Slope reliability analysis considering geological uncertainty and spatial variability of soil parameters
DENG Zhi-ping1,2, LI Dian-qing1,2, CAO Zi-jun1,2, PHOON Kok Kwang1,2
1. State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China; 2. School of Water Resources and Hydropower Engineering, Wuhan University, Wuhan 430072, China
Abstract：The inherent variability of soil properties has currently received considerable attention in slope reliability analysis. However, the geological uncertainty is often ignored in analysis. This paper proposes a method for the slope reliability analysis considering geological uncertainty and spatial variability of soil parameters. The coupled Markov chain model is adopted to simulate the geological uncertainty. The midpoint method based on the Cholesky decomposition technique is used to discretize the random fields of different soil type parameters. The safety factor is calculated using the finite element-strength reduction method. The slope reliability analysis is conducted by Mote Carlo simulation. The procedure for this method is presented. A slope reliability problem is analyzed using the borehole data in Perth, Australia to illustrate the importance of considering geological uncertainty and spatial variability of soil parameters in slope reliability analysis and investigate the effect of layout scheme of boreholes on evaluating slope reliability. The results indicate that the proposed method can effectively reflect the effect of two types of soil heterogeneity on slope reliability. When there is less number of boreholes, the difference between the simulated and the real soil type distribution of slope is large, and ignoring the geological uncertainty will result in inaccurate estimation for slope reliability. The layout scheme of boreholes has a significant effect on safety factor and failure probability of slope. Boreholes should be placed as many as possible in the critical influence zone of the slope. The relationships between the statistics of safety factor and failure probability of slope and the number of boreholes are not monotonic, but the statistics of safety factor and failure probability of the slope converge to the accurate value with the increasing borehole number.
[1] ELKATEB T, CHALATURNYK R, ROBERTSON PK. An overview of soil heterogeneity: quantification and implications on geotechnical field problems[J]. Canadian Geotechnical Journal, 2003, 40(1): 1-15. [2] PHOON K K, KULHAWY F H. Characterization of geotechnical variability[J]. Canadian Geotechnical Journal, 1999, 36(4): 612-624. [3] EVANS S G. Landslides and surficial deposits in urban areas of British Columbia: a review[J]. Canadian Geotechnical Journal, 1982, 19(3): 269-288. [4] HANSEN L, EILERTSEN R, SOLBERG I L, et al. Stratigraphic evaluation of a Holocene clay-slide in Northern Norway[J]. Landslides, 2007, 4(3): 233-244. [5] 刘 润, 闫澍旺. 渤海湾地基土随机场特性及可靠度分析[J]. 岩土工程学报, 2004, 26(4): 464-467. (LIU Run, YAN Shu-wang. Random field model and reliability analysis of foundation soil in Bohai gulf[J]. Chinese Journal of Geotechnical Engineering, 2004, 26(4): 464-467. (in Chinese)) [6] 朱红霞, 闫澍旺. 天津港地基土随机场特性及可靠度分析[J]. 岩石力学与工程学报, 2007, 26(增刊2): 3959-3965. (ZHU Hong-xia, YAN Shu-wang. Random field model and reliability analysis of foundation soil in Tianjin port[J]. Chinese Journal of Rock Mechanics and Engineering, 2007, 26(S2): 3959-3965. (in Chinese)) [7] 张继周, 缪林昌. 基于随机场理论的地基概率沉降分析[J]. 岩土工程学报, 2010, 32(7): 1059-1064. (ZHANG Ji-zhou, MIAO Lin-chang. Probabilistic foundation settlement based on random field theory[J]. Chinese Journal of Geotechnical Engineering, 2010, 32(7): 1059-1064. (in Chinese)) [8] 李典庆, 蒋水华, 周创兵. 等. 考虑参数空间变异性的边坡可靠度分析非侵入式随机有限元法[J]. 岩土工程学报, 2013, 35(8): 1413-1422. (LI Dian-qing, JIANG Shui-hua, ZHOU Chuang-bing, et al. Reliability analysis of slopes considering spatial variability of soil parameters using non-intrusive stochastic finite element method[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(8): 1413-1422. (in Chinese)) [9] 祁小辉, 李典庆, 周创兵, 等. 考虑土体空间变异性的边坡最危险滑动面随机分析方法[J]. 岩土工程学报, 2013, 35(4): 745-753. (QI Xiao-hui, LI Dian-qing, ZHOU Chuang-bing, et al. Stochastic analysis method of critical slip surfaces in soil slopes considering spatial variability[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(4): 745-753. (in Chinese)) [10] 邓志平, 蒋水华, 曹子君, 等. 考虑参数空间变异性边坡可靠度分析的 Kriging 方法[J]. 武汉大学学报: 工学版, 2014, 47(6): 743-749. (DENG Zhi-ping, JIANG Shui-hua, CAO Zi-jun, et al. Reliability analysis of slope stability considering spatially varying soil properties using Kriging method[J]. Engineering Journal of Wuhan University, 2014, 47(6): 743-749. (in Chinese)) [11] GRIFFITHS D V, FENTON G A, MANOHARAN N. Undrained bearing capacity of two-strip footings on spatially random soil[J]. International Journal of Geomechanics, 2006, 6(6): 421-427. [12] CHO S E, PARK H C. Effect of spatial variability of cross-correlated soil properties on bearing capacity of strip footing[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2010, 34(1): 1-26. [13] WANG Y, HUANG K, CAO Z. Bayesian identification of soil strata in London clay[J]. Géotechnique, 2014, 64(3): 239. [14] EISBACHER GH. Natural slope failure, northeastern Skeena mountains[J]. Canadian Geotechnical Journal, 1971, 8(3):384-390. [15] TANG WH, SIDI I, GILBERT RB. Average property in random two-state medium[J]. Journal of Engineering Mechanics, 1989, 115(1): 131-144. [16] HALIM IS. Reliability of geotechnical systems considering geological anomaly[D]. Urbana-Champaign: University of Illinois at Urbana-Champaign, 1991. [17] KOHNO S, ANG A, TANG W H. Reliability evaluation of idealized tunnel systems[J]. Structural Safety, 1992, 11(2): 81-93. [18] ELFEKI A, DEKKING M. A Markov chain model for subsurface characterization: theory and applications[J]. Mathematical Geology, 2001, 33(5): 569-589. [19] QI X H, LI D Q, PHOON K K, et al. Simulation of geologic uncertainty using coupled Markov chain[J]. Engineering Geology, 2016, 207: 129-140. [20] LI D Q, QI X H, CAO Z J, et al. Evaluating slope stability uncertainty using coupled Markov chain[J]. Computers and Geotechnics, 2016, 73: 72-82. [21] HALDAR S, BABU G L S. Effect of soil spatial variability on the response of laterally loaded pile in undrained clay[J]. Computers and Geotechnics, 2008, 35(4): 537-547. [22] SRIVASTAVA A, BABU G L S, HALDAR S. Influence of spatial variability of permeability property on steady state seepage flow and slope stability analysis[J]. Engineering Geology, 2010, 110(3): 93-101. [23] KASAMA K, WHITTLE A J, ZEN K. Effect of spatial variability on the bearing capacity of cement-treated ground[J]. Soils and Foundations, 2012, 52(4): 600-619. [24] 蒋水华, 李典庆, 周创兵, 等. 考虑自相关函数影响的边坡可靠度分析[J]. 岩土工程学报, 2014, 36(3): 508-518. (JIANG Shui-hua, LI Dian-qing, ZHOU Chuang-bing, et al. Slope reliability analysis considering effect of autocorrelation functions[J]. Chinese Journal of Geotechnical Engineering, 2014, 36(3): 508-518. (in Chinese)) [25] CHING J, PHOON K K. Effect of element sizes in random field finite element simulations of soil shear strength[J]. Computers & Structures, 2013, 126: 120-134. [26] SIVAKUMAR BABU GL, SRIVASTAVA A, MURTHY DSN. Reliability analysis of the bearing capacity of a shallow foundation resting on cohesive soil[J]. Canadian Geotechnical Journal, 2006, 43(2): 217-223.
