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Gap-graded soils are poorly graded soils, which have a deficiency of certain particle sizes, one example is a mixture of coarse and finer sand grains with no intermediate-sized particles. While current knowledge of soil behaviour has been mainly established by considering the response of well-graded soils, natural soils encountered in geotechnical engineering practice can be gap-graded. In this research, both numerical and experimental approaches are applied to study the mechanical behaviour of gap-graded soils; materials with continuous particle size distributions are also investigated using the same analytical tools to provide a benchmark against which the gap-graded materials can be considered. Using discrete element method (DEM) simulations, the stress transmission within granular materials with a broad range of particle size distributions was investigated. The first series of analyses took a rather simplistic binary approach and considered grains to be either active or inactive grains. These analyses showed that for both continuous and gap-graded soils, the proportion by volume of inactive grains can be sufficiently large to influence widely used measures of state such as void ratio and bulk density. The nature of the stress transmission was then analysed, which shows that for materials with a continuous, linear gradation, the proportion of stress carried by a particle aligns with its particle volume; this is not the case in gap-graded soils. Using DEM, the small-strain stiffness of gap-graded soils was considered in detail. The results show that the particle-scale distribution of stress influences the stiffness of gap-graded soils. A new semi-empirical state variable, e_α, was proposed that weights the contribution of particles to the solids volume used in calculating e by the particle stress. The strong correlation of G_0 with e_α shows how the heterogeneity of stress influences stiffness. The difference between the stiffness obtained from the quasi-static small strain probes and the stiffness obtained from the dynamic bender element tests can qualitatively capture the proportion of inactive particles. The potential to use this observation in physical laboratory experiments was explored.

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.

Flows involving polydisperse granular media are widespread in nature and industry. Knowledge of the momentum coupling between the fluid and solid phases comes mostly from empirical and numerical correlations based on studies involving monodisperse materials and treatment of polydispersity has had little attention. Accurate predictions of the flow induced forces acting on grains are required to understand problems of relevance to geotechnical engineering involving sand particle migration such as seepage induced instabilities and filtration processes. The Discrete Element Method (DEM) is widely used in the geomechanics community to study particle scale behaviour of sands and soils, and is often combined with Computational Fluid Dynamics (CFD) to simulate saturated materials. The popular coarse grid DEM-CFD approach, in which fluid cells contain multiple particles, relies on empirical drag force relations to predict the interaction between phases based on the flow Reynolds number and the fluid cell porosity. Highly resolved simulations of interstitial fluid flow at low Reynolds numbers in dense polydisperse sphere packings were conducted using the Immersed Boundary Method (IBM). Fluidparticle interaction forces from IBM simulations were used to investigate the role of grain size polydispersity on drag and to critically assess the suitability of popular drag correlations for use in geomechanics research. Polydispersity was systematically controlled by considering linearly graded particle size distributions (PSDs) with uniformity coefficients between Cu = 1.01 - 2.50, and bimodal PSDs with diameter ratios 2 and 4. Flow fields obtained from the IBM were used to validate Stokes flow simulations with a Pore Network Model (PNM) and to investigate the role of constrictions in pore scale head loss. The Ergun and Di Felice correlations are shown to not adequately predict the particle drag forces in polydisperse systems. The polydispersity correction of van der Hoef et al. is shown to predict the meso-scale drag adequately but fail to capture the correct partitioning of the drag between different sized particles. An approach to correcting the predictions of monodisperse drag models using local porosities for each particle calculated from the radical Voronoi tessellation is shown to provide good predictions at the particle and meso scales. The PNM studied is shown to accurately predict flow paths through porous media and provide accurate predictions of fluidparticle interaction forces using the method of Chareyre et al.

Internal erosion is a major safety concern for embankment dams and flood embankments and is the focus of much research internationally. Suffusion is a mechanism of internal erosion which affects gap-graded or broadly graded cohesionless soils and is characterised by selective removal of fine material, leaving behind a coarse material with increased hydraulic conductivity. Early studies on suffusion proposed design criteria based on laboratory testing, and presented conceptual models to explain the results in terms of grain-scale behaviour. The study by Kenney & Lau (1985) identified three criteria for suffusion: 1 – Fine particles must be free to move (mechanical criterion); 2 – Fine particles must be small enough to fit through the void space between coarse particles (geometric criterion); 3 – Fluid flowing through the void space must have sufficient velocity to transport the fine particles (hydraulic criterion). Recent studies have examined the first two criteria using grain-scale models with idealised particles, including analytical models and discrete element models (DEM) with circular or spherical particles. This thesis presents a new methodology, using non-destructive 3D imaging (micro-CT) to characterise the internal microstructure in physical specimens of sands and glass beads. This methodology involved the development of innovative image processing and numerical techniques to quantify unstable particle assemblies and to measure particle size distributions and void constriction size distributions. The new method was validated and was shown to produce good agreement with existing methods for idealised particle configurations, however the results for real sand specimens provided new insights into the effects of particle shape, particle size distribution and density on void constriction sizes. Furthermore, the 3D images of real specimens have provided new insights into the appropriateness of existing conceptual models for gap-graded particle structures. These results were used to critically examine and evaluate existing mechanical and geometric criteria for suffusion. The 3D images showed, qualitatively, that the void structures in sands varied significantly from those in porous rocks – which had been the basis for the majority of existing grain-scale fluid flow models. To examine this issue quantitatively, computational fluid dynamics (CFD) simulations were performed within the 3D images of sands and glass beads, in parallel to laboratory permeameter tests on the same materials. The results presented in this thesis provided entirely new insights into the patterns of fluid flow in sands, they allowed correlations to be made between fluid flow and void constriction sizes and also showed how local velocities varied from volume-average discharge and seepage velocities. This study provides new information to support, clarify and improve upon the current understanding of suffusion, filtration and seepage flows in sands. The detailed methodology and results also highlight issues of great importance to future micro-scale modelling of these phenomena.

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.

Embankment dams consisting of broadly graded materials have been found to be susceptible to internal erosion. The need to minimise both the cost and risk requires an accurate characterisation of a range of materials, in terms of their susceptibility. Despite significant theoretical and experimental developments, there is a lack of consensus as to how to determine the susceptibility of a material to internal erosion, and what force conditions are required to initiate erosion in susceptible materials. A significant weakness in current geotechnical modelling is the limitation to the use of a large-scale averaged representation of the flow. The immersed-boundary method alternative is a small-scale resolving method capable of elucidating the flow at arbitrarily small scales, rectifying this limitation. In this research the Immersed-Boundary Method (IBM) is used to accurately model the interaction of the particle surface and the fluid flow. The method is adapted and applied to modelling internal erosion, with the intention of understanding the micro-scale mechanisms involved. In particular, the fluid-particle coupling in the IBM model is adapted to be suitable to the case of densely packed particles, characteristic of embankment structures. In this thesis significant improvements are made to the immersed-boundary method’s ability to model fluid particle flows. Improvements to the momentum exchange between the particles surface both when the particle is removed from others, and when two particles are within each others range of influence, are made. Additionally the dependence on mesh resolution of the flow field in proximity of the particle’s surface is reduced, allowing more tractable simulation of the large scale problems characteristic of geotechnical problems. The removal of sporadic pressure fluctuations improves the accuracy of predictions. The resulting tool will provide insight into the science under-pinning internal erosion, guiding best practice with regards to predicting and preventing the onset and propagation of internal erosion.

The stiffness of soil is an important parameter that has implications on soil-structure interaction, on the response to earthquake motion and on the response of soils to dynamic loadings. Stiffness reduces and behaves plastically at medium to high strains; however, at small-strain the stiffness has been observed to be a constant value and elastic. Small-strain stiffness governs the soil-structure interaction during construction projects and site response during dynamic loading due to earthquakes and man-made operations. Quantifying stiffness, in particular shear stiffness, at small-strain is difficult due to the effect of sample fabric on the values measured and the resolution of the testing equipment that is available. Wave propagation has been used to measure the stiffness of samples by propagating waves in different directions and in different planes. This thesis aims to examine the propagation of stress waves through a granular medium. Samples were created using the numerical discrete element method (DEM) in two- and three-dimensions. Waves, created by a point source, were propagated through the samples and this propagation was measured using micromechanical data. The speed of the propagating wave was assessed using existing techniques and novel methods developed during the research. The effect of macro-scale parameters, such as sample boundary conditions, and the effect of micro-scale parameters, such as interparticle contact laws, on sample stiffness were examined. Randomly packed samples were created with a quantifiable fabric tensor, measured using the contact force network. Wave propagation in different directions was examined to quantify the effect of inherent anisotropy on the sample stiffness. Samples were confined at anisotropic confining pressures to isolate the effect of induced anisotropy on the sample stiffness. Wave propagation results were compared with the results of small amplitude stress probes for a number of simulations and with experimental work carried out in the University of Bristol.

This study used synchrotron X-ray micro computed tomography (μCT) to investigate the response of soil to one dimensional compression both at room temperature and below freezing. Synchrotron tomography at the Diamond Light Source in Oxfordshire was used in order to capture high resolution (in the order of μm) images of the soil in situ as it was subject to loading and temperature change. Custom apparatuses were designed and built to control the loading and temperature of the experiment at all times. Two sets of experiments were carried out; one set on dry sands in 'mini-oedometer' tests and another examining the effects of temperatures below zero on sands and silts saturated with water. The particle-scale response of sand in an oedometer test was investigated by examining the evolution of both scalar and directional properties of Leighton Buzzard sand and Reigate sand samples. The scalar properties included void ratio, particle shape, particle size distribution and particle contact area. The variation of void ratio within a sample was examined to determine the boundary effects. The directional properties measured included the particle orientation, contact normals and branch vectors. Tracking of the particle positions for the larger sand during loading was also carried out. This study presents the documentation of many of these properties for a sample under load in situ for the first time. In the second set of experiments the micromechanics of frozen soil, in particular the phenomenon of ice lensing, was investigated. Temperature controlled mini-oedometers developed for this study were used to directly observe the behaviour of saturated soil under temperature conditions below 0°C. Micro-cracks within the ice phase of the frozen soil were observed and it is proposed that under field conditions such micro-cracks are likely to represent the initiation of ice-lenses by providing a conduit for water migration.

The critical state soil mechanics (CSSM) framework originally proposed by Schofield & Wroth (1968) has been shown to capture the mechanical behaviour of soils effectively. The particulate implementation of the discrete element method (DEM) can replicate many of the complex mechanical characteristics associated with sand. This research firstly shows that the CSSM framework is useful to assess whether a DEM simulation gives a response that is representative of a real soil. The research then explores the capacity of DEM to extend understanding of soil behaviour within the CSSM framework. The influence of sample size on the critical-state response observed in DEM simulations that use rigid-wall boundaries was examined. The observed sensitivity was shown to be caused by higher void ratios and lower contact densities adjacent to the boundaries. When the void ratio (e) and mean stress (p') of the homogeneous interior regions were considered, the influence of sample size on the position of the critical state line (CSL) in e-log(p') space diminished. A parametric study on the influence of the interparticle friction (μ) on the load-deformation response was carried out. The macro-scale stress-deformation characteristics were nonlinearly related to μ and the particle-scale measures (fabric, contact force distribution, etc.) varied systematically with μ. The limited effect of increases in μ on the overall strength at high μ values (μ > 0.5) is attributable to transition from sliding-dominant to rolling-dominant contact behaviour. A μ value higher than 0.5 leads to a CSL in e-log(p') space that does not capture real soil response. True-triaxial simulations with different intermediate stress ratios (b) were performed. The dependency of strength on b agreed with empirical failure criteria for sands and was related to a change of buckling modes of the strong force chains as b increased. DEM simulations showed that the position of the CSL in e-log(p') space depends on the intermediate stress ratio b. This sensitivity seems to be related to the dependency of the directional fabric anisotropy on b. The link between the state parameter and both soil strength and dilatancy proposed by Jefferies & Been (2006) was reproduced in DEM simulations. A new rotational resistance model was proposed and it was shown that the new model can qualitatively capture the influence of particle shape on the mechanical behaviour of sand. However, it was shown that the effect of rotational resistance is limited and to quantitatively compare the DEM simulation results with laboratory testing data, e.g., the critical-state loci, it is necessary to use non-spherical particles.

Granular filters are considered to be among the most safety critical elements of embankment dams. The behaviour of such filters is poorly understood, which is reflected in the empirically derived rules used for filter design, which have been shown to be conservative and to contradict each other in some cases. In this thesis particle-scale numerical analysis is used to improve the understanding of internal stability, a requirement for granular filters, and to assess the fundamental basis for some commonly used empirical design rules. Internal stability describes the ability of the coarse fraction of a broadly or gap-graded cohesionless soil to prevent the erosion of the finer fraction under seepage. Two conditions for internal instability are that: (i) the fine particles carry relatively lower stress than the coarse particles (hydromechanical condition) and (ii) the fine particles should be small enough to pass through the void constrictions between the coarse particles (geometric condition). Each of these conditions is assessed in turn. The hydromechanical condition is assessed by using discrete element modelling (DEM) to analyse the fabric and effective stress distribution within soils of varying internal stability according to empirical criteria. In particular the hypothesis of Skempton and Brogan (1994) that a prerequisite for internal instability is a reduction of the effective stress in the finer fraction is explored. The results show that the stress transferred by the fines is related to the soil fabric, in particular the number and strength of contacts between particles. This is in turn shown to be influenced by the particle size distribution (PSD), fines content and relative density of the material. A conceptual framework to describe this behaviour is introduced. The geometric condition is intimately linked to the size of the constrictions within the void space. The constriction size distribution (CSD) within DEM samples with differing PSDs and relative densities is quantified using two approaches: the Weighted Delaunay method (Reboul et al., 2010) and the Maximal Ball method (Dong and Blunt, 2009). CSD curves are shown to have similar shapes which can be usefully normalised using characteristic filter particle diameters. The results show very good qualitative agreement with the experimental work of Kenney et al. (1985), and lend scientific support to the use of characteristic particle diameters in filter design. An analysis of constrictions within DEM samples with stress-induced anisotropy shows that larger and smaller constrictions align with the major and minor principal stresses respectively. A random walk network model describing void space is proposed to simulate the movement of a polydisperse fine material through a granular filter. This model is useful for identifying effective and ineffective base/filter combinations.

Over the past 50 years, experimental studies have repeatedly demonstrated that the mechanical behaviour of sand is sensitive to the material fabric, i.e., the arrangement of the grains. Up until now there have been relatively few attempts to describe quantitatively the fabric of sands. In fact, most of our understanding of the link between the particle movements and interactions and the macro-scale response of granular materials, including sand, comes from discrete element modelling (DEM) and experiments on “analogue” sands with simple, idealized shapes. The aim of this study had been to describe quantitatively the particle morphology and fabric of real sand and their evolution under loading. The material investigated was Reigate sand (from Southeast England), a geologically old sand which, in its intact state, exhibits significant grain interlocking and no bonding. To explore the effects of fabric on the mechanical response of the soil, intact and reconstituted specimens both having similar densities were tested under triaxial compression. The specimens were impregnated with an epoxy resin at three different stages of shear deformation and small cores from each specimen were scanned using X-ray micro-tomography. Different systems and scanning parameters were explored in order to obtain three-dimensional high-resolution images with a voxel size of 5/im (0.018^50) and a quality level required for the identification of the individual particles and the surface defining each particle-particle contact. The quantification of particle size and shape has shown that breakage of fractured grains, along existing fissures, occurs both during reconstitution and shearing of the intact soil, a phenomenon that cannot be observed using invasive techniques such as sieve analysis. Statistical analyses of the distribution of fabric directional data in terms of particle orientations, contact normals, branch vectors and void orientations were carried out at each loading stage. It has been shown that the initial particle orientation fabric that develops during the deposition of the material tends to persist during shearing, while the contact normals seem to be reorientated along the direction of the major principal stress in the post-peak regime. Different patterns were observed within the shear band as both the particles and the contact normals appeared to rotate towards the direction of the shear plane. The measurements from the tomographic data were complemented with a qualitative description of the morphology and fabric using SEM and optical microscope images of thin sections.