Analytical Method for Calculating the Volume of Rock Blocks Using Available Mapping Data Field

The calculation of the volumes of rock blocks delimited by discontinuity planes in rock masses is essential for the design of excavations and supports, applied to various engineering activities, like mining and tunneling. Furthermore, the block volumes control the rock mass behavior. If very small blocks are predominant, the rock mass tends to act as a continuum media and exhibit failure through the rock material. In case of prevalence of large blocks the rock mass acts as a discrete block set and failure through discontinuities can occur. There are many analytical methods in technical literature to calculate the volume of rock blocks but most of them are not realistic in relation to data input. In some cases a detailed knowledge of block geometry is required; such condition is rarely available in a field survey. This paper presents an analytical solution for block volume calculation using an easily obtained data in the field. Tetrahedral, tabular or prismatic blocks can be considered. An extension of the solution for polyhedral blocks is also presented.