The objective of the present study was to develop a fluid flow-coupled distinct element model capable of capturing the undrained behaviour of granular soils by considering fundamental physical mechanisms that involve fluid flow and particle interaction. The method considers granular media as assemblies of ellipsoidal particles arranged on a plane and interacting by means of contact forces. Saturation effects are incorporated by assuming that particles are immersed in fluid, the flow of which is simulated as occurring through a network of conduits. The flow through conduits is according to a Hagen-Poiseuille relation; a transient solution is obtained by solving a system of differential equations. The developed fluid-flow coupled distinct element was used to conduct various numerical simulations and the mechanisms of undrained deformations were examined from a micromechanical point of view. The dissertation begins with a literature review on the undrained behaviour of granular materials as observed in laboratory experiments. A review of previous attempts to simulate undrained tests micromechanically is also presented, and the advantages and disadvantages of various methods are examined. The capability of the developed model to simulate two-dimensional fluid-flow and pressure dissipation problems is demonstrated by means of comparisons with analytical solutions. Fluid pressure dissipation problems are qualitatively compared with Terzaghi's one-dimension theory of consolidation. It is shown that transient flow problems are accurately modelled by the fluid flow network approach. Simulated compression tests were carried out to examine the effects of different confining pressures and initial densities on the macroscopic response. The results compare favorably with those commonly observed in undrained laboratory experiments. Simulated tests are analyzed from a micromechanical point of view. It is shown that macroscopic behaviour can be traced to changes in micromechanical fabric descriptors. The effects of the interparticle friction angle on the undrained behaviour of the assemblies are investigated. The undrained strength is considerably increased by increasing interparticle friction. The main mechanism found to be responsible for the development of higher strength is the tendency of the specimens to dilate during shear distortion. The effects of the principal stress direction on the macroscopic response are examined. The behaviour of initially anisotropic samples is significantly altered by the direction of the principal stresses relative to the anisotropy direction. It is demonstrated that macroscopic permeability of the media has a considerable effect on the strength. This behaviour is attributed to the inhomogeneity of pore pressure distributions which increases with decreased permeability. The results presented are generally in agreement with observations previously reported from laboratory experiments. The possible applications of the model for future research are also discussed.

The objective of the present study was to develop a fluid flow-coupled distinct element model capable of capturing the undrained behaviour of granular soils by considering fundamental physical mechanisms that involve fluid flow and particle interaction. The method considers granular media as assemblies of ellipsoidal particles arranged on a plane and interacting by means of contact forces. Saturation effects are incorporated by assuming that particles are immersed in fluid, the flow of which is simulated as occurring through a network of conduits. The flow through conduits is according to a Hagen-Poiseuille relation; a transient solution is obtained by solving a system of differential equations. The developed fluid-flow coupled distinct element was used to conduct various numerical simulations and the mechanisms of undrained deformations were examined from a micromechanical point of view. The dissertation begins with a literature review on the undrained behaviour of granular materials as observed in laboratory experiments. A review of previous attempts to simulate undrained tests micromechanically is also presented, and the advantages and disadvantages of various methods are examined. The capability of the developed model to simulate two-dimensional fluid-flow and pressure dissipation problems is demonstrated by means of comparisons with analytical solutions. Fluid pressure dissipation problems are qualitatively compared with Terzaghi's one-dimension theory of consolidation. It is shown that transient flow problems are accurately modelled by the fluid flow network approach. Simulated compression tests were carried out to examine the effects of different confining pressures and initial densities on the macroscopic response. The results compare favorably with those commonly observed in undrained laboratory experiments. Simulated tests are analyzed from a micromechanical point of view. It is shown that macroscopic behaviour can be traced to changes in micromechanical fabric descriptors. The effects of the interparticle friction angle on the undrained behaviour of the assemblies are investigated. The undrained strength is considerably increased by increasing interparticle friction. The main mechanism found to be responsible for the development of higher strength is the tendency of the specimens to dilate during shear distortion. The effects of the principal stress direction on the macroscopic response are examined. The behaviour of initially anisotropic samples is significantly altered by the direction of the principal stresses relative to the anisotropy direction. It is demonstrated that macroscopic permeability of the media has a considerable effect on the strength. This behaviour is attributed to the inhomogeneity of pore pressure distributions which increases with decreased permeability. The results presented are generally in agreement with observations previously reported from laboratory experiments. The possible applications of the model for future research are also discussed.

<p>In this work, we have focused on the jamming properties of systems composed of semi-2D elliptical shaped particles. In order to study these systems, we have performed three types of experiments: Couette shear, biaxial isotropic compression, and biaxial pure shear. In each experimental scheme, we take data for both systems of ellipses an bi-disperse disks, in order to probe the effect of broken spherical symmetry at the particle scale, on the global behavior. We use two synchronized cameras to capture the flow of particles and the local stress at the same time.</p><p>In Couette experiments, we study the rheological properties, as well as the stress fluctuations for very large strains (up to 20 revolutions of the inner wheel). The system is sheared for densities below the isotropic jamming point (point J). From these studies we learn that over a small range of packing fractions, ($0.85 \leq \phi \leq 0.86$),</p><p>systems of ellipses demonstrate exceptionally slow dynamical evolution when they are sheared. For</p><p>fixed density, and starting from an essentially unstressed state, the application of shear strain leads to</p><p>first a growth of average particle displacements in the system through a Reynolds dilatancy effect,</p><p>and then for very large strains, a steady decrease in particle displacements. In an intermediate</p><p>range of shear strains, the system exists in effectively meta-stable states for a very long time</p><p>before relaxing to an unjammed state, in which the flow of particles stops completely, and the</p><p>stress fluctuations drop to zero. The strain scale for this relaxation depends on the global packing</p><p>fraction. We characterize this slow dynamics by measuring the evolution of mean velocity, density,</p><p>and orientational order throughout the experiments. In a similar set of experiments performed on</p><p>disks, slow relaxation was observed as well. However, the increasing average displacement build-up</p><p>before relaxation, which was observed in ellipses, did not occur for disks. This suggests that the</p><p>slow relaxation towards an unjammed state in ellipses is associated with the possibility of small and</p><p>slow changes in their orientations, which then allow a more efficient packing.</p><p>In order to study the stress fluctuations, we implement photoelastic properties of the particles. We are able to track the $g^{2}$ (a measure of local stress) of each particle throughout the entire experiment. </p><p>Unlike disks, the power spectra of $g^2$, $P(\omega)$, is not rate invariant for ellipses. In other words, all curves of $R P(\omega)$ vs. $\omega / R$ (where $R$ is the shear rate) with different values of $R$, collapse to a single curve for disks, but not for ellipses.</p><p>The rate invariance of spectra was previously studied for sheared spherical glass beads and semi-2D pentagonal particles. This is the first experimental work in which the fluctuations of granular systems composed of elongated particles is addressed. </p><p>We have also studied the formation and destruction of stress avalanches during Couette shear in both systems of disks and ellipses. In particular, we introduce measures which characterize the size and shape of stress avalanches. Analysis of these measures shows that the build-up and release of stress in both systems of disks and ellipses have similar distributions which indicates that the deformation of particles in a Couette cell does not resemble stick-slip behavior. We also find that the build-up and release of stress is faster is larger avalanches.</p><p>Cyclic isotropic compression is performed on semi-2D systems of bi-disperse disks and identical ellipses with aspect ratio 2, which are composed of photoelastic particles. In each compression cycle, the system is compressed with a total strain of $1.6\%$ and then expanded to the initial state. After completion of each half cycle, the system is allowed to relax, then imaged by two synchronized cameras. The packing fraction, $\phi$, of compressed states are chosen above the isotopic jamming point (point J). In both systems of disks and ellipses, we observed relaxation of global stress over long compression cycles. We find that the global stress drops with a power law over time ($\sigma \sim C t^{-A}$). The exponent of decay, $A$, drops linearly with increasing $\phi$, and hits zero at $\phi \simeq 0.89$ for disks, and $\phi \simeq 0.93$ for ellipses. Above these packing fractions, the system is stable with respect to its global stress. </p><p>In order to understand the origin of this slow stress dilation, we have studied the structural changes of the system, including Falk-Langer measures of affine and non-affine deformations, as well as average contact per particle.</p> / Dissertation