土体参数空间变异性对边坡失效模式间相关性及系统可靠度的影响

Effect of spatial variability on correlation between slope failure modes and system reliability of slope stability

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。

The commonly used approximation for evaluating the correlation coefficients between failure modes has a certain degree of error. This paper uses Pearson correlation coefficient to characterize the correlation between different slope failure mechanisms. Based on the correlation coefficients calculated from two different methods, this paper studies the effect of soil spatial variability on correlation coefficients between failure modes, the number of failure modes of a slope and the bimodal bounds of system failure probability. A brief introduction to risk aggregation method aiming at selecting representative slip surfaces, and Ditlevsen＇s formulas for calculating bimodal bounds of system failure probability is presented. A single-layered and a two-layered slopes are studied to evaluate applicability of the approximation correlation coefficients. The results show that the commonly used approximation correlation coefficients cannot reflect the effect of soil spatial variability on correlation between failure modes, whereas the Pearson correlation coefficients can. When the spatial variability of soil properties is weak, there is large discrepancy between approximation correlation coefficients and Pearson correlation coefficients. Too many representative slip surfaces are selected and the representative failure modes cannot be reflected effectively based on approximate correlation coefficients. Furthermore, the upper-bound limit of system failure probability calculated by approximation correlation coefficients is probably greater than 1, and the bimodal bounds of system failure probability are too wide, all of these make system failure probability become meaningless. By contrast, the calculated bimodal bounds of system failure probability based on Pearson correlation coefficients are narrower, showing the changes of system failure probability effectively.