A procedure to estimate the accuracy of circular and elliptical discs for representing the natural discontinuity facet in the discrete fracture network models

Abstract This paper develops a procedure to estimate the accuracies of circular and elliptical disc models with respect to the natural discontinuity facet that represents various irregular shapes. The core of calculating the Accuracy Representation Index (ARI) was to obtain the area of the overlap between a fracture shape and an ellipse or a circle. The point radial method and Monte Carlo simulation were adopted to calculate the overlap area. Moreover, several rectangular fractures were generated, circular and elliptical disc models were respectively used to represent them and their representation accuracies were calculated. For the elliptical disc model, one important conclusion is that the ARI reaches the maximum when the elliptical disc has the same aspect ratio and rotation angle as the rectangular discontinuity. Furthermore, this method is applied to an actual slope rock mass of an open-pit mine, and the results showed that the simulation effect of the elliptical disc model was superior to that of the circular disc model, and the mean values of ARI for the elliptical and circular disc models were 0.898 and 0.739, respectively. Essentially, the optimum long-short axes ratio and the rotation angle of an elliptical disc model to represent the fracture can be obtained.