Research On Some Problems Of Extended Finite Element Method And Its Application In Rock Slope Engineering

In the past twenty years,extended finite element method(XFEM)had become a mature method and shown great advantage in solving crack and discontinuity problems in engineering.XFEM can model the crack propagation without considering the remeshing,it also can easily solve holes,gaps,weak discontinuity problems in composite material.Therefore,the research of XFEM is still an active area in the recent studies.However,many researches aim at extending the usage of XFEM in a certain field,they are lack of in-depth research on some complex crack problems and practical engineering problems.Based on the previous studies,this paper aims to improve the ability of XFEM in modelling the complex multi-crack propagation problem.Meanwhile,the application of the enhanced XFEM in rock slope engineering is discussed.The research mainly contains the following aspects.(1)The novel method to description the crack is proposed in the framework of level set method.Firstly,the crack function is discretized by the piecewise linear function and the sides of mesh can also constitute a line segment set.Next,the posit ional relationship between line segments can be used to determine the location of the crack surface element.Then,the location of the crack surface node can also be determined.Because the positional relationship between line segments can be easily determined by some local mesh information,the novel method can greatly facilitate the modeling of complex cracks.Meanwhile,the new scheme for crack propagation is introduced into XFEM,which can promote the description of the curve crack.(2)The novel direct method is proposed to calculate the stress intensity factor(SIF)in the framework of XFEM.By coupling the new mesh technique and the least squares algorithm,a novel method to obtain the SIFs is built based on the crack-tip stress in a particular area at crack tips.The method is independent of the mesh and it can obtain accurate solution for mode I crack,mode II crack and mixed mode crack.In some condition,the novel method can obtain the better solution than that obtained by the indirect method,such as the J-integral method.Therefore,the novel method can greatly enhance the application of direct method in engineering calculation.(3)The paper proposes a novel method to model the complex multi-crack problem.By coupling the phantom node method and the mesh cut method in XFEM,the enhanced XFEM can model the complex multi-crack problem.In fact,phantom node method and mesh cut method can increase the degree of freedom in the local mesh,the increased degrees of freedom can make it easy for the descrip tion of the complex multi-crack state,and the complex multi-crack problem can be solved.(4)The paper also handle the frictional contact problem in XFEM.Based on the characteristic of the shape function of triangle element,the constitutive law of frict ional contact is built on the node of crack surface element.The new method has introduced the bearing capability of the element into the model to reconstruct the mechanism of stress redistribution on the node.Then,the new method can overcome the locking phenomenon of displacement in solving the frictional contact problem.Therefore,the new frictional contact algorithm can improve the ability of the XFEM in the dealing with the complex multi-crack problem.(5)The application of the XFEM is discussed in the paper.By introducing the coalescence mode of cracks,state function and the strength reduction method,the rock slope with several echelon joints are modelled to analyze the stability of rock slopes.Firstly,the compression test of the specimen with two cracks and the problem of the stability of rock slope with a joint are employed to illustrate the ability of XFEM in modelling the propagation and coalescence of cracks.Then,two types of rock slopes with different arrangements of echelon joints are simulated to illustrate that the arrangement pattern for joint can greatly affect the stability of rock slope.