Fast calculation method for soil dynamics under harmonic loads by 2.5D FEM and RBM combination technique

Abstract

A comprehensive analysis of soil dynamics is essential for accurately predicting the environmental impacts of subway operations. However, traditional finite element methods become computationally expensive when dealing with high-frequency disturbances and large-scale effects. To overcome the challenge, this study proposes a hybrid approach that integrates 2.5D FEM with the reduced basis method (RBM) to enhance computational efficiency. First, the solution of vibration transfer functions of the soil system is derived based on 2.5D FEM, and its accuracy is validated against two benchmark examples. Subsequently, RBM is introduced to establish reduced-order models in both the frequency and wavenumber domains. In this case study, the proposed method demonstrates higher accuracy than the linear interpolation method, significantly reducing truncation errors. Specifically, the statistical error of the linear interpolation method is found to be 3 to 35 times greater than that of the proposed approach. Moreover, the proposed method achieves an approximately 75 % reduction in computational effort by avoiding inefficient repeat calculations when new parameters are introduced in traditional FEM approaches. However, it is important to note that the effectiveness of the proposed method depends significantly on the number of pre-computed solutions used to construct the reduced basis space. Computational efficiency improves as the sampling interval decreases. Thus, the proposed method is recommended when there are a sufficient number of pre-computed solutions, in addition to the linear interpolation method. Moreover, its application in reproducing the high-frequency subway-induced ground vibrations shows that the proposed method has a good effect. In conclusion, this study provides a novel computational method with high accuracy and efficiency, which has a significant potential for application in more complex soil dynamic problems in transportation and earthquake engineering.