小样本岩土参数下考虑矩估计偏差的土质边坡可靠度分析  

Reliability analysis of soil slope considering moment estimation bias using small sample geotechnical parameters

作　　者：张文生[1,2] 罗强[1,2] 蒋良潍[1,2] 李昂[1,2] ZHANG Wen-sheng;LUO Qiang;JIANG Liang-wei;LI Ang(School of Civil Engineering,Southwest Jiaotong University,Chengdu,Siehuan 610031,China;MOE Key Laboratory of High-speed Railway Engineering,Southwest Jiaotong University,Chengdu,Sichuan 610031,China)

机构地区：[1]西南交通大学土木工程学院,四川成都610031 [2]西南交通大学高速铁路线路工程教育部重点实验室,四川成都610031

出　　处：《岩土力学》2019年第1期315-324,共10页Rock and Soil Mechanics

基　　金：国家基础研究发展规划项目(973计划)(No.2013CB036204)~~

摘　　要：以样本平均值和样本方差为表征的矩估计值在小样本岩土参数下具有较大不确定性,直接用于可靠度分析可能导致结果出现较大误差。根据抽样获得的同一小样本X可能来自不同总体W~*的事件发生概率关系,基于正态总体均值、方差与相应矩估计值的偏差分别服从t及χ~2分布的基本规律,依据条件概率原理构建了由W~*组成的岩土参数虚拟总体空间Ω_(POP)及对应发生概率空间Ω_(OCC)。以简单土坡为对象,采用MonteCarlo法获得了不同强度参数总体W~*下的失效概率空间Ω_(FAI),应用全概率公式建立了考虑样本矩估计偏差影响的边坡稳定可靠指标β_T计算方法,分析了多批次小样本抽样下β_T空间分布特征。研究表明:以小样本岩土参数矩估计偏差发生概率为权重的矩偏权值法能有效收窄β_T分布区间,减小参数估计误差传递至β_T空间的不确定性,且β_T空间平均值收敛于真值,表现出良好的有效性和无偏性;针对实际勘察工作中的单批次小样本取样特点,矩偏权值法能较好地降低数据在偏差偶然过大情况下造成的可靠性计算结果失真程度。The moment estimations, such as mean and variance of samples, are quite uncertain in the context of limited geotechnical parameters, which may lead to a large bias in reliability analysis. The same small sample X may come from different populations W*, and the biases between the population mean and variance and the corresponding moment satisfy the law of t and χ2 distribution under assumption of normal distribution. Based on conditional probability principle, virtual population space ΩPOP and corresponding occurrence probability space ΩOCC composed of W* are constructed. The Monte-Carlo simulation methods is used to obtain the failure probability space ΩFAI for a simple soil slope. Underlying the full probability formula, a momentary weighting method, denoted by MWM, is proposed to calculate reliability index βT. The numerical examples show that MWM could effectively narrow the βT range, and simultaneously reduce the uncertainty caused by parameter estimation error. The mean value of βT converges to the true value, showing good validity and unbiasedness. Aiming at the characteristics of single batch sampling in actual investigation work, MWM can reduce the distortion degree of reliability analysis in large occasional moment estimation bias cases.

关 键 词：小样本岩土参数 矩估计偏差 矩偏权值法 土质边坡 可靠度分析 

分 类 号：U213.13[交通运输工程—道路与铁道工程]