Spatial variability of the poroelastic response of the heterogeneous medium

In this work, a stochastic methodology is applied to analyze the variability of the poroelastic response of the heterogeneous medium at the field scale. To solve the problem analytically, we restrict our attention to the one-dimensional models, where fluid flow as well as deformation occurs in one direction only under a constant applied stress. Assuming statistic homogeneity, the closed-form solutions that describe the variability of fluid pressure head, and a solid's strain and displacement are developed using a spectral approach based on Fourier-Stieltjes representations for the perturbed quantities. The influence of the correlation length of the log hydraulic conductivity on these results is investigated. It is found that the variances of the solid's strain and displacement increase with the correlation length of the log hydraulic conductivity, while the correlation length of the log hydraulic conductivity plays the role in reducing the variability of the specific discharge.