Engineering Mechanics ›› 2018, Vol. 35 ›› Issue (8): 154-161.doi: 10.6052/j.issn.1000-4750.2017.04.0308

Previous Articles     Next Articles

MODEL CORRECTION FACTOR METHOD BASED APPROACH FOR RELIABILITY ANALYSIS OF SPATIALLY VARIABLE SLOPES

JIANG Shui-hua, YAO Chi, YANG Jian-hua, JIANG Qing-hui, HUANG Jin-song   

  1. School of Civil Engineering and Architecture, Nanchang University, Nanchang, Jiangxi 330031, China
  • Received:2017-04-25 Revised:2017-09-22 Online:2018-08-29 Published:2018-08-29

Abstract: Reliability analysis of spatially variable slopes involves repeatedly evaluating the slope stability using a deterministic analysis method such as the limit equilibrium method (LEM) or the finite element method (FEM). The LEM is conceptually simple and computationally efficient, while the FEM tends to give a more realistic prediction of slope failure mechanism, particularly when considering the spatial variability of soil properties. Thus, it is of great interest to adopt advantages of both LEM and FEM in estimating the reliability of slope stability. This paper aims to propose a model correction factor method (MCFM) based approach for reliability analysis of spatially variable slopes. In this approach, first-order reliability method is adopted for slope reliability analysis considering spatial variation. A model correction factor is introduced to modify the idealized LEM-based limit-state surface to the more accurate FEM-based limit-state surface. Finally, a line sampling is adopted to estimate the probability of slope failure based on the corrected LEM model with the model correction factor. The reliability assessment of a cohesive-frictional slope example is studied to investigate the performance of the proposed approach considering the spatial variability of the soil strength parameters. The results indicate the proposed approach not only provides an accurate estimation of probability of failure consistent with that obtained from the FEM-based subset simulation, but also significantly reduces the number of finite element analyses of slope stability. Thus, it provides an effective and versatile tool for slope reliability analysis at low-probability levels considering the spatial variability of the soil strength parameters.

Key words: slope reliability, spatial variability, finite element method, first order reliability method, model correction factor

CLC Number: 

  • TU311
[1] Phoon K K, Kulhawy F H. Characterization of geotechnical variability[J]. Canadian Geotechnical Journal, 1999, 36(4):612-624.
[2] 张继周, 缪林昌, 王华敬. 土性参数不确定性描述方法的探讨[J]. 岩土工程学报, 2009, 31(12):1936-1940. Zhang Jizhou, Miao Linchang, Wang Huajing. Methods for characterizing variability of soil parameters[J]. Chinese Journal of Geotechnical Engineering, 2009, 31(12):1936-1940. (in Chinese)
[3] Griffiths D V, Fenton G A. Probabilistic slope stability analysis by finite elements[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2004, 130(5):507-518.
[4] Low B K, Lacasse S, Nadim F. Slope reliability analysis accounting for spatial variation[J]. Georisk, 2007, 1(4):177-189.
[5] Cho S E. Probabilistic assessment of slope stability that considers the spatial variability of soil properties[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2009, 136(7):975-984.
[6] Jiang S H, Li D Q, Cao Z J, et al. Efficient system reliability analysis of slope stability in spatially variable soils using Monte Carlo simulation[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2015, 141(2):04014096.
[7] 蒋水华, 李典庆, 周创兵, 等. 考虑自相关函数影响边坡可靠度分析[J]. 岩土工程学报, 2014, 36(3):508-518. Jiang Shuihua, Li Dianqing, Zhou Chuangbing, et al. Slope reliability analysis considering effect of autocorrelation functions[J]. Chinese Journal of Geotechnical Engineering, 2014, 36(3):508-518. (in Chinese)
[8] Javankhoshdel S, Luo N, Bathurst R J. Probabilistic analysis of simple slopes with cohesive soil strength using RLEM and RFEM[J]. Georisk, 2017, 11(3):231-246.
[9] Low B K, Zhang J, Tang W H. Efficient system reliability analysis illustrated for a retaining wall and a soil slope[J]. Computers and Geotechnics, 2011, 38(2):196-204.
[10] 张浮平, 曹子君, 唐小松, 等. 基于蒙特卡罗模拟的高效边坡可靠度修正方法[J]. 工程力学, 2016, 33(7):55-64. Zhang Fuping, Cao Zijun, Tang Xiaosong, et al. Efficient slope reliability updating method based on Monte Carlo simulation[J]. Journal of Engineering Mechanics, 2016, 33(7):55-64. (in Chinese)
[11] 谭晓慧, 王建国. 边坡的弹塑性有限元可靠度分析[J]. 岩土工程学报, 2007, 29(1):44-50. Tan Xiaohui, Wang Jianguo. Slope reliability analysis using elastoplastic finite element method[J]. Chinese Journal of Geotechnical Engineering, 2007, 29(1):44-50.
[12] Duncan J M. State of the art:limit equilibrium and finite-element analysis of slopes[J]. Journal of Geotechnical Engineering, 1996, 122(7):577-596.
[13] 孙玉进, 宋二祥, 杨军. 基于非线性强度准则的土工结构安全系数有限元计算[J]. 工程力学, 2016, 33(7):84-91. Sun Yujin, Song Erxiang, Yang Jun. Finite element analysis of earth structure stability with general nonlinear failure criterion[J]. Chinese Journal of Engineering Mechanics, 2016, 33(7):84-91. (in Chinese)
[14] Griffiths D V, Lane P A. Slope stability analysis by finite elements[J]. Géotechnique, 1999, 49(3):387-403.
[15] 李典庆, 肖特, 曹子君, 等. 基于极限平衡法和有限元法的边坡协同式可靠度分析[J]. 岩土工程学报, 2016, 38(6):1004-1013. Li Dianqing, Xiao Te, Cao Zijun, et al. Auxiliary slope reliability analysis using limit equilibrium analysis and finite element analysis[J]. Chinese Journal of Geotechnical Engineering, 2016, 38(6):1004-1013. (in Chinese)
[16] Xiao T, Li D Q, Cao Z J, et al. Three-dimensional slope reliability and risk assessment using auxiliary random finite element method[J]. Computers and Geotechnics, 2016, 79:146-158.
[17] Ditlevsen O, Arnbjerg-Nielsen T. Model-correction-factor method in structural reliability[J]. Journal of Engineering Mechanics, 1994, 120(1):1-10.
[18] Vanmarcke E H. Random fields:analysis and synthesis. Revised and expanded new edition[M]. Beijing:World Scientific Publishing, 2010.
[19] Li C C, Der Kiureghian A. Optimal discretization of random fields[J]. Journal of Engineering Mechanics, 1993, 119(6):1136-1154.
[20] Jiang S H, Huang J S, Yao C, et al. Quantitative risk assessment of slope failure in 2-D spatially variable soils by limit equilibrium method[J]. Applied Mathematical Modelling, 2017, 47:710-725.
[21] Hasofer A M, Lind N C. Exact and invariant second-moment code format[J]. American Society of Civil Engineers, Journal of Engineering Mechanics, 1974, 100:111-121.
[22] Rackwitz R, Fiessler B. Structural reliability under combined random load sequences[J]. Computers and Structures, 1978, 9(5):489-494.
[23] Franchin P, Ditlevsen O, Der Kiureghian A. Model correction factor method for reliability problems involving integrals of non-Gaussian random fields[J]. Probabilistic Engineering Mechanics, 2002, 17(2):109-122.
[24] Leander J, Al-Emrani M. Reliability-based fatigue assessment of steel bridges using LEFM-A sensitivity analysis[J]. International Journal of Fatigue, 2016, 93:82-91.
[25] Hohenbichler M, Rackwitz R. Improvement of second-order reliability estimates by importance sampling[J]. Journal of Engineering Mechanics, 1988, 114(12):2195-2199.
[26] 陈磊, 吕震宙, 宋述芳. 模糊可靠性灵敏度分析的线抽样方法[J]. 工程力学, 2008, 25(7):45-51. Chen Lei, Lü Zhenzhou, Song Shufang. Line sampling algorithm for fuzzy reliability sensitivity analysis[J]. Chinese Journal of Engineering Mechanics, 2008, 25(7):45-51. (in Chinese)
[27] 吕召燕, 吕震宙, 张磊刚, 等. 基于条件期望的改进线抽样方法及其应用[J]. 工程力学, 2014, 31(4):34-39. Lü Zhaoyan, Lü Zhenzhou, Zhang Leigang, et al. An improved line sampling method and its application based on conditional expectation[J]. Chinese Journal of Engineering Mechanics, 2014, 31(4):34-39. (in Chinese)
[28] 李典庆, 蒋水华. 边坡可靠度非侵入式随机分析方法[M]. 北京:科学出版社, 2016:73-106. Li Dianqing, Jiang Shuihua. A non-intrusive stochastic method for slope reliability analysis[M]. Beijing:Science Press, 2016:73-106. (in Chinese)
[29] Smith I M, Griffiths D V, Margetts L. Programming the finite element method[M]. 5th ed. Chichester, UK:John Wiley & Sons, 2014.
[30] Tu Y, Liu X, Zhong Z, et al. New criteria for defining slope failure using the strength reduction method[J]. Engineering Geology, 2016, 212:63-71.
[31] Au S K, Beck J L. Estimation of small failure probabilities in high dimensions by subset simulation[J]. Probabilistic Engineering Mechanics, 2001, 16(4):263-277.
[1] XIE Jiang, ZHANG Xue-han, SU Xuan, MOU Hao-lei, ZHOU Jian, FENG Zhen-yu, LAN Yuan-pei. INFLUENCE OF LAYER SEQUENCE ON ENERGY ABSORPTION CHARACTERISTICS OF THIN-WALLED COMPOSITE CIRCULAR TUBES UNDER AXIAL COMPRESSION [J]. Engineering Mechanics, 2018, 35(6): 231-239.
[2] WANG Shan. A STRESS RECOVERY METHOD FOR CRACKS IN KIRCHHOFF PLATE BASED ON THE SYMPLECTIC EIGENSOLUTIONS NEAR THE CRACK TIPS [J]. Engineering Mechanics, 2018, 35(5): 10-16.
[3] ZHAO Xiao-gang, ZHAO Xin, WEN Ze-feng, JIN Xue-song. INFLUENCE OF WHEEL-RAIL ADHESION COEFFICIENT ON TRANSIENT PROPAGATION OF A VERTICAL RAIL CRACK [J]. Engineering Mechanics, 2018, 35(5): 239-245.
[4] HONG Jun-qing, LIU Wei-qing, FANG Hai, ZHANG Fu-bin. STRESS ANALYSIS OF COMPOSITE SANDWICH PANELS UNDER UNIDIRECTIONAL BENDING [J]. Engineering Mechanics, 2018, 35(4): 41-51.
[5] LI Ke, GE Yao-jun, ZHAO Lin, XIA Jin-lin. NUMERICAL STUDY OF THE RESPONSIBILITY OF STRUCTURAL AEROSTATIC RESPONSES IN AERO-ELASTIC MODEL TESTS OF LONG-SPAN CABLE-STAYED BRIDGES [J]. Engineering Mechanics, 2018, 35(3): 79-85.
[6] ZHANG Peng-fei, WANG Zhi-heng, XI Guang. STUDY ON STRESS ANALYSIS METHOD AND RADIAL SIZE OPTIMIZATION DESIGN METHOD FOR MULTI-LAYER HIGH SPEED ROTATING SHRINK-FITTED CYLINDERS [J]. Engineering Mechanics, 2018, 35(10): 212-221.
[7] JIANG Shui-hua, YANG Jian-hua, YAO Chi, HUANG Jin-song. QUANTITATIVE RISK ASSESSMENT OF SLOPE FAILURE CONSIDERING SPATIAL VARIABILITY OF SOIL PROPERTIES [J]. Engineering Mechanics, 2018, 35(1): 136-147.
[8] DI Qin-feng, SONG Hai-tao, CHEN Feng, WANG Wen-chang, ZHANG He, JIN Ze-zhong. THE DEVELOPMENT AND APPLICATION OF NUMERICAL PLATFORM FOR THREADED CONNECTIONS UNDER COMPLEX LOADS [J]. Engineering Mechanics, 2017, 34(增刊): 295-299.
[9] CHEN Hao-dong, WANG Qing-song, SUN Jin-hua. NUMERICAL PREDICTION ON THE FIRST BREAKING TIME OF GLASS IN FIRE CONDITIONS [J]. Engineering Mechanics, 2017, 34(增刊): 210-213.
[10] YIN Guan-sheng, YAO Ru-yang, ZHAO Zhen-yu. STUDY ON OPTIMIZATION AND CONTROL PARAMETERS OF A CONCEPT MODEL OF HIGHWAY CRASH CUSHIONS [J]. Engineering Mechanics, 2017, 34(增刊): 220-226.
[11] CHEN Xiao-dong, NIE Guo-jun. BENDING ANALYSIS OF LAMINATES WITH VARIABLE ANGLE TOWS [J]. Engineering Mechanics, 2017, 34(9): 248-256.
[12] YANG Zhi-yong, CAO Zi-jun, LI Dian-qing, PHOON Kok-kwang. EFFECT OF SPATIALLY VARIABLE FRICTION COEFFICIENT OF GRANULAR MATERIALS ON ITS MACRO-MECHANICAL BEHAVIORS USING BIAXIAL COMPRESSION NUMERICAL SIMULATION [J]. Engineering Mechanics, 2017, 34(5): 235-246.
[13] WANG Xiao-qing, JIN Xian-long, YANG Zhi-hao. PARALLEL NUMERICAL SIMULATION FOR DYNAMIC RESPONSE OF LARGE-SCALE WATER CONVEYANCE TUNNEL UNDER SEISMIC EXCITATION BASED ON ALE METHOD [J]. Engineering Mechanics, 2017, 34(3): 247-256.
[14] WANG Wei-hao, FENG Hai-quan, ZHU Ming-xin, LIU Jia. INFLUENCE OF DIFFERENT DILATATION SIZE ON MECHANICAL PROPERTIES OF ASYMMETRIC VERTRBRAL ARTERY STENTS [J]. Engineering Mechanics, 2017, 34(3): 232-240.
[15] LI Rong, LIANG Bin, NODA Nao-Aki. A CONVENIENT ADHESIVE STRENGTH PREDICTION METHOD FOR ADHESIVE BUTT JOINT IN TERMS OF THE CRITICAL STRESS INTENSITY FACTOR [J]. Engineering Mechanics, 2017, 34(11): 218-224.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
[1] ZHANG Dong-juan;CUI Zhen-shan;LI Yu-qiang;RUAN Xue-yu. SPRINGBACK OF SHEET METAL AFTER PLANE STRAIN STRETCH-BENDING[J]. Engineering Mechanics, 2007, 24(7): 0 -071 .
[2] LI Zhong-xian,HUANG Xin. INFLUENCE OF TRAVELING WAVE EFFECT ON SEISMIC RESPONSES OF CONTINUOUS RIGID-FRAMED BRIDGE IN DEEP WATER[J]. Engineering Mechanics, 2013, 30(3): 120 -125 .
[3] WANG Jin-ting;ZHANG Chu-han;JIN Feng. ON THE ACCURACY OF SEVERAL EXPLICIT INTEGRATION SCHEMES FOR DYNAMIC EQUATION WITH DAMPING[J]. Engineering Mechanics, 2006, 23(3): 1 -5 .
[4] XIONG Tie-hua;CHANG Xiao-lin. APPLICATION OF RESPONSE SURFACE METHOD IN SYSTEM RELIABILITY ANALYSIS[J]. Engineering Mechanics, 2006, 23(4): 58 -61 .
[5] GE Xin-sheng;CHEN Li-qun;LIU Yan-zhu. OPTIMAL CONTROL OF A NONHOLONOMIC MOTION PLANNING FOR MUTILBODY SYSTEMS[J]. Engineering Mechanics, 2006, 23(3): 63 -68 .
[6] GU Zhi-ping;HE Xing-suo;FANG Tong. EFFECT OF THE DIFFERENTIAL LINKING CONDITION ON SUB-HARMONIC RESONANCE[J]. Engineering Mechanics, 2006, 23(4): 62 -66 .
[7] JIA Chao;ZHANG Chu-han;JIN Feng;CHENG Wei-shuai. SENSITIVITY ANALYSIS OF STRUCTURAL RELIABILITY TO RANDOM VARIABLES AND FAILURE-MODE CORRELATION FACTORS AND ITS APPLICATION IN ENGINEERING[J]. Engineering Mechanics, 2006, 23(4): 12 -16,1 .
[8] LI Yi;ZHAO Wen;ZHANG Yan-nian. AN ACCELERATING ALGORITHM FOR RELIABILITY ANALYSIS OF SYSTEM STIFFNESS[J]. Engineering Mechanics, 2006, 23(3): 17 -20 .
[9] SHI Bao-jun;YUAN Ming-wu;SONG Shi-jun. LEAST-SQUARE POINT COLLOCATED MESHLESS METHOD BASED ON KERNEL REPRODUCING FOR HYDRODYNAMIC PROBLEMS[J]. Engineering Mechanics, 2006, 23(4): 17 -21,3 .
[10] YANG Pu;LIU Ying-hua;YUAN Hong-yan;CEN Zhang-zhi. A MODIFIED ELASTIC COMPENSATION METHOD FOR THE COMPUTATION OF LIMIT LOADS[J]. Engineering Mechanics, 2006, 23(3): 21 -26 .