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

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##### Data

2016

##### Título da Revista

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##### Título de Volume

##### Editor

##### Resumo

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.

##### Descrição

##### Palavras-chave

Analytical methods, Block volume calculation, Rock masses, Discontinuity planes

##### Citação

LOPES, P. F. T.; LANA, M. S. Analytical method for calculating the volume of rock blocks using available mapping data field. Mathematical Geosciences, v. 49, p. 217-229, 2016. Disponível em: <https://link.springer.com/article/10.1007/s11004-016-9635-0>. Acesso em: 25 ago. 2017.