Grain-based Model Research Articles

Modeling Injection-Induced Fracture Propagation in Crystalline Rocks by a Fluid–Solid Coupling Grain-Based Model

Modeling Injection-Induced Fracture Propagation in Crystalline Rocks by a Fluid–Solid Coupling Grain-Based Model

A 3D grain‐based reconstruction method from a 2D surface image for the Distinct Lattice Spring Model

AbstractIn this work, a surface image‐based 3D grain‐based model (GBM) reconstruction method based on the digital image processing (DIP) technique, periodic random packing and the simulated annealing algorithm is proposed. Taking a surface digital image of Beishan granite as an example, a K‐means clustering algorithm is employed to extract the mineral compositions, the distribution of which is quantified by the two‐point probability function (TPPF). Given the 3D volume fraction of each mineral composition, their corresponding 3D two‐point probability functions can be evaluated from their 2D forms by the linear interpolation method. The 3D GBM reconstruction is generated by a simulated annealing algorithm, with the Monte Carlo algorithm extending the calculation of the two‐point probability function as the target function to the random particle model. To improve the computational efficiency, the periodic boundary condition is applied to both the random particle generator and the evaluation of the two‐point probability function, allowing large‐scale GBM to be generated for the Distinct Lattice Spring Model (DLSM). The elastic response and advantages of the random particle model for the DLSM are investigated. Finally, the DLSM is further enriched with a tension‐cutoff Mohr‐Coulomb failure criterion, and the GBM reconstruction method is successfully tested for reproducing the mechanical behaviours of granite and interpreting the failure mechanism at the mesoscale under different loading conditions.

Effect of the mineral spatial distribution heterogeneity on the tensile strength of granite: Insights from PFC3D-GBM numerical analysis

The mechanical characteristics of crystalline rocks are affected by the heterogeneity of the spatial distribution of minerals. In this paper, a novel three-dimensional (3D) grain-based model (GBM) based on particle flow code (PFC), i.e. PFC3D-GBM, is proposed. This model can accomplish the grouping of mineral grains at the 3D scale and then filling them. Then, the effect of the position distribution, geometric size, and volume composite of mineral grains on the cracking behaviour and macroscopic properties of granite are examined by conducting Brazilian splitting tests. The numerical results show that when an external load is applied to a sample, force chains will form around each contact, and the orientation distribution of the force chains is uniform, which is independent of the external load level. Furthermore, the number of high-strength force chains is proportional to the external load level, and the main orientation distribution is consistent with the external loading direction. The main orientation of the cracks is vertical to that of the high-strength force chains. The geometric size of the mineral grains controls the mechanical behaviours. As the average grain size increases, the number of transgranular contacts with higher bonding strength in the region connecting both loading points increases. The number of high-strength force chains increases, leading to an increase in the stress concentration value required for the macroscopic failure of the sample. Due to the highest bonding strength, the generation of transgranular cracks in quartz requires a higher concentrated stress value. With increasing volume composition of quartz, the number of transgranular cracks in quartz distributed in the region connecting both loading points increases, which requires many high-strength force chains. The load level rises, leading to an increase in the tensile strength of the numerical sample.

Effect of Grain Size on the Dynamic Flexural Tensile Strength of Granite: Insight from GBM3D-PFC Simulations

For reproducing the heterogeneous structure of granites, a novel three-dimensional grain-based model based on particle flow code (GBM3D-PFC) was proposed in this paper. Then, dynamic semicircular bending tests under different impact velocities were conducted on the numerical samples with different grain sizes by the coupled split Hopkinson pressure bar system. On the one hand, with increasing grain size, the dynamic flexural tensile strength and proportion of transgranular cracks increase, while the total crack number decreases. On the other hand, as the loading rate increases, the dynamic flexural tensile strength and transgranular crack proportion increase. Based on the GBM3D-PFC, the evolution of the load applied to the sample can be reasonably described. The relationship between the contact force network and the sample’s strength can be established. The microcracking behavior obtained by numerical simulations can be used to explain the variation of the macroscopic mechanical parameters.

Mode I fracture behavior of heterogeneous granite: Insights from grain-based FDEM modelling

The failure of brittle rock has a significant influence on engineering stability. The purpose of this study is to understand the progressive fracture mechanism of heterogeneous granite from a mesoscopic perspective. In the present work, the fracture process zone (FPZ) model is used to characterize the constitutive relationship of rock cracking in the combined finite-discrete element method (FDEM). Moreover, the breakable grain-based model (bGBM) is established to study the fracture behavior of granite via the semi-circular bending (SCB) tests. To rebuild the meso-structure of granite specimens, an algorithm that considers the mesoscopic grain geometry characteristics and grain contact mechanical properties is utilized. Then, three classic examples, namely, a uniaxial compressive test, a Brazilian splitting test and a semi-circular bending test, are investigated with the numerical model. A good agreement of the load–displacement curves and crack propagation paths can be found between the simulation and laboratory tests. The meso-heterogeneity of granite cause the macroscopic fracture surface of the slit tip to be nearly upright, with local roughness and zigzag. The slit length has a significant effect on the damage distribution range of the SCB specimen, and the peak load and mode I fracture toughness decreases with increasing slit length and supporting span. The accurate measurement of the mode I fracture toughness of SCB specimens needs to consider the FPZ, and the average increment is 39% and 41% under different slit length and supporting span conditions, respectively.

A three-dimensional grain-based model for studying the microscopic fracture behaviour of granite

Grain-based models (GBMs) are widely used to analyse the micromechanical characteristics of granite. However, the classical two-dimensional (2D)-GBM has some shortcomings: poor matching of mineral composition and grain size distribution to the rock, small number of intragranular microcracks, and inability to represent the three-dimensional (3D) structure of the grains. Therefore, we propose a new method to establish a 3D-GBM in the particle flow code (PFC). The PFC3D-GBM parameters are obtained by calibrating the experimental data, such as the elastic modulus, Poisson's ratio, tensile strength, compressive strength, Hoek-Brown (HB) strength criterion, and fracture characteristics. The fracture mode of granite is analysed on the basis of the experimental and simulation results. In addition, the fracture characteristics and microscopic fracture mechanisms of granite are analysed from the perspective of mineralogy. The results reveal that the mineral composition and the grain size distribution of PFC3D-GBM match well with those of the rock, and the model can simulate the macroscopic and microscopic fracture characteristics of granite. This provides an effective way to study the relationship between microscopic parameters and macroscopic behaviours in a 3D model.

Microcracking behavior and damage mechanism of granite subjected to high temperature based on CT-GBM numerical simulation

Studying the high-temperature impact on microcracking behavior of granite is of great significance to geothermal energy extraction and deep engineering disaster prevention. Therefore, a thermo-mechanical coupled numerical model of granite is established based on computed tomography and grain-based model (CT-GBM) to investigate the impact of high temperature upon microcracking behavior of granite, and to further discuss the thermal damage mechanism. The results show that the thermal damage of granite mainly develops in the form of tensile failure. The development of intra grain cracks can be roughly divided into three periods featuring quiet (room temperature ∼ 300℃), stable development (300℃∼450℃) and unstable development (450℃∼600℃). The development of grain boundary cracks first appeared at the feldspar-quartz grain boundary, but the feldspar-feldspar grain boundary cracks prevail at high temperature (above 332℃) due to the large proportion of feldspar in granite. The phenomenon of stress concentration in granite under high temperature becomes growingly obvious with the increase of temperature, and such phenomenon is more obvious in grain boundaries than in mineral grains, which is the reason of microcracking and prevail of grain boundary cracks. In addition, the thermal damage degree of mineral grains and grain boundaries is described quantitatively through the self-defined crack coefficient. It is discovered that under the joint influence of thermal expansion characteristics and mechanical properties of minerals, the damage of grain boundaries between different minerals is more serious than that in identical minerals, and the damage of quartz grain is more serious than that of feldspar and mica.

Numerical modelling technique for rock mass in underground coal mine by using grain-based model

The stability of rock mass around longwall or excavation in underground coal mine is a prerequisite for the safe and continuous coal production. In practice, instability incidents commonly occur at longwall face or longwall roof that causes serious occupational injury or even death. Current research on the instability has not sufficiently interpreted the formation and propagation of rock mass failure, mostly due to the discontinuous, anisotropic, inhomogeneous and non-elastic nature of rock mass. To assist interpretation of the above stability behaviour, this paper presents a study to improve the numerical modelling technique of rock mass around longwall by using Grain-Based Model. The modelling technique uses Discrete Element Methods and the grain structure Voronoi. A procedure for calibrating rock properties in modelling technique is proposed and validated through application for field rock mass at Ha Lam coal mine, Quang Ninh province, Vietnam. The paper also presents a technique for selecting grain size and monitoring the modelling efficiently. The proposed procedure along with the modelling code are useful for investigation of rock mass around underground excavations from which technical solutions for safe and continuous production can be established.

NUMERICAL INVESTIGATION OF GRANITE FAILURE MECHANISM BASED ON FINITE-ELEMENT VORONOI GRAIN-BASED MODEL

NUMERICAL INVESTIGATION OF GRANITE FAILURE MECHANISM BASED ON FINITE-ELEMENT VORONOI GRAIN-BASED MODEL

FDEM numerical study on the mechanical characteristics and failure behavior of heterogeneous rock based on the Weibull distribution of mechanical parameters

Rock materials are typically heterogeneous. Traditional digital image processing (DIP) technology and the grain-based model (GBM) method are difficult to apply to engineering-scale problem studies, such as tunnel excavation. Based on the combined finite-discrete element method (FDEM), a random parameter assignment method is proposed to simulate the mechanical properties and failure behavior of heterogeneous rock. The elastic moduli of triangular elements, as well as the strength parameters of quadrilateral joint elements, assigned by this method obey a Weibull distribution. The simulation results of uniaxial compression, triaxial compression and Brazilian disc show that with the increase in the heterogeneity m value, the uniaxial compressive strength, elastic modulus, triaxial compressive strength, equivalent cohesion, equivalent internal friction angle and tensile strength all increase exponentially and approach those of the homogeneous rock sample. In addition, the heterogeneous rock samples mainly shear fail along their corresponding theoretical failure angle under uniaxial and triaxial compression. The simulation results of tunnel excavation indicate that for heterogeneous rock with different m values, the overall fracture morphology of the surrounding rock remains unchanged, and X-shaped conjugate shear failures mainly occur followed by a small amount of tensile failures, which are similar to the homogeneous surrounding rock. However, with the increase in the m value, the failure degree and the maximum fracture propagation range of the surrounding rock decrease exponentially. Moreover, the simulation results of uniaxial compression and tunnel excavation with different element sizes suggest that the random parameter assignment method proposed in this paper is reliable.

Size effects on process performance and product quality in progressive microforming of shafted gears revealed by experiment and numerical modeling

As one of the indispensable actuating components in micro-systems, the shafted microgear is in great production demand. Microforming is a manufacturing process to produce microgears to meet the needs. Due to the small geometrical size, there are uncertain process performance and product quality issues in this production process. In this study, the shafted microgears were fabricated in two different scaling factors with four grain sizes using a progressively extrusion-blanking method. To explore the unknown of the process, grain-based modeling was proposed and employed to simulate the entire forming process. The results show that when the grains are large, the anisotropy of single grains has an obvious size effect on the forming behavior and process performance; and the produced geometries and surface quality are worsened; and the deformation load is decreased. Five deformation zones were identified in the microstructures with different hardness and distributions of stress and strain. The simulation by using the proposed model successfully predicted the formation of zones and revealed the inhomogeneous deformation in the forming process. The undesirable geometries of microgears including material unfilling, burr and inclination were observed on the shaft and teeth of gear, and the inclination size is increased obviously with grain size. To avoid the formation of inclination and material unfilling, the punch was redesigned, and a die insert was added to constraint the bottom surface of the gear teeth. The new products had then the better forming quality.

Effect of the crystal habit on micromechanical extensile behaviors of the crystalline rock during compression

The crystal habit controls the microstructure heterogeneity of the crystalline rock and significantly affects its mechanical behaviors. However, thus far, this effect has not been quantitatively characterized. Here we established a grain-based model to investigate effects of the crystal habit on compression-induced micromechanical extensile behaviors of the crystalline rock. Alteration of the grain morphology heterogeneity from the euhedral to anhedral was quantitatively depicted by the fractal dimension. Meanwhile, heterogeneity of grain-scale mechanical properties was also considered, which depended on the stress state. We identified two effects related to the crystal habit that affected mechanical behaviors of the crystalline rock: the tensile stress concentration effect (TSCE) and the grain boundary interlocking effect (ILE). These two effects counteracted with each other with modulating the crystal habit. The stress threshold of the crack initiation of the crystalline rock generally decreased as the crystal habit modulated from the euhedral to anhedral, while the stress thresholds of the crack damage and the peak stress first decreased and then increased. The crystal habit had important influences on the stress distributions and further affected the progressive failure characteristics of the crystalline rock. The intergranular cracking was throughout the whole process while the transgranular failure mainly emerged adjacent to the crack damage stage. With modulating the crystal habit from the euhedral to anhedral, the number of the transgranular failure zone first decreased then increased. We acquired new insights into the microcracking behaviors of the crystalline rock in which the transition to the anhedral microstructure could favor the transgranular failure.

Numerical Investigation of Brittleness Effect on Strength and Microcracking Behavior of Crystalline Rock

Brittleness has a significant influence on rock failure under compression; however, the mechanism is rarely comprehensively discussed. This study numerically investigates the brittleness effect on microcracking behavior of crystalline rock using a grain-based model implemented into a two-dimensional particle flow code, with a focus on the discussion of how rock brittleness affects the failure mechanism. The simulated failure mode changes from tension to shear with decreasing rock brittleness, which is consistent with previous laboratory test results. As the brittleness gradually decreases in the model, the grain boundary (GB) tensile crack to shear crack ratio increases, and the corresponding fractures change from vertical or subvertical to an angle about 45° along the vertical direction. The propagation and coalescence of generated microcracks result in a transition of failure pattern from splitting to shear under uniaxial compression with a decreasing brittleness level in the rock. A transition from GB tensile crack to shear crack is also observed under direct tension when the brittleness index gradually decreases. The tension to shear transition mechanism is closely related to the relative strength of the mineral grain and mineral bonding. The relative strength of mineral and mineral bonding could be used as a parameter to characterize rock brittleness from a microscale viewpoint.

Three-dimensional grain-based model study on triaxial mechanical behavior and fracturing mechanism of granite containing a single fissure

In order to investigate the mechanical behavior and failure mechanism of fissured granite under triaxial compression, a three-dimensional grain-based model (GBM3D) was established in particle flow code (PFC) for simulating the triaxial compression of granite specimens with various fissure inclinations (α = 0°, 30°, 45°, 60° and 90°) under different confining pressures (0, 5, 10 and 20 MPa). First, a group of micro-parameters used in GBM3D was calibrated based on the experimental triaxial compression results of intact specimens, the simulation results of fissured specimens based on these parameters are in good agreement with the experimental results. Compared with intact granite, the fissured granite has smaller peak strength, crack damage threshold, elastic modulus and axial peak strain. Confining pressure can improve the mechanical properties of granite at the same fissure angle, and under the same confining pressure, the mechanical properties increase with the increase of fracture angle. With the increase of axial stress, the cracks first emerge from the crack apices and propagate toward the ends of the specimen along the direction of the principal stress, and the cracks penetrate each other and eventually lead to the failure of the specimens. The displacement field shows that the main cracks are all generated at the interfacial locations where large relative displacements occur between the particles. The three-dimensional spatial crack distribution characteristics of the damaged specimens are not only influenced by the confining pressure, but also related to the fissure angle. The confining pressure not only complicates the crack distribution characteristics, but also increases the total count of cracks. As the fissure angle increases, anti-tensile wing crack is more likely to appear in the specimen.

Determining Young's modulus of granite using accurate grain-based modeling with microscale rock mechanical experiments

It is critical to rigorously determine the mechanical properties of granitic rocks to effectively analyze and manage subsurface engineering activities, such as geothermal energy exploitation and nuclear waste disposal. However, the required deep drilling and sampling for macroscale rock mechanics experiments (macro-RME) are challenging and expensive. In this study, we developed a novel accurate grain-based modeling (AGBM) using the results of microscale rock mechanics experiments (micro-RME) to determine the elastic properties of arbitrarily shaped granite . The microstructure of each sample and Young's modulus of rock-forming minerals were measured with a TESCAN Integrated Mineral Analyzer (TIMA) and nanoindentation test . The geometry and Young's modulus of interphases between different minerals were determined using an advanced algorithm with atomic force microscopy (AFM) test. With the microstructure and microscale mechanical properties obtained from the micro-RME, the AGBM was applied to derive the macroscale mechanical properties of the granite samples. This new methodology was demonstrated on small test specimens extracted from granite fragments. Because we can use test specimens from arbitrarily shaped and small rock fragments, this new methodology has been proven to be a breakthrough from the conventional technology of macro-RME. • Minerals and interphase in granites were measured by microscale mechanics experiments. • Accurate Grain-Based Modeling was developed to determine the macroscale property. • Specimens can be arbitrarily-shaped, avoiding the difficulty of drilling intact rock.

Effects of inhomogeneity on mechanical properties of granites in Songliao Basin using the grain-based model

Effects of inhomogeneity on mechanical properties of granites in Songliao Basin using the grain-based model

Microcracking behaviors and acoustic emission characteristics of granite subjected to direct shear based on a novel grain-based model

In this study, we numerically examine the microcracking behaviors of Alxa porphyritic granite under direct shear using a novel grain-based model considering particle-scale softening mechanism. Associated acoustic emission (AE) activities were monitored using a moment tensor algorithm, and then the effects of normal stress on the microcracking behaviors and AE characteristics of granite were investigated. The shear fracture systems primarily comprised linked tensile crack arrays, of which the proportion of shear cracks increases with an increase in normal stress. Furthermore, additional intra-grain cracks formed because of the strengthening grain interlocking effect, and the thickness of shear band gradually increased. Moreover, with the normal stress increasing, the decreasing b-value of AE events indicated that the proportion of large-magnitude AE events increased. We reported that the maximum-magnitude AE event in the prepeak stage could be used to identify the crack damage point, which could be considered as a potential failure precursor of granites. The displacement ratio of the peak strength point to crack damage point slightly increased with an increase in normal stress, providing a potential warning indicator for the granite failure. Overall, this study provides certain novel insights into the damage behaviors and failure prediction of granites under direct shear.

Reconstruction of 3D Shapes of Granite Minerals and Generation of Random Numerical Specimens

Abstract The existing methods of generating random mineral grains in numerical rock specimens mostly adopt random polygons (in 2D) or random polyhedrons (in 3D) to represent mineral grains. Although this simplification is effective and reasonable, the complex three-dimensional (3D) shape of mineral grains can be reconstructed by computed tomography (CT) scan and image processing techniques, and then, random grains with real shape can be generated in a numerical specimen. In this paper, we proposed an improved grain-based model to construct random mineral grains with real 3D shape in numerical specimens. The granite specimens with granular minerals are scanned by CT. After the CT slices are denoised and corrected, the minerals, including biotite, quartz, and feldspar, are segmented from the CT slices to reconstruct the 3D mineral shapes; these shapes are stored in grain library. By importing the grain library in PFC (Particle Follow Code, a simulation software), heterogeneous specimens with random mineral grains are constructed, and uniaxial compression tests are carried out on them. Results show that the ranges of Young’s modulus, Poisson’s ratio, and uniaxial compressive strength of these numerical specimens are similar to those of real specimens measured in the laboratory. Therefore, the proposed method is feasible and reasonable. This work can provide a reference for the study of constructing heterogeneous numerical rock specimens in rock mechanics.

Fracture behavior of granite specimen containing a single fissure under uniaxial compression by grain-based model 3D

Fracture behavior of granite specimen containing a single fissure under uniaxial compression by grain-based model 3D

A breakable grain-based model for bi-modular rocks

This article proposes a breakable grain scheme and a method to achieve bi-modular elastic material behavior in grain-based models of rocks using the Hybrid Lattice/Discrete Element Method; a version of the Discrete Element Method that employs Rigid Body Spring Network interactions. First, the paper presents both contributions and two validation exercises regarding bi-modular elastic behavior. Subsequently, a set of comprehensive parametric analyses defines the impact that numerical input parameters have on macroscale results, including: crack initiation and damage stresses; unconfined compression and direct tensile strengths ; and material’s characteristic length. Of note, the analyses investigate the influence of heterogeneity, based on the application of the Weibull probability distribution to compressive and tensile Young moduli and inter and intragranular strength parameters. Afterwards, simulations based on three theoretical rock types show the capabilities of the Hybrid LDEM with the proposed contributions in representing typical macroscale properties of rocks observed in laboratory tests. Lastly, visual comparisons between grain breakage processes from numerical simulations and laboratory thin-section analyses indicate consistent correspondence, which evidences the potential application of the developed methods to future research focused on rocks’ microcracking phenomena. This work concludes that the proposed breakable grains and bi-modular material behavior schemes widen the range of macroscale properties that grain-based models can produce while preserving simplicity. • A novel breakable grain-based model is proposed for bi-modular rocks. • The model is based on the Hybrid Lattice/Discrete Element Method. • Breakable grain approach operates by effectively slicing the rigid particles. • Bi-modular elastic behavior is realized by a fictitious stress scheme. • The methods widen the range of macroscale properties that grain-based models produce.