Structure deformation analysis of the deep excavation based on the local radial basis function collocation method

This study introduces a local radial basis function collocation method (LRBFCM) to analyzing structural deformation in deep excavation within a two dimensional geotechnical model. To mitigate the size effect caused by a large length-to-width ratio, a technique known as the 'direct method' is employed. This method effectively reduces the influence of the shape parameter, thereby improving the accuracy of the partial derivative calculations in LRBFCM. The combination of LRBFCM with the direct method is applied to the deep excavation problem, which consists of both the soil and support structures. The soil is modeled using the Drucker-Prager (D-P) elastic-plastic model, while an elastic model is employed for the support structure. Elastic-plastic discretization is performed using incremental theory. The proposed approach is validated through four different examples, comparing the results with numerical solutions obtained from traditional finite element methods (FEM). This study advocates the use of the direct method to optimize the distribution of local influence nodes, particularly in cases involving large length-to-width ratios. The combination of LRBFCM with incremental theory is shown to be effective for addressing elastic-plastic problems.