Uncertainty in the Volume Strain Field of the Solid in Unsaturated Heterogeneous Deforming Media

Abstract

In a partially saturated, heterogeneous deforming aquifer, we analyzed the solid's volume strain field within a stochastic framework. The differential equations describing the first two moments of the solid's volume strain field were developed through the perturbation approach. To solve the problem analytically, focus was placed on the one-dimensional model. The resulting closed-form solutions (namely, the first two moments of the solid's volume strain field) were obtained using the nonstationary spectral approach in conjunction with the principle of superposition. They are functions of the statistical properties of the logarithm of the saturated hydraulic conductivity and a soil pore size distribution parameter. It can be concluded from the analytical solutions that the correlation length of the logarithm of the hydraulic conductivity is important in increasing the variability of the solid's volume strain field, while the soil pore size distribution parameter plays the role of decreasing the variability in the solid's volume strain field.