Abstract
1 INTRODUCTIONIn recent years the principal method of analysis of earth and rock structures has been the finite element technique in which, once properties are assumed or determined for the material, the structure is analyzed as a continuum. The method has been widely used in the analyses of geotechnical problems as well as in a wide range of other engineering problems. However, in the study of fractured rock masses, a question arises with the use of the finite element method. It is apparent that the nature and orientation of the fracture systems should play a substantial part in the performance of a fractured geological structure during an earthquake. It is generally not easy to adopt the finite element method to represent a fractured, jointed, and essentially discontinuous material. An alternative approach is therefore proposed to study the behavior of fractured rock masses during an earthquake. In 1978, a computational technique was devised by Cundall and Strack(1978-1979) in order to study the behavior of an assemblage of disks. Cundall(1980) extended this technique to examine the behavior of jointed rock masses subjected to static forces, and called it the "distinct element method". Since their code operated by evaluating the forces, velocities, and displacements of the components of the mass, it was easily extendable to dynamic inputs for seismic studies. The modified program will be referred as UDEC II. It has since been used in the analysis of the seismic stability of a fractured rock mass. This report summarizes the distinct element method and describes its application to the seismic stability of a fractured ridge. 2 THE DISTINCT ELEMENT METHODThe distinct element method, which Cundall and Strack(1979) developed, is summarized in the following section.2.1 Block geometryFor reasons of simplicity, only rigid blocks have been used in dynamic analysis. Each block is a simply connected domain defined by its corners, which are rounded off by circles of variable radius but with a constant distance d as defined in the figures of Table 1. This arbitrary rounding technique is used to define the exact contact location, at which the contact force is to be applied. Such contacts may be of three different types: corner-to-corner, corner-to-edge, or edge-to-edge. The two first types of contact are defined geometrically only by one point and one direction, while the latter type, which is distributed along a larger surface and therefore cannot be concentrated at a single point, is described by a combination of two corner-to-edge contacts. Point and normal direction of a contact are defined in Table 1. Table 1. Definition of position and direction of contact (available in full paper)2.2 Force-displacement relation at contactThe relative velocity of two blocks at a contact point C, with n and s the components in the normal and tangential contact directions, is calculated from the rigid body movement of each block and from the linear and angular velocities at each block centroid. The corresponding relative displacement at a contact C during a time interval ¿t has components ¿n and ¿s: (mathematical equation) (available in full paper)