Uncertainty analysis of the EPR models.

It is imperative to understand how foundations behave on earthen slopes to accurately predict their allowable carrying capacity in geotechnical engineering. A comprehensive finite element (FE) simulation with PLAXIS 2D was conducted to assess the effects of various parameters on the bearing capacity (BC) of single- and double-strip foundations placed near the earth’s slope crest. The specified parameters include foundation width (B) and depth (Df/B); setback distance between the slope edge and foundation (b/B); soil internal friction (ϕ) and cohesion (c); slope inclination (β); and spacing between foundations (S/B). In addition, the numerically simulated database was used to develop simple mathematical expressions for predicting the capacities in both cases using evolutionary polynomial regression (EPR). The results revealed that the bearing capacity of single- and double-strip foundations increased with an increase in all studied parameters except slope inclination. For single-strip foundations, the outcomes demonstrated that slope inclination has no impact on BC when it is located 6B from the slope edge. However, under interference conditions, the critical center-to-center spacing between foundations is 3–4B, beyond which they behave as individual foundations. Additionally, EPR provides a robust method of predicting the BC of single- and double-strip foundations within slope crests based on the strong correlation of various statistical criteria between simulated and predicted results from training, validation, and testing. Finally, according to sensitivity analysis, in both single and double-strip foundations resting on an earthen slope crest, b/B, B, and ϕ are the most important input parameters that impact the output results.在岩土工程领域，精准预测地基的容许承载力，必先明确地基在土坡上的工作性状。本研究采用PLAXIS 2D软件开展了全面的有限元（FE）模拟，以评估各类参数对设置于边坡坡顶附近的单条形与双条形基础承载力（BC）的影响。所考量的参数包括基础宽度（B）与基础埋深比（Df/B）、边坡边缘与基础间的退距（b/B）、土体黏聚力（c）与内摩擦角（ϕ）、边坡倾角（β），以及基础间距比（S/B）。 此外，本研究利用数值模拟生成的数据集，通过进化多项式回归（EPR）方法构建了两类基础承载力的简易预测数学表达式。研究结果表明：除边坡倾角外，单条形与双条形基础的承载力均随其余各研究参数的增大而提升。针对单条形基础，结果显示当其与坡边间距为6B时，边坡倾角对其承载力无影响。而在基础相互干扰的工况下，基础间的临界中心间距为3~4B，当间距超过该范围时，双条形基础的工作性状将与独立单条形基础一致。 EPR方法展现出可靠的预测性能：训练、验证与测试阶段的模拟结果与预测结果之间，各项统计准则均呈现极强的相关性，可实现边坡坡顶单、双条形基础承载力的精准预测。最后，通过敏感性分析可知，对于设置于土坡坡顶的单条形与双条形基础而言，b/B、B与ϕ是对输出结果影响最为显著的输入参数。