Evolution Of Coordination Number Research Articles

A 3D DEM modeling of soil-rock mixture considering spatial distribution orientation of blocks

Spatial distribution orientations of blocks can cause significant errors in the discrete element model (DEM) calculation of soil-rock mixture (SRM). To avoid this error, spherical harmonic (SH) series whose harmonization degrees fixed at 15 were proposed for block reconstruction. This research refers to the case-history of a deep excavation rift valley spanning from the Mabian to Zhaojue section of the Leshan-Xichang Expressway, mainly containing moderately-weathered silty mudstone, in the Leshan City, Sichuan Province, China. The appropriate degree of finite-term SH series is selected by the volume, surface area. 100 blocks were scanned on site, and sphericity and angularity of the blocks were calculated. The sphericity and angularity of 50 reconstructed blocks were considered for the error analysis of SH method. Moreover, stochastic polyhedron method was considered for comparing different block reconstructions. The maximum block placement angle was defined to control the spatial distribution orientations of the blocks. Large scale direct tests were carried. Numerical simulations of large-scale direct shear tests were conducted to study the influence of the spatial distribution orientations of the blocks on the mechanical properties of the SRMs. The results revealed that the finite-term SH series fixed at 15 accurately reflected the shape characteristics and mechanical behaviors of actual blocks. The spatial distribution orientations of the blocks had a minimal impact on the friction angle and cohesion of SRM constructed through the SH method. The SRMs developed via the SH method exhibited marginal variations in contact force and anisotropy index of contact across diverse block placement strategies. The evolution of coordination number was closer when employing the SH method under varied block placement methods. Blocks reconstructed by the SH method, could mitigate errors in DEM calculation caused by the spatial distribution orientations of the blocks.

DEM simulations on the influence of carbonate precipitation on liquefaction mitigation of sand

Microbially induced carbonate precipitation (MICP) is an effective method to mitigate liquefaction of sands under cyclic shear loading. In this paper, discrete element method (DEM)-based simulations of the cyclic direct simple shear (CyDSS) tests are carried out using a three-dimensional shear box geometry to evaluate the liquefaction resistance of untreated, MICP-cemented, and reconstituted sands. A six-parameter contact model previously used for undrained and drained triaxial tests on sand is used in the DEM analysis. Verification and validation of the DEM model is implemented through modeling of experimental CyDSS results on loose Fraser River sand at several values of cyclic stress ratios (CSR). The DEM model parameters for untreated and microbially treated Ottawa 20–30 sand are obtained by matching the simulated deviatoric stress and excess pore pressure from strain-controlled undrained isotopically consolidated triaxial compression tests. The DEM model is shown to be capable of accurately representing the cyclic strength curves for untreated, treated, and treated but reconstituted sand using parameters derived from the triaxial test data. The simulated stress path, shear strain evolution, and the evolution of coordination number are used to further examine the effect of MICP on liquefaction in CyDSS tests. The DEM model can be used to design cementation levels and develop cyclic strength curves for different types of sands to aid engineers in designing liquefaction mitigation strategies using MICP.

DEM simulation of cyclic thermal consolidation tests considering the effects of relative density and temperature magnitude

The effect of temperature cycles on the granular particles surrounding energy-related structures has received more and more attention. In this paper, thermal consolidation tests with granular materials were simulated by the discrete element method, and different densities and magnitudes of temperature change were considered. The features of densification of the granular materials are effectively reflected in the simulation process. It demonstrates that thermal cycling induces a rising of the stress level and accumulation of volumetric strain within granular materials. The evolution of coordination number and anisotropy was investigated. It demonstrates that temperature cycling induces a significant stress dilation and strain contraction within granular materials, while the corresponding granular anisotropy paraments such as contact number, normal contact force, and tangential contact force has also a small change. Moreover, the relative density and the magnitude of temperature change have a significant effect on the micro-anisotropy of the material.

High heating rate sintering and microstructural evolution assessment using the discrete element method

An original discrete element model for coupling thermo-mechanics with sintering is presented to disclose the thermo-micromechanical behavior of particulate systems and their densification process under rapid firing. This paper focuses on the numerical model formulation and application on the fast firing of Al2O3, including its verification with literature. Particular emphasis is given to the evolution of thermal and densification gradients over sintering conditions and sample length, zeroing in on the shrinkage evolution and the characteristic densification phenomena. Relationships between defects, microstructure, and sintering parameters are also explored. Finally, the time-dependent change of material microstructure concerning coordination number evolution, cohesive neck size distribution, gradients of temperature, and sample length are analyzed. The numerical results present good agreement with experimental data from the literature.

DEM simulation of the thermo-geomechanical effect of recycled concrete aggregate assemblies in geothermal pavement bases

This paper studies the discrete element modeling (DEM) of the thermal-geomechanical effect of recycled concrete aggregate (RCA) assemblies when harnessing renewable geothermal energy from pavement bases. This research study aims to simulate the behavior of RCA under repeated load triaxial test (RLT) at temperatures varying from 20 °C to 80 °C, to simulate temperature effects when harnessing geothermal energy from pavements. The DEM approach was used to simulate unsaturated soil considering interparticle water meniscus and the variation in its force due to the temperature fluctuation. In this research study, RCA samples with different particle size distributions were simulated under RLT test condition for various temperature conditions. According to the macro-geomechanical results, the resilient modulus (MR), porosity, and accumulated strain of samples showed different trends under varying temperatures. Comparing the micro-geomechanical behavior of the samples indicated that matric suction decreased with increasing temperature. Furthermore, the particle scale matric suction was found to be affected by the size ratio of the contacted particles. It was observed that varying the size ratio between 1 and 4 led to a higher average matric suction. The evolution of coordination number (CN), contact normal and contact normal force indicated that samples with higher sand content experienced decrease in CN and magnitude of contact normal by increasing temperature. Meanwhile, samples with lower sand content tended to have an increased CN and magnitude of contact normal in the direction of anisotropy at increased temperatures. An equation was also proposed to predict MR based on matric suction and the ratio of fine over coarse content, based on the RCA particle sizes.

Effect of Intermediate Principal Stress on the Behavior of Granular Materials at a Low Mean Stress by DEM

This study examines the macro- and micro-mechanical behaviors of granular materials at a low mean stress in general triaxial loading using the discrete element method. Spheres were used to model the particles to reduce the computational costs. They were placed in the grid points of a cube with their random values of diameters. The generated cubical sample was compressed isotropically with periodic boundaries to reach the target mean stress of 25 kPa. The isotropically compressed dense sample prepared in this way was subjected to shear by varying a non-dimensional parameter, $$b = (\sigma^{\prime}_{2} - \sigma^{\prime}_{3} )/(\sigma^{\prime}_{1} - \sigma^{\prime}_{3} )$$ from 0 to 1. From the numerical study, it is observed that the simulated macro-results agree well with the experimental results. The evolution of principal stress and strain components and angle of shearing resistance is strongly dependent on b. However, the evolution of coordination number and slip coordination is not a function of b. The evolution of the components of contact fabric tensor considering the strong contacts has excellent similarity with that of stress components. The ratio of strong contact to total contact strongly depends on the values of b and it decreases at small strain level regardless of b and starts accumulating afterward as the strain increases.

A stochastic particle breakage model for granular soils subjected to one-dimensional compression with emphasis on the evolution of coordination number

Prediction of the evolution of particle size distribution (PSD) is of great importance for studying particle breakage. This paper presents a stochastic approach, namely a Markov chain model, for predicting the evolution of PSD of granular materials during one-dimensional compression tests. The model requires the survival probability of each size group particles in an assembly, named as the survival probability matrix. The Weibull distribution is used to capture the particle size and particle strength effects of single particles. The evolution of the coordination number is investigated via 3D discrete element simulations. The proposed analytical form of survival probability matrix with consideration of the coupling effect of particle-scale factors (i.e., particle size, particle strength) and evolution of the coordination number during one-dimensional compression shows that the largest particles in an assembly do not always have the maximum breakage probability (or the minimum survival probability). This also confirms the dominant role of the coordination number on the balance of evolution of PSD within granular soils. The proposed model is validated against experimental data from one-dimensional compression tests on different granular materials. The limitations as well as possible future developments of the model are discussed.

Discrete element method investigation on thermally-induced shakedown of granular materials

Temperature change, as a common kind of internal perturbation performed on granular materials, has a significant effect on the bulk properties of granular materials. However, few studies on thermally-induced shakedown under a long-term thermal cycling were reported. In this work, the discrete element method was used to give insight into the thermally-induced shakedown on the fabric and stress states within non-cohesive, frictional granular assemblies. Assemblies were submitted to thermal cycling at a stationary boundary condition after experiencing a one-dimensional compression. Evolution of coordination number, entropy and anisotropy was investigated as well as boundary forces and contact forces. At the same time, effects of the heating rate, the initial vertical load and the magnitude of temperature change were examined. It demonstrates that thermal cycling induces a significant force relaxation within granular materials, while the corresponding granular fabric has a small change. In addition, the entropy and anisotropy decreases with thermal cycling. Moreover, the initial vertical load can constrain the development of thermally-induced fabric change, thereby limiting force relaxation to some degree. Both high heating rate and larger magnitudes of temperature change contribute to more significant force relaxation. However, they cause smaller fabric changes even though they provide larger perturbations.

Deformation Modes for Assemblies of Frictionless Polydisperse Spheres

The challenge of dealing with cohesive powders during storage, handling and transport are widely known in the process and pharmaceutical industries. Simulations with the discrete element method (DEM) provide further insight into the local microstructure of bulk materials. In this work, the DEM approach is presented to investigate the flow behavior of granular systems subjected to different modes of deformations. When uniaxial compression is applied of frictionless, polydisperse spheres above jamming (transition from fluid-like state to solid-like state), the evolution of coordination number (average number of contacts per particle) and pressure as functions of the volume fraction are, astonishingly, identical to results obtained for purely isotropic compression. Analytical predictions for the evolution of pressure and coordination number under isotropic strain can thus be separated from different deformation modes, as applied in this study. After two different modes of volume-conserving deviatoric shear, the results still compare quite well with results for purely isotropic compression. The difference between the two deviatoric modes and uniaxial deformation is examined with respect to the anisotropic stress response as a function of deviatoric strain.

Constitutive relations for the isotropic deformation of frictionless packings of polydisperse spheres

The isotropic compression of polydisperse packings of frictionless spheres is modeled with the Discrete Element Method (DEM). The evolution of coordination number, fraction of rattlers, isotropic fabric, and pressure (isotropic stress) is reported as function of volume fraction for different system parameters. The power law relationship, with power ≈ 1 / 2 , between coordination number and volume fraction is confirmed in the jammed state for a broad range of volume fractions and for different (moderate) polydispersities. The polydispersity in the packing causes a shift of the critical volume fraction, i.e., more heterogeneous packings jam at higher volume fractions. Close to jamming, the coordination number and the jamming volume fraction itself depend on both history and rate. At larger densities, neither the deformation history nor the loading rate have a significant effect on the evolution of the coordination number. Concerning the fabric tensor, comparing our DEM results to theoretical predictions, good agreement for different polydispersities is observed. An analytical expression for the pressure as function of isotropic (volumetric) strain is proposed for polydisperse packings, based on the assumption of uniform deformation. We note that, besides the implicit proportionality to contact number density (or fabric), no single power-law is evidenced in the relation between pressure and isotropic strain. However, starting from zero pressure at the jamming point, a linear term with a quadratic correction describes the stress evolution rather well for a broad range of densities and for various polydispersities. Finally, an incremental evolution equation is proposed for both fabric and stress, as function of isotropic strain, and involving the coordination number and the fraction of rattlers, as starting point for further studies involving anisotropic deformations.