小样本岩土参数的Bootstrap估计及边坡稳定分析

 针对岩土参数小样本下t分布法区间估计较宽将导致工程设计偏于保守的问题，根据描述土体固有变异性的c，?总体开展小样本随机取样勘察模拟，运用Bootstrap法进行数据重构得到区间估计和点估计结果，对比与t分布法所得参数估计的差异。基于充足次数重复抽样构建的参数估计空间，分析与之映射的边坡稳定安全系数离散特征。研究表明：对应于同一置信水平，能充分利用小样本经验分布信息的Bootstrap法可有效收窄c，?均值置信区间，保证率下限值较传统t分布法结果更接近真值；虽然2种方法得到点估计结果的均值和方差相同，即对应的边坡稳定可靠指标相等，但采用Bootstrap法保证率下限值计算的边坡稳定安全系数均值相对较大，离散性更小，且这种改善效果随参数变异水平上升愈加明显；在保证相同可靠度条件下，Bootstrap法能更合理地对小样本统计不确定性导致的边坡安全风险进行补偿。

Bootstrap estimation for geotechnical parameters of small samples and slope stability analysis

The confidence interval of geotechnical parameters calculated by the t-distribution method is too wide under the small sample condition which leads to the conservative engineering design. The simulation on the random sampling survey for small samples was therefore conducted based on the population of c，φ which reflect the inherent variability of soil. The interval and point estimation results were obtained using the Bootstrap method to reconstruct the datum. The differences of the parameter estimation from the t-distribution method and Bootstrap method were compared. The discrete characteristics of safety factors of slope stability were analyzed based on the parameter estimation space built by the sufficient number of repeated sampling. For the same confidence level，the Bootstrap method sufficiently takes advantage of the empirical distribution information of small samples and effectively narrow the mean confidence interval of c，φ，and their lower limit values with guarantee rate are closer to the true values compared to t-distribution method. The two methods yield the same results of mean and variance of point estimation，namely their reliability indexes of slope stability are equal，but the means of safety factors of slope stability calculated by the lower limit value with guarantee rate using the Bootstrap method are relatively large，the discreteness of safety factors decrease. The improvement becomes more obvious with the increase of the variance level of parameters. On the condition of the same reliability，the Bootstrap method can reasonably compensate the safety risk of slope caused by the statistical uncertainty from small samples.