Analytical method for calculating the volume of rock blocks using available mapping data field.

Abstract

The occurrence of potentially unstable rock blocks in rock masses is very common. These blocks are delimited by discontinuity planes and can have various shapes, depending on the orientation of the discontinuities which form them. Discontinuity planes are breakouts of the rock material continuity created due to geological events which took place during the rock mass formation throughout geologic periods. These planes normally present a geometrical pattern. They form families of discontinuity which are defined as plane sets that have similar orientation in tridimensional space. The behavior of rock masses is extremely dependent on block size. As discussed by Hoek (1983) rock masses may behave as a pseudo-continuum in case of block size is very small in relation to the excavation size. Palmström (1995) also discussed the influence of block size in geomechanical behavior of rock masses. Estimates of block volume were used in the geomechanical index RMi, proposed by Palmströn, as a measure of the degree of jointing of a rock mass. Palmströn proposed empirical methods for volume calculation based on geomechanical parameters, such as the volumetric count jointing index and the RQD. This author explained that block volume is also an expression of the overall geometry of the rock mass, as it is a three-dimensional measure. The calculation of the volume of rock blocks is also essential for stability analysis and support design. Equilibrium limit methods have been used to analyze stability of rigid blocks in excavations in rock masses. Body forces must be considered in this analysis and the most important is the block weight which is primarily the function of the block dimension. Calculation of rock block volume is not trivial because the block geometry is three dimensional in most of the situations. Although blocks are considered regular solids they might assume many different shapes, depending on the number of discontinuity planes which form them. Tetrahedral and complex polyhedral blocks are examples of these shapes. In this paper, an analytical solution to calculate the volume of rock blocks is presented. It was developed for tabular, prismatic and tetrahedral blocks and further extended to apply in polyhedral blocks. In addition, statistical distributions for rock block volumes are also presented. They can provide a model of rock mass structure (pseudo-continuum or an array of discrete blocks) by the knowledge of typical block sizes.