Rock joints determine the size of the blocks and the rock fracture degree; at the same time joints influence the mechanic and hydraulic behaviour of the rock mass due to its geometrical and mechanical characteristics. Considering major discontinuities, presents in little amount (faults, dikes etc.) and minor discontinuities in great amount and a very variable space distribution (fissures, contacts and discontinuities), former ones (or joints) should be studied statistically and modelled its space distribution applying probabilistic methods, Kulatilake (1993). In this work is presented a probabilistic model of joint distribution applied to the Southeast Slope of Timbopeba iron mine, the fractured rock mass was adopted homogeneous and isotropic, with joints considered as plane circular disks, with parameters like orientation, diameter and location. With the probabilistic model for each joint parameter and the Monte Carlo method, it was simulated and built the fractured rock mass in three dimensions of the Timbopeba Southeast Slope. The contribution of this model is the probable representation of the rock mass structure and its inference in future excavations of slopes in the rock mass. This tool aids in the determination of critical situations where the joint concentration could be higher than a mean concentration value normally used.


The mechanical and hydraulic behaviour of a fractured rock is very influenced by the joint sets which have complex characterization due to, its geometric variability, limitation in the observation and quantification of their geometric parameters, when made in outcrops, rock cores, or tunnel surfaces. With help on a survey joint mapping in a sampling plane of the Southeast Slope, the probabilistic model proposed will have the function of predict the distribution of joints in a no accessible volume of rock. Later it was simulated a traverse cut of the slope where the most probable joints are observed for the geological type formation of the case study. This probabilistic model of joint distribution allows to enlarge the knowledge of the structure of the rock mass, for the case study, and in the future it will be possible, with help on limit equilibrium methods and numeric tools, to simulate the mechanical and hydraulic behaviour of the rock mass, aiding this way in projects in fractured rock.


In most of the geo-science areas, the studies focus the external part of the globe, basing their studies on observations of the surface and to a certain depth of the Earth crust. These observations have a lot of uncertainties as for the own heterogeneous formation of the Earth, in this sense the statistics is an important tool of research in this area. In a statistical study the random variables can be described approximately in terms of parameters, as the measures of central tendency and measures of dispersion (mean and standard deviation respectively). Also we can use the distribution of frequencies or histograms that represents the number of times that each value of the variable is repeated in the collected sample.

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