Using Boundary Transform Method to Solve Geotechnical Problems with Mixed-Type Boundary Conditions

Abstract

In geotechnical engineering, mixed-type boundary problems cannot be solved directly by the integral transform method due to the diversity of boundary conditions. In view of this, the relationships between different boundaries are figured out from the perspectives of physical meaning and mathematical derivation. A novel boundary transform method is then proposed to transform a complex mixed-type boundary into a simple one, and the transform rules for different types of boundaries are graphically presented. Subsequently, the procedures to solve geotechnical problems with mixed-type boundaries are comprehensively elaborated. The application of the proposed boundary transform method for a two-dimensional steady flow problem with mixed-type boundaries is systemically considered. The results show that the boundary transform method can effectively deal with mixed-type boundary problems, rendering accurate solutions when compared with numerical analyses.