Numerical Study on Behavior of Groundwater Flow in Single Rough Fractures Under Mechanical Effect

Abstract

This paper numerically investigates the characteristics of groundwater flow in spatially correlated variable aperture fractures under the mechanical effect. Spatially correlated aperture distributions are generated using the geostatistical method (i.e., turning bands algorithm in this study). To represent a nonlinear relationship between the effective normal stress and the fracture aperture, a simple mechanical formula is combined with a local flow model. Numerical results indicate that the groundwater flow is significantly affected by the geometry of aperture distribution, varying with the applied effective normal stress as well as the spatial correlation length of aperture distribution. Moreover, using the flow results simulated in this study, two empirical formulae are proposed: (1) the first one (modified Louis formula) is to represent the relationship between the effective normal stress and the effective permeability of fracture and (2) the second one is to represent the relationship between relative roughness and effective permeability.