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| System reliability of geotechnical problems using quasi-Newton approximation-based sorm |
| ZENG Peng,CHEN Yu,LI Tianbin |
(State Key Laboratory of Geohazard Prevention and Geoenvironment Protection,Chengdu University of Technology,
Chengdu,Sichuan 610059,China) |
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Abstract Multi-failure modes inherently exist in geotechnical engineering practices,which are typically considered as series system problems in literature. However,the existing system reliability methods can hardly achieve a good balance between the computational cost and accuracy. Given this limitation,a novel method integrates a highly efficient second order reliability method(SORM) and a practical system reliability approach was proposed in this paper. Specifically,the quasi-Newton approximation-based SORM was used to approximate the second order reliability index for each limit state function(LSF),providing a basis for the further linearization transformation,so as to ultimately implement the improved linearization approach to obtain the system reliability results. In addition,two examples of common geotechnical problems featuring series system reliability analyses-a semi-gravity retaining wall and a soil slope with multiple layers were reviewed for illustration. The computed results with the proposed method show good computational efficiency and accuracy.
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[1] PHOON K K,CHING J. Risk and reliability in geotechnical engineering[M]. [S. l.]:CRC Press,2014:139–147.
[2] 李典庆,蒋水华,张利民,等. 考虑锚杆腐蚀作用的岩质边坡系统可靠度分析[J]. 岩石力学与工程学报,2013,32(6):1 137–1 144. (LI Dianqing,JIANG Shuihua,ZHANG Liming,et al. System reliability analysis of rock slopes considering rock bolt corrosion[J]. Chinese Journal of Rock Mechanics and Engineering,2013,32(6):1 137–1 144.(in Chinese))
[3] 张俊芝,李桂青. 服役重力坝系统可靠度及概率寿命探讨[J]. 水利学报,2000,(4):40–45.(ZHANG Junzhi,LI Guiqing. A study on system reliability and expectancy of gravity dam in service[J]. Journal of Hydraulic Engineering,2000,(4):40–45.(in Chinese))
[4] 宋玉香,景诗庭,朱永全. 隧道结构系统可靠度研究[J]. 岩土力学,2008,29(3):780–784.(SONG Yuxiang,JING Shiting,ZHU Yongquan. Research on reliability of tunnel structural system[J]. Rock and Soil Mechanics,2008,29(3):780–784.(in Chinese))
[5] 谭晓慧. 多滑面边坡的可靠性分析[J]. 岩石力学与工程学报,2001,20(6):822–825.(TAN Xiaohui. Reliability analysis on a slope with several slide surfaces[J]. Chinese Journal of Rock Mechanics and Engineering,2001,20(6):822–825.(in Chinese))
[6] 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.
[7] LÜ Q,CHAN C,LOW B. System reliability assessment for a rock tunnel with multiple failure modes[J]. Rock Mechanics and Rock Engineering,2013,46(4):821–833.
[8] CHO S E. First-order reliability analysis of slope considering multiple failure modes[J]. Engineering Geology,2013,154:98–105.
[9] ZENG P,JIMENEZ R. An approximation to the reliability of series geotechnical systems using a linearization approach[J]. Computers and Geotechnics,2014,62:304–309.
[10] ZENG P,JIMENEZ R,LI T. An efficient quasi-Newton approximation- based SORM to estimate the reliability of geotechnical problems[J]. Computers and Geotechnics,2016,76:33–42.
[11] 高 谦. 土木工程可靠性理论及其应用[M]. 北京:中国建材工业出版社,2007:129–131.(GAO Qian. Reliability theory and application in civil engineering[M]. Beijing:China Building Material Press,2007:129–131.(in Chinese))
[12] 傅方煜,郑小瑶,吕 庆,等. 基于响应面法的边坡稳定二阶可靠度分析[J]. 岩土力学,2014,35(12):3 460–3 466.(FU Fangyu,ZHENG Xiaoyao,LÜ Qing,et al. Second order reliability analysis of slope stability using response surface method[J]. Rock and Soil Mechanics,2014,35(12):3 460–3 466.(in Chinese))
[13] TVEDT L. Two second-order approximations to the failure probability[R]. Oslo:Det Norske Veritas,1983.
[14] BREITUNG K. Asymptotic approximations for multinormal integrals[J]. Journal of Engineering Mechanics,1984,110(3):357–366.
[15] HOHENBICHLER M,RACKWITZ R. Improvement of second order reliability estimates by importance sampling[J]. Journal of Engineering Mechanics,1988,114(12):2 195–2 199.
[16] HONG H. Simple approximations for improving second-order reliability estimates[J]. Journal of Engineering Mechanics,1999,125(5):592–595.
[17] ZHAO Y,ONO T. New approximations for SORM:Part 1[J]. Journal of Engineering Mechanics,1999,125(1):79–85.
[18] PHOON K K. Reliability-based design in geotechnical engineering:computations and applications[M]. PHOON K K ed. New York:Taylor Francis,2008:78–91.
[19] PERIÇARO G A,SANTOS S R,RIBEIRO A A,et al. HLRF-BFGS optimization algorithm for structural reliability[J]. Appl Math Model,2015,39(7):2 025–2 035.
[20] LIM J,LEE B,LEE I. Second-order reliability method—based inverse reliability analysis using Hessian update for accurate and efficient reliability—based design optimization[J]. International Journal for Numerical Methods in Engineering,2014,100(10):773–792.
[21] 杜永峰,余 钰,李 慧. 重力式挡土墙稳定性的结构体系可靠度分析[J]. 岩土工程学报,2008,30(3):349–353.(DU Yongfeng,YU Yu,LI Hui. Analysis of reliability of structural systems for stability of gravity retaining walls[J]. Chinese Journal of Geotechnical Engineering,2008,30(3):349–353.(in Chinese))
[22] ZENG P,JIMENEZ R,JURADO-PIÑA R. System reliability analysis of layered soil slopes using fully specified slip surfaces and genetic algorithms[J]. Engineering Geology,2015,193:106–117.
[23] 王 宇,王春磊,汪 灿,等. 边坡可靠性评价的向量投影响应面研究及应用[J]. 岩土工程学报,2011,33(9):1 434–1 439.(WANG Yu,WANG Chunlei,WANG Can,et al. Reliability evaluation of slopes based on vector projection response surface and its application[J]. Chinese Journal of Geotechnical Engineering,2011,33(9):1 434–1 439.(in Chinese))
[24] 褚雪松,王旭春,张勇强,等. 基于代表性滑动面的边坡系统可靠度分析[J]. 煤炭学报,2014,39(6):1 077–1 083.(CHU Xuesong,WANG Xuchun,ZHANG Yongqiang,et al. Slope system reliability analysis based on representative slip surfaces[J]. Journal of China Coal Society,2014,39(6):1 077–1 083.(in Chinese))
[25] 李静萍,程勇刚,李典庆,等. 基于多重响应面法的空间变异土坡系统可靠度分析[J]. 岩土力学,2016,37(1):147–155.(LI Jingping,CHENG Yonggang,LI Dianqing,et al. System reliability analysis of spatially variable soil slopes using the multiple response surfaces method[J]. Rock and Soil Mechanics,2016,37(1):147–155.(in Chinese))
[26] 蒋水华,祁小辉,曹子君,等. 基于随机响应面法的边坡系统可靠度分析[J]. 岩土力学,2015,36(3):809–818.(JIANG Shuihua,QI Xiaohui,CAO Zijun,et al. System reliability analysis of slope with stochastic response surface method[J]. Rock and Soil Mechanics.,2015,36(3):809–818.(in Chinese))
[27] DUNCAN J M,SONG K S. SLOPE8R:A computer program for slope stability analysis with non-circular slip surfaces[R]. Berkeley,CA:Department of Civil Engineering,University of California,1984:99–114. |
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