Abstract
In this paper, factor of safety (FOS) considering three-dimensional (3D) and nonlinear shear strength of geomaterials is formulated based on the modified spatial mobilized plane (MSMP) model. The MSMP model has the desirable features of considering 3D strength and the nonlinear shear behavior of soils, compared with the widely used Mohr-Coulomb (M-C) model. The MSMP model is developed from the spatial mobilized plane model by relating the internal friction angle to the mean effective stress within the framework of critical state soil mechanics. Based on the developed MSMP model and the geometric relationships in the mobilized effective normal-shear stress plane, the nonlinear 3D FOS is defined as the ratio of mobilized shear strength to shear stress. The developed nonlinear 3D FOS is applied to slope parametric and case studies. The parametric studies show significant differences between the nonlinear 3D FOS by the MSMP model and the traditional linear two-dimensional (2D) FOS by the M-C model. The case study shows that the MSMP model and nonlinear 3D FOS can better capture the developed failure slope zone than the M-C model and linear 2D FOS.
Similar content being viewed by others
References
Abaqus (2013) ABAQUS user’s manual. Version 6.13-EF. Providence, RI, USA: Hibbitt, Karlsson & Sorensen, Inc.
Bishop AW, Webb DL, Lewin PI (1965) Undisturbed samples of London clay from the Ashford common shaft: Strength-effective stress relationships. Geotechnique 15:1–31, DOI: https://doi.org/10.1680/geot.1965.15.1.1
Camargo J, Velloso R, Vargas EA (2016) Numerical limit analysis of three-dimensional slope stability problems in catchment areas. Acta Geotechnica 11:1369–1383, DOI: https://doi.org/10.1007/s11440-016-0459-3
Charles JA, Soares MM (1984) The stability of slopes in soils with nonlinear failure envelopes. Canadian Geotechnical Journal 21(3): 397–406, DOI: https://doi.org/10.1139/t84-044
Chen SL, Liu K (2019) Undrained cylindrical cavity expansion in anisotropic critical state soils. Geotechnique 69(3):189–202, DOI: https://doi.org/10.1680/jgeot.16.P.335
Davis RO, Selvadurai APS (2002) Plasticity and geomechanics. Cambridge University Press: New York, USA
Drucker DC, Prager W (1952) Soil mechanics and plastic analysis or limit design. Quarterly of Applied Mathematics 10(2):157–165
Duncan JM, Wright SG, Brandon TL (2014) Soil strength and slope stability. John Wiley & Sons, Inc.
Fu WX, Liao Y (2010) Non-linear shear strength reduction technique in slope stability calculation. Computers and Geotechncis 37:288–298, DOI: https://doi.org/10.1016/j.compgeo.2009.11.002
Gamez JA, Stark TD (2014) Fully softened shear strength at low stresses for levee and embankment design. Journal of Geotechnical and Geoenvironmental Engineering 140(9):06014010, DOI: https://doi.org/10.1061/(ASCE)GT.1943-5606.0001151
Geostudio (2021) GEO-SLOPE International, Ltd., https://www.geoslope.com
Hasebe N, Wang XF (2003) Irregular elastic half-plane gravity problem. International Journal of Rock Mechanics and Mining Sciences 40(6):863–875, DOI: https://doi.org/10.1016/S1365-1609(03)00054-6
Iverson RM, Reid ME (1992) Gravity-driven groundwater flow and slope failure potential 1. Elastic effective-stress model. Water Resources Research 28(3):925–938, DOI: https://doi.org/10.1029/91WR02694
Lade PV (2010) The mechanics of surficial failure in soil slopes. Engineering Geology 114:57–64, DOI: https://doi.org/10.1016/j.enggeo.2010.04.003
Lee KL, See HB (1967) Drained strength characteristics of sand. Journal of the Soil Mechanics and Foundation Division 93(6):117–141, DOI: https://doi.org/10.1061/JSFEAQ.0001048
Li X (2007) Finite element analysis of slope stability using a nonlinear failure criterion. Computers and Geotechnics 34(3):127–136, DOI: https://doi.org/10.1016/j.compgeo.2006.11.005
Liu K, Chen SL (2019) Analysis of cylindrical cavity expansion in anisotropic critical state soils under drained conditions. Canadian Geotechnical Journal 56(5):675–686, DOI: https://doi.org/10.1139/cgj-2018-0025
Liu K, Chen SL, Gu XQ (2020) Analytical and numerical analyses of tunnel excavation problem using an extended Drucker-Prager model. Rock Mechanics and Rock Enngineering 53:1777–1790, DOI: https://doi.org/10.1007/s00603-019-01992-5
Liu K, Chen SL, Voyiadjis GZ (2019) Integration of anisotropic modified Cam Clay model in finite element analysis: Formulation, validation, and application. Computers and Geotechnics 116:103198, DOI: https://doi.org/10.1016/j.compgeo.2019.103198
Liu K, Zhang HJ, Yuan P, Xiao LF (2023) Theoretical solution for stress and strain distributions induced by generalized elastic constant variation in rock mass. International Journal of Geomechanics 24(9), DOI: https://doi.org/10.1061/IJGNAI.GMENG-8342
Martel SJ, Muller JR (2000) A two-dimensional boundary element method for calculating elastic gravitational stresses in slopes. Pure and Applied Geophysics 157:989–1007, DOI: https://doi.org/10.1007/s000240050014
Matsuoka H, Nakai T (1974) Stress-deformation and strength characteristics of soil under three different principal stresses. Proceedings of the Japan Society of Civil Engineers 232:59–70, DOI: https://doi.org/10.2208/jscej1969.1974.232_59
Mitchell JK, Soga K (2005) Fundamentals of soil behavior. New York: Wiley
Mualem Y (1976) A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resources Research 12(3):513–522, DOI: https://doi.org/10.1029/WR012i003p00513
Muir Wood, DM (1990) Soil behaviour and critical state soil mechanics. Cambridge University Press, Cambridge, UK
Niandou H, Shao JF, Henry JP, Fourmaintraux D (1997) Laboratory investigation of the mechanical behaviour of Tournemire shale. International Journal of Rock Mechanics and Mining Science 34(1): 3–16, DOI: https://doi.org/10.1016/S1365-1609(97)80029-9
Qiu W, Kong C, Liu K (2015) Three-dimensional numerical analysis of the tunnel for polyaxial state of stress. Mathematical Problems in Engineering 301241:1–8, DOI: https://doi.org/10.1155/2015/301241
Rabczuk T, Belytschko T (2004) Cracking particles: A simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering 61(13):2316–2343, DOI: https://doi.org/10.1002/nme.1151
Rabczuk T, Zi G, Bordas S, and Nguyen-Xuan H (2010) A simple and robust three-dimensional cracking-particle method without enrichment. Computer Methods in Applied Mechanics and Engineering 199(37–40):2437–2455, DOI: https://doi.org/10.1016/j.cma.2010.03.031
Rowe PW (1962) The stress-dilatancy relation for static equilibrium of an assembly of particles in contact. Proceedings of the Royal Society A 269(1339):500–527, DOI: https://doi.org/10.1098/rspa.1962.0193
Schofield AN, Wroth CP (1968) Critical state soil mechanics. London, UK: McGraw-hill
Seo HJ, Jeong KH, Choi H, Lee IM (2012) Pullout resistance increase of soil nailing induced by pressurized grouting. Journal of Geotechnical and Geoenvironmental Engineering 138(5):604–613, DOI: https://doi.org/10.1061/(ASCE)GT.1943-5606.0000622
Seo HJ, Lee IM, Ryu YM, Jung JH (2019) Mechanical behavior of hybrid soil nail-anchor system. KSCE Journal of Civil Engineering 23:4201–4211, DOI: https://doi.org/10.1007/s12205-019-2268-3
Seo HJ, Pelecanos L, Kwon YS, Lee IM (2017) Net load-displacement estimation in soil-nail pullout tests. Proceedings of the Institution of Civil Engineers-Geotechnical Engineering 170(6):534–547, DOI: https://doi.org/10.1680/jgeen.16.00185
Silvestri V, Tabib C (1983) Exact determination of gravity stresses in finite elastic slopes, Part I. Theoretical considerations. Canadian Geotechnical Journal 20:47–54, DOI: https://doi.org/10.1139/t83-005
Stark TD, Fernandez R (2019) Fully softened shear strength measurement and correlations. Geotechnical Testing Journal 43(5):1201–1215, DOI: https://doi.org/10.1520/GTJ20190124
Thompson MJ, VandenBerge DR (2017) Shear strength of remolded and compacted beaumont clay. In Geotechnical Frontiers 2017: Geotechnical Materials, Modeling and Testing 82–91. Reston, VA: American Society of Civil Engineers, DOI: https://doi.org/10.1061/9780784480472.009
van Genuchten MT (1980) A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal 44(5):892–898, DOI: https://doi.org/10.2136/sssaj1980.03615995004400050002x
Wang L, Wu CZ, Tang LB, Zhang WG, Lacasse S, Liu HL, Gao L (2020) Efficient reliability analysis of earth dam slope stability using extreme gradient boosting method. Acta Geotechnica 15:3135–3150, DOI: https://doi.org/10.1007/s11440-020-00962-4
Ye GL, Zhang F, Yashima A, Sumi T, Ikemura T (2005) Numerical analyses on progressive failure of slope due to heavy rain with 2D and 3D FEM. Soils and Foundations 45(2):1–15, DOI: https://doi.org/10.3208/sandf.45.2_1
Yuan P, Cai CS, Liu K, Wang XJ, Ke L (2023) Dynamic performance-based assessment for tied-arch bridges subjected to heavy multiaxial tractor-trailers. Structure and Infrastructure Engineering, DOI: https://doi.org/10.1080/15732479.2022.2155975
Zhang Y, Wang X, Wang X, Mang H (2022) Virtual displacement based discontinuity layout optimization. International Journal for Numerical Methods in Engineering 123(22):5682–5694, DOI: https://doi.org/10.1002/nme.7084
Zhang HJ, Zhang S, Fang W, Liu G, Gao W, Jiang Z, Liu K (2023) Study on the vehicle-induced LTAS law of the tunnel in diatomite area. KSCE Journal of Civil Engineering 27(4):1838–1849, DOI: https://doi.org/10.1007/s12205-023-1940-9
Zoback MD (2010) Reservoir geomechanics. Cambridge University Press, New York
Acknowledgments
This research is sponsored by the National Natural Science Foundation of China (Grant No. 52178364).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Liu, K., Wang, G., Yuan, P. et al. Case Study: Slope Stability Assessment Considering 3D Nonlinear Shear Strength. KSCE J Civ Eng 28, 124–138 (2024). https://doi.org/10.1007/s12205-023-2264-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12205-023-2264-5