Numerical Modeling of 3D Slopes with Weak Zones by Random Field and Finite Elements
Abstract
:1. Introduction
2. Methodology
2.1. Method for Generating 3D Random Fields
2.2. Method of Generating 3D Random Field
2.3. Method for Characterization of Anisotropic Correlation Structure
2.4. Simulation and Model Verification of Weak Zones in Slopes
- (1)
- Use Abaqus to build a 3D finite element slope model, including defining the material parameters of the rocks and weak zones, and setting the grid and boundary conditions of the model in the analysis step. Then output an inp file (a file executed by the Abaqus software).
- (2)
- Associate the yield strength in the material parameters of the slope with the user-defined field variable User Defined Field, and set the state variable Depvar at the same time.
- (3)
- Call the random field generated by the USDFLD subroutine to replace the yield strength in the original slope model.
- (4)
- Carry out the stability calculation of the slope model with weak zones constructed in (3), and obtain the safety factor of the slope model.
- (5)
- According to the above steps, perform 100 Monte-Carlo simulations on the established model, and perform statistical analysis on the calculation results.
3. Slope Stability Analysis
4. Results and Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Reference | Method | Investigation Approach | Remarks |
---|---|---|---|
Liang et al., 1999 [35] | Limit equilibrium method | Analytical | Simple calculation method, only suitable for regular slopes |
Griffiths & Lane, 1999 [36] | Strength reduction method | Numerical | Calculate more complex models, but need to predict the slip surface in advance |
Ling & Wu, 2009 [4] | Centrifuge modeling | Physical model | Show the plastic failure but cannot reflect the complex engineering geological conditions |
Liu et al., 2013 [37] | Finite element strength reduction method | Numerical | Reflect the influence of the weak zones on the stability of the slope, but cannot reflect the spatial heterogeneity of the weak zones |
Liu et al., 2018 [33] | Two-phase random media | Numerical | Reflect the characteristics of the rock-soil slope, but limited to a two-dimensional model, and cannot reflect the spatial variability of the slope shape |
Huang et al., 2020 [38] | Discrete element method | Numerical | Simulate the nonlinear large deformation characteristics, but have low solution efficiency for complex models |
Wang et al., 2021 [28] | Random finite element method | Numerical | Characterize the stratification of the soil inside the slope, but cannot reflect the slope of the soil–rock mixture. |
Parameter | Unit | Value |
---|---|---|
(a) Deterministic parameter | ||
Yield strength of weak zones | kPa | 10 |
Yield strength of rocks | kPa | 50 |
Young’s modulu of weak zones | kPa | 105 |
Young’s modulu of rocks | kPa | 5 × 105 |
Poisson’s ratio | – | 0.3 |
Correlation length along x direction θx | m | 5 |
Correlation length along y direction θy | m | 1 |
Correlation length along z direction θz | m | 10,000 |
(b) Variable parameter | ||
Volume fraction of weak zones | – | [0~1] |
Material | Volumetric Weight γ (kN/m3) | Elastic Modulus E (GPa) | Poisson Ratio v | Cohesion c (kPa) | Internal Friction Angle φ (°) |
---|---|---|---|---|---|
Rock (weathered flint strips dolomite) | 28.0 | 100 | 0.2 | 50 | 30 |
Weak zones (residual cohesive soil) | 18.0 | 0.002 | 0.3 | 10.73 | 20 |
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Xia, Y.-X.; Cheng, P.; Liu, M.-M.; Hu, J. Numerical Modeling of 3D Slopes with Weak Zones by Random Field and Finite Elements. Appl. Sci. 2021, 11, 9852. https://doi.org/10.3390/app11219852
Xia Y-X, Cheng P, Liu M-M, Hu J. Numerical Modeling of 3D Slopes with Weak Zones by Random Field and Finite Elements. Applied Sciences. 2021; 11(21):9852. https://doi.org/10.3390/app11219852
Chicago/Turabian StyleXia, Yu-Xiang, Po Cheng, Man-Man Liu, and Jun Hu. 2021. "Numerical Modeling of 3D Slopes with Weak Zones by Random Field and Finite Elements" Applied Sciences 11, no. 21: 9852. https://doi.org/10.3390/app11219852
APA StyleXia, Y.-X., Cheng, P., Liu, M.-M., & Hu, J. (2021). Numerical Modeling of 3D Slopes with Weak Zones by Random Field and Finite Elements. Applied Sciences, 11(21), 9852. https://doi.org/10.3390/app11219852