APPROXIMATE FORMS OF WAVE EQUATIONS FOR WATER-SATURATED POROUS MATERIALS AND RELATED DYNAMIC MODULUS

Abstract

On the basis of the information concerning the compressibilities of water, solid particle and solid skeleton, the material constants appearing in the theory of water-filled porous elastic materials developed by M. A. Biot were computed and their order of magnitude was examined. Such check-up permitted to simplify considerably the theory for the case of dynamical problems and led to wave equations which are identical in form with those derived for the elastic theory. This shows that the elastic theory can serve as a substitute for the poro-elastic theory, especially when the latter is associated with the undrained condition like dynamical problems. Young's modulus and Poisson's ratio in the equivalent elastic theory were related with the constants of the materials constituting a two-phase porous medium. Furthermore, the expression for the pore pressure coefficient B proposed by A. W. Skempton was derived and extended to the case of one-dimensional compression. Finally, a relationship between Poisson's ratio and the pore pressure coefficients was disclosed.