Compaction Dynamics in Porous Media: a Combined Experimental, Numerical, and Analytical Approach

Abstract

Porous media are a broad class of materials made of a solid skeleton and void spaces that are prevalent in natural and man-made environments. They are of critical importance to various fields ranging from material science to geomechanics. When compressed, porous media may exhibit sudden and repeated stress drops linked with meso-scale damage and the formation of localised deformation zones called compaction bands that can propagate cyclically. This Thesis provides an experimental, numerical and analytical basis for modelling localisation in a variety of porous materials.

The influence of shaped boundaries on those bands is first explored experimentally. The bands are found to conform to the shape of nearby boundaries, yet revert to planar form some distance away. Surprisingly, the band shape can be inferred from a linear elastic model.

Secondly, a nonlocal continuum model that produces recurrent stress drops is developed. These drops are driven by the rise and fall in meso-related temperature, which characterises fluctuating velocities at the meso-scale.

The choice of a nonlinear elastic law in the continuum model prompted questions regarding the wave speed in such materials. Nonlinear elasticity wave speeds are derived for hypo and hyperelastic models. While both models yield identical results in isotropic compression, hyperelasticity predicts changes in the ratio of wave speed under shear without necessarily needing fabric, as often assumed in previous investigations.

Finally, a finite element analysis is performed to apply the developed model to a boundary value problem. The findings show that a variety of experimentally observed compaction patterns can be recovered.