基于强度折减采样与高斯过程回归的空间变异土坡自适应可靠度分析

Adaptive reliability analysis of spatially variable soil slopes using strength reduction sampling and Gaussian process regression

土体参数空间变异性对土坡稳定性的影响已受到岩土工程界的广泛关注,繁冗的计算量是空间变异土坡可靠度分析面临的瓶颈问题。基于强度折减采样(SRS)和高斯过程回归(GPR)模型,提出一种适用于高维空间的空间变异土坡自适应可靠度分析方法(SRS-GPR)。首先采用Karhunen-Loève展开法将空间变异土体强度参数离散为高维随机变量,随后根据SRS生成土坡临界样本点,接着通过GPR构建土体参数随机场与边坡安全系数之间的高维非线性函数关系,并基于主动学习策略自动搜寻最优训练样本点,迭代更新GPR模型。在此基础上,结合GPR模型和蒙特卡洛模拟进行边坡可靠度分析。最后,通过两个典型算例验证所提方法的准确性、高效性、鲁棒性和适用性。结果表明:所提方法可有效识别靠近极限状态面附近的最优样本点,使得迭代更新的GPR模型在该区域的预测精度逐渐提高。此外,所提方法不受随机变量维度的影响,可直接在高维参数空间应用,且对边坡稳定性模型的调用次数较少,在计算效率方面具有显著优势。

Spatial variability of soil parameters has significant impact on slope stability.The critical problem for the slope reliability analysis considering the spatial variability is the dramatic computational demand.Based on the strength reduction sampling(SRS)and Gaussian process regression(GPR),an adaptive reliability analysis method(SRS-GPR)for soil slopes considering the spatial variability is proposed.Firstly,the spatially variable soil strength parameters are discretized into high-dimensional random variables by the Karhunen-Loève expansion method.Then the critical sample points are generated according to the SRS.Next,the nonlinear relationship between the random fields of soil parameters and the safety factor of slopes is established by the GPR.With the active learning strategy,the best training sample points can be automatically identified,so the GPR model can be sequentially updated.Subsequently,the trained GPR model and Monte Carlo simulation are adopted to perform slope reliability analysis.Finally,the accuracy,efficiency,robustness and applicability of the proposed method are testified by two examples.The results show that the proposed method can effectively identify the best training sample points near the limit state surface,and the prediction accuracy of the updated GPR model in this region is gradually improved.Moreover,this method can be directly applied in the original high-dimensional parameter space with marginal impact of dimensionality of random variables,and a small number of evaluations of the slope stability model are required,which indicates a significant advantage in terms of the computational efficiency.