Evolution of displacement and pore fluid pressure due to a point fluid source at the centre of a porous elastic sphere : Starfield Festschrift

An exact solution and an asymptotic solution for small values of time are derived for the displacement and pore fluid pressure in a porous elastic sphere undergoing dilation due to a point fluid source at the centre of the sphere. No pore fluid can escape from the surface of the sphere. The pore fluid pressure at points within the sphere first decreases for some time interval, reaches a minimum value and then steadily increases. The initial value of the time derivative of the pore fluid pressure is finite and independent of the distance from the source. The steady decrease in the pore fluid pressure lasts for a longer time and is greater in magnitude for points at a greater distance from the source and for more compressible elastic skeletons. The effect is due to stress redistribution, which takes place to maintain compatibility of strains. It is compared with the initial increase in pore fluid pressure in the consolidation of a porous elastic sphere from which fluid can drain freely at the surface. Applications of the results to geophysics are briefly discussed.