Granular media are ubiquitous and important to a wide range of engineering applications and industries. A granular material under shear may exhibit exceedingly complicated behavior which is notoriously difficult to characterize and model, including anisotropy, dilatancy, plasticity, non-coaxiality, critical state and fluid-solid-phase transition. The macroscopic shear responses of a granular material reflect non-trivial micromechanical mechanisms originated from the grain scale of the material. The thesis aims to examine the behavior of granular media subjected to quasi-static shear from a multiscale perspective, based on two complementary approaches: a micromechanics approach based on the discrete element method (DEM) and a hierarchical multiscale approach based on coupled fi...[ Read more ]

Granular media are ubiquitous and important to a wide range of engineering applications and industries. A granular material under shear may exhibit exceedingly complicated behavior which is notoriously difficult to characterize and model, including anisotropy, dilatancy, plasticity, non-coaxiality, critical state and fluid-solid-phase transition. The macroscopic shear responses of a granular material reflect non-trivial micromechanical mechanisms originated from the grain scale of the material. The thesis aims to examine the behavior of granular media subjected to quasi-static shear from a multiscale perspective, based on two complementary approaches: a micromechanics approach based on the discrete element method (DEM) and a hierarchical multiscale approach based on coupled finite element method (FEM) and DEM. The micromechanical study is endeavored to develop an improved cross-scale understanding of key continuum concepts and phenomena in constitutive modeling of granular media, such as granular anisotropy and granular plasticity. The second approach aims to abandon the phenomenological nature of conventional constitutive modeling and to remove the scale limitation of the micromechanics approach in modeling practical boundary value problems (BVPs), by developing a novel hierarchical coupling between FEM and DEM. With a computational bridging scheme in this hierarchical framework, the macro observations and micro mechanisms in granular media can be linked intimately, which is exemplified with simulations of strain localization in various BVPs. Major findings from this thesis are summarized as follows:

(i) Signature characteristics of shear-induced anisotropy at liquefaction, phase transformation, and critical states are identified based on micromechanical study. Static liquefaction is found to occur when the geometrical anisotropy dominates the mechanical anisotropy and the weak force network features an exceptionally high proportion of sliding contacts and develops certain degree of anisotropy. Phase transformation corresponds to a transitional, unstable state associated with a dramatic change in both coordination number and sliding contacts. The critical state in a granular material is always associated with a highly anisotropic fabric structure wherein both the critical void ratio and critical fabric anisotropy depends on the mean effective stress.

(ii) The concept of the critical state in granular soils needs to make proper reference to the fabric structure. A unique relationship between the mean effective stress and a fabric anisotropy parameter, K, defined by the first joint invariant of the deviatoric stress tensor and the deviatoric fabric tensor, is found following power-law at critical state, and is path-independent based on DEM simulations under different loading conditions and intermediate principal stress ratios. Based on the findings, a new definition of critical state for granular media is proposed. In addition to the constant stress and volume required by the conventional critical state concept, an additional constraint that K reaches a unique value at critical state is proposed.

(iii) Fluctuations of local volume, local anisotropy, local shear strain and non-affine displacement are examined. A constant temperature-like compactivity is found for the material under constant-volume shear from the volume fluctuations. The compactivity is not, however, equilibrated among different particle groups in a polydisperse assembly. The local anisotropic orientation evolves towards the coaxial direction of the stress anisotropy with shear. The local shear strain field depicts clear shear transformation zones which act as plasticity carriers. The spatial correlation of the local shear strains exhibits a fourfold pattern which is stronger in the stress deviatoric planes than in the stress isotropic plane. The fluctuations of non-affine displacement suggest an isotropic spatial correlation. Both the local strain and the non-affine displacement exhibit a power-law decayed distribution with a long-range correlation showing strong cooperativity of plastic events.

(iv) A hierarchical multiscale framework is proposed to model the mechanical behavior of granular media. The framework employs a rigorous hierarchical coupling between FEM and DEM. The problem domain is discretized and solved by FEM, while DEM packings are embedded at each Gauss point of the FEM mesh to derive the constitutive relation required at the local material points. The hierarchical scheme helps to avoid the phenomenological assumptions or fitting parameters of constitutive law and retains the computational efficiency of FEM in solving BVPs. Moreover, the framework offers rich information on the particle level with direct link to the macroscopic material responses, which helps to shed lights on cross-scale understanding of granular media.

(v) Inherent anisotropy and strain localization in granular soil are studied using the coupled FEM/DEM multiscale modeling approach. The inherent anisotropy is introduced by using elongated particles in the local DEM packings. By varying bedding plane angles, specimens with different inherent anisotropies can be generated and are biaxially compressed with both smooth and rough loading platens. Varied strain localization patterns are observed with different inherent anisotropies and different boundary conditions. In the case of smooth boundary condition, non-coaxiality is found to be the symmetry breaker and major trigger of strain localization, leading to either a type-a or a type-b shear band. In the case of rough boundary condition, the non-coaxial material response and the boundary constraint work jointly to cause cross-shape double shear bands. Local analyses indicate the DEM packings inside the shear band(s) undergo extensive shear deformation, fabric evolution as well as particle rotation, and may reach the critical state, while those outside the shear band(s) experience only mild deformation with negligible fabric evolution and particle rotation.

(vi) The multiscale modeling approach is further applied to solve geotechnical engineering problems including retaining wall, footing, and cavity expansion. The method is competitive to calculate passive/active lateral earth pressure coefficients, bearing capacity and cavity pressure compared with traditional analytical and numerical methods. Complicated shear localization patterns can also be captured and predicted using this method due to its natural incorporation of material nonlinearity and plasticity. The merit of the method is that it can offer multiscale perspectives to the classical problems.