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We adopt a two-dimensional granular assembly in a direct shear box to systematically investigate the role of rolling resistance during the shearing process. A discrete element method with parallel computation and a rolling friction model is utilized in this paper. The macro- and microscale responses are sensitively subjected to a change in the rolling friction. The critical-state indices are found to be linearly related to each other, and the linear relationship between the critical-state indices and the rolling friction coefficient is evidently observed. The macro- and microscopic relationships are discussed from the connections between the stress and fabric properties. For microscale behaviors, different rolling frictions can generate various magnitudes of arching effects caused by antirotation and pose different characteristics to the force chains. The algorithm related to the extraction of force chains is adopted to explain the local sustaining structures. The localization, length, number and magnitude distribution of the force chains depend on the rolling friction. The influence of the rolling resistance on the friction mobilization is evident. A transition of the force distribution from the exponential to the Gaussian distribution is observed when the rolling resistance conditions change. The strong–weak contact systems and various anisotropic parameters are utilized to characterize the mechanical and geometrical roles of rolling resistance.

This paper presents simulations of true triaxial tests on crushable granular materials. Considering both the shear and tensile fracture modes of the particle, the Mohr–Coulomb model with tension cut-off is employed as the fracture criterion of single particle. When the particle stresses satisfy the fracture criterion, three new balls are generated to replace the broken particle. The new balls overlap enough within the bounding parent sphere to obey the mass conservation law. A polydisperse assembly consisting of 7935 spheres was isotropically compressed until the desired confining pressure was reached. Then the sample with no bias in initial fabric was subjected to axial compression at a constant minor principal stress under different intermediate principal stress ratios, b. The simulated stress–strain–dilation responses were in agreement with the experimental observations. The macro–micro responses including stress–strain characteristics, fabric tensors, anisotropies, the orientation tensor and force chain characteristics were discussed in details. It is shown that volumetric responses is affected by b. The anisotropies vary with b, but a unique macro–micro linkage exists between the anisotropies and stress ratio, q / p, irrespective of the value of b. A linear relationship is found between the obliquity of $${\sigma _{1} }/{\sigma _{3} }$$ and the strength indicator ( $$\beta =\ln ({\tau _{1} }/{\tau _{3} }))$$ using the orientation tensor method.

We adopt the discrete element method with a periodic boundary to investigate the comprehensive effects of initial anisotropic consolidation derived from an initial stress ratio ( $$K_{\mathrm{c}})$$ under complex stress paths (b). Both the initial stiffness and deformation mechanisms are systematically analyzed. The dilatancy rate and the stress–dilatancy relationship depend on stress paths and $$K_{\mathrm{c}}$$ . Meanwhile, the distinction between the critical-state mechanical responses under different stress paths also depends on the initial stress ratio. The equation of the relationship between the excess friction angle and peak state parameter is conceptually given, where the coefficients are related to both the initial stress ratio and stress path. At the microscopic level, the properties of contact forces, coordination number, and anisotropies of the assemblies are discussed. The samples with different initial stress ratios exhibit different extents of distinction in terms of various coordinate numbers. The probability density functions of both contact normal and tangential forces are evidently affected by the initial stress ratio, and the effects of the initial stress ratio gradually vanish as shearing proceeds. The strong force chain networks under different conditions of $$K_{\mathrm{c}} $$ and b are explored, showing the comprehensive mechanism of force transmission. At the same strain level, the proportion and the magnitude of strong contact forces strengthen with the improvement of initial anisotropic consolidation, and the initial anisotropic consolidation can evidently improve the ability of the assemblies to cluster along the intermediate principal direction with the increase of b. Different anisotropy parameters show different sensitivities to the initial stress ratio. The fabric-based strength descriptor is linearly correlated to the stress ratio under different $$K_{\mathrm{c}} $$ conditions. The fabric and small-strain stiffness are combined to investigate the macro- and microscopic connections that are subject to inherent anisotropic consolidation as well as the intermediate stress ratio.

A method of modeling convex or concave polygonal particles is proposed. DEM simulations of shear banding in crushable and irregularly shaped granular materials are presented in this work. Numerical biaxial tests are conducted on an identical particle assembly with varied particle crushability. The particle crushing is synchronized with the development of macroscopic stress, and the evolution of particle size distribution can be characterized by fractal dimension. The shear banding pattern is sensitive to particle crushability, where one shear band is clearly visible in the uncrushable assembly and X-shaped shear bands are evident in the crushable assembly. There are fewer branches of strong force chains and weak confinement inside the shear bands, which cause the particles inside the shear bands to become vulnerable to breakage. The small fragments with larger rotation magnitudes inside the shear bands form ball-bearing to promote the formation of shear bands. While there are extensive particle breakages occurring, the ball-bearing mechanism will lubricate whole assembly. With the increase of particle crushability the shear band formation is suppressed and the shear resistance of the assembly is reduced. The porosity inside the shear bands are related to the particle crushability.

The effects of particle size ratio on the mechanical behaviors of binary mixtures are investigated using three-dimensional discrete element method. The samples with three types of particle size ratios (SR, $$\hbox {SR}=3.0$$ , 4.5 and 6.0) are prepared at the maximum packing efficiency state, which appears at 70 % of the large particle volume content. The results demonstrate that the maxima of peak deviator stress are obtained at the sample with $$\hbox {SR}=4.5$$ . The initial elastic modulus, $$E_{0}$$ , increases with increasing SR. The value of deviator stress increases with increasing SR at the softening stage, whereas an opposite trend is observed at the critical state. The evolutions of the effective particle ratio can capture the differences among the evolutions of the deviator stress of different samples during the softening stage and the critical state to some degree. In addition, different SRs generate different packing structures of the binary mixtures and have apparent influences on the force chain networks in the binary mixtures. With increasing SR, the strong force chains become stronger, and the weak force chains become weaker. The deviator stress contributed by the contacts between large particles and between large and small particles constitutes a major part of the overall deviator stress of the binary mixtures at the maximum packing efficiency state. Furthermore, the positions of the critical state lines of binary mixtures in the $$p-q$$ plane and $$v-\ln p$$ plane are sensitive to SR, and the lubrication effect of small particles in the binary mixtures is enhanced with increasing SR.

Four sets of individual-particle crushing tests were carried out on sandstone grains of different size with geometric similarity. The tensile strength was analyzed using Weibull statistics, and the size-hardening law was obtained. The experimental data also validated that the Weibull modulus is independent of the grain size. Considering both the shear and tensile fracture modes of the particle, the Mohr–Coulomb model with a tension cut-off was employed as the fracture criterion of a single particle. When the particle stresses satisfied the fracture criterion, three new fragments modeled by the ‘clump’ were generated to replace the broken particle. Nine spheres with four different sizes were released from the clump and allowed to continue crushing if the fragment stresses fulfilled the criterion again. Two polydisperse assemblies with different particle sizes but same initial fabrics were prepared. DEM simulations of triaxial shear tests with different grain sizes were carried out on the crushable granular material with varied confining pressures. The simulated stress–strain–dilation responses were in agreement with the experimental observations. The macro–micro responses of the two samples, including the stress–strain–dilation behavior, the particle crushing, and the normal contact force distribution, were discussed in detail. The cause of the size effect on the shear strength and deformation was thoroughly investigated through a variety of mechanism demonstrations and micromechanical analysis.

It is well known that particle breakage plays a critical role in the mechanical behavior of granular materials and has been a topic subject to intensive studies. This paper presents a three dimensional fracture model in the context of combined finite-discrete element method (FDEM) to simulate the breakage of irregular shaped granular materials, e.g., sands, gravels, and rockfills. In this method, each particle is discretized into a finite element mesh. The potential fracture paths are represented by pre-inserted non-thickness cohesive interface elements with a progressive damage model. The Mohr–Coulomb model with tension cut-off is employed as the damage initiation criterion to rupture the predominant failure mode at the particle scale. The particle breakage modeling using combined FDEM is validated by the qualitative agreement between the results of simulated single particle crushing tests and those obtained from laboratory tests and prior DEM simulations. A comprehensive numerical triaxial tests are carried out on both the unbreakable and breakable particle assemblies with varied confining pressure and particle crushability. The simulated stress–strain–dilation responses of breakable granular assembly are qualitatively in good agreement with the experimental observations. The effects of particle breakage on the compressibility, shear strength, volumetric response of the fairly dense breakable granular assembly are thoroughly investigated through a variety of mechanism demonstrations and micromechanical analysis. This paper also reports the energy input and dissipation behavior and its relation to the mechanical response.