考虑地层变异特征一致性的围岩变形不确定性分析
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摘要
目前地层变异性分析大多基于地层重复性沉积和变异特征一致性假设,而未考虑地质构造和风化作用的影响,忽略了地层变异性特征一致性的检验。为此,提出地层变异特征一致性的检验和分区方法,采用岩土相局部状态转移概率矩阵的相关系数作为一致性的定量判据,基于耦合Markov链模型模拟地层分布,并通过MonteCarlo方法分析隧道围岩变形的不确定性。利用青岛轨道交通某斜井的地质钻孔数据,探讨了地层变异特征一致性对地层分布和变形模拟精度的影响,分析了所提方法的有效性。结果表明,当地质构造和风化作用导致地层变异特征不一致时,增加钻孔数量无法提高地层分布模拟精度,采用所提方法对地层变异特征一致性检验并分区后,可避免状态转移概率矩阵中局部地层分布特征缺失的问题,提高围岩变形不确定性分析的准确性。
Most analyses of geological heterogeneity are based on the assumption of repetitive deposition and stationary transition probabilities. However, the effects of tectonism and weathering are ignored, which leads to the absence of consistency verification of geological heterogeneity features(GHFs). A test method for the consistency of GHFs is herein proposed, as well as a partition method to detect stationary Markovian zones. The correlation coefficients between local transition probability matrices are adopted as quantitative criteria of consistency. The stratigraphic distribution is simulated by the coupled Markov chain model, and the deformation analysis of surrounding rock uncertainty is accomplished through Monte-Carlo simulations. Taking advantage of the borehole data in Tsingtao, the effect on stratigraphic distribution and uncertainty analyses induced by the consistency of GHFs is discussed, and the effectiveness of the proposed method is illustrated. The results indicate that the accuracy of uncertainty analyses cannot be improved with increased number of boreholes when there are conflicting GHFs. After the consistency verification of GHFs and the partition of stationary Markovian zones, the absence of local features can be avoided to improve the accuracy of uncertainty analyses of surrounding rock deformation.
Most analyses of geological heterogeneity are based on the assumption of repetitive deposition and stationary transition probabilities. However, the effects of tectonism and weathering are ignored, which leads to the absence of consistency verification of geological heterogeneity features(GHFs). A test method for the consistency of GHFs is herein proposed, as well as a partition method to detect stationary Markovian zones. The correlation coefficients between local transition probability matrices are adopted as quantitative criteria of consistency. The stratigraphic distribution is simulated by the coupled Markov chain model, and the deformation analysis of surrounding rock uncertainty is accomplished through Monte-Carlo simulations. Taking advantage of the borehole data in Tsingtao, the effect on stratigraphic distribution and uncertainty analyses induced by the consistency of GHFs is discussed, and the effectiveness of the proposed method is illustrated. The results indicate that the accuracy of uncertainty analyses cannot be improved with increased number of boreholes when there are conflicting GHFs. After the consistency verification of GHFs and the partition of stationary Markovian zones, the absence of local features can be avoided to improve the accuracy of uncertainty analyses of surrounding rock deformation.
引文
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[7]刘东海,周云晴,王帅,等.岩性Markov预测下的长隧洞TBM施工进度随机仿真分析[J].系统仿真学报,2009,21(2):558-562.LIU Dong-hai,ZHOU Yun-qing,WANG Shuai,et al.Stochastic simulation and risk analysis of water tunnel TBM construction scheduling based on geologic prediction using Markov process[J].Journal of System Simulation,2009,21(2):558-562.
[8]刘东海,黄培志,冯守中.地质条件不确定性下TBM管片结构失事概率计算[J].岩土力学,2010,31(4):1181-1186.LIU Dong-hai,HUANG Pei-zhi,FENG Shou-zhong.Breakage probability assessment of TBM construction tunnel lining segments considering geologic uncertainty[J].Rock and Soil Mechanics,2010,31(4):1181-1186.
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[11]祁小辉,李典庆,曹子君,等.考虑地层变异的边坡稳定不确定性分析[J].岩土力学,2017,38(5):1385-1396.QI Xiao-hui,LI Dian-qing,CAO Zi-jun,et al.Uncertainty analysis of slope stability considering geological uncertainty[J].Rock and Soil Mechanics,2017,38(5):1385-1396.
[12]祁小辉,李典庆,周创兵,等.基于钻孔资料的耦合马尔可夫链水平方向转移概率矩阵估计[J].应用基础与工程科学学报,2017,(5):967-984.QI Xiao-hui,LI Dian-qing,ZHOU Chuang-bing,et al.Estimation of horizontal transition probability matrix for coupled Markov chain based on borehole data[J].Journal of Basic Science and Engineering,2017,(5):967-984.
[13]QI X H,ZHOU W,LI D Q.Uncertainty analysis of slope stability considering geological heterogeneity[M]//Landslides and Engineered Slopes Experience,Theory and Practice.London:Taylor and Francis Group Press,2016:1685-1693.
[14]邓志平,李典庆,曹子君,等.考虑地层变异性和土体参数变异性的边坡可靠度分析[J].岩土工程学报,2017,39(6):986-995.DENG Zhi-ping,LI Dian-qing,CAO Zi-jun,et al.Slope reliability analysis considering geological uncertainty and spatial variability of soil parameters[J].Chinese Journal of Geotechnical Engineering,2017,39(6):986-995.
[15]DENG Z P,LI D Q,QI X H,et al.Reliability evaluation of slope considering geological uncertainty and inherent variability of soil parameters[J].Computers and Geotechnics,2017,(92):121-131.
[16]ELFEKI A M M,DEKKING F M.Reducing geological uncertainty by conditioning on boreholes:the coupled Markov chain approach[J].Hydrogeology Journal,2007,15(8):1439-1455.
[17]LEE S Y,CARLE S F,FOGG G E.Geologic heterogeneity and a comparison of two geostatistical models:sequential Gaussian and transition probabilitybased geostatistical simulation[J].Advances in Water Resources,2007,30(9):1914-1932.
[18]ZHANG L M,EKYALIMPA R,HAGUE S,et al.Updating geological conditions using bayes theorem and Markov chain[C]//Winter Simulation Conference.[S.l.]:IEEE Press,2015:3367-3378.
[19]WANG X,LI Z,WANG H,et al.Probabilistic analysis of shield-driven tunnel in multiple strata considering stratigraphic uncertainty[J].Structural Safety,2016,62:88-100.
[20]QI X H,ZHOU W H,YUEN K V.Detection of stationary Markovian zones in a geologically heterogeneous area[J].Journal of Risk and Uncertainty in Engineering Systems,Part A:Civil Engineering,2017,3(4):04017026.
[21]景毅,王世称,苑清扬.马尔柯夫过程在地质学中的应用[M].北京:地质出版社,1986:5-115.JING Yi,WANG Shi-cheng,YUAN Qing-yang.Application of Markov chain in geology[M].Beijing:Geology Press,1986:5-115.
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[23]ELFEKI A,DEKKING M.A Markov chain model for subsurface characterization:theory and applications[J].Mathematical Geology,2001,33(5):569-589.
[24]ELFEKI A.Prediction of contaminant plumes(shapes,spatial moments and macrodispersion)in aquifers with insufficient geological information[J].Journal of Hydrology,2006,44(6):841-856.
[25]ELFEKI A,DEKKING M.Modelling subsurface heterogeneity by coupled Markov chains:directional dependency,Walther’s law and entropy[J].Geotechnical&Geological Engineering,2005,23(6):721-756.
[26]刘振峰,郝天珧,方辉.用Markov链模型随机模拟储层岩相空间展布[J].石油学报,2005,26(5):57-60.LIU Zhen-feng,HAO Tian-yao,FANG Hui.Modeling of stochastic reservoir lithofacies with Markov chain model[J].Acta Petrolei Sinica,2005,26(5):57-60.
[27]YARUS J M,CHAMBERS R L.随机建模和地质统计学--原理、方法和实例研究[M].穆龙新,陈亮,译.北京:石油工业出版社,2000:52-61.YARUS J M,CHAMBERS R L.Stochastic modeling and geostatistics:principle,methods and case studies[M].Translated by MU Long-xin,CHEN Liang.Beijing:Petroleum Industry Press,2000:52-61.
[28]TONG H.Determination of the order of a Markov chain by Akaike’s information criterion[J].Journal of Applied Probability,1975,12(3):488-497.
[29]GATES P,TONG H.On Markov chain modeling to some weather data[J].Journal of Applied Meteorology,1976,15(11):1145-1151.
[30]高华喜,殷坤龙.降雨与滑坡灾害相关性分析及预警预报阀值之探讨[J].岩土力学,2007,28(5):1055-1060.GAO Hua-xi,YIN Kun-long.Discuss on the correlations between landslides and rainfall and threshold for landslide early-warning and prediction[J].Rock and Soil Mechanics,2007,28(5):1055-1060.
[31]孙长宁,曹净,宋志刚,等.基坑体系可靠度的条件概率计算方法[J].岩土力学,2014,35(4):1211-1216.SUN Chang-ning,CAO Jing,SONG Zhi-gang,et al.Calculation method of foundation pit system reliability based on conditional probability[J].Rock and Soil Mechanics,2014,35(4):1211-1216.
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