The study of macroscopic discrete granular materials holds significance in hydraulic engineering, geotechnical engineering, as well as road and bridge engineering. Its foundational scientific exploration bears profound theoretical implications and is of pivotal practical value to engineering endeavors. Within the realm of engineering construction, issues such as dam breakages, earth-rock dam damage, and geological disasters involving loose particles pose substantial threats to the safety of both national livelihoods and property. Thus, delving into the examination of the structural stability of granular materials at the mesoscopic scale becomes an imperative pursuit. In this study, the topological structure of granular materials is identified and segmented based on image processing techniques, and the relationship between the compressive capacity of polygonal structures and the number of polygonal sides is studied. The redundancy function is defined to evaluate the structural stability of granular materials. In addition, the definition of structure tensor is introduced, and redundancy and structure tensor are applied to the study of biaxial compression of shale materials. The research results contribute to improving engineering safety and have guiding merits for the research and application of granular materials. Future work could focus on extending these methods to other types of granular materials and exploring their behavior under different loading conditions. (c) 2025 Published by Elsevier B.V. on behalf of Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences.

This paper presents a mathematical description of the failure law of anisotropic properties from the following three aspects. Firstly, a generalized nonlinear failure criterion, revision Matsuoka-Nakai-Lade-Duncan (RMNLD) criterion, is proposed, which can describe a series of failure curves via von Mises and spatial mobilized plane (SMP) criterion on the partial plane. Secondly, a new stress tensor with a fabric tensor is proposed to describe the particle arrangement characteristics of rock or soil materials in 3D space, and it can be adapted to express the anisotropic RMNLD. Finally, the mapping relationship from anisotropic RMNLD to isotropic von Mises criterion was established on the deviatoric plane. The validity and feasibility of the proposed anisotropic RMNLD criterion and stress transformation method are experimentally verified.

This study investigates the influence of micro -scale entities such as inherent and induced fabric anisotropy on the stress-strain behaviour of granular assemblies. In tandem with this exploration, our objective is to formulate a novel correlation that quantifies the evolution of fabric tensor across diverse loading paths. This correlation can be introduced to enhance the micro -mechanical insights in conventional constitutive models. Employing the Discrete Element Method (DEM), we simulate the drained and undrained responses of 680 transversely isotropic particulate assemblies with diverse initial fabrics and particle Aspect Ratio (AR) under true triaxial loading conditions. We consider a second -order fabric tensor based on inter -particle contact orientations to trace fabric evolution during loading. To account for fluid-solid interaction under undrained conditions, we adopted the DEM-Coupled Fluid Method (CFM). The simulation results highlight the significant influence of the Lode angle, particle shape and initial fabric on the stress-strain behaviour of granular materials, with fabric evolution primarily affected by the stress state, void ratio and particle AR. Lastly, we propose a new correlation for the quantification of the fabric tensor using a multi -layer feed -forward neural network. The satisfactory performance of the suggested correlation is demonstrated through a comparison between DEM data and predicted fabric tensor values.

The macroscopic mechanical behavior of granular materials is closely related to the fabric anisotropy and contact force anisotropy. In order to investigate the microevolution of fabric and force anisotropy of rock masses containing non-coplanar intermittent joints under direct shear loading, this paper establishes a numerical model using the particle flow code (PFC) based on the distinct element method (DEM) and investigates the effects of non-coplanar intermittent joints on the evolutions in the fabric and force anisotropy and the distributions of contact forces of rock specimens by setting up specimens with different ligament angles of joints. Meanwhile, the shear strength, deformation characteristics and failure mode, energy dissipation were analyzed to deepen the understanding of the macroscopic mechanical behavior of the specimens from the microscopic mechanism. Three anisotropic tensors aijc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${a}_{ij}{c}$$\end{document}, aijn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${a}_{ij}{n}$$\end{document} and aijt\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${a}_{ij}{t}$$\end{document} are defined to characterize the anisotropic behavior of the granular materials which can show the evolution law of fabric and mechanical anisotropy of the system under direct shear load. The findings indicate that the degree of fabric anisotropy increases with increasing ligament, and the length of the load side significantly influences the initial mechanical anisotropy of the specimen. Concurrently, a rise in the ligament angle impedes the progression of anisotropy within the specimen, leading to a substantial reduction in the macroscopic mechanical strength of the rock.

A multiscale method is presented to develop a constitutive model for anisotropic soils in a three-dimensional (3D) stress state. A fabric tensor and its evolution, which quantify the particle arrangement at the microscale, are adopted to describe the effects of the inherent and induced anisotropy on the mechanical behaviors at the macroscale. Using two steps of stress mapping, the deformation and failure of anisotropic soil under the 3D stress state are equivalent to those of isotropic soil under the triaxial compression stress state. A series of discrete element method (DEM) simulations are conducted to preliminarily verify this equivalence. Based on the above method, the obtained anisotropic yield surface is continuous and smooth. Then, a fabric evolution law is established according to the DEM simulation results. Compared with the rotational hardening law, the fabric evolution law can also make the yield surface rotate during the loading process, and it can grasp the microscopic mechanism of soil deformation. As an example, an anisotropic modified Cam-clay model is developed, and its performance validates the ability of the proposed method to account for the effect of soil anisotropy.

Various constitutive formulations have been developed over the years to reproduce the cyclic resistance of sands. A common challenge for existing models is the accurate simulation of the cyclic strength of sands for a wide range of initial conditions and different cyclic stress levels when adopting a single calibration. Many liquefaction models tend to overpredict the resistance of the soil under large-amplitude loading, while underestimating the strength at low-amplitude cyclic shearing. This manifests itself in slopes of simulated cyclic resistance ratio curves (CRR-curves) which are steeper than experimental studies indicate. This paper provides a discussion on the effects of large-amplitude and low-amplitude cyclic shearing on a granular material based on micromechanical and experimental investigations presented in the literature. A constitutive model with a shear-history threshold is proposed, which accounts for a shift of the apparent angle of phase transformation under cyclic loading. In addition, a novel expression for a deviatoric fabric tensor is introduced to describe the evolution of shear-induced fabric anisotropy while a soil is dilating and contracting. Combining these two features in one formulation within the bounding surface plasticity framework enables an accurate prediction of cyclic strength of sands under a wide range of cyclic stress ratios.

Characterisation of the permeability of soils is of practical importance and, for cohesionless or granular soils, it can be predicted from the void ratio and the particle size distribution (PSD). However, the effect of fabric anisotropy on the permeability is rarely discussed. Restricting consideration to granular (cohesionless) soil, this study combines a variety of numerical methods to investigate (1) how the anisotropy of the permeability evolves as the soil fabric anisotropy evolves in triaxial deformation and (2) establish a link between the anisotropy of the permeability and the fabric anisotropy. The Discrete Element Method (DEM) was employed to create linearly graded virtual samples of spheres (Cu of 1 to 2). Initially isotropic sphere packings were subjected to triaxial compression or triaxial extension up to 30% of absolute axial strain to induce an anisotropic fabric. Pore Network Models (PNMs) present a computationally efficient option for simulation of flow through the pore space. A PNM models fluid flow between pores (nodes) connected by pipes ( edges) whose geometry is defined by the topology of the connected pores and the mass balance equation is solved at each pore. After demonstrating the accuracy of the PNM framework adopted here, this contribution presents data from PNM simulations that used the positions of individual particles in the sheared spherical packings as input data. The fabric and permeability anisotropies during triaxial shear deformation were compared at axial strain intervals of 1%. Detailed microscale analyses suggest that the anisotropy in the permeability can be attributed to an increase in the local conductance of fluid pipes in the direction of the major principal stress, which is related to the evolution of the pore topologies during the shear deformation.