Grain-Level Numerical Simulations for the Effective Elasticity of Weakly Cemented Sandstones

Abstract

Weakly cemented sandstones are characteristic of loose-bonding contacts, large porosities, and high-clay contents. This study presents a discrete element method (DEM)-based numerical study for the effective elasticity of such rocks that mainly depends on the mechanical behavior of intergranular contact regions. The DEM scheme employs a set of normal and shear springs to phenomenologically describe the mechanical behavior of intergranular finite-sized cements defined by three morphological parameters: cement thickness, bonding radius, and grain radius. Applications to two digital models established in terms of contact-bonding and distant-bonding modes, respectively, where spherical quartz grains are randomly packed together with adding cements under the specified confining pressure, are compared with the theoretical predictions by the contact-bonding and distant-bonding cement theories, which demonstrates a good agreement generally for small contact widths, small contact thicknesses, and large-magnitude moduli, especially for the effective shear modulus. Applications to a series of artificial sandstone samples made in terms of different proportions of quartz grains and clays (a mixture of epoxy and kaolinite) under loose compaction for weak cementation demonstrate a good agreement with ultrasonic measurements. Numerical investigations for the micromechanical characteristics (differential stress fields, force chains, and fabric tensors) of artificial samples subject to applied axial strains demonstrate that the strong mechanical behavior of weakly cemented sandstones tends to appear inside the cohesive aggregates of stiff grains because of their relatively large sizes with loose compaction.