Displacement Calculation of a Multi-Stage Homogeneous Loess Slope Under Seismic Action
Abstract
1. Introduction
2. Effect of the Comprehensive Slope Ratio on Slope Displacement
2.1. Influence of the Number of Slope Stages on the Multi-Stage Loess Slope Displacement
2.2. Effect of the Slope Ratio on the Displacement of Multi-Stage Loess Slopes
3. Displacement Calculation of Multi-Stage Homogeneous Loess Slopes Under Seismic Action
3.1. Basic Assumptions
- (1)
- The slope soil body is a linear viscoelastic body.
- (2)
- The motion of the slope is horizontal shear motion under the horizontal seismic action [16].
- (3)
- It is a two-dimensional plane strain problem.
3.2. Equations of Motion
3.3. Boundary Conditions
- (1)
- Initial conditions [15]:
- (2)
- Continuous deformation conditions:
3.4. Displacement Calculation of Slope Soil
4. Calculation Validation
4.1. Calculation Model
4.2. Theoretical Calculation
4.3. Numerical Calculation
4.4. Comparative Analysis
5. Conclusions
- (1)
- Based on the basic theory of soil dynamics, this paper introduces the comprehensive slope ratio, takes the damping and deformation of the soil body into full consideration, establishes the displacement calculation model of a multi-stage homogeneous loess slope under seismic action, and provides the analytical expression.
- (2)
- In this paper, a multi-stage homogeneous loess slope model for each working condition is established using finite element software. It is found that, under the condition of an unchanged comprehensive slope ratio, a single change in the number of slope stages or slope ratio of all stages has a small influence on the horizontal displacement of a multi-stage slope, and the slope horizontal displacements along the direction of the slope height show the phenomenon of increasing first and then decreasing. Therefore, when calculating the horizontal displacement of a multi-stage homogeneous loess slope under seismic action, the geometric characteristics of a multi-stage loess slope can be simplified by adopting the comprehensive slope ratio.
- (3)
- Comparing the theoretical and numerical calculation results of this paper, it can be seen that the peak displacement of a multi-stage homogeneous loess slope at each height position does not deviate much (5.5%), which indicates that the theoretical calculation method of this paper is reasonable.
- (4)
- The analytical model could be extended in future work to account for stratified loess, anisotropy, or inhomogeneity, which would enhance the model’s realism and field applicability.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Working Condition | Slope Stage | Comprehensive Slope Ratio | Working Condition | Slope Stage | Comprehensive Slope Ratio |
---|---|---|---|---|---|
A1 | 1 | 1:0.75 | A-9 | 1 | 1:1.25 |
A-2 | 2 | A-10 | 2 | ||
A-3 | 3 | A-11 | 3 | ||
A-4 | 4 | A-12 | 4 | ||
A-5 | 1 | 1:1.0 | A-13 | 1 | 1:1.5 |
A-6 | 2 | A-14 | 2 | ||
A-7 | 3 | A-15 | 3 | ||
A-8 | 4 | A-16 | 4 |
Working Condition | Slope Ratio of Each Stage | Working Condition | Slope Ratio of Each Stage |
---|---|---|---|
B-1 | 1:1.0 1:1.0 1:1.0 | B-7 | 1:0.7 1:1.3 1:1.0 |
B-2 | 1:0.9 1:1.0 1:1.1 | B-8 | 1:0.6 1:1.0 1:1.4 |
B-3 | 1:0.9 1:1.1 1:1.0 | B-9 | 1:0.6 1:1.4 1:1.0 |
B-4 | 1:0.8 1:1.0 1:1.2 | B-10 | 1:0.5 1:1.0 1:1.5 |
B-5 | 1:0.8 1:1.2 1:1.0 | B-11 | 1:0.5 1:1.5 1:1.0 |
B-6 | 1:0.7 1:1.0 1:1.3 | / | / |
Parameter | Cohesion/(kPa) | Internal Friction Angle/(°) | Damping Coefficient/(kN·s/m) | Shear Modulus G/Mpa | Unit Weight of Soil γ/(kN/m3) |
---|---|---|---|---|---|
Value | 15 | 30 | 10 | 7.7 | 16.8 |
Slope Height/m | Peak Displacement/mm | |
---|---|---|
Theoretical Calculation | Numerical Simulation Calculation | |
0 | 18.0 | 18.9 |
5 | 19.3 | 19.8 |
10 | 19.4 | 19.6 |
15 | 18.5 | 18.6 |
20 | 17.5 | 17.9 |
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Li, J.; Ye, S.; Cui, X.; Liu, B.; Li, N. Displacement Calculation of a Multi-Stage Homogeneous Loess Slope Under Seismic Action. Buildings 2025, 15, 1484. https://doi.org/10.3390/buildings15091484
Li J, Ye S, Cui X, Liu B, Li N. Displacement Calculation of a Multi-Stage Homogeneous Loess Slope Under Seismic Action. Buildings. 2025; 15(9):1484. https://doi.org/10.3390/buildings15091484
Chicago/Turabian StyleLi, Jingbang, Shuaihua Ye, Xinzhuang Cui, Biao Liu, and Nianxiang Li. 2025. "Displacement Calculation of a Multi-Stage Homogeneous Loess Slope Under Seismic Action" Buildings 15, no. 9: 1484. https://doi.org/10.3390/buildings15091484
APA StyleLi, J., Ye, S., Cui, X., Liu, B., & Li, N. (2025). Displacement Calculation of a Multi-Stage Homogeneous Loess Slope Under Seismic Action. Buildings, 15(9), 1484. https://doi.org/10.3390/buildings15091484