CONDITIONAL PROBABILITY METHOD FOR SOIL SLOPE STABILITY WITH SMALL SAMPLE

As a significant source of uncertainty, the statistical uncertainty due to limited samples considerably affects the result of slope stability evaluation. In this paper, a conditional probability approach(CPA)was proposed to lower the effects of statistical uncertainty on slope stability evaluation without adding further samples. First, the bias between the mean (μ) of a Gaussian population and the averaged value (X) of a small sample ( X ) taken from the population obeys the t distribution. Based on this condition, given a set of survey sample data X , a series of potential mean values (μ_i^*) of the corresponding unknown population with random deviations from the X can be created(denoted by event B_i, i=1, 2, …). The occurrence probability of each case is quantified and denoted by P(B_i). Then, the stability analysis for each case can be performed. The result(e.g., failure probability P_fi) is seen as the conditional probability of event B_i(denoted by P(A|B_i)), where A stands for the event of slope failure. Finally, from the law of total probability, the sum of the product of P(B_i) and P(A|B_i) for all cases is treated as the slope failure probability(denoted by P(A)). To investigate the established method, a series of case studies were carried out. The result indicates that the CPA can efficiently reduce the discretion of the stability analysis result (i.e. P(A)), thereby lead to a more precise outcome than the conventional analysis method where the sample mean is directly utilized.