Stability Analysis of Inhomogeneous Slopes in Unsaturated Soils Optimized by a Genetic Algorithm
Publication: International Journal of Geomechanics
Volume 22, Issue 9
Abstract
Most theoretical analysis for the assessment of the stability of soil slopes is commonly performed under completely dry or saturated and homogeneous conditions, the effect of suction and soil inhomogeneity are generally ignored in stability assessments. This paper presents an analytical framework to investigate the stability of three-dimensional (3D) inhomogeneous slopes in unsaturated soils under one-dimensional steady flow. Based on the kinematic limit analysis method, a 3D rotational failure mechanism is adopted, and three possible failure mechanisms of soil slopes (e.g., toe, face, and base failure) are considered. A closed-form solution for the factor of safety is derived by the energy balance equation, which takes the effects of the suction stress, effective unit weight, and inhomogeneity of soil simultaneously into account. To improve optimize efficiency, a genetic algorithm (GA), which has the advantages of high efficiency and good accuracy, is applied to search for the minimum of the factor of safety of the slope. This methodology is well validated through comparison with existing solutions and numerical simulation. Parameter analyses are performed to investigate the effects of different parameters on slope stability. The results of the present study indicate that the stability of the slope will be underestimated if the suction stress and the change in effective unit soil weight are not considered. The inhomogeneity of soil can reduce the stability of slopes.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or codes that support the findings of this paper are available from the corresponding author upon reasonable request. To be specific, all data that support all the figures in this paper can be provided by the corresponding author.
Acknowledgments
The authors would like to thank the editor and the anonymous reviewers for their valuable suggestions to improve this paper. This research was supported by the National Natural Science Foundation of China (Grant No. 41807295). The financial support is greatly appreciated.
Notation
The following symbols are used in this paper:
- a
- distances from the centerline of the conical volume to the slope crest;
- B
- maximum width of the rotational failure mechanism;
- maximum width of the 3D portion;
- b
- width of plane insert block;
- c′
- effective cohesion strength;
- capp
- apparent cohesion;
- c0
- effective cohesion strength of the slope base;
- cf
- effective cohesion strength of the slope face;
- c3D and c2D
- effective cohesion in 3D and 2D portions of slope, respectively;
- and
- rate of the internal energy dissipation of 3D and 2Ds portion achieved by soil cohesion, respectively;
- and
- rate of the internal energy dissipation of 3D and 2D portions achieved by apparent cohesion, respectively;
- d
- distances from the centerline of the conical volume to the slope face;
- e
- distance from the centerline of the conical volume to the slope base;
- Fs
- factor of safety of slope;
- Gs
- specific gravity of soil;
- H
- slope height;
- H′
- auxiliary height of slope;
- hf
- distance from the slope face to the slope crest;
- hs
- distance from the slip face to the slope crest;
- ks
- saturated hydraulic conductivity;
- n
- distribution of the soil’s pore size;
- nw and nd
- pore size distribution parameter of wet and dry paths, respectively;
- n0
- inhomogeneous coefficient;
- q
- vertical steady flow rate;
- R
- radius of the conical volume;
- r and r′
- radius of log spiral and inner log spiral, respectively;
- r0 and
- initial radius of log spirals OA and OA′, respectively;
- rf
- distance from the slope face to the center of rotation O;
- rh
- final radius of the log spiral;
- rm
- average radius of both spirals;
- S
- degree of pore water saturation;
- Se
- normalized degree of saturation;
- Sr
- residual degree of saturation;
- matric suction;
- ua
- pore air pressure;
- uw
- pore water pressure;
- and
- rate of external forces achieved by the effective soil weight of the 3D and 2D parts, respectively;
- ,
- rate of external forces achieved by the effective soil weight of the 3D and 2D parts, respectively;
- z0
- vertical distance from the water table to the slope toe elevation;
- z3D
- vertical distance from any one point of failure block to the water table level;
- z2D
- vertical distance from the point on the sliding surface of the plane insert block to the water table level;
- α
- inverse of air entry pressure;
- αw and αd
- inverse of air entry pressure of wet and dry paths, respectively;
- β
- slope inclination angle;
- β′
- auxiliary slope inclination angle;
- γ′
- effective unit soil weight;
- γsat
- unit weight of saturated soil;
- γw
- unit weight of water;
- γH/c
- stability factor of slope;
- σ
- total stress;
- σ′
- effective stress;
- σs
- suction stress;
- ϕ′
- effective internal friction angle;
- τf
- shear strength;
- θ
- rotational angle;
- θ0
- initial rotational angle;
- θB and θc
- rotational angles from horizontal line to the line that passes through points B and C, respectively;
- θh
- final rotational angle of log spiral;
- θs
- saturated volumetric water content; and
- θr
- residual volumetric water content.
References
Bishop, A. W. 1959. “The principle of effective stress.” Teknisk Ukeblad 106 (39): 859–863.
Chen, H. H., and L. Zhang. 2022. “A machine learning-based method for predicting end-bearing capacity of rock-socketed shafts.” Rock Mech. Rock Eng. 55: 1743–1757. https://doi.org/10.1007/s00603-021-02757-9.
Chen, H. H., L. Li, J. P. Li, and D. A. Sun. 2022. “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. H., and P. Q. Mo. 2022. “An undrained expansion solution of cylindrical cavity in SANICLAY for K0-consolidated clays.” J. Rock Mech. Geotech. Eng. https://doi.org/10.1016/j.jrmge.2021.10.016.
Chen, J., J.-H. Yin, and C. F. Lee. 2003. “Upper bound limit analysis of slope stability using rigid finite elements and nonlinear programming.” Can. Geotech. J. 40 (4): 742–752. https://doi.org/10.1139/t03-032.
Chen, W. F. 1975. Limit analysis and soil plasticity. Amsterdam, Netherlands: Elsevier.
Chen, Z. Y. 2002. “Limit analysis for the classic problems of soil mechanics.” Chin. J. Geotech. Eng. 24 (1): 1–11.
Deng, B., and M. Yang. 2019. “Analysis of passive earth pressure for unsaturated retaining structures.” Int. J. Geomech. 19 (12): 06019016. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001518.
Fredlund, D. G., and N. R. Morgenstern. 1977. “Stress state variables for unsaturated soils.” J. Geotech. Eng. Div. 14 (4): 56.
Gao, Y. F., F. Zhang, G. H. Lei, and D. Y. Li. 2013. “An extended limit analysis of three-dimensional slope stability.” Géotechnique 63 (6): 518–524. https://doi.org/10.1680/geot.12.T.004.
Gao, Y., D. Zhu, F. Zhang, G. H. Lei, and H. Qin. 2014. “Stability analysis of three-dimensional slopes under water drawdown conditions.” Can. Geotech. J. 51 (11): 1355–1364. https://doi.org/10.1139/cgj-2013-0448.
Griffiths, D. V., and R. M. Marquez. 2007. “Three-dimensional slope stability analysis by elasto-plastic finite elements.” Géotechnique 57 (6): 537–546. https://doi.org/10.1680/geot.2007.57.6.537.
Han, C.-y., J.-j. Chen, X.-h. Xia, and J.-h. Wang. 2014. “Three-dimensional stability analysis of anisotropic and non-homogeneous slopes using limit analysis.” J. Cent. South Univ. 21: 1142–1147. https://doi.org/10.1007/s11771-014-2047-8.
Hou, C.-T., and X.-L. Yang. 2020. “Seismic stability of 3D tunnel face considering tensile strength cut-off.” KSCE J. Civ. Eng. 24 (7): 2232–2243. https://doi.org/10.1007/s12205-020-1804-5.
Leshchinsky, D., and C. Huang. 1993. “Generalized three-dimensional slope stability analysis.” J. Geotech. Eng. Div. 30 (3): 1748–1764.
Li, Z. W., and X. L. Yang. 2018. “Stability of 3D slope under steady unsaturated flow condition.” Eng. Geol. 242: 150–159. https://doi.org/10.1016/j.enggeo.2018.06.004.
Likos, W. J., N. Lu, and J. W. Godt. 2014. “Hysteresis and uncertainty in soil water-retention curve parameters.” J. Geotech. Geoenviron. Eng. 140 (4): 04013050. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001071.
Lim, K., A. V. Lyamin, M. J. Cassidy, and A. J. Li. 2016. “Three-Dimensional slope stability charts for frictional fill materials placed on purely cohesive clay.” Int. J. Geomech. 16 (2): 04015042. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000526.
Lu, N., J. W. Godt, and D. T. Wu. 2010. “A closed-form equation for effective stress in unsaturated soil.” Water Resour. Res. 46 (5): W05515.
Lu, N., and D. V. Griffiths. 2004. “Profiles of steady-state suction stress in unsaturated soils.” J. Geotech. Geoenviron. Eng. 130 (10): 1063–1076. https://doi.org/10.1061/(ASCE)1090-0241(2004)130:10(1063).
Lu, N., and W. J. Likos. 2004. Unsaturated soil mechanics. Hoboken, NJ: Wiley.
Lu, N., and W. J. Likos. 2006. “Suction stress characteristic curve for unsaturated soil.” J. Geotech. Geoenviron. Eng. 132 (2): 131–142. https://doi.org/10.1061/(ASCE)1090-0241(2006)132:2(131).
Lu, N., A. Wayllace, and S. Oh. 2013. “Infiltration-induced seasonally reactivated instability of a highway embankment near the Eisenhower Tunnel, Colorado, USA.” Eng. Geol. 162: 22–32. https://doi.org/10.1016/j.enggeo.2013.05.002.
Michalowski, R. L. 2010. “Limit analysis and stability charts for 3D slope failures.” J. Geotech. Geoenviron. Eng. 136 (4): 583–593. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000251.
Michalowski, R. L., and A. Drescher. 2009. “Three-dimensional stability of slopes and excavations.” Géotechnique 59 (10): 839–850. https://doi.org/10.1680/geot.8.P.136.
Mualem, Y. 1976. “A new model for predicting the hydraulic conductivity of unsaturated porous media.” Water Resour. Res. 12 (3): 513–522. https://doi.org/10.1029/WR012i003p00513.
Nian, T. K., G. Q. Chen, M. T. Luan, Q. Yang, and D. F. Zheng. 2008. “Limit analysis of the stability of slopes reinforced with piles against landslide in nonhomogeneous and anisotropic soils.” Can. Geotech. J. 45 (8): 1092–1103. https://doi.org/10.1139/T08-042.
Pan, Q., J. Xu, and D. Dias. 2017. “Three-dimensional stability of a slope subjected to seepage forces.” Int. J. Geomech. 17 (8): 04017035. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000913.
Saada, Z., S. Maghous, and D. Garnier. 2012. “Stability analysis of rock slopes subjected to seepage forces using the modified Hoek-Brown criterion.” Int. J. Rock Mech. Min. Sci. 55: 45–54. https://doi.org/10.1016/j.ijrmms.2012.06.010.
Sengupta, A., and A. Upadhyay. 2009. “Locating the critical failure surface in a slope stability analysis by genetic algorithm.” Appl. Soft Comput. 9 (1): 387–392. https://doi.org/10.1016/j.asoc.2008.04.015.
Sorbino, G., and M. V. Nicotera. 2013. “Unsaturated soil mechanics in rainfall-induced flow landslides.” Eng. Geol. 165: 105–132. https://doi.org/10.1016/j.enggeo.2012.10.008.
Sun, D., L. Wang, and L. Li. 2019. “Stability of unsaturated soil slopes with cracks under steady-infiltration conditions.” Int. J. Geomech. 19 (6): 04019044. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001398.
Vahedifard, F., B. A. Leshchinsky, K. Mortezaei, and N. Lu. 2015. “Active earth pressures for unsaturated retaining structures.” J. Geotech. Geoenviron. Eng. 141 (11): 04015048. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001356.
Vahedifard, F., D. Leshchinsky, K. Mortezaei, and N. Lu. 2016. “Effective stress-based limit-equilibrium analysis for homogeneous unsaturated slopes.” Int. J. Geomech. 16 (6): D4016003. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000554.
van Genuchten, M. T. 1980. “A closed-form equation for predicting the hydraulic conductivity of unsaturated soils.” Soil Sci. Soc. Am. J. 44 (5): 892–898. https://doi.org/10.2136/sssaj1980.03615995004400050002x.
Viratjandr, C., and R. L. Michalowski. 2006. “Limit analysis of submerged slopes subjected to water drawdown.” Can. Geotech. J. 43 (8): 802–814. https://doi.org/10.1139/t06-042.
Wang, H., H. Moayedi, and L. Kok Foong. 2021. “Genetic algorithm hybridized with multilayer perceptron to have an economical slope stability design.” Eng. Comput. 37 (4): 3067–3078. https://doi.org/10.1007/s00366-020-00957-5.
Wang, L., D. Sun, B. Chen, and J. Li. 2019a. “Three-dimensional seismic stability of unsaturated soil slopes using a semi-analytical method.” Comput. Geotech. 110: 296–307. https://doi.org/10.1016/j.compgeo.2019.02.008.
Wang, L., D. Sun, and L. Li. 2019b. “Three-dimensional stability of compound slope using limit analysis method.” Can. Geotech. J. 56 (1): 116–125. https://doi.org/10.1139/cgj-2017-0345.
Yang, M., and B. Deng. 2019. “Stability study of slope reinforced with piles under steady unsaturated flow conditions.” Comput. Geotech. 109: 89–98. https://doi.org/10.1016/j.compgeo.2019.01.020.
Yang, X., and Z. Li. 2018. “Kinematical analysis of 3D passive earth pressure with nonlinear yield criterion.” Int. J. Numer. Anal. Methods Geomech. 42 (7): 916–930. https://doi.org/10.1002/nag.2771.
Yang, X.-L., and J.-s. Xu. 2017. “Three-dimensional stability of two-stage slope in inhomogeneous soils.” Int. J. Geomech. 17 (7): 06016045. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000867.
Zheng, L., L. Li, and J. Li. 2020. “Development of three-dimensional failure mechanisms and genetic algorithm for limit analysis of two-layer slopes.” Nat. Hazard. 103: 3181–3212. https://doi.org/10.1007/s11069-020-04126-1.
Zhou, X. P., and H. Cheng. 2013. “Analysis of stability of three-dimensional slopes using the rigorous limit equilibrium method.” Eng. Geol. 160: 21–33. https://doi.org/10.1016/j.enggeo.2013.03.027.
Information & Authors
Information
Published In
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Mar 2, 2021
Accepted: Mar 7, 2022
Published online: Jul 7, 2022
Published in print: Sep 1, 2022
Discussion open until: Dec 7, 2022
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited by
- Yunong Li, Wei Zhao, Chang Liu, Liwei Wang, Limit Analysis for 3D Stability of Unsaturated Inhomogeneous Slopes Reinforced with Piles, International Journal of Geomechanics, 10.1061/IJGNAI.GMENG-7802, 23, 4, (2023).
- Jiaping Sun, Tiantang Yu, Pingting Dong, Three-dimensional soil slope dynamic stability assessment using minimum potential energy approach, Soil Dynamics and Earthquake Engineering, 10.1016/j.soildyn.2023.107837, 168, (107837), (2023).