ANALYTICAL SOLUTIONS FOR STEADY AND TRANSIENT FLOW IN NONHOMOGENEOUS AND ANISOTROPIC ROCK JOINTS

Analytical solutions are presented for the distributions of head and velocity due to flow of water in a single rectangular rock joint with anisotropic and non-homogeneous hydraulic properties. The joint can be intersected by point sources or sinks representing boreholes or drains. The flow is laminar, steady or transient. The solutions are based on integral transforms such as Fourier and Laguerre transforms and provide continuous and differentiable expressions for the head and velocity components at each point in the joint domain and at any time t. Thus, there is no need to discretize the joint surface into elements as with finite element and finite difference methods. The solutions can handle any arbitrary variations of joint aperture and surface roughness. Preferential flow paths and channel flow can be predicted once the joint void space is characterized. Deviations from the cubic law due to joint variable aperture and surface roughness can also be studied in a non-empirical manner. Numerical examples are presented illustrating some applications of the proposed solutions.