岩土力学数值模拟结果的概率评估方法研究

Probabilistic evaluation of numerical simulation of geomechanics

提出了一种用于评估多参数随机变异情况下岩土力学非线性数值模拟结果可靠性的多维高效直接积分型随机分析方法。它首先根据多维积分理论和可靠性分析的直接积分法确定多维随机输入参数的计值点;然后利用非线性数值模拟方法,比如有限元法或有限差分法等,完成所有计值点上的计算任务,据此就可以利用多维高效积分程序计算待评估响应量的前几阶矩(一般包括1～6阶矩);最后利用多种方法,包括曲线拟合法、加权余量法及最大熵法计算响应量的概率分布,并据此算出响应量的概率置信区间,用于定量评估响应量的可靠性。数值算例表明,此法具有精度和计算效率较高的优点。

A high efficient direct integration method is proposed for evaluating the variation effect of nonlinear numerical simulation results of geomechanics subject to multi-random parameters. In this method, taking the interested results as stochastic implicit response variables, firstly the integration points are determined by the multidimensional integration theory and direct integration reliability analysis method. Then the sample points are calculated by using the numerical simulation software; and then high order probability moments of response functions are evaluated by integration subroutine; at last the numerical probability density function of response variable then the confidence interval is obtained from several proposed method including curve fitting method, the weighted residual method and the maximum entropy distribution solver software developed by the authors. The numerical examples show that this method has higher accuracy and the computational efforts are reduced.