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From page 153... ... 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  where RM is the resilient modulus, 3 is the confining pressure, and 1k and 2k are regression coefficients. Read the entire page →
From page 154... ... B-2 2 1 2 R I JM M Pa R Pa Pa             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 Poisson's ratio; and M and  are model coefficients.   log 1 exp ln R Ropt m opt M b aa bM k S S a          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        ; b is the maximum of log R Ropt M M        ; mk is the regression parameter; and  optS S is the variation of degree of saturation expressed in decimal. Read the entire page →
From page 155... ... B-3 2 3 1 1 1 3 3 k km oct oct R II f h M k Pa Pa Pa                        where RM is the resilient modulus; 1I is the first invariant of stress tensor; oct is the octahedral shear stress; Pa is the atmospheric pressure;  is the volumetric water content; f is the saturation factor; mh is the matric suction;  and  are the Henkel pore water pressure coefficients; and 1k , 2k , and 3k are regression coefficients.   21 k R d w mM k     where RM is the resilient modulus; d is the deviatoric shear stress; w is the Bishop's effective stress coefficient; m is the matric suction; and 1k and 2k are regression coefficients. Read the entire page →
From page 156... ... B-4 2 3 4 1 3 1 k k w oct R a a a k SVM k P P P               where RM is the resilient modulus;  is the bulk stress; oct 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                where VRM is the resilient modulus in the vertical direction; 1I is the first invariant of stress tensor; oct 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. Read the entire page →
From page 157... ... B-5       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 wopt                     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. Read the entire page →
From page 158... ... B-6 PERMANENT DEFORMATION MODELS OF UNBOUND LAYERS AND SUBGRADE  1 P r N N N         where P is the accumulated plastic strain; r is the resilient strain of granular material; N is the number of load cycles; and  and  are regression coefficients. p b r aN    where p is the accumulated plastic strain; r is the resilient strain of granular material; N is the number of load cycles; and a and b are regression coefficients. Read the entire page →
From page 159... ... B-7 1 b p RCN R    ' f qb d c q         where P 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      , 6sin 3 sin M     , 0 6cos 3 sin cq      , where c and  are cohesion and friction angle; and d and 'c are material parameters. max D fB C p dAN            where P is the accumulated plastic strain; N is the number of load cycles; d is the deviatoric shear stress; f is shear stress; m ax is shear strength; and A , B , C , and D are regression coefficients.    0 2 1m nNp e J I K             2sin 3 3 sin       6cos 3 3 sin cK      where P is the accumulated plastic strain; N is the number of load cycles; and 0 ,  , and  are regression coefficients; 2J is the second invariant of the deviatoric stress tensor; 1I is the first invariant of the stress tensor; 0 ,  ,  , m and n are model coefficients; and c and  are cohesion and friction angle, respectively. Read the entire page →
From page 160... ... B-8     910 0 1 9 9 0.15 20 2 log 0.61119 0.017638 4.8928510 1 10 r c e e W                                         where 0 ,  , and  are Pavement ME Design model coefficients; r 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                         where 0 ,  , and  are Pavement ME Design model coefficients; MBV is methylene blue value; pfc is the percent fines content; T is the scale factor of texture index; Aa is the shape factor of angularity index; A is the scale factor of angularity index; d is the dry density; Ga is the shape factor of gradation; Ta is the shape factor of texture index; and G is the scale factor of gradation. Read the entire page →
From page 161... ... B-9    ' tan ' tan bf n a a wc S           where f is the shear strength; n is the normal stress; 'c is the cohesion; ' is the effective angle of shearing resistance for a saturated soil; b 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.    ' tan ' tan bf n a a wc             where f is the shear strength; n is the normal stress; 'c is the cohesion; ' is the effective angle of shearing resistance for a saturated soil; b is the angle of shearing resistance with respect to matric suction; au is the air pressure; wu is the pore water pressure;  is the normalized volumetric water content; and  is the fitting parameter. Read the entire page →
From page 162... ... B-10 EROSION MODELS OF UNBOUND LAYERS ESALg          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  is the model coefficient. log 1.07 0.34 i dP m ESAL f m D       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. Read the entire page →
From page 163... ... B-11 v is time delay before the appearance of visible (measurable) damage; and  is shape factor related to the erosion rate. Read the entire page →

From page 153...

... 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  where RM is the resilient modulus, 3 is the confining pressure, and 1k and 2k are regression coefficients.

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From page 154...

... B-2 2 1 2 R I JM M Pa R Pa Pa             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 Poisson's ratio; and M and  are model coefficients.   log 1 exp ln R Ropt m opt M b aa bM k S S a          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        ; b is the maximum of log R Ropt M M        ; mk is the regression parameter; and  optS S is the variation of degree of saturation expressed in decimal.

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From page 155...

... B-3 2 3 1 1 1 3 3 k km oct oct R II f h M k Pa Pa Pa                        where RM is the resilient modulus; 1I is the first invariant of stress tensor; oct is the octahedral shear stress; Pa is the atmospheric pressure;  is the volumetric water content; f is the saturation factor; mh is the matric suction;  and  are the Henkel pore water pressure coefficients; and 1k , 2k , and 3k are regression coefficients.   21 k R d w mM k     where RM is the resilient modulus; d is the deviatoric shear stress; w is the Bishop's effective stress coefficient; m is the matric suction; and 1k and 2k are regression coefficients.

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From page 156...

... B-4 2 3 4 1 3 1 k k w oct R a a a k SVM k P P P               where RM is the resilient modulus;  is the bulk stress; oct 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                where VRM is the resilient modulus in the vertical direction; 1I is the first invariant of stress tensor; oct 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.

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From page 157...

... B-5       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 wopt                     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.

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From page 158...

... B-6 PERMANENT DEFORMATION MODELS OF UNBOUND LAYERS AND SUBGRADE  1 P r N N N         where P is the accumulated plastic strain; r is the resilient strain of granular material; N is the number of load cycles; and  and  are regression coefficients. p b r aN    where p is the accumulated plastic strain; r is the resilient strain of granular material; N is the number of load cycles; and a and b are regression coefficients.

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From page 159...

... B-7 1 b p RCN R    ' f qb d c q         where P 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      , 6sin 3 sin M     , 0 6cos 3 sin cq      , where c and  are cohesion and friction angle; and d and 'c are material parameters. max D fB C p dAN            where P is the accumulated plastic strain; N is the number of load cycles; d is the deviatoric shear stress; f is shear stress; m ax is shear strength; and A , B , C , and D are regression coefficients.    0 2 1m nNp e J I K             2sin 3 3 sin       6cos 3 3 sin cK      where P is the accumulated plastic strain; N is the number of load cycles; and 0 ,  , and  are regression coefficients; 2J is the second invariant of the deviatoric stress tensor; 1I is the first invariant of the stress tensor; 0 ,  ,  , m and n are model coefficients; and c and  are cohesion and friction angle, respectively.

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From page 160...

... B-8     910 0 1 9 9 0.15 20 2 log 0.61119 0.017638 4.8928510 1 10 r c e e W                                         where 0 ,  , and  are Pavement ME Design model coefficients; r 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                         where 0 ,  , and  are Pavement ME Design model coefficients; MBV is methylene blue value; pfc is the percent fines content; T is the scale factor of texture index; Aa is the shape factor of angularity index; A is the scale factor of angularity index; d is the dry density; Ga is the shape factor of gradation; Ta is the shape factor of texture index; and G is the scale factor of gradation.

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From page 161...

... B-9    ' tan ' tan bf n a a wc S           where f is the shear strength; n is the normal stress; 'c is the cohesion; ' is the effective angle of shearing resistance for a saturated soil; b 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.    ' tan ' tan bf n a a wc             where f is the shear strength; n is the normal stress; 'c is the cohesion; ' is the effective angle of shearing resistance for a saturated soil; b is the angle of shearing resistance with respect to matric suction; au is the air pressure; wu is the pore water pressure;  is the normalized volumetric water content; and  is the fitting parameter.

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From page 162...

... B-10 EROSION MODELS OF UNBOUND LAYERS ESALg          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  is the model coefficient. log 1.07 0.34 i dP m ESAL f m D       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.

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From page 163...

... B-11 v is time delay before the appearance of visible (measurable) damage; and  is shape factor related to the erosion rate.

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