Dynamics of Saturated Rocks. IV: Column and Borehole Problems

Abstract

The one‐dimensional dynamic column and borehole problems of rock mechanics are solved analytically and numerically on the assumption that the water fully saturated, elastic rock medium is characterized by two degrees of porosity—one due to the pores and the other due to the fissures. Use of Laplace transform with respect to time reduces the governing equations of the column and borehole problems to ordinary differential equations with constant and variable coefficients, respectively. The transformed solution of these problems is obtained analytically for the column and by finite differences for the borehole problem and after a numerical Laplace transform inversion produces the time domain response to suddenly applied or harmonically varying with time loads. The quasi‐static counterparts of these problems are analyzed as special cases of the dynamic ones. Numerical studies reveal that inertial effects depend on the kind of the applied load, the influence of porosities and permeabilities is rather small, and that the response is rather close to the one for the single‐porosity model.