Modeling Macro-scale Clay Behavior at Micro-scale Clay Particle Interfaces
Clay consolidation has generally been considered from a macro-scale perspective by measuring the macro-scale compression of a clay soil over time. Clay particles in consolidation tests experience shear and normal forces at the inter-particle level due to force applied to the soil at the macro-scale. These shear and normal forces cause the particles to slide at the micro-scale and produce macro-scale changes in soil volume and shape. By considering the inter-particle interactions at the micro-scale, the shear force - normal force - velocity relationship can be described by the Rate Process Theory (RPT). This research investigated the use of the RPT for analyzing sliding at individual clay particle contacts during secondary compression to describe macro-scale clay behavior.
The novel micro-scale friction experiments conducted in this research demonstrated that an Atomic Force Microscope (AFM) can be used to obtain coefficient of friction (μ) measurements for montmorillonite. This method allows for the measurements to be performed over spatial scales of a few microns, can be done under dry conditions or a wide range of aqueous solutions, and requires no calibration beyond making a few microscopic measurements of the probe. Control tests of silica on mica (μ = 0.29 ± 0.02) agree with literature values where limits indicate one standard deviation.μ values for wet and dry sodium montmorillonite were determined to be 0.20 ± 0.03 and 0.72 ± 0.03, respectively.
The micro-scale AFM and macro-scale triaxial shear, ring shear, and direct shear experimental data ofμ as a function of sliding velocity were found to match well with those calculated using common RPT parameter values. The activation energy for the macro-scale triaxial shear and corresponding micro-scale friction regime experiments fall within the expected range for pure montmorillonite of 84–109 kJ/mol. Additionally, the micro-scale and macro-scale experimental results fall within the expected range for the number of bonds per unit of normal force of 10^7–10^9 bonds/N.
A discrete element method (DEM) model was developed to calculate thin, disk-shaped clay particle movement in three dimensions during compression using the RPT as a contact model. The DEM compression results were compared to macro-scale consolidation experiments conducted on the same reference clay as the micro-scale AFM experiments. The influences on the compression of the number of bonds at each clay contact per unit of normal contact force and the activation energy were quantified. Increasing the activation energy decreased the compression, as expected. Similarly, increasing the number of bonds per unit of normal force at the contacts decreased the compression, as expected. Realistic clay fabrics with varying particle sizes, particle size distributions, and aspect ratios led to a compression model with behavior similar to the macro-scale laboratory compression tests.
This research provides evidence of the close correspondence between macro-scale and micro-scaleμ measurements and contributes to multi-disciplinary understanding of factors that control friction between clay particles and deformation of clay masses. The results from this work can be applied to a wide range of time-dependent phenomena such as clay secondary compression, shear deformation, and fault dynamics behavior.