伪蒙特卡罗法及其在边坡可靠度分析中的应用

在确定具有最小可靠度指标的滑动面（即临界可靠度滑动面）时，由于常规的蒙特卡罗法抽样耗时巨大，临界可靠度滑动面的获得较为耗时。对于均质边坡，利用简化Bishop法构建了可靠度分析的功能函数，设计了6种随机变量的标准差组合，假定了随机变量的4种抽样范围，利用抽样次数较小的蒙特卡罗法即伪蒙特卡罗法对随机生成的132组可行滑动面进行了伪可靠度指标的计算并与蒙特卡罗法计算得到的可靠度指标进行了比较分析，研究发现：只有一个随机变量的前提下，滑动面的伪可靠度指标与蒙特卡罗法计算的可靠度指标呈完全线性关系，在其它条件相同的情况下，伪蒙特卡罗法抽样范围越大，伪可靠度指标与蒙特卡罗法计算的可靠度指标之间的拟合直线斜率越小，反之亦然；伪蒙特卡罗法抽样次数越大，伪可靠度指标与蒙特卡罗法计算的可靠度指标之间的拟合直线斜率越大，反之亦然。对均质边坡，可应用伪蒙特卡罗法快速计算其临界可靠度指标。

Analysis on the Quasi Monte-Carlo Method and its Application in the Slope Reliability

The critical reliability slip surface with minimum value of reliability index is difficult to be obtained by the Monte-Carlo method. The simplified Bishop method was adopted to calculate the factor of safety for given circular slip surface thereby defining the performance function in reliability analysis. Six variance values of random variables were designed and four sample ranges were assumed. A quasi-Monte Carlo method was defined with fow samples. One hundred and thirty-two potential slip surfaces were randomly generated. The reliability indexes regarding those slip surfaces were calculated by Monte-Carlo method and quasi-Monte Carlo method, respectively. The comparative results show that in the case of one random variable, the reliability index from Monte Carlo method is found to be linear with that from quasi-Monte Carlo method. In the similar conditions, the wider the sample range, the smaller the tangent value of line, and Vice versa. In addition, the bigger the sample number, the bigger the tangent value of line. The Quasi-Monte Carlo method is approved to be practicable for the determination of critical reliability slip surface for homogeneous slope.