Geosynthetic reinforcement is a lucrative solution for stabilizing the recurring failure of slopes. This paper presents an efficient probabilistic approach to analyze the internal stability of geosynthetic reinforced slopes (GRSs) resting on a soil deposit subjected to harmonic base shaking. Collocation based Stochastic Response Surface (SRS) method is used for the same. The deterministic analysis is performed employing a rigorous formulation of Horizontal Slice Method (HSM) in a modified pseudo-dynamic framework. The formulation satisfies the horizontal, vertical, and the moment equilibrium equations of each slice. The algorithm is made efficient using the non-linear constrained optimization. The effect of exciting frequency of soil on the stability of GRS is examined in detail. The accuracy of the proposed probabilistic formulation is also compared with the results of the FORM. Four input parameters are considered to be random in nature namely internal soil friction angle, unit weight, ultimate tensile strength of reinforcement, and shear wave velocity of reinforced soil (GRS). The Gaussian copula is used to correlate the input random variables. The results depict that the proposed formulation is effective and precise in predicting the probability of failure (P_f) of GRSs. The performance function is evaluated only 376 times in comparison to the direct Monte-Carlo Simulation where it is evaluated at least 10⁵ times, reducing the computation time from approximately 2 days to 25 min. To the best of author’s knowledge, the proposed method is original.

土工合成材料的加固是稳定斜坡反复破坏的有利可图的解决方案。本文提出了一种有效的概率方法来分析土基合成加固边坡（GRS）的内部稳定性，该边坡位于发生谐和基振动的土壤沉积物上。基于配置的随机响应面（SRS）方法也是如此。确定性分析是在修改的伪动态框架中使用严格的“水平切片法”（HSM）公式进行的。该公式满足每个切片的水平，垂直和弯矩平衡方程。使用非线性约束优化使该算法高效。详细研究了土壤激发频率对GRS稳定性的影响。提议的概率公式的准确性也与FORM的结果进行了比较。本质上，四个输入参数被认为是随机的，即内部土壤摩擦角，单位重量，增强材料的极限抗拉强度和增强土壤的剪切波速度（GRS）。高斯copula用于关联输入的随机变量。结果表明，所提出的公式在预测失效概率方面是有效且精确的（P _f）的GRS。与直接蒙特卡洛模拟相比，性能函数仅被评估376次，而直接蒙特卡洛模拟至少被评估10 ⁵次，从而将计算时间从大约2天减少到25分钟。据作者所知，所提出的方法是原始的。