Bond Contact Model Research Articles

An empirical strength criterion for deep rock incorporating the effect of fracture intensity using distinct element method

Deep rock strength is one of the most important research areas in rock mechanics and engineering which is closely related to bearing capacity and stability of underground structures. Due to high ground stress, the mechanical behaviours of deep rock are different from those of shallow rock. In order to characterize deep rock strength precisely, a great number of rock strength criterions have been proposed over the past few decades to quantitatively describe the relationship between complex stress state and rock strength parameters. Some microscopic characteristics like fracture intensity(P32 ) have received some attention. They are thought to have significant influences on the strength of deep rock. Currently, most of the constitutive models and strength criterions focused on the shallow rock and macro mechanical parameters, and they can not directly explain the relationship between the microscopic fracture characteristics and the strength of deep rock. In this research, the effects of fracture characteristics and confining pressure on deep rock strength were investigated using distinct element method(DEM). Firstly, an improved bond contact model incorporating rolling and twisting resistances was implemented in the rock numerical specimens, and the Smooth-Joint contact model was used for simulating fractures of rocks. The fracture length distributions in specimens were characterised by an exponent parameter a. Then numerical simulation of triaxial compression tests were carried out on numerical rock specimens under different confining pressures and P32 . The results show an approximate linear relationship between the maximum principal stress and P32 . Rock strength decreases with the increase of P32 , and it decreases rapidly at a higher confining pressure. Based on the results, a new empirical strength criterion is proposed. The criterion considers the nonlinear relationship between maximum principal stress and confining pressure of deep rock, additionally reveals the correlation between microscopic fracture characteristics and rock strength. In principle stress space, the corresponding failure envelopes projected onto the π-Plane showed a good agreement with DEM simulation results, which indicates a good applicability for the prediction of deep rock strength.

Mechanical response and deformation mechanisms of porous PZT95/5 ceramics under shock-wave compression

A series of plate impact experiments were performed to investigate the shock response of porous PZT95/5 ceramics. Based on the measured free surface velocity profiles, the influences of impact velocity and porosity on the shock response of porous PZT95/5 ceramics were explored. Then, the shock response of porous PZT95/5 ceramics was numerically simulated by using the discrete element method (DEM) based on flat-joint bonded contact model to analyze the microscopic deformation mechanisms. The simulation results of the free surface velocity profiles agreed well with experimental results. The macroscopic deformation process of porous PZT 95/5 ferroelectric ceramics under shock-wave compression can be divided into four stages: elastic deformation, cracks spread deformation, void collapse deformation and Hugoniot state. The microscopic deformation mechanisms of porous PZT95/5 ceramics under shock-wave compression could be mainly attributed to the nucleation and growth of large numbers of shear cracks and tension cracks around voids, as well as the collapse of voids in ceramics.

A Micromechanical Model for Simulation of Rock Failure Under High Strain Rate Loading

Quasi-brittle materials such as rock are rate sensitive materials and their behaviour under dynamic loading is not identical with that under static loading. In this study, numerical Brazilian tensile tests are conducted using a Split Hopkinson Pressure Bar system in an attempt to reproduce the dynamic increase factors (DIF) of the experimental tests. The rock is modelled by a bonded particle system made of spherical particles which interact at the contact points. The numerical results indicate that while the bonded particle system with a simple contact bond model can closely mimic the static behaviour of the sandstone specimens, it lacks what is needed for a rate dependent material. Therefore, a micromechanical model in which the contact bond strength is allowed to vary in proportion to the relative velocity of the involved particles is introduced. It is shown that the modified model can reproduce the physical tests data reported in the literature. In particular, with the application of strength enhancement coefficients in the range of 0–16 × 105, DIF values of 1.1–13 are obtained in the indirect tensile Brazilian tests, and the induced strain rate in the specimen is in 10–1000 s−1 range. Our preliminary study indicates that the model, consistent with the fact reported for the quasi-brittle materials, shows different rate-dependent sensitivity and dynamic strength enhancement in tension and compression. The micromechanical parameters in the proposed model can be adjusted to reproduce the physical rock strength, and that the shape of the reflected and transmitted numerical waves can be modified to approach those in the physical tests.

Calibration of the microparameters of the discrete element method using a relevance vector machine and its application to rockfill materials

To accurately simulate the mechanical properties of rockfill materials under triaxial stress using the discrete element method (DEM), the microparameters of the rockfill material DEM model are calibrated based on the macroparameters of a constitutive model. For the calibration model, a refined 3-D numerical triaxial test is established to obtain the deformation curves of the rockfill under different confining pressures. Deformation curves with different microparameters in the contact model are then calculated by numerical triaxial tests to determine the macroparameters of the constitutive model. Then, a nonlinear relationship between the macroparameters of the E-B model and the microparameters of the contact bond model is built by a relevance vector machine. A memetic algorithm is employed to calibrate the microparameters of the rockfill, thereby establishing a calibration model based on a relevance vector machine and a memetic algorithm. Afterwards, a numerical triaxial test example of rockfill materials is used to verify the feasibility of this calibration model, and then the fabric microparameters under different confining pressures are analysed. In addition, to determine the influence region, a failure process of a rockfill slope is simulated with the calibrated microparameters of the DEM model. In summary, this calibration method substantially improves the numerical results, thereby enhancing the ability to determine the mechanical properties of construction materials and solve various problems in engineering.

Numerical simulation of land subsidence caused by subway train vibration using PFC

Abstract. Subsidence induced by human activity and urbanization is distributed in an area or along a line. In Shanghai, China, land subsidence is distributed along the belt near a subway line. The subsidence is caused by train vibration as well as regional land subsidence and other engineering activity. In order to figure out the mechanical response of the tunnel surroundings, the PFC2D software based on a discrete element method is introduced to simulate a section of the metro tunnel. The linear contact bond model was employed to reflect the characteristics of clay. Based on the analysis of stress and settlement caused by dynamic cyclic loading, the mechanical response law and subsidence mechanism were investigated. In addition, the influence of frequency on settlement was also analyzed: the greater the frequency, the more particles were rearranged and the larger the settlement. The fraction of sliding contacts was introduced to explain this phenomenon. The results can be used to understand, predict and control land subsidence to protect the geological environment.

Experimental and Numerical Study on Cutting Performance of Coal Plow

Coal plow is one of the important equipment for thin seam mining, it is very important to improve the performance of plow for efficient coal mining. In order to study the cutting performance of the coal plow, the cutting test is carried out in National Energy Mining Equipment Research Center, and the forces of the plow bit with different cutting speeds and depths are obtained. According to the properties of simulated coal wall, the intrinsic parameters of coal wall material are determined, and the three-dimensional bond contact model of coal wall is established by EDEM software. The force information of coal plow, the distribution of coal particles and the residual state of the coal wall surface are obtained through the numerical simulation. The results show that the maximum error of the force obtained by DEM simulation and experiment is 7.849 %, and the error of the width the residual coal ridge is 6.5 %. The force distribution of the plow bit is analyzed by combining the discrete element method with the finite element method. The high dynamic stress area of the plow bit is mainly concentrated in the back of the body and the alloy head inlay position. In order to reduce the consumption of the plow bit, local heat treatment is carried out on the plow bit, which can improve the mechanical properties of the plow bit. The simulation results are verified by experiments and industrial production, which proves the accuracy and feasibility of using DEM to study the cutting performance of coal plow.

A van der Waals contact-bond model for low-dimensional nanoscale carbon materials based on the quasi-continuum method

Abstract

DEM analysis of geobag wall system filled with recycled concrete aggregate

This paper investigates numerically a novel geobag wall system using recycled concrete aggregate. The analysis of the performance of the geobag wall system as a flexible retaining wall to support an embankment was conducted employing the discrete element method (DEM) code PFC2D. The slope soil was simulated as bonded balls utilizing the contact-bond model, and the recycled concrete aggregate was treated as unbonded balls based on the linear contact stiffness model. The geotextile of the geobags was set as ball clusters with the parallel bond model. The corresponding parameters of the slope soil, aggregate, and geotextile were derived from biaxial tests, large-scale direct shearing tests, tensile tests, and modified shearing tests. These parameters were calibrated by contrasting the measured data with the numerical results. Utilizing the calibrated parameters, numerical models were established for slopes strengthened by the geobag wall systems, which had been investigated in a series of experimental indoor 1-g model tests. The numerical results were contrasted with the measured data in terms of settlement, horizontal displacement, soil pressure, and crack distribution. Additionally, the coordination numbers, porosities and displacement vectors of the DEM models were also investigated. The modeling methods and results presented in this paper can provide researchers with more insights into the DEM modeling of geobag wall systems and recycled concrete aggregate.

Study of deformation and failure in an anisotropic rock with a three-dimensional discrete element model

This paper is devoted to numerical analysis of deformation and failure of transversely isotropic rocks. A three-dimensional discrete element (DEM) model is proposed in the framework of the particle flow code (PFC). The anisotropic rocks are characterized by a matrix phase in which non-persistent weak layers are embedded. The mechanical behavior of the matrix is described by a non-linear bond contact model while that of weak layers by a smooth joint contact model. The local elastic and strength properties in the bond and smooth joint models are calibrated from the corresponding macroscopic properties. Numerical predictions are compared with experimental data obtained from triaxial compression tests performed on a clayey rock, Tournemire shale. The anisotropic behavior of both elastic modulus and failure strength is well reproduced. The influence of confining stress on the failure strength of shale rock is also captured. A series of three dimensional numerical simulations are further performed for different orientations of weak layers and confining stresses. The effect of weak layers and confining stress on both local cracking process and macroscopic failure mode of rock samples is investigated and discussed.

Determination of Parameters of the Discrete Element Bond Model for Asphalt Mixture Based on Splitting Test

A discrete element method (DEM) has widely been used to simulate asphalt mixture characteristics, and DEM models can consider the effect of aggregate gradation and interaction between particles. However, proper selection of model parameters is crucial to obtain convincing results from DEM‐based simulations. This paper presents a method to appropriately determine the mechanical parameters to be used in DEM‐based simulation of asphalt concrete mixture. Splitting test specimens are prepared by using asphalt mixture, and the splitting test results are compared with simulation results from two‐dimensional (2D) DEM and three‐dimensional (3D) DEM. Basing on the DEM results, the effects of contact model parameters on the simulation results are analyzed. The slope of the load‐displacement curve at the beginning stage is mainly affected by the stiffness parameters, and the peak load is mainly determined by using the value of the bond strength. The laboratory splitting test of AC‐20 and AC‐13 specimens were performed at different temperatures, namely, −10°C, 0°C, 10°C, and 20°C, and the load‐displacement relationships were plotted. According to the real load‐displacement curve’s slope at the beginning stage and peak load applied, the range of DEM bond model parameters is determined. On the basis of DEM results of the splitting test, the relationships between simulation load‐displacement curve’s characteristics and bond model parameters are fitted. The values of the parameters of the DEM contact bond model at different temperatures are obtained depending on the actual load‐displacement curve’s initial slope and peak load. Lastly the DEM and laboratory test results are compared, which illustrates that the parallel bond model can well simulate the behavior of asphalt mixture.

Distinct element modeling of rock fragmentation by TBM cutter

There are many tunneling engineering practices all over the world, in which the tunnel boring machine (TBM) is a main construction way due to its serial advantages such as safety, high efficiency and environment-friendly. TBM cutters are the crucial parts, whose interaction is one of main factors to affect the efficiency of TBM. In this article, a two-dimensional (2D) distinct element method (DEM) code, PFC2D, incorporating an improved microscopic bond contact model proposed for rock, is used to investigate the macro- and micro-mechanical responses during the invasion process of cutter. The influences of the cutter’s geometrical parameters, that is, cutter width and cutter angle, and confining pressure, are investigated in study. The DEM results show that: (1) the whole cutter invasion process can be described into three stages: loading stage, unloading stage and residual leaping broken stage; (2) cutter width has more influence on the capability and efficiency of TBM than cutter angle, and both the capability and efficiency of TBM are the best when confining pressure ratio equals to 0.1; (3) consistent with microscopic information, the analyses on specimen failure modes show that cutter with large width and small angle is helpful to rock fragmentation.

Exploring the undrained cyclic behavior of methane-hydrate-bearing sediments using CFD–DEM

Based on the mechanical experimental results of methane hydrate (MH), a bond contact model considering the rate-dependency of MH is proposed. A CFD–DEM scheme considering fluid compressibility is used to simulate a series of undrained cyclic shear tests of numerical methane-hydrate-bearing sediment (MHBS) samples. The dynamic behavior, including stress–strain relationship, dynamic shear modulus, and damping ratio, is investigated. In addition, the force chains, contact fabric and averaged pure rotation rate (APR) are examined to investigate the relationships between micromechanical variables and macromechanical responses in the DEM MH samples. The effects of temperature, confining pressure and MH saturation are also analyzed. Due to the micro-structural strengthening by the MH bonds, no obvious change in microscopic quantities is observed, and the samples remain at the elastic stage under the applied low-shear stress level. When confining pressure and MH saturation increase, the dynamic elastic modulus increases, while the damping ratio decreases. An increasing temperature (leading to weakening of MH bonds) can lower the dynamic elastic modulus, but has almost no impact on the damping ratio. On the contrary, an increasing cyclic shear stress level lowers the damping ratio, but has almost no effect on the dynamic elastic modulus.

Distinct element method analysis of jointed rock fragmentation induced by TBM cutting

The mechanism of rock breaking and optimal design of the cutters are especially significant in tunnel excavation by Tunnel Boring Machine (TBM). In order to investigate the jointed rock fragmentation induced by TBM cutting, and to improve the capability and efficiency in rock breaking, a series models of jointed rock cutting were simulated by the Distinct Element Method, where an improved zero-thickness bond contact model was implanted to capture the main mechanical behaviour of the hard and brittle rocks. The fragmentation of intact and jointed rock induced by TBM cutting with double cutters was simulated to investigate the influence of jointed angle, spacing and cutter penetration depth on the rock breaking. The main results show that: the process of intact rock or jointed rock fragmentation can be divided into loading stage, unloading stage and residual leaping broken stage and the existence of the joint will make unloading phase in advance; the failure modes for jointed rock breaking can be classified into four types: joint-prevent failure mode, joint-propagation failure mode, joint-tendency failure mode and joint-initiation failure mode; the optimum cutter spacing can be found in the process of jointed rock fragmentation. The result will be useful in the optimisation design of cutters and estimation of penetration depth.

DEM analysis of the effect of joint geometry on the shear behavior of rocks

In order to comprehensively investigate the effect of different joint geometries on the shear behavior of rocks, the Distinct Element Method (DEM) was utilized with a new bond contact model. A series of direct shear tests on coplanar and non-coplanar jointed rocks was simulated using the PFC2D software, which incorporates our bond contact model. Both coplanar jointed rocks with different joint persistence and non-coplanar ones with different joint inclinations were simulated and investigated numerically. The numerical results were compared and discussed with relevant laboratory tests as well as some reported numerical works. The results show that for coplanar jointed rocks, the peak shear stress decreases nonlinearly with the joint persistence, and the failure process can be divided into four stages: elastic shearing phase, crack propagation, failure of rock bridges, and residual phase. For non-coplanar jointed rocks, as the absolute value of the inclination angle of the rock joints increases, its shear strength increases, changing the failure patterns and the length of new fractures between existing cracks. When the absolute value increases from 15° to 30°, the average shear capacity increases the most as 39%, while the shear capacity increases the least as 2.9% when the absolute value changes from 45° to 60°. There is a good consistency of the failure patterns obtained from experiments and numerical tests. All these demonstrate that the DEM can be further applied to rock mechanics and practical rock engineering with confidence in the future.

Multiscale modeling and analysis of compaction bands in high-porosity sandstones

We present a multiscale investigation on the initiation and development of compaction bands in high-porosity sandstones based on an innovative hierarchical multiscale approach. This approach couples the finite element method and the discrete element method (DEM) to offer direct, rigorous linking of the microscopic origins and mechanisms with complex macroscopic phenomena observed in granular rocks such as strain localization and failure. To simulate compaction band in granular cementitious sandstone, we adopt a bonded contact model with normal and tangential interparticle cohesions in the DEM and propose a dual-porosity structure consisting of macro-pores and interstitial voids for the representative volume element to mimic the typical meso-structure of high-porosity sandstones. In the absence of particle crushing, our multiscale analyses identify debonding and pore collapses as two major contributors to the formation of compaction bands. The critical pressures predicted by our simulations, corresponding to surges of debonding and pore collapse events, agree well with the estimations from field data. The occurrence patterns of compaction band are found closely related to specimen heterogeneity, porosity and confining pressure. Other deformation band patterns, including shear-enhanced compaction bands and compactive shear bands, were also observed under relatively low confining pressure conditions with a rough threshold at $$0.55P^{*}$$ ( $$P^{*}$$ is the critical pressure) on the failure envelop. Key microscopic characteristics attributable to the occurrence of these various deformation patterns, including fabric anisotropy, particle rotation, debonding and pore collapse, are examined. Shear-enhanced compaction bands and pure compaction bands bear many similarities in terms of these microscopic characteristics, whereas both differ substantially from compactive shear bands.

Influences of Micro Parameters of Discrete Element on Macro Parameters of Clay

Based on the discrete element software PFC2D, the biaxial test of clay is simulated. Contact bond model simulates the physical and mechanical behaviors of the clay, and is used to research the influences between the seven microscopic parameters, such as particle radius, particle radius ratio, stiffness ratio, friction coefficient, contact modulus, contact normal bond strength, contact shear bond strength and the macroscopic parameters of the clay, such as Young’s modulus, Poisson’s ratio, cohesion and internal friction angle, respectively. In order to make calibration process of clay efficiently, screen out the two most significant microscopic parameters for each response by design of experiment—the Plackett-Burman design method, and obtain the linear regression equation of macroscopic parameters. After that, estimate the nonlinear relationship between the two microscopic parameters and macroscopic parameters by the Response Surface Methods—Central Composite Design method, and obtain an optimum set of microscopic parameters.

Size-dependent mechanical behavior of an intergranular bond revealed by an analytical model

The size of intergranular bonds significantly affects the macroscopic mechanical properties of geomaterials. A size-dependent bond contact model is desired in the distinct element method (DEM) for geomaterials formed by aggregates of bonded particles. This paper proposes an analytical solution of highly-precise stress fields of a biconcave bond between two identical disc-shaped particles under different loading paths based on Dvorkin’s solution. The Unified Strength theory is then introduced to obtain the initial failure domain in the bond. The proposed solution is consistent with results predicted by finite element simulations and experimental observations. The functions of bond stiffness with respect to all influencing parameters, i.e. bond width/thickness, particle radius and elastic parameters of bond material, are provided by the solution and empirically formulated by fitting a large number of analytical results. Additionally, the failure criterion or envelope under different combined loads is formulated for typical brittle bonds. The resulting failure criterion, approximated as an ellipsoid, depends on the size and material properties of the bonds. The proposed solution and equation can be implemented into a bond contact model used in DEM simulations of a geomaterial, where variation of bond sizes is significant and size-dependent contact model is important.

The estimation of uniaxial compressive strength conversion factor of trona and interbeds from point load tests and numerical modeling

The point load (PL) test is generally used for estimation of uniaxial compressive strength (UCS) of rocks because of its economic advantages and simplicity in testing. If the PL index of a specimen is known, the UCS can be estimated using conversion factors. Several conversion factors have been proposed by various researchers and they are dependent upon the rock type. In the literature, conversion factors on different sedimentary, igneous and metamorphic rocks can be found, but no study exists on trona. In this study, laboratory UCS and field PL tests were carried out on trona and interbeds of volcano-sedimentary rocks. Based on these tests, PL to UCS conversion factors of trona and interbeds are proposed. The tests were modeled numerically using a distinct element method (DEM) software, particle flow code (PFC), in an attempt to guide researchers having various types of modeling problems (excavation, cavern design, hydraulic fracturing, etc.) of the abovementioned rock types. Average PFC parallel bond contact model micro properties for the trona and interbeds were determined within this study so that future researchers can use them to avoid the rigorous PFC calibration procedure. It was observed that PFC overestimates the tensile strength of the rocks by a factor that ranges from 22 to 106.

Calibrating the Micromechanical Parameters of the PFC2D(3D) Models Using the Improved Simulated Annealing Algorithm

PFC2D(3D) is commercial software, which is commonly used to model the crack initiation of rock and rock‐like materials. For the PFC2D(3D) numerical simulation, a proper set of microparameters need to be determined before the numerical simulation. To obtain a proper set of microparameters for PFC2D(3D) model based on the macroparameters obtained from physical experiments, a novel technique has been carried out in this paper. The improved simulated annealing algorithm was employed to calibrate the microparameters of the numerical simulation model of PFC2D(3D). A Python script completely controls the calibration process, which can terminate automatically based on a termination criterion. The microparameter calibration process is not based on establishing the relationship between microparameters and macroparameters; instead, the microparameters are calibrated according to the improved simulated annealing algorithm. By using the proposed approach, the microparameters of both the contact‐bond model and parallel‐bond model in PFC2D(3D) can be determined. To verify the validity of calibrating the microparameters of PFC2D(3D) via the improved simulated annealing algorithm, some examples were selected from the literature. The corresponding numerical simulations were performed, and the numerical simulation results indicated that the proposed method is reliable for calibrating the microparameters of PFC2D(3D) model.

Scaling of the fracture process zone in rock

The zone of microcracks surrounding a notch tip—the process zone—is a phenomenon observed in fracture of quasi-brittle materials, and the characterization of the process zone is the topic of the paper. Specimens of different sizes with a center notch fabricated from a granite of large grain (Rockville granite, average grain size of 10 mm), were tested in three-point bending. Acoustic emissions were recorded and locations of microcracks were determined up to peak load. The results show that both the length and width of the process zone increase with the increase of the specimen size. Furthermore, the suitability of a proposed theoretical relationship between the length and width of the process zone and specimen size was studied experimentally and numerically. The discrete element method with a tension softening contact bond model was used to investigate the development of the process zone with the specimen size. A synthetic rock composed of rigid circular particles that interact through normal and shear springs was tested in the numerical simulations. It was shown that the limiting specimen size, beyond which no further noticeable increase in the length of the process zone is observed, is significantly larger than the limiting specimen size beyond which the width of the process zone shows no size effect.