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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。
Based on the Bootstrap sampling technique, a method of slope reliability analysis under finite data is proposed. This paper briefly introduces the traditional method of slope reliability analysis. The statistical uncertainty of the probability distribution function of shear strength parameters was simulated by Bootstrap method. Taking the infinite slope as an example, the influence of shear strength distribution parameters and distribution type uncertainty on slope reliability is studied. The results show that the sample mean value, sample standard deviation and AIC value based on the limited data have great variability. This variability further leads to obvious statistical uncertainty of the probability distribution function of the shear strength parameter. When considering the statistical uncertainty of the probability distribution function of shear strength parameters, the slope reliability index should be a confidence interval with a certain confidence level instead of a fixed value in the traditional reliability analysis. The range of confidence interval of slope reliability index increases with the increase of safety factor. Meanwhile, the reliability index calculated by the distribution parameter and distribution type uncertainty has greater variability and wider range of confidence interval. The Bootstrap method provides an effective way to simulate the statistical uncertainty of the probability distribution function of shear strength parameters and evaluate the reliability of slope under the condition of limited data.