Calculation of and Key Influencing Factors Analysis on Equivalent Resilient Modulus of a Submerged Subgrade
Abstract
:1. Introduction
2. Materials and Methods
2.1. Typical Submerged Subgrade Model
2.2. Constitutive Model of Resilent Modulus
2.3. Calculation of Equivalent Resilient Modulus
2.3.1. Equivalent Iteration
- Set the reference value. The value εt was calculated using the nonlinear model under the peak load.
- Calculate the linear elastic response. A linear elastic model was established with the initial modulus Ei between the maximum and minimum values in the modulus distribution of the nonlinear model, and the corresponding response εt’ under the same load was calculated.
- Iterative convergence algorithm. The convergence criterion is that the error between the linear elastic response and the reference value must be less than the permitted value (0.5%), and the bisection method was applied to ensure convergence of the iterations.
2.3.2. Weighted Average
3. Results
3.1. Validation of Constitutive Model
3.2. Distribution of Resilient Modulus
3.3. Dynamic Response
3.4. Equivalent Resilient Modulus
4. Discussion
4.1. Influence of Material Parameters
4.2. Influence of Structural Parameters
4.3. Design Framework for Submerged Subgrade
- Determine the model parameters, including boundary conditions, the constitutive model, structural parameters, and material parameters. The constitutive model of Equation (5) must be adopted, and other parameters need to be preliminarily determined in combination with local construction conditions and in consideration of engineering experience.
- Calculate the mechanical response. Calculate the tensile strain at the bottom of the asphalt layer, εt, and the compressive strain at the top of the subgrade, εc, under FWD loading as representative dynamic response indicators. At the same time, these two indicators will also be used as the basis for calculating the equivalent resilient modulus of the subgrade.
- Calculate the equivalent resilient modulus. The equivalent resilient modulus can be calculated via equivalent iteration with tensile strain and weighted average with compressive strain. Theoretically, the equivalent iteration method has higher accuracy, while the weighted average method has higher computational efficiency. Designers can choose a method according to the requirements of the task at hand.
- Carry out decision making. Judge whether the results of the equivalent resilient modulus meet the requirements. If so, then complete this design. If not, the design parameters can be modified with reference to the results of the key influencing factors analysis given in this study until the design requirements are met.
5. Conclusions
- The effect of water level rise on the tensile strain at the bottom of the asphalt layer and the compressive strain at the top of the subgrade is obvious, and its trend is similar to an exponential change. At a low water level, the change in compressive strain is more obvious, while the change in tensile strain is more significant when the water level rises to a point where the subgrade is close to saturation. In fact, a situation in which near-saturation occurs is very rare, so the indicator of compressive strain is especially important in the design of a submerged subgrade.
- The equivalent resilient modulus of the subgrade calculated using the equivalent iteration and weighted average methods has a strong correlation with the moisture content of the subgrade, and the modulus of the subgrade basically decreases linearly with the increase in the water level. The results of the weighted average based on the distribution of compressive strains at the top of the subgrade under FWD load are in high agreement with the results of the equivalent iteration, which is a more accurate method in theory. Therefore, it can be concluded that the method of determining the weighted average based on the distribution of compressive strain is feasible.
- Among the subgrade materials and structural parameters considered in this study, the saturated permeability coefficient and subgrade height have the most significant effect on the resilient modulus of the subgrade, while SWCC and subgrade width have a slight effect on the modulus, and the effect of slope can be approximately ignored. Therefore, during the process of designing a submerged subgrade, the influence of the above parameters on the dynamic response of the structure should be emphasized, and the corresponding suggested values of the resilient modulus of the subgrade should be proposed according to the actual construction conditions.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Layer | Material | Thickness (cm) | Elastic Modulus (MPa) | Poisson’s Ratio | Dry Density (g·cm−3) |
---|---|---|---|---|---|
Top layer | AC13 | 4 | 8200 | 0.25 | 2.40 |
Bottom layer | AC20 | 6 | 8000 | 0.25 | 2.40 |
Base course | Graded Aggregate | 20 | 300 | 0.35 | 2.32 |
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Tang, J.; Chen, S.; Ma, T.; Zheng, B.; Huang, X. Calculation of and Key Influencing Factors Analysis on Equivalent Resilient Modulus of a Submerged Subgrade. Materials 2024, 17, 949. https://doi.org/10.3390/ma17040949
Tang J, Chen S, Ma T, Zheng B, Huang X. Calculation of and Key Influencing Factors Analysis on Equivalent Resilient Modulus of a Submerged Subgrade. Materials. 2024; 17(4):949. https://doi.org/10.3390/ma17040949
Chicago/Turabian StyleTang, Junyao, Siyu Chen, Tao Ma, Binshuang Zheng, and Xiaoming Huang. 2024. "Calculation of and Key Influencing Factors Analysis on Equivalent Resilient Modulus of a Submerged Subgrade" Materials 17, no. 4: 949. https://doi.org/10.3390/ma17040949