Upper bound solution for active thrust of nonhomogeneous cohesive soil considering effects of intermediate principal stress

Abstract

Considering the variation of cohesion along the depth, the upper bound solution of active earth pressure for a rough inclined wall with sloped backfill is formulated based on a log-spiral failure mechanism. For a more accurate prediction, the influence of intermediate principal stress is taken into consideration using the unified strength theory. Converting the search for the active pressure to an optimization problem, the most critical failure surface can be located by a natural selection-based gravitational search algorithm (GSA). The proposed method is validated compared with existing methods for noncohesive and cohesive cases and proved to be more accordance with the limit equilibrium solution. The influences of the variation of soil cohesion and intermediate principal stress on active earth pressure coefficient are then fully studied. It can be concluded that both the variations of soil cohesion and intermediate principal stress have a significant influence on the active earth pressure coefficient.

Keywords

unified strength theory / earth pressure / logarithmic spiral failure surface / upper bound method / gravitational search algorithm

References

[1] XuS-Y, ShamsabadiA, TacirogluE. Evaluation of active and passive seismic earth pressures considering internal friction and cohesion [J]. Soil Dynamics and Earthquake Engineering, 2015, 70: 30-47

[2] MccookD K. Limit analysis and soil plasticity [J]. Soil Science Society of America Journal, 1976, 40(4): IV

[3] ShamsabadiA, XuS-Y, TacirogluE. A generalized log-spiral-Rankine limit equilibrium model for seismic earth pressure analysis [J]. Soil Dynamics and Earthquake Engineering, 2013, 49: 197-209

[4] YangX L, HuangF. Collapse mechanism of shallow tunnel based on nonlinear Hoek-Brown failure criterion [J]. Tunnelling and Underground Space Technology, 2011, 26(6): 686-691

[5] PatkiM A, MandalJ N, DewaikarD M. Determination of passive earth pressure coefficients using limit equilibrium approach coupled with the Kötter equation [J]. Canadian Geotechnical Journal, 2015, 52(9): 1241-1254

[6] YangX-L, LiZ-W. Upper bound analysis of 3D static and seismic active earth pressure [J]. Soil Dynamics and Earthquake Engineering, 2018, 10818-28

[7] ChenW F, SnitbhanN, FangH Y. Stability of slopes in anisotropic, nonhomogeneous soils [J]. Canadian Geotechnical Journal, 1975, 12(1): 146-152

[8] DuD-C, DiasD, YangX-L. Analysis of earth pressure for shallow square tunnels in anisotropic and non-homogeneous soils [J]. Computers and Geotechnics, 2018, 104: 226-236

[9] QinC-B, ChenC S. Kinematic stability of a two-stage slope in layered soils [J]. International Journal of Geomechanics, 2017, 17(9): 06017006

[10] MohammadiM, TavakoliH. Comparing the generalized Hoek-Brown and Mohr-Coulomb failure criteria for stress analysis on the rocks failure plane [J]. Geomechanics and Engineering, 2015, 91115-124

[11] YuM-H. Twin shear stress yield criterion [J]. International Journal of Mechanical Sciences, 1983, 25(1): 71-74

[12] DengL-S, FanW, YinY-P, et al.. Parametric study of the unified strength theory for a loess foundation supporting a strip footing [J]. Environmental Earth Sciences, 2019, 78(12): 1-14

[13] ZhangC-G, ZhaoJ-H, ZhangQ-H, et al.. A new closed-form solution for circular openings modeled by the Unified Strength Theory and radius-dependent Young’s modulus [J]. Computers and Geotechnics, 2012, 42: 118-128

[14] LiZ W, YangX L, LiY X. Active earth pressure coefficients based on a 3D rotational mechanism [J]. Computers and Geotechnics, 2019, 112: 342-349

[15] AntãoA N, SantanaT G, VicenteD S M, et al.. Three-dimensional active earth pressure coefficients by upper bound numerical limit analysis [J]. Computers and Geotechnics, 2016, 79: 96-104

[16] RaoP-P, ChenQ-S, ZhouY-T, et al.. Determination of active earth pressure on rigid retaining wall considering arching effect in cohesive backfill soil [J]. International Journal of Geomechanics, 2016, 16(3): 04015082

[17] SanthoshkumarG, GhoshP. Seismic passive earth pressure on an inclined cantilever retaining wall using method of stress characteristics — A new approach [J]. Soil Dynamics and Earthquake Engineering, 2018, 107: 77-82

[18] ShamsabadiA, Khalili-TehraniP, StewartJ P, et al.. Validated simulation models for lateral response of bridge abutments with typical backfills [J]. Journal of Bridge Engineering, 2010, 15(3): 302-311

[19] GaoW, WangX, DaiS, et al.. Study on stability of high embankment slope based on black hole algorithm [J]. Environmental Earth Sciences, 2016, 75(20): 1-13

[20] KhajehzadehM, TahaM R, El-ShafieA, et al.. A modified gravitational search algorithm for slope stability analysis [J]. Engineering Applications of Artificial Intelligence, 2012, 25(8): 1589-1597

[21] RashediE, Nezamabadi-PourH, SaryazdiS. GSA: A gravitational search algorithm [J]. Information Sciences, 2009, 179(13): 2232-2248

[22] RashediE, RashediE, Nezamabadi-PourH. A comprehensive survey on gravitational search algorithm [J]. Swarm and Evolutionary Computation, 2018, 41141-158

[23] FanW, BaiX Y, YuM H. Formula of ultimate bearing capacity of shallow foundation based on unified strength theory [J]. Rock and Soil Mechanics, 2005, 26(10): 1617-1622(in Chinese)

[24] YangX-L. Upper bound limit analysis of active earth pressure with different fracture surface and nonlinear yield criterion [J]. Theoretical and Applied Fracture Mechanics, 2007, 47(1): 46-56

[25] ZhuD-Y, QianQ-H. New approach for computation of earth pressure coefficients based on limit equilibrium method [J]. China Civil Engineering Journal, 2000, 33(1): 63-68

[26] TangD, JiangZ-M, YuanT, et al.. Stability analysis of soil slope subjected to perched water condition [J]. KSCE Journal of Civil Engineering, 2020, 24(9): 2581-2590