Grain-based Model Research Articles

Numerical simulation of failure and micro-cracking behavior of non-persistent rock joint under direct shear

Persistency, as a key geometric parameter of joints, significantly affects shear strength parameters of jointed rock mass. A good understanding of how persistency affects shear behavior of joint is therefore crucial for better evaluation of stability of rock slope. To investigate the failure and micro-cracking behavior of non-persistent rock joint under direct shear, a novel Voronoi generation algorithm is first used to establish an improved grain-based model (GBM) of granite which considers the shape of feldspar. The calibrated model is then used to simulate the direct shear test of numerical models possessing different joint persistency under various normal stresses. The results reveal that the developed micro-cracks generally increase rapidly when the shear strain reaches to a value approximately 50 % of the peak shear strain and the grain boundary tensile micro-crack is dominant among these initiated micro-cracks. Micro-cracks generally initiate at the ends of rock bridge, and then gradually propagate to the central of rock bridge, forming en-echelon fractures. The failure mode of numerical model is closely related to the generated en-echelon fractures. An increase in both joint persistency and normal stress can lead to a shear failure. The finding in this study provides an important basis for understanding the mechanical behavior and failure mechanism of jointed rock mass.

Rate and negative Poisson’s ratio effects on Compressive Mechanical behaviors of Thermal-Damaged Crystalline Rocks using a grain-based model

Rate and negative Poisson’s ratio effects on Compressive Mechanical behaviors of Thermal-Damaged Crystalline Rocks using a grain-based model

Stress evolution in rocks around tunnel under uniaxial loading: Insights from PFC3D-GBM modelling and force chain analysis

In underground engineerings, the evolution of the stress state in the surrounding rocks can effectively reveal its fracture mechanism. To precisely describe this microscopic information, the present study utilizes the three-dimensional Grain-based model based on Particle Flow Code (PFC3D-GBM) to construct a square numerical specimen with a pre-existing hole representing a tunnel and subjected it to uniaxial loading. In this model, different types of mineral structures and internal force chain networks are distinguished at a three-dimensional scale. Furthermore, the evolution of force chain networks in the top, bottom, left and right regions around the tunnel is quantitatively characterized. The anti-fracture capability depending on stress state of various structures is calculated and then the fracture mechanism from the point of anti-fracture capability is discussed. The research results indicate that at at the beginning of loading, some red force chains with higher level have appeared on both sides of the tunnel. As the load goes on, red force chain network extending from both sides of the tunnel to the upper and lower ends of the specimen have emerged. The average value and sum value of all force chains show an increasing trend before the peak load and a decreasing trend after the peak load. The average value of force chains within a specific structure can accurately reflect the microscopic mechanical properties of that structure. The average values of force chains on the left and right sides of the tunnel are higher, both in terms of starting points and ascending rates, than those in the upper and lower regions of the tunnel. The orientation distribution of all force chains is relatively uniform, but force chains with higher level are generally align with the loading direction. The fundamental reason for the high degree of fragmentation on the left and right sides of the tunnel is that these regions bear more external load than the upper and lower regions, rather than being inherently more prone to fracture.

Investigating Mechanical Characteristics of Rocks Under Freeze–Thaw Cycles Using Grain-Based Model

AbstractBased on the discrete element method (DEM), a water-contained grain-based model (GBM) is developed in this study to evaluate the effects of freeze–thaw cycles (FTCs) on the mechanical characteristics of the rock. A set of freeze–thaw and uniaxial compression tests is carried out to explore the impact of micro damage caused by FTCs on the mechanical prosperities of rock samples. By monitoring the development and distribution of micro-cracks during freeze–thaw test and uniaxial compression test, the damage mechanism of FTCs is revealed from a microscopic perspective, which shows that FTCs deteriorate the strength and brittleness parameters as exponential functions. The parametric analysis is carried out to explore the influence of porosity and mineral components on the mechanical behaviors of rock against freeze–thaw and uniaxial loadings. Based on the parametric analysis results, it is found that UCS, Young’s modulus, and total strain energy at peak stress decrease with the increase of porosity and clay content, which emphasizes the contributions of porosity and mineral components on the mechanical properties of rock samples. It is proved that the water-contained grain-based model developed in this study can capture the damage caused by FTCs on the mechanical performance of rock from a microscopic perspective, which provides novel perspectives on the phenomenon of rock degradation in response to fluctuations in temperature.

Loading/Unloading Response of Crystalline Rocks with Varied Thermal-Damaged Degrees to Cyclic Compression Using a Grain-Based Model

Loading/Unloading Response of Crystalline Rocks with Varied Thermal-Damaged Degrees to Cyclic Compression Using a Grain-Based Model

Analysis of Granite Deformation and Rupture Law and Evolution of Grain-Based Model Force Chain Network under Anchor Reinforcement

In actual underground rock engineering, to prevent the deformation and damage of the rock mass, rock bolt reinforcement technology is commonly employed to maintain the stability of the surrounding rock. Therefore, studying the anchoring and crack-stopping effect of rock bolts on fractured granite rock mass is essential. It can provide significant reference and support for the design of underground engineering, engineering safety assessment, the theory of rock mechanics, and resource development. In this study, indoor experiments are combined with numerical simulations to explore the impact of fracture dip angles on the mechanical behavior of unanchored and anchored granite samples from both macroscopic and microscopic perspectives. It also investigates the evolution of the anchoring and crack-stopping effect of rock bolts on granite containing fractures with different dip angles. The results show that the load-displacement trends, displacement fields, and debris fields from indoor experiments and numerical simulations are highly similar. Additionally, it was discovered that, in comparison to the unanchored samples, the anchored samples with fractures at various angles all exhibited a higher degree of tensile failure rather than shear failure that propagates diagonally across the samples from the regions around the fracture tips. This finding verifies the effectiveness of the numerical model parameter calibration. At the same time, it was observed that the internal force chain value level in the anchored samples is higher than in the unanchored samples, indicating that the anchored samples possess greater load-bearing capacity. Furthermore, as the angle αs increases, the reinforcing and crack-stopping effects of the rock bolts become increasingly less pronounced.

Grain-based coupled thermo-mechanical modeling for stressed heterogeneous granite under thermal shock

Microscopic damage and macroscopic mechanical properties of granite under the coupling effect of thermal load and initial stress are crucial considerations for the safe construction of underground geo-energy engineering. However, visualizing real-time micro-crack processes in rocks under high-temperature and high-pressure conditions using the current experimental techniques remains challenging. In this study, a numerical method is developed to analyze the thermally induced damage in heterogeneous granite under the coupled influence of initial stress and thermal loading. A biaxial thermo-mechanical grain-based model considering real mineral distribution is established based on digital image processing technology, the grain-based modeling method, and heat conduction theory. The microscopic parameters are calibrated and the effectiveness of the model is verified based on thermal shock and uniaxial compression experiments. The thermal destruction mechanism of granite under initial stress from a microscopic perspective was unveiled for the first time. During the thermal shock process, the stress within the rock does not remain constant at the initial stress value. Instead, it changes continuously with the progression of heat conduction. The impact of the initial stress on the thermally induced cracks is relatively minor. Cooling causes more damage to the rock than heating during thermal shock. The intragranular cracks of quartz consistently outnumber other intragranular or intergranular cracks during thermal shock. The initial stress and thermal shock damage enhance and weaken the biaxial peak strength of granite, respectively. The weakening effect of thermal shock on the peak strength becomes more pronounced at a higher initial stress. These research findings and proposed research techniques contribute to the management and optimization of underground geo-energy engineering.

Effects of temperature on pure mode-I and mode-Ⅱ fracture behaviors and acoustic emission characteristics of granite using a grain-based model

To investigate the effects of thermally induced microcracks on the pure mode-I and mode-Ⅱ fracture behaviors of the granite, a Grain-based model (GBM) was used to build cracked straight-through Brazilian disc (CSTBD) granite specimens. Splitting tests were conducted on the CSTBD specimens treated at various temperatures under pure mode-I and mode-Ⅱ loadings, and the moment tensor algorithm was utilized to record the acoustic emission (AE) events generated by fracture during loading. The results indicate that thermally induced microcracks predominantly consist of intergranular and intragranular tensile cracks, with quartz phase transition significantly increasing the number of intragranular tensile cracks. With the increase in heat-treatment temperature, thermally induced microcracks gradually guide the initiation direction of load-induced cracks, making the crack propagation path more tortuous. The AE characteristics reveal that the fracture behavior of the CSTBD specimen heat-treated at 600 ℃ transitions from brittle to ductile. Furthermore, thermally induced microcracks can constrain the propagation distance of load-induced cracks, increasing the small-scale AE events and the b-value, thereby reducing the AE magnitude during failure.

Does double pre-notches have a greater impact than single pre-notch on the mechanical and fracture behavior of rock? Insights from three-point bending tests using the numerical approach of grain-based model

The mechanical performance of rock masses is significantly impacted by the existence of cracks. Distribution of the cracks may result in different mechanical or fracture behaviors of rock. To gain a preliminary understanding of such problems, a series of numerical tests of three-point bending (TPB) are designed and carried out with the consideration of single pre-notch and double pre-notches. The numerical method of grain-based model (GBM) approach is employed in this paper, with a validation implemented by comparing the results with previous experiments to demonstrate the reliability of this model. Afterward, a comprehensive investigation, including the mechanical behavior, strength characteristics, crack evolution and progressive failure mechanism of the above mentioned TPB tests are conducted. The conclusions are as follows: (1) During TPB tests, as the offset distance increases, the fracture mode of the single pre-notched specimens gradually transitions from Mode I to Mode II, with the peak fracture toughness occurring at a mixed Mode I-II fracture condition (2p/s = 0.4). Moreover, the failure angle, notch open degree and expansion area all tend to rise regardless of specimens of single or double pre-notches. (2) A thorough exploration of crack evolution shows that the specimens primarily fracture during the crack propagation and failure stages. Shear failure predominates among these stages, with microcracks mostly occurring inside the rock mineral grains. (3) When offset distance increases to a certain degree (2p/s = 0.8), the fracture of specimen ceases to be governed by the pre-notch; instead, it occurs directly from the middle of the beam specimen. This phenomenon can be attributed to the reduction of stress concentration at the notch tip, as inferred from analysis of the contact force chain. (4) In double pre-notched specimen, microcracks initiate at both pre-notches, but the final failure results from crack propagation at one notch tip. Compared to single pre-notched specimen, the presence of double pre-notches exhibits superior fracture resistance performance.

Grain-Based Modeling for Heterogeneous Rock Fragmentation Under Stressed Conditions and TBM Cutter Spacing Optimization

Grain-Based Modeling for Heterogeneous Rock Fragmentation Under Stressed Conditions and TBM Cutter Spacing Optimization

Dynamic fracture mechanism from a pre-existing flaw in granite: Insights from grain-based modelling

Both heterogeneity and pre-existing flaws are closely associated with the mechanical response of crystalline granite. To uncover the underlying mechanism, grain-based model (GBM) based on particle flow code (PFC), i.e., PFC-GBM, with different contacts between any two grains, was employed to carry out numerical calculations to investigate the effect of a single flaw with various inclination angles on the dynamic behavior of LdB granite. The failure pattern is identified through density and spatial distributions of microcracks, and the primary fracture directions are obtained by microcrack orientations. Microcracks are divided into inter-Grain and intra-Grain types, and these two types are further classified into more subtypes according to mineral composition. IG cracks typically form during the pre-peak stage and tend to emerge earlier than TG cracks. Conversely, TG cracks are predominantly created during the post-peak stage but constitute a significant proportion irrespective of flaw inclination angle. A novel method is also proposed to acquire high-stress particles, which promote the identification of dominant macrocrack paths. Finally, the effect of particle size is also systemically analyzed.

Study on the Meso-Failure Mechanism of Granite under Real-Time High Temperature by Numerical Simulation

In the development of geothermal resources in hot dry rocks, deep underground rock masses are typically subjected to real-time high-temperature environments. High temperatures alter the physical and mechanical properties of the rocks, directly affecting the safe and efficient utilization of hot dry rock resources. Therefore, a grain-based model (GBM) of particle flow code (PFC) was constructed based on uniaxial compression tests, and the model was verified according to macroscopic mechanical parameters and damage modes, in order to carry out the simulation study of the uniaxial compression of granite and explore the meso-failure mechanism of granite under real-time high temperature. The relationships between stress–strain curves and crack derivation, the evolution of microcracks, and the characteristics of acoustic emission activity and energy changes at different temperatures were investigated in conjunction with the results of laboratory tests. The results show that crack development, acoustic emission activity, and energy evolution during uniaxial compression include four main stages: initial compression, elasticity, plastic strengthening, and post-peak damage. The failure of granite is primarily controlled by mica and feldspar. During loading, intergranular tensile cracks first emerge within the granite, followed by intragranular tensile cracks, with shear cracks appearing last. As the temperature increases, the total number of microcracks continuously rises, the frequency of acoustic emission events increases, and both dissipated energy and boundary energy gradually decrease, showing an upward trend in the energy dissipation ratio, indicating an increase in thermal damage due to high temperatures. At 400 °C, the rate of microcrack formation increases significantly, with intergranular and intragranular cracks starting to coalesce into macroscopic cracks that extend outward. In the post-peak stage, the phenomenon of multiple peaks in acoustic emission events begins to appear. At 600 °C, the rate of microcrack formation reaches its maximum, with cracks extending throughout the sample to form a network of fractures, resulting in the granite exhibiting ductile failure characteristics.

Effect of heat treatment on microcracking behaviors and Mode-I fracture characteristics of granite: An experimental and numerical investigation

Combining thermal stimulation and tensile fracture induced by cold water injection can synergistically enhance hydraulic fracturing, improving geothermal reservoir connectivity. To investigate the heat effect on the Mode-I fracture characteristics of granite, notched semi-circular bend (SCB) granite specimens were prepared and heat-treated at five temperatures ranging from 25 to 600 ℃. Mineralogical analysis and three-point bending tests were performed on the SCB specimens, and a grain-based model (GBM) incorporating four types of mineral particles was developed. The model was simulated for heat treatment and Mode-I loading and then validated against experimental results. The behavior and evolution of intra- and intergranular microcracks in the SCB specimens during heating, cooling, and mechanical loading were analyzed. Moreover, the fracture surface morphology and microcracking mechanisms observed in the SCB specimens at different heat-treatment temperatures were discussed. The results reveal a nonlinear trend in the Mode-I fracture toughness of the SCB specimens, initially increasing and then decreasing with heat-treatment temperature. The number of thermally induced cracks escalates with increasing heat-treatment temperature, predominantly as intergranular tensile cracks, followed by intragranular tensile cracks. Under Mode-I loading, the SCB specimens heat-treated below 450 ℃ predominantly exhibit intergranular cracks, while intragranular tensile cracks become more prevalent at 600 ℃. Thermally induced cracks can alter the propagation direction and path of mechanically induced cracks, causing macrocracks to deviate from the initial straight propagation path. Scanning electron microscope (SEM) analysis illustrates that at 300 ℃ and above, the fracture surface morphology becomes more fragmented and longer microcracks appear.

Cross-scale mechanical softening of Marcellus shale induced by CO2-water–rock interactions using nanoindentation and accurate grain-based modeling

Mechanical softening behaviors of shale in CO2-water–rock interaction are critical for shale gas exploitation and CO2 sequestration. This work investigated the cross-scale mechanical softening of shale triggered by CO2-water–rock interaction. Initially, the mechanical softening of shale following 30 d of exposure to CO2 and water was assessed at the rock-forming mineral scale using nanoindentation. The mechanical alterations of rock-forming minerals, including quartz, muscovite, chlorite, and kaolinite, were analyzed and compared. Subsequently, an accurate grain-based modeling (AGBM) was proposed to upscale the nanoindentation results. Numerical models were generated based on the real microstructure of shale derived from TESCAN integrated minerals analyzer (TIMA) digital images. Mechanical parameters of shale minerals determined by nanoindentation served as input material properties for AGBMs. Finally, numerical simulations of uniaxial compression tests were conducted to investigate the impact of mineral softening on the macroscopic Young’s modulus and uniaxial compressive strength (UCS) of shale. The results present direct evidence of shale mineral softening during CO2-water–rock interaction and explore its influence on the upscale mechanical properties of shale. This paper offers a microscopic perspective for comprehending CO2-water-shale interactions and contributes to the development of a cross-scale mechanical model for shale.

Study on the characteristics of granite rock impact crack based on grain-based model

The type and heterogeneity of minerals control the initiation, aggregation, and expansion of rock blasting cracks and significantly affect the rock failure process. Granite was used to investigate the law of rock cracking under impact loading at the scale of mineral particles, and a two-dimensional grain-based model (GBM) was developed using PFC based on CT) scanning and laboratory mechanical tests. The GBM’s reliability was validated using laboratory uniaxial compression tests and numerical simulations. The specimen failure modes and evolution of microcracks during rock impact were analyzed, as well as the impact cracks’ characteristics under various impact velocities. The findings show that the GBM can simulate the microfracture behavior of several types of mineral fractures during rock impact. The evolution of granite cracks under impact loading can be divided into three stages: rapid growth, decreased growth, and gradual stabilization. The impact failure cracks of the samples were primarily tensile and intragranular. Granite’s tensile and shear fractures and intergranular and intergranular cracks of granite exhibit various trends with varying impact velocities. The GBM is viable for researching the dynamics of crystalline rocks and is a powerful tool for exploring the dynamic characteristics of rocks at the mineral particle level.

Compression-Hardening Memory of the Microstructure and Its Effect on the Cyclic Loading/Unloading Response of Crystalline Rock Using a Grain-Based Model

Compression-Hardening Memory of the Microstructure and Its Effect on the Cyclic Loading/Unloading Response of Crystalline Rock Using a Grain-Based Model

Discrete element simulation study on effects of grain preferred orientation on micro-cracking and macro-mechanical behavior of crystalline rocks

Abstract Grain-preferred orientation significantly influences the brittle fracture mechanism and failure mode of crystalline rocks. However, current grain-based models (GBMs) based on particle flow code (PFC) software are mostly proposed on the basis of the Voronoi tessellation method for grain boundary generation, which is difficult to simulate the heterogeneity of microstructure such as shape and orientation of rock minerals. To study the effect of grain-preferred orientation on macroscopic mechanical properties and microscopic characteristics of crystalline rocks, a novel grain-based microstructure transformation method (MTM) is proposed. Based on the MTM, a GBM with a target aspect ratio and crystal orientation is obtained by transforming the Voronoi crystal geometry through a planar coordinate mapping. Specifically, embedded FISH language is used to control random mineral seed size and distribution pattern to generate Tyson polygons. A polygon geometry that satisfies the rock texture is obtained as a grain boundary by spatially transforming the vertex of the Tyson polygon. The transformed complex geometry is taken as the crystal structure of the GBM, and the Lac du Bonnet granite models with different aspect ratios and crystal orientations were developed in PFC2D. Finally, a series of unconfined compressive strength tests are performed in PFC2D to verify the proposed modeling methods for the geometric variation of the crystals and to study the effects of the preferred orientation of the grains on the macroscopic mechanical properties and microscopic fracture mechanisms of the crystalline rocks from different perspectives.

Numerical insight into hydraulic fracture propagation in hot dry rock with complex natural fracture networks via fluid-solid coupling grain-based modeling

Abundant natural fractures (NFs) in hot dry rock (HDR) reservoirs serve as a crucial element in hydraulic fracturing technology and reservoir production. Nevertheless, the interaction mechanism between hydraulic fractures (HFs) and natural fracture networks (NFNs) remains poorly understood. This study combines the novel hydro-grain-based model (hydro-GBM) and discrete fracture network (DFN) model to investigate the effects of in-situ stress, fracture number, and fracture length on hydraulic fracturing behaviors in mineral-scale granite with NFNs. Results indicate that as the complexity of NFs increases, the stress shadow effect is amplified during HF propagation, while the spatial arrangement of NFs governs the propagation of secondary paths. Additionally, a downward trend is observed in average activity levels of acoustic emission (AE) events and proportions of large events within NFs and matrix. Damage and activation degrees in both NFs and matrix decrease with an increase in the number of NFs. The inability of main hydraulic paths to propagate over long distances can be attributed to the dispersion of fracturing fluid and the rapid decay of pressure within densely distributed, short NFs. These numerical findings shed light on the process of HFs activating NFNs and provide valuable insights for enhancing heat extraction efficiency in HDR reservoirs.

A novel grain growth algorithm for grain-based models for investigating the complex behavior of crystalline rock

The mineralogical composition and microstructure of crystalline rock affect its mechanical properties. However, it is challenging to analyze and quantify the associated mechanisms using experimental methods. A potential solution to this problem is to apply microscopic simulation methods, such as a combination of the discrete element method and grain-based model (GBM). A prerequisite for microscopic simulations is to accurately reproduce the microscopic features, especially the interactions between grains. Inspired by the crystallization of polycrystalline rocks, a novel grain growth algorithm that constructs a GBM by simulating the sequential crystallization process is proposed in this paper. The results of comprehensive analyses show that the proposed modeling method can accurately reproduce the mineralogical compositions, euhedral-to-anhedral morphology transitions, and grain size distributions during different crystallization processes. By accurately reproducing the interlocking structure between grains, the proposed method can simulate typical mechanical behaviors, such as the nonlinear strength envelope, uniaxial compressive strength-to-tensile strength ratio, and bimodularity, which are consistent with the experimental findings. The effectiveness of this method in modeling porphyritic structures and grain-scale anisotropic textures is demonstrated, and the microscopic mechanism of fracture mode transition associated with the difference in grain structures is discussed.

Impact of soft minerals on crack propagation in crystalline rocks under uniaxial compression: A grain‐based numerical investigation

AbstractVarying external conditions in the metallogenetic process of crystalline rocks contribute to the complex mineral and textural characteristics, rendering the mechanical properties highly heterogeneous at the mineral scale. This research focused on the influences of minerals with relatively low strength and stiffness (soft minerals) in crystalline rocks on their cracking behavior. A particle‐based discrete element method (DEM) was first employed to establish random grain‐based models (GBM) of crystalline rocks containing soft minerals with different contents, strengths, and stiffnesses. On this basis, responses of the mechanical properties and crack propagation to these parameters were systematically investigated and an optimized micro‐parameter calibration method for real CT (computed‐tomography) ‐based GBM was then proposed considering the characteristics of soft minerals. The results demonstrate that with the decrease of the strength of soft mica, the intragranular cracks are prone to initiate and propagate inside the soft minerals and lead to the final crack coalescence. The decrease in the stiffness of soft minerals enhances their controlling effects on the cracking propagation. Based on the CT‐based granite model, it was found that a heterogeneous stress field is produced due to the spatial distribution of the soft (mica) and hard (quartz and feldspar) minerals, and the mica minerals tend to terminate cracks or force cracks to deflect or bypass individual grains during crack propagation. This study sheds light on the damage and failure processes of crystalline rocks with contrast mineral components.