An investigation of integrating the finite element method (FEM) with grey system theory for geotechnical problems

Numerical simulation is very important to solve geotechnical problems. However, it is difficult to obtain required comprehensive and accurate information such as parameters, boundary conditions, and etc. In this paper, a grey distributed parameter model, which integrates the finite element method (FEM) with the grey system theory, was proposed to address the issue. The analysis of grey properties on rock and soil system was performed. The equilibrium equations, geometric equations, physics equations and related differential equations were obtained, each of the equations contains grey parameters and variables. And the discretization and solution methods of the FEM with the grey variables were discussed. An example of deep-buried circular mining tunnel was applied to test the proposed model. The calculation results were compared with those of the exact solution (analytical solution) and the classical FEM, respectively, through which the rationality of the proposed model was demonstrated. For the first time, grey variables and grey parameters are defined in geotechnical numerical simulation. The expressions of basic equations with grey variables are given respectively. A grey distributed parameter model which integrates the FEM with the grey system theory is proposed to solve geotechnical problems, and the optimal solution to the proposed model is determined through calculation and comparison of an application example. The proposed numerical model with grey variables not only has the advantage of grey system theory, but also greatly improves the adaptability and application effect of the model, which contributes to the prediction and evaluation problems in geological engineering, geotechnical engineering, water conservancy engineering and civil engineering with complex structures.