Bond Contact Model Research Articles

Approach for determining micro-strength parameters of rock based on particle flow code

Discrete Element Method (DEM) has been successfully utilized to model rock behavior based on particle flow code (PFC), which is extensively employed in solving various problems related to rock engineering and geomechanics. Therefore, a convenient method for selecting appropriate microparameters of PFC for model generation is necessary. The present study aims to develop a novel approach that calculates proper micro-strength parameters for the contact bond model (CBM). Firstly, based on Plackett–Burman (PB) design, qualitative research is conducted and it is found that the main factors that influence the Brazilian tensile strength is microscopic tensile strength. We analyzed the stress conditions of a Brazilian disc’s vertical diameter using both continuum models and DEM. From this analysis, we establish a theoretical relationship between rock tensile strength and micro-strength parameters. Subsequently, a large number of numerical Brazilian tests were conducted to obtain the statistical relationship between the geometric parameters of balls, micro-strength parameters and the Brazilian tension strength. The results of the numerical simulation were then used to refine the theoretical equation mentioned above, resulting in a modified equation for rock tensile strength and micro-strength parameters. Finally, after verification, we confirm the feasibility of the method in this paper.

Numerical research method of rock slope with intermittent fractures based on parallel bond contact model

Within the domain of rock slopes characterized by intermittent fracturing, the fracture distribution and the mechanical properties of the interstitial rock bridges significantly influence the stability of the slope. The parallel bond contact model is advantageous in replicating the mechanical behavior of rock particles. This research introduces a numerical methodology for analyzing rock slopes with intermittent fractures using the parallel bond contact model. Initially, the model’s microscale parameters are refined through calibration with empirical data derived from macroscopic mechanical tests on rocks. Following this, the discrete element modeling software is employed to construct a detailed rock slope model. This model incorporates a smooth joint approach to define the intermittent fractures, enabling the creation of slope models with varying configurations of coplanar rock bridges and diverse rock types. The research methodologically investigates the mechanical properties and failure patterns of rock slopes under a spectrum of variable combinations. The findings reveal that slopes with multiple rock bridges demonstrate progressive failure and interlocking phenomena during their load-deformation cycles. These insights provide a foundational understanding for the analysis of catastrophic mechanisms and the stability assessment of rock slopes.

Discrete element modelling of the size-dependent mechanical behavior of Al2O3 ceramic under quasi-static uniaxial compression

The size-dependent mechanical behavior of Al2O3 ceramic under quasit-static uniaxial compression was simulated via two-dimensional discrete element method. The numerical sample of Al2O3 ceramic was established by adopting the linear parallel bond contact model, and the inherent defects was further generated by randomly removing a subset of elementary discs. The uniaxial compressive strength of Al2O3 ceramic samples with different sizes follows the Weibull distribution. With an increase in sample size, the magnitude of the uniaxial compressive strength decreases, while its variability increases. Additionally, with sample size increases, both the Young's modulus and Poisson's ratio decrease. Meanwhile, the variability in Young's modulus and Poisson's ratio is more pronounced in larger samples than in smaller ones. The progressive fracture process of Al2O3 ceramic sample can be categorized into four typical stages, namely linear-elastic stage, crack initiation stage, crack propagation stage and complete failure stage. The final fragment size distributions of Al2O3 ceramic samples of different sizes can be accurately described by the fractal model. Notably, smaller samples tend to exhibit a greater breakage extent compared to larger samples. Finally, a size-dependent statistical equation of uniaxial compressive strength of Al2O3 ceramic is proposed based on the numerical results and the inverse function of the Weibull distribution, which can provide a theoretical basis for the design and production of ceramic materials.

Influence of freeze–thaw cycles on mechanical properties of pervious concrete: From experimental studies to discrete element simulations

In this paper, pervious concrete (PC) was prepared using fly ash, granulated blast furnace slag, and rice husk ash as supplementary cementitious materials (SCMs), and the mechanical properties, water permeability, and freeze–thaw durability of permeable concrete were mainly investigated. Discrete elements (DEM) were used to mimic the freeze–thaw cycle process of pervious concrete to assess better how freeze–thaw cycles affect the mechanical properties of pervious concrete. To allow water particles of various sizes to fill the model pores, new algorithms were developed. However, since some connected pores release some of the pressure generated by water expansion when undergoing FTCs, two different water particles must be defined. Meanwhile, an elastoplastic parallel bond contact model (EPPBM) was created to account for any residual strain brought on by water freeze–thaw expansion at the aggregate bond. Through experiments, it was determined that adding SCMs increased the compressive strength of the pervious concrete by 1.22 %, 15.32 %, 32.34 %, and 35.20 % at 7, 28, 56, and 90 days compared to the control group. The microstructure of the hydrated calcium silicate (C-S-H) gel could be relatively dense by SEM. The width of the interfacial transition zone (ITZ) was found to have been effectively shortened by further scanning using EDS. As a result, in the tests of mechanical properties after freeze–thaw cycles (25, 50, 75, and 100 cycles), there was a significant improvement in the loss of strength compared to the control group, which was 2.13 %, 6.91 %, 10.04 %, and 17.40 %, respectively. Using numerical simulation to correct the functional correlation between FTCs and the mechanical characteristics of permeable concrete, the trend essentially aligns with the experiment's results, demonstrating the model's viability. Acoustic emission monitoring of model rupture location and strain energy loss after FTCs were utilized and the effect of different porosity and initial uniaxial compressive strength (UCS) on the attenuation constant of the freeze–thaw resistance of pervious concrete was analyzed. The decay constant of UCS increased with increasing porosity and elastic modulus while decreasing with increasing initial UCS. Therefore, the decay constant of UCS and elastic modulus after arbitrary FTCs can be easily estimated using the initial parameters of the pervious concrete.

DEM analyses of mesoscopic failure mechanism and stress bearing mechanism of compacted snow subjected to unconfined compressive loading

In order to explore the mesoscopic failure mechanism and bearing mechanism of compacted snow under loading. First, the skeleton of dendritic snow crystal was constructed by 13 ice rigid sphere particles which are bonded together using a completed bond contact model. Second, a "falling snow method" was proposed and used to simulate the whole process of natural snowfall, i.e. snow generation, snow falling, snow deposition, and snow compaction. Third, the compacted snow sample was sintered at different temperatures with different times; in sintering process, the snow particles were bonded together by the completed bond contact model. Finally, after contact model parameter calibration by reported snow test results, the unconfined compression tests on the finished sintering snow were carried out and the mesoscopic failure mechanism and stress bearing mechanism were analyzed. Take the sintering temperature of −10 °C and finished sintering samples for example, the results show that the number of compacted snow bond breaks was mainly contributed by tension bond breaks. Meanwhile, with the increase of density, the ratio of bond breaks in tension and compression was higher. When the density was below 475 kg·m−3, the bond breakage was dominated by bending. While the density was above 475 kg·m−3, the bond breakage was mainly shearing. The contribution of the normal contact force to the total axial stress accounted for about 65% which was greater than that of the tangential contact force (ρ = 400 kg m−3). This study can provide support for the mesomechanical failure theory of compacted snow engineering, such as snow roads, compacted snow runways, and snow foundations.

A two-surface contact model for DEM and its application to model fatigue crack growth in cemented materials

This paper proposes a modelling approach that combines the discrete element method (DEM) and a novel bonded contact model to characterise the fatigue response of cemented materials. While DEM is commonly used to simulate bonded materials undergoing cracking, the centrepiece of the present method is the development of the novel bonded fatigue model. This new model couples damage mechanics and bounding surface plasticity theory to capture fatigue crack growth in cement bridges between aggregates. Thanks to the incorporation of the bounding surface plasticity, the proposed model provides a smooth transition from static to fatigue damages and vice-versa in a unified manner, making it more flexible to capture damage responses of cemented materials under different loading conditions (i.e. monotonic and cyclic loadings). Moreover, the proposed approach automatically captures the hysteretic response in cement bridges between aggregates under fatigue loadings without ad-hoc treatments. More importantly, by removing the direct dependence of the fatigue damage variable on the number of loading cycles, the modelling approach can be applied to simulate the fatigue behaviour of cemented materials under cyclic variable load amplitudes. The proposed modelling approach is evaluated against several strength tests to examine its predictive capability. Satisfactory agreements with fatigue experiments are achieved for flexural modulus degradations, lifetimes and sensitivity of stress levels under constant and variable amplitude cycles. This result suggests that the proposed discrete modelling approach can be used to conduct numerical experiments for insights into the fatigue behaviour of cemented materials.

Discrete-element method modelling of structural clay

Clay structures are mainly formed by cementation between particles, and play an important role in the weakening and failure of foundations when disturbed. Existing constitutive models reflect the failure characteristics of clay from the phenomenological aspect, while the mechanism of clay damage from a microscopic perspective remains unclear. Herein, the discrete-element method is used together with the bond and cohesive contact model (to capture the cohesion and structure of soft clay, respectively) to reproduce the cementation of clay; numerical models of the confined compression test, vane shear test and triaxial test are established, aiming to reveal the influence of a clay's structure on its deformation and failure process. Results show that the deformation and stress–strain development agree well with experimental findings at the macroscopic level. Moreover, the relationship between structural failure and macroscopic mechanical behaviour can be established, which is helpful for revealing the failure mechanism of structural clay. Considering the development of a failure surface at the micro scale, optimised suggestions are proposed for conventional shear stress calculation in the vane shear test. The method used has potential to simulate the mechanical behaviour of structural clay and carries significant implications for improvement of constitutive models and engineering design.

Toward a fundamental understanding of the impact mechanisms of analog proppant-clastic rock systems through numerical analysis

The understanding of the collision behavior of proppants with clastic rocks comprises an important step to model, at a larger-scale, problems involving hydraulic fracturing, especially during the stage of high-pressure injection of fluids with proppants to initiate rock fracturing. This paper presents a multiscale study on the interaction problem of proppant simulant (impactor) colliding on the surface of a block (analog rock) by performing 3-dimensional discrete element analysis. Three variants of the block material representing strong, medium-strength and weak clastic rock are simulated considering a variation in bond and contact stiffness as well as bond strength using the linear parallel bond contact model. The interaction between the rock (made of bonded particles) and the impactor (proppant particle) was defined by the Hertz-Mindlin contact model which truly represented the force-displacement response for a grain-block system. A parametric study was conducted to assess the effect of the size of the impactor and the velocity at collision on the damage characteristics of the base rock. It was found that there exist significant differences in the impact response when different impactor and rock attributes are considered. Emphasis was placed in the analysis of macroscale parameters such as stress and energy transfer, mesoscale parameters such as penetration depth and contact formation, as well as microscale parameters such as contact force network and fracture network.

Evaluation of the dynamic behavior of cemented granular soil by the three-dimensional discrete element bonded contact model

Evaluation of the dynamic behavior of cemented granular soil by the three-dimensional discrete element bonded contact model

A discrete element analysis for general failure behavior of basalt

Discrete element method is a commonly used numerical method in rock mechanics and rock engineering. In this research, the flat-joint contact bond model is used to reproduce the macro-properties of basalt on an assembly of particles. A series of laboratory tests, including uniaxial compression test, Brazilian tension test, and fracture toughness test are used to simulate progressive degradation of rock mass strength in a size-independent model with a unique set of micro-properties. The work involves a detailed analysis for estimating compressive elastic modulus, Poisson's ratio, bimodularity, mode I fracture toughness, crack closure, crack initiation, and crack damage thresholds, as well as the tensile and compressive strengths. The constructed flat-jointed material yields a realistic uniaxial compression to tensile strength ratio and nonlinear stress-strain response through sustaining adequate particle interlocking and embedded pre-existing microcracks. The role of sample size on the compressive elastic modulus, crack initiation and crack damage stress limits is demonstrated in detail. A model size-independency analysis was also performed to examine the effect of particle size on the results. The numerical results presented in this study are within 10% of the laboratory results.

Discrete element method for simulations of the jack-up foundation penetration

This paper presents the application of a novel discrete element-based method to simulate the continuous penetration process of jack-up foundations in various soil profiles. A special application of the linear contact bond model is proposed to reproduce the strength distributions of offshore clay. The calibrated inter-particle parameters accurately describe the sophisticated soil characteristics. The effects of particle size, boundary size, model scale, and penetration rate are investigated in this study. The established model balances the accuracy of the results and the computational efficiency. The results of the discrete element simulation are verified by comparison with three published examples. The numerical simulation results provide a microscopic perspective to understand the penetration process and show its advantages in coping with large deformation problems in geomechanics.

A Strength Criterion for Deep Rock with Stochastic Fractures via DEM Simulations

Criteria for rock strength mostly focus on macromechanical parameters, which cannot directly explain the relationship between microscopic fracture characteristics and strength. This paper analyses the strength characteristics of deep jointed rock with stochastic fractures by the distinct element method (DEM) and proposes a new strength criterion. First, an improved bond contact model and the smooth-joint contact model are implemented within the framework of DEM to simulate the characteristics of deep rock. Then, triaxial compression tests on Berea sandstone are also numerically simulated under various confining pressures and fracture intensities (P32). Finally, a strength criterion is proposed and validated based on the numerical and experimental results. The criterion can capture the nonlinear relationship between the major principal stress and the confining pressure and reveal the microscopic fracture characteristics of deep rock. However, the criterion does not consider the influence of the intermediate principal stress. The average deviation between all the predicted strengths and the experimental results is 5.12%, which demonstrates that the criterion has good applicability.

Experimental and numerical studies of a three-dimensional bonded contact model of cemented granular soils

Experimental and numerical studies of a three-dimensional bonded contact model of cemented granular soils

The use of frictional and bonded contact models in finite element analysis for internal fixation of tibia fracture

Tibia is one of the bones that often fracture, generally occurring due to a car accident, falling from high places, work accidents, and sports injuries. Internal fixation is one of the solutions to repair broken bones. In some cases, internal fixation also failed to carry out its function, so the healing process was disturbed and did not run according to the plan. Factors that might interfere with the process can be analyzed using FEM. The objective of this study is to study the effect of the contact model used to model the connection between broken bones of the tibia, to stress distribution that occurs on fixation plate for walking conditions. Analysis was carried out by using ANSYS software with fine-sized tetrahedrons mesh. Two contact models were used. Namely, friction and bonded. The load amount used is based on the average weight of Indonesian Adults, i.e. 63 kg. The results of the analysis show that, for the friction contact model, higher stress is found in the middle area plate, adjacent to the broken location on the bone. Different results are found in the bonded contact model, larger stress occurs in the upper-end area fixation plate.

DEM simulations of spherical particle–particle collisions

AbstractThe randomness, diversity, and complexity of the high‐speed particle crushing process bring great difficulties to the theoretical analysis of powder engineering. In this paper, the discrete element method is used to simulate the collision of spherical particles, which provides a reference for studying the process and mechanism of crushing between particles under impact load. The Hertz–Mindlin with bonded contact model is used as the particle–particle contact model. The central collisions of particles with different diameter ratios under different high‐speed motions and the eccentric collisions with different eccentricities are discussed. The results show that the bond damage increases with the increase of relative velocity in both centre impact and eccentric impact. In centre collisions, particles of smaller objects are more fragmented than particles of larger objects. For smaller target particles, the larger the diameter ratio is, the more particle elements are detached from the target particles, and the greater the bond breakage rate. For larger target particles, the larger the diameter ratio is, the less the particle element falls off and the smaller the bond breakage rate. This provides guidance for the collision and crushing of particles with different particle size ratios and different eccentricities during high‐speed motion in engineering applications in the future.

Establishing an oblique impact breakage master curve using a DEM bonded contact model

This paper aims to establish a breakage master curve of oblique impact using a DEM bonded contact model. Despite numerous advantages of particle impact breakage by DEM, there exist two major issues in hindering the distinct power of DEM with a fully predictive capacity. The first barrier is the notable discrepancy of breakage probability evaluation, i.e. breakage ratio in experiments and damage ratio in DEM. The second barrier is the lack of an oblique impact model where the breakage probability subject to various impact angles can be unified. In this work, these two longstanding barriers are addressed by conducting digital twin of impact breakage using a DEM bonded contact model. A newly developed oblique impact model is used to account for the effect of impact angle. The equivalent velocity proposed in the oblique impact model is shown to successfully establish a remarkable breakage master curve for all the impact angles.

DEM analysis of cyclic liquefaction behaviour of cemented sand

This study presents an investigation of cyclic liquefaction response of cemented sand using discrete element method (DEM). To reproduce the effect of cementation for cemented sand, an existing bond contact model was introduced in a DEM code, and then a series of undrained cyclic triaxial tests were simulated, where different cement contents (CCs) and cyclic stress ratios (CSRs) were considered. Finally, the evolutions of some important macro and micro-scale variables were analyzed. For cemented sand, if the CC is large or the CSR is small, few bond breakages occur, the mechanical coordination number almost remains unchanged, and the input work mainly contributes to the increase in the elastic energies at particle contacts and bond contacts, not leading to the onset of liquefaction. In the case of the liquefied cemented sand, with increasing CSR, bonds break more intensely, and the mechanical coordination number declines faster. The elastic energies at particle contacts and bond contacts tend to be zero faster, and the dissipated energies due to sliding friction, rolling rotation, and twisting rotation reach their maximum more promptly. In addition, the normal orientations for the bonded contacts, unbonded contacts, broken bond contacts, and total contacts, all tend to be isotropic more rapidly.

Love Wave or Slip Wave?

Abstract Conventional models of the structure of the Earth, such as the Preliminary Reference Earth Model (PREM), assume a bonded interface between the crust and the upper mantle. The bonded contact model is consistent with the observation of Love waves during an earthquake. However, anomalies in the Love wave dispersion have been reported in the literature. When slip occurs at the crust-mantle interface, another kind of an interfacial wave, called the slip wave can exist. It is shown that the dispersion relation of the slip wave, with a slip weakening friction law, appears to be in agreement with the observations at seismic frequencies. This suggests that slip could occur at the crust-mantle interface.

Coupled CFD–DEM numerical modelling of perforation damage and sand production in weak sandstone formation

A coupled microscopic simulation method was implemented to investigate the bond breakage behaviour during perforation and sand production in a weak cemented sandstone. A new contact bond model was implemented in the open-source program CFDEM to simulate a large cylindrical sample of one hundred thousand numerical particles using a high-performance computer (HPC) system. The coupled simulation of the particle–fluid phases and the information exchange between them required intensive computational power and highly efficient parallelization algorithms, yet it provided the detailed information on the distribution of bond and bond breakage, new contact formation, particle migration and the associated change in the internal porosity across the sample. The perforation process was found to create a damage zone that contained a compacted core of unbonded particles. The compacted core expanded quickly under fluid flow condition and released its particles to migrate towards the perforation tunnel. Small particles were produced first from the perforation damage zone, while fewer particles of larger sizes were produced later in an overall transient sand production phenomenon.

Instability analysis of jointed rock slope subject to rainfall using DEM strength reduction technique

Uncertain climatic factors like rainfall can induce the complex hydro-chemo mechanical processes within the rock mass, and thus substantially increase the failure probability of rock slope. This paper presents a numerical investigation into the rainfall-induced instability mechanism of jointed rock slope with two joint inclinations of dipping 45° and 60° and the corresponded safety factor using the two-dimensional Distinct Element Method (DEM), where the non-uniform strength reduction approach is employed. For this purpose, some crucial aspects were mainly discussed, i.e. the quantifications of water softening and chemical weathering effects in the micro bond contact model, the necessary fitted functional relationships used in the safety factor, and determinations on the intensities of water softening and chemical weathering. The results show that the proposed DEM strength reduction provides a feasible approach to analyze the rainfall-triggered instability of jointed rock slope. The significant rise of bond breakage and the accompanied large displacement of sliding block indicate the achieved critical infiltration depth of rainfall and the consequent destabilization of jointed rock slope. The jointed rock slope with steeper dipping joints has lower safety factor, and thus is more prone to instability under the same rainfall effect.