Reliability Analysis Of Progressive Failure Of Homogeneous Earth Slope

The reliability theory has been widely used in analysis of slope stability, and the research considering progressive failure mechanism develops gradually and becomes one of the important research subjects at present.Firstly, the uncertainty source of soil parameter is analyzed and quantified. At the same time, the statistical analysis of soil parameter is presented and the artificial error is eliminated to reserve natural inherent characteristics of soil. Based on the previous analysis, the expression of the coefficient of spatial variation for parameters is given out.Then, using statistics of soil parameters, the formulas of progressive failure probability for brittle and strain softening earth slopes are elicited considering the force between soil bars on the basis of the progressive failure model, and the influences of inherent variability, systematic uncertainty, correlation distance, correlation coefficient of the soil parameter are studied carefully. It is shown that the systematic uncertainty and the inherent variability have coordinative influences on the progressive failure probability, and the regularities are similar;the sensitivity of the inherent variability or systematic uncertainty of the cohesive strength c is much stronger than that of coefficient of friction μ to the progressive failure probability.It can also be shown that progressive failure probability of brittle earth slope may reach an ultimate value, which decreases with the increase of the combined mean values of c,μ. The larger are the combined mean values, the greater the inherent variability or systematic uncertainty. It cannot be found for the strain softening earth slope. Compared progressive failure probabilities of brittle and strain softening earth slope, it is found that the probability of strain softening earth slope increases quickly with the coefficient of variation when the combined mean value is less than certain limit value. In such cases the probability is much larger than that of brittle earth slope. Otherwise, it increases very slowly when the combined mean value is large than certain limit value, and it is far less than that of brittle earth slope.Afterwards, the formulations of probability and the variability coefficient of safety factor are derived from FOSM method with the consideration of spatial variability. The influences of all sorts of uncertainties on the coefficient of variability are also studiedcarefully. It is suggested that the double indexes of safety factor and probability index or failure probability should be used by calculating the coefficient of variability of safety factor in the analysis of slope stability.Finally, two engineering examples of different cases are calculated and analyzed. The conclusions arrived at in this paper may be helpful to earth slope stability analysis.