Micromechanics of shear wave propagation and non-linear stiffness of granular materials
Creators: name: Nguyen, Hoang
Publisher: name: Imperial College London
Year: 2020

description: Analysis of the micro-mechanics of shear wave propagation is shown in this work to be a powerful method to study soil stiffness at small-strain levels. Discrete element modelling of triaxial tests successfully captures the small-strain stiffness of granular materials. Various interpretative methods are adopted to determine the travel time for shear waves that are transmitted through assemblies of perfectly spherical particles with different densities, allowing small-strain stiffness under anisotropic stress states to be measured. Along with the micro-scale data gathered from true triaxial simulations, the stiffness anisotropy data are used to assess the effect of each principal stress on the small-strain stiffness. In addition, these dynamic stiffnesses allow the void correction function that quantifies the effect of sample density on stiffness to be studied. A notable conclusion obtained is that the inclusions of micro-scale data (i.e. the coordination number) will likely give a more accurate void ratio correction function when compared with the traditional function used in the interpretation of laboratory test data where particle level information is unavailable. Non-linear stiffness of soil is a long-standing topic of interest in geomechanics, with the degree of nonlinearity being influenced by many factors including the stress path, the sample density and the particle size distribution. These issues are extensively studied here using discrete method simulations of triaxial tests in which samples were sheared along with different stress paths. Both the macro-scale and the micro-scale data gathered from the true-triaxial DEM simulations allow the non-linearity of stiffness and the interactions at the particle scale to be further understood. The coordination number and the second-order fabric tensor provide a complementary insights to further understanding of macro-scale response of granular materials. At a given strain level, both the dynamic stiffness and the static stiffness are measured, allowing the degree of nonlinearity of stiffness to be studied. The framework of kinematic modified yielding points proposed by Jardine (1992) that identifies three main zones (i.e. linear elastic behaviour, non-linear elastic behaviour and elasto-plastic behaviour) provides a benchmark for the gap between the dynamic stiffness and the static stiffness to be studied in an effective manner. A key observation is that the dynamic shear stiffness tends to increase to a peak value before experiencing of a decrease in magnitude. Simulations of triaxial tests in which the samples were sheared along different stress paths allow the yield surfaces to be captured, reconfirming that the sub-yield surfaces are dependant upon the sample density and the confining effective stress. The stress history and the particle size distribution (PSDs) have a large influence on the shape of the non-linear stiffness degradation curve. In conjunction with the static stiffness, the dynamic stiffness was measured to quantify the effect of the over-consolidation ratio (OCR) on the shear stiffness, resulting in the observation that the reductions in stiffness with increasing the OCR values has strong link to drops in coordination number, while the input work required during shearing triaxial tests is almost identical for samples with different OCR values. The stress history has a measurable impact on the shear wave propagation, with higher travel time for samples with higher values of OCR, indicating that both the dynamic stiffness and the static stiffness obtained from DEM simulations reduce as OCR increases. The mathematical formulations used to capture the non-linear stiffness degradation curves are examined in detail, the hyperbolic form is found to closely capture the reductions in shear stiffness with increasing strain. Several DEM simulations that consider effects of the coefficient of uniformity (Cu) on the non-linear behaviour of granular materials are performed, arriving at some key observations that: (i) samples with lower values of Cu have higher stiffness at small-strain levels; (ii) a higher amount of work should be input for samples with coarse particles to attain a particular strain level; (iii) more energy dissipation is observed for samples with a lower Cu value.