Grain-based Model Research Articles

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.

Modelling micro-cracking behaviour of granite during direct tensile test using cohesive GBM approach

We employed a cohesive grain-based model (GBM) to investigate the mechanical behaviour and micro-cracking response of Neuhauser granite under direct tensile loading. The microstructural properties of Neuhauser granite were incorporated into the numerical model, and hourglass-shaped specimens were generated based on the geometrical configuration of specimens. We proposed an alternative calibration procedure, and the numerical observations revealed that the cohesive GBM could accurately reproduce the failure behaviour of physical specimen. At the same time, the conventional GBM failed to return a reliable output. The calibration procedure was augmented by examining the impacts of the random distribution of minerals and tensile loading rate on the fracture behaviour of GBM specimens. Besides, pre-cracked granite was generated to investigate the influence of pre-existing cracks on mechanical and fracture behaviour. By increasing the flaw inclination angle, the peak tensile strength of both single and double flaw specimens was increased. The micro-cracks initiated from flaw tips and extended horizontally towards the side of specimens. At low flaw inclination angles, the macroscopic tensile fracture was almost identical to that of intact rock while the fracture pattern was different at high flaw angles.

On the Failure Mechanism of Brittle Granite in 2-D Rock Indentation

Abstract Rock indentation is one of the main mechanical rock breaking approaches, in which the indenter moves perpendicular to the rock surface. A detailed understanding of the failure mechanism of brittle granite is of great importance to achieve high efficiency in rock breaking and to optimize the cutting parameters during deep hard formation drilling. In the present study, a rock indentation simulation model of Ya’an granite is carried out, using the grain-based model (GBM), which is based on the discrete element method of Particle Flow Code (PFC2D), to reproduce the crack initiation, propagation, and coalescence processes in intact rock. This study also includes an experimental program to examine the crack initiation, propagation, and the acoustic emissions in rock specimens. The results show that the microcracks generate gradually in intact rock with respect to penetration depth, and some of the microcracks coalesce with the crack number increasing, eventually resulting in the macrofracture formation. Four types of microcracks will generate during the indentation: intragrain tensile crack, intragrain shear crack, intergrain tensile crack, and intergrain shear crack. Among these four types of cracks, the intergrain tensile crack and intragrain shear crack are the two main crack types generated in indentation, especially the intergrain tensile crack. The rock failure mechanisms are different with the variation of grain size, and the lateral fragmentation of rock is restricted because of the chip hold-down effect of hydrostatic pressure. This study leads to an enhanced understanding of rock breaking mechanisms of Ya’an granite and provides the basis for improving the rock excavation machine design.

A grain-based model considering pre-existing cracks for modelling mechanical properties of crystalline rock

Mechanical properties of crystalline rock are greatly affected by its micro-structures which are characterized as highly-interlocked polygon grains and presence of micro-defects. Due to insufficient consideration of micro-structures in crystalline rock, previous simulations using discrete element method (DEM) cannot realistically reproduce the mechanical properties of crystalline rock including crack closure behaviour and high ratio of uniaxial compressive strength (UCS) against tensile strength (TS). The irregular shape of minerals in crystalline rock is modelled by discrete element method (DEM) using grain-based model (GBM). Presence of initial cracks is incorporated into GBM by introducing two notional contact surfaces to model gradual closure behaviour under compressive loading, and to obtain a higher UCS/TS ratio. The stress-strain response and crack evolution including crack closure, crack initiation, crack coalescence as well as development of macroscopic shear failure can be realistically reproduced with the proposed model. A calibration procedure is proposed to match properties of Remiremont granite under room temperature. The influence of initial cracks on the rock is then comprehensively studied. The simulation results show a good agreement with the experimental outputs under various treatment temperatures. By modelling the polygon grain and pre-existing cracks, the simulated UCS/TS ratio can be more realistic and increased up to a value of 49.

Modeling Damage Evolution in Heterogeneous Granite Using Digital Image-Based Grain-Based Model

A particle-based discrete element model combined with digital image processing to take into account the grain geometry and size distribution is used to investigate the mechanical and microcracking behavior of Beishan granite (BG), a typical crystalline rock potential for nuclear waste disposal in China. First, the procedure to construct a digital image-based grain-based model is introduced. The unsupervised K-means clustering algorithm is used to determine mineral boundaries, and four micro-parameters are assigned according to the Weibull distribution to reflect micro-heterogeneity of rock. Then, the model is calibrated to the macro-properties of BG obtained from laboratory tests, and consistency between model simulation and laboratory test results of both microcracking processes and failure modes is found. It is shown that intragrain cracks are initiated successively in quartz, feldspar, and mica; and their numbers in quartz and feldspar are much more than that in mica. Crack cluster, forking cracks and cataclastic microcracking are typical in quartz, while the “voids” is found in mica. Grain property heterogeneity has a significant impact on micro-cracking behavior and macro-properties of the model, with greater heterogeneity resulting in a lower uniaxial compression strength and elastic modulus, and a more scattered distribution of microcrack inclination. The modeling procedures presented here provide an effective method for investigating mechanical and damage behavior of granites, with specific consideration of heterogeneity involving the distribution of mineral grains and their mechanical properties.

Grain-scale failure mechanism of porous sandstone: An experimental and numerical FDEM study of the Brazilian Tensile Strength test using CT-Scan microstructure

Many widely used numerical models of rock fracture based on mesoscale laboratory test characterisation of effective ‘intact’ strength parameters neglect microstructure effects. They therefore cannot explain grain boundary and pore effects on crack propagation and consequently are inadequate for models of rock destruction that exploit point and indentation stresses. Understanding deep drilling processes involving drill-bit buttons and/or water-jetting where rock loading is concentrated in domains with fewer mineral grains will therefore require models with microstructure. To investigate microscale failure mechanisms of granular rocks in diverse scenarios, we target a porous sandstone and introduce a novel workflow consisting of a computerized tomography (CT) based microstructure construction approach and a complementary mechanical numerical approach. The construction approach extracts the realistic rock microstructure and transforms the large voxel number CT-scan data into significantly fewer triangular elements. The finite-discrete element method (FDEM) with grain-based model (GBM) is adopted to solve the mechanics. The microscale failure mechanism of sandstone during the Brazilian test was thoroughly analysed using the numerical results together with the post failure CT-scan test data. The build-up of compressive and tensile stress chains, micro-crack nucleation, local relaxation, chain switching and final crack-path development exploiting pores was illustrated, revealing the micro-to-macro failure mechanism in time and space. Fracture paths in the specimens during Brazilian tensile test were dominated by the pores and the inter-grain boundaries. The tensile strength of the inter-grain joints was estimated to be at least 3.67 times the mesoscale specimen's intact tensile strength, while the pores account for 72.76% of the fracture path. The influence of the cementation distribution and microscale discontinuities was investigated with numerical cases.

Numerical investigation of micro-cracking behavior of brittle rock containing a pore-like flaw under uniaxial compression

Pore-like flaws, which are commonly encountered in brittle rock, play an important role in the engineering performance of structures constructed in or on rock. Experimental and numerical investigations of micro-cracking mechanism of rock containing a pore-like flaw can enhance our knowledge of rock damage/failure from a microscopic view. In this study, the influences of a two-dimensional circular pore-like flaw with respect to its diameter and position on the strength and micro-cracking behavior of brittle rock under uniaxial compression are numerically investigated. The results reveal that the strength and elastic modulus are significantly affected by the diameter and position in the pore. The uniaxial compressive strength and elastic modulus of the numerical model with a pore diameter of 15.44 mm located in the center of the model are found to decrease by 58.6% and 56.4% respectively when compared with those of the intact model without a pore. As the pore position varies while the porosity remains unchanged, the simulated uniaxial compressive strength and elastic modulus are also found to be generally smaller than those of the intact model without a pore. When a pore-containing numerical model is loaded, the micro-cracks are found to mostly initiate at the top and bottom of the pore, due to the local tensile stress increase. The simulation results of the early-stage micro-cracking process and stress distribution are in a generally good agreement with the analytical solution obtained from the Kirsch equations. The grain-based model used in this study can not only study the crack initiation on the boundary of the pore but also provide a convenient means to analyze and visualize the temporal and spatial micro-cracking process after the crack initiation, which accounts for the variations in the simulated strength and modulus satisfactorily from a micro-cracking view.

A 3D Grain-Based Model for Simulating the Micromechanical Behavior of Salt Rock

A novel 3D grain-based model (3D-GBM) based on Voronoi tessellation technology is proposed and implemented into a three-dimensional particle flow code (PFC3D) to investigate the micromechanical properties of salt rock at the grain scale. Parameter calibration is performed for numerical test configurations with various microparameters matched with the macroresponses observed in laboratory experiments (e.g., uniaxial compression test, triaxial compression test, and the Brazilian splitting test). Verifications comparing the simulated results and laboratory tests indicate that the 3D-GBM provides an alternative and promising approach for efficiently reproducing the micromechanical behavior of crystalline salt rocks.

Mesoscopic time-dependent behavior of rocks based on three-dimensional discrete element grain-based model

Abstract A three-dimensional discrete element grain-based stress corrosion model incorporating the theories of subcritical crack growth and chemical reaction rate was built to explore the time-dependent behavior of damage evolution and fracture patterns of brittle rocks on a mesoscopic scale. The model was first validated and the model accurately captured the evolution of damage (tensile and shear microcracks) on the mesoscopic scale and the macroscopic mechanical behavior (the strength, and failure patterns) observed in laboratory experiments. The subcritical parameters of the model were calibrated to match the time-dependent damage deformation behavior observed in laboratory experiments. The time-dependent numerical results replicated the typical decelerating-accelerating axial strain behavior seen in laboratory brittle creep experiments. The crack propagation pattern in the simulation indicated that tension cracks were dominant. The results of numerical simulation showed that the time-to-failure during brittle creep decreased with the increase of the stress level, while the initial strain value, initial damage value, and minimum creep strain rate increased, as observed previously in the laboratory. We conclude therefore that the presented model supports a rich set of grain-scale discontinuities that can be related to microstructural features and provides a deeper understanding of the evolution of time-dependent damage on the mesoscale.

Numerical Study of the Influence of Joint Angle on the Failure Behavior of Randomly and Nonpersistently Jointed Rock Mass

The generation of nonpersistent joints in numerical specimens is not easy to achieve in some geotechnical numerical software. In this paper, the synthetic rock mass modeling method was used to construct a group of numerical specimens based on triangular grain-based model and random joint set (RJS) model in universal discrete element code. The randomly distributed nonpersistent joints have seven dominant inclination angles. Then the unconfined compressive strength (UCS) tests of the seven groups of specimens were carried out numerically to obtain some insight into the influence of dominant inclination angle on strength behaviors, failure modes and fracture development. The inclination angles of the nonpersistent RJS have fluctuant effect on the UCS of the specimens. The maximum UCS appeared when the RJS angle is 90°, and small UCS values appeared when the RJS angles are 45°, 60° and 75°. With decreasing RJS angle, the brittleness gradually changes into ductility, and strain hardening occurs. During the whole uniaxial compression process, shear fractures take the dominant role during the preliminary stage and then reduce gradually, while the tensile fractures have an inverse variation trend during the initial stage and significantly increase when the axial strain exceeds 0.6% and then keeps growing until the compression ending. The nonpersistent RJSs with small and large angles have little contribution to the shear fracture development, and only the RJSs with median inclination angles (45°, 60°) significantly promote the shear fracture propagation and development, while the RJS makes an increasing contribution to the tensile fracture propagation and development with the increase in the RJS inclination angle.

3D Grain-Based Mesoscale Modeling of Short Fatigue Crack Growth for Bridge Weldments Considering Crack-Front Evolution

AbstractTo evaluate short crack growth and fatigue damage accumulation in steel structures, efforts have been made based on a two-dimensional (2D) grain-based model for fatigue life assessment unde...

FDEM Simulation of Rocks with Microstructure Generated by Voronoi Grain-Based Model with Particle Growth

Rock strength variation is closely related to its microstructure. With the development of computer technology, the numerical model of rocks can be constructed via computer programming, and the numerical simulation avoids a mass of redundant experimental tests and usually limited by the samples retrieved from the sub-surfaces. In previous studies, the microstructure in the numerical model is generated randomly. In this paper, a novel methodology for generating the polycrystalline rock microstructure by a Voronoi grain-based model with particle growth is proposed. The 3D Voronoi tessellations in this numerical model generation procedure do not consist of random poly-crystals; the distribution of the poly-crystals varies in shapes and sizes, which represent different mineral grains, and is determined by petrographic data with the 3D particle growth method. The uniaxial compression tests and tension tests are simulated via a combined FDEM and cohesive crack propagation model. The results demonstrate that the numerical simulation agrees well with the experimental study. More importantly, the fracture patterns in the micro-scale are gained, similar to the results obtained from laboratory experiments. The novel Voronoi grain-based model with the particle growth method can reconstruct the microstructure of polycrystalline rocks and provide further information in understanding the micro-behaviors of rock materials.

A grain-based time-to-failure creep model for brittle rocks

Long-term stability analysis and stand-up time prediction of underground excavations are important in engineering design and construction. A Time-to-Failure (TtoF) creep model is proposed for the simulation of lifetime of intact brittle rock under uniaxial and triaxial loading conditions. In the TtoF model, the grain-based modeling approach using UDEC is adopted to describe the heterogeneity and micro-fractures of rock. The time-dependent deformation behavior of a grain cell is assumed to obey the Burgers creep model. The viscosity coefficient of the Maxwell component is modified to relate it to stress. The time to enter the acceleration creep deformation stage is considered as a function of the stresses and the strength parameters of the grain cell. A damage index is defined as a function of the strength parameters and the center-driving-stress ratio at a given time. Degradation of grain boundary is considered to measure the roughness corrosion of contact. The validity of the TtoF model is verified using laboratory uniaxial and triaxial compression test data of brittle rocks. The model can be useful for investigating time-dependent deformation behaviors of brittle rock and determining stand-up time of rock structures.

Numerical modeling of geomaterial fracture using a cohesive crack model in grain-based DEM

This paper aims to study the mechanical behavior of rocks using the cohesive crack model (CCM) and grain-based model (GBM) within the distinct element method (DEM) simulations. In the GBM-DEM, the Voronoi tessellation scheme is used and the intact material is simulated as assemblies of a number of particles bonded together at their contact areas. Implemented CCM defines the nonlinear behavior of the grain interfaces under various modes of loading. Numerical simulation of a tension–compression and direct shear tests is conducted to verify the correct implementation of CCM. Moreover, in the application of such a numerical framework, the uniaxial and biaxial compression tests as well as the Brazilian disc test are simulated in the universal distinct element code using a calibration process and then the results are compared with the relevant responses of the rock sample. Finally, the capability of soft computing method, i.e., artificial neural network (ANN) for predicting macromechanical parameters of rock, i.e., UCS based on input cohesive contact shear strength parameters, i.e., cohesion and friction angle, is explored. Results indicate that the ANN model can be quite accurate predictor of uniaxial compressive strength (UCS) and therefore used as a potential tool to aid in estimating target values.

Meso-Scale Simulation of Concrete Uniaxial Behavior Based on Numerical Modeling of CT Images.

It is important to study the failure mechanism of concrete by observing the crack expansion and capturing key structures at the mesoscale. This manuscript proposed a method for efficiently identifying aggregate boundary information by X-ray computed tomography technology (CT) and a discrete element modeling method (DEM) for equivalent random polygon aggregates. This method overcomes the shortcomings of the Grain Based Model (GBM) which is impossible to establish a mesoscopic model with a large difference in grain radius. Through the above two methods, the CT slice images were processed in batches, and the numbers of edges, axial length, elongation of the aggregate were identified. The feasibility of the method was verified by the comparison between experimental and simulating results. Three mesoscopic models for different porosities were established. Based on aggregate statistics, this manuscript achieved the meso-model recovery to the maximum extent. The test results show that the crack appeared at the tip of the aggregate firstly, and then the broken boundary was applied in the direction of the applied load and around the pores. Finally, the crack was selectively expanded under the axial force. During the loading process, the minor principal stress was normally distributed. As the porosity and loading time increased, the heterogeneity increased.

A cohesive grain based model to simulate shear behaviour of rock joints with asperity damage in polycrystalline rock

A cohesive grain based model is proposed to simulate the fracture behaviour of polycrystalline rocks. The model was employed to characterize the cracking response of both inter- and intra-grain contacts in the grain based model (GBM). The model was implemented in distinct element codes and its ability to mimic the mechanical and failure behaviour of polycrystalline rocks was demonstrated through calibration of several granitic rocks including Adelaide black granite, Eibenstock II granite, and Aue granite. The calibrated model of Aue granite was used to assess the effect of joint roughness coefficient (JRC) on asperity damage and shear mechanism of rock joints (i.e. grain crushing) under constant normal load (CNL) and constant normal stiffness (CNS) conditions. The bond-break in intra-grain contacts contributed to asperity damage in form of grain crushing. The numerical observations showed that under CNS condition asperity damage increased with increasing initial normal stress and JRC, and rough rock joints exhibited more dilative response.

Weibull grain-based model (W-GBM) for simulating heterogeneous mechanical characteristics of salt rock

This research presents a Weibull statistical grain-based model in two-dimensional Particle Flow Code (PFC2D) to describe the microstructural heterogeneity induced by grain shapes based on centroidal Voronoi tessellation technology. A consistent parameterization strategy based on macroscopically measured data of Qianjiang salt rock was implemented to determine the microparameters of the numerical model. Deformation response, strength characteristics as well as microcracking behavior are examined by varying heterogeneity of numerical specimens under uniaxial compression and compressive tests with various confining pressures. The simulated results indicate that the proposed model is capable of predicting the mechanical behavior of salt rock in the laboratory and numerical conclusions.

Factors Controlling the Difference in Brazilian and Direct Tensile Strengths of the Lac du Bonnet Granite

Laboratory tests showed that the average direct tension strength (DTS0) of the Lac du Bonnet granite was 6.9 MPa, and significantly less than its average Brazilian tension strength (BTS0), i.e., 8.8 MPa. In this paper, a grain-based model (GBM) with a 2D universal discrete element code (UDEC) was used to explore factors that could control the difference in the direct tension strength (DTS) and Brazilian tension strength (BTS) of the Lac du Bonnet granite from the micromechanical point of view. Micro parameters of the grain contacts were investigated, i.e., the tensile strength (T), cohesion (c), friction angle (φ), and the ratio of the shear to normal stiffness (λ). Results show that both BTS and DTS highly depended on log(λ). With an increase in log(λ), the BTS first increased nonlinearly and decreased instead after achieving a peak while the DTS always increased nonlinearly. The BTS was sensitive to T and c, while the DTS was mainly sensitive to T. The ratio of DTS to BTS first decreased with the increase of log(λ) and then increased instead from a minimum. It was found that the GBM with UDEC can well reproduce the uniaxial compression, direct tension and Brazilian tests of the Lac du Bonnet granite simultaneously only on condition that λ = 2.51. This indicated that the shear stiffness of the grain boundary in the Lac du Bonnet granite may be several times larger than its normal stiffness. This may be the main factor controlling the difference in the BTS and DTS of the Lac du Bonnet granite.

Refined Approaches for Estimating the Strength of Rock Blocks

Micro-discrete fracture networks (μDFNs) have been integrated into grain-based models (GBMs) within the numerical software UDEC to assess rock block strength through a series of unconfined compressive strength (UCS) tests of progressively larger in size numerical specimens. GBMs were generated by utilizing a Voronoi tessellation scheme to capture the crack evolution processes within the intact rock material, and μDFNs were separately created and embedded into the GBMs to simulate the effect of pre-existing defects. Various μDFNs realisations were generated stochastically within the software FracMan to assess the combined impact of defect intensity, persistence, strength and specimen size. The resulting synthetic rock block models were used to assess the “flawed” material strength at block scale through a rigorous sensitivity numerical analysis. The acquired results predict a progressive strength reduction with decreasing intact rock quality and certain trends are captured when rock block strength is expressed as a function of a newly proposed “Defect Intensity× Persistence” factor. This allow us to standardise the data along specific strength reduction envelopes and to propose generic relationships that cover a wide range of defect geometrical combinations, defect strengths and sample sizes. Accordingly, an attempt is undertaken to refine two existing empirical approaches that consider the effect of scale and micro-defects explicitly for predicting the UCS of rock blocks.

Numerical Investigation of Radial Strain-Controlled Uniaxial Compression Test of Äspö Diorite in Grain-Based Model

A complete stress–strain curve is difficult to obtain for Class II rocks because of the abrupt failure after peak stress. Although the servo-controlled loading system has been used successfully in laboratory tests to analyze the failure of Class II rocks, improved simulation techniques are still needed to control the failure of Class II rocks. In this study, the Class II behavior of Aspo diorite was reproduced explicitly using the GBM-UDEC model. The relative differentiations in all mechanical properties between the simulation and laboratory tests were within ± 5%, such as Young’s modulus, and slope of the post-peak stress–strain curve. Based on the stress and crack generation in UCS test simulation, the failure behavior of the Aspo diorite in the post-peak stress region could be classified into three stages: (V) unstable crack growth with decreasing stress, (VI) stable crack growth with increasing stress, (VII) unstable crack growth, and failure of the rock specimen with decreasing stress. Throughout the simulation, the microcrack investigation was conducted in the aspect of number, angle, relative strength of contacts, and location. In the pre-peak stress region, the cracks between 0° and 20° with respect to axial stress was dominant with over 62% of population among total cracks. Cracks were generated preferentially in relatively weak contacts. The ratio of brakeage in the weakest contact was 22%, while the average breakage value of the other stronger contacts was 16%. In the post-peak stress region, the number of cracks generated between 20° and 40° was approximately 1.4 times higher than those between 0° and 20° at Stages V and VII. There was a significant increase in the number of cracks in the strongest contacts when the model was at the beginning of Stage V and Stage VII. In Stage VII, microcracks were generated intensively in central column of the rock model. Moreover, crack coalescence was monitored in the inner column and rock spalling, complete detachment of block in rock specimen model, was observed at the lateral side of the rock model in Stage VII. In the energy calculation, 23% of the strain energy stored in the model was extracted immediately after peak stress to prevent the violent failure of the rock and most of the energy extracted resulted from grain blocks compared to contacts.