Poroelastic Center of Dilation Revisited

In both elasticity and poroelasticity, the nucleus of strain is usually used to refer to a singular solution such as the point force, the force dipole, the centers of rotation and dilation, etc. These fundamentals solutions constitute the building blocks for various problems of practical importance and are, therefore, relatively well understood. However, a comparison of the original elastic solution for the center of dilation with the classic Lamé solution reveals an unexpected dependence of the center of dilation solution on the Poisson’s ratio. This inconsistency is investigated by means of two alternative representations of the singularity and leads to the identification of a compressed zone inside the singularity. The poroelastic equivalent to this nucleus of strain is shown to be the superposition of the elastic one with drained material parameters and an instantaneous point fluid source associated with a finite volume of fluid that is expelled from the compressed region inside the singularity and is injected in the porous medium.