Proposed Enhancements to Pavement ME Design: Improved Consideration of the Influence of Subgrade and Unbound Layers on Pavement Performance (2019)

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C-1 Appendix C. Evaluation and Screening of Unbound Layer and Subgrade Models A suitable unbound layer/subgrade model to enhance Pavement Mechanistic-Empirical (ME) Design should be equipped with the following capabilities: 1. Adequately reflects the influence of unbound layer/subgrade on pavement performance. 2. Offers availability of the data or the testing methods and equipment to provide the needed input data for model development. 3. Is relatively easy to implement within Pavement ME Design. To satisfy these requirements, researchers proposed a set of three criteria in the evaluation of unbound layer/subgrade models:  Susceptibility criterion.  Accuracy criterion.  Development criterion. Each criterion is elaborated below. SUSCEPTIBILITY CRITERION The susceptibility criterion refers to how the model responds to the changes in the operational conditions, including moisture, heat, traffic stress, and load-induced/particle-induced anisotropy. As listed in Tables 2 to 5 of the final report, the performance of flexible and rigid pavement is closely related to the operational conditions of unbound layers and subgrade. For example, as shown in Table 2, a flexible pavement is more susceptible to the load-related cracking (alligator and longitudinal cracking) when the modulus of the base course decreases. When the cross-anisotropy is considered, the fatigue life is normally shorter than when using an isotropic modulus for the base course. In addition, the modulus of the base course significantly reduces as the degree of moisture increases, which results in more severe load-related cracking. Based on the results in Tables 2 to 5, each unbound layer/subgrade model should be evaluated under these operational conditions. The degree of susceptibility of the model is divided into the following three levels:  High level.  Medium level.  Low level. ACCURACY CRITERION The accuracy criterion refers to how close the predictions made by an unbound layer/subgrade model are to the actual behaviors of these underlying materials. More specifically, the model should be verified by comparing to the laboratory measurements on unbound layer and subgrade materials. In addition, the model needs to be compared with the performance prediction that is made by its counterpart in Pavement ME Design through a sensitivity analysis. The degree of accuracy is described by three levels:

C-2  High level.  Medium level.  Low level. DEVELOPMENT CRITERION The development criterion refers to the efforts required to develop, validate, and α-test the unbound layer/subgrade model for the enhancements of Pavement ME Design. It is used to ensure that essential development issues can be identified and solved (e.g., whether the data elements that are needed for the model are available and/or whether the test methods and equipment that are needed to provide inputs for the model are available). Furthermore, the model can be validated by making predictions of the observed performance of pavements in the Long- Term Pavement Performance (LTPP) database and/or from state departments of transportation. This criterion will serve as the basis of the development and implementation of enhancements for Pavement ME Design in Phase II of this project. The ease of development of an unbound layer/subgrade model is rated as three levels:  Simple level.  Involved level.  Complex level. Based on the evaluation criteria established above, researchers developed a scoring method to rank the models of unbound layer and subgrade listed in Tables 2.6 to 2.11. Each model is scored against each criterion on a scale of 1 to 3. For the susceptibility criterion, the high, medium, and low levels are given 1 point, 2 points, and 3 points, respectively. For the accuracy criterion, the high, medium, and low levels are regarded as 1 point, 2 points, and 3 points, respectively. For the development criterion, the simple, involved, and complex levels are given 1 point, 2 points, and 3 points, respectively. Based on the descriptions in the collected literature, the unbound layer/subgrade model is graded for the particular level. The evaluation of susceptibility, which involves moisture, heat, traffic stress, and load-induced/particle-induced anisotropy, is conducted by reviewing whether the model considers these aspects. The assessment for accuracy depends on the extent of match between the predicted values and the measured/observed values. The determination of ease of development depends on whether the model coefficients can be obtained conveniently and efficiently, whether the tests conducted to attain the model inputs are accessible, and the degree of compatibility with Pavement ME Design. The results of applying the scoring method to each model are presented in Tables C.1 to C.6 corresponding to Tables 2.6 to 2.11. The total score in the last column of the following tables is the sum of the scores for each evaluation criterion.

C-3 Table C.1. Scoring Results of Modulus Models of Unbound Layers and Subgrade. Model Evaluation Criteria Total Score OC 1 DA2 ED3 M4 H5 A6 T7 Nonlinear Stress-dependent Model (51) 2 1 3 k RM k  3 3 3 2 3 2 16 Nonlinear Stress-dependent Model (52) 2 1 k RM k  3 3 3 2 3 2 16 Nonlinear Stress-dependent Model (53)  2 3 1R dM k k k    1 dk   2 4 1R dM k k k   1 dk  3 3 3 2 3 2 16 Nonlinear Stress-dependent Model (54) ' ' d R d a bM     3 3 3 2 3 2 16 Nonlinear Stress-dependent Model (55) 32 1 kk R dM k   3 3 3 2 3 2 16 Nonlinear Stress-dependent Model (56) 2 3 1 1 k k oct R IM k Pa Pa Pa             3 3 3 1 2 2 14 Nonlinear Stress-dependent Model (57) 2 3 1 1 1 k k oct R IM k Pa Pa Pa             3 3 3 1 2 2 14 Nonlinear Stress-dependent Model (58) 2 1 2 R I JM M Pa R Pa Pa             3 3 3 1 2 2 14 Moisture-sensitive Model (19)   log 1 exp ln R Ropt m opt M b aa bM k S S a          2 3 3 1 2 2 13 Moisture-sensitive and Stress-dependent Model (59)    2 3 1R d s a wM k k k k u u     2 3 3 2 2 2 14 1 Operational condition 2 Degree of accuracy 3 Ease of development 4 Moisture 5 Heat 6 Anisotropy 7 Traffic

C-4    2 4 1R d s a wM k k k k u u     Moisture-sensitive and Stress-dependent Model (60) 2 3 1 4 1 3 k koct R I kM k Pa Pa Pa             2 3 3 1 2 2 13 Moisture-sensitive and Stress-dependent Model (61) 2 3 1 1 3 k km oct R I fhM k Pa Pa Pa              1 3 3 1 2 2 12 Moisture-sensitive and Stress-dependent Model (12) 2 3 1 1 1 3 3 k km oct oct R II f h M k Pa Pa Pa                        1 3 3 1 2 3 13 Moisture-sensitive and Stress-dependent Model (42)   21 k R d w mM k     2 3 3 2 2 2 14 Moisture-sensitive and Stress-dependent Model (62) 2 3 1 1 k k w m oct R a a a M k P P P                 2 3 3 1 2 2 13 Moisture-sensitive and Stress-dependent Model (9) ' 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                         1 3 3 1 2 2 12 Moisture-sensitive and Stress-dependent Model (8)   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                     1 3 3 1 2 3 13 Moisture-sensitive and Stress-dependent Model (63) 2 3 4 1 3 1 k k w oct R a a a k SVM k P P P               1 3 3 1 1 2 11 Stress-dependent and Cross-anisotropic Model (64) 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 Gn m M M                3 3 1 1 2 2 12

C-5 Stress-dependent and Cross-anisotropic Model (65) 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                                             3 3 1 1 2 2 12 Moisture-sensitive, Stress-dependent, and Cross-anisotropic Model (66) 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 Gs r M M                 1 3 1 1 1 2 9 Regression Models for Stress-dependent Model Coefficients (67)     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 LL wcwopt opt s wopt                            3 3 3 1 2 1 13 Regression Models for Moisture-sensitive and Stress- dependent Model Coefficients (Error! Bookmark not  defined.)               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                        1 3 1 1 2 3 11 Empirical Regression Model for Resilient Modulus (68)  0.642555rM CBR 3 3 3 2 2 1 14 Empirical Regression Model for Resilient Modulus (68) 1155 555rM R  3 3 3 3 2 1 15 Empirical Regression Model for Resilient Modulus (69)  30000 0.14r iM a 3 3 3 3 2 1 15 Empirical Regression Model for Resilient Modulus (69)   0.64 752555 1 0.728r M wPI        3 3 3 3 2 1 15 Empirical Regression Model for Resilient Modulus (68) 0.64 1.12 2922555rM DCP       3 3 3 2 2 1 14

C-6 Table C.2. Scoring Results of Permanent Deformation Models of Unbound Layers and Subgrade. Model Evaluation Criteria Total Score OC DA ED M H A T Non-stress-dependent Mechanistic-empirical Model (70)  1 P r N N N         3 3 3 1 2 1 13 Non-stress-dependent Mechanistic-empirical Model (71) p b r aN    3 3 3 1 2 2 14 Non-stress-dependent Mechanistic-empirical Model (72) 0 N p e         3 3 3 1 2 1 13 Non-stress-dependent Mechanistic-empirical Model (73)    , 0 kzp p zz e   3 3 3 3 2 2 16 Stress-dependent Mechanistic-empirical Model (68) 0 N p s v r e               3 3 3 1 2 1 13 Stress-dependent Mechanistic-empirical Model (71) 6 0 1 2 6 0 1 2 log .log p oct r oct ka a a Pa Pa kb b b N Pa Pa                                       3 3 3 1 2 3 15 Stress-dependent Mechanistic-empirical Model (74) 1 b p RCN R    2 3 3 1 2 2 13 Stress-dependent Mechanistic-empirical Model (75) max D fB C p dAN            2 3 3 1 2 2 13 Stress-dependent Mechanistic-empirical Model (76)    0 2 1m nNp e J I K           1 3 3 1 1 3 12

C-7 Regression Models for Pavement ME Design Model Coefficients (72) 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                                          3 3 3 2 3 1 15 Regression Models for Pavement ME Design Model Coefficients (68)     910 0 1 9 9 0.15 20 2 log 0.61119 0.017638 4.8928510 1 10 r c e e W                                         2 3 3 1 3 1 13 Regression Models for Pavement ME Design Model Coefficients (77) 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                         2 3 3 1 1 1 11

C-8 Table C.3. Scoring Results of Shear Strength Models of Unbound Layers and Subgrade. Model Evaluation Criteria Total Score OC DA ED M H A T Non-moisture-sensitive Model (78) tannc    3 3 3 1 3 1 14 Moisture-sensitive Model (79)    ' tan ' tan bf n a a wc            1 3 3 1 2 3 13 Moisture-sensitive Model (80)   tantan nba wc u u     1 3 3 1 2 3 13 Moisture-sensitive Model (81)    ' tan ' tan bf n a a wc S           1 3 3 1 2 3 13 Moisture-sensitive Model (82)    ' tan ' tan bf n a a wc            1 3 3 1 2 3 13 Moisture-sensitive Model (83)         ' tan ' tanf n a a w a w a w b c                         1 3 3 1 2 3 13 Moisture-sensitive Model (77)  ' 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                          1 3 3 1 1 1 10 Moisture-sensitive Model (84) 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                       2 3 3 1 2 1 12

C-9 Table C.4. Scoring Results of Erosion Models of Unbound Layers. Model Evaluation Criteria Total Score OC DA ED M H A T Empirical Model (85) ESALg          3 3 3 1 3 2 15 Empirical Model (86) log 1.07 0.34 i dP m ESAL f m D       3 3 3 1 3 2 15 Empirical Model (87) exp 2.884 1.652 log 10,000 ESAL DE NPI               3 3 3 1 3 2 15 Empirical Model (88) 36.67 2.884 1.652 log 10,000 P NPI ESAL DE NPI F                  3 3 3 1 3 2 15 Empirical Model (89)  0.1031 2 1 log 14.524 6.777 9.0 100 m i i i N C P C nPercent erosion damage N      3 3 3 1 3 2 15 Empirical Model (68) Table-based Erodibility Class Assessment 3 3 3 2 3 1 15 Mechanistic-empirical Model (23)    0% D Nf Erosion f e          2 2 3 1 2 2 12

C-10 Table C.5 Scoring Results of Foundation Models of Subgrade Model Evaluation Criteria Total Score OC DA ED M H A T No-shear Model (90) (x,y) kw(x,y)p  3 3 3 1 3 1 14 No-shear Model (91) 2(x,y) kw(x,y) (x,y)p T w   3 3 3 1 3 2 15 No-shear Model (92) 2 2(x,y) kw(x,y) (x,y)p D w    3 3 3 1 3 2 15 Shear-included Model (93) 2(x,y) kw(x,y) G (x,y)p w   3 2 3 1 2 2 13 Shear-included Model (94) 2 2(1 ) p kw(x, y) G (x, y)k G p w c c       3 3 3 1 2 2 14 Table C.6. Scoring Results of Thickness Sensitive Models of Unbound Layers. Model Category Model Type Item Score Total Score Modulus Models Nonlinear Stress-dependent Models in Table 6 See Table 6 See Table 6 Moisture-sensitive and Stress-dependent Models in Table 6 Stress-dependent and Cross-anisotropic Models in Table 6 Moisture-sensitive, Stress-dependent, and Cross-anisotropic Model in Table 6 Permanent Deformation Models Stress-dependent Mechanistic-empirical Models in Table 7 See Table 7 See Table 7 Regression Models for Pavement ME Design Model Coefficients in Table 7 Shear Strength Models Moisture-sensitive Models in Table 8 See Table 8 See Table 8 Erosion Models Mechanistic-empirical Models in Table 9 See Table 9 See Table 9