Grain-based Model Research Articles

Numerical investigation of the effects of the micro-parameters of the transgranular contact on the mechanical response of granite

In this work, a novel three-dimensional grain-based model based on the Discrete Element Method (GBM3D-DEM) was proposed, and then the granite’s internal structure was reproduced in a realistic way. The effects of the micro-strength and micro-elastic modulus of the transgranular contact on the macroscopic mechanical characteristics and micro-cracking behavior of the sample in the Brazilian splitting test were investigated. Moreover, the variation of the fracture energy required for a single intergranular/transgranular contact was discussed. The consistency between the experimental and numerical results indicates that the proposed GBM3D-DEM is reliable. Results indicate that as the micro-strength of transgranular contact increases, the slope of the load–displacement curves in the linear elastic stage increases. The external load value required the macro-scale fracture of sample increases. The energy required for the transgranular contact fracture increases. In the propagation process of the main crack, the grain boundary structure is more easily destroyed, increasing the intergranular crack number. When the micro-elastic modulus of the transgranular contact rises, the stress region in the disk sample decreases gradually. In this case, the maximum external load value that the sample can withstand decreases. The transgranular contact is more likely to be destroyed under loading. The numerical results based on the GBM3D-DEM can predict the energy required for macro-scale fracture of crystalline granite, which is of great significance to rock mechanics.

Rock grain-scale mechanical properties influencing hydraulic fracturing using Hydro-GBM approach

Rock cracking is of key concern to many geological applications. On a grain scale, rock fracturing depends on not only the external load but also the mechanical properties of the mineral grain and grain boundary. In this study, we investigated the effect of rock grain-scale mechanical parameters on fluid-driven cracking behaviours and discussed the identification of micro mechanical parameters in the grain-based model. A coupled hydro-grain-based DEM model (Hydro-GBM) is used to reconstruct rock microstructures and simulate hydraulic fracturing. We analyzed the influences of the main micro-mechanical parameters of mineral grain and grain boundary and explored the responsible micro-mechanisms. Results including crack initiation pressure, breakdown pressure, partitions of intragranular and grain boundary cracks in tension/shear are presented in detail. Then, based on the parameter analysis, some issues in identifying micro parameters in existing DEM simulations are discussed. We proposed a formulation to determine contact friction angle, which could eliminate the long-standing mismatch of shear cracking between experiment and simulation. We also suggested the importance of calibrating micro results in grain-based modelling. The presented study systematically revealed the effects of rock grain-scale properties on hydraulic fractures and could provide valuable references to the selection of micro mechanical parameters in future modelling.

Thermomechanical Properties of Granite after Air Cooling and Water Cooling Investigated by Grain-Based Model 3d

Thermomechanical Properties of Granite after Air Cooling and Water Cooling Investigated by Grain-Based Model 3d

Influence of grain-to-particle size ratio on the tensile mechanical response of granite based on a novel three-dimensional grain-based model

In this paper, we developed a novel three-dimensional grain-based model based on the discrete element method (DEM) and reproduced the heterogeneous structure of crystalline granite. We carried out static Brazilian splitting tests to analyze the mechanical properties and micro-cracking behavior of granite samples. Furthermore, we investigated the effect of grain-to-particle size ratio on the tensile strength and discussed the difference in mechanical response of granite samples with different grain sizes and particle sizes under static loading. Our results show that the load–displacement curve of the sample can be divided into initial compaction stage, linear elasticity stage, damage stage, and post-peak stage. Tensile failure is the main failure mode leading to the macroscopic fracture of the sample, and intergranular failure is dominant. As the grain-to-particle size ratio increases, the proportion of the number of transgranular contacts to the number of total contacts increases and stabilizes. Compared with intergranular contact, transgranular contact has a higher bonding strength, and its fracture requires a larger stress concentration magnitude, which leads to an increase in the external load required for the macroscopic fracture of the sample.

A meso-mechanical approach to time-dependent deformation and fracturing of partially saturated sandstone

In the present paper, we investigate how water acts to weaken rock in two complementary ways: mechanically through the generalized effective stress principle, and chemically through time-dependent rock-fluid reactions that allow subcritical crack growth. These processes, together with capillary suction and stress corrosion , were incorporated into a three-dimensional discrete element grain-based model to investigate both the time-independent and the time-dependent mechanical behavior of partially saturated sandstone at the mesoscale . The capillary parameters related to capillary suction and subcritical parameters related to stress corrosion in the model were calibrated to match the deformation behavior of partially saturated sandstone observed in laboratory. Following this calibration, numerical simulations of partially saturated sandstone with different levels of saturation were performed in uniaxial compression. The simulations show that both the peak strength and elastic modulus of the sandstone decrease as a function of increasing saturation and that the relationships between these properties can be expressed by negative exponential functions. The simulations are in good agreement with the experimental results. Second, the long-term brittle deformation of partially saturated sandstone with different levels of saturation under a constant stress level was modeled. The results show that time-to-failure during brittle creep decreases, and the initial strain and the minimum creep strain rate increases, as a function of increasing saturation, as also observed in laboratory. The simulations also highlight the formation of tensile cracks as the main deformation mechanism during brittle creep. Finally, brittle creep in partially saturated sandstone samples with different levels of saturation was studied under different stress levels. These simulations show that the minimum creep strain rate and the time-to-failure as a function of stress can be well described by exponential relations. We conclude that the proposed model permits a deeper understanding of time-independent and time-dependent deformation and failure of partially saturated sandstone at the mesoscale.

Fluid-driven micro-cracking behaviour of crystalline rock using a coupled hydro-grain-based discrete element method

The grain-scale heterogeneity of rock has been found to greatly affect the cracking behaviour in mechanical tests. However, the heterogeneity has been insufficiently considered in hydraulic fracturing. To fill the gap, this paper proposes a coupled hydro-grain-based discrete element model and explores the fluid-driven micro-cracking of crystalline rock. The micro-heterogeneity of the rock is represented by a grain-based model. Three laboratory-scale fracturing cases over granite under different in-situ stresses are simulated. First, typical micro behaviour and hydro/hydro-mechanical responses are presented and interpreted. Next, sensitivity analysis of in-situ stress conditions is carried out. It is found that hydraulic fracturing of crystalline rock involves many unique behaviours on grain-scale such as non-symmetrical propagation, “zipper mode” initiation time order, generations of isolated and branching cracks, and re-closure of the cracks earlier initiated. Cracks can be induced in mineral grains and along the grain interfaces. The cracking mode is dominated by tension failure, with a small proportion in shear (between 3.5% and 1.5%). The interplays among orientation, aperture and number of different types of crack show that: 1. The inclination of cracks to the direction of maximum confining stress may occupy the entire range from 0° to 180°; 2. The aperture of cracks decreases statistically with their orientations turning to the direction of the minimum confining stress (σ3); 3. Increases in σ3 suppress the generation of total cracks and tend to force cracks to propagate in mineral grains; 4. A small in-situ stress difference results in fewer branching and isolated cracks. In this paper, evolutions of injection pressure and rock deformation during hydraulic fracturing are also discussed.

INVESTIGATION ON THE ROCK CUTTING MECHANISM OF HETEROGENEOUS GRANITE USING A GRAIN-BASED MODELING APPROACH

A good understanding of rock cutting mechanism is of great importance for improving the cutting efficiency and reducing the costs in hard heterogeneous formation drilling. This paper implements the grain-based modeling approach to mimic the granite considering the highly heterogeneous mechanical behaviors of grains in granite. The rock cutting mechanism of granite, accounting for the influence of hydrostatic pressure, mineral size, random distribution, rake angle, cutting depth and velocity of cutter, are investigated. The research results demonstrate that the inter-grain shear crack and intra-grain tensile crack are the two main crack types generated during rock cutting process. The cutting force responses show strong vibration with respect to the cutting distance. The magnitude of cutting force sharply drops and abruptly rises during the cutting process, which becomes more obviously with the increasing hydrostatic pressure, cutting depth and rake angle of cutter. The hydrostatic pressure, grain size and random distribution of grains have great influence on chip morphology. In contrast, comparing with the above three factors, the cutting depth, rake angle of cutter and cutting velocity have little influence on the chip morphology. These results lead to an enhanced understanding of rock breaking mechanisms in granite, and provide a basis for improving the design of rock-breaking bits.

Investigation of Damage Evolution in Heterogeneous Rock Based on the Grain-Based Finite-Discrete Element Model.

Granite exhibits obvious meso-geometric heterogeneity. To study the influence of grain size and preferred grain orientation on the damage evolution and mechanical properties of granite, as well as to reveal the inner link between grain size‚ preferred orientation, uniaxial tensile strength (UTS) and damage evolution, a series of Brazilian splitting tests were carried out based on the combined finite-discrete element method (FDEM), grain-based model (GBM) and inverse Monte Carlo (IMC) algorithm. The main conclusions are as follows: (1) Mineral grain significantly influences the crack propagation paths, and the GBM can capture the location of fracture section more accurately than the conventional model. (2) Shear cracks occur near the loading area, while tensile and tensile-shear mixed cracks occur far from the loading area. The applied stress must overcome the tensile strength of the grain interface contacts. (3) The UTS and the ratio of the number of intergrain tensile cracks to the number of intragrain tensile cracks are negatively related to the grain size. (4) With the increase of the preferred grain orientation, the UTS presents a “V-shaped” characteristic distribution. (5) During the whole process of splitting simulation, shear microcracks play the dominant role in energy release; particularly, they occur in later stage. This novel framework, which can reveal the control mechanism of brittle rock heterogeneity on continuous-discontinuous trans-scale fracture process and microscopic rock behaviour, provides an effective technology and numerical analysis method for characterizing rock meso-structure. Accordingly, the research results can provide a useful reference for the prediction of heterogeneous rock mechanical properties and the stability control of engineering rock masses.

Strength and failure mechanism of highly interlocked jointed pillars: Insights from upscaled continuum grain-based models of a jointed rock mass analogue

An optimum design of mine pillars necessitates a reliable estimation of the rock mass strength. It is known that the Hoek-Brown failure criterion, with its strength parameters obtained using the Geological Strength Index, tends to underestimate the confined strength of interlocked jointed hard rock masses. Therefore, geomechanical designs based on this approach could lead to oversized pillars due to the underestimation of the pillar core strength. In this study, a two-dimensional finite element program was used to investigate the strength and failure mechanisms of jointed pillars. For this purpose, a previously calibrated grain-based model of heat-treated marble, an analogue for a highly interlocked jointed rock mass, was upscaled to simulate jointed pillars of various width-to-height ratios. The simulation results showed that the slope of the pillar stability curve obtained from this approach is steeper than those of existing continuum and discontinuum models of jointed pillars. This is attributed to the high degree of block interlock leading to higher rock mass strength at the pillar core. It is demonstrated that this modeling approach provides more realistic results in terms of pillar failure process compared to other continuum models, in which the rock mass is simulated as a homogeneous material.

Investigating asperity damage of natural rock joints in polycrystalline rocks under confining pressure using grain-based model

A cohesive grain-based model (GBM) was employed to investigate the asperity damage response of jointed Aue granite under confined compression. The cohesive GBM was able to characterise both inter- and intra-grain contacts in distinct element method (DEM). We calibrated the model against the laboratory data, including confined and unconfined compression tests as well as Brazilian tensile test of Aue granite. We generated synthetic Aue granite specimens, including three different rock joint profiles with various joint roughness coefficients (JRC) from smooth to very rough (i.e. 4.6, 10.2, and 17.5). We conducted confined compression tests on the synthetic specimens under 2, 5, 10, and 40 MPa of confining pressures. The numerical results revealed that at high confining pressure (i.e. 40 MPa), the rock joint profile had a negligible influence of the damage response of the specimen, and only contributed to the reduction of strength. For the other numerical experiments, the intensity of asperity damage caused by grain crushing was more pronounced when the confining pressure was high. We concluded that the cohesive GBM framework has the potential to be used as a virtual laboratory for investigating the shear behaviour of jointed granitic rocks, which is challenging to be studied in the laboratory.

Grain-Based DEM for Particle Bed Comminution

The comminution at the grain size level for liberating the valuable minerals usually requires the highest size-specific energy. Therefore, a full understanding of the comminution process at this level is essential. Models based on the Discrete Element Method (DEM) can become a helpful tool for this purpose. One major concern, however, is the missing representativeness of mineral microstructures in the simulations. In this study, a method to overcome this limitation is presented. The authors show how a realistic microstructure can be implemented into a particle bed comminution simulation using grain-based models in DEM (GBM-DEM). The improved algorithm-based modeling approach is exemplarily compared to an equivalent real experiment. The simulated results obtained within the presented study show that it is possible to reproduce the interfacial breakage observed in real experiments at the grain size level. This is of particular interest as the aim of comminution in mineral processing is not only the size reduction of coarse particles, but often an efficient liberation of valuable components. Simulations with automatically generated real mineral microstructures will help to further improve the efficiency of ore processing.

Influence of grain size on strength of polymineralic crystalline rock: New insights from DEM grain-based modeling

Grain size effect on rock strength is a topic of great interest in geotechnical engineering. A consensus obtained from earlier laboratory tests is that rock strength generally decreases with the increase of grain size for both silicate and carbonate rocks; however, some recent numerical results conflict with such laboratory test results. To address this intriguing issue, the effect of grain size on strength of polymineralic crystalline rock with low porosity is investigated numerically using the grain-based modeling (GBM) approach in discrete element method (DEM) by interpreting micro-cracking process in response to loading. In agreement with some previous DEM simulation results, the simulated rock strength is found to increase with increasing grain size for both homogeneous and heterogeneous models, even when the number of assembled disks in one mineral grain changes. The mechanism of strength increase with increasing grain size is mainly associated with the number of assembled smooth-joint contacts along grain interfaces and the generation of grain boundary cracks in response to loading. The grain interfaces significantly weaken the integrity of the rock model, which is similar to effects of inherent defects in real rock. As the grain size increases, fewer grain interfaces are built in the model and the rock strength becomes much higher. Hence, by solely changing the mineral grain size in a model, the mechanism of grain size effect as observed in laboratory tests cannot be replicated. To address this issue, a method of degradation of grain boundary strength parameters is used to mimic the possible mechanism of grain size effect. The simulated strength using the method becomes comparable with those obtained from laboratory tests when the heterogeneity in the rock is considered. Degradation of grain boundary parameters with increasing grain size provides a plausible explanation for the grain size effect on rock strength.

Analysis of capillary water imbibition in sandstone via a combination of nuclear magnetic resonance imaging and numerical DEM modeling

The physics of water imbibition into initially unsaturated sandstone is critical to the understanding of displacement processes and fluid transport in the vadose zone. The distribution of water within rock is important due to its significant influence on rock mechanical behavior. Here, therefore, we used nuclear magnetic resonance (NMR) technology to visualize and quantify the dynamics of water infiltration and distribution in initially unsaturated sandstone. The progression of water imbibition in sandstone specimens under the following two conditions were analyzed: (1) specimens soaked in water for different durations and (2) specimens soaked in water for the same duration and then held in this state for different durations. An analytic function was developed to estimate the sandstone moisture profile and to determine the unsaturated flow within the sandstone when the water distribution matched laboratory observations. Finally, a three-dimensional discrete element grain-based model was formulated that incorporates the local parallel-plate method, the unsaturated flow function, and the generalized effective stress principle. We used this model to effectively reproduce the process of water imbibition in the laboratory sandstone specimens. The effect of water imbibition on the mechanical properties of the studied sandstone was also evaluated. These results show that the strength of the core of the sample was reduced as water migrated from its surface to its center, resulting in a decrease in bulk sample strength as standing duration (i.e. water distribution uniformity) increased. The results of this study aid in our understanding of the influence of water imbibition on the mechanical behavior of sandstone, which is important for rock slope stability assessments following rainfall.

A modeling study of the micro-cracking behavior of brittle crystalline rocks under uniaxial loading considering different scenarios of grain-based models

The grain-based model (GBM) in two-dimensional Particle Flow Code (PFC2D) is widely used to simulate the deformation and brittle failure of crystalline rocks. However, the original GBM consisting of the parallel-bond (PB) and the smooth-joint (SJ) produces unrealistic micro-cracking processes in which excessive microcracks are distributed along the interfaces of mineral grains under uniaxial loading. To solve the problem, this research presents a discussion of the mechanical behavior of six GBMs composed of different contact models including PB, SJ, and flat-joint (FJ). After the uniaxial compressive and direct tensile tests of numerical granites, it is found that the different contact types in GBMs have a limited influence on the tensile strength (TS), elastic modulus (E), and Poisson’s ratio (ν) but have a great impact on the uniaxial compressive strength (UCS) and microcrack pattern. The UCS calculated by the PB/FJ GBM is higher than the actual value. Microcrack distributions simulated by the FJ/SJ and FJ/PB GBMs show that numerous mineral grains are cut across under uniaxial loading instead of their interfaces. While the FJ/SJ and FJ/PB GBMs may well reproduce the brittle failure process of crystalline rocks, it remains to be seen whether they will be applicable to other rock mechanics issues, including triaxial compression, thermal cracking, and hydraulic fracturing.

An advanced grain-based model to characterize mechanical behaviors of crystalline rocks with different weathering degrees

Laboratory tests revealed that by enhancing the weathering degree, a transition of pre-peak stress-strain mechanical responses of crystalline rocks under unconfined compression from approximate linearity to nonlinearity was evident, as was the weakening of macro-mechanical properties. However, thus far, very few numerical studies have been conducted to quantitatively characterize the strong-to-weak transition of the mechanical behaviors of crystalline rocks modulated by the weathering degree. We propose an advanced grain-based model (AGBM) using Universal Distinct Element Code (UDEC) to characterize mechanical characteristics of crystalline rocks with different weathering degrees. The weathering-induced deterioration of microstructures was treated as loosening of grain contacts and weakening of their properties. It was proved that the grain contact model that considered hardening nonlinear deformation in compression and linearly elastic deformation in tension or shear was feasible and applicable to characterize the mechanical behaviors of crystalline rocks with different weathering degrees. The compression hardening deformation of grain contacts significantly affected the macro nonlinear stress-strain relation and stress thresholds of crack closure, crack imitation, stable crack growth, and unstable crack growth. We acquired new insights on the weathering-induced weakening of macro-mechanical characteristics of crystalline rock, which resulted from weakening of deformation properties of the grain contact more than grain contact strength.

Compression-Induced Tensile Mechanical Behaviors of the Crystalline Rock under Dynamic Loads.

Characterization of the tensile mechanical behaviors of rocks under dynamic loads is of great significance for the practical engineering. However, thus far, its micromechanics have rarely been studied. This paper micromechanically investigated the compression-induced tensile mechanical behaviors of the crystalline rock using the grain-based model (GBM) by universal distinct element code (UDEC). Results showed that the crystalline rock has the rate- and heterogeneity-dependency of tensile behaviors. Essentially, dynamic Brazilian tensile strength increased in a linear manner as the loading rate increased. With the size distribution and morphology of grain-scale heterogeneity weakened, it increased, and this trend was obviously enhanced as the loading rate increased. Additionally, the rate-dependent characteristic became strong with the grain heterogeneity weakened. The grain heterogeneity prominently affected the stress distribution inside the synthetic crystalline rock, especially in the mixed compression and tension zone. Due to heterogeneity, there were tensile stress concentrations (TSCs) in the sample which could favor microcracking and strength weakening of the sample. As the grain heterogeneity weakened or the loading rate increased, the magnitude of the TSC had a decreasing trend and there was a transition from the sharp TSC to the smooth tensile stress distribution zone. The progressive failure of the crystalline rock was notably influenced by the loading rate, which mainly represented the formation of the crushing zone adjacent to two loading points. Our results are meaningful for the practical engineering such as underground protection works from stress waves.

A continuum grain-based model for intact and granulated Wombeyan marble

The discontinuum numerical modeling approaches widely used to simulate brittle rock failure employ the Voronoi tessellation technique to generate polygonal grain-like structures. Using this approach, called the grain-based model (GBM), the progressive micro-cracking leading to macroscopic fracturing and failure of brittle rocks can be realistically simulated. In this paper, a GBM is developed using the continuum numerical program RS2 to reproduce the laboratory behavior of intact and heat-treated (granulated) Wombeyan marble. An iterative calibration procedure is utilized to match the macro-properties of RS2-GBM to those of marble. It is found that RS2-GBM captures some of the most important characteristics of brittle rocks, including the non-linear strength envelope and the change in the failure mode and post-peak response with increasing confinement. It is demonstrated that the peak strength and failure mode of RS2-GBM are comparable to those of previously calibrated discontinuum GBMs. The advantage of the continuum over the discontinuum GBM is its shorter computation time. It is discussed that since the granulated marble serves as an analogue for a highly interlocked jointed rock mass, its calibrated continuum GBM can be used as an alternative tool for stability analyses and design of excavations and mine pillars in jointed rock masses.

Parameter studies on the mineral boundary strength influencing the fracturing of the crystalline rock based on a novel Grain-Based Model

The grain-based model (GBM) in two-dimensional Particle Flow Code (PFC2D) is widely employed to investigate the mechanical response characteristics of crystalline rocks under external load considering the realistic petrographic texture. However, due to the poor self-locking effect of the Parallel-Bond (PB) inside the minerals and unreasonable parametric assignment for the Smooth-Joint (SJ) at the mineral boundaries, the original GBM cannot reproduce the exact microcracking process of brittle rocks. To solve the problem, the novel grain-based model (nGBM) composed of the Flat-Joint (FJ) and the SJ was proposed in our previous research, which not only enhances the rotational resistance of particles, but also improves the simulation of the mineral boundaries. In this study, the nGBM was carefully established and calibrated based on the properties of Alxa porphyritic granite. A series of simulation tests of uniaxial compression, triaxial compression and direct tension under different mineral boundary parametric conditions were carried out to observe the deformation, microcracking and failure behaviors of the nGBM. Quantitative analyses of the mineral boundary properties and the mechanical behaviors of the numerical specimen revealed the extremely complicated relationships between them, which can help explain the micromechanical damage process of crystalline rocks and provide valuable reference for the model calibration.

Time-dependent deformation analysis of the surrounding rock mass around a tunnel

A numerical time-dependent model is established by incorporating the stress corrosion model into the three-dimensional discrete element grain-based model (3DEC-GBM) to analyze the fracture evolution and instability mechanism of the surrounding rock mass around a circular tunnel. The surrounding rock of the tunnel is assumed to be made from intact Yunnan sandstone formation, whose material properties were found using laboratory experiments (ignoring scale effects). The mesoscale mechanical stress corrosion parameters in the model are calibrated to reproduce the time-independent and -dependent deformation and failure of Yunnan sandstone observed in a laboratory. The model is validated against laboratory data and then further applied to analyze the time-independent and -dependent deformation of the surrounding rock of the tunnel. The fracture evolution around the tunnel instability is numerically visualized. The failure zone around the tunnel gradually extends deeper into the surrounding rock with time, and the location of failure at the roof and floor of the circular tunnel becomes more evident as the lateral pressure coefficient increases. We conclude that the model is not only able to simulate the location of the concentrated tensile and shear stress around the tunnel but also has important theoretical guidance and practical significance for the long-term stability study of tunnels.

Calibration of coupled hydro-mechanical properties of grain-based model for simulating fracture process and associated pore pressure evolution in excavation damage zone around deep tunnels

The objective of this paper is to develop a methodology for calibration of a discrete element grain-based model (GBM) to replicate the hydro-mechanical properties of a brittle rock measured in the laboratory, and to apply the calibrated model to simulating the formation of excavation damage zone (EDZ) around underground excavations. Firstly, a new cohesive crack model is implemented into the universal distinct element code (UDEC) to control the fracturing behaviour of materials under various loading modes. Next, a methodology for calibration of the components of the UDEC-Voronoi model is discussed. The role of connectivity of induced microcracks on increasing the permeability of laboratory-scale samples is investigated. The calibrated samples are used to investigate the influence of pore fluid pressure on weakening the drained strength of the laboratory-scale rock. The validity of the Terzaghi's effective stress law for the drained peak strength of low-porosity rock is tested by performing a series of biaxial compression test simulations. Finally, the evolution of damage and pore pressure around two unsupported circular tunnels in crystalline granitic rock is studied.