A Finite Element Approach For Contact Problems And Its Application In Geotechnical Engineering

One of distinct characters of geotechnical problems is that there exiSt variousinterfaces such as interface between the StrUctUre and geotechncal medi8, the jointsin rock maSs, sliding face in soi1 and so on, which will effect the mecbocalbehaviors of the geotecndcal media and the StructUres significanly So far thoughthe finite element method has been wildly used in geotecbocal field, it still remainsan inthectable problem to simulate these inteffoces idealIy in the numerical analysis.The author deems that it is a PraCtical way to tr6at these uncontinuous PrOblems ascontact problem in solid mecbocs tmiformly. The main intension of this paPer is todeveloP a finite element aPProach for contact problem and aPPly it to geotecbocalproblems.Presently, as a widely used technique in finite element analysis for geOtechnical, problems, the contact interfaces usually are taken as the joint element, Which wasintroduced by Goodman eary in l968. Othendse, the discreet element method isalso a rather popplar method to deal with uncontinuous media, eSPeCially theso-called discreet medias that consists of rock blocks, granlars and so on.Nevertheless, in these aPproaches the contact intethee are charactered sboly edstiffeess K. and K.' which is not PerfeCt and rigorous in thc vitw of solidmechanics and rather rough for the description of the behavior of the iDtfores. Incollbet, taken as a contact Problem, the principal chatrs of the iDtCthees can bereflected: (l) the cbntact inifore is of shear strength Which imPlies tha a genericpair of contact points on the inidse will displace coincidentally if the tangentialfbrce at this POint has not reahed the 1imit resistance, else, relative s1ide betwee the\ points will occur along the tangental direction. (2) No matter the relative slideoccurs or not, the contact bodies cannot invade each Other in any wise.M there are considerable number of research concendng finie elemenmethod on contat problem and lot of techniques such as iteraion methd,mathematics propoming, Penalty method, Langrange multiplier and so on haVbeen developed, it is not easy to popularize the presemed methods tO engineering.' field due to their complicate techniques. ms promPts the author to develop anWash that is simpler in teChniques and can be @plied to geotecIlllital PrOblemsivwith less difficulty. Obviously, the critical step is the construction of the relevant FEM formulae.The contact problem FEM formulae in this paper are constructed by means of principle of virtual work instead of variational principle which has been wildly used for classical problems, for it is difficult to found the corresponding function expression for contact problems. To achieve the object, firstly, the theory of virtual work principles for deformable body is established. Then, by means of the principle, the expressions for classical problems and contact problems are constructed, which are the basis of the following FEM. Sequentially, the FEM formulae for contact problem can be obtained with no difficulty. Also, the procedure to implement the elasto-plastic contact problems is presented in details. Moreover, a special contact problems implying herein the contact between deformable body and rigid body such as rigid foundation and base, rigid retaining wall and backfill is studied.Five typical examples concerning pressure distribution under shallow foundation, earth pressure of retaining wall, behavior of a axially loaded bored pile, a metro tunnel constructed with shield machine, and a landslide with tunnels in it are solved successfully, which verifies the validity of the method developed in this paper. At the end, some unsolved problems in the presented method are discussed briefly.In conclusion, taken . as contact problems, the mechanical properties of contact interface can be reflected more perfectly. Moreover, because the method is based on a more rigorous mechanical theory, a much more satisfactory result would be obtained. Otherwise, th...