DEVELOPMENT OF AN EMPIRICAL MODEL RELATING PERMEABILITY AND SPECIFIC STIFFNESS FOR ROUGH FRACTURES

The coupling between hydraulic and mechanical properties of porous and fractured geologic media are critical for many geophysical processes and practical applications. Thus, the prediction of linkage between these properties are broadly important. Here we present a predictive model that links fracture permeability and specific stiffness with empirical coefficients dependent on fracture roughness, correlation length of aperture field, and rock mechanical properties. The model was developed empirically from results of modeling the deformation and flow through synthetic fractures with aperture fields that follow a normal distribution. The fractures were subjected to increasing normal stress. Specific stiffness was directly quantified from these numerical experiments with resultant displacement. Moreover, intrinsic permeability was estimated through the modified Local Cubic Law that considers effects of local fracture roughness and tortuosity.

We found that fracture displacement increases non-linearly with applied normal stress, while specific stiffness is expectedly sub-proportional to normal stress. Most importantly, permeability decreases exponentially with increasing specific stiffness regardless of fracture morphology. Based on the calculated permeability and specific stiffness, we propose an empirical model that relates specific stiffness to permeability accounting for fracture roughness, correlation length, and moduli. The model can capture the transition from effective medium to percolation flow regimes with increasing specific stiffness.