Determining Probability Distribution Functions of Rock Joint Geometric Properties

The mechanisms of deformation and failure of the structures in and on the jointed rock masses are often governed by the characteristics of the geometrical properties of joints. Since the joint geometry properties have a range of values, it is helpful to understand the distribution of these values in order to predict how the extreme values may be compared with the values obtained from a small sample. This work studies three datasets of joint systems (1652 joint data) from nine outcrops of igneous, sedimentary, and metamorphic rocks in order to determine the probability distribution function of the rock joint geometry properties. Consequently, the goodness-of-fit (GOF) tests are applied to obtain the data. According to these GOF tests, the Lognormal is the best probability distribution function representing the joint spacing, aperture, and trace length. The Cauchy is the best probability distribution function for the joint dip angle. It is found that the Cauchy distribution function is the best probability distribution function to represent the joint dip direction of igneous rocks, and the Burr distribution function is the best probability distribution function to define the joint dip direction of the sedimentary and metamorphic rocks.