A Semianalytical Model for Three-Dimensional Stability Analysis of Potentially Rotational Slopes in Unsaturated Soils
Publication: International Journal of Geomechanics
Volume 22, Issue 10
Abstract
Stability analysis of slopes subjected to steady infiltration is a hot topic in geotechnical engineering. However, the existing three-dimensional (3D) upper-bound limit analyses of unsaturated rotational slopes failed to take variable strength parameters and hydraulic parameters in space into account. To fill this gap, a semianalytical model is developed to capture the factor of safety (FS) and the critical failure region of unsaturated slopes based on the kinematical approach of limit analysis (KALA). A 3D rotational failure mechanism of unsaturated slopes subjected to steady vertical infiltrations is generated by a “point-by-point” technique, which can readily incorporate spatially variable strength parameters and hydraulic parameters. The work rates are calculated to formulate the objective function of FS, and the critical FS are optimized. The proposed model is validated through comparisons with the existing solutions and numerical solutions in terms of both the FSs and the failure patterns. The combined effects of hydraulic parameters and the size of slopes are investigated. An application to the stability analyses of unsaturated slopes with spatially variable physical parameters demonstrates that the proposed model has the potential to serve as a benchmark for the KALA of unsaturated slopes under complex geological conditions. Generally, the described framework can help geotechnical designers quickly evaluate the stability of unsaturated slopes in the preliminary design phase if the water table elevation is available and the hydraulic and strength parameters have been calibrated.
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Acknowledgments
The authors have received financial support from the Innovation Foundation of Central South University (Grant No. 1053320192343), the National Key R&D Program of China (Grant No. 2017YFB1201204), the Systematic Project of Guangxi Key Laboratory of Disaster Prevention and Engineering Safety (Grant No. 2020ZDK010), and the Fundamental Research Funds for the Central Universities (Grant No. JUSRP121055).
Notation
The following symbols are used in this paper:
- cap
- apparent cohesion;
- c′
- effective cohesion of soils;
- ct
- total cohesion;
- COV(i) (i
- ks, φ′, c′, 1/α, n) = variation coefficients of the mechanical and hydraulic parameters;
- Gs
- specific gravity of soils;
- H
- slope height;
- ks
- saturated hydraulic conductivity;
- Ly: (Lz)
- autocorrelation distances in the Y (Z) direction;
- n
- pore size distribution of soils;
- q
- specific discharge under vertical steady flow condition;
- Ri,j
- polar radius of the gravity centers of regular triangle Ti,j;
- polar radius of the gravity centers of inverted triangle T′i,j;
- S
- water saturation degree;
- Sr
- residual degrees of saturation;
- Se
- effective degrees of saturation;
- Si,j
- area of regular triangle Ti,j;
- area of regular triangle T′i,j;
- uw
- pore water pressures;
- Vi,j
- volume of regular triangle Ti,j;
- volume of regular triangle ;
- vi,j
- velocity magnitude of regular triangle Ti,j;
- velocity magnitude of inverted triangle ;
- W
- slope width;
- internal energy dissipation;
- work rate done by soil weight;
- W1
- width of the initial cross section of the 3D discretized failure mechanism;
- z
- vertical distance between the water table and the specified point within slopes;
- zu
- vertical distance between the slope toe and the location of water table elevation;
- α
- inverse of the air entry pressure;
- β
- slope inclination;
- δψ
- discretization angle between two adjacent points on a radial plane of the 3D discretized failure mechanism;
- δθ
- discretization angle between two adjacent radial planes of the 3D discretized failure mechanism;
- φ′
- effective friction angle of soils;
- γsat
- saturated unit weight of soils;
- γw
- water unit weight;
- η
- radial angle of the maximum cross section of the 3D discretized failure mechanism;
- λi,j
- length parameter of the discretized point Pi,j of the 3D discretized failure mechanism;
- μi
- (i = ks, φ′, c′, 1/α, n) means of the mechanical and hydraulic parameters;
- ρi
- (i = ks, φ′, c′, 1/α, n) autocorrelation coefficients of the mechanical and hydraulic parameters;
- cross-correlation coefficient of the effective soil cohesion and frictional angles;
- cross-correlation coefficient of the pore size distribution coefficient of soils and the air entry pressure;
- σ
- total stresses of soils;
- σ′
- effective stresses of soils;
- σs
- suction stress;
- τ
- shear stress;
- ω
- rotational angular velocity; and
- ψi,j
- angular parameter of the discretized point Pi,j of the 3D discretized failure mechanism.
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© 2022 American Society of Civil Engineers.
History
Received: Nov 8, 2021
Accepted: May 8, 2022
Published online: Jul 27, 2022
Published in print: Oct 1, 2022
Discussion open until: Dec 27, 2022
ASCE Technical Topics:
- Analysis (by type)
- Continuum mechanics
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering mechanics
- Failure analysis
- Geomechanics
- Geotechnical engineering
- Limit analysis
- Mathematics
- Motion (dynamics)
- Parameters (statistics)
- Rotation
- Slope stability
- Slopes
- Soil analysis
- Soil mechanics
- Soil properties
- Solid mechanics
- Statistics
- Three-dimensional analysis
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