基于帕德逼近响应面法的边坡可靠度分析

边坡工程在进行稳定性分析评价时，通常其功能函数呈现出高度非线性隐式特性，从而导致无 法直接求解其可靠度。因此，提出将数值分析中的帕德有理逼近与可靠度分析中的响应面法相结合，利用帕 德逼近有理多项式拟合响应面函数。并采用拉丁超立方试验构造样本，将样本数据代入简化 Bishop 算法中 得到边坡功能函数值，求解得到代理模型待定系数，从而实现隐式功能函数显式化。且基于 Matlab 程序语 言编制 JC 法可靠度指标计算程序，建立了基于帕德逼近有理多项式的边坡稳定可靠度分析新方法（PRSM）。 通过两个经典的边坡算例，验证了所提方法的可行性、计算的高效性及准确性。最后，将所提方法应用于某 实际边坡工程中，计算结果表明，该边坡工程失稳的可能性较低，与实际监测结果吻合。

Slope Reliability Analysis Based on Pad Approximation Response Surface Method

In the stability analysis and evaluation of slope engineering, its function usually presents highly nonlinear implicit characteristics, which makes it impossible to directly solve its reliability. Therefore, a combination has been proposed of Pade rational approximation in numerical analysis with the response surface method in reliability analysis, thus fitting the response surface function by using the Pade approximation rational polynomial. By adopting the Latin hypercube test, samples can be constructed, with the sample data substituted into the simplified Bishop algorithm, thus obtaining the value of slope function function, followed by the solution of the undetermined coefficients of proxy model, so as to realize the explicit expression of implicit function function. Based on the Matlab programming language, the JC method reliability index calculation program is compiled, thus establishing a new slope stability reliability analysis method (PRSM) based on the Pade approximation rational polynomial as well. The feasibility, efficiency and accuracy of the proposed method can be verified by two classic slope calculation examples. Finally, with the proposed method applied to an actual slope project, the calculation results show that the slope project is characterized with a low instability possibility, which is consistent with the actual monitoring results.