Analytical Method for Calculating the Volume of Rock Blocks Using Available Mapping Data Field
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Analytical Method for Calculating the Volume of Rock Blocks Using Available Mapping Data Field Paulo Lopes1 · Milene Lana2
Received: 13 November 2015 / Accepted: 5 April 2016 © International Association for Mathematical Geosciences 2016
Abstract 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. Keywords Analytical methods · Block volume calculation · Discontinuity planes · Rock masses
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Paulo Lopes [email protected] Milene Lana [email protected]
1
Vale Institute of Technology (ITV), Ouro Preto, Brazil
2
Department of Mining Engineer (DEMIN), Federal University of Ouro Preto (UFOP), Ouro Preto, Brazil
123
Math Geosci
1 Introduction 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 e
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