|
|
|
| Spatial variability characterization of the mechanical parameters of structural planes and reliability analysis of rock slopes |
| JIANG Shuihua1，2，LI Jianping1，HUANG Jinsong1，ZHOU Chuangbing1 |
(1. School of Infratructure Engineering，Nanchang University，Nanchang，Jiangxi 330031，China；2. State Key Laboratory of Geomechanics and Geotechnical Engineering，Institute of Rock and Soil Mechanics，Chinese Academy of Sciences，
Wuhan，Hubei 430071，China) |
|
|
|
|
Abstract Characterization of the spatial variability of rock mass parameters differs significantly from that of soil parameters due to complex structures inherently existing in the rock masses. At present，the spatial variability modeling of the mechanical parameters of highly fractured/weathered rock masses and those dominated by a single structural plane and associated slope reliability analysis have been extensively studied. However，few attempts have been made to depict the spatial variability of the mechanical parameters of wedge and anti-dip rock masses and conduct associated slope reliability analysis. In this paper，a method for spatial variability modeling of the mechanical parameters of structural planes and slope reliability analysis is proposed for the wedge and anti-dip rock masses. The varying ranges of the autocorrelation distances and scales of fluctuation of the mechanical parameters for different types of rock masses are systematically summarized. An interface program between the spatial variability modeling of the mechanical parameters and probabilistic slope stability analysis with FLAC3D software is developed. An explicit function relationship between the factor of safety of the slope and the random field vectors of structural plane parameters is constructed using the Back-Propagation(BP) neural network. Then the non-intrusive stochastic finite difference method is adopted to explore the influence of the spatial variability of the mechanical parameters of structural planes on the probability of slope failure. The results indicate that the autocorrelation distances and scales of fluctuation of the mechanical parameters are different among different types of rock masses. The single exponential autocorrelation function is the most widely used theoretical autocorrelation function. The direction simulation and direct Monte-Carlo simulation methods are adopted to validate the effectiveness of the proposed method. The proposed method can provide an effective means for the spatial variability characterization of the mechanical parameters of structural plans for the wedge and anti-dip rock masses in the slope reliability analysis. In addition，the probability of slope failure will be overestimated if the spatial variability of mechanical parameters is ignored，which can further result in conservative slope reinforcement design schemes.
|
|
|
|
|
|
[1] 谭文辉，王家臣，周汝弟. 岩体强度参数空间变异性分析[J]. 岩石力学与工程学报，1999，18(5)：546–549.(TAN Wenhui，WANG Jiachen，ZHOU Rudi. Analysis of spatial variability of rock mass strength parameters[J]. Chinese Journal of Rock Mechanics and Engineering，1999，18(5)：546–549.(in Chinese))
[2] 王家臣，骆中洲. 基于岩体性质空间变异性的边坡可靠性分析[J]. 化工矿山技术，1996，25(3)：1–4.(WANG Jiachen，LUO Zhongzhou. Slope reliability analysis based on spatial variability of rock mass properties[J]. Industrial Minerals and Processing，1996，25(3)：1–4.(in Chinese))
[3] 王家臣，王艳青，宁 柯. 应用地质统计学研究岩体强度的空间变异性[J]. 黄金科学技术，1999，45：51–54.(WANG Jiachen，WANG Yanqing，NING Ke. The spatial variability of rock mass strength is studied by geostatistics[J]. Gold Science and Technology，1999，45：51–54.(in Chinese))
[4] 常 远，任富强，常来山，等. 混合岩与绿泥石英片岩强度空间变异性实验研究[J]. 中国矿业，2016，25(10)：142–145.(CHANG Yuan，REN Fuqiang，CHANG Laishan. Experimental study on spatial variability of strength of mixed rock and chlastonite schist[J]. China Mining Magazine，2016，25(10)：142–145.(in Chinese))
[5] EIVAZY H，ESMAIELI K，JEAN R. Modelling geomechanical heterogeneity of rock masses using direct and indirect geostatistical conditional simulation methods[J]. Rock Mechanics and Rock Engineering，2017，50(12)：3 175–3 195.
[6] ZHANG W，MENG F，CHEN F，et al. Effects of spatial variability of weak layer and seismic randomness on rock slope stability and reliability analysis[J]. Soil Dynamics and Earthquake Engineering，2021，146：106735.
[7] CHEN D，XU D，REN G，et al. Simulation of cross-correlated non-Gaussian random fields for layered rock mass mechanical parameters[J]. Computers and Geotechnics，2019，112：104–119.
[8] 高 谦，王思敬. 水电站船闸边坡稳定性分析及可靠度评价[J]. 水文地质工程地质，1993，20(5)：5–9.(GAO Qian，WANG Sijing. Stability analysis and reliability evaluation of slope of shiplock of hydropower station[J]. Hydrogeology and Engineering Geology，1993，20(5)：5–9.(in Chinese))
[9] HOEK E，LONDE P. The design of rock slopes and foundations[R]. Denver：General Report for Third Congress of the International Society for Rock mechanics，1974：1–78.
[10] SRIVASTAVA A. Spatial variability modelling of geotechnical parameters and stability of highly weathered rock slope[J]. Indian Geotechnical Journal，2012，42(3)：179–185.
[11] 徐根洪. 可靠性理论在强风化岩石边坡稳定性分析中的应用[J]. 长江科学院院报，2016，33(3)：65–69.(XU Genhong. Stability Application of reliability theory to stability analysis of strongly weathered rock slope[J]. Journal of Yangtze River Scientific Research Institute，2016，33(3)：65–69.(in Chinese))
[12] RENANI H R，MARTIN C D，VARONA P，et al. Stability analysis of slopes with spatially variable strength properties[J]. Rock Mechanics and Rock Engineering，2019，52(10)：1–18.
[13] 张社荣，王 超，孙 博. Bayes约束随机场下坝基溶蚀区随机模拟方法及其影响分析[J]. 岩土力学，2013，34(8)：2 337–2 346. (ZHANG Sherong，WANG Chao，SUN Bo. Random simulation method of dam foundation erosion zone under Bayes constrained random field and its influence analysis[J]. Rock and Soil Mechanics，2013，34(8)：2 337–2 346.(in Chinese))
[14] HSU S C，NELSON P P. Material spatial variability and slope stability for weak rock masses[J]. Journal of Geotechnical and Geoenvironmental Engineering，2006，132(2)：183–193.
[15] GRAVANIS E，PANTELIDIS L，GRIFFITHS D V. An analytical solution in probabilistic rock slope stability assessment based on random fields[J]. International Journal of Rock Mechanics and Mining Sciences，2014，71：19–24.
[16] HUANG X C，ZHOU X P，MA W，et al. Two-dimensional stability assessment of rock slopes based on random field[J]. International Journal of Geomechanics，2016，17(7)：04016155.
[17] 牛燚炜，周小平，钱七虎. 基于随机场的岩石边坡三维稳定性分 析[J]. 土木建筑与环境工程，2017，39(3)：129–137.(NIU Yiwei，ZHOU Xiaoping，QIAN Qihu. Three-dimensional stability analysis of rock slope based on random field[J]. Journal of Civil and Environmental Engineering，2017，39(3)：129–137.(in Chinese))
[18] TANG H，YONG R，EZ ELDIN M A M. Stability analysis of stratified rock slopes with spatially variable strength parameters：the case of Qianjiangping landslide[J]. Bulletin of Engineering Geology and the Environment，2017，76(3)：839–853.
[19] 宋胜武，向柏宇，杨静熙，等. 锦屏一级水电站复杂地质条件下坝肩高陡边坡稳定性分析及其加固设计[J]. 岩石力学与工程学报，2010，29(3)：16–32.(SONG Shengwu，XIANG Baiyu，YANG Jingxi，et al. Three-dimensional stability analysis of rock slope based on random field[J]. Chinese Journal of Rock Mechanics and Engineering，2010，29(3)：16–32.(in Chinese))
[20] ZHOU J W，JIAO M Y，XING H G，et al. A reliability analysis method for rock slope controlled by weak structural surface[J]. Geosciences Journal，2017，21(3)：1–15.
[21] 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 Shuihua，LI Dianqing，ZHOU Chuangbing，et al. Slope reliability analysis considering the influence of autocorrelation function[J]. Chinese Journal of Geotechnical Engineering，2014，36(3)：508–518.(in Chinese))
[22] AL-BITTAR T，SOUBRA A H. Bearing capacity of spatially random rock masses obeying Hoek–Brown failure criterion[J]. Georisk，2017，11(2)：215–229.
[23] CHING J，HU Y G，YANG Z Y，et al. Reliability-based design for allowable bearing capacity of footings on rock masses by considering angle of distortion[J]. International Journal of Rock Mechanics and Mining Sciences，2011，48(5)：728–740.
[24] 程勇刚，常晓林，李典庆. 考虑岩体空间变异性的隧洞围岩变形随机分析[J]. 岩石力学与工程学报，2012，31(增1)：2 767–2 775. (CHENG Yonggang，CHANG Xiaolin，LI Dianqing. Random analysis of tunnel surrounding rock deformation considering spatial variability of rock mass[J]. Chinese Journal of Rock Mechanics and Engineering，2012，31 (Supp.1)：2 767–2 775.(in Chinese))
[25] 方 超，薛亚东. 围岩空间变异性对隧道结构可靠度的影响分 析[J]. 现代隧道技术，2014，51(5)：41–47.(FANG Chao，XUE Yadong. Analysis of the influence of surrounding rock spatial variability on tunnel structure reliability[J]. Modern Tunnelling Technology，2014，51(5)：41–47.(in Chinese))
[26] 代庆礼. 考虑参数空间变异的高风化岩质边坡可靠性分析[J]. 长江科学院院报，2015，32(10)：57–64.(DAI Qingli. Reliability analysis of highly weathered rock slope considering spatial variation of parameters[J]. Journal of Yangtze River Scientific Research Institute，2015，32(10)：57–64.(in Chinese))
[27] 文 明，张顶立，房 倩. 高速铁路隧道围岩参数空间变异性的力学响应分析[J]. 岩石力学与工程学报，2017，36(7)：1 697–1 709. (WEN Ming，ZHANG Dingli FANG Qian. Mechanical response analysis of spatial variability of surrounding rock parameters in high-speed railway tunnel[J]. Chinese Journal of Rock Mechanics and Engineering，2017，36(7)：1 697–1 709.(in Chinese))
[28] LÜ Q，XIAO Z P，ZHENG J，et al. Probabilistic assessment of tunnel convergence considering spatial variability in rock mass properties using interpolated autocorrelation and response surface method[J]. Geoscience Frontiers，2018，9(6)：1 619–1 629.
[29] LIU H X，QI X H. Random field characterization of uniaxial compressive strength and elastic modulus for intact rocks[J]. Geoscience Frontiers，2018，9(6)：1 609–1 618.
[30] CHEN F，WANG L，ZHANG W. Reliability assessment on stability of tunnelling perpendicularly beneath an existing tunnel considering spatial variabilities of rock mass properties[J]. Tunnelling and Underground Space Technology，2019，88：276–289.
[31] 程红战，陈 健，王占盛，等. 考虑旋转各向异性相关结构的黏土边坡稳定性分析[J]. 岩石力学与工程学报，2017，36(增2)：3 965– 3 973.(CHENG Hongzhan，CHEN Jian， WANG Zhansheng，et al. Stability analysis of a clay slope accounting for the rotated anisotropy correlation structure[J]. Chinese Journal of Rock Mechanics and Engineering，2017，36(Supp.2)：3 965–3 973.(in Chinese))
[32] 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，2016：27–47.(LI Dianqing，JIANG Shuihua. Non-intrusive stochastic analysis method for slope reliability[M]. Beijing：Science Press，2016：27–47.(in Chinese))
[33] 李典庆，周创兵，陈益峰，等. 边坡可靠度分析的随机响应面法及程序实现[J]. 岩石力学与工程学报，2010，29(8)：1 513–1 523.(LI Dianqing，ZHOU Chuangbing，CHEN Yifeng，et al. Random response surface method and program implementation for slope reliability analysis[J]. Chinese Journal of Rock Mechanics and Engineering，2010，29(8)：1 513–1 523.(in Chinese))
[34] 徐 军，张利民，郑颖人. 基于数值模拟和BP网络的可靠度计算方法[J]. 岩石力学与工程学报，2003，22(3)：395–399.(XU Jun，ZHANG Liming，ZHENG Yinren. Reliability calculation method based on numerical simulation and BP network[J]. Chinese Journal of Rock Mechanics and Engineering，2003，22(3)：395–399. (in Chinese))
[35] HE X，XU H，SABETAMAL H，et al. Machine learning aided stochastic reliability analysis of spatially variable slopes[J]. Computers and Geotechnics，2020，126：103711.
[36] CHO S E. Probabilistic stability analyses of slopes using the ANN-based response surface[J]. Computers and Geotechnics，2009，36(5)：787–797.
[37] 朱 勇，周 辉，冯夏庭，等. 岩质边坡楔形体破坏概率的方向模拟[J]. 岩土力学，2017，38(增1)：157–163.(ZHU Yong，ZHOU Hui，FENG Xiating，et al. Directional simulation of failure probability of rock slope wedge[J]. Rock and Soil Mechanics，2017，38(Supp.1)：157–163.(in Chinese))
[38] 杨宝全，张 林，陈 媛，等. 锦屏一级高拱坝整体稳定物理与数值模拟综合分析[J]. 水利学报，2017，48(2)：175–183.(YANG Baoquan，ZHANG Lin，CHEN Yuan，et al. Comprehensive analysis of overall stability of Jinping High arch dam based on physics and numerical simulation[J]. Journal of Hydraulic Engineering，2017，48(2)：175–183.(in Chinese))
[39] CHING J，PHOON K K. Effect of element sizes in random field finite element simulations of soil shear strength[J]. Computers and Structures，2013，126(9)：120–134.
[40] 张社荣，谭尧升，王 超，等. 多层软弱夹层边坡岩体破坏机制与稳定性研究[J]. 岩土力学，2014，35(6)：1 695–1 702.(ZHANG Sherong，TAN Yaosheng，WANG Chao，et al. Study on failure mechanism and stability of multi-layer soft interlayer slope rock mass[J]. Rock and Soil Mechanics，2014，35(6)：1 695–1 702.(in Chinese))
[41] 蒋水华，李典庆，黎学优，等. 锦屏一级水电站左岸坝肩边坡施工期高效三维可靠度分析[J]. 岩石力学与工程学报，2015，34(2)：349–361.(JIANG Shuihua，LI Dianqing，LI Xueyou，et al. Three- dimensional reliability analysis of the left bank abutment slope during construction of Jinping I Hydropower Station[J]. Chinese Journal of Rock Mechanics and Engineering，2015，34(2)：349–361.(in Chinese)) |
|
|
|
2022, Vol. 41 
