Presenting an algorithm for determining the distribution functions for orientation and location of discontinuities in space and its use in the rock slopes stability analysis

Determining the type and characteristics of the distribution functions for orientation and location of discontinuities in rock mechanics and engineering geology is important. Generally, the distribution functions of orientation parameters, including the dip and dip direction, are either hypothetically determined or determined independently and the spatial dependence of these parameters is ignored in determining their distribution functions. This creates uncertainty in determining the distribution functions for orientation and location of discontinuities. In this study, using statistical, probabilistic and reliability methods, an algorithm for determining the distribution functions is presented. Studies show the high ability of this algorithm to determine the orientation distribution functions and spatial location of discontinuities. Then distribution functions of orientation and location for discontinuities were determined in the western wall of Sarcheshmeh copper mine. Stability of the wall was investigated using the identified distribution functions. The results showed that the Log Logistic – 3 parameter Weibull combined distribution function is the best distribution function for describing orientation and location of discontinuities. Instability was investigated using the combined distribution function detected and under different dips of the final wall. The results showed that the probability of occurrence of instability in the western wall is maximum under the 45 ° of the final wall dip and final wall is completely stable under the 30 ° of wall dip. The optimal dip of the western wall of the Sarcheshmeh copper mine is 29 °.