ABSTRACT: This Bureau of Mines study describes the development of a large-scale, three-dimensional, finite-element model of a deep-vein Coeur d'Alene District mine. The three-dimensional model was prepared from combined digitized mine maps and generated levels that may also be analyzed as independent two-dimensional models. A comparison of the stress changes and displacements was made following a simulated vein excavation in both the three-dimensional and two-dimensional models. A one-cut excavation was simulated with the two-dimensional model and a multiple-cut excavation was simulated with the three-dimensional model. The compared results from the two analyses are discussed in terms of the inherent differences between the models.


In the 100 years since discovery, the mines of northern Idaho's Coeur d'Alene Mining District have undergone continued development. Silver/ lead deposits are generally found in near-vertical, narrow veins in a host rock of hard quartzite that usually fails by brittle fracture. The method most often employed to mine the high-grade veins has been overhand cut-and-fill. However, with development to greater depths, and consequently into more highly stressed rock, rock bursting has become a very serious problem.

At the Lucky Friday Mine, located near the town of Mullan, Idaho, toward the eastern end of the district, numerical modeling methods were employed to aid in understanding rock bursts. Mining-induced stresses in the vicinity of an excavation were calculated to yield insight into the energy sources and mechanisms that combine to produce rock bursts. Prior to this study, models using the finite-element method have all been two-dimensional because available mainframe computers have been limited in size and capacity. The development of ever-faster and higher-capacity computers has made the analysis of large-scale, three-dimensional, finite-element models more practical. An important question that arises with the availability of both two- and three-dimensional models is when should one be used rather than the other?

The purpose of this study was to compare the results of a simulated single-cut excavation from a two-dimensional model with a simulated multiple-cut excavation from a three-dimensional model. The two models were identical in plan section through the center of the excavation to provide an accurate basis for comparing the results. The main difference between the simulated excavations involved the physical extent of the excavation. In the case of the two-dimensional model, the excavation was unlimited in the direction normal to the plane of the model, while in the three-dimensional model, the excavation was generally limited in the three coordinate directions.

Figure 1. Plot of two-dimensional, finite-element mesh of the 5100 level showing excavated and unexcavated vein and sericitic quartzite. (available in full paper)

The question then became: When will analysis of an excavation enlarged by multiple cuts in a three-dimensional model produce stresses and displacements that are nearly identical to those produced by a similar single-cut excavation in a two-dimensional model?


The two- and three-dimensional finite-element models were prepared by first constructing a two-dimensional mesh of the 5100 level and then combining levels above and below this level to form the three-dimensional mesh.

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