中文摘要：

基于Bootstrap抽样技术提出了有限数据条件下边坡可靠度分析方法。简要介绍了传统的边坡可靠度分析方法。采用Bootstrap方法模拟了抗剪强度参数概率分布函数的统计不确定性。以无限边坡为例研究了抗剪强度分布参数和分布类型不确定性对边坡可靠度的影响规律。结果表明：基于有限数据估计的样本均值、样本标准差和AIC值具有较大的变异性,这种变异性进一步导致了抗剪强度参数概率分布函数存在明显的统计不确定性。在考虑抗剪强度参数概率分布函数的统计不确定性时,边坡可靠度指标应为具有一定置信度水平的置信区间,而不是传统可靠度分析中的固定值。边坡可靠度指标的置信区间变化范围随安全系数的增加而增大,同时考虑分布参数和分布类型不确定性计算的可靠度指标具有更大的变异性和更宽的置信区间变化范围。Bootstrap方法为有限数据条件下抗剪强度参数概率分布函数统计不确定性的模拟以及边坡可靠度的评估提供了一条有效的途径。

英文摘要：

A slope reliability analysis method based on limited shear-strength parameter data is proposed by adopting the Bootstrap sampling method. The traditional method of slope reliability analysis is first introduced briefly, and then the Bootstrap method is adopted to model the statistical uncertainty in probability distributions of shear strength parameters. An example of the infinite slope is given, the influence of the distribution parameters of shear strength and the uncertainty of distribution type on the reliability of the slope is studied. The results indicate that the sample mean, sample standard deviation and AIC values derived from the limited data of shear strength parameters show a large variability. This variability further aggravates the statistical uncertainty in the probability distributions of shear strength parameters. By considering the statistical uncertainty in the probability distributions of shear strength parameters, the reliability index of a slope is presented as a confidence interval instead of a single, fixed index derived from a classical reliability analysis. The range of this confidence interval increases with increasing slope safety factor. Meanwhile, when both the uncertainties in distribution parameters and distribution types of shear strength parameters are taken into account, the reliability index has a higher variability and thus a wider range of confidence interval. The Bootstrap method provides a practical access to modeling the uncertain probability distributions of shear strength parameters and to determining the associated slope reliability with limited data of shear strength parameters.