FUNDAMENTAL-SOLUTIONS OF BIOTS EQUATIONS OF DYNAMIC POROELASTICITY

Fundamental solutions pertaining to Biot's equation of three-dimensional dynamic poroelasticity are derived in the Laplace transform domain. These solutions define the displacement field in fluid-saturated media due to point forces in the solid and fluid phases. In addition, for the two extreme cases of a medium with low and high permeabilities, time domain approximations of the fundamental solutions are derived by inverting Laplace transform expressions. Finally, numerical results are presented to highlight the salient features of the problem as well as investigate the accuracy of the time domain solutions. These analytical expressions are also used to define the equivalent one-phase material properties for the more usual undrained dynamic analyses.