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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.

A utilização de gabaritos visuais de teores é uma ferramenta por vezes utilizada, principalmente em atividades de campo, para a avaliação prévia e estimativa de teores e concentração de fases visualmente distintas. Estes padrões geométricos de superfície podem ser simulados com métodos estatísticos, possibilitando a utilização eficaz de outras ferramentas, como a análise computacional de imagens. Neste trabalho propõe-se a utilização do método de Monte Carlo para a simulação destes padrões (gabaritos), usando-se previamente a modelagem matemática das fases mineralógicas/tipológicas imersas no maciço. Apenas alguns parâmetros das distribuições estatísticas associadas à distribuição espacial das fases constituintes são alterados, permitindo uma correlação entre valores desses parâmetros e o padrão dos gabaritos. Tal ferramenta serve, por exemplo, para estimação expedita de teor de blocos de lavra, a partir da análise visual das faces expostas da bancada, bem como para análise petrográfica ou metalográfica PALAVRAS-CHAVE: gabarito visual, estereotomia, método estocástico, números pseudoaleatórios. STEREOTOMIC EVALUATION OF CONTENT VIA MONTE CARLO METHOD ABSTRACTThe use of visual templates for content calculation is a useful tool, especially in field activities, prior to the evaluation and estimation the amount of useful materials and visually distinct phases. These geometric surface patterns can be simulated by statistical methods, enabling the effective use of other tools such as computational imaging. In this paper we propose the use of Monte Carlo method for simulation of these patterns (templates), using previously mathematical modeling of mineralogical/typological phases disseminated in a matrix. Only some parameters of statistical distributions linked to spatial distribution of the constituent phases are changed, allowing correlation between values of these parameters and the standards of surface pattern. Such a tool serves, for instance, to expeditiously estimation of ore contents in exploitable blocks, from visual analysis of the exposed bench faces, or to petrographic or metallographic analyses as well.

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