Critical Stability Analysis of Slopes Using Stress Characteristics in Purely Cohesive Soil
Publication: International Journal of Geomechanics
Volume 23, Issue 1
Abstract
This paper investigates the critical stability of purely cohesive soil (ϕ = 0) slopes under seismic conditions using a novel concept of the critical slope surface (CSS). A theoretical model is devised on the basis of a unified framework of the method of stress characteristics and the pseudostatic approach. In the presence of pseudostatic seismic forces, a system of differential equations governing the equilibrium stress field is combined with the Mohr–Coulomb yield criterion. Subsequently, the curvilinear CSS derived at the state of critical equilibrium with a factor of safety of 1.0 is endorsed to operate as an autoguided measure for slope stability. Unlike the traditional limit equilibrium and limit analysis methods, the present method does not involve any preordained failure mechanism in the analysis. The CSSs obtained from the present analysis mostly anticipate steeper profiles with lesser height than the traditional linear slopes reported in the literature. In addition, the curvilinear CSS exhibits a certain morphological resemblance with naturally occurring soil slopes. A finite-element simulation of the CSS further establishes the versatility of the proposed concept to design an equivalent linear profile with a prescribed height. A set of design charts based on the CSS concept is provided to mandate a quick and inexpensive stability analysis in practice.
Practical Applications
In slope stability analysis, the optimal inclination of a linear slope often becomes a prerequisite to ensure a sufficient margin of safety by providing a flat slope geometry compared with that required for critical stability with a factor of safety of 1.0. The present critical slope surface-based stability concept ensures critical stability at minimal computational costs. The critical slope surface appears to be a boundary between the zone of stability and instability. Hence, for site-specific soil properties and seismic conditions, flat slope profiles compared with the derived critical slope surface ensure a stable configuration and vice versa. Therefore, the guidelines for designing proposed linear slopes can be orientated in advance to prevent an imminent collapse. In the case of existing slopes, the necessity for a remedial measure to maintain critical stability can also be assessed a priori using the current concept.
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References
Akhlaghi, T., and A. Nikkar. 2014. “Evaluation of the pseudostatic analyses of earth dams using FE simulation and observed earthquake-induced deformations: Case studies of upper San Fernando and Kitayama dams.” Sci. World J. 2014: 585462. https://doi.org/10.1155/2014/585462.
Baker, R., R. Shukha, V. Operstein, and S. Frydman. 2006. “Stability charts for pseudo-static slope stability analysis.” Soil Dyn. Earthq. Eng. 26 (9): 813–823. https://doi.org/10.1016/j.soildyn.2006.01.023.
Bishop, A. W. 1955. “The use of the slip circle in the stability analysis of slopes.” Géotechnique 5 (1): 7–17. https://doi.org/10.1680/geot.1955.5.1.7.
Bray, J. D., and T. Travasarou. 2007. “Simplified procedure for estimating earthquake-induced deviatoric slope displacements.” J. Geotech. Geoenviron. Eng. 133 (4): 381–392. https://doi.org/10.1061/(ASCE)1090-0241(2007)133:4(381).
CEN (European Committee for Standardization). 2004. Design of structures for earthquake resistance—Part 1: General rules, seismic actions and rules for buildings. Eurocode 8. Brussels, Belgium: CEN.
Chakraborty, D., and J. Kumar. 2013. “Bearing capacity of foundations on slopes.” Geomech. Geoengin. 8 (4): 274–285. https://doi.org/10.1080/17486025.2013.770172.
Chanda, N., S. Ghosh, and M. Pal. 2016. “Analysis of slope considering circular rupture surface.” Int. J. Geotech. Eng. 10 (3): 288–296. https://doi.org/10.1080/19386362.2016.1142270.
Chen, H., and L. Zhang. 2022. “A machine learning-based method for predicting end-bearing capacity of rock-socketed shafts.” Rock Mech. Rock Eng. 55 (3): 1743–1757. https://doi.org/10.1007/s00603-021-02757-9.
Chen, H., L. Li, J. Li, and D. Sun. 2022a. “A generic analytical elastic solution for excavation responses of an arbitrarily shaped deep opening under biaxial in situ stresses.” Int. J. Geomech. 22 (4): 04022023. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002335.
Chen, H.-b., F.-q. Chen, and Y.-j. Lin. 2022b. “Slip-line solution to earth pressure of narrow backfill against retaining walls on yielding foundations.” Int. J. Geomech. 22 (5): 04022051. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002356.
Chen, H., H. Zhu, and L. Zhang. 2022c. “A three-dimensional (3D) semi-analytical solution for the ultimate end-bearing capacity of rock-socketed shafts.” Rock Mech. Rock Eng. 55 (2): 611–627. https://doi.org/10.1007/s00603-021-02710-w.
Chen, W. F., and C. R. Scawthorn. 1970. “Limit analysis and limit equilibrium solutions in soil mechanics.” Soils Found. 10 (3): 13–49. https://doi.org/10.3208/sandf1960.10.3_13.
Chen, Z., N. Wang, L. Wang, P. Sun, and B. Chen. 2022d. “Theoretical studies and applications of an upper-bound stability analysis method based on the failure mode of inclined slices.” Comput. Geotech. 142: 104540. https://doi.org/10.1016/j.compgeo.2021.104540.
Cheng, Y. M., L. Li, and S. C. Chi. 2007. “Performance studies on six heuristic global optimization methods in the location of critical slip surface.” Comput. Geotech. 34 (6): 462–484. https://doi.org/10.1016/j.compgeo.2007.01.004.
Cui, H., J. Ji, J. Song, and W. Huang. 2022. “Limit state line-based seismic stability charts for homogeneous earth slopes.” Comput. Geotech. 146: 104749. https://doi.org/10.1016/j.compgeo.2022.104749.
Deng, D.-p., L. Li, and L.-h. Zhao. 2019. “Stability analysis of a layered slope with failure mechanism of a composite slip surface.” Int. J. Geomech. 19 (6): 04019050. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001417.
DOC (Department of Conservation Division of Mines and Geology). 1997. Special publication 117: Guidelines for evaluating and mitigating seismic hazards in California. Sacramento, CA: DOC.
Duncan, J. M. 1996. “State of the art: Limit equilibrium and finite-element analysis of slopes.” J. Geotech. Eng. 122 (7): 577–596. https://doi.org/10.1061/(ASCE)0733-9410(1996)122:7(577).
Fang, H. W., Y. F. Chen, and Y. X. Xu. 2020. “New instability criterion for stability analysis of homogeneous slopes.” Int. J. Geomech. 20 (5): 04020034. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001665.
Georgiadis, K., and E. Chrysouli. 2011. “Seismic bearing capacity of strip footings on clay slopes.” In Proc., 15th European Conf. on Soil Mechanics and Geotechnical Engineering, edited by A. Anagnostopoulos, M. Pachakis, and C. Tsatsanifos, 723–728. Rotterdam, Netherlands: Millpress.
Gray, D. 2013. “Influence of slope morphology on the stability of earthen slopes.” In Proc., Geo-Congress 2013: Stability and Performance of Slopes and Embankments III, Geotechnical Special Publication 231, edited by C. Meehan, D. Pradel, M. A. Pando, and J. F. Labuz, 1902–1911. Reston, VA: ASCE.
Huang, C.-C. 2019. “Experimental verification of seismic bearing capacity of near-slope footings using shaking table tests.” J. Earthq. Eng. 26 (1): 162–191. https://doi.org/10.1080/13632469.2019.1665148.
Jeldes, I. A., E. C. Drumm, and D. C. Yoder. 2015a. “Design of stable concave slopes for reduced sediment delivery.” J. Geotech. Geoenviron. Eng. 141 (2): 04014093. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001211.
Jeldes, I. A., N. E. Vence, and E. C. Drumm. 2015b. “Approximate solution to the Sokolovskiĭ concave slope at limiting equilibrium.” Int. J. Geomech. 15 (2): 04014049. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000330.
Jellali, B., and W. Frikha. 2017. “Constrained particle swarm optimization algorithm applied to slope stability.” Int. J. Geomech. 17 (12): 06017022. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001019.
Kumar, J., and P. Ghosh. 2007. “Ultimate bearing capacity of two interfering rough strip footings.” Int. J. Geomech. 7 (1): 53–62. https://doi.org/10.1061/(ASCE)1532-3641(2007)7:1(53).
Kumar, J., and V. B. K. Mohan Rao. 2003. “Seismic bearing capacity of foundations on slopes.” Géotechnique 53 (3): 347–361. https://doi.org/10.1680/geot.2003.53.3.347.
Lee, M.-G., J.-G. Ha, S.-B. Jo, H.-J. Park, and D.-S. Kim. 2017. “Assessment of horizontal seismic coefficient for gravity quay walls by centrifuge tests.” Géotechnique Lett. 7 (2): 211–217. https://doi.org/10.1680/jgele.17.00005.
Li, C., L. Su, H. Liao, C. Zhang, and S. Xiao. 2021. “Modeling of rapid evaluation for seismic stability of soil slope by finite element limit analysis.” Comput. Geotech. 133: 104074. https://doi.org/10.1016/j.compgeo.2021.104074.
Lim, K., A. J. Li, A. Schmid, and A. V. Lyamin. 2016. “Slope-stability assessments using finite-element limit-analysis methods.” Int. J. Geomech. 17 (2): 06016017. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000715.
Macedo, J., J. Bray, N. Abrahamson, and T. Travasarou. 2018. “Performance-based probabilistic seismic slope displacement procedure.” Earthq. Spectra 34 (2): 673–695. https://doi.org/10.1193/122516EQS251M.
Michalowski, R. L. 2002. “Stability charts for uniform slopes.” J. Geotech. Geoenviron. Eng. 128 (4): 351–355. https://doi.org/10.1061/(ASCE)1090-0241(2002)128:4(351).
MOHURD (Ministry of Housing and Urban–Rural Development of the People’s Republic of China). 2013. Technical code for building slope engineering. GB 50330. Beijing: MOHURD.
Mononobe, N., and H. Matsuo. 1929. “On the determination of earth pressure during earthquakes.” In Proc., World Engineering Conf., 177–185. Tokyo, Japan.
Morgenstern, N. R., and V. E. Price. 1965. “The analysis of the stability of general slip surfaces.” Géotechnique 15 (1): 79–93. https://doi.org/10.1680/geot.1965.15.1.79.
Nandi, S., G. Santhoshkumar, and P. Ghosh. 2021. “Determination of critical slope face in c – φ soil under seismic condition using method of stress characteristics.” Int. J. Geomech. 21 (4): 04021031. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001976.
Okabe, S. 1926. “General theory of earth pressures.” J. Jpn. Soc. Civ. Eng. 12 (6): 1277–1323.
Qin, C., and S. C. Chian. 2017. “Kinematic stability of a two-stage slope in layered soils.” Int. J. Geomech. 17 (9): 06017006. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000928.
Qin, C., and S. C. Chian. 2018. “New perspective on seismic slope stability analysis.” Int. J. Geomech. 18 (7): 06018013. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001170.
Ranjan, G., and A. S. R. Rao. 2014. Basic and applied soil mechanics. 2nd ed. Delhi, India: New Age.
Sahoo, P. P., and S. K. Shukla. 2019. “Taylor’s slope stability chart for combined effects of horizontal and vertical seismic coefficients.” Géotechnique 69 (4): 344–354. https://doi.org/10.1680/jgeot.17.P.222.
Sahoo, P. P., and S. K. Shukla. 2021. “Time-history analysis of soil slope subjected to seismic loadings.” Soil Mech. Found. Eng. 58 (2): 130–137. https://doi.org/10.1007/s11204-021-09717-z.
Santhoshkumar, G., and P. Ghosh. 2021. “Plasticity-based estimation of active earth pressure exerted by layered cohesionless backfill.” Int. J. Geomech. 21 (11): 06021028. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002182.
Sarkar, S., and M. Chakraborty. 2021. “Seismic stability of non-homogenous cohesive soil by using calculus of variation.” In Proc., Local Site Effects and Ground Failures, edited by T. G. Sitharam, R. Jakka, and L. Govindaraju, 229–240. Singapore: Springer.
Shinoda, M. 2015. “Seismic stability and displacement analyses of earth slopes using non-circular slip surface.” Soils Found. 55 (2): 227–241. https://doi.org/10.1016/j.sandf.2015.02.001.
Sokolovski, V. V. 1960. Statics of soil media. 2nd ed. London: Butterworths.
Stockton, E., B. A. Leshchinsky, M. J. Olsen, and T. M. Evans. 2019. “Influence of both anisotropic friction and cohesion on the formation of tension cracks and stability of slopes.” Comput. Geotech. 249: 31–44. https://doi.org/10.1016/j.enggeo.2018.12.016.
Sun, J., T. Yu, and P. Dong. 2022. “Evaluation of 3D slope stability based on the minimum potential energy principle.” Comput. Geotech. 146: 104717. https://doi.org/10.1016/j.compgeo.2022.104717.
Taylor, D. W. 1937. “Stability of earth slopes.” J. Bost. Soc. Civ. Eng. 24 (3): 197–246.
Taylor, D. W. 1948. Fundamentals of soil mechanics. New York: Wiley.
Tiwari, R. C. 2014. “Simplified numerical implementation in slope stability modeling.” Int. J. Geomech. 15 (3): 04014051. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000399.
Wang, Q., S. Gao, B. Jiang, S. Li, M. He, H. Gao, and Q. Qin. 2018. “Rock-cutting mechanics model and its application based on slip-line theory.” Int. J. Geomech. 18 (5): 04018025. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001136.
Xu, J.-s., and X.-l. Yang. 2018. “Seismic and static stability analysis for 3D reinforced slope in nonhomogeneous and anisotropic soils.” Int. J. Geomech. 18 (7): 04018065. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001177.
Yang, X.-g., E.-d. Zhai, Y. Wang, and Z.-b. Hu. 2018. “A comparative study of pseudo-static slope stability analysis using different design codes.” Water Sci. Eng. 11 (4): 310–317. https://doi.org/10.1016/j.wse.2018.12.003.
Zhang, J., Y. Gao, F. Zhang, Y. Wan, and M. Liu. 2018. “Influence of anisotropy and nonhomogeneity on stability analysis of slurry-support trenches.” Int. J. Geomech. 18 (5): 04018028. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001151.
Zhou, A., X. Huang, N. Li, P. Jiang, and W. Wang. 2020. “A Monte Carlo approach to estimate the stability of soil–rock slopes considering the non-uniformity of materials.” Symmetry 12 (4): 590. https://doi.org/10.3390/sym12040590.
Zhou, A., C. Li, P. Jiang, K. Yao, N. Li, and W. Wang. 2018. “Slip line theory based stability analysis on the influence of deep excavation on adjacent slope.” Math. Probl. Eng. 2018: 2041712. https://doi.org/10.1155/2018/2041712.
Zhou, X. P., and H. Cheng. 2014. “Stability analysis of three-dimensional seismic landslides using the rigorous limit equilibrium method.” Eng. Geol. 174: 87–102. https://doi.org/10.1016/j.enggeo.2014.03.009.
Zhou, Y., F. Zhang, and B. Li. 2019. “Static and seismic stability charts for three-dimensional cut slopes and natural slopes under short-term undrained conditions.” Adv. Civ. Eng. 2019: 1914674. https://doi.org/10.1155/2019/1914674.
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Published In
International Journal of Geomechanics
Volume 23 • Issue 1 • January 2023
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© 2022 American Society of Civil Engineers.
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Received: Mar 23, 2022
Accepted: Aug 12, 2022
Published online: Nov 4, 2022
Published in print: Jan 1, 2023
Discussion open until: Apr 4, 2023
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