The breakage phenomenon has gained attention from geotechnical and mining engineers primarily due to its pivotal influence on the mechanical response of granular soils. Numerous researchers performed laboratory tests on crushable soils and incorporated the corresponding effects into numerical simulations. A systematic review of various studies is crucial for gaining insight into the current state of knowledge and for illuminating the required developments for upcoming research projects. The current state-of-the-art study summarizes both experimental evidence and numerical approaches, particularly focusing on discrete element simulations and constitutive models used to describe the behavior of crushable soils. The review begins by exploring particle breakage quantification, delving into experimental evidence to elucidate its influence on the mechanical behavior of granular soils, and examining the factors that affect the breakage phenomenon. In this context, the accuracy of various indices in estimating the extent of breakage has been assessed through ten series of experiments conducted on different crushable soils. Furthermore, alternative breakage indices are suggested for constitutive models to track the evolution of particle crushing under continuous shearing. Regarding numerical modeling, the review covers different approaches using the discrete element method (DEM) for simulating the behavior of crushable particulate media, discussing the advantages and disadvantages of each approach. Additionally, different families of constitutive models, including elastoplasticity, hypoplasticity, and thermodynamically based approaches, are analyzed. The performance of one model from each group is evaluated in simulating the response of Tacheng rockfill material under drained triaxial tests. Finally, new insights into the development of constitutive models and areas requiring further investigation utilizing DEM have been highlighted.

An appropriate interface constitutive model is crucial to the simulation of soil-structure interface behavior. Currently, most models are only capable of describing the mechanical properties of rough interface. However, they are unable to simultaneously account for the effects of surface roughness and particle breakage. This study proposes an elastoplastic interface constitutive model considering the effects of normal stress, relative density, particle breakage, and surface roughness. It describes the variations of critical void ratio and critical stress ratio with normalized surface roughness by exponential functions. Change in critical void ratio caused by particle breakage is denoted by input work. An expression of the critical state line and a modified dilatancy function are derived based on the state-dependent dilatancy theory, uniformly describing the influences of relative density, particle breakage, normal stress, and surface roughness. The yield and hardening functions are introduced by including the plastic shear displacement as the hardening parameter based on the Mohr-Coulomb criterion. Finally, experimental data from the literature are utilized to validate the accuracy of the proposed model for various materials under different conditions.

One of the main problems of carbonate sands is the fragile nature of particles and their susceptibility to breakage. Carbonate sands are affected by volumetric strain even at low stress levels, which is not the case with silicate sands. By defining a simple breakage model, the current study develops an elastoplastic critical state constitutive model that considers the impact of particle breakage on the mechanical behavior of carbonate sands. The particle breakage model depends on mean effective stress and critical breakage stress, which is assumed to correspond with the precompression pressure of soil in the oedometer test. In the proposed model, critical state line movement with the breakage parameter (alpha) considers the particle breakage effect. Based on the unified clay and sand model (CASM), a novel dynamic yield surface with a shape parameter affected by particle breaking has been created. Certain modifications are made to the modified Cam-Clay stress dilatancy to predict the behavior of carbonate sand. The current model has only ten parameters that simulate the carbonate sands' behavior even at high-stress levels without any breakage test. Experimental data with different soil densities, loading stress paths, and stress levels were compared with the model, and the results demonstrated satisfactory conformance.

Crushable porous soils, such as volcanic pumice, are distributed worldwide and cause a variety of engineering problems, such as slope hazards. The mechanical properties of these soils are complicated by their high compressibility due to voids in the particles themselves and changes in the soil gradation due to particle crushing. They are usually classified as problematic soils and discussed separately from ordinary granular soils, and their behaviour is not systematically understood. In this study, isotropic and triaxial compression tests were conducted on artificial pumice in order to determine the relationship between the mechanical properties and the particle crushing of crushable porous granular materials. The results showed that the mechanical behaviour of artificial pumice, representative of such materials, can be explained using a particle crushing index, which is related to the degree of efficient packing. Furthermore, a new critical state surface equation was proposed. It is applicable to crushable porous granular materials and shows the potential for expressing the critical state or isotropic consolidation state of such materials as a single surface in a three-dimensional space consisting of three axes: the stress - void ratio - crushing index. The validity of this new equation was confirmed by applying it to natural pumice from previous research. (c) 2025 Production and hosting by Elsevier B.V. on behalf of The Japanese Geotechnical Society. This is an open access article under the CC BY- NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

The effects of confining pressure and particle breakage on the mechanical behavior of tailings were investigated using the discrete-element method to simulate conventional triaxial tests. The particle breakage was simulated using the octahedral shear stress breakage criterion and 14 Apollonian fragments replacement method. The macroscopic behavior of tailings revealed that the peak shear stress ratio is sensitive to confining pressure and the critical shear stress ratio is less sensitive to particle breakage. Confining pressure and particle breakage affect shear expansion, leading to changes in shear damage patterns. The quantitative study shows that particle breakage is the main factor influencing the nonlinear variation of the tailing strength. However, the influence proportion of particle breakage is gradually decreasing with the increase in the confining pressure. Microscopic analysis reveals a positive correlation between the overall anisotropy and the shear stress ratio, with the anisotropy of the normal contact force distribution contributing the most. The variation of the overall anisotropy is caused by the variation of the contact state, in which the sliding contact state is the main influencing factor.

Due to the widespread prevalence of respiratory diseases such as COVID-19 and H1N1, the use of disposable masks has increased significantly. Consequently, the environmental issues arising from their accumulation have become increasingly severe. This study, therefore, aims to investigate the potential of using masks as soil reinforcement materials. This study conducted triaxial and seepage tests on mask-calcareous sand mixtures with varying ratios to examine the effects of mask content on the strength, modulus, particle fragmentation, and permeability coefficient of calcareous sand, as well as the influence of different mask sizes on shear strength and shear dilation. The results demonstrate that with an increase in mask content, the peak stress ratio of the mask-calcareous sand mixture increases by 4% per level, and the internal friction angle rises by approximately 1.6% per level. Conversely, water permeability and shear swelling are reduced, and particle loss decreases by over 70%. The reinforcing effect of the mask is attributed to the high friction between the mask and the calcareous sand at the contact interface, which restricts the movement of soil particles during deformation, thereby enhancing the overall strength of the mixture. Among the three mask sizes, the smallest mask-calcareous sand mixture exhibited the greatest improvement in shear strength, and the shear shrinkage effect was more pronounced. This indicates that particle size also significantly influences the mechanical properties of the mixtures. The reinforcing effect of the mask on the soil results from the high friction at the interface between the mask and the calcareous sand. When the soil deforms, the mask enhances the overall strength of the mixture by restricting the movement of soil particles. Considering the impact of masks on the performance of calcareous sand, it can be concluded that the optimal mass content of masks is 0.3%. This study offers a new perspective on the reuse of discarded masks in civil engineering applications.

The distinct particle breakage characteristics of calcareous sand can induce extra settlement in calcareous sand foundations, posing a significant challenge to the safety of island and reef engineering. To explore the particle breakage, settlement characteristics and internal stress variations of calcareous sand foundations, the laboratory loading tests for calcareous sand foundations with different particle gradations were conducted. Particle Image Velocimetry (PIV) technology and tactile pressure sensor systems were also utilized. The study reveals that the tested calcareous sand foundations have differential settlements subjected to external loading, which has a strong relationship with the particle breakage. It is found that the nonuniform internal stresses between the sand particles can induce different degrees of the particle breakage, which in turn changes internal stresses and redistribution of particle positions in calcareous sands, and further causes the uneven settlement of the foundation. The degree of uneven settlement in calcareous sand foundations increases with an increase of external load and decreases with an increase of the coefficient of uniformity Cu for calcareous sands. During creep, the vertical and lateral stresses on the inter-particle contacts within the calcareous sand foundation exhibit an overall trend of decrease in weak forces and increase in strong forces. This continuous increase in strong forces results in a growth of creep deformation in calcareous sand foundation, while the degree of differential settlement in the foundation decreases with the progression of creep.

Particle shape and local breakage significantly affect the deformation characteristics of crushable granular materials. However, in the existing constitutive model research, there is less introduction of particle shape on particle breakage. A quantitative parameter for the three-dimensional particle shape (Average spherical modulus GM\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{G_{M}}$$\end{document}) is proposed in this study. Combined with GM\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{G_{M}}$$\end{document}, the triaxial compression test of granular materials with different particle shapes was carried out, and the particle size distribution before and after the test was determined. The results indicate that the local damage mechanism governs the macroscopic deformation behavior of granular materials, as influenced by the particle gradation of the samples before and after the triaxial compression test. Based on these findings, a binary medium model with a friction element weakening factor is proposed. This model incorporates the effects of particle shape and breakage behavior, significantly enhancing its calculation accuracy. Experimental results demonstrate that the model effectively predicts the deformation of crushable granular materials, accounting for particle shape.

Particle breakage is an important factor affecting the mechanical properties of granular materials. In this study, the influence of particle breakage under different fine particle content is investigated by DEM. Through 3D scanning and Voronoi tessellations, the breakable particle model with realistic shape is constructed. A series of confined cyclic loading tests were performed at different fine particle content. Then, the particle breakage characteristics, including the degree of breakage and the breakage pattern, were evaluated. In addition, the compaction deformation was analyzed according to the evolution of porosity. Finally, the influence mechanism of particle breakage is explained from two perspectives of particle contact and particle motion. On the one hand, with the increase of fine particle content, the number of contacts on the coarse particles is increasing. Hence, the coarse particles can withstand greater forces without breaking. On the other hand, the displacement of coarse particles and the porosity decrement have very similar evolution curve. This indicates that the Z-axis displacement of coarse particles can directly reflect the variation of sample porosity. In addition, particle breakage has little effect on particle rotation. The effect of particle breakage on porosity is mainly realized through the effect of particle translation rather than particle rotation.

The plastic strain of calcareous sand is related to its stress path and particle breakage, rendering the hardening process complex. An expression for the stress-path-dependence factor was developed by analyzing the variations in plastic strain across different initial void ratios. A stress-path-independent hardening parameter was derived from the modified plastic work and was subsequently validated. Constant-proportion loading tests on calcareous sands confirmed the applicability of this hardening model. The results indicated that under isotropic compression, the plastic volumetric strain increased with increasing average effective stress, albeit at a decreasing growth rate. A positive linear relationship was observed between the volumetric strain modulus and relative breakage index. The proposed hardening parameter effectively captured the particle breakage and stress path effects in calcareous sand and was validated through theoretical calculations and laboratory tests, offering valuable insights into the mechanical behavior of fragile granular soils.