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The shear strength of granular materials has been found to increase nonlinearly with particle asphericity before reaching a steady value independent of particle asphericity. Although the origin of shear strength has been extensively studied, the underlying mechanism of its nonlinear dependency on particle shape remains unclear. In this study, we present a microscopic investigation of shape-dependent shear strength from the perspective of particle dynamics. A series of numerical simple shear tests on assemblies of ellipsoids with different aspect ratios are performed using the discrete element method. It is confirmed that the power-law scaling in nonlocal granular rheology is still valid for granular materials composed of non-spherical particles, such that the macroscopic shear strength and microscopic dynamics can be bridged using granular temperature. Analogous to other amorphous solids, granular materials with higher granular temperature are much softer and exhibiting less resistance to shear. The statistics of the clusters of the particles with higher granular temperature indicate that granular systems with different particle shapes showing different collective motion patterns. We further explore the coupling between rotational and translational particle dynamics and their long-range correlations. The macroscopic shear strength shows a clear monotonic relation with the intrinsic length scale reflecting long-range dynamic correlations. Finally, we propose a picture illustrating the negative feedback mechanism between particle rolling and sliding, which leads to the nonlinear increase and steady value of shear strength with particle asphericity. Our finding may shed light not only on the particle shape effects, but also on the fundamental understanding of the microscopic origin of shear strength of granular materials.

The multi-scale characteristics of particle morphology, including the overall form, local roundness and surface roughness, affect the critical state behavior of sands and should be considered in modern critical state-based continuum constitutive modeling. Despite extensive experimental and numerical studies, no consensus has been reached as to how particle morphology may quantitatively dictate the critical state response of sands. This study presents a numerical investigation based on discrete element method (DEM) in an attempt to address this outstanding issue. Five DEM samples of uniformly graded sands consisting of realistic shape clumps and ideal spheres of different mass proportions are prepared and subjected to conventional drained and undrained triaxial compression under different initial void ratios and stress states. A 3D overall regularity (OR) index is adopted to quantify both the overall form and local roundness characteristics of these assemblies. It is shown that this shape parameter OR may effectively help to elucidate the correlation between mechanical properties, especially the critical state behavior of sand and particle shape, and has a great potential for incorporation into the framework of anisotropic critical state theory for constitutive modeling of sand behavior. The study helps to advance our cross-scale understanding of microscopic grain-scale morphology information in relation to macroscopic soil behavior.

This paper presents a novel computational-geometry-based approach to generating random packing of complex-shaped 3D particles with quantitatively controlled sizes and shapes for discrete modeling of granular materials. The proposed method consists of the following five essential steps: (1) partitioning of the packing domain into a prescribed number of random polyhedrons with desired sizes and form-scale shapes using the constrained Voronoi tessellation; (2) extraction of key points from the edges and facets of each polyhedron; (3) construction of a freeform curve network in each polyhedron based on Bezier curve fitting; (4) generation of solid particles with smooth, convex surfaces using the biharmonic-based surface interpolation of the constructed network; and (5) creation of concavity by superimposing spherical harmonic-based random noise. To ensure that the obtained shape descriptors (e.g., the elongation, flatness, roundness and convexity ratio) match the hypothesized values, an inverse Monte Carlo algorithm is employed to iteratively fine-tune the control parameters during particle generation. The ability of the proposed approach to generate granular particles with the desired geometric properties and packing is demonstrated through several examples. This study paves a viable pathway for realistic modeling of granular media pertaining to various engineering and industrial processes.

The at-rest coefficient of lateral pressure, $$K_0$$ , is a critical macroscopic parameter for evaluating stress transmission in granular media for engineering practice. This paper revisits the microscopic origin of $$K_0$$ and its corresponding underlying physics based on micromechanics-based theories and numerical simulations, with a focus placed on the effect of particle shape. Two typical kinds of distortion (elongation and blockiness) in particle shape are considered, modeled by ellipsoids and superballs in the discrete element method. One-dimensional compression tests are performed on numerical specimens with dense and loose initial states for different particle shapes. An analytical relationship between $$K_0$$ and anisotropy of fabric measures (i.e., contact normal, contact force, and shape-related anisotropy) is established within the stress-force-fabric framework. It is found that the analytical $$K_0$$ is consistent with the measured one directly from the simulation regardless of particle shape, verifying a well-established relationship between $$K_0$$ and fabric. It is further found that contact force partition of $$K_0$$ plays the most prominent role in $$K_0$$ compared to contact normal and shape-related partitions. Results also reveal the different influence of shape distortion on $$K_0$$ and the corresponding mechanical properties related to $$K_0$$ , such as void ratio, mobilized friction angle, and coordination number. More specifically, $$K_0$$ has a ‘W’-shape relationship with elongation for dense ellipsoids and an ‘M’-shape relationship with blockiness for superballs.

The shearing behaviour of reproduced flat LBS grains artificially bonded with ordinary Portland cement (OPC) and plaster of Paris (PP) was examined using micromechanical experiments. Monotonic shearing tests showed a distinct variation in the load–displacement relationship at low, medium and high normal loads, and a nonlinear shear strength envelope was proposed. For OPC-bonded sand grains, a brittle–ductile transition at 20–30 N normal load was observed and three breakage mechanisms in shearing (chipping, shear cracks and crushing) were distinguished in accordance with the changes in the load–displacement curves. OPC-bonded sands showed a predominant dilation at lower normal loads, whereas PP-bonded sands were highly compressive. Based on previously published works using element-scale tests, a new mechanism for dilation under micromechanical testing was proposed in the study. Cyclic shearing tests were conducted on OPC-bonded sands, and the effects of increased displacement amplitude and normal load were highlighted.

The flow direction is generally different from the gravity direction in geotechnical structures or slopes, the effect of which during suffusion remains unclear. This paper presents a coupled computational fluid dynamics and discrete element method approach to simulate the particle–fluid interaction relevant to this problem. The CFD-DEM approach is first benchmarked by a classic granular system problem, which is then used to investigate the characteristics of suffusion and its impact on the mechanical behavior. Five different angles between gravity and seepage directions for gap-graded soils with two fines contents are examined. Both the macroscopic and microscopic characteristics during suffusion and triaxial loading tests are analyzed. The direction angle is found to play a significant role affecting the erosion process and the mechanical consequence of soils. The results show that the greater the angle is, the harder it is for suffusion to occur and continue.

We present a study on compaction band in a high-porosity limestone (Tuffeau de Maastricht) based on comparison and analysis of X-ray tomography observations and computational multiscale simulations. We employ a hierarchical multiscale approach coupling the finite element method (FEM) with the discrete element method (DEM) to simulate the formation of compaction bands in Tuffeau de Maastricht. A high-porosity RVE is prepared according to X-ray tomography observations of material microstructure, and its grain-scale parameters are calibrated by data from laboratory isotropic compression and triaxial compression tests. Triaxial compression tests are simulated by FEM as a boundary value problem to observe compaction bands. The generated RVE is embedded into each integration point of the FE mesh, receiving displacement gradient as DEM boundary conditions, and is solved accordingly to produce the required mechanical responses for FEM computation without assuming phenomenological constitutive relations. The simulated global mechanical responses of the triaxial tests are found to show qualitative agreement with the experimental data. The evolution of compaction band patterns in the simulation matches remarkably well with the experimental observations in terms of fields of porosity and incremental strains. Both show two compaction fronts initiating from the two ends of the specimen and propagating toward the middle. By virtue of the multiscale approach, useful microstructural information is further extracted from the simulations to offer cross-scale insights into compaction bands. The study confirms that significant debonding accompanied by collapse of macropores and grain rearrangements is the major microstructural mechanisms causing the formation of compaction bands in high-porosity Tuffeau de Maastricht.

We present a multiscale investigation on the initiation and development of compaction bands in high-porosity sandstones based on an innovative hierarchical multiscale approach. This approach couples the finite element method and the discrete element method (DEM) to offer direct, rigorous linking of the microscopic origins and mechanisms with complex macroscopic phenomena observed in granular rocks such as strain localization and failure. To simulate compaction band in granular cementitious sandstone, we adopt a bonded contact model with normal and tangential interparticle cohesions in the DEM and propose a dual-porosity structure consisting of macro-pores and interstitial voids for the representative volume element to mimic the typical meso-structure of high-porosity sandstones. In the absence of particle crushing, our multiscale analyses identify debonding and pore collapses as two major contributors to the formation of compaction bands. The critical pressures predicted by our simulations, corresponding to surges of debonding and pore collapse events, agree well with the estimations from field data. The occurrence patterns of compaction band are found closely related to specimen heterogeneity, porosity and confining pressure. Other deformation band patterns, including shear-enhanced compaction bands and compactive shear bands, were also observed under relatively low confining pressure conditions with a rough threshold at $$0.55P^{*}$$ ( $$P^{*}$$ is the critical pressure) on the failure envelop. Key microscopic characteristics attributable to the occurrence of these various deformation patterns, including fabric anisotropy, particle rotation, debonding and pore collapse, are examined. Shear-enhanced compaction bands and pure compaction bands bear many similarities in terms of these microscopic characteristics, whereas both differ substantially from compactive shear bands.

Strength anisotropy is an important soil behavior which is closely related to the microstructural characteristics in soil. Proper consideration of the microscopic properties of a soil is key to accurate description of its strength anisotropy. This paper presents a failure criterion for cross-anisotropic soils based on the Spatially Mobilized Plane (SMP) criterion. In the new criterion, the shear-normal stress ratio defined in the SMP is related to the relative orientation of the loading direction with respect to the axes of material anisotropy through a microstructure-based tensor. The formulation includes only two parameters which can be easily calibrated by conventional triaixal tests. By comparison with tests data, the criterion is shown to offer good characterization of the strength anisotropy for a variety of geomaterials with cross-anisotropy.