Abstract

An innovative approach that combines isogeometric analysis (IGA), limit analysis, machine learning, and the multivariate adaptive regression splines (MARS) model is presented in this paper to investigate sinkhole stability of circular cavity. The upper bound limit analysis method using IGA and second-order cone programming (SOCP) is employed to analyze circular cavity stability. Based on Bézier extraction, the non-uniform rational B-spline (NURBS) is used to generate a set of NURBS surfaces that define the boundary of the soil domain. The proposed approach is validated through comparative analysis with previous studies, demonstrating its effectiveness in accurately predicting soil stability. A large dataset consisting of 5000 randomly generated runs is used to train the machine learning algorithm that is integrated with the MARS model. The results show high accuracy, with a small mean squared error of 10^–3, in predicting the undrained stability of circular cavities. The integration of IGA, limit analysis, machine learning, and the MARS model contributes significantly to advancing computational techniques for assessing soil stability. The proposed approach offers a comprehensive and precise tool for engineers and researchers, providing an accurate design formula for evaluating the undrained stability of circular cavities.

中文翻译：

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圆形空腔不排水天坑稳定性：基于等几何分析与机器学习相结合的综合方法

摘要

本文提出了一种结合等几何分析（IGA）、极限分析、机器学习和多元自适应回归样条（MARS）模型的创新方法来研究圆形空腔的沉孔稳定性。采用IGA和二阶锥规划（SOCP）的上限分析方法来分析圆形腔的稳定性。基于贝塞尔提取，使用非均匀有理 B 样条 (NURBS) 生成一组定义土壤域边界的 NURBS 曲面。通过与以往研究的比较分析验证了所提出的方法，证明了其在准确预测土壤稳定性方面的有效性。由 5000 次随机生成的运行组成的大型数据集用于训练与 MARS 模型集成的机器学习算法。结果显示，在预测圆形空腔的不排水稳定性方面具有很高的准确性，均方误差很小，为 10 ^{–3 。}IGA、极限分析、机器学习和 MARS 模型的集成极大地促进了评估土壤稳定性的计算技术的发展。所提出的方法为工程师和研究人员提供了全面而精确的工具，为评估圆形空腔的不排水稳定性提供了准确的设计公式。