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74 Santha (1994) presented several model constant correla- (54) tions based on the resilient moduli data from Georgia. Cor- relations developed by Santha (1994) as a function of soil where (µ a − µw) is matric suction; k1, k 2, k 3, k6, and k 7 are properties are presented in Table 14. Validation of the corre- model constants; and α1 and β1 are regression constants lations proposed by Santha (1994) showed that these models estimated from clay content or plastic limit. This expression predicted close to the measured values. Limitations of these is a simplification of the five-parameter model. The fitting correlations include the requirement for several characteris- parameters (k6, and k 7) were reported to be close to 0 and tics and possible collinearity problems. 1 as per the experimental results and analy- ses reported by Gupta et al. (2007). Further Table 13 details on this model are reported by Gupta et Bulk Stress Based Model (Model 2I-1) Constants Developed by Rada and Witczak (1981) (Richter 2006) al. (2007). The previous equations are valid for both granular and cohesive soil types. Ooi et al. (2004) acknowledged that, although the above equations account for the effects of external stress state on the resilient modulus, they do not account for the internal tensile stress (suc- tion) caused by the soil type, soil structure, and the soil physical state. Overall, however, these equations address and capture both external confinement and shear stress effects on the resilient properties of granular and cohesive soils. Also, as stated by Irwin (n.d.), these non- linear models can be used in a semi-log format, which can result in better analysis of subgrade stresses including tensile stresses. Correlations Development and Evaluation Table 14 Correlations Developed from Model by Santha To address the effects of soil type and test-related variables, (1994) (Adapted from Richter 2006) several researchers analyzed their test data with the previ- ous model formulations and then determined the model constants. Different forms of regression equations were developed between model constants and soil properties. A summary of these studies is presented in the following sec- tions. Richter (2006) discussed a few of these correlations and their findings with respect to these models. Some of the findings presented here are based on the information pro- vided in Richter (2006). Other factors including the degree of anisotropy and its influence on moduli of aggregates were reported by Tutumleur and Thompson (1997). Rada and Witczak (1981) provided model constants based on the bulk stress model (Model MR2I-1) for various types of unbound granular materials including aggregates. Table 13 presents the model constants. Richter (2006) observed that a considerable range of model constants for various base materials was reported by Rada and Witczak Note: MC = moisture content; MOIST = optimum moisture content; SATU = percent saturation; COMP = percent compaction; (1981). The variation was attributed to moisture and den- S40 and S60 = percents passing numbers 40 and 60 sieves; sity variations as well as material characteristics (Richter CLY = percent clay (CLY); SLT = percent silt (SLT); 2006). SW = percent swell (SW); SH = percent shrinkage; DEN = density; and CBR = California Bearing Ratio.
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75 Another study conducted by Titus-Glover and Fernando erably based on different material types. Maher et al. (2000) (1995) presented model constants derived using MR3I-1 also reported several model constant parameters based on on various materials. Table 15 presents these constants and MR3I-1 on various New Jersey subgrades. Table 16 presents results. Richter (2006) noted that these results ranged consid- these results. Wolfe and Butalia (2004) attempted a comprehensive Table 15 evaluation of various models, including both direct and indi- Model Constants from Titus-Glover and Fernando 1995 Study (Richter 2006) rect models, to predict various resilient moduli properties. Figure 83 presents comparisons of various model predictions of resilient properties with measured moduli. The models termed in the figure correspond to the U.S. Department of Agriculture model, Hyperbolic model (MRDS 7), Georgia DOT model (Table 14), TxDOT model (MRDS 11), [spell out]UCS model (MRDS 4), and Ohio model (MRDS 4). From Figure 83, it can be mentioned that the MR pre- dicted from the six models shows large variations with the laboratory results for all the soil samples. Wolfe and Buta- lia (2004) noted that the existing models are not capable of providing accurate predictions of moduli. Variations in the model predictions and measured moduli can be attributed to differences in soil types and test procedures. The resilient Table 16 Model Constants for NJ Subgrades from Maher et al. (2000)
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76 FIGURE 83 Comparisons of various model predictions and measured moduli (Wolfe and Butalia 2004).
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77 moduli were measured using the AASHTO T294-94 Titi et al. (2006) used the MR3I-6 correlation, which was procedure, whereas the predicted moduli were based on recommended by the MEPDG guide. This study determined earlier AASHTO procedure data. This eventually resulted the model constant parameters for different Wisconsin sub- in the development of a new Model 2I-5. This model has grades and these constant parameters are then correlated with two constant parameters. Researchers analyzed their resil- various basic soil properties. A total of 136 test results were ient moduli data with this model and provided the following analyzed in the determination of model constant parameters, model constant equations as a function of soil properties (see k1, k 2, and k 3. Figure 84). Backcalculation of the moduli and their compar- isons for select soils are also presented in Figure 85, which indicates an excellent match with the measured moduli. Malla and Joshi (2006) used the MR3I-2 formulation and analyzed several subgrades from New England states. Vari- ous constant parameters derived from this study were then correlated with soil properties and compaction variables. Table 17 provides various model constant parameters devel- oped for coarse-grained soils, coarse-grained soils with CU ≤ 100, and fine-grained soils. Prediction of resilient moduli using these relationships was made with the measured moduli in the same tables. The coefficients of determination for most of these relationships are close to 0.40, indicating that these correlations could be considered as average at best. Malla and Joshi (2006) also developed individual soil correlations (AASHTO soil type) based on the measured test data. These correlations have higher R2 values, suggesting that these correlations are bet- ter than those developed for the grouped soil correlations of FIGURE 85 Comparisons between model predictions and Table 17. measured resilient moduli (Wolfe and Butalia 2004). FIGURE 84 Model 2I-5 constant equations recommended by Wolfe and Butalia (2004).