Abstract
An approach of limit state equation for surrounding rock was put forward based on deformation criterion. A method of symmetrical sampling of basic random variables adopted by classical response surface method was mended, and peak value and deflection degree of basic random variables distribution curve were took into account in the mended sampling method. A calculation way of probability moment, based on mended Rosenbluth method, suitable for non-explicit performance function was put forward. The first, second, third and fourth order moments of functional function value were calculated by mended Rosenbluth method through the first, second, third and fourth order moments of basic random variable. A probability density the function(PDF) of functional function was deduced through its first, second, third and fourth moments, the PDF in the new method took the place of the method of quadratic polynomial to approximate real functional function and reliability probability was calculated through integral by the PDF for random variable of functional function value in the new method. The result shows that the improved response surface method can adapt to various statistic distribution types of basic random variables, its calculation process is legible and need not iterative circulation. In addition, a stability probability of surrounding rock for a tunnel was calculated by the improved method, whose workload is only 30% of classical method and its accuracy is comparative.
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SU Yong-hua, JIANG De-song, ZHAO Ming-hua. Estimation of stability reliability degree of tunnel structure in soft and loose rock mass[J]. Journal of Hunan University, 2006, 33(2): 10–14. (in Chinese)
LI Zhi-ye, ZENG Yan-hua. Design Principle and Ways for Underground Structure[M]. Chengdu: South-West Traffic University Press, 2005: 304–310. (in Chinese)
BUCHER C G, BOUGUND U. A fast and efficient response surface approach for structural reliability problem[J]. Structural Safety, 1990, 34(1): 57–66.
SCHÜELLER G I. On efficient computational scheme to calculate structural failure probability[J]. Probability Engineering Mechanics, 1989, 4(1): 10–18.
LIU Y W, MOSES F. A sequential response surface methods and its application in the reliability analysis of aircraft structural system[J]. Structural Safety, 1994, 16(1/2): 39–46.
FARAVELLI L A. Response surface approach for reliability analysis[J]. Journal of Engineering Mechanics, 1989, 115(12): 2763–2781.
ROSENBLUETH E. Point estimate for probability moment[C]// Proc Nat Acad Sci, USA, 1975, 72: 3812–3814.
TONG Xiao-li. Improved Rosenbluth method and its application in structure stability reliability degree analysis[J]. Journal of Dalian Science and Technology of University, 1997, 37(3): 316–321. (in Chinese)
ZHAO Guo-fan. Engineering Structural Reliability Theory and Its Application[M]. Dalian: Dalian Technology University Press, 1996: 145–148. (in Chinese)
ZHAO Wen-gui. Fourth order moment analysis method for structure stability reliability degree[J]. Journal of Dalian Science and Technology of University, 1992, 32(4): 455–459. (in Chinese)
SU Yong-hua, HE Man-chao, GAO Qian. Applying of Rosenblueth method in evaluating stability reliability of anchor-shotcrete net support system for soft-fracture surrounding rock[J]. Chinese Journal of Geotechnical Engineering, 2004, 26(3): 373–379. (in Chinese)
SU Yong-hua, HE Man-chao. Simplified calculation approach of response surface method reliability index by point estimation of probability moment[J]. Engineering Mechanics, 2007, 24(7): 11–15. (in Chinese)
ZHANG Xiao-qing, KANG Hai-gui, WANG Fu-ming. A new method for reliability problem without explicit performance function[J]. Journal of Dalian University of Technology, 2003, 43(5): 650–654. (in Chinese)
SU Yong-hua, ZHAO Ming-hua, ZHANG Yue-ying, et al. On analysis of reliability of slope stability based on Spencer model by the method of difference[J]. Journal of Rock Mechanics and Engineering, 2006, 25(S1): 2750–2756. (in Chinese)
SU Yong-hua, ZHAO Ming-hua. Application of response surface method in stability reliability degree analysis for slope[J]. Chinese Journal of Rock Mechancis and Engineering, 2006, 25(7): 1417–1425. (in Chinese)
HAN Bin, WU Ai-xiang, DENG Jian, et al. Backfill technical analysis based on reliability theory in the underhand drift cut and filling stoping[J]. Journal of Central South University: Science and Technology, 2006, 37(3): 583–587. (in Chinese)
HE Yue-gang, LI Zhi-wei, YANG Xiao-li. Hazard development mechanism and deformation estimation of water solution mining area[J]. Journal of Central South University of Technology, 2006, 13(6): 738–742.
XIE Xue-bin, PAN Chang-ling, CAO Ping, et al. An optimization method of stope structure parameter for rock burst tendency mine[J]. Journal of Central South University: Natural Science, 1999, 30(2): 121–125. (in Chinese)
DENG Jian, BIAN Li, LI Xi-bing, et al. Analysis of factors and countermeasures of mining subsidence in Kaiyang phosphorus mine[J]. Journal of Central South University of Technology, 2006, 13(6): 733–737.
TU Wen-ge, LIN Li-chuan. Analysis on fuzzy reliability of structure[J]. Journal of Central South University of Technology: Natural Science, 2000, 31(4): 371–375. (in Chinese)
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Foundation item: Project(50378036) supported by the National Natural Science Foundation of China; Project (200503) supported by the Foundation of Communications Department of Hunan Province, China
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Su, Yh., Zhang, P. & Zhao, Mh. Improved response surface method and its application in stability reliability degree analysis of tunnel surrounding rock. J. Cent. South Univ. Technol. 14, 870–876 (2007). https://doi.org/10.1007/s11771-007-0165-2
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DOI: https://doi.org/10.1007/s11771-007-0165-2