抗剪强度参数概率分布的最大熵估计及边坡可靠度分析

提出了基于最大熵原理的抗剪强度参数概率分布估计方法。首先简要介绍了最大熵原理估计抗剪强度参数概率分布的基本步骤。其次，基于模拟数据分别验证了最大熵原理估计抗剪强度参数概率分布和边坡失效概率的有效性，并比较了最大熵原理、选优识别和核密度估计方法的不确定性建模精度和稳健性。最后，以一组残积土抗剪强度参数试验数据并结合无限边坡稳定分析为例研究了最大熵原理在抗剪强度参数概率分布和边坡失效概率估计中的应用。结果表明：最大熵原理能够有效地估计抗剪强度参数的概率分布和边坡失效概率。与传统的选优识别和核密度估计相比，最大熵原理估计抗剪强度参数概率分布和边坡失效概率的精度和稳健性都更高。最大熵原理避免了核密度估计过分依赖有限样本数据的缺点，又克服了选优识别可能未将真实分布包括在备选概率分布集合中的缺陷。此外，基于有限数据估计的抗剪强度参数概率分布和边坡失效概率具有较大的离散性。

Probability distribution of shear strength parameters using maximum entropy principle for slope reliability analysis

This paper proposes a new method for modeling the probability distributions of shear strength parameters using maximum entropy principle (MEP). First, the procedure for constructing the probability density functions (PDFs) of shear strength parameters using MEP is presented. Then, Monte Carlo simulations are conducted to validate MEP for modeling the PDFs of shear strength parameters and probability of slope failure. Moreover, the accuracy and robustness of MEP, Akaike Information Criterion (AIC) and kernel density estimation (KDE) are compared. Finally, a dataset of shear strength parameters for residual soil is compiled, and an infinite slope is adopted to demonstrate the application of MEP to the estimation of the probability distributions of shear strength parameters and probability of slope failure. The results indicate that with limited shear strength data, MEP can effectively model the PDFs of shear strength parameters and probability of slope failure. In comparison with AIC and KDE, MEP produces more accurate and robust results for the PDFs of shear strength parameters and probability of slope failure. MEP not only avoids relying too much on the limited shear strength data in KDE, but also overcomes the possibility of excluding the true probability distribution in the set of candidate probability distributions in AIC. Furthermore, there are significant variations in the probability distributions of shear strength parameters and probability of slope failure estimated from limited data.