Application Of The Improved Element-free Galerkin Method In Fracture Analyses Of Rock Mass

As a type of geomaterials naturally formed, rock mass is usually composed of many natural joints and cracks or other types of intact discontinuities due to long-term deformation and damage. When loaded, cracks will be initiated and expand in the rock mass and the then mechanical properties of rock mass will change. The actual defom}ation and failure process of geo-materials and geo-struchues is a complex progressive evolution involving initially elastic deformation, crack propagation, large-scale displacement and even movement of a discrete system. The study on the crack expansion is very important for the evaluation of damage and stability of rock masses.In order to simulate the real failure process of rock mass,for the local problems at the tip of the discontinuity,the extended numerical EFG method is presented based on the partition of unity method.The local trial functions at the tip of the discontinuity are enriched with the analysis solution at the tip.So the method in the paper can solved the problems of the fractured rockmass and the localization with continuity and discontinuity.At the same time,the method can enhance the precision of the numerical result to discontinuous and its tip. With this method crack expansion of rock mass is analyzed.This paper presents an improved moving least-squares(IMLS).The IMLS approximation has greater computational efficiency and precision than the existing moving least-squares approximation,and does not lead to an ill- conditioned system of equations.By combining the element-free Galerkin method and the IMLS approximation ,an improved element-free Galerkin method is derived. The examples reveal the method has the advantages of excellent convergence rate,high accuracy and efficiency.It is very promising in engineering application.One of the major difficulties in the implementation of element-free Galerkin method is the noninterpolatory character of the approximation.As a consequence,the imposition of boundary conditions is quite awkwat.So a coupled improved element-free Galerkin-finite element method is suggested.With the coupled suggested before crack promblem and the crack propagation are calculated.