A Simulation of the Closure of a Small-scale Hydraulic Fracture in a Granite

Abstract

A simulation model for the closure of a mated fracture under nomal stress was developed by modifying the theory of Brown and Scholz. The initial aperture, instead of the height of composite topography, was used as a variable, and then the dependence of the radius at.a three-dimensional local minimum of aperture of the minimum value was considered. Furthermore, each term in a basic formu-la was evaluated independently. A chi-square distribution was fitted to the probability density function of the initial aperture determined experimentally for hydraulic fractures created in Inada granite in the laboratory. The relationships among normal stress, crack closure, and true contact area were simulated and compared to the experimental results. The simulation code reproduced the normal stress-crack closure diagrams obtained in the experi-ment above the stress levels of 0.07MPa except for the case where there were initially many secondary cracks open behind the main fracture surfaces. The true contact area was estimated to be less than 0.2010 of the nominal one even when the normal stress was 40MPa. The mechanical initial aperture esti-mated by the simulation was about double the hydraulic initial aperture determined in the experiments even if the mean value of the aperture minima was taken as the mechanical initial aperture.