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In the present study, the authors describe a method for a coupled analysis of saturated porous media together with the consideration of convection using the mixture theory, in which density and the coefficient of kinematic viscosity are treated to be depending on temperature variation. The density of water also considered to be a function of pore pressure. Then we performed a series of analyses for some typical situations. The results emphasis the importance of consideration of convection in heat transport. We further checked the effect of temperature and pore pressure on the density of water. It should be noted that the classical Boussinesq approximation implies the density depends only on the temperature change. However, we found out that the results are not different from those of the classical Boussinesq approximation.
Recently, the use of underground space is being considered in many countries due to its benefits such as isolation, earthquake-resistance and constant temperature. When structures are constructed on the ground or underground, the underground construction cost is likely to be more expensive than that on surface. But, the maintenance cost for underground structures may be much cheaper than surface structures and the disturbance to environment due to construction would be less in case of underground structures than in surface structures. If any substance is stored or disposed in rock mass below the underground water level, the seepage through discontinuities may accelerate the transportation and diffusion of the substances. Therefore, it is necessary to predict accurately the seepage in rock mass for better assessment of the safe disposal of such substances. Cheng(1978) reported analyses and experiments on rock mass to investigate its coupled behavior. Following this work, Lapwood(1948), Combarnous et al.(1975), Wooding(1957) and Sato et al.(1985) pointed out that the water density was a function of temperature change when free convection occurred. The governing equation was based on the momentum conservation law of Navier-Stokes and they assumed that water only transports sub- stances. Bear et al. (1981) solved the problem of drawing up underground water from a well by using the momentum conservation law of ground skeleton. Ohnishi et al. (1986) performed a series of numerical analyses on both saturated and non- saturated ground. Lewis et al. (1987) described a procedure for deriving governing equation for saturated porous ground and he performed a series of numerical analyses. In this paper, the authors present mass, momentum and energy conservation laws for fluid and skeleton to describe the coupled seepage, stress and thermal behavior of rock mass using the mixture theory. These governing equations include constitutive laws such as Darcy's law, Hooke's law and Fourier's law. It is assumed that water density depends on temperature and pressure. Darcy's law includes kinematic viscosity which is influenced by temperature variation to represent free convection. Finally, we carried out numerical analyses for shallow and deep underground which includes a heat source to clarify its influence on surrounding. It is shown that Boussinesq's approximation can represent free convection.
In this paper, the authors present mass, momentum and energy conservation laws for fluid and skeleton to describe the coupled seepage, stress and thermal behavior of rock mass using the mixture theory. These governing equations include constitutive laws such as Darcy's law, Hooke's law and Fourier's law. It is assumed that water density depends on temperature and pressure. Darcy's law includes kinematic viscosity which is influenced by temperature variation to represent free convection. Finally, we carried out numerical analyses for shallow and deep underground which includes a heat source to clarify its influence on surrounding. It is shown that Boussinesq's approximation can represent free convection.
