A Multiscale Method to Develop Three-Dimensional Anisotropic Constitutive Model for Soils
Abstract
:1. Introduction
2. Inherent Anisotropy
2.1. Modified Stress Tensor
2.1.1. Basic Idea
2.1.2. Formula
2.1.3. A Simple DEM Verification
2.2. Transformed Stress Tensor
2.2.1. Basic Idea
2.2.2. Formula
2.3. Brief Summary
3. Anisotropic Yield Surface
3.1. In 3D Stress Space
3.2. On the Triaxial Meridian Plane
3.3. On the Deviatoric Plane
4. Induced Anisotropy
5. Anisotropic MCC Model
5.1. Plastic Flow Rule
5.2. Hardening Law
5.3. Elastic Stiffness Matrix
5.4. Elastoplastic Stiffness Matrix
5.5. Comparison between the Isotropic and Anisotropic MCC Models
6. Verification of the Proposed Method
7. Conclusions
- The inherent anisotropy is considered using two steps of stress mapping. From to , anisotropic soil is equivalent to isotropic soil; from to , the true triaxial yield/failure behaviors are similar to those of triaxial compression.
- The induced anisotropy is represented by a fabric evolution law, which plays the same role as the rotational hardening law but can capture the microscopic mechanism behind soil deformation.
- Based on an isotropic constitutive model, , the anisotropic model can be easily developed to predict the stress–strain relation of anisotropic soil in a three-dimensional stress state.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Reference | Anisotropic Yield Function | Rotational Hardening Law |
---|---|---|
Sekiguchi and Ohta [4] | / | |
Wheeler et al. [6] | ||
Dafalias and Manzari [11] | ||
Zhang et al. [12] | where | |
Anastasopoulos et al. [13] | ||
Seidalinov and Taiebat [14] | ||
Hong et al. [15] | ||
Shirmohammadi and Hajialilue-Bonab [16] | ||
Dejaloud and Rezania [17] | ||
Macias and Rotta Loria [18] |
Isotropic MCC Model | Anisotropic MCC Model | |
---|---|---|
Stress tensor | ||
Yield function | ||
Plastic flow rule | ||
Hardening law | ||
Elastic stiffness matrix | ||
Elastoplastic stiffness matrix | ||
Parameters | M, λ, κ, and ν | M, λ, κ, ν, Δ, C, and β |
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Tian, Y.; Chen, H.; Yao, Z.; Fang, Y. A Multiscale Method to Develop Three-Dimensional Anisotropic Constitutive Model for Soils. Buildings 2024, 14, 307. https://doi.org/10.3390/buildings14020307
Tian Y, Chen H, Yao Z, Fang Y. A Multiscale Method to Develop Three-Dimensional Anisotropic Constitutive Model for Soils. Buildings. 2024; 14(2):307. https://doi.org/10.3390/buildings14020307
Chicago/Turabian StyleTian, Yu, Hao Chen, Zijun Yao, and Yufei Fang. 2024. "A Multiscale Method to Develop Three-Dimensional Anisotropic Constitutive Model for Soils" Buildings 14, no. 2: 307. https://doi.org/10.3390/buildings14020307