**Suggested Citation:**"Appendix B. Definitions of Model Parameters of Unbound Layer and Subgrade Models." National Academies of Sciences, Engineering, and Medicine. 2019.

*Proposed Enhancements to Pavement ME Design: Improved Consideration of the Influence of Subgrade and Unbound Layers on Pavement Performance*. Washington, DC: The National Academies Press. doi: 10.17226/25583.

**Suggested Citation:**"Appendix B. Definitions of Model Parameters of Unbound Layer and Subgrade Models." National Academies of Sciences, Engineering, and Medicine. 2019.

*Proposed Enhancements to Pavement ME Design: Improved Consideration of the Influence of Subgrade and Unbound Layers on Pavement Performance*. Washington, DC: The National Academies Press. doi: 10.17226/25583.

**Suggested Citation:**"Appendix B. Definitions of Model Parameters of Unbound Layer and Subgrade Models." National Academies of Sciences, Engineering, and Medicine. 2019.

*Proposed Enhancements to Pavement ME Design: Improved Consideration of the Influence of Subgrade and Unbound Layers on Pavement Performance*. Washington, DC: The National Academies Press. doi: 10.17226/25583.

**Suggested Citation:**"Appendix B. Definitions of Model Parameters of Unbound Layer and Subgrade Models." National Academies of Sciences, Engineering, and Medicine. 2019.

**Suggested Citation:**"Appendix B. Definitions of Model Parameters of Unbound Layer and Subgrade Models." National Academies of Sciences, Engineering, and Medicine. 2019.

**Suggested Citation:**"Appendix B. Definitions of Model Parameters of Unbound Layer and Subgrade Models." National Academies of Sciences, Engineering, and Medicine. 2019.

**Suggested Citation:**"Appendix B. Definitions of Model Parameters of Unbound Layer and Subgrade Models." National Academies of Sciences, Engineering, and Medicine. 2019.

**Suggested Citation:**"Appendix B. Definitions of Model Parameters of Unbound Layer and Subgrade Models." National Academies of Sciences, Engineering, and Medicine. 2019.

**Suggested Citation:**"Appendix B. Definitions of Model Parameters of Unbound Layer and Subgrade Models." National Academies of Sciences, Engineering, and Medicine. 2019.

**Suggested Citation:**"Appendix B. Definitions of Model Parameters of Unbound Layer and Subgrade Models." National Academies of Sciences, Engineering, and Medicine. 2019.

**Suggested Citation:**"Appendix B. Definitions of Model Parameters of Unbound Layer and Subgrade Models." National Academies of Sciences, Engineering, and Medicine. 2019.

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

B-1 Appendix B. Definitions of Model Parameters of Unbound Layer and Subgrade Models MODULUS MODELS OF UNBOUND LAYERS AND SUBGRADE 2 1 3 k RM k ï³ï½ where RM is the resilient modulus, 3ï³ is the confining pressure, and 1k and 2k are regression coefficients. 2 1 k RM k ï±ï½ where RM is the resilient modulus, ï± is the bulk stress, and 1k and 2k are regression coefficients. ï¨ ï©2 3 1R dM k k k ï³ï½ ï« ï 1 dk ï³ï³ ï¨ ï©2 4 1R dM k k kï³ï½ ï« ï 1 dk ï³ï¼ where RM is the resilient modulus; dï³ is the deviatoric shear stress; and 1k , 2k , 3k , and 4k are regression coefficients. ' ' d R d a bM ï³ ï³ ï« ï½ where RM is the resilient modulus, dï³ is the deviatoric shear stress, and 'a and 'b are regression coefficients. 32 1 kk R dM k ï± ï³ï½ where RM is the resilient modulus; dï³ is the deviatoric shear stress; ï± is the bulk stress; and 1k , 2k , and 3k are regression coefficients. 2 3 1 1 k k oct R IM k Pa Pa Pa ï´ï¦ ï¶ ï¦ ï¶ï½ ï§ ï· ï§ ï· ï¨ ï¸ ï¨ ï¸ where RM is the resilient modulus; 1I is the first invariant of stress tensor; octï´ is the octahedral shear stress; Pa is the atmospheric pressure; and 1k , 2k , and 3k are regression coefficients. 2 3 1 1 1 k k oct R IM k Pa Pa Pa ï´ï¦ ï¶ ï¦ ï¶ï½ ï«ï§ ï· ï§ ï· ï¨ ï¸ ï¨ ï¸ where RM is the resilient modulus; 1I is the first invariant of stress tensor; octï´ is the octahedral shear stress; Pa is the atmospheric pressure; and 1k , 2k , and 3k are regression coefficients.

B-2 2 1 2 R I JM M Pa R Pa Pa ï¬ ï© ï¹ï¦ ï¶ï½ ï´ ï«ïª ïºï§ ï· ï¨ ï¸ïª ïºï« ï» where RM is the resilient modulus; 1I is the first invariant of stress tensor; 2J is the second invariant of shear stress tensor; Pa is the atmospheric pressure; R is a function of the Poissonâs ratio; and M and ï¬ are model coefficients. ï¨ ï© log 1 exp ln R Ropt m opt M b aa bM k S S a ï ï½ ï« ïï© ï¹ï« ï« ïïª ïºï« ï» where RM is the resilient modulus at a given degree of saturation; RoptM is the resilient modulus at reference condition; a is the minimum of log R Ropt M M ï¦ ï¶ ï§ ï·ï§ ï· ï¨ ï¸ ; b is the maximum of log R Ropt M M ï¦ ï¶ ï§ ï·ï§ ï· ï¨ ï¸ ; mk is the regression parameter; and ï¨ ï©optS Sï is the variation of degree of saturation expressed in decimal. ï¨ ï© ï¨ ï©2 3 1R d s a wM k k k k u uï³ï½ ï« ï ï« ï ï¨ ï© ï¨ ï©2 4 1R d s a wM k k k k u uï³ï½ ï« ï ï« ï where RM is the resilient modulus; dï³ is the deviatoric shear stress; au is the air pressure; wu is the pore water pressure; and 1k , 2k , 3k , 4k , and sk are regression coefficients. 2 3 1 4 1 3 k koct R I kM k Pa Pa Pa ï´ïï¦ ï¶ ï¦ ï¶ï½ ï§ ï· ï§ ï· ï¨ ï¸ ï¨ ï¸ where RM is the resilient modulus; 1I is the first invariant of stress tensor; octï´ is the octahedral shear stress; Pa is the atmospheric pressure; and 1k , 2k , 3k , and 4k are regression coefficients. 2 3 1 1 3 k km oct R I fhM k Pa Pa Pa ï± ï´ïï¦ ï¶ ï¦ ï¶ï½ ï§ ï· ï§ ï· ï¨ ï¸ ï¨ ï¸ where RM is the resilient modulus; 1I is the first invariant of stress tensor; octï´ is the octahedral shear stress; Pa is the atmospheric pressure; ï± is the volumetric water content; f is the saturation factor; mh is the matric suction; and 1k , 2k , and 3k are regression coefficients.

B-3 2 3 1 1 1 3 3 k km oct oct R II f h M k Pa Pa Pa ï± ï¢ ï¡ï´ ï´ ï© ï¹ï¦ ï¶ï ï« ï«ï§ ï·ïª ïº ï¦ ï¶ï¨ ï¸ïª ïºï½ ï§ ï· ï¨ ï¸ïª ïº ïª ïºï« ï» where RM is the resilient modulus; 1I is the first invariant of stress tensor; octï´ is the octahedral shear stress; Pa is the atmospheric pressure; ï± is the volumetric water content; f is the saturation factor; mh is the matric suction; ï¡ and ï¢ are the Henkel pore water pressure coefficients; and 1k , 2k , and 3k are regression coefficients. ï¨ ï© 21 k R d w mM k ï³ ï£ ï¹ï½ ï« where RM is the resilient modulus; dï³ is the deviatoric shear stress; wï£ is the Bishopâs effective stress coefficient; mï¹ is the matric suction; and 1k and 2k are regression coefficients. 2 3 1 1 k k w m oct R a a a M k P P P ï± ï£ ï¹ ï´ï¦ ï¶ ï¦ ï¶ï« ï½ ï«ï§ ï· ï§ ï· ï¨ ï¸ ï¨ ï¸ where RM is the resilient modulus; ï± is the bulk stress; octï´ is the octahedral shear stress; Pa is the atmospheric pressure; wï£ is the Bishopâs effective stress coefficient; mï¹ is the matric suction; and 1k , 2k , and 3k are regression coefficients. ' 2 4 4 ' 1 3 1 1o k k k m mnet w sat oct R a a a a uM k P P P P ï¹ ï¹ï± ï´ï ï ïï¦ ï¶ ï¦ ï¶ ï¦ ï¶ï ïï½ ï« ï«ï§ ï· ï§ ï· ï§ ï· ï¨ ï¸ ï¨ ï¸ ï¨ ï¸ where RM is the resilient modulus; netï± is the net bulk stress; octï´ is the octahedral shear stress; Pa is the atmospheric pressure; w satu ïï is the build-up of pore water pressure under saturated conditions; 0mï¹ is the initial matric soil suction; mï¹ï is the relative change of matrix soil suction with respect to 0mï¹ ; and ' 1k , ' 2k , ' 3k , and ' 4k are regression coefficients. ï¨ ï© 2 3 6 1 7 3 k k b oct R a us a a w a a kM k p k k p p p ï«ï³ ï´ ï ï ï¦ ï¶ ï¦ ï¶ï ï½ ï« ï« ï ïï§ ï· ï§ ï· ï¨ ï¸ ï¨ ï¸ where RM is the resilient modulus; bï³ is the bulk stress; octï´ is the octahedral shear stress; Pa is the atmospheric pressure; au is the air pressure; wu is the pore water pressure; ï is the normalized volumetric water content; ï« is the fitting parameter; and 1k , 2k , 3k , 6k , 7k , and usk are regression coefficients.

B-4 2 3 4 1 3 1 k k w oct R a a a k SVM k P P P ï± ï´ï¦ ï¶ ï¦ ï¶ï« ï½ ï«ï§ ï· ï§ ï· ï¨ ï¸ ï¨ ï¸ where RM is the resilient modulus; ï± is the bulk stress; octï´ is the octahedral shear stress; Pa is the atmospheric pressure; wV is the volumetric water content; S is the soil suction; and 1k , 2k , 3k , and 4k are regression coefficients. 2 3 1 1 1 ; k k V oct R a a a H R VH V V R R IM k P P P M Gs r M M ï´ï¦ ï¶ ï¦ ï¶ ï½ ï«ï§ ï· ï§ ï· ï¨ ï¸ ï¨ ï¸ ï½ ï½ where VRM is the resilient modulus in the vertical direction; 1I is the first invariant of stress tensor; octï´ is the octahedral shear stress; Pa is the atmospheric pressure; 1k , 2k , and 3k are regression coefficients; HRM is the resilient modulus in the horizontal direction; VHG is the shear modulus in the horizontal-vertical plane; and s and r are the modulus ratios. 2 3 5 6 8 9 1 4 7 ; ; k k k k V Hoct oct R a R a a a a a k k oct VH a a a M k P M k P P P P P G k P P P ï± ï´ ï± ï´ ï± ï´ ï¦ ï¶ ï¦ ï¶ ï¦ ï¶ ï¦ ï¶ ï½ ï½ï§ ï· ï§ ï· ï§ ï· ï§ ï· ï¨ ï¸ ï¨ ï¸ ï¨ ï¸ ï¨ ï¸ ï¦ ï¶ ï¦ ï¶ ï½ ï§ ï· ï§ ï· ï¨ ï¸ ï¨ ï¸ where VRM is the resilient modulus in the vertical direction; octï´ is the octahedral shear stress; Pa is the atmospheric pressure; HRM is the resilient modulus in the horizontal direction; VHG is the shear modulus in the horizontal-vertical plane; and 1k , 2k , 3k , 4k , 5k , 6k , 7k , 8k , and 9k are regression coefficients. 2 3 1 1 3 ; k k V m oct R a a a H R VH V V R R I fhM k P P P M Gn m M M ï± ï´ï¦ ï¶ ï¦ ï¶ï ï½ ï§ ï· ï§ ï· ï¨ ï¸ ï¨ ï¸ ï½ ï½ where VRM is the resilient modulus in the vertical direction; 1I is the first invariant of stress tensor; octï´ is the octahedral shear stress; Pa is the atmospheric pressure; ï± is the volumetric water content; f is the saturation factor; mh is the matric suction; 1k , 2k , and 3k are regression coefficients; HRM is the resilient modulus in the horizontal direction; VHG is the shear modulus in the horizontal-vertical plane; and n and m are the modulus ratios.

B-5 ï¨ ï© ï¨ ï© ï¨ ï© 1 2 3 1.3577 0.0106 % 0.0437 0.5193 0.0073 4 0.0095 40 0.0027 200 0.003 0.0049 1.4258 0.0288 4 0.0303 40 0.0521 200 0.0251 % 0.0535 0.0672 0.0026 0.0025 0.6055 k clay wc k P P P LL wopt k P P P silt wcLL wopt opt s woptï§ ï§ ï½ ï« ï ï½ ï ï« ï ï ï ï½ ï ï« ï ï« ï« ï ï ï« ï where 1k , 2k , and 3k are resilient modulus model coefficients; %clay is the clay content in percentage; % silt is the silt content in percentage; 4P is the percent of material passing sieve No. 4; 40P is the percent of material passing sieve No. 40; 200P is the percent of material passing sieve No. 200; LL is the liquid limit; wopt is the optimum water content; wc is the water content; and optï§ is the dry density at optimum water content. ï¨ ï© ï¨ ï© ï¨ ï© ï¨ ï© ï¨ ï© ï¨ ï© ï¨ ï© 1 2 3 ln 137.19 13.60ln 4.35ln 0.62ln 36.14 0.04 3.81ln 0.22 0.77ln 4.39 0.45ln 0.01 0.05 0.15ln d A T A s T d s T k k pfc a k pfc a ï§ ï¬ ï¬ ï¬ ï¬ ï§ ï¬ ï½ ï ï« ï« ï ï½ ï« ï ï ï ï½ ï ï« ï ï« ï« where 1k , 2k , and 3k are resilient modulus model coefficients; dï§ is the dry density; Aï¬ is the scale factor of angularity index; Tï¬ is the scale factor of texture index; pfc is the percent fines content; and sa is the shape factor of angularity index. ï¨ ï©0.642555rM CBRï½ where rM is the resilient modulus, and CBR is the California bearing ratio. 1155 555rM Rï½ ï« where rM is the resilient modulus, and R is the resistance R-value. 30000 0.14 i r aM ï¦ ï¶ï½ ï§ ï· ï¨ ï¸ where rM is the resilient modulus, and ia is the AASHTO layer coefficient. ï¨ ï© 0.64 752555 1 0.728r M wPI ï¦ ï¶ ï½ ï§ ï·ï§ ï·ï«ï¨ ï¸ where RM is the resilient modulus, wPI is the weighted plasticity index. 0.64 1.12 2922555rM DCP ï¦ ï¶ï½ ï§ ï· ï¨ ï¸ where RM is the resilient modulus, and DCP is the dynamic cone penetrometer index.

B-6 PERMANENT DEFORMATION MODELS OF UNBOUND LAYERS AND SUBGRADE ï¨ ï©1 P r N N N ï¡ï¥ ï ï¥ ïï© ï¹ï¶ ï½ïª ïºï¶ï« ï» where Pï¥ is the accumulated plastic strain; rï¥ is the resilient strain of granular material; N is the number of load cycles; and ï and ï¡ are regression coefficients. p b r aN ï¥ ï¥ ï½ where pï¥ is the accumulated plastic strain; rï¥ is the resilient strain of granular material; N is the number of load cycles; and a and b are regression coefficients. 0 N p e ï¢ï² ï¥ ï¥ ï¦ ï¶ïï§ ï· ï¨ ï¸ï½ where pï¥ is the accumulated plastic strain; N is the number of load cycles; and 0ï¥ , ï² , and ï¢ are regression coefficients. ï¨ ï© ï¨ ï©, 0 kzp p zz eï¥ ï¥ ïï½ï½ where ï¨ ï©p zï¥ is the plastic strain at depth z; , 0p zï¥ ï½ is the vertical plastic strain at the top of subgrade; z is the depth measured from the top of subgrade; and k is the model coefficient. 0 N p s v r e ï¢ï²ï¥ï¥ ï¢ ï¥ ï¥ ï¦ ï¶ïï§ ï· ï¨ ï¸ï¦ ï¶ï½ ï§ ï· ï¨ ï¸ where pï¥ is the accumulated plastic strain; rï¥ is the resilient strain of granular material; N is the number of load cycles; 0ï¥ , ï² , and ï¢ are regression coefficients; sï¢ is a global calibration coefficient, 1.673 for granular materials; rï¥ is the resilient strain imposed in the laboratory test; and vï¥ is the average vertical resilient strain in the base layer of the flexible pavements. 6 6 0 1 2 0 1 2log .log p oct oct r k ka a a b b b N Pa Pa Pa Pa ï¥ ï± ï±ï´ ï´ ï¥ ï© ï¹ ï© ï¹ï¦ ï¶ ï¦ ï¶ï¦ ï¶ ï¦ ï¶ ïª ïº ïª ïºï§ ï· ï§ ï·ï§ ï· ï§ ï· ï¨ ï¸ ï¨ ï¸ïª ïº ïª ïºï¨ ï¸ ï¨ ï¸ï« ï» ï« ï» ï« ï«ï½ ï« ï« ï« ï« ï« where Pï¥ is the accumulated plastic strain; rï¥ is the resilient strain of granular material; N is the number of load cycles; ï± is the bulk stress; Pa is the atmospheric pressure; octï´ is the octahedral shear stress; and 0a , 1a , 2a , 0b , 1b , and 2b are model coefficients.

B-7 1 b p RCN R ï¥ ï½ ï ' f qb d c q ï¦ ï¶ ï½ ï«ï§ ï·ï§ ï· ï¨ ï¸ where Pï¥ is the accumulated plastic strain; N is the number of load cycles; C is the permanent strain in the first loading cycle; b is a shear ratio parameter; R is the shear failure ratio 1 3 0f q q q Mp ï³ ï³ï ï½ ï½ ï« , 6sin 3 sin M ï¦ ï¦ ï½ ï , 0 6cos 3 sin cq ï¦ ï¦ ï ï½ ï , where c and ï¦ are cohesion and friction angle; and d and 'c are material parameters.Â max D fB C p dAN ï´ ï¥ ï³ ï´ ï¦ ï¶ ï½ ï§ ï· ï¨ ï¸ where Pï¥ is the accumulated plastic strain; N is the number of load cycles; dï³ is the deviatoric shear stress; fï´ is shear stress; m axï´ is shear strength; and A , B , C , and D are regression coefficients. ï¨ ï© ï¨ ï©0 2 1m nNp e J I K ï¢ï² ï¥ ï¥ ï¡ ï¦ ï¶ïï§ ï· ï¨ ï¸ï½ ï« ï¨ ï© 2sin 3 3 sin ï¦ï¡ ï¦ ï½ ï ï¨ ï© 6cos 3 3 sin cK ï¦ ï¦ ï ï½ ï where Pï¥ is the accumulated plastic strain; N is the number of load cycles; and 0ï¥ , ï² , and ï¢ are regression coefficients; 2J is the second invariant of the deviatoric stress tensor; 1I is the first invariant of the stress tensor; 0ï¥ , ï² , ï¢ , m and n are model coefficients; and c and ï¦ are cohesion and friction angle, respectively. 60 6 4 2 3 2 6 log 0.80978 0.06626 0.003077 10 log 0.9190 0.03105 0.001806 1.5 10 log 1.78667 1.45062 3.784 10 2.074 10 1.05 10 c r r c r c c r W E W E W W E ï± ï± ï± ï± ï¥ ï³ ï¥ ï¢ ï³ ï² ï³ ï³ ï ï ï ï ï ï¦ ï¶ ï½ ï ï ï«ï§ ï· ï¨ ï¸ ï½ ï ï« ï« ï ï´ ï½ ï ï« ï ï´ ï ï´ ï ï´ where 0ï¥ , ï² , and ï¢ are Pavement ME Design model coefficients; rï¥ is the resilient strain of granular material; N is the number of load cycles; cW is the water content; ï±ï³ is the bulk stress; and rE is the resilient modulus of granular material.

B-8 ï¨ ï© ï¨ ï© 910 0 1 9 9 0.15 20 2 log 0.61119 0.017638 4.8928510 1 10 r c e e W ï¢ ï¢ ï² ï² ï¢ ï¢ ï¥ ï¥ ï¢ ï² ï¦ ï¶ ï§ ï· ï¨ ï¸ ï¦ ï¶ ï§ ï·ï´ ï« ï´ ï§ ï· ï¨ ï¸ï½ ï½ ï ï ï¦ ï¶ ïï§ ï·ï½ ï´ï§ ï·ï© ï¹ïï§ ï·ïª ïºï« ï»ï¨ ï¸ where 0ï¥ , ï² , and ï¢ are Pavement ME Design model coefficients; rï¥ is the resilient strain of granular material; and cW is the water content. 0ln 10.24 0.03 0.10 0.88 3.95 ln ln 6.74 0.02 0.04 0.85 0.03 0.13 ln 10.17 2.75 ln 0.05 2.00 1.61ln 0.34 A T G G T d G A T MBV pfc a MBV pfc a a pfc a a ï¥ ï¬ ï² ï¬ ï¢ ï§ ï¬ ï½ ï ï« ï« ï ï½ ï« ï« ï ï« ï ï½ ï ï ï ï ï where 0ï¥ , ï² , and ï¢ are Pavement ME Design model coefficients; MBV is methylene blue value; pfc is the percent fines content; Tï¬ is the scale factor of texture index; Aa is the shape factor of angularity index; Aï¬ is the scale factor of angularity index; dï§ is the dry density; Ga is the shape factor of gradation; Ta is the shape factor of texture index; and Gï¬ is the scale factor of gradation. SHEAR STRENGTH MODELS OF UNBOUND LAYERS AND SUBGRADE tanncï´ ï³ ï¦ï½ ï« where ï´ is the shear stress; nï³ is the normal stress; c is the cohesion; and ï¦ is the friction angle. ï¨ ï© ï¨ ï©' tan ' tan bf n a a wcï´ ï³ ï ï¦ ï¡ ï ï ï¦ï½ ï« ï ï« ï Â where fï´ is the shear strength; nï³ is the normal stress; 'c is the cohesion; 'ï¦ is the effective angle of shearing resistance for a saturated soil; bï¦ is the angle of shearing resistance with respect to matric suction; au is the air pressure; wu is the pore water pressure; and ï¡ is the fitting coefficient. ï¨ ï© tantan nba wc u uï´ ï³ ï¦ï¦ï½ ï«ï¢ï« ï where ï´ is the shear stress; nï³ is the normal stress; au is the air pressure; wu is the pore water pressure; 'c is the cohesion; ï¦ is the friction angle for a saturated soil; and bï¦ is the angle of shearing resistance with respect to matric suction.

B-9 ï¨ ï© ï¨ ï©' tan ' tan bf n a a wc Sï´ ï³ ï ï¦ ï ï ï¦ï½ ï« ï ï« ï where fï´ is the shear strength; nï³ is the normal stress; 'c is the cohesion; 'ï¦ is the effective angle of shearing resistance for a saturated soil; bï¦ is the angle of shearing resistance with respect to matric suction; au is the air pressure; wu is the pore water pressure; and S is the degree of saturation. ï¨ ï© ï¨ ï©' tan ' tan bf n a a wc ï«ï´ ï³ ï ï¦ ï ï ï¦ï½ ï« ï ï« ï ï where fï´ is the shear strength; nï³ is the normal stress; 'c is the cohesion; 'ï¦ is the effective angle of shearing resistance for a saturated soil; bï¦ is the angle of shearing resistance with respect to matric suction; au is the air pressure; wu is the pore water pressure; ï is the normalized volumetric water content; and ï« is the fitting parameter. ï¨ ï© ï¨ ï© ï¨ ï© ï¨ ï©' tan ' tanf n a a w a w a w bc ï¢ ï´ ï³ ï ï¦ ï ï ï¦ ïª ï ï ï ïï© ï¹ï½ ï« ï ï« ï ï ï ï ïï« ï» where fï´ is the shear strength; nï³ is the normal stress; 'c is the cohesion; 'ï¦ is the effective angle of shearing resistance for a saturated soil; ï¦ is the angle of shearing resistance with respect to matric suction; au is the air pressure; wu is the pore water pressure; and ïª and ï¢ are model coefficients. ï¨ ï©' tan ' ' 1676.624 2.088 13.260 0.113 270.722ln 38.778 ' 2.827 0.016 0.0005 0.051 0.763ln 0.008 n m A A d G A S d c c MBV a fh a MBV a pfc ï´ ï³ ï¦ï± ï¬ ï§ ï¦ ï¬ ï§ ï½ ï« ï½ ï ï ï ï ï ï« ï« ï½ ï ï ï ï ï« ï where ï´ is the shear stress; nï³ is the normal stress; 'c is the cohesion; 'ï¦ is the friction angle; ï± is the volumetric water content; f is the saturation factor; mh is the matric suction; MBV is the methylene blue value; Aa is the shape factor of angularity index; Aï¬ is the scale factor of angularity index; dï§ is the dry density; Ga is the shape factor of gradation; Sa is the shape factor of shape index; and pfc is the percent fines content. 2 tan 83.95 1.58 40 2.57 0.043 40 6.88 0.14 0.81 tan 1.61 0.96 0.88 4.13 31.82 n N N sN sb c c N n N PL G PI n G ï´ ï³ ï¦ ï¹ ï¹ ï¦ ï¦ ï¹ ï½ ï« ï½ ï« ï ï ï ï« ï ï½ ï ï ï ï« where 40N is the percent of material passing 0.42 mm sieve size; n is the porosity; 40NN is normalized 40N = ï¨ ï©40 55.89N ï ; NPL is normalized plastic limit = 15.89PL ï ; sNG is normalized specific gravity of aggregate = 2.61sG ï ; ï¹ is matric suction; PI is plasticity index; and sbG is specific gravity of binder content.

B-10 EROSION MODELS OF UNBOUND LAYERS ESALg ï¢ ï² ï¦ ï¶ ï½ ï§ ï· ï¨ ï¸ where g is the amount of distress as a fraction of a pumping level of 3; ESAL is the equivalent 80 kN single axle loads; and ï¢ is the model coefficient. log 1.07 0.34 i dP m ESAL f m D ï½ ï ï ï½ ï ï¥ where iP is the pumping index; ESAL is the equivalent 80 kN single axle loads; df is the drainage adjustment factor; m is the model coefficient; and D is the slab thickness. exp 2.884 1.652 log 10,000 ESAL DE NPI ï© ï¹ï¦ ï¶ï ï½ ï ï« ïïª ïºï§ ï· ïª ïºï¨ ï¸ï« ï» ï¥ where NPI is the normalized pumping index of volume of pumped material; ESAL is the equivalent 80 kN single axle loads; and DE is the deformation energy per one application of ESAL. 36.67 2.884 1.652 log 10,000 P NPI ESAL DE NPI F ï½ ï ï© ï¹ï¦ ï¶ï ï½ ï ï ï« ïïª ïºï§ ï· ïª ïºï¨ ï¸ï« ï» ï¥ where P is the volume of pumped material; NPI is the normalized pumping index of volume of pumped material; ESAL is the equivalent 80 kN single axle loads; and DE is the deformation energy per one application of ESAL. ï¨ ï©0.1031 2 1 log 14.524 6.777 9.0 100 m i i i N C P C nPercent erosion damage Nï½ ï½ ï ï ï½ ï¥ where N is the allowable number of load repetitions based on a pressure of a PSI of 3.0; 1C is the adjustment factor; P is the pressure on the foundation under the slab corner; m is the total number of load groups; 2C is the model coefficient; in is the predicted number of repetitions for the ith load group; and iN is the allowable number of repetitions for the ith load group. ï¨ ï© ï¨ ï©0% D Nf Erosion f e ï¢ ï² ï® ï¦ ï¶ ïï§ ï·ï§ ï·ïï¨ ï¸ï½ where 0f is maximum faulting; ï¨ ï©%f Erosion is percent of maximum faulting; ï² is scale calculation factor based on laboratory erosion test; ï¨ ï©D N is damage after N load repetitions;

B-11 v is time delay before the appearance of visible (measurable) damage; and ï¢ is shape factor related to the erosion rate. FOUNDATION MODELS OF SUBGRADE (x,y) kw(x,y)p ï½ where ï¨ ï©,p x y is the distributed load applied in the x-y plane; ï¨ ï©,w x y is the displacement in the vertical direction; and k is the foundation modulus. 2(x, y) kw(x, y) (x, y)p T wï½ ï ï where ï¨ ï©,p x y is the distributed load applied in the x-y plane; w is the displacement in the vertical direction; 2ï is the Laplace operator in x and y ( 2 2 2 2 2x y ï¦ ï¶ï¶ ï¶ ï ï½ ï«ï§ ï·ï¶ ï¶ï¨ ï¸ ); and T is the constant tension of a stretched elastic membrane of the top ends of the springs. 2 2(x, y) kw(x, y) (x, y)p D wï½ ï ï ï where ï¨ ï©,p x y is the distributed load applied in the x-y plane; w is the displacement in the vertical direction; 2ï is the Laplace operator in x and y ( 2 2 2 2 2x y ï¦ ï¶ï¶ ï¶ ï ï½ ï«ï§ ï·ï¶ ï¶ï¨ ï¸ ); and D is the flexural rigidity of the plate. 2(x, y) kw(x, y) G (x, y)p wï½ ï ï where ï¨ ï©,p x y is the distributed load applied in the x-y plane, w is the displacement in the vertical direction; 2ï is the Laplace operator in x and y; and G is the constant of the shear layer. 2 2(1 ) p kw G c 3k 4 3 4 9 f f k G p w c c E k H G HG ï« ï ï ï½ ï ï ï½ ï½ ï½ where p is the distributed load; w is the displacement in the vertical direction; 2ï is the Laplace operator in x and y ( 2 2 2 2 2x y ï¦ ï¶ï¶ ï¶ ï ï½ ï«ï§ ï·ï¶ ï¶ï¨ ï¸ ); c is the spring constant of upper spring layer; k is the spring constant of lower spring layer; G is the constant of the shear layer; fE is Youngâs modulus; fG is the shear modulus of the foundation material; and H is the thickness of the foundation.