Advancements in rock block volume calculation by analytical method for geological engineering applications

The shape, the volume, and the distribution of the rock blocks represent important geomechanical factors of a rock mass behavior in engineering works. Several methods have been developed for estimating these parameters, including numerical models, as well as analytical and empirical methods. However, their determination in actual in-situ conditions can be quite challenging. The existing analytical methods show limitations in determining the in-situ rock blocks volume. Numerical models provide more reliable estimates of these parameters, but they are not accessible to all, and they require a good working knowledge. Increasing the accuracy of existing analytical methods, or developing more reliable and accessible methods, are more realistic approaches to obtain better estimates of rock block volumes. This paper presents a new method to obtain more accurate estimates of in-situ rock block volume. The method is developed for rock a mass consisting of three persistent joint sets, each set having constant spacing and orientation values. It is based on vector products to obtain exact block volumes, an improvement as compared to previous methods. The volumes of the rock blocks are calculated through the multiplication of the blocks' edge vector. The results of the developed equation are validated with the output of numerical simulations using 3DEC version 7.0 software, and the results indicate that the developed method makes it possible to determine in-situ rock block volume more reliably than the existing methods.

Automated summary

The shape, volume, and distribution of rock blocks are important factors in the behavior of rock masses in engineering works. Existing analytical methods have limitations in determining in-situ rock block volume. Numerical models provide more reliable estimates but require specialized knowledge. Improving existing analytical methods or developing more accessible methods are more realistic approaches for better estimates of rock block volumes.