中文摘要：

实际工程中的岩土参数往往是小样本情况，利用经典概率分布（如正态分布、对数正态分布、贝塔分布、威布尔分布等）推断其最优概率类型时，存在样本分布区间不匹配、限定范围选择和单峰值概率分布函数无法反映参数随机波动性等三个未解决的基本问题。为此，选取了五种不同取值区间，利用10组小样本岩土参数的实测样本，以勒让德多项式和第二类切比雪夫多项式对岩土参数的概率分布函数进行推断，利用K-S检验法对所得的概率分布函数进行检验。通过区间取值匹配、拟合检验值和累积概率值的比较，提出了以3σ原则为基础，同时考虑偏度进行调整的积分区间确定标准。研究结果表明：以有限比较法原理确定最优概率分布的阶数，所得最优概率分布能够反映小样本数据的随机波动；而且正交多项式推断方法所得概率分布函数的检验值均小于传统分布的检验值，说明所得分布更加符合岩土参数的实际情况。

英文摘要：

Geotechnical parameters obtained in engineering practice are usually small samples, and the typical probability distributions such as normal distribution, logarithmic normal distribution, beta distribution and Weibull distribution were used to fit their optimal probability models in general. However, three basic problems have not been solved in the aforementioned inference, including the unmatched integral interval of sample distribution, the selection in limited range and that single peak probability distribution function cannot reflect the random fluctuation of parameters. To investigate these three problems, five different intervals were selected firstly, and Legendre polynomial and Chebyshev polynomial of the second class were used to infer the probability distribution function of 10 groups of geotechnical parameters. The K-S method was used to test the optimal property of the thus-obtained probability functions. Through the comparison of the interval value matching, fitting test values and cumulative probability values, a new integral interval standard that combines 3σ principle and the effect of skewness was put forward. The results also show that the order of the optimal probability distribution can be determined by the finite comparison method, and all the test values of orthogonal polynomial inference method are smaller than that of traditional method. The optimal probability distribution can reflect the random fluctuation of small sample data, which is more accordant with the actual conditions for geotechnical parameters.