Stability analysis of three-dimensional two-bench unsaturated soil slopes under seismic loading

Abstract

Due to rainfall infiltration, groundwater activity, geological processes, and natural erosion, soil often exhibits heterogeneity and unsaturation. Additionally, seismic events can compromise slope stability. Existing analytical solutions typically consider a single failure mode, leading to inaccurate slope stability assessments. This study analyzes the impact of matric suction through three nonlinear shear strength models and adopts a heterogeneous soil model where cohesion linearly increases with depth. An improved pseudo-dynamic method is used to account for seismic effects. Based on a three-dimensional (3D) trumpet-shaped rotational failure mechanism, a new framework is established to analyze the stability of 3D two-bench slopes in heterogeneous unsaturated soil under seismic effects. The internal energy dissipation rate and external power at failure are calculated, and the gravity increase method is introduced to derive an explicit expression for the safety factor (F _s). The results are compared with previously published results, demonstrating the effectiveness of the proposed method. Sensitivity analyses on different parameters are conducted, discussing the influence of various factors on F _s. This study proposes a new formula for calculating the F _s of 3D two-bench slopes in heterogeneous unsaturated soil under seismic effects, providing a practical application for slope engineering.

References

[[1]] Lam L, Fredlund D G. A general limit equilibrium model for three-dimensional slope stability analysis [J]. Canadian Geotechnical Journal, 1993, 30(6): 905-919

[[2]] Zhang H, Hu X-L, Boldini D, et al.. Evaluation of the shear strength parameters of a compacted S-RM fill using improved 2-D and 3-D limit equilibrium methods [J]. Engineering Geology, 2020, 269: 105550

[[3]] Zhang R-H, Ye S-H, Tao H. Stability analysis of multistage homogeneous loess slopes by improved limit equilibrium method [J]. Rock and Soil Mechanics, 2021, 42(3): 813-825

[[4]] Wang X-F, Hu S-B, Wang E-Y. Study of slope vibration site effects and energy analysis from CO₂ static blasting [J]. Journal of Central South University, 2024, 31(1): 210-224

[[5]] Qin H, Tang H, Yin X-T, et al.. Disturbed zone calculation and stability evaluation method of footwall slope with slip-shear failure under excavation [J]. Journal of Central South University, 2024, 31(2): 589-601

[[6]] Lyu Y-N, Chen X, Tang J-B, et al.. Application assessment of hybrid smoothed finite element method for geotechnical deformation and stability analysis [J]. Journal of Central South University, 2023, 30(3): 919-933

[[7]] Sun R, Yang F, Yang J-S, et al.. Investigation of upper bound adaptive finite element method based on second-order cone programming and higher-order element [J]. Rocks and Soils Mechanics, 2020, 41(2): 687-694

[[8]] Yang J, Liu B, Wang Y-J, et al.. Roof control mechanism and partition compensation support technology of gob-side entry formed by N00 mining method in thin coal seam [J]. Journal of Central South University, 2024, 31(2): 602-620

[[9]] Zhou J-F, Qin C-B. Finite-element upper-bound analysis of seismic slope stability considering pseudo-dynamic approach [J]. Computers and Geotechnics, 2020, 122: 103530

[[10]] Chen W F. Limit analysis and soil plasticity [M], 1975, New York, Elsevier Scientific Pub. Co.

[[11]] Li T-Z, Gong W-P, Tang H-M, et al.. A meshed kinematical approach for 3D slope stability analysis [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2022, 46(15): 2913-2930

[[12]] Michalowski R L, Drescher A. Three-dimensional stability of slopes and excavations [J]. Géotechnique, 2009, 59(10): 839-850

[[13]] Yao Y, Wang Z. Study on upper bound limit analysis of horizontal layers slope stability based on optimization method [J]. Scientific Reports, 2023, 13(1): 6106

[[14]] Qu C-L, Fu D, Liu S-W, et al.. Upper limit analysis for ultimate bearing capacity of heterogeneous stratified slope [J]. Rock and Soil Mechanics, 2022, 43(10): 2923-2932

[[15]] Yang X L, Li L, Yin J H. Seismic and static stability analysis for rock slopes by a kinematical approach [J]. Géotechnique, 2004, 54(8): 543-549

[[16]] Yang X-L, Yin J-H. Slope stability analysis with nonlinear failure criterion [J]. Journal of Engineering Mechanics, 2004, 130(3): 267-273

[[17]] Yang X-L, Yin J-H. Upper bound solution for ultimate bearing capacity with a modified Hoek-Brown failure criterion [J]. International Journal of Rock Mechanics and Mining Sciences, 2005, 42(4): 550-560

[[18]] Zhong J-H, Yang X-L. Pseudo-dynamic stability of rock slope considering Hoek–Brown strength criterion [J]. Acta Geotechnica, 2022, 17(6): 2481-2494

[[19]] Drescher A. Limit plasticity approach to piping in bins [J]. Journal of Applied Mechanics, 1983, 50(3): 549-553

[[20]] Silvestri V. A three-dimensional slope stability problem in clay [J]. Canadian Geotechnical Journal, 2006, 43(2): 224-228

[[21]] Zhang Z L, Yang X L. Unified solution of safety factors for three-dimensional compound slopes considering local and global instability [J]. Computers and Geotechnics, 2023, 155: 105227

[[22]] Steedman R S, Zeng X. The influence of phase on the calculation of pseudo-static earth pressure on a retaining wall [J]. Géotechnique, 1990, 40(1): 103-112

[[23]] Bellezza I. A new pseudo-dynamic approach for seismic active soil thrust [J]. Geotechnical and Geological Engineering, 2014, 32(2): 561-576

[[24]] Hou C-Q, Zhang T-T, Sun Z-B, et al.. Seismic analysis of nonhomogeneous slopes with cracks using a discretization kinematic approach [J]. International Journal of Geomechanics, 2019, 19(9): 04019104

[[25]] Nian T K, Chen G Q, Luan M T, et al.. Limit analysis of the stability of slopes reinforced with piles against landslide in nonhomogeneous and anisotropic soils [J]. Canadian Geotechnical Journal, 2008, 45(8): 1092-1103

[[26]] Rao P-P, Zhao L-X, Chen Q-S, et al.. Three-dimensional limit analysis of slopes reinforced with piles in soils exhibiting heterogeneity and anisotropy in cohesion [J]. Soil Dynamics and Earthquake Engineering, 2019, 121: 194-199

[[27]] Ip S C Y, Rahardjo H, Satyanaga A. Three-dimensional slope stability analysis incorporating unsaturated soil properties in Singapore [J]. Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards, 2021, 15(2): 98-112

[[28]] Silvestri V. A three-dimensional slope stability problem in clay [J]. Canadian Geotechnical Journal, 2006, 43(2): 224-228

[[29]] Zhang L L, Fredlund D G, Fredlund M D, et al.. Modeling the unsaturated soil zone in slope stability analysis [J]. Canadian Geotechnical Journal, 2014, 51(12): 1384-1398

[[30]] Xu J-S, Yang X-L. Three-dimensional stability analysis of slope in unsaturated soils considering strength nonlinearity under water drawdown [J]. Engineering Geology, 2018, 237: 102-115

[[31]] Tan M-X, Vanapalli S K. Foundation bearing capacity estimation on unsaturated soil slope under transient flow condition using slip line method [J]. Computers and Geotechnics, 2022, 148: 104804

[[32]] Fredlund D G, Xing A-Q, Fredlund M D, et al.. The relationship of the unsaturated soil shear strength to the soil-water characteristic curve [J]. Canadian Geotechnical Journal, 1996, 33(3): 440-448

[[33]] Khalili N, Khabbaz M H. A unique relationship for χ for the determination of the shear strength of unsaturated soils [J]. Géotechnique, 1998, 48(5): 681-687

[[34]] Vanapalli S K, Fredlund D G, Pufahl D E, et al.. Model for the prediction of shear strength with respect to soil suction [J]. Canadian Geotechnical Journal, 1996, 33(3): 379-392

[[35]] Escario V, Sáez J. The shear strength of partly saturated soils [J]. Géotechnique, 1986, 36(3): 453-456

[[36]] Fredlund D G, Morgenstern N R, Widger R A. The shear strength of unsaturated soils[J]. Canadian Geotechnical Journal, 1978, 15(3): 313-321

[[37]] Wang Z, Cao L-Z, Wang D. Evaluation on upper limit of heterogeneous slope stability [J]. Rock and Soil Mechanics, 2019, 40(2): 737-742

[[38]] Zhou J-F, Qin C-B. Influence of soft band on seismic slope stability by finite-element limit-analysis modelling [J]. Computers and Geotechnics, 2023, 158: 105396

[[39]] Sun W-Y, Lin J-C, Ma Q-G, et al.. Seismic fragility assessment of circular metro tunnels in loess deposit [J]. Journal of Central South University, 2024, 31(3): 950-964

[[40]] Gazetas G, Garini E, Georgarakos T. Effects of near-fault ground shaking on sliding systems [C]. Geotechnical Earthquake Engineering and Soil Dynamics IV. Sacramento, California, USA, 2008, Reston, VA, American Society of Civil Engineers 1906-1921