A monte carlo simulation for discontinuity orientations using bivariate empirical distribution

There exist some probability distributions for describing rock discontinuity, e.g., Fisher distribution, Bingham distribution, and bivariate normal distribution. But in reality they are not suitable to represent the statistical characteristics of rock discontinuity orientation data in most cases. In such cases one should use the bivariate empirical distributions obtained for the discontinuity orientations in representing the statistical distributions of discontinuity orientations. The paper introduces the empirical bivariate distribution into the Monte Carlo simulation (MSC) of rock discontinuity orientations and develops a corresponding computer code, named as EMCSDO. EMCSDO is a freeware designed for researchers and practicing engineers, and can be easily mastered by them with little computer knowledge. Two examples with satisfactory results are presented to show the validity of the code. The second example also show if a theoretical distribution can be found to fit discontinuity orientations well, we should prefer to use the theoretical distribution to simulate the orientations based on Monte Carlo technique.