Stochastic fracture geometry modeling in 3-D including validations for a part of Arrowhead East Tunnel, California, USA

Eight-hundred and fifty nine fractures of a gneissic rock mass were mapped using 16 scanlines placed on steep rock exposures that were within 300 m of a tunnel alignment before the tunnel excavation. These data were analyzed using the software package FRACNTWK to find the number of fracture sets that exist in the rock mass, 3-D fracture frequency for each set and the probability distributions of orientation, trace length, fracture size in three dimensions (3-D) and spacing for each of the fracture sets. In obtaining these distributions corrections were applied for sampling biases associated with orientation, trace length, size and spacing. Developed stochastic 3-D fracture network for the rock mass was validated by comparing statistical properties of observed fracture traces on the scanlines with the predicted fracture traces on similar scanlines. The one-dimensional (1-D) fracture frequency of the rock mass in all directions in 3-D was calculated and is presented in terms of a stereographic plot. The 1-D fracture frequency along the tunnel alignment direction was predicted to be about 6.5 fractures/m before the tunnel excavation. This prediction was found to be in excellent agreement with the observed values obtained about 1 year later during the tunnel excavation. This was another validation conducted for the developed 3-D fracture network.