Numerical Analysis of Slope Stability under Surcharge Effects Using Convex Crossover Optimization
DOI:
https://doi.org/10.22399/ijcesen.4274Keywords:
Slope stability, Numerical optimization, Critical failure surface, Genetic algorithm, Surcharge load, Convex crossoverAbstract
An important problem in geotechnical engineering is slope stability analysis, yet it remains highly complex due to the nonlinear nature of failure mechanisms. The evaluation requires determining the critical failure surface (CFS) and the minimum factor of safety (FOS), which poses a challenging optimization problem. In this study, the limit equilibrium method (LEM), based on the Fellenius approach, is applied to assess slope stability under varying surcharge conditions, including surcharge intensity, position, and width. Results show that higher surcharge intensity combined with reduced position distance and width significantly undermines slope stability. Traditional optimization algorithms are often inadequate for such problems, as they rely on initial guesses and may converge only to local optima. To address this, a Multi-Parametric Genetic Algorithm (MPGA) with a Convex Crossover (CC) operator is developed. The CC operator parameters are calibrated using benchmark test functions, while a time-dependent decay factor is incorporated to improve variable interaction and prevent premature convergence. The proposed MPGA consistently identifies more accurate critical failure surfaces and provides lower safety factors compared to conventional approaches. Overall, the method demonstrates superior efficiency and robustness, offering a reliable tool for slope stability optimization under surcharge conditions.
References
[1] Baker .R (1980). Determination of critical slip surface in slope stability computations. International journal for Numerical and Analytical Methods in Geomechanics, 4:333-359.DOI: 10.1002/nag.1610040405
[2] Revilla.J ,Castillo.E.(1977). Détermination of variations applied to stability slope. GCotechnique, 27:1-11. https://doi.org/10.1680/geot.1977.27.1.1
[3] Fellenius W (1936). Calculation of the stability of earth dams. Transactions of the 2nd congress on large dams, Washington, DC, vol 4, pp 445–463. International Commission on Large Dams (ICOLD), Paris.
[4] Bishop A.W (1955). The use of the slip circlein the stabilityanalysis of slopes. Geotechnique 5(1):7–17.https://doi.org/10.1680/geot.1955.5.1.7
[5] Janbu. N (1975). Slope stability computations: In Hirschfeld RC, Poulos SJ. Embankment-dams engineering. https://DOI: 10.1016/0148-9062(75)90139-4
[6] MORGENSTERN.N R,Price. VE (1965). The analysis of the stability of general slip surfaces. Geotechnique. Lecturer in Civil Engineering, Imperial College of Science and Technology, London, England. https://doi.org/10.1680/geot.1965.15.1.79
[7] Spencer.E (1967). A method of analysis of the stability ofembankments assuming parallel inter-slice forces. Geotechnique17(1):11–26. https://doi: 10.1680/geot.1967.17.1.11
[8] Sarma.SK (1973). Stability analysis of embankments and slopes. Geotechnique23, No. 3, 423433. https://doi: 10.1680/geot.1973.23.3.423
[9] Fredlund. D.G; Krahn. J (1977). Comparison slope stability methods of analysis. Can. Geotech. J. 14,429. DOI: 10.1139/t77-045
[10] Duncan.JM (1996). State of the art: limit equilibrium and finite element analysis of slope. J. Geotech.Eng 122(7): 577-596. DOI: 10.1061/(asce)0733-9410(1996)122:7(577)
[11] Griffiths.DV, Lane.PA(1999). Slope stability analysis by finite elements. Geotechnical 49(3):387-403. DOI: 10.1680/geot.1999.49.3.387
[12] Zheng .H, Sun.G;Liu.D(2009). A practical procedure for searching critical slip surface of slope based on the strength reduction technique. Comput Geotech 36(1):1-5. DOI: 10.1016/j.compgeo.2008.06.002
[13] Cheng. YM, Lansivaara.T, Wei.WB (2007). Tow dimension slope stability analysis by limit equilibrium and strength reduction methods. Comput Geotech 34(3): 137-150. DOI: 10.1016/j.compgeo.2007.05.006
[14] Liu.SY, Shao.LT,Li HJ (2015). Slope stability analysis using the limit equilibrium method and tow finite element methods. Comput Geotech 63:291-298. DOI: 10.1016/j.compgeo.2014.10.008
[15] Soren.K, Budi.G, Sen.P (2014). Stability analysis of open pit slope by finite difference method. Int J Res Eng Technol 3:326-334.
[16] Baker.R, Garber.M(1978). Theoretical analysis of the stability of slope. Geotechnique 28(4):395-411. DOI: 10.1680/geot.1978.28.4.395
[17] Greco.VR (1996). Efficient Monto Carlo technique for locating critical slip surface. J Geotech Eng 122(7):517-525. DOI: 10.1061/(ASCE)0733-9410(1996)122:7(517)
[18] Gaw,W. (2016). Determination of the noncircular critical slip surface in slope stability analysis by meeting ant colony optimization.J.Comput.Civ.Eng.30(2), 06015001.DOI: 10.1061/(asce)cp.1943-5487.0000475
[19] Goh, ATC (1999). Genetic algorithm search for critical slope surface multiple-wedge stability analysis. Can.Geotech.J.6(2),383-391.DOI: 10.1139/t98-110
[20] Zolfaghari. A, Heath. R, MccombieP. (2005). Simple genetic algorithm search for critical non-circular failure surface in slope stability analysis. Computers and Geotechnics 32 139–152,. DOI: 10.1016/j.compgeo.2005.02.001
[21] Chen, Y.M (2007). Global optimization analysis of slope stability by simulated annealing with dynamic bounds and Dirac function. Eng.optim.39 (1), 17-32. DOI: 10.1080/03052150600916294
[22] Li. Chen. Y.U, Y.M, Chen.Y.M, Zhan.L.T.(2010). An efficient approach for locating the critical slip surface in slope stability analyses using a real-coded genetic algorithm. Can. Geotech.J.47 (7), 806-820.DOI: 10.1139/t09-124
[23] Shinoda.M, Miyata.Y. (2019). PSO-based stability analysis of unreinforced and reinforced soil slope using non-circular slip surface. Acta Geotech. 14(3), 907-919. DOI: 10.1007/s11440-018-0678-x
[24] Khajehzadeh.M, Tahha.M.R, El-shafie.A,Mohammad.K (2011). Search for critical failure surface in slope stability analysis by gravitational search algorithm. Int J Phys Sci 6(21): 5012-5021. DOI: 10.5897/IJPS11.694
[25] Khajehzadeh.M, Taha.M.R,El-shafie.A,Mohammad.K (2012). A modified gravitational search algorithm for stability analysis. Eng App Artif Intell 25(8): 1589-1597. DOI: 10.1016/j.engappai.2012.01.011
[26] Tongchun. H (2012). Stability calculation of slope by tabu search method. In: Fourth joint international symposium on information technology in civil engineering, towards a vision for information technology in civil engineeringhttps://doi.org/10.1061/40704(2003)3
[27] Aniruddha.S, Upadhyay.A.(2009). Locating the critical failure surface in a slope stability analysis by Genetic Algorithm. App Soft Comput 9(1): 387-3. DOI: 10.1016/j.asoc.2008.04.015
[28] Pina.R.J, Jimenez.R(2015). A genetic algorithm for slope stability with concave slip surface using custom operators. Eng Optim 47(4): 453-472. https://doi.org/10.1080/0305215X.2014.895339
[29] Mennaai. A, Zatar.A(2024). An efficient genetic algorithm for locating critical failure surface in slope stability analysis with limit equilibrium method.Vol. 5 No. 2. Studies in Engineering and Exact Sciences, Curitiba, v.5, n.2, 2024.https://doi.org/10.54021/seesv5n2-823
[30] Manouchehrian .A, Gholmanejad.J.(2014).Development of model for analysis of slope stability for circular mode failure using genetic algorithm. Environ Earth Sci 71(3) : 1267-1277.DOI: 10.1007/s12665-013-2531-8
[31] Mc Combie.P, Wilkinson.P(2002). The use of the simple genetic algorithm in finding the critical factor of safety in slope stability analysis. Comput Geotech 29(8): 699-714.
[32] DOI: 10.1016/s0266-352x (02)00027-7
[33] Xiao.Z, Tian.B, Lu X. (2017). Locating the critical slip surface in a slope stability analysis by enhanced fireworks algorithm. Cluster Comput 22:1-11. DOI: 10.1007/s10586-017-1196-6
[34] Gao.W, Wang.X, Dai.S, Chen.D (2016). Study on stability of high embankment slope based on black hole algorithm. Environ Earth Sci 75(20): 1381. DOI: 10.1007/s12665-016-6208-y
[35] Gao.W (2015). Slope stability analysis based on immunised evolutionary programming. Environ Earth Sci74(4): 3357-3369. DOI: 10.1007/s12665-015-4372-0
[36] Gandomi.A.H,Kashani.A.R, Mousavi.M.(2016). Slope stability analysis using evolutionary optimization techniques. Int J Numer Anal methods Geomech 41(2): 251-264.DOI: 10.1002/nag.2554
[37] Singh.J,Banka.H,Verma.A.K.(2018). A BBO-based algorithm for slope stability analysis by locating critical failure surface. Comput Appl 31:1-18. DOI: 10.1007/s00521-018-3418-0
[38] Gandomi.AH,Kashani.A.R,Mousavi.M.(2014). Slope stability analysis using recent swarm intelligence techniques. Int J Numer Anal Methods Geomechv39 (3): 295-309.https://doi.org/10.1002/nag.2308
[39] Liangxing. J, Junjie. W, Chunwa. L. (2023). Slope stability analysis based on improved radial movement optimization considering seepage effect. Alex Engi J 79 591-607.
[40] https://doi.org/10.1016/j.aej.2023.08.029
[41] KozaJ.R.(1992). Genetic Programming II Automatic Discovery of Reusable Subprograms, MIT Press, Cambridge, MA.
[42] Dorigo. M, Maniezzo. M, Colorin. A.(1996).Ant system optimization by a colony of cooperating agents, IEEE Trans. Syst.Man Cybern.B 26 29-41. DOI: 10.1109/3477.484436
[43] Himanshu. N, Burman. A. (2019). Determination of critical failure surface of slope using Particle swarm optimization technique considering seepage and seismic loading.Geotech.Geol.Eng.37 (3), 1261-1281. https://doi.org/10.1007/s10706-018-0683-8
[44] Kashani.A.R,Gandomi.A.H, Mousavi. M. (2016). Imperialistic competitive algorithm a metaheuristic algorithm for locating the critical slip surface in 2-Dimensional soil slope.Geosci. Front 7(1), 83-89. https://doi.org/10.1016/j.gsf.2014.11.005
[45] Gao.W. (2014). Forecasting of landslide disasters based on bionics algorithm-Part 1: Critical slip surface searching. Comput.Geotech.61, 370-377. DOI: 10.1016/j.compgeo.2014.06.007
[46] Loke K.F, Hossein.M.(2022). Neural network optimized by equilibrium optimization and vortex search algorithm. Volume 38, pages 1269-1283. https://doi.org/10.1007/s00366-021-01282-1
[47] Chao.W, Shuai .Q. Tuanhui. W. (2025).GSWOA-KELM model for prediction slope stability and its engineering application. https://doi.org/10.1007/s11069-025-07260-w
[48] Mansheng.L, Limei.Z, Shuai.T. (2024). Prediction of stability of slope with weak layers using convolutional neural networks. Volume 120, pages 12081-21105.https://doi.org/10.1007/s11069-024-06674-2
[49] Yuqi .S, Ruren.L. (2025).Predictive Analysis of slope stability via Metaheuristic Algorithms Helping Neural Networks. https://doi.org/10.1002/gj.5184
[50] ShuaiHua.Y, GuangWen.F,XiaoRui.M.(2019).Reliability Analysis of Grillage Flexible Slope Supporting Structure with Anchors Considering Fuzzy Transitional Interval and Fuzzy Randomness of Soil Parameters.Arab.J.Sci Eng 44(10): 8849-8857https://doi.org/10.1007/s1336 9-019-03912-9
[51] Zhang.R.H,Goh.ATC, Zhang.W.(2019). System reliability assessment on deep-branched excavation to adjacent to an existing upper slope in mountainous terraina case study SN.App Sci 1:876.
[52] Cheng.YM, Chi.SC. (2007). Performance studies on six heuristic global optimization methods in the location of critical slip surface. Comput.Geotech.34 (6): 462-484.DOI: 10.1016/j.compgeo.2007.01.004
[53] Chen .ZY, Shaao.CM (1988). Evolution of minimum factor of safety in slope stability analysis. Can.Geotech.J 25(4): 735-748. https://doi.org/10.1139/t88-084
[54] Ahangar, A.; faramarzi, A.; Javadi, A.A(2010). A new approach for prediction of the stability of soil and rock slopes. Eng Comput27(7):878–893. DOI: 10.1108/02644401011073700.
[55] Cheng .Y.M, Lau.CK (2014). Slope stability analysis and stabilization. New methods and insight. CRC Press, Boca Raton.
[56] Huang.YH (2014). Slope stability analysis by the limit equilibrium methods: fundamentals and methods. Amer. Soci.Civil.Engin. https://doi.org/10.1061/9780784412886
[57] Sun.J,Li.J,Liu.Q (2008). Search for critical slip surface in slope stability analysis by spline- based GA method. Geotech Geoenviron Eng 134(2):252-256. DOI: 10.1061/(ASCE)1090-0241(2008)134:2(252)
[58] Wu. A (2012). Locating general failure surfaces in slope analysis via cuckoo search. Accessed 27 Jan 2017 https://www.rocscience.com/help/slide/web help7/pdf files/theory/.
[59] Cheng.Y.M(2003). Location of critical failure surface and some further studies on slope stability analysis. Comput Geotech 30(3):255-267. DOI: 10.1016/s0266-352x(03)00012-0
[60] Jade.S, Shanker.KD (1995). Modelling of slope failure using a global optimization technique. Eng Optim+ A35-23(4):255-266.DOI: 10.1080/03052159508941357
[61] Simon.D (2008). Biogeography-based optimization. IEEE Trans Evol Comput 12(6):702-713.
[62] DOI: 10.1109/TEVC.2008.919004
[63] Holland John H (1975). Adaptation in Natural and artificial systems. University of Michigan press, Ann Arbor, MI, 1975; MIT Press, Cambridge, MA, 1992.
[64] Back.T.(1996). Evolutionary Algorithms in Theory and Practice, Oxford University press, New York.DOI: 10.1002/(sici)1099-0526(199703/04)2:4<26::aid-cplx6>3.0.co;2-7
[65] Michalewics. Z (1995). A survey of constraint handling techniques in evolutionary computation methods, in: Proceeding of the 4th Annual Conference on Evolutionary Programming, Mit press, Cambridge, MA, PP.135-155.
[66] Coello.C (2000). An updated survey of GA –based multiobjective optimization techniques. ACM. Comput. Surveys 32(2) 109-143.https://doi.org/10.1145/358923.358929
[67] Hedberg. S.R (2005). Evolutionary computing: the rise of electronic breeding. IEEE syst.20(6) 12-15.
[68] Goldberg. D.E (2002). The design of innovation: lessons from and for competent genetic algorithms, Addision-Wesley, Reading,MA
[69] Yang.C.X ,Tham. L.G, Feng.X.T,Lee.P.K.K (2004). Two-stepped evolutionary algorithm and its application to stability analysis of slope. J.Comput, Civil.Eng.18 (2) 145-153. https://doi.org/10.1061/(ASCE)0887-3801(2004)18:2(145)
[70] Nian .T, Zheng .D (2006). Application of a simple genetic to the stability of slope subjected to pore-water pressure, in Proceeding of 6th World Congress on intelligent control and automation,Dalian, China,PP.3668-3671.https://doi.org/10.1088/1742-2132/5/3/008
[71] Davis, L. (1991). Handbook of Genetic Algorithms. Van Nostrand Reinhold, New York.
[72] Slide search methods (2016).
[73] https://www.rocsience.com/help/slide/webhelp7/pdf_files/developer_tips/Slide_Search_Methods. Pdf/.
[74] Kostic.S, Vasovic.N,Sunaric.D (2015). A new approach to grid search method is slope stability analysis using box-behnken statistical design. Appl Math Comput 256: 425-437. https://doi.org/10.1016/j.amc.2015.01.022
[75] Yamagami. T, Ueta. Y (1986). Noncircular slip surface of the stability of slope. Landslides 22(4): 8-16. https://doi.org/10.3313/jls1964.22.4_8
[76] Cheng.Y.M, Lansivaara.T,Chi.S.C,Sun.Y.J (2008). An improved harmony search minimization algorithm using different slip surface generation methods for slope stability analysis. Eng. Optim 40(2):95-115. https://doi.org/10.1080/03052150701618153
[77] Jianping.S,Li.J,Liu.Q (2008). Search for critical slip surface in slope stability analysis by spline-based GA method. J Geotech Geoenviron Eng 134(2):252-256.
[78] https://doi.org/10.1061/(ASCE)1090-0241(2008)134:2(252)
[79] Kahatadeniya. K.S, Nanakorn. P,Neaupane. K.M (2009). Determination of the critical failure surface for slope stability analysis using ant colony optimization. Eng Geol 108:133-141. https://doi.org/10.1016/j.enggeo.2009.06.010
[80] Khajehzadeh.M, Taha.M.R,El-Shafie.A, Eslami.M (2012). Locating the general failure surface of earth slope using particle swarm optimization. Civil Eng Environ Syst (1): 41-57.
[81] http://dx.doi.org/10.1080/10286608.2012.663356
[82] Kang .F,Li.J,Ma.Z (2013). An artificial bee colony algorithm for locating the critical slip surface in slope stability analysis. Eng Optim 45(2):207-233.https://doi.org/10.1080/0305215X.2012.665451
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