Parallel Bond Model Research Articles

Study on Meso-Material Parameters of Submarine Weathered Granite Based on Parallel Bond Model.

In order to study the mechanical properties of submarine weathered granite under marine geological conditions, uniaxial compression tests were carried out on the original medium weathered granite of the seafloor of an offshore area in Pingtan, Fujian Province by using triaxial experimental apparatus to analyze the fracture characteristics, stress–strain characteristics, and compressive strength indexes. Based on the theory of discontinuous medium, the uniaxial compression and uniaxial tensile tests of rocks were simulated, and the microscopic mechanical parameters of discrete elements of granite samples were determined based on the indoor macroscopic mechanical tests: effective modulus Et, compressive elastic modulus Ec, macro Poisson’s ratio μ, and uniaxial compressive strength σc. The results show that the parallel bond model has good simulation results for the uniaxial compression test, but the tensile strength and tensile–compression ratio were quite different from the experimental values. When the confining pressure is large, the calibrated parameter adaptability by uniaxial compression is poor. The reason for certain errors is a large resistance of the parallel bond model to particle rotation and the influence of normal stress on shear strength is not considered. The cementation model can be modified by adding coefficients based on laboratory test results.

Optimizing RAP sieving efficiency of linear vibrating sieve using DEM simulation

Producing recycled hot-mix asphalt mixtures (RHMA) requires an adequate stockpile of reclaimed asphalt pavement (RAP). To improve the content of RAP in RHMA and maintain the quality stability of RHMA, crushing and sieving technology was applied to pretreat RAP, which is mentioned in various technical standards across the world. However, the obstacle that affects the RHMA output during continuous production in any real-life project is the low efficiency of RAP crushing and sieving. A model of a three-dimensional, three-layer linear vibrating sieve was established in the numerical software of the Discrete Element Method (DEM) by considering the sieving combination commonly used in engineering. The Linear Model and Linear Parallel-Bond Model were defined for the contact properties of the RAP particles. Based on DEM simulation, the influence of sieving parameters such as vibration amplitude and frequency as well as inclination and length of the sieve mesh were evaluated by sieving efficiency. Furthermore, the optimal RAP sieving parameters were obtained and verified in the project. The results show that the sieving efficiency first increases and then decreases with an increase in amplitude, frequency, and inclination; however, the length of the sieve mesh has little effect on the sieving efficiency. The order of influence of the different parameters on the RAP sieving efficiency is as follows: amplitude > frequency > inclination > length. The optimal sieving parameters of RAP were 20 Hz, 3 mm, and 10°, respectively, for frequency, amplitude, inclination. The optimum sieve inclination of virgin aggregate was 20° higher than that of RAP. The deviation between the sieving efficiency of the DEM simulation test and the plant sieving test was within 15%, indicating that the DEM simulation had high accuracy. The study could be of interest to sieving plant manufacturers, pavement maintenance sector, and construction contractors.

Construction of Discrete Element Constitutive Relationship and Simulation of Fracture Performance of Quasi-Brittle Materials.

In order to solve the problem that the built-in parallel bond model in the discrete element software cannot adequately simulate the post-peak fracture behavior of quasi-brittle materials, a linear cohesive model was established. First, two particles are used to simulate the interface constitutive behavior in different modes. The results show that the new model can better simulate the behavior of Mode-I fracture, Mode-II fracture, and Mixed-mode fracture. Then, the influence of micro-parameters on the newly constructed constitutive model is analyzed, which provides a basis for the determination of micro-parameter values. Finally, the proposed softening model is applied to a three-point bending test of mortar, and the fracture behavior obtained is compared to the acoustic emission results. The simulation results also show that the constitutive model we built can be used to simulate the fracture behavior of quasi-brittle materials such as mortar and concrete.

Single-Molecule Force Probing of RGD-Binding Integrins on Pancreatic Cancer Cells.

Integrin-targeting arginine-glycine-aspartic acid (RGD)-based nanocarriers have been widely used for tumor imaging, monitoring of tumor development, and delivery of anticancer drugs. However, the thermodynamics of an RGD-integrin formation and dissociation associated with binding dynamics, affinity, and stability remains unclear. Here, we probed the binding strength of the binary complex to live pancreatic cancer cells using single-molecule binding force spectroscopy methods, in which RGD peptides were functionalized on a force probe tip through poly(ethylene glycol) (PEG)-based bifunctional linker molecules. While the density of integrin αV receptors on the cell surface varies more than twofold from cell line to cell line, the individual RGD-integrin complexes exhibited a cell type-independent, monovalent bond strength. The load-dependent bond strength of multivalent RGD-integrin interactions scaled sublinearly with increasing bond number, consistent with the noncooperative, parallel bond model. Furthermore, the multivalent bonds ruptured sequentially either by one or in multiples, and the force strength was comparable to the synchronous rupture force. Comparison of energy landscapes of the bond number revealed a substantial decrease of kinetic off-rates for multivalent bonds, along with the increased width of the potential well and the increased potential barrier height between bound and unbound states, enhancing the stability of the multivalent bonds between them.

Numerical study on full-field stress evolution and acoustic emission characteristics of rocks containing three parallel pre-existing flaws under uniaxial compression

A linear parallel bond model combined with Weibull distribution to take into account the mechanical heterogeneity of brittle rocks is used to investigate the cracking behavior, acoustic emission (AE) characteristics and full-field stress evolution of rocks containing three parallel pre-existing flaws under uniaxial compression. The intact model is calibrated to the macro mechanical properties of rocks obtained from laboratory tests. The numerical results indicate that the presence of three parallel pre-existing flaws weakens the mechanical properties of rocks. As the flaw inclination increases, uniaxial compression strength shows a trend of first decreasing and then increasing, and the elastic modulus and Poisson's ratio are roughly increasing. The displacement localization zones chronologically formed around pre-existing flaws can interact with each other, and the damage or fracture processes of pre-cracked samples are complicated. And the tensile stress in x direction concentrates around pre-existing flaws. As the flaw inclination increases, the tensile stress concentration area at the end of the pre-existing flaws in the x direction also changes, at the same time, the area of the tensile stress concentration area in the y direction gradually decreases. And AE events with high fracture intensity are located in the macroscopic shear zone or split zone.

Mechanical behaviour and energy evolution of polyurethane-mixed ballast under revised bonding constitutive model

The bonding contact presents complex modes in polyurethane-mixed ballast. The commonly used parallel bond model is revised and four different contact models are developed including Ballast-Ballast Contact Bonding, Ballast-Ballast Noncontact Bonding, Ballast-Sleeper Contact Bonding, and Ballast-Sleeper Noncontact Bonding. The mechanical behaviour and energy evolution of polyurethane-mixed ballast with various amounts of glue are studied from the macro and mesoscopic properties. Results show that the elastic strain energy has always been the main form in polyurethane-mixed bed, followed by viscous strain energy, frictional energy, and damping energy. Compared with the common ballast bed, there are more contacts in polyurethane-mixed ballast bed and, when more glue is used, the amount of contacts is further increased while the maximum contact force is reduced. After bonding, the amount of contacts is significantly increased and all forms of energy become more evenly distributed at different surfaces of the sleeper. The kinetic energy of polyurethane-mixed ballast fluctuates with smaller amplitude and convergences more quickly under cyclic loading, which is reflected in the macroscopic aspect that the settlement of polyurethane-mixed ballast bed is relatively small and can be fast completed.

Discrete Element Simulations of Ice Load and Mooring Force on Moored Structure in Level Ice

Moored structures are suitable for operations in ice-covered regions owing to their security and efficiency. This paper aims to present a new method for simulating the ice load and mooring force on the moored structure during ice-structure interaction with a spherical discrete element method (DEM). In this method, the level ice and mooring lines consist of bonded sphere elements arranged in different patterns. The level ice model has been widely validated in simulation of the ice load of fixed structures. In the mooring line simulation, a string of spherical elements was jointed with the parallel bond model to simulate the chains or cable structure. The accuracy of the mooring line model was proved by comparing the numerical results with the nonlinear FEM results and model towing experiment results. The motion of the structure was calculated in the quaternion method, considering the ice load, mooring force, and hydrodynamic force. The hydrodynamic force comprised wave-making damping, current drag, and buoyancy force. Based on the proposed model, the interaction of a semi-submersible structure with level ice was simulated, and the effect of ice thickness on the ice load was analyzed. The numerical results show that the DEM method is suitable to simulate the ice load and mooring force on moored floating structures.

Stability Analysis of Jointed Rock Cutting Slope Based on Discrete Element Method

The joints in the rock mass are essential for the stability of rocky slopes, and the destabilization damage of the slope is often directly related to the joints. In this study, in order to reveal the instability process and mechanism of rock slopes from a microscale perspective, the DEM simulations for rocky slopes of the K88 + 400∼K88 + 540 section of Zhongkai Expressway are carried out considering the influence of joints. Based on the findings of the on‐site jointed structural surfaces, a rocky slope model containing two sets of intermittent joints was constructed, and the linear parallel bond model and the smooth joint model are used to characterize the rock body and joints, respectively. The evolution of microfracture, contact force chain, and particle displacement are analyzed to explore the micromechanism of slope instability. Finally, the triple reinforcement scheme of anchor cable frame and grass planting is proposed. The research results can provide a reference for stability analysis and reinforcement of similar rocky slope projects.

Cracking Behavior and Acoustic Emission Characteristics of Rock Containing a Single Preexisting Flaw

The existence of flaws in brittle rocks or rock-like materials has an obvious influence on the material mechanical properties and cracking behavior of civil engineering projects. In this work, the two-dimensional particle flow code PFC2D was used to study the deformation and strength properties, failure processes, and acoustic emission (AE) characteristics of mudstone with a single preexisting flaw. First, the procedure to construct a parallel bond model is introduced. The Weibull distribution is used to reflect the mechanical heterogeneity of rocks. Then, the microscopic parameters used in PFC2D are calibrated to the macroproperties of mudstone obtained from laboratory tests under the uniaxial compression. The results indicate that the increases of the flaw inclination lead to the increasing uniaxial compressive strength and elastic modulus. In terms of microcrack evolution, the initiation, propagation, and coalescence of microcracks are closely related to the force chain. Specifically, an “X” shaped tension force chain concentrated area around the preexisting flaw is founded, which is the most prone area for microcracks to initiate. With an increase in flaw inclination, the b value of AE also shows an increasing trend. By incorporating the AE event numbers into a damage variable, this paper derives a constitutive model, which is verified by numerical results on brittle rocks with a single preexisting flaw under uniaxial compression.

Experimental Study on the Calibration of Microparameters of Dolomite in the Barun Open-Pit Mine on the Basis of the Parallel Bond Model

The microparameter calibration of the particle flow parallel bond model (PBM) is mostly based on a uniaxial compression test. The microparameters calibrated only by uniaxial compression tests cannot be directly used to study the mechanical properties of rocks with surrounding pressure conditions. To analyze the relationship between the macroparameters and microparameters in the model and select appropriate particle flow model parameters, this study conducted a particle flow numerical simulation experiment based on the basic test principles of the uniaxial compression, Brazilian splitting, and triaxial compression tests. An orthogonal experimental design was performed for the calibration of the microparameters of the particle flow PBM, and multifactor analysis of variance was used to screen out the factors that have a considerable influence on the experimental indicators. Regression analysis was performed on the significant influencing factors and test indicators, and the corresponding linear and nonlinear relationships between the macroparameters and microparameters were obtained. Lastly, the microparameters of the model were determined in accordance with the macroparameters of the mechanical test of the Barun open-pit mine dolomite, and a numerical simulation test was conducted. Simulation test results were consistent with the actual test results, thus providing a basis for a subsequent numerical simulation study on the mechanical properties of dolomite.

Effect of heterogeneity and injection borehole location on hydraulic fracture initiation and propagation in shale gas reservoirs

The breakdown pressure and fracture propagation are essential problems in hydraulic fracturing, but how they are affected by rock heterogeneity and injection borehole location has been unclear. In this study, a hydro-mechanical coupling model in micromechanics was established to investigate the mechanisms of fracture initiation and propagation in shale formations. The dependence of the breakdown pressure and fracture propagation on approach angle of bedding plane, particle heterogeneity and borehole location was numerically studied. First, a hydro-mechanical coupling model was developed with both parallel bond model (PBM) and smooth joint model (SJM) for heterogeneous shale formations. Then, this model was validated by theoretical analysis and experimental observations. Finally, the effects of rock heterogeneity and borehole location on the breakdown pressure, fracture modes, stress distribution were analyzed through numerical simulations. It is found that the approach angle of bedding has significant effects on breakdown pressure and fracture network, but has only limited impact on the stress distribution near borehole. The stress distribution near borehole is heavily affected by particle size distribution. The lowest breakdown pressure and hydraulic injection volume are observed at the borehole located at the bedding plane. These results can deepen our understanding on the micro-mechanisms in hydraulic fracture initiation and propagation.

Influence of Parallel-Joint Position on Mechanical Behavior and Acoustic Emission Characteristics of Rock Pillar

In this paper, the parallel-joint rock column model is established based on PFC software, and the effects of different joint positions on the mechanical properties, acoustic emission characteristics, and damage evolution characteristics of rock columns are analyzed. In the PFC models, the intact rock is simulated by parallel-bond model, and the joints are simulated by flat-joint contact model. The research result shows that on the whole, when the joint is outside the rock pillar, the UCS of the rock pillar is higher than that of the joint inside the rock pillar, while the elastic modulus is less than that of rock pillar with joint inside. The evolution characteristics of acoustic emission of rock pillars at different joint positions are basically the same. However, the maximum value of acoustic emission events and corresponding deformation of rock pillars at different joint positions are different. The damage of jointed rock mass can generally show three stages: no damage, slow damage increase, and sharp damage increase.

Unloading Response Characteristics of Cross Fault Caverns: Effect of Fault Angles

The research of unloading response characteristics of caverns with weak structure has important engineering value for the development and construction of underground space. In this paper, firstly, the cross fault cavity model is established based on particle flow code (PFC) software, considering different fault dip angles. The parallel bond model (PBM) is used in the cavern model and the smooth joint model (SJM) is used in the fault model. Then, the mechanical, acoustic emission (AE), energy response characteristics and failure modes of the cavern model with different fault angles are explored. The research result show that the fault angle has a great influence on the stress distribution and failure modes of surrounding rock. The existence of faults does not change the overall law of AE evolution curve, that is, the number of AE hits increases first and then decreases. However, the existence of faults changes the maximum number of AE hits and the duration of AE. When the cavern is unloaded, the strain energy of the model first decreases and then increases.

Numerical and Experimental Study on Strain Rate Effect of Ordinary Concrete under Low Strain Rate

The strain rate effect of ordinary concrete is researched through the particle discrete element method. A random construction method of three-dimensional aggregate is used, and the numerical sample consistent with the experimental specimen is constructed using particle flow code. Moreover, the simulation method that can properly reflect the strain rate effect with the parallel bond model is proposed. The meso-parameters are calibrated by triaxial compression test. Based on the proposed simulation method and calibrated meso-parameters, the numerical tests of direct tension, uniaxial compression, and cyclic loading under strain rates from 10−5 s−1 to 10−1 s−1 are carried out. The results show that the strain rate effect of concrete can be simulated with particle flow code by assuming that the micromechanical properties of materials vary with the strain rate, and the strength and failure characteristics of numerical samples under different strain rates are described well by the proposed method. In addition, the different mechanical responses of the samples to the strain rate in the compression test and the tensile test are obtained, and the changes of mechanical parameters and damage degree with strain rates in the cyclic loading test are also successfully simulated. This study can provide a feasible numerical method for the follow-up research of dynamic mechanical behavior of concrete and offer theoretical guidance for the stability assessment of concrete engineering.

DEM simulations of cemented sands with a statistical representation of micro-bond parameters

The heterogeneity of cemented sands influences its mechanical behavior, and the investigation of heterogeneity properties is a crucial part of the micro-mechanical analysis. This study combined the discrete element method (DEM) model with the Weibull statistics to analyze the effect of heterogeneity on the mechanical properties of cemented sands from macroscopic and particle levels. First, to consider the effect of the irregular particle shape, the two-dimensional (2D) images of realistic particle shape were obtained from an X-ray sample and incorporated into DEM simulations. Then, a flexible membrane boundary was applied in the DEM simulation to allow flexible deformation subjected to external loading. After that, we combined the parallel bond model with Weibull statistics to model the heterogeneity of the cemented sands. Finally, a parametric study was conducted using the established DEM model, considering a range of homogeneity indices and confining pressures. Simulation results not only offer new insights to the ground improvement technology, but also can contribute to the research of the mechanical behavior of cemented sands.

A simple approach of calibrating input parallel bond model parameters for DEM simulations of rock behaviour

The mineral bonds between grains of rock are usually simulated by parallel bonds in discrete element method (DEM) simulations. The existence of multiple input parameters makes the calibration process tedious and time-consuming. In this paper, a series of parametric studies are firstly conducted by varying the value of each input parameter independently, based on which their distinct influences on the strength and deformation characteristics of simulated specimens are obtained. One-way and multiple-way analysis of variance are conducted to evaluate the sensitivity of macro strength and deformation parameters to the change of input parallel bond model parameters. The order of influence level of these input parameters on the macro behaviour of simulated specimens is obtained and the input parameters with the dominating influences on the macro mechanical properties are identified. Then, empirical correlations between the macro mechanical properties and their dominating input parameters are established separately. These empirical correlations are taken as the basic components in the regression analysis of multiple variables for each macro mechanical property. The regression equations serve as the first estimation of input parameters for the calibration. The adjustment of input parameters is conducted with reference to the partial differentials of the regression equations considering the difference between the simulation results and the experimental data as the increments/decrements. The effectiveness of the proposed calibration approach is validated by simulating a series of triaxial compression tests on mudstone.

3D continuum-discrete coupled modelling of triaxial Hopkinson bar tests on rock under multiaxial static-dynamic loads

Rock engineering projects at depth are frequently subjected to dynamic loadings under in-situ stress state, and the studies should be conducted to decipher the coupled effect of confining pressure and strain rate on the behaviour of rocks. The triaxial Hopkinson bar system has been applied to investigate the responses of materials to the coupled multiaxial static-dynamic loads. In this study, a three-dimensional (3D) continuum-discrete coupled method is employed to establish a numerical-based triaxial Hopkinson bar system, and the steel bars and a cubic specimen are modelled by continuum zones and bonded-particle material, respectively. Firstly, the detailed numerical modelling is performed to verify some prerequisites and uncertainties in the experiments, including stress wave propagation and attenuation in three directions, dynamic stress equilibrium, boundary effects, interfacial frictions, and controversial methodologies for applying confining pressure, by using the flat-joint model and parallel bond model. Then, both experimental tests and numerical modelling are carried out on sandstone under multiaxial pre-stress conditions (i.e., uniaxial, biaxial and triaxial compression) followed by dynamic loads. The dynamic responses of rock, including stress-strain curves, dynamic strength, energy evolutions, and damage patterns, exhibit confinement dependence, which is in good agreement with experimental observations. Under uniaxial compression, the specimens are broken into fragments by multiple fractures; while under biaxial compression, two symmetrically distributed V-shaped damage zones form near the free surfaces. Under triaxial compression, the degree of damage is substantially reduced, and microcrack localisation zones are initiated from the surface, propagate to the interior and eventually form macroscopic fractures. Moreover, a series of numerical simulations is conducted to investigate the strain rate dependence of sandstone under multiaxial load conditions. Both dynamic strength and peak lateral dynamic stresses increase with increasing strain rate. The increase of dynamic strength and failure strain becomes obvious at high strain rates with the enhancement of lateral confinement.

Numerical Investigation on the Evolution of Mechanical Properties of Rock Affected by Micro-Parameters

Investigating the micro-parameters of rock is vital for understanding the macro-properties of rock, such as the uniaxial compressive strength (UCS), Young’s modulus, failure patterns, etc. In this paper, based on the experimental results of rock material, a parallel-bond model in three-dimensional particle flow code (PFC3D) was applied to investigate the effects of the joint action of bond stiffness ratio and bond stress ratio on macro-properties of rock. The uniaxial compressive strength, stress–strain relationships, and failure characteristics, as well as underlying compression and failure mechanisms, in the process of parameter calibration, were systematically studied. The results indicated that the interaction of several micro-parameters would obviously change the response characteristics of the macro-properties of the model. The mechanism of the effects of various micro-parameters on the macro-properties of the model was further revealed. The change of the micro-parameters would change the strength and stress state of the bond between particles. The research results could promote the understanding of the failure mechanism of rock and improve the efficiency of micro-parameter calibration and the accuracy of calibration results.

Mesoscale numerical simulation of fracture of cement treated base material during semi circular bending test with discrete element model

The fracture of Cement Treated Base (CTB) is greatly influenced by its mesoscale structure and characteristics. The Discrete Element Method (DEM) was adopted to build a mesoscale Semicircular Bending (SCB) model of CTB. The DEM models were built based on two methods including the Digital Image Process (DIP) of actual aggregate distribution and randomization algorithm to generate aggregates. The mesoscale heterogeneity of the model consisted of aggregates, cement mortar, Interface Transition Zone (ITZ) and air voids. Analysis results showed that the DEM models based on both DIP and randomization with the Linear Parallel Bond Model (LPBM) presented satisfying results, compared with laboratory tests. It was found that the main cracks occurred along ITZ between mortar and aggregates. The gradation and distribution of aggregate, and air voids have all significant influence on the fracture resistance and the crack propagation of the CTB. The lime-ash treated material simulation results showed relatively higher fracture toughness over strength ratio.

Numerical investigation of interaction between hydraulic and natural fractures under various geologic and engineering parameters using particle flow code method

ABSTRACT Gaining a better understanding on the mechanism of the interaction between the hydraulic fracture (HF) and the natural fracture (NF) is essential for increasing the stimulated reservoir volume (SRV) of shale gas fracturing. In this study, a two-dimensional (2D) numerical model for simulating the behavior of HF/NF interaction using particle flow code (PFC) method was established, and this model can consider the fluid-mechanical coupling effect, the fluid flow in permeable NFs, and the heterogeneity of particle size. The numerical model was verified by KGD analytical model and Gu and Weng’s analytical model. The input micro-parameters for PFC simulation were calibrated to match with the experimental macro-parameters of Longmaxi shale by trial-and-error method. The effects of various geologic and engineering parameters on the HF/NF interaction were investigated using PFC method. The modeling results show that there are six kinds of HF/NF interaction patterns observed from the results of PFC simulation. The HF will hardly cross the NF directly when the permeability of NF reaches a higher value of 100 mD. When the in-situ stress difference reaches 13 MPa, the HF will cross the NF even if the other factors are not favorable to the occurrence of “crossing”. The product of injection rate and fracturing fluid viscosity (Q·μ) is suggested to be used to study the HF/NF interaction, and the HF tends to cross the NF under a higher value of Q·μ. Moreover, the scenario of “crossing” is extremely likely to occur under orthogonal approach angle, and frictional coefficient of NF has little effect on orthogonal HF/NF interaction. The cases with the same HF/NF interaction pattern have a similar variation trend of borehole pressure history curve. Through analyzing the numerical results, the technical measures such as variable pump rate fracturing method and alternate injection method of slickwater-linear gel fluid were suggested to be applied to increase the complexity of fracture network. Abbreviation: 2D: Two-dimensional; 3D: Three-dimensional; PFC: Particle flow code; EIA: Energy Information Administration; SRV: Stimulated reservoir volume; BPM: Bonded particle model; PBM: Parallel bond model; FEM: Finite element method; BEM: Boundary element method; DEM: Discrete element method; XFEM: Extended finite element method; CZM: Cohesive zone model; UDEC: Universal distinct element code; 3DEC: Three-dimensional distinct element code; DDM: Displacement discontinuity method; SJM: Smooth joint model