UNCONFINED FLOW THROUGH JOINTED ROCK1

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Abstract
The two‐dimensional, steady‐state, unconfined flow of a homogeneous fluid through jointed rock is studied for both laminar and turbulent conditions by use of a method which is based on previously developed theoretical and experimental flow relationships. However, only the independent unknowns are selected in order to reduce the complexity of the problem and render it more readily tractable. The intact rock is assumed to be impermeable, and two intersecting systems of plane, parallel joints are used in the mathematical model, taking into account the surface roughness of the joints. The mathematical solution of the resulting nonlinear (due to turbulent flow in some joints) system of equations is obtained by use of a rapidly converging iterative procedure, wherein each iteration takes special advantage of the banded nature of the associated matrix. For the particular case where a free surface exists, the general flow equations are not satisfied, because some of the joints in the vicinity of the free surface do not flow full; therefore, new equations must be established to handle this condition. Once the development of the mathematical model is accomplished, several cases involving different geometric characteristics (width, orientation, and roughness of joints) are solved for a rectangular domain, and graphs are given to illustrate the influence of the various parameters on the manifested flow behavior.

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