Numerical methods are very important in geotechnical and geological engineering. This study presents a reduced-order numerical model to approximate the displacement and stress field in geotechnical and geological engineering contexts by combining numerical methods, proper orthogonal decomposition (POD), and multi-output support vector machine (MSVM). Snapshots were generated using Latin hypercube sampling. POD was used to compute POD-based vectors and their coefficients. Training samples were constructed from the numerical model and POD coefficients input. The MSVM algorithm was adopted to present the relationship based on these training samples. A reduced-order model was developed by predicting the POD coefficients using MSVM, and the displacement and stress field was then predicted based on the POD vectors and predicted POD coefficients. The proposed method was verified and demonstrated for a circular tunnel. The results show the displacement and stress fields are in excellent agreement with the analytical solution and with the numerical solution, and the predicted deformations are consistent with rock mechanics theory. The proposed method predicts the deformation and mechanical behavior of geomaterials well and may be used to replace numerical models for back analysis, for optimal design, and for uncertainty analysis in geotechnical and geological engineering, all of which involve repeated computation.

数值方法在岩土工程和地质工程中非常重要。本研究通过结合数值方法，适当的正交分解（POD）和多输出支持向量机（MSVM），提出了一种简化的数值模型，用于近似岩土和地质工程环境中的位移和应力场。使用拉丁超立方体采样生成快照。POD用于计算基于POD的向量及其系数。根据数值模型和POD系数输入构建​​训练样本。在这些训练样本的基础上，采用了MSVM算法来表示这种关系。通过使用MSVM预测POD系数来开发降阶模型，然后基于POD向量和预测的POD系数预测位移和应力场。所提出的方法在圆形隧道中得到了验证和证明。结果表明，位移场和应力场与解析解和数值解都非常吻合，并且预测的变形与岩石力学理论是一致的。所提出的方法可以很好地预测土工材料的变形和力学行为，可用于代替数值模型进行反分析，优化设计以及岩土工程和地质工程中的不确定性分析，所有这些都需要重复计算。