Displacement measurements made over a period of several years with an array of three-point bore hole extensometers in the immediate and remote hanging wall zones of the Homestake Mine study site when compared with two and three dimensional finite element model displacements result in a three dimensional elastic properties scale factor that is only 80 percent of the two dimensional result. Thus, if circumstances do not justify the use of a two dimensional model for forward design analysis, then a three dimensional analysis cannot be avoided.
The validation and calibration of finite element models for design analysis are fundamental problems in rock mechanics. Although some progress is being made, no generally accepted theory yet exists that allows one to determine field scale rock mass properties from laboratory scale test data. Consequently, the identification of rock mass properties is usually done through comparisons of field measurements with estimates obtained from numerical models. Back-analysis of displacement data is, perhaps, the most common practical identification procedure in use. Young's modulus largely determines displacements within the elastic range, so that most back-analyses are used to determine rock mass elastic moduli. Within the elastic range, regression analysis of calculated on measured displacements is a simple but rigorous identification procedure (Cividini, et al, 1981). A high degree of linearity indicated by a high correlation coefficient validates the essential correctness of the model. The slope of the regression line is the scale factor for the elastic moduli (Pariseau, et al, 1985). The reason that scale factors are needed, of course, arises from the presence of discontinuities in the rock mass that are absent in laboratory test specimens. An important question in this regard concerns the differences in rock properties scale factors determined by back analysis of the same field data using two and three dimensional models. The question concerning the role of model dimensionality is not only theoretically interesting, but it is of considerable practical importance because of the much greater cost associated with any decision to require three dimensional design analyses. Reviews (Gioda, 1985; Gioda and Sakurai, 1987) of the identification problem and associated theory do not address this question. The approach to the problem in the present study is computationally oriented and consists of an extended series of two and three dimensional finite element analyses. Emphasis is on the analysis of displacements that were measured during a rock mechanics investigation in a deep, underground gold mine. This paper summarizes the results obtained to date.
The Homestake Mining Company, the U.S. Bureau of Mines and the University of Utah initiated a cooperative rock mechanics study at the Homestake Mine in the Autumn of 1983. The mine is located in the state of South Dakota as shown in Figure 1. Three adjacent panels between the 6950 and 7100 Levels (feet below surface, about 2100 meters) were selected for the study and subsequently instrumented with three point bore hole extensometers and vibrating wire stress gages as shown in Figure 2.
