The capillary pressure vs. saturation curve for a fractured rock mass: fracture and matrix contributions

The fractal topography of fracture surfaces challenges the upscaling of laboratory test results to the field scale, therefore the study of rock masses often requires numerical experimentation. We generate digital fracture analogues and model invasion percolation to investigate the capillarity-saturation P(c)-S(w) fracture response to changes in boundary conditions. Results show that aperture is Gaussian-distributed and the coefficient of variation is scale-independent. The aperture contraction during normal stress increments causes higher capillary pressures and steeper P(c)-S(w) curves, while shear displacement results in invasion anisotropy. The three-parameter van Genutchen model adequately fits the fracture capillary response in all cases; the capillary entry value decreases with fracture size, yet the fracture P(c)-S(w) curve normalized by the entry value is size-independent. Finally, we combine the fracture and matrix response to infer the rock mass response. Fracture spacing, aperture statistics and matrix porosity determine the rock mass capillarity-saturation P(c)-S(w) curve. Fractures without gouge control the entry pressure whereas the matrix regulates the residual saturation at high capillary pressure P(c).