In this paper the dynamic interaction between an embedded object and surrounding media (elastic rocks without joints) with an unilateral frictional contact interface is studied. The Coulomb friction law is supposed. The incident wave is assumed strong enough so that local slip or separation may take place along the interface. Therefore, the present problem is indeed a nonlinear boundary value problem. The mixed boundary conditions involve unknown intervals (the slip, separation and stick zones). A boundary element scheme together with an iterative technique is developed to solve this problem. Slip/stick/separation zones are determined. The numerical results of the interface traction and relative slip velocity are presented. The method is proved to be effective.


With the increasing use of underground structures such as nuclear power stations or oil reservoirs, it becomes more and more important to know the dynamic behaviors of the embedded structures as well as their influences on the surrounding medium from earthquake resistant point of view. In most previous studies concerning this problem, the interface between the structures and their surrounding media (soils or rocks) are assumed to be perfectly bonded, i.e, the displacements and stresses are continuous across the interface. However, this is not always true in practical cases. Partial or total debonding and other kinds of imperfections often occur along the interfaces. The dynamic analysis for these cases is particular important. In this paper, we assume the interface to be frictionally contact and examine the dynamic interaction between an embedded structure (which is treated as an elastic inclusion) and its surrounding media (which is modeled as elastic rocks without joints). The time domain boundary element method (BEM) will be used. We believe the BEM is probably the best suited for solving the present problem since the variables of interest of both the problem and the solution procedure are on the boundaries. In addition, the present problem deals with wave propagation in an infinite medium and the BEM is a good way of modeling this kind of situation. For the development and application of dynamic BEM, we refer to the review articles by Bescos (1987,1997). Here we particularly notice some works dealing with the dynamic contact problems (Abascal, 1995 and Antes and Steinfeld, 1991).


Consider the problem shown in µ Fig. I. The system µ, is divided into the rock region µ, and inclusion region µ.

BEM formulation in the rocks region

The governing equations of dynamic equilibrium for an elastic, isotropic, homogeneous body having a small amplitude displacement field can be written, with the use of a constitutive relation. The general BEM formulation in elasto dynamic problems can be found in many published papers and books (e.g. Manolis and Beskos (1988) and Dominguez (1993)).


Since the boundaries between slip, stick and separation zones are unknown and vary with time, they should be determined by an iterative method. For the present problem, iteration is carried out in each time step.

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