Three-dimensional stability of two-step slope with crack considering temperature effect on unsaturated soil

Abstract

In existing studies, most slope stability analyses concentrate on conditions with constant temperature, assuming the slope is intact, and employ the Mohr-Coulomb (M-C) failure criterion for saturated soil to characterize the strength of the backfill. However, the actual working temperature of slopes varies, and natural phenomena such as rainfall and groundwater infiltration commonly result in unsaturated soil conditions, with cracks typically present in cohesive slopes. This study introduces a novel approach for assessing the stability of unsaturated soil stepped slopes under varying temperatures, incorporating the effects of open and vertical cracks. Utilizing the kinematic approach and gravity increase method, we developed a three-dimensional (3D) rotational wedge failure mechanism to simulate slope collapse, enhancing the traditional two-dimensional analyses. We integrated temperature-dependent functions and nonlinear shear strength equations to evaluate the impact of temperature on four typical unsaturated soil types. A particle swarm optimization algorithm was employed to calculate the safety factor, ensuring our method’s accuracy by comparing it with existing studies. The results indicate that considering 3D effects yields a higher safety factor, while cracks reduce slope stability. Each unsaturated soil exhibits a distinctive temperature response curve, highlighting the importance of understanding soil types in the design phase.

References

[1] MichalowskiR L. Stability assessment of slopes with cracks using limit analysis. Canadian Geotechnical Journal, 2013, 50(10): 1011-1021 J]

[2] HuY-n, JiJ, SunZ-b, et al.. First order reliability-based design optimization of 3D pile-reinforced slopes with Pareto optimality. Computers and Geotechnics, 2023, 162: 105635 J]

[3] LiY-x, YangX-l. Seismic displacement of 3D slope reinforced by piles with nonlinear failure criterion. International Journal of Geomechanics, 2019, 19(6): 04019042 J]

[4] ParkD, MichalowskiR L. Three-dimensional stability analysis of slopes in hard soil/soft rock with tensile strength cut-off. Engineering Geology, 2017, 229: 73-84 J]

[5] LamL, FredlundD G. A general limit equilibrium model for three-dimensional slope stability analysis. Canadian Geotechnical Journal, 1993, 30(6): 905-919 J]

[6] ZhangR-h, YeS-h, TaoH. Stability analysis of multistage homogeneous loess slopes by improved limit equilibrium method. Rock and Soil Mechanics, 2021, 42(3): 813-825[J]

[7] ZhangH, HuX-l, BoldiniD, et al.. Evaluation of the shear strength parameters of a compacted S-RM fill using improved 2-D and 3-D limit equilibrium methods. Engineering Geology, 2020, 269: 105550 J]

[8] SunR, YangF, YangJ-s, ZhaoY-d, ZhengX-c, LuoJ-j, YaoJ. Investigation of upper bound adaptive finite element method based on second-order cone programming and higher-order element. Rocks and Soils Mechanics, 2020, 41(2): 687-694[J]

[9] SwanC C, SeoY K. Limit state analysis of earthen slopes using dual continuum/FEM approaches. International Journal for Numerical and Analytical Methods in Geomechanics, 1999, 23(12): 1359-1371 J]

[10] LyuY-n, ChenX, TangJ-b, et al.. Application assessment of hybrid smoothed finite element method for geotechnical deformation and stability analysis. Journal of Central South University, 2023, 30(3): 919-933 J]

[11] ZhouJ-f, QinC-b. Finite-element upper-bound analysis of seismic slope stability considering pseudo-dynamic approach. Computers and Geotechnics, 2020, 122: 103530 J]

[12] YangX L, LiZ W. Comparison of factors of safety using a 3D failure mechanism with kinematic approach. International Journal of Geomechanics, 2018, 18(9): 04018107 J]

[13] ZhanM-j, XiaL-j, ZhanL-f, et al.. Recognition of changes in air and soil temperatures at a station typical of China’s subtropical monsoon region (1961–2018). Advances in Meteorology, 2019, 2019: 6927045 J]

[14] ShiX, WangG-j, ChenT-x, et al.. Long-term changes in layered soil temperature based on ground measurements in Jiangsu Province, China. International Journal of Climatology, 2021, 41(5): 2996-3009 J]

[15] MazdiyasniO, AghakouchakA. Substantial increase in concurrent droughts and heatwaves in the United States. Proceedings of the National Academy of Science, 2015, 112(37): 11484-11489 J]

[16] AbeyrathneA, JayasundaraC, CostaS, et al.. Deviatoric behaviour of compacted unsaturated soils within (q, v_w, p) space: An experimental study. Acta Geotechnica, 2023, 18(3): 1651-1669 J]

[17] ZhangL L, FredlundD G, FredlundM D, et al.. Modeling the unsaturated soil zone in slope stability analysis. Canadian Geotechnical Journal, 2014, 51(12): 1384-1398 J]

[18] VahedifardF, CaoT D, ThotaS K, et al.. Nonisothermal models for soil-water retention curve. Journal of Geotechnical and Geoenvironmental Engineering, 2018, 144(9): 04018061 J]

[19] CampanellaR G, MitchellJ K. Influence of temperature variations on soil behavior. Journal of the Soil Mechanics and Foundations Division, 1968, 94(3): 709-734 J]

[20] GrantS A, SalehzadehA. Calculation of temperature effects on wetting coefficients of porous solids and their capillary pressure functions. Water Resources Research, 1996, 32(2): 261-270 J]

[21] AlsherifN A, MccartneyJ S. Thermal behaviour of unsaturated silt at high suction magnitudes. Géotechnique, 2015, 65(9): 703-716 J]

[22] MaghsoodiS, CuisinierO, MasrouriF. Thermal effects on mechanical behaviour of soil-structure interface. Canadian Geotechnical Journal, 2020, 57(1): 32-47 J]

[23] SeniorR B. Tensile strength, tension cracks, and stability of slopes. Soils and Foundations, 1981, 21(2): 1-17 J]

[24] HeY, LiuY, ZhangY-b, et al.. Stability assessment of three-dimensional slopes with cracks. Engineering Geology, 2019, 252: 136-144 J]

[25] YoungT. An essay on the cohesion of fluids. Abstracts of the Papers Printed in the Philosophical Transactions of the Royal Society of London, 1832, 1: 171-172[J]

[26] BachmannJ, HortonR, GrantS A, et al.. Temperature dependence of water retention curves for wettable and water-repellent soils. Soil Science Society of America Journal, 2002, 66(1): 44[J]

[27] WatsonK M. Thermodynamics of the liquid state. Industrial & Engineering Chemistry, 1943, 35(4): 398-406 J]

[28] VanapalliS K, FredlundD G, PufahlD E, et al.. Model for the prediction of shear strength with respect to soil suction. Canadian Geotechnical Journal, 1996, 33(3): 379-392 J]

[29] FredlundD G, XingA-q. Erratum: Equations for the soil-water characteristic curve. Canadian Geotechnical Journal, 1994, 31(6): 1026 J]

[30] FredlundD G, XingA-q, FredlundM D, et al.. The relationship of the unsaturated soil shear strength to the soil-water characteristic curve. Canadian Geotechnical Journal, 1996, 33(3): 440-448 J]

[31] KhaliliN, KhabbazM H. A unique relationship for χ for the determination of the shear strength of unsaturated soils. Géotechnique, 1998, 48(5): 681-687 J]

[32] MichalowskiR L, DrescherA. Three-dimensional stability of slopes and excavations. Géotechnique, 2009, 59(10): 839-850 J]

[33] QinC B, ChianS C. Kinematic analysis of seismic slope stability with a discretisation technique and pseudo-dynamic approach: A new perspective. Géotechnique, 2018, 68(6): 492-503 J]

[34] ZhongJ-h, HouC-t, YangX-l. Bearing capacity of foundations resting on rock masses subjected to Rayleigh waves. Soil Dynamics and Earthquake Engineering, 2023, 167: 107791 J]

[35] ZhangZ L, WuY M. A general kinematic approach to the seismic stability assessment of slopes. Computers and Geotechnics, 2023, 160: 105519 J]

[36] ZhangZ L, YangX L. Unified solution of safety factors for three-dimensional compound slopes considering local and global instability. Computers and Geotechnics, 2023, 155: 105227 J]

[37] UtiliS. Investigation by limit analysis on the stability of slopes with cracks. Géotechnique, 2013, 63(2): 140-154 J]

[38] MariniF, WalczakB. Particle swarm optimization (PSO). A tutorial. Chemometrics and Intelligent Laboratory Systems, 2015, 149: 153-165 J]

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