【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χ²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。更多还原

【Abstract】 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 Ω_POP and corresponding occurrence probability space Ω_OCC composed of W^* are constructed. The Monte-Carlo simulation methods is used to obtain the failure probability space Ω_FAI for a simple soil slope. Underlying the full probability formula, a momentary weighting method, denoted by MWM, is proposed to calculate reliability index β_T. The numerical examples show that MWM could effectively narrow the β_T range, and simultaneously reduce the uncertainty caused by parameter estimation error. The mean value of β_T 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.更多还原