The dilative intake of poroelastic inclusions an alternative to the Mandel-Cryer effect

This study examines the time-dependent poromechanics behavior of a fluid-saturated spherical inclusion embedded inside a fluid-saturated porous medium with different poroelastic properties. Both media comprise compressible constituents with distinctively defined poroelastic parameters. It is assumed that the inclusion is subjected to a fluid source at the center. The problem is formulated and solved using Biot theory of poromechanics. The contrasts in inclusion and the medium matrix stiffnesses and their respective hydraulic conductivities can be recognized as two competing factors, which affect the inclusion's rate of expansion during fluid injection. Findings show a certain type of behavior that the inclusion exhibits at the onset of fluid injection when having greater stiffness than the medium matrix, where the inclusion experiences some decrease in the pore pressure. Compared to what announced as the stress redistribution due the Mandel-Cryer effect in earlier researches on dilation of free spheres, this study shows that the associated phenomenon would be likewise attributed to the coupled nature of pressures and deformations in the theory of poroelasticity. However, it is a consequence of the inclusion-matrix stiffness contrast where a dilating free sphere can be regarded as a special case of this new problem. The asymptotic expansions of pressure terms verify the existence of such an effect. The results of this study would put forward very good insight in some engineering applications.