and Lytton, R.L. (2001). Cross-Anisotropic Characterization of Unbound Granular Materials. Transportation Research Record: Journal of the Transportation Research Board, No. 1757, pp. 82â91. 4. Gauch, H.G., Hwang, J.T., and Fick, G.W. (2003). Model Evaluation by Comparison of Model-Based Predictions and Measured Values. Agronomy Journal, No. 95, pp. 1442â1446.