تجزیه و تحلیل حساسیت اعمال شده برای تثبیت شیب در هنگام شکست

This article discusses how sensitivity analysis is a sound assessment tool for selecting the most efficient stabilization method of slopes at failure. A discretized form of the variational approach is used not only for performing sensitivity analysis but to locate the critical slip surface, i.e., the sensitivity analysis is carried out in the same way as it is done in optimization problems. This method supplies a robust formulation and methodology for obtaining the sensitivities of the safety factor with respect to both the soil parameters and the slope profile, stating the slope stabilization design as a relatively simple minimization problem. Two well known examples, as the Selset landslide and the Sudbury Hill slip are used to illustrate the application of the method and to highlight both its capabilities and limitations.

Today, engineers are not completely satisfied with the solutions to given problems and they also require knowledge of how these solutions depend on data. Thus, for instance, in minimization problems, such as those associated with slope stability, it is not enough to know the optimal value of the objective function (the safety factor) and the solution (slip line) where the minimum is attained. In this sense, approaches as the “safety maps” introduced by Baker and Leshchinsky [1] provides a valuable information to determine how and how much specific changes in the parameters of the system modify both the optimal objective function value and the optimal solution. In the field of slope stability, sensitivity analysis is generally conducted by means of a series of calculations in which each significant parameter is varied systematically over its maximum credible range in order to determine its influence upon the safety factor [2]. If one is interested in characterizing the variation in safety when encounter minor modifications in the parameters, these incremental techniques define an approximation of the safety factor gradient. In this case, for discrete problems (i.e., slices) the sensitivity may be calculated in a simpler and compact way by using the techniques that have been developed in the area of non-linear optimization [3]. When dealing with continuous problems as those linked to the variational approach of slope stability analysis, the formulation put forth by Castillo et al. [4] can be used. In any event, regardless of how the sensitivity analysis is done, when instability occurs, a sensitivity analysis allows to know which qualitative or quantitative actions are more appropriate to stabilize the given slope. Therefore, the sensitivity analysis is a useful tool able to provide a sound assessment for the selection of the slope stabilization method. Our main objective in this article is to analyze the use of this sensitivity analysis tool.

A new sensitivity analysis of slope stability has been presented. The approach is especially appropriate to be used with computational modules in which the location of the critical slip surface is resolved as an optimization problem. In schemes of this type, which may be interpreted as a discretization of the classic variational approach to solving the slope stability problem, Castillo et al. [9] have reported that the sensitivity analysis can be carried out in the same way as is done with optimization techniques. Hence, Eqs. (6) and (10) provide a quick way for obtaining the sensitivities. The sensitivities obtained could be introduced into Eq. (7) to solve Eq. (9), and thus lead to the relatively simple formulation of slope stabilization design as a minimization problem. The main drawback to the method stems from the applicability of Eq. (7). Only in cases where the action to be undertaken does not entail a major change in the system is it reasonable to assume that the variation in the safety factor may be calculated by means of the linear approach defined by Eq. (7). At failure, when urgent actions must be adopted, it is often of interest to use procedures of this kind which will result in only a slight increase in F. However, when sensitivity with respect to a parameter is small, even a slight increase in the safety factor will mean a substantial variation in the parameter, so the formulation put forth here will not be applicable.