Numerical study of the hydromechanical behavior of two rough fracture surfaces in contact

Abstract

Flow in fractures is traditionally modeled by characterizing the aperture distribution with some deterministic function or set of stochastic parameters. Other models generate the aperture distribution by the closure of two stochastic surfaces. The objective of this research is to develop a model where the aperture distribution is determined during the closure of two random elastic surfaces with complete hydromechanical interaction. Because stress and strain conditions required to generate a given aperture distribution are calculated during closure, the model is used to couple the mechanical and hydraulic characteristics of the fracture. Stochastic realizations of clay fracture surfaces are generated by measuring one‐dimensional profiles of a fracture surface. Next, the spectral representation of the profile is related to the fractal dimension of the fracture. Using the fractal dimension determined from one‐dimensional clay profiles, an equivalent two‐dimensional fractal surface is generated. Conceptually, each surface consists of linear elastic rectangular asperities resting upon a linear elastic half‐space. During closure, asperities that come into contact deform and punch into the half space creating mechanical interaction between all the asperities on the grid. Once we determine the aperture distribution at an applied stress level, a hydraulic gradient is applied across the fracture and fluid flow is determined. Nodal pressures created by flow deform the aperture distribution coupling hydraulic to mechanical behavior. Stress versus relative closure results indicate that stress increases nonlinearly with relative closure. Fluid pressures in the aperture distribution exert a significant influence on the mechanical characteristics of a fracture. Fluid discharge through the fracture decreases exponentially with an increase in relative closure. Flow calculated in the rough walled aperture distribution deviates increasingly from the parallel plate model with the geometric mean aperture as the percent contact area increases. The deviation results from an increase in tortuosity and channelling of the flow field in the aperture distribution. We can use this model to develop stress and flow versus relative closure constitutive relationships for a single fracture as a function of fracture surface geometry.