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97 CHAPTER 5. INTERPRETATIONS, APPRAISAL, AND APPLICATIONS INTRODUCTION This project developed several models as described in previous chapters for unbound granular materials and subgrade, which are intended to enhance the sensitivity of predicted pavement performance to these underlying layers. The sensitivity of these enhanced models is evaluated in this chapter for both flexible and rigid pavements. The common performance indicators contained in the Pavement ME Design that will be evaluated here include fatigue cracking, rutting, and IRI for flexible pavements, and faulting for rigid pavements. The sensitivity analysis will demonstrate whether the predicted performance changes with the change of traffic load, operational conditions, material properties, and thickness of the structural layers. In addition, the proposed enhanced models are compared with the corresponding models in the Pavement ME Design, which shows the resulting difference in the prediction of pavement performance. MOISTURE-SENSITIVE, STRESS-DEPENDENT, AND CROSS-ANISOTROPIC RESILIENT MODULUS Unbound granular materials are generally applied in the bases and subbases to support pavement surfaces and transfer vehicle loads to the subgrades. The stiffness of the bases and subbases in the pavement design are described using MR, which is the ratio of axial stress and recoverable axial strain (196). However, in most pavement designs, the bases and subbases are treated as linear elastic and isotropic materials using one MR and Poissonâs ratio, which do not represent realistic properties of unbound granular materials. Researchers have shown that the MR of unbound granular materials depends upon the confining pressure (or sum of the principle stresses) and the octahedral shear stress. Predicted results using models (50, 51, 54, 197â201) that consider the effects of bulk and shear stresses have shown good to experimental results. In addition to the effects of stress conditions of materials, characterization of the MR can also be achieved with the density, moisture content, and gradation (4, 196). The anisotropy of unbound granular materials is mainly due to the preferred orientation and the compact force. Researchers generally believe that the modulus of unbound granular materials in the vertical direction is greater than that in the horizontal direction. The ignorance of this property will cause overestimation of tensile stresses in base layers, which affect further pavement performance models. Studies with the anisotropic base and subbase layers showed better predictions with field measurements compared with isotropic models (202). This section presents a pavement structure model with stress-dependent, moisture- sensitive, and anisotropic base layers using the commercial FE software COMSOL (Error! Reference source not found.). The responses of the pavement under different loading levels and the effects of some base material properties will also be shown. FE MODEL OF PAVEMENT STRUCTURES To simulate the responses of the pavement structure, researchers built a 2D axisymmetric model using the FE software COMSOL (Error! Reference source not found.). The 2D axisymmetric model can precisely represent the 3D cylindrical structure with axially symmetric geometry and loading conditions. It was applied and studied for large-scale tank tests (203) and
98 FWD tests (205). Figure 55 and Table 23 show the configuration of the model built in the software. Figure 55. The 2D Axisymmetric Model Used in FE Analysis. Table 23. Material Properties of Pavement Layers. Layer Material Description Material Properties Surface Linear Viscoelastic, Isotropic v=0.35 Base Nonlinear, Anisotropic, Moisture-Sensitive - Subgrade Nonlinear, Moisture-Sensitive, Isotropic v=0.4 The surface material is modeled as viscoelastic and isotropic. Due to the incomplete implementation of the constitutive model for viscoelastic materials as Eq. 5.1 (206, 207) in COMSOL, a method using the Partial Differential Equation Module coupling with the Linear Elastic Solid Module is applied and can successfully model linear viscoelastic materials (208). For solid-like viscoelastic materials such as asphalt concrete, a generalized Maxwell model is applied to represent the relaxation modulus of the material in terms of Prony series as in Eq. 5.2: 2ij kk ij ije eï³ ï¬ ï¤ ïï½ ï« (5.1) where ,ï¬ ï are Lameâs constant. ,ij ijeï³ are stress and strain components. kke is the first invariant of stress tensor. ijï¤ is Kronecker delta.
99 1 (t) exp( t/ ) n i i i E E E ï´ï¥ ï½ ï½ ï« ïï¥ (5.2) where (t)E is relaxation modulus. Eï¥ is long-term modulus. n is the number of Prony series. iï´ is relaxation time. The stress-dependent nonlinearity of unbound granular base materials can be characterized using Eq. 5.3 from the Pavement ME Design Guide: 321 1 ( ) ( 1) kk oct z IE k Pa Pa Pa ï´ ï½ ï« (5.3) In addition, researchers proposed an improved model to characterize the MR of unbound granular materials, which takes the moisture condition of the material into consideration. The formula is expressed as Eq. 5.4: 321 1 3( ) ( )kkm octz I f hE k Pa Pa Pa ï± ï´ï ï½ (5.4) where zE is vertical modulus of the material (assuming z axis is the vertical axis). 1 2 3, ,k k k are regression coefficients from laboratory tests. aP is atmosphere pressure. 1I is the first invariant of stress tensor. octï´ is the octahedral shear stress. ï± is volumetric water content. f is saturation factor. mh is matric suction. Table 24 shows an example of the base information. Table 24. Example of Base Material Information. State: Georgia, State Code: 13, SHRP ID: 4111 Moisture Condition Volumetric Water Content, % Matric Suction, kPa af, kPa bf cf hr, kPa Base Dry 8.76 527 27.44 0.58 1.07 20684 Medium 9.73 309 Wet 10.7 187 Subgrade Medium 23.34 308 45.57 0.88 0.56 20684 The anisotropy of the unbound granular base is modeled as cross-anisotropy, which requires five independent parameters to characterize the materials as shown in Eq. 5.5 (209):
100 2 2 0 2 2 0 2 0 0 0 0 0 0 0 0 0 (1 ) ( ) 0 0 0 ( ) (1 ) 0 0 0 1 0 0 0 10 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 zx xy zx zx xx xy zx zx zx yy zx zx xy zz z xy yz zx n n n n n n n n n n n nE n m m ïµ ïµ ïµ ïµ ï¡ï³ ïµ ïµ ïµ ïµ ï¡ï³ ïµ ï¡ ïµ ï¡ ïµï³ ï³ ï¡ ï¢ ï¢ ï³ ï¡ ï¢ ï³ ï¡ ï¢ ï¦ ï¶ï ï«ï¦ ï¶ ï§ ï·ï§ ï· ï« ïï§ ï·ï§ ï· ï§ ï·ïï§ ï· ï§ ï·ï½ï§ ï· ï§ ï·ï§ ï· ï§ ï·ï§ ï· ï§ ï·ï§ ï· ï§ ï·ï§ ï· ï§ ï·ï¨ ï¸ ï¨ ï¸ (5.5) in which: /x zn E Eï½ (5.6) /zx zm G Eï½ (5.7) 0 1 xyï¡ ïµï½ ï« (5.8) 2 0 1 2xy zxnï¢ ïµ ïµï½ ï ï (5.9) where zE is vertical modulus of the material. xE is the horizontal modulus of the material. zxG is the shear modulus in the z-x plane. xyïµ is Poissonâs ratio in the x-y plane. zxïµ is Poissonâs ratio in the z-x plane. Table 25 presents the material parameters applied in the models.
101 Table 25. Material Parameters of Pavement Layers. Surface Eï¥ 42 E , MPa; ï´ , s 1E 6564 1ï´ 4.09E-06 2E 6582 2ï´ 0.000256 3E 3200 3ï´ 0.00771 4E 1342 4ï´ 0.21 5E 299 5ï´ 3.88 6E 103 6ï´ 66.3 Base 1k 1637 n 0.45 2k 0.42 m 0.35 3k â0.20 zxïµ 0.38 0.43 Subgrade 1 k 1220 2k 0.28 3k â2.28 PAVEMENT PERFORMANCE PREDICTED BY THE PROPOSED MODEL AND PAVEMENT ME DESIGN MODEL As documented in the Pavement ME Design Guide, the performance of pavements is affected by the material properties of pavements including the stiffness and responses of pavements under traffic loading including strains at critical locations. In this chapter, the pavement performance predicted by the Pavement ME Design Guide distress models was used to investigate how the pavement structure, material properties, and the loading level influence the pavement performance. Additionally, the modulus models for unbound granular base proposed by researchers and Pavement ME Design Guide was compared in terms of distresses such as fatigue cracking and rutting. Fatigue Cracking in Asphalt Mixtures The approach explained in the Pavement ME Design Guide to predict fatigue life of the pavement is based on the calculation of damage at either the surface for top-down cracking or the bottom for bottom-up cracking (67). The final form to predict the number of load repetitions to failure is from the Asphalt Institute (AI) model (210) with the national field calibrated model. Since the original form of AI model was proposed to only predict load repetitions in the phase of crack initiation (211) and the difference between national and local conditions, the prediction model for top-down cracking is limited in its accuracy and variability (202). The performance of fatigue cracking in this section is evaluated using bottom-up fatigue cracking model in Pavement ME Design. For top-down cracking, alternative models can be found in recent research (194, 212): 3.9492 1.281 1 1 10.00432 ( ) ( )f t N k C Eï¥ ï¢ï½ (5.10)
102 in which, for the bottom-up cracking: 1 (11.02 3.49h ) 1 0.0036020.000398 1 ac k e ï ï¢ ï½ ï« ï« (5.11) 10MC ï½ (5.12) 4.84( 0.69)b a b VM V V ï½ ï ï« (5.13) where fN is the number of load repetitions to failure. tï¥ is tensile strain at the critical location. E is stiffness of the material. hac is thickness of the asphalt layer. ,a bV V are contents of air voids and effective binder. Permanent Deformation in the Base Layer To predict the permanent deformation of the pavement, the Pavement ME Design Guide applies models corresponding to the material type and computes the accumulated plastic strain at each sublayer. For the unbound granular materials, the proposed model (67) with the calibrated coefficient to predict the permanent deformation is presented as Eq. 5.14: ( /N)0(N) ( )a GB v r e h ï¢ï²ï¥ï¤ ï¢ ï¥ ï¥ ïï½ (5.14) in which: log 0.61119 0.017638 cWï¢ ï½ ï ï (5.15) 9 91 ( /10 ) 0 1 9 2 bb r r r e a E e a E ï¢ ï¢ï² ï²ï¥ ï¥ ï ï« ï½ (5.16) 1 9 1 0 9 ln( ) b r b r a EC a E ï½ (5.17) 9 1/0 910 ( )1 10 C ï¢ ï¢ï² ï½ ï (5.18) where GBï¢ is the national calibration factor, 1.673. cW is water content, %. rE is the MR of the layer/sublayer, psi. 0, ,ï¥ ï¢ ï² are material properties. rï¥ is resilient strain imposed in laboratory test to obtain material properties.
103 vï¥ is the average vertical strain in the layer/sublayer as obtained from the primary response model. h is the thickness of layer/sublayer, in; 1a =0.15; 9a =20.0; 1b =0; 9b =0. Researchers have developed a new ME rutting model, as noted in Chapter 4, to predict the rut depth in unbound granular materials with the load cycle. The formula of the model is presented as the following equation: 2( /N) ( )1 0(N) ( ) ( ) ( )1 m n m na p a a J PI K P P ï¢ï² ï¡ï¥ ï¥ ï ï ï«ï«ï½ (5.19) 2sin 3(3 sin ) ï¦ï¡ ï¦ ï¢ ï½ ï¢ï (5.20) 6 cos 3(3 sin ) cK ï¦ ï¦ ï¢ ï¢ ï½ ï¢ï (5.21) 0.2214 4.6 455.62 1262.75satc PI SGï±ï¢ ï½ ï ï« ï« ï (5.22) 0.0272 0.638 1.487 69.92opt satPIï¦ ï± ï±ï¢ ï½ ï ï ï« (5.23) 0 2000.083 0.237 0.072 0.404optP PIï¥ ï±ï½ ï« ï« ï (5.24) 00.679 0.74410 ï¥ï² ï«ï½ (5.25) 2000.026 0.029 2.647dPï¢ ï§ï½ ï ï« ï (5.26) 00.237 0.15310m ï¥ ïï½ (5.27) 0.827 0.277n mï½ ï ï (5.28) where cï¢ is the cohesion of the material, kPa. ï¦ï¢ is the friction angle of the material, degree. PI is the plasticity index of the material. SG is the specific gravity of the material. 200P is the percent passing No. 200 sieve. optï± is the optimum volumetric water content, %. satï± is the saturated volumetric water content, %. dï§ is dry density of the material, 3lb/ ft . 1I is the first invariant of the stress tensor. 2J is the second invariant of the deviatoric stress tensor. aP is atmosphere pressure, kPa.
104 COMPARISONS OF PROPOSED MODELS AND PAVEMENT ME DESIGN MODELS Before the sensitivity analysis, several cases are run to check the nonlinearity and anisotropy of the base layer in the pavement model. Different from most of current simulations that treat the subgrade as a linear elastic material, the pavement models with moisture-sensitive subgrade are shown in the following three sections. Check the Nonlinearity of the Unbound Granular Base Based on the Eq. 3.2, the nonlinearity of the base material reflects on its sensitivity to the stress state and the moisture condition of the base layer. In this case, four loading levels 201 kPa, 566 kPa, 755 kPa, and 1006 kPa and two moisture conditions are applied to determine the pavement responses. Figure 56 and Figure 57 show the critical responses and modulus contours at different loading levels. As the loading increases, the strains at critical points increase accordingly. The modulus in the base course increases with the loading level and decreases with the distance from the loading area, which matches with its stress-dependent property and previous research (213, 214). (a) (b) Figure 56. (a) Tensile Strain at the Bottom of the Surface and (b) Average Compressive Strain in the Centerline of the Base under Different Loading Levels. 0 100 200 300 400 500 600 St ra in ,Â Âµ É 201Â kPa 566Â kPa 755Â kPa 1006Â kPa 0 200 400 600 800 1000 1200 St ra in ,Â Âµ É 201Â kPa 566Â kPa 755Â kPa 1006Â kPa
105 (a) (b) (c) (d) Figure 57. Vertical Modulus Contours in the Base Layer under the Loading Level (a) 201 kPa, (b) 566 kPa, (c) 756 kPa, and (d) 1006 kPa (Unit: MPa). Figure 58 shows the modulus contours at different moisture conditions while other factors are the same. The modulus in the base course is higher in the dryer condition, which reflects that the moisture softens the base material. (a) (b) (c) Figure 58. Vertical Modulus Contours in the Base Layer at (a) Dry Condition, (b) Medium Condition, and (c) Wet Condition (unit: MPa). Check the Anisotropy of the Unbound Granular Base The anisotropy of the granular base material reflects on the ratio of vertical modulus to the horizontal modulus, which is the value of 1/n in the Eq. 5.6. Figure 59 shows that as the value of 1/n increases, the tensile strain at the bottom of the surface and the compressive strain at the top of subgrade show an ascending trend, which matches the conclusion of a previous study (215).
106 (a) (b) Figure 59. (a) Tensile Strain at the Bottom of the Surface; (b) Compressive Strain at the top of the Subgrade the Pavement with Different Anisotropy (1/n) of Base Layers. From the cases above, the FE model applied in the study shows differences with the loading level and the value of n, which demonstrates that the model proposed in this project is sensitive in terms of both the stress-dependent and anisotropic characteristics of the base. Check the Nonlinearity of the Subgrade In most of the current simulation of pavement structures, the subgrade was considered as linear and isotropic. However, the properties of the subgrade should also be characterized and modeled like base materials. It is necessary to study the effects of the stress-dependent and moisture-dependent MR to the pavement performance. In this section, the MR of the subgrade is modeled as in Eq. 3.2, and the coefficients are obtained and calculated from data in the LTPP database. Table 24 and Table 25 show the basic information of the subgrade. Figure 60 shows that 1) with the increase of the loading level, the modulus of the subgrade increases accordingly; and 2) with the increase of the depth, the modulus first increases and then decreases. Figure 60. Vertical Modulus Contours in the Subgrade at Different Loading Levels. Next, the models were applied to study the effects of the pavement structure, properties, and moisture conditions of the base and subgrade materials to the pavement performance. The models for the MR of the unbound base layer and the permanent deformation (rut depth) in the 310 315 320 325 330 335 340 St ra in ,Â Âµ É 0.67 1 2.22 520 560 600 640 680 720 760 St ra in ,Â Âµ É 0.67 1 2.22 â400 â350 â300 â250 â200 â150 â100 â50 0 30 40 50 60 70 De pt h, Â c m VerticalÂ Modulus,Â MPa 566Â kPa 755Â kPa 1006Â kPa
107 unbound base layer proposed by the Pavement ME Design Guide and researchers were compared. Comparison of Resilient Modulus Models for Unbound Granular Base The validation of the proposed model and comparison between the proposed model and the model in the Pavement ME Design were presented in previous studies (213, 214). The proposed model by researchers predicts the MR change of unbound materials due to moisture change more accurately since it considers the influence of the moisture change on the stress state of the material. Comparison of Rutting Models in Unbound Granular Base Eqs. 5.15 and 5.20 present the rut depth that is the permanent deformation in the base layer under repeated loads. The material properties required in these two models are obtained from LTPP database and presented in Table 26. Table 26. Base Material Information for Rut Depth Calculation. Information Value Volumetric Water Content in FE Model, % 9.73 P200 (Percent Passing No. 200 Sieve) 8.5 Maximum Dry Density, lb/ft3 135 PI (Plasticity Index) 14 Optimum Water Content, % 9 Specific Gravity 2.687 Load Number 100,000 Figure 61 shows the rut depth in the base layer using two models when other factors such as the pavement structure, material properties, loading level, and number of load repetitions are the same. When using the model proposed by researchers, the rut depth is greater. Figure 61. Rut Depth in the Base Layer Using Different Models. 0 0.1 0.2 0.3 0.4 To ta lÂ R ut Â D ep th ,Â i n ModelÂ in PavementÂ ME Design NewÂ Model
108 SENSITIVITY ANALYSIS OF PROPOSED MODELS AND PAVEMENT ME DESIGN MODELS The sensitivity analyses were performed on the FE models with the proposed base/subgrade models to determine the effects of the load level, pavement structure, material properties, and moisture conditions on the pavement performance, in which the rutting model is the proposed rutting model. Different Loading Levels Figure 62 presents the pavement performance under different loading levels as computed with the COMSOL using models developed by researchers. For the fatigue cracking, the loading repetitions are calculated based on the Pavement ME Design Guide criteria. The number of load repetitions decreases dramatically with the increase of the loading level. The total rut depth in the base layer is calculated using the permanent deformation model proposed by researchers when the loading repetition number is 100,000. The rut depth increases with the increase of the loading level. (a) (b) Figure 62. Pavement Performance Including (a) Load Repetitions to the Fatigue Cracking Failure; (b) Rut Depth in the Base at Different Loading Levels. 0.00E+00 5.00E+04 1.00E+05 1.50E+05 2.00E+05 2.50E+05 3.00E+05 3.50E+05 4.00E+05 N 566Â kPaÂ (9Â kips) 755Â kPaÂ (12Â kips) 1006Â kPaÂ (16 kips) 0 0.5 1 1.5 2 2.5 3 3.5 4 To ta lÂ R ut Â D ep th ,Â i n 566Â kPaÂ (9Â kips) 755Â kPaÂ (12Â kips) 1066Â kPaÂ (16 kips)
109 Different Thicknesses of the Asphalt Layer Figure 63 presents the pavement performance when using stresses and strains as computed with COMSOL and material models developed by researchers and when the thickness of the asphalt layer varies. Based on the Eqs. 5.10â11, the thickness has opposite effects on the terms kâ1 and the tensile strain at the critical location. Hence, an increase of the thickness of the asphalt layer delays the top-down cracking when the thickness is small. In terms of bottom-up cracking and the total rut depth in the base layer, the increase of the asphalt layer improves the pavement performance. (a) (b) Figure 63. Pavement Performance Including (a) Load Repetitions to the Fatigue Cracking Failure; (b) Rut Depth in the Base at Different Thickness of the Asphalt Layer. Different Thicknesses of the Base Layer Figure 64 presents the pavement performance when using stresses and strains as computed with COMSOL and material models developed by researchers and when the thickness 0.00E+00 2.00E+05 4.00E+05 6.00E+05 8.00E+05 1.00E+06 1.20E+06 1.40E+06 N 4âinÂ AC 6âinÂ AC 8âinÂ AC 0 0.5 1 1.5 2 2.5 3 3.5 To ta lÂ R ut Â D ep th ,Â i n 4âinÂ AC 6âinÂ AC 8âinÂ AC
110 of the base layer varies. As the thickness of the base layer increases, the tensile strain at the bottom of the asphalt layer decreases, which reduces the load repetitions to the fatigue cracking. For the rut depth in the base layer, an increase of the base layer thickness reduces the rut depth in the base layer. (a) (b) Figure 64. Pavement Performance Including (a) Load Repetitions to the Fatigue Cracking Failure and (b) Rut Depth in the Base at Different Thickness of the Base Layer. Different Moisture Conditions of the Base Layer Figure 65 presents the pavement performance when stresses and strains computed with COMSOL and the material models developed by researchers and when the moisture of the base layer varies. As the moisture content of base layer increases, the modulus of the base decreases, which reduces the load repetitions to the fatigue cracking. For the rut depth, when the moisture content of the base layer changes from 8.76 percent to 10.70 percent, the total rut depth also increases. 3.00E+05 3.20E+05 3.40E+05 3.60E+05 3.80E+05 4.00E+05 N 6âinÂ Base 10âinÂ Base 15âinÂ Base 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 To ta lÂ R ut Â D ep th ,Â i n 6âinÂ Base 10âinÂ Base 15âinÂ Base
111 (a) (b) Figure 65. Pavement Performance Including (a) Load Repetitions to the Fatigue Cracking Failure and (b) Rut Depth in the Base at Different Moisture Conditions of the Base Layer. SENSITIVITY ANALYSIS OF PROPOSED FAULTING MODELS The sensitivity analysis was performed on both the proposed first (or full) and second (or load-related) faulting models to assess the effect of various relevant performance-related variables on the development of faulting. Because the effect on the development of faulting not only depended on the designated variable but also on the interactions with other variables, the sets of selected variables should be values at their most normal scales when varying the designated variable. For simplicity, a LTPP pavement section of 1-3028 was used for conducting sensitivity analysis of the proposed faulting models. Figure 66 shows the pavement structure for the LTPP section 1-3028. Table 27 presents the basic information of the LTPP section 1-3028 for sensitivity analysis. 0.00E+00 5.00E+04 1.00E+05 1.50E+05 2.00E+05 2.50E+05 3.00E+05 3.50E+05 4.00E+05 4.50E+05 N DryÂ Condition Optimum Condition WetÂ Condition 0 0.1 0.2 0.3 0.4 0.5 0.6 To ta lÂ R ut Â D ep th ,Â i n DryÂ Condition Medium Condition Wet Condition
112 Figure 66. Pavement Structure for LTPP Section 1-3028. Table 27. Basic Information of LTPP Section 1-3028 for Sensitivity Analysis. Information Value State Alabama County Jefferson Climatic zone WNF Thickness of surface 10.2" Thickness of base layer 7" Type of base layer Unbound Use of dowel No Freeze-thaw cycles 60.88 Annual number of wet days 124 Annual number of days temperature greater than 32Â°C 52 Annual number of days temperature lower than 0Â°C 63 The designated variables to investigate the effect on faulting include: ï· Use of dowels (Yes or No). ï· Type of base layer (Bound or Unbound). ï· Thickness of base layer. ï· Annual average number of days with temperature greater than 32Â°C. ï· Freeze-thaw cycles. ï· Climatic zones (WF, WNF, DF, and DNF). Use of Dowel The effect of whether to use dowels in jointed concrete pavement on the development of faulting was investigated. The results of the investigation based on both faulting models are shown in Figure 67 indicating use of dowels in jointed concrete pavement always results in lower faulting based on both proposed faulting models. The effect of the use of dowels on faulting is to greatly diminish faulting.
113 (a) (b) Figure 67. Effect of Use of Dowels on Faulting Based on (a) Full Faulting Model and (b) Load-Related Faulting Model. Type of Base Layer The effect of the type of base layer (bound or unbound) on the development of faulting was studied. From Figure 68a, even though the faulting begins earlier when bound base layer was applied, the ensuing faulting depth grows faster and greater when unbound baser layer was applied. For the second faulting model, Figure 68b shows that selection of bound base layer diminishes faulting depth. (a) (b) Figure 68. Effect of Types of Base Layer on Faulting Based on (a) Full Faulting Model and (b) Load-Related Faulting Model.
114 Thickness of Base Layer Figure 69 shows the sensitivity of the thickness of the base layer on the development of faulting based on both the first and the second faulting models. From Figure 69a, it seems that the effect of the thickness of the base layer has slight impact on development of faulting. The thicker base layer can reduce the faulting depth even if it causes earlier occurrence of faulting. Obviously, in Figure 69b, an increase in thickness of base results in a decrease in the development of faulting. (a) (b) Figure 69. Effect of Thickness of Base Layer on Faulting Based on (a) Full Faulting Model and (b) Load-Related Faulting Model. Freeze-Thaw Cycles To illustrate the effect of the annual average freeze-thaw cycles on faulting, three different values of this variable are used in the sensitivity analysis. Figure 70 shows that by varying the freeze-thaw cycles in the two faulting models. A larger freeze-thaw cycle results in more faulting. This is consistent with the fact that a major cause of faulting is temperature variations. The greater the freeze-thaw cycles, the larger temperature variations that can severely curve slabs upward or downward and produce more faulting.
115 (a) (b) Figure 70. Effect of Freeze-Thaw Cycles on Faulting Based on (a) Full Faulting Model and (b) Load-Related Faulting Model. Annual Average Number of Days with Temperature Greater than 32Â°C The effect of the annual average number of days with temperature greater than 32Â°C (days32C) on faulting was studied. Figure 71b shows that the greater days32C results in less faulting based on the load-related faulting model, which indicates the deformation of underlying layers. In Figure 71a, for the full model, the initial segments of the three curves prior to the critical inflection point basically tally with the results in Figure 71b. After passing the critical inflection point where erosion begins to dominate the rate of faulting, the order of the faulting magnitude reverses the order in Figure 71b. Thus, prior to reaching the critical inflection point, the greater the number of days with days32C, the less the pre-critical faulting. After passing the critical point where erosion is the principal cause of accelerating faulting, the order of faulting magnitude reverses. (a) (b) Figure 71. Effect of Number of Days with Temperature Greater than 32Â°C on Faulting Based on (a) Full Faulting Model and (b) Load-Related Faulting Model.
116 Effect of Climatic Zone Figure 72 shows the development of faulting in different climate zones. The faulting develops faster and greatest in the WF climatic zone and accumulates slowest and lowest in the DF climate zone from Figure 72a but in WNF climate zone from Figure 72b. This difference comes from the unbalanced data sets regression, which indicates section sizes for four different climatic zones were unbalanced for first and second faulting model regressions. (a) (b) Figure 72. Effect of Climatic Zone on Faulting Based on (a) First Faulting Model and (b) Second Faulting Model. SENSITIVITY ANALYSIS OF PROPOSED MODULUS OF SUBGRADE REACTION MODEL Researchers developed a moisture and suction dependent MR model, as noted in Eq. 4.20. Similarly, to improve the slab-base interface bond sensitivity in rigid pavement performance, an ANN model was developed in Chapter 4. To examine the sensitivity of the moisture and degree of bonding on pavement performance, the proposed models were applied in eight LTPP pavement sections listed in Table 28.
117 Table 28. Selected LTPP Pavement Sections and FWD Backcalculated Modulus Values for Each Layer. Climate zone State State code SHRP ID Slab thickness (in.) Base thickness (in.) Backcalculated values Î´ Slab modulus (psi) Base modulus (psi) Subgrade modulus (psi) Wet- Freeze Minnesota 27 4034 10 3.6 5342000 98000 11000 0.52 Kentucky 21 4025 9.8 6 5693000 195000 25000 0.9 Wet- Nonfreeze Alabama 01 0606 10.3 6.3 7798000 195000 8000 0.5 North Carolina 37 5037 7.8 15.1 4875000 20000 14000 0.11 Dry- Freeze Colorado 08 7776 10.7 15.3 4147000 100000 27000 0.48 North Dakota 38 3006 8.5 3.8 10000000 199000 50000 0.37 Dry- Nonfreeze New Mexico 35 3010 7.9 6.9 7171000 64000 22000 0.22 Arizona 04 0214 8.3 6.1 7087000 98000 25000 0.32 Each pavement section in Table 29 consisted of one surface, one base, and a subgrade layer. The modulus values for each layer are calculated using FWD backcalculation procedure. To illustrate the effect of moisture in subgrade k-value and therefore, pavement performance, MR values were calculated first at three different moisture conditions. Table 29 lists the MR values for each pavement structure at three selected moisture conditions: 1) equilibrium volumetric water content + 10 percent; 2) equilibrium volumetric water content; and 3) equilibrium volumetric water content â10 percent. Equilibrium suction and the corresponding volumetric water content were calculated using Eq. 4.15 and the SWCC equation developed by Fredlund and Xing as shown in Eqs. 4.1 and 4.2. The four fitting parameters (af, bf, cf, and hr) of the SWCC equation were predicted from the ANN model developed by researchers.
118 Table 29. Calculated MR Values at the Mid-depth of Base Layer at Different Moisture Conditions. State Code SHR P ID Î´ Saha et al. (133) Î¸ -hm(kPa) f Saha et al. (216) MR (MPa) af bf cf hr k1 k2 k3 27 4034 0 4.91 2.62 1.65 3000 0.0030 6 2621 1 689.3 0.66 -0.03 37.2 0.52 0.0034 1931 1 33.9 1 0.00374 1635 1 32.8 21 4025 0 5.86 0.34 1.74 2999 0.0418 5976 1 945.55 0.67 -0.29 880.2 0.9 0.0465 3845 1 707.5 1 0.0511 2498 1 569.2 01 0606 0 6.71 1.01 0.07 2998 0.1265 9386 1 913.7 0.73 -0.03 1397.2 0.5 0.1406 1750 2.74 930.3 1 0.1546 41 5.81 115.8 37 5037 0 7.57 0.98 1.08 2999 0.0606 732 1 431.43 0.92 -0.23 126.3 0.11 0.067 533 1 105.7 1 0.0741 403 1 91.5 08 7776 0 1.06 1.01 0.69 2999 0.072 3832 1 983.52 0.207 -0.027 167.2 0.48 0.08 1858 1 147.6 1 0.088 975 1 132.4 38 3006 0 1.00 1.01 0.79 2999 0.038 3778 1 544.43 0.65 -0.08 184.2 0.37 0.042 1961 1 131.1 1 0.046 1100 1 98.5 35 3010 0 5.30 3.35 1.05 2998 0.012 3189 1 859.5 0.73 -0.025 114.3 0.22 0.013 2093 1 92.5 1 0.015 1565 1 84.8 04 0214 0 5.05 0.12 2.18 2999 0.066 1995 1 900.14 0.509 0.047 162.9 0.32 0.073 533 1 92.3 1 0.08 124 1 54.7 The coefficients of the proposed MR model were predicted using the ANN model shown in Figure 17. To compare the sensitivity of moisture on subgrade k-value, the MR values were calculated at different moisture conditions using the proposed model and the Pavement ME Design model. After that, the subgrade k-values were calculated using the developed ANN model shown in Figure 36 and Pavement ME Design approach. Table 29 also list three different bonding conditions for each pavement structure: 1) no bond, 2) partially bonded, and 3) fully bonded. Each bonding condition was applied as an input in the developed ANN model and compared with the predicted k-values from Pavement ME Design. Figure 73 presents the sensitivity of degree of bonding on subgrade k-value using the developed ANN model and the Pavement ME Design model. Figure 74 illustrates the effect of moisture on subgrade k-value.
119 (a) (b) Figure 73. Sensitivity of Degree of Bonding on Subgrade k-value Using (a) ANN Model and (b) Pavement ME Design Model. 0.E+00 2.E+07 4.E+07 6.E+07 8.E+07 A N N p re di ct ed k -v al ue (N /m 3 ) LTPP pavement section identification number (State code-SHRP ID) NoÂ bond Partial bond Full bond 1.88% 2.74% 9.82% 13.99% 3.07% 10.18% 2.66% 13.82% 18.4% 38.44% 1.07% 2.97% â0.22% â0.33% 0.46% 2.87% 0.E+00 2.E+07 4.E+07 6.E+07 8.E+07 Pa ve m en t M E k- va lu e (N /m 3 ) LTPP pavement section identification number (State code-SHRP ID) NoÂ bond Full bond 13.63% 9.98% 13.74% 38.07% 2.76% â0.34% 2.83% 2.51%
120 (a) (b) Figure 74. Sensitivity of Moisture on Subgrade k-value Using (a) ANN Model and (b) Pavement ME Design Model. Figure 73 shows that both ANN model and the Pavement ME Design have similar sensitivity of degree of bonding on k-value. But, as shown in Figure 73a, ME design model has no partial bonding condition whereas ANN model can predict k-value at any bonding conditions. In both cases, degree of bonding has higher sensitivity when the base-slab modulus ration is relatively higher. LTPP section 21-4025 and 08-7776 have a higher modulus ratio compared to the other sections and therefore shows a significant change in k-value due to the change in degree of bonding. 0.E+00 2.E+07 4.E+07 6.E+07 8.E+07 A N N p re di ct ed k -v al ue (N /m 3 ) LTPP pavement section identification number (State code-SHRP ID) Eq.Â vol.Â wc.Â +Â 10% Eq. vol. wc. Eq. vol. wc. - 10% 0.08% 0.30% 2.23% 4.89% 14.237% 20.42% 2.73% 6.37% 0.83% 1.78% â2.75% â5.34% 3.18% 0.12% 0.40% â0.0037% 0.E+00 2.E+07 4.E+07 6.E+07 8.E+07 Pa ve m en t M E k- va lu e (N /m 3 ) LTPP pavement section identification number (State code-SHRP ID) Eq.Â vol.Â wc.Â +Â 10% Eq. vol. wc. Eq. vol. wc. - 10% 1.2Eâ05% 2.5Eâ05% â0.37% â0.68% â0.49% â1.09% 1.68% 3.50% 0.27% 1.20% â0.07% â0.03% 1.5Eâ04% 2.3Eâ04% 0.65% 1.16%
121 Figure 74 compares the sensitivity of moisture on k-value using the ANN model and Pavement ME Design model. Pavement ME Design has almost no sensitivity of moisture on subgrade k-value. But the proposed ANN model shows relatively higher sensitivity. Although the combination of moisture-sensitive MR model and the developed ANN model show large sensitivity to moisture and slab-base degree of bonding on k-value, it is still necessary to evaluate the effect of moisture and degree of bonding on pavement performance. The next section describes the prediction of the fatigue cracking (top-down and bottom-up) and faulting performance for various bonding and moisture conditions and compares with the predicted performance using Pavement ME Design model. SENSITIVITY ANALYSIS OF RIGID PAVEMENT PERFORMANCE TO PROPOSED MODELS The Pavement ME Design Guide adopted an incremental distress calculation procedure that requires hundreds of thousands of stress and deflection calculations to compute monthly damage (i.e., different loads, load positions, and temperature gradients) over a design period. ISLAB2000 FE software is used in the design guide to accurately compute rigid pavement responses, such as stresses and deflections under the influence of traffic and environmental load. The structural distress considered for JPCP design are fatigue related transverse cracking of PCC slabs and differential deflection related transverse joint faulting. Transverse cracking of PCC slab initiates either at the top surface of the PCC slab and propagate downward (top-down cracking) or vice-versa (bottom-up cracking) depending on the loading and environmental conditions. Both types of fatigue cracking and the faulting performance are considered in this study for sensitivity analysis. The fatigue damage at the top of the slab occurs due to repeated loading by heavy axles when the pavement is exposed to high negative temperature gradient (the top of the slab cooler than bottom of the slab). The critical loading condition for top-down cracking involves a combination of axles that loads the opposite ends of a slab simultaneously. In the presence of high negative temperature gradient, such load combinations cause a high tensile stress at the top of the slab near the critical edge. Similarly bottom-up transverse cracking initiate due to a critical tensile bending stress at the bottom of the slab. This bending stress is maximum when the truck axles are near the longitudinal edge of the slab, midway between the transverse joints. Moreover, this stress increases greatly when there is a high positive temperature gradient through the slab (the top of the slab is warmer than the bottom of the slab). A difference in elevation across a joint or crack is classified as faulting distress. Repeated heavy axle loads crossing transverse joints creates the potential for joint faulting. In this study, to compute the critical stress for top-down cracking, two single axles load, weighing 22,000 lb each, were applied at opposite ends of the transverse joint in addition to a negative 3Â°C temperature gradient. While for bottom-up cracking, one single axle load of 22,000 lb at midway between the transverse joints was exposed to a positive 3Â°C temperature gradient. Last, one tandem axle load, weighing 57,000 lb near the edge of transverse joint was applied for the computation of joint faulting. No temperature gradient was applied for faulting distress calculation. Figure 75 shows the effect of degree of bonding on pavement performance (i.e., tensile stress at surface, tensile stress at slab bottom, and differential deflection across the transverse joint) using the k-value predicted from ANN model and Pavement ME Design model.
122 ANN model Pavement ME Design (a) ANN model Pavement ME Design (b) 0 0.3 0.6 0.9 1.2 1.5 Te ns ile st re ss a t s ur fa ce (M Pa ) LTPP pavement section identification number FullÂ bond Partial bond No bond 0. 96 % 1. 8% â0 .1 3% 12 .4 1% 3. 85 % 4. 27 % 6. 94 % 8. 11 % 7. 55 % 17 .4 9% 1. 54 % 2. 50 % 0. 23 % 2. 46 % 2. 01 % 3. 01 % 0 0.3 0.6 0.9 1.2 1.5 Te ns ile st re ss a t s ur fa ce (M Pa ) LTPP pavement section identification number FullÂ bond No bond 0. 43 % 3. 45 % 7. 40 % â 2. 04 % 2. 65 % 2. 96 % 0. 89 % 0. 64 % 0 0.4 0.8 1.2 1.6 2 Te ns ile st re ss a t s la b bo tto m (M Pa ) LTPP pavement section identification number FullÂ bond Partial bond No bond 0. 99 % 1. 91 % 2. 01 % 7. 2% 4. 27 % 6. 44 % 7. 53 % 8. 76 % 9. 31 % 21 .2 8% 1. 66 % 2. 68 % 0. 29 % 3. 18 % 2. 41 % 3. 63 % 0 0.4 0.8 1.2 1.6 2 Te ns ile st re ss a t s la b bo tto m (M Pa ) LTPP pavement section identification number FullÂ bond No bond 1. 34 % 5. 2% â0 .8 3% 9. 02 % 14 .2 6% â0 .1 1% 2. 74 % 3. 41 %
123 ANN model Pavement ME Design (c) Figure 75. PCC Slab-Base Interface Bond Sensitivity on (a) Tensile Stress at Top of Slab; (b) Tensile Stress at Bottom of Slab; and (c) Deferential Deflection on Transverse Joints. The developed ANN model has larger sensitivity of tensile stress and differential deflection due to change in degree of bonding at slab-base interface. For both ANN model and Pavement ME Design model, fully bonded condition shows the lowest tensile stress and differential deflection whereas no bonding between slab and base develop largest tensile stress and deflection. As seen, Pavement ME Design model can only calculate tensile stress and deflection at two extreme bonding conditions, but the developed ANN model has the capability of predict tensile stress and deflection at partially bonded condition as well. Figure 76 shows the sensitivity of moisture on tensile stress and differential deflection using the proposed moisture and suction dependent MR model and Pavement ME Design model. 0 0.1 0.2 0.3 0.4 D iff er en tia l s la b de fle ct io n (m m ) LTPP pavement section identification number FullÂ bond Partial bond No bond 0. 37 % 0. 90 % 1. 28 % 4. 51 % 1. 66 % 2. 46 % 3. 46 % 4. 15 % 6. 16 % 13 .2 1% 0. 73 % 1. 16 % 0. 07 % 0. 87 % 1. 16 % 1. 60 % 0 0.1 0.2 0.3 0.4 D iff er en tia l s la b de fle ct io n (m m ) LTPP pavement section identification number FullÂ bond No bond 0. 77 % 4. 18 % 2. 20 % 3. 83 % 12 .6 5% 7. 99 % 0. 73 % 1. 49 %
124 ANN model Pavement ME Design (a) ANN model Pavement ME Design (b) 0 0.3 0.6 0.9 1.2 1.5 Te ns ile st re ss a t s ur fa ce (M Pa ) LTPP pavement section identification number Eq.Â vol.Â wc.Â +10% Eq. vol. wc. Eq. vol. wc. - 10% 0. 00 04 6% 0. 50 % â0 .1 5% 3. 33 % â0 .0 2% 0. 22 % 1. 10 % 1. 96 % 0. 59 % 1. 10 % 0. 33 % 0. 50 % 0. 12 % 0. 12 % 0. 33 % 0. 48 % 0 0.3 0.6 0.9 1.2 1.5 Te ns ile st re ss a t s ur fa ce (M Pa ) LTPP pavement section identification number Eq.Â vol.Â wc.Â +10% Eq. vol. wc. Eq. vol. wc. - 10% 0% 0% 0 % 0% 0% 0% 0% â0 .0 00 2% 0% 0% 0% 0% 0. 00 02 % 0. 00 05 % 0 0.4 0.8 1.2 1.6 2 2.4 Te ns ile st re ss a t s la b bo tto m (M Pa ) LTPP pavement section identification number Eq.Â vol.Â wc.Â +10% Eq. vol. wc. Eq. vol. wc. - 10% 0. 01 1% 0. 01 5% 0. 97 % 1. 69 % 0. 00 1% 0. 00 1% 1. 23 % 2. 19 % 0. 70 % 1. 29 % 0. 16 % 0. 16 % 0. 15 % 0. 15 % 0. 42 % 0. 59 % 0 0.4 0.8 1.2 1.6 2 2.4 Te ns ile st re ss a t s la b bo tto m (M Pa ) LTPP pavement section identification number Eq.Â vol.Â wc.Â +10% Eq. vol. wc. Eq. vol. wc. - 10% 0. 03 % 0. 03 % â0 .0 1% â0 .0 3% â0 .0 2% â0 .0 3% 0. 10 % 0. 20 % â0 .0 00 1% 0. 00 02 % 0% 0% 0. 01 % 0. 00 1%
125 ANN model Pavement ME Design (c) Figure 76. Base Layer Moisture Sensitivity on (a) Tensile Stress at Top of Slab; (b) Tensile Stress at Bottom of Slab; and (c) Deferential Deflection on Transverse Joints. As shown in Figure 76, the Pavement ME Design model shows very low sensitivity of tensile stress at slab top and bottom and differential deflection due to the change in moisture at middle of base layer. However, the proposed MR model and the corresponding k-value from ANN model shows higher sensitivity in tensile stress and differential deflection for change in moisture. Tensile stress at slab top and bottom increases with the increase of moisture in base layer. In summary, the models developed in this project are sensitive and capable of identifying various pavement responses including stress and strain at the bottom and top of asphalt layer, and distresses including cracking and rutting in asphalt pavement and faulting in concrete pavement with different base and subgrade properties under different moisture and temperature conditions, while in the Pavement ME Design such obvious differences cannot be observed. 0 0.1 0.2 0.3 0.4 D iff er en tia l s la b de fle ct io n (m m ) LTPP pavement section identification number Eq.Â vol.Â wc.Â +10% Eq. vol. wc. Eq. vol. wc. - 10% 0. 03 % 0. 04 % 0. 76 % 1. 38 % 0. 03 % 0. 06 % 1. 03 % 1. 82 % 0. 37 % 0. 71 % â0 .4 5% â0 .9 7% 0. 06 % 0. 06 % 0. 04 % 0. 17 % 0 0.1 0.2 0.3 0.4 D iff er en tia l s la b de fle ct io n (m m ) LTPP pavement section identification number Eq.Â vol.Â wc.Â +10% Eq. vol. wc. Eq. vol. wc. - 10% 0% 0% â 0. 04 % â0 .1 % â0 .0 2% â0 .0 2% 0. 25 % 0. 49 % 0. 21 % 0. 31 % 0% 0% 0% 0% 0. 12 % 0. 24 %