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常用的计算失效模式间近似相关系数存在一定的误差,采用Pearson相关系数准确地表征边坡失效模式间相关性。基于近似相关系数和Pearson相关系数,研究了土体参数空间变异性对边坡失效模式间相关性、代表性失效模式数目、边坡系统失效概率上、下限3方面的影响。简要介绍了选取边坡代表性滑动面的风险聚类法以及系统失效概率上、下限的Ditlevsen双模界限公式。以单层和两层边坡为例研究了近似相关系数的适用性。结果表明:常用的近似相关系数不能考虑土体参数空间变异性对边坡失效模式间相关性的影响,而Pearson相关系数能够有效地反映土体参数空间变异性对边坡失效模式间相关性的影响。当土体参数空间变异性较弱时,近似相关系数与Pearson相关系数间差别明显,基于近似相关系数会选取过多的代表性滑动面,不能有效地反映边坡代表性破坏模式。此外,基于近似相关系数计算的边坡系统失效概率上限会超过1,系统失效概率上、下限范围很宽,使得系统失效概率上、下限失去了意义。相比之下,基于Pearson相关系数计算的边坡系统失效概率上、下限范围较窄,能够有效地反映系统失效概率变化情况。
There is a certain error in the commonly used approximate correlation coefficient between failure modes. Pearson correlation coefficient is used to accurately characterize the correlation between failure modes. Based on the approximate correlation coefficient and the Pearson correlation coefficient, the influence of spatial variability of soil parameters on the correlation among failure modes of slopes, the number of representative failure modes, the upper and lower bounds of failure probability of slope system was studied. This paper briefly introduces the risk clustering method which selects the representative slip surface of slope and the Ditlevsen bimodulus formula of upper and lower limit of system failure probability. The applicability of the approximate correlation coefficient is studied by taking single and double slope as an example. The results show that the commonly used approximate correlation coefficient can not consider the influence of spatial variability of soil parameters on the correlation between failure modes of slope and Pearson correlation coefficient can effectively reflect the correlation between spatial variability of soil parameters and failure modes of slope influences. When the spatial variability of soil parameters is weak, the difference between the approximate correlation coefficient and the Pearson correlation coefficient is obvious. Based on the approximate correlation coefficient, too many representative sliding surfaces are selected and the representative failure modes of the slope can not be effectively reflected. In addition, the upper bound of the failure probability of slope system based on the approximate correlation coefficient will exceed 1, and the upper and lower limits of the system failure probability are very wide, making the upper and lower limits of the system failure have no meaning. In contrast, the slope failure probability calculated based on the Pearson correlation coefficient has a narrow range of lower limit, which can effectively reflect the change of system failure probability.