1 INTRODUCTION
Development of computer technology and numerical modeling techniques in the last decade have made feasible large-scale computations of geotechnical problems. General purpose finite element programs have been developed that provide a capability for static and dynamic analyses of rock masses with material inhomogeneity, complex non- linear behavior, and structural discontinuities. While detailed calculations incorporating these attributes of rock masses are theoretically possible, there are practical constraints that create a limit of resolution beneath which the rock must be considered as homogeneous. In other words, a representative element of some average dimension must be treated as "continuum" and be assigned homogeneous stress-strain relations (Fig. 1). The length of resolution, denoted here as k is dependent upon the size and requirements of the problems modeled and in practice may correspond to the size of the smallest region represented in a numerical idealization; such as the smallest element in a finite element model. For large scale analysis, this resolution length k may be one, two, or more orders of magnitude greater than the dimension of the rock samples tested in the laboratory. This is not a problem if the rock is genuinely continuous and isotropic. In practice, because the laboratory sample and the "representative" element contain discontinuities that may influence the material behavior differently at the two levels of resolution, the average stress-strain relation can differ substantially. Several empirical procedures for scaling the laboratory values of the elastic moduli and strength of the rock to in-situ values on the basis of quality indices, such as RQD, Q, or RHR have been proposed (e.g., Bieniawski 1979). However, these procedures are generally deficient because they fail to account for the resolution at which numerical modeling is performed. Accordingly, several investigators have developed semiempirical procedures in which the material properties of a given volume are related to the corresponding proper- ties of a laboratory sample via relationships involving sample dimensions as well as quality (e.g., Hardy and Hocking 1978). These have found most application in development of the properties of rock pillars, but are conceptually suited for numerical modeling, providing that the material properties of each zone in the model are adjusted in accordance with its dimensions. The alternatives to simple empirical procedures involve developing models that directly account for the presence of the fractures. Along those lines, equivalent anisotropic models and ubiquitous joint models have received much attention. As discussed in the following section, these approaches have their limitations. A better, but often impractical approach, is to explicitly model each fracture. Here we propose a more practical alternative; one that involves two levels of definition of the rock mass. The first, or global level corresponds to the continuum representation at the scale of resolution we designated k. The second, is a macroscopic level, at which the discontinuities and inhomogeneties of the rock can be treated.
FIGURE 1. EQUIVALENT CONTINUUM FOR LARGE SCALE MODELING(available in full paper)
2 BACKGROUND
Equivalent continuum models for fractured rock mass are based on the assumption that single or multiple set of parallel joints exist in the rock mass, and that the precise location of the joints is unimportant.
