Validation of Monte Carlo simulation for discontinuity locations in space

Baecher disk model is the most commonly accepted and widely used 3-D discontinuity network model (3DDNM). Monte Carlo simulation (MCS) for discontinuity locations is an important step for constructing Baecher disk model. Uniform distributions are usually used to simulate the locations, based on the assumption that trace spacings along a sampling line (SL) obey an exponential distribution. However, no researchers have validated whether the trace spacings simulated using aforementioned method obey the observed exponential distribution in the field. The aim of this study is to perform the validation using a hypothetical 3DDNM. This study includes a brief review of the MCS procedure for discontinuity locations, construction of a hypothetical 3DDNM, and the goodness-of-fit test procedure for simulated trace spacings along SL. Seven sampling line groups (SLG) are used, and each SLG contains twenty SL having a same direction vector. The possible points of intersection between each SL and all simulated discontinuities are obtained, the spacings of those points are calculated, Kolmogorov–Smirnov tests are used to test the goodness-of-fit to the spacings along different SL, and the theoretical values and simulated values of parameter λ of exponential distributions for different SL are also calculated. The results show that: (a) for all SL the trace spacings obey exponential distributions at the 5% significance level; (b) for all SLG the simulated values of λ fluctuate around their theoretical values, and the mean simulated values are very close to its theoretical values; (c) therefore, it is valid to use uniform distributions to simulate locations in space for those discontinuities, whose observed trace spacings follow exponential distributions. The validation procedure developed in this study are also applicable to 3DDNM constructed for field cases.