Thermally induced deformation and effects on groundwater flow in a discontinuous granite mass.

Abstract

Existing analytical treatments of groundwater flow have mostly been founded on classical hydrodynamics, that groundwater motion is derivable from a velocity potential. This conception is in contradiction with the principle of conservation of energy, although it conforms with the principle of the conservation of mass (Hubbert, 1940, p. 285; Scheidegger, 1960, pps. 74-75; Bear, 1972, pps. 122-123). This dissertation shows that both principles can be utilized, based on the fact that a force potential at a point is equal to the work required to transfer a unit mass from this point to another point. This potential is given the symbol φ - gh - gz + (p/ρ) and is incorporated in the force field E. This potential is related to the flow field (q) by the anisotropic hydraulic conductivity. This relation forms a solid formulation for the theory of the flow of fluids through fractured porous media. This relation is applied to develop two basic equations. One partial differential equation, representing flow in the fracture, depending on the actual geometry of the fracture and incorporating the anisotropic parameter of the hydraulic conductivity based on the thermal induced stress and the force potential. A second partial differential equation (storage equation) in two-dimensions for non-steady groundwater flow in confined and saturated aquifers. This storage equation incorporates time, hydraulic conductivity and the radial coordinates. It is solved analytically using the Bessel's functions Jₒ and Kₒ. The two equations represent two models. Both the potential and the thermal hydraulic conductivity constitute a coupling between the two models to render the models a thermohydromechanical model. This aspect is the essential theme underlying this work and is implemented through a matrix-fracture system based on the slow flow and the fast flow behavior. The evaluation of the transient parameters including the aperture becomes possible and falls in line with the physics of the problem. This comprehensive analytical model is found to satisfy the transient demands of the mathematical physics. The application of the phenomena observed in the field from different sources and from Stripa Granite, rendered the model realistic and appropriate to the fractured porous media.