Testing and Modeling on Particle Breakage for Granular Soils

The special collection on Testing and Modeling on Particle Breakage for Granular Soils is available in the ASCE Library (https://ascelibrary.org/ijgnai/testing_modeling_granular_soils).

Coarse grains, such as calcareous sands, angular rockfills, and ballast, are prone to fracture under higher stress or larger displacements. This phenomenon is called particle breakage, a hot topic in geotechnics that has been widely and extensively studied (Einav 2007; Bolton et al. 2008; Liu and Zou 2013; Xiao and Liu 2017; Cil et al. 2020; Xiao et al. 2020a). Particle breakage could greatly influence the soil's mechanical properties (e.g., strength, dilatancy, and deformation) and the settlement and stability of piles, rockfill dams, and railway. Indeed, many studies on the discrete nature of granular geomaterials and particle breakage have been published in the International Journal of Geomechanics, whose topics cover geomechanical applications of discrete element modeling or combined finite–discrete element method (Lobo-Guerrero et al. 2006; Abbas et al. 2007; Camusso and Barla 2009; Indraratna et al. 2010; O’Sullivan 2011; Barla et al. 2012b; Graziani et al. 2012; Mahabadi et al. 2012; Li et al. 2016; Vallejos et al. 2017; Zhao et al. 2019; Ngo and Indraratna 2020), testing and modeling of rock fracture or particle breakage (Mahabadi et al. 2012; Villeneuve et al. 2012; Kong et al. 2016; Jia et al. 2017; Yu 2017; Mao et al. 2018; Wei et al. 2018; Jia et al. 2019; Liu et al. 2020b), and continuum-based modeling of particle breakage (Varadarajan et al. 2006; Desai et al. 2011; Dolezalova and Hladik 2011; Elia et al. 2011; Barla et al. 2012a; Indraratna et al. 2012; Xiao et al. 2012; Fu et al. 2014; Honkanadavar and Sharma 2014; Xiao et al. 2016; Liu and Gao 2017; Xiao et al. 2017; Xiao and Desai 2019). Some of them have even been included in special issues (e.g., Material and Computer Modeling, Advances in Modeling Rock Engineering Problems, etc.). Herein, this special collection dives into the specific topic of particle breakage and covers studies through experimental investigations, theoretical analyses, and numerical simulations. All the presented papers in this special collection are the authors' original works and have undergone rigorous peer reviews.

Laboratory testing is a significant way to investigate the strength distribution, stress–dilatancy relationship, and deformation of granular soils undergoing particle breakage. There are 11 papers that present experimental investigations on crushable soils. Xiao et al. (2019) investigated the influence of particle size (e.g., 2.5, 5, and 10 mm) and acidic erosion (pH = 2, 4, and 7 with immersion days of 5, 10, and 15, respectively) on the tensile strength, characteristic stress (corresponding to 37% particles survived), and surviving probability (i.e., the ratio of the number of uncrushed particles to the number of total particles) of limestone through a series of single-grain crushing tests. The Weibull distribution was adopted to describe the relationship between particle tensile strength and particle size at different pH values and immersion days. The predictions by the proposed function of the peak force considering the effect of particle size and acidic erosion agreed well with the observed values. Chen et al. (2020) studied the combined behavior of grain crushing and flooding of a crushable soil through a series of one-dimensional compression tests, including constant rate of strain tests and multistage loading oedometer tests, and microhardness tests under dry and saturated conditions. The saturated and flooded specimens possessed the same stress–strain relationship but different stress relaxation coefficients. The addition of water weakened microhardness and strength of particles, resulting in an increase in particle breakage and particle surface corrugation. Two hyperbolic functions between the plastic work and the particle breakage extent were established for the dry and saturated/flooded conditions, respectively. Xiao et al. (2020b) investigated the effect of loading duration, vertical stress, and fines content on the volumetric strain, particle size distribution (PSD), and particle breakage of carbonate sands through a series of one-dimensional compression tests. Particle breakage increased with decreasing fines content and increasing vertical stress and loading duration. Notably, the loading duration significantly influenced the particle breakage within 100 min.

Zhang and Luo (2020) carried out a series of drained triaxial compression tests on calcareous sand and found out that the dilatancy, stress–strain relationship, and critical state were significantly affected by particle breakage. A modified dilatancy equation considering particle breakage was proposed to describe the stress–dilatancy behavior of calcareous sand. Yu (2019) carried out a series of isotropic compression tests and drained and undrained triaxial tests to investigate the effects of particle breakage on the compression and shearing behaviors of precrushed coral sands. Isotropic compression tests showed that the compression of precrushed coral sands increased with increasing particle breakage. An increase in particle breakage from drained and undrained triaxial tests could result in a decrease in stress ratio, peak-state friction angle, maximum dilatancy angle, and void ratio, and an increase in volumetric strain or excess pore water pressure. The critical state line (CSL) in the compression plane moved downward and rotated counterclockwise as the particle breakage increased, which is in line with the findings by Xiao et al. (2016). Wu et al. (2020) introduced the compression and particle breakage characteristics of silica sand through a series of high stress–level monotonic and cyclic loadings with different stress paths (i.e., isotropic compression, anisotropic compression, and constant-mean effective stress shearing). It was found that the degree of particle breakage was larger for anisotropic compression than for isotropic compression and the particle breakage increased as the cyclic loading number increased for a given stress path. The relative breakage under different loading conditions well correlated with the plastic work per unit volume. Meanwhile, the loading mode and drainage condition could influence this relationship between the relative breakage and plastic work. Liu et al. (2020a) carried out a series of drained and undrained triaxial compression tests on two types of calcareous sands (different PSDs) under monotonic, cyclic, and creep loading conditions. The peak strength increased and the axial strain corresponding to the peak strength decreased as the confining pressure increased in the monotonic drained triaxial tests. Increasing the stress level, cyclic numbers, and grain size resulted in more particle breakage, similar to the work by Wu et al. (2020). A unique relationship between the breakage extent and the total input energy per unit volume was established for the calcareous sand with a given PSD regardless of the loading conditions, which is slightly different from that of the findings by Wu et al. (2020). Ning et al. (2020) studied the stress–strain behavior, critical state, and gradation evolution of rockfill materials influenced by particle breakage through a series of large-scale triaxial tests under conditions of constant lateral stress, constant mean effective stress, and constant vertical stress, respectively. The CSL in the stress plane was described by a power function, while the CSL in the compression plane was depicted by a linear function. A unique relationship between the critical-state void ratio, critical-state mean effective stress, and grading state index was found for this rockfill material, which is independent of stress path. Pan et al. (2020) studied the effects of intermediate principal stress ratio on the strength, dilatancy, and particle breakage of the rockfill material through a series of large-scale true triaxial tests. It was found that the internal friction angle and particle breakage at a given minor principal stress increased with increasing intermediate principal stress ratio. Increasing minor principal stress at a given intermediate principal stress ratio resulted in a decrease in the internal friction angle but an increase in particle breakage.

In addition, two new methods were proposed to quantify the particle breakage in crushable soils under loading. Mao et al. (2020) provided an image analysis approach to evaluate the location and extent of particle breakage below a flat-ended pile tip by black-coating particles. The assembled gray images in different positions can form a quasi-stereoscopic graph that was adopted to evaluate the particle crushing below the pile tip based on the change of grayscale values. Zheng et al. (2020) utilized X-ray computed tomography to obtain evolutions of particle breakage and particle shape of crushable sands through a series of one-dimensional compression tests. The particle size was better described by the intermediate Feret diameter and the particle shape was well characterized by elongation, flatness, and sphericity. The smaller fragments of crushed sand had higher elongation, flatness, and convexity.

Numerical simulation is an effective way to investigate micro- and macroscale perspectives for coarse grains. Two papers discussed the characteristics of grain crushing of coarse grains using numerical analysis. Yao et al. (2020) studied the shear characteristics of rockfill–structure interfaces by the combined finite–discrete element method (FDEM) with irregularly shaped particles represented by polyhedrons. The proposed method provided comprehensive details of the macroscopic and microscopic responses on the shear-induced phenomena of rockfill–structure interfaces, and these responses were influenced by surface roughness. The macroscopic behaviors (such as the strain softening and volumetric dilation behaviors of the rough interface and the strain hardening and volumetric contraction behaviors of the smooth interface) strongly correlated with the microstructural anisotropy evolution. Ciantia and O’Sullivan (2020) proposed a method to modify the state parameter for crushable soils in the critical state plane that was formed by introducing the grading state index into the compression plane. The employment of this revised state parameter could overcome the limitation that was found during the estimation of the liquefaction susceptibility of crushable soils based on the common state parameter in the compression plane. In addition, the peak-state friction angle, the excess friction angle (i.e., the difference between the peak-state friction angle and the critical-state friction angle), and the maximum dilatancy angle can be uniquely correlated with this revised state parameter. Furthermore, two papers discussed the grain crushing by combining experimental and numerical analyses. Li et al. (2020) introduced a new method combining hammer weight and drop height to evaluate the efficiency of dynamic compaction considering particle breakage through a series of large-scale dynamic compaction tests and numerical simulations. The effect of the drop height was overestimated through tamping energy or tamping momentum. Indraratna et al. (2020) investigated the effect of recycled rubber energy-absorbing mats (REAMs) on the deformation and degradation responses of railway ballast through a series of large-scale dynamic triaxial tests and a series of numerical simulations by the coupled discrete element method–finite difference method (DEM–FDM). The REAMs effectively reduced the particle breakage of ballast. The coupled DEM–FDM model could well capture the deformation and degradation of ballast improved by REAMs under cyclic loading, implying that the micromechanics of ballast improved by REAMs can be explored using the coupled DEM–FEM method.

Two papers focused on the establishment of a constitutive model for crushable soils incorporating particle breakage. Bauer and Safikhani (2020) proposed an extended micropolar hypoplastic model by incorporating the mean grain diameter and solid hardness to investigate the effect of particle breakage on the mechanical responses. The predictions of plane strain compression tests showed that the mean grain diameter decreased significantly in zones of shear strain localization, and the localization patterns depended on the boundary condition. Wang et al. (2020) conducted a series of drained and undrained triaxial compression tests of carbonate sand to investigate the effect of particle breakage on CSLs in the stress and compression planes. It was found that a nonlinear CSL in the stress plane correlated with the relative breakage index. A CSL in the compression plane was extended to a critical state plane (CSP) by incorporating the effect of particle breakage, which is similar to that in those studies (Liu and Zou 2013; Xiao and Liu 2017; Ciantia and O’Sullivan 2020). The evolution of particle breakage was expressed as a hyperbolic function of axial strain. A breakage state-dependent constitutive model was finally established to capture the drained and undrained stress–strain responses and the evolution of particle breakage.