Particle scale analysis of soil stiffness and elastic wave propagation

Soils are granular materials consisting of many particles, and the overall response of a soil can be considered to be a complex accumulation of the inter-particle responses. Small-strain soil stiffness is important to predict the ground deformation in situ and in practice and is often deduced from elastic wave velocity in laboratory experiments. The dynamic properties of soils are also important for dynamic analyses including site response analysis. Stress waves propagate through soil via the grain contact network, thus the actual particle-scale mechanics differ from those assumed in continuum mechanics which is often used to simulate and analyse stress wave propagation. Thus the particle properties including surface characteristics should have a direct impact on the overall response of soil to stress wave disturbances. Surface roughness effects on the inter-particle response have previously been considered in the experimental work of Cavarretta (2009) and in the dynamic analyses using the discrete element method (DEM) described by O’Donovan (2013). This research aims to develop understanding of the extent of the sensitivity of soil stiffness to the contact rheology by adopting theoretical, numerical (DEM) and experimental approaches. The theoretical approach follows Yimsiri & Soga (2000) who combined micromechanical effective medium theory and a rough surface contact model; their approach is revisited here considering more recent UK-based tribology studies. The contact laws considered in the DEM analyses presented here include particle surface roughness, partial slip at tangential contacts, and spin resistance based on these developments by the work of O’Donovan (2013). The experimental approach used two types of dynamic tests: bender element tests in a cubical cell apparatus, and shear plate tests in a triaxial apparatus. For both test types, smooth and rough surface spherical ballotini are used to study the surface roughness effects on the sample shear modulus. Shear plates are not commonly used in soil mechanics dynamic testing and so the study also included an assessment of this technology. The data generated show that the small-strain stiffness of granular materials is measurably reduced sensitively with the surface roughness especially at a low stress level. This explains partially a higher exponent n value in the relationship between the shear modulus and the confining stress (n > 0.5). As the stress level increases the shear modulus of the assembly of rough particles approach the smooth equivalent.Open Acces

Influence of packing density and stress on the dynamic response of granular materials

Laboratory geophysics tests including bender elements and acoustic emission measure the speed of propagation of stress or sound waves in granular materials to derive elastic stiffness parameters. This contribution builds on earlier studies to assess whether the received signal characteristics can provide additional information about either the material’s behaviour or the nature of the material itself. Specifically it considers the maximum frequency that the material can transmit; it also assesses whether there is a simple link between the spectrum of the received signal and the natural frequencies of the sample. Discrete element method (DEM) simulations of planar compression wave propagation were performed to generate the data for the study. Restricting consideration to uniform (monodisperse) spheres, the material fabric was varied by considering face-centred cubic lattice packings as well as random configurations with different packing densities. Supplemental analyses, in addition to the DEM simulations, were used to develop a more comprehensive understanding of the system dynamics. The assembly stiffness and mass matrices were extracted from the DEM model and these data were used in an eigenmode analysis that provided significant insight into the observed overall dynamic response. The close agreement of the wave velocities estimated using eigenmode analysis with the DEM results confirms that DEM wave propagation simulations can reliably be used to extract material stiffness data. The data show that increasing either stress or density allows higher frequencies to propagate through the media, but the low-pass wavelength is a function of packing density rather than stress level. Prior research which had hypothesised that there is a simple link between the spectrum of the received signal and the natural sample frequencies was not substantiated

An appraisal of the influence of material fabric and stress anisotropy on small-strain stiffness

This paper examines the effect of a non-isotropic, true triaxial stress state on soil stiffness using discrete element method (DEM) simulations. Samples of uniform spheres with a very stable face centred cubic (FCC) are considered to isolate the effect of stress from stress-induced fabric changes. At the same time the anisotropic nature of the lattice fabric enables the effect of fabric on the observed responses to be explored. The elastic or small strain stiffness was determined by applying small amplitude displacement perturbations to the samples and measuring the resultant shear wave velocity. Two different mean stress levels were considered and at both stress levels the magnitudes of the three principal stresses were varied. The data obtained confirm that the stresses in direction of wave propagation and shear wave oscillation have a measurable influence on shear modulus values. The extent of sensitivity depends on the material fabric. The stress component orthogonal to the plane of wave motion has, however, a less marked effect on shea

An appraisal of the influence of material fabric and stress anisotropy on small-strain stiffness

This paper examines the effect of a non-isotropic, true triaxial stress state on soil stiffness using discrete element method (DEM) simulations. Samples of uniform spheres with a very stable face centred cubic (FCC) are considered to isolate the effect of stress from stress-induced fabric changes. At the same time the anisotropic nature of the lattice fabric enables the effect of fabric on the observed responses to be explored. The elastic or small strain stiffness was determined by applying small amplitude displacement perturbations to the samples and measuring the resultant shear wave velocity. Two different mean stress levels were considered and at both stress levels the magnitudes of the three principal stresses were varied. The data obtained confirm that the stresses in direction of wave propagation and shear wave oscillation have a measurable influence on shear modulus values. The extent of sensitivity depends on the material fabric. The stress component orthogonal to the plane of wave motion has, however, a less marked effect on shea

Evaluation of soil fabric using elastic waves during load-unload

It is essential to assess the evolution of soil fabric as it has an important role in the mechanical responses of soils during complex loading conditions. This contribution carries out the physical experiments using three granular materials in the laboratory. The variations of compression and shear wave velocities (Vp and Vs) are investigated during load-unload cycles under dry and drained conditions. Supplementary discrete element method (DEM) simulations are performed to understand the evolution of soil fabric during the equivalent load-unload cycles using spherical particles. Vp and Vs are not always reversible even though the stress state regains its isotropic condition after unload, indicating that Vp and Vs are governed by not only the stress state but also the fabric change. The variations of Vp/Vs are density- and stress-dependent; a higher level of stress ratio (σ1′/ σ3′) threshold is observed for denser packings to trigger a significant change in wave velocity ratio (Vp/Vs) for experimental results using spherical glass beads and simulation data using spherical particles. Considering the particle shape, a higher σ1′/ σ3′ threshold is found for more angular particles than rounded particles. The DEM result reveals that Vp/Vs of spherical particles can be correlated linearly with the evolution of fabric ratio (Φver/ Φhor) during load-unload in a pre-peak range under dry and drained conditions

Effects of seepage flow on liquefaction resistance of uniform sand and gap-graded soil under undrained cyclic torsional shear

Internal erosion is the transportation of soil particles from within or beneath geotechnical structures, caused by seepage flow, that impacts the subsequent mechanical and hydraulic behaviour of the soil. However, it is difficult to predict the liquefaction resistance of eroded soil due to several factors related to the soil fabric. The present study investigates the impact of seepage flow on the undrained cyclic behaviour of two types of soil: uniform sand and gap-graded soil with a fines content of 20%, using a novel erosion hollow cylindrical torsion shear apparatus. From the results for the uniform sand, the soil fabric formed by moist tamping (MT) leads to higher liquefaction resistance than that formed by air-pluviation (AP). However, after applying seepage flow, the liquefaction resistance of the eroded MT specimens becomes even lower than that of the non-eroded AP specimen. Therefore, the liquefaction resistance of soil is expected to decrease due to the rearrangement of the initially stable coarse particles during seepage flow. On the other hand, the liquefaction resistance of the gap-graded soil tends to increase after the removal of fines as the number of stable contacts between the coarse particles is increased. Under these test conditions, the latter effect is found to be greater for the given gradation, leading to a slight increase in the liquefaction resistance of the tested gap-graded soil after internal erosion. Furthermore, the intergranular void ratio and small-strain shear modulus are seen to be well correlated with the liquefaction resistance of the tested soil

CLUMP: A Code Library to generate Universal Multi-sphere Particles

Particle shape plays a key role in the mechanical and rheological behaviour of particulate and granular materials. The simulation of particulate assemblies typically entails the use of Molecular Dynamics, where spheres are the predominant particle shape, and the Discrete Element Method (DEM). Clumps and clusters of spheres have been used to simulate non-spherical particles, primarily due to the simplicity of contact detection among spheres and their ability to approximate practically any irregular geometry. Various approaches have been proposed in the literature to generate such clumps or clusters, while open-source numerical codes applying these are scanty. The CLUMP code, proposed in this paper, provides a unified framework, where a particle morphology can be approximated using different clump-generation approaches from the literature. This framework allows comparing the representations of the particle generated by the different approaches both quantitatively and qualitatively, providing the user with the tools to decide which approach is more appropriate for their application. Also, one novel generation technique is proposed. Outputs are provided in formats used by some of the most popular DEM codes. Moreover, the resulting clumps can be transformed into surface meshes, allowing for easy characterisation of their morphology. Finally, the effect of clump-generation techniques on the mechanical behaviour of granular assemblies is investigated via triaxial compression tests

Using geophysical data to quantify stress-transmission in gap-graded granular materials

The behaviour of gap-graded granular materials, i.e. mixtures of coarse and cohesionless finer grains having a measurable difference in particle size, does not always confirm to established frameworks of sand behaviour. Prior research has revealed that the role of the finer particles on the stress-strain response, liquefaction resistance, and internal stability of non-cohesive gap-graded soils is significant and complex, and highly dependent on both the volumetric proportion of finer particles in the material and the coarse-particle to finer-particle size ratio. Quantifying the participation of the finer particles on the stress transmission and overall behaviour is central to understanding the behaviour of these materials. However, no experimental technique that can directly quantify the contribution of finer particles to the overall behaviour has hitherto been proposed. This paper explores to what extent the participation of finer particles can be assessed using laboratory geophysics, recognizing that granular materials act as a filter to remove the high frequency components of applied seismic / sound waves. Discrete element method simulations are performed to understand the link between particle-scale stress transmission and the overall response observed during shear wave propagation. When the proportion of finer particles is increased systematically both the shear wave velocity (VS) and low-pass frequency (flp) increase sharply once a significant amount of the applied stress is transferred via the finer particles. This trend is also observed in equivalent laboratory experiments. Consequently, the flp–VS relationship can provide useful insights to assess whether the finer particles contribute to stress transmission and hence the mechanical behaviour of the gap-graded materials