Flow Code Research Articles

Experimental and Numerical Simulation Study on the Mechanism of Fracture-Increasing and Permeability-Increasing in Granite Pore Walls by the Air DTH Hammer Percussion Drilling

Air DTH (Down-The-Hole) hammer percussion drilling (vibration percussion drilling) has proven to be a highly efficient geothermal drilling technique, and percussion fractures near the wellbore benefit geothermal energy development in many ways (such as hydraulic fracturing, perforation, etc.). However, no research has been done on the mechanism of fracture-increasing and permeation-increasing in granite pore walls by air DTH hammer percussion drilling. This article: (1) using an air drilling test device, an air DTH hammer whole bit impact rock fragmentation test was conducted on granite in an atmospheric environment; (2) dyeing experiments, CT scanning, and 3D reconstruction modeling were used to characterize and identify wellbore cracks; (3) research the strength, porosity, and permeability changes of granite wellbore through mechanical and permeability testing experiments; and (4) numerical simulation of impact stress waves using particle flow code (PFC) 6.0 software to demonstrate the rationality of impact experimental results. The results show that the air DTH hammer impact can induce micro-cracks in the wellbore, and the distribution of cracks is regionalized, mainly due to the attenuation of the impact stress wave. The numerical results are consistent with the experimental results. The average strength of granite decreased by 16.5%, the average porosity increased by 9.5%, the average permeability increased by 63.3%, the porosity increased from 0.0025% to 0.03%, and the porosity increased by about 12 times under the air DTH Hammer percussion drilling. The above results provide the theoretical basis and experimental proof for the ability of air DTH hammer drilling to produce wellbore cracks and improve wellbore permeability. The presented experimental results can be a useful reference for building numerical models.

Effects of weathering depth and thickness on rock failure: Experimental approach and particle flow code simulation

This study investigated the effects of weathering depth and thickness on the failure mechanisms of rock samples through experimental and numerical methods. The first configuration involved conducting artificial weathering on limestone using the freezing and thawing (F-T) for 40 cycles. The mechanical parameters of the samples were measured at the end of the 40th cycle. In the second configuration, a series of specimens underwent salt crystallization (S-C) tests for 20 cycles. Experimental results were validated using discrete element method (DEM). Next, the weathered limestone model with dimensions of 108 mm × 54 mm were prepared. The weathering layers were tested at four different thicknesses (i.e. 2.5 mm, 5 mm, 7.5 mm, and 10 mm) and three different positions (at the surface, 5 mm under the rock surface, and 10 mm under the rock surface). According to the results, weathering depth and thickness have a considerable effect on the failure process. The results also showed a correlation between the values of compressive strength and failure mechanisms associated with the weathering layer. The numerical results revealed that the tension crack was the dominant factor. Additionally, with increasing weathering thickness, Young's modulus, crack initiation stress, and final strength decreased in constant weathering depth. The results also demonstrated that the failure progress of the numerical models was similar to that observed in the laboratory.

Migration trajectories and blocking effect of the fine particles in porous media based on particle flow simulation

The particle flow code method based on the discrete element method was used to establish the seepage migration model of fine particles [fine particles (FPs), i.e., suspended particles] in a porous medium. A series of numerical simulations were carried out by changing the particle size, seepage velocity, particle injection number, and wide particle size gradation. The research showed that large FPs play a major role in blocking porous medium channels when the injected FPs have a wide size gradation. Due to the blocking effect, small FPs that would not otherwise have deposited also deposit. Moreover, by increasing the number of large FPs in the mixed particles, the total number of particles deposited and the number of smaller FPs deposited will also increase. The distribution of FPs in porous mediums can be divided into three types: surface deposition, internal deposition, and non-deposition. When the seepage velocity increases and reaches a seepage threshold, which is the critical seepage velocity, the deposited FPs will once again be in a suspended state and undergo migration. On the contrary, the FPs will continue to maintain their sedimentary state, and the critical seepage velocity will also increase correspondingly with increasing particle size.

Numerical Simulations for Deformation and Failure of Layered Rock Slopes and Their Support Design by Particle Flow Code

Numerical Simulations for Deformation and Failure of Layered Rock Slopes and Their Support Design by Particle Flow Code

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.

Effect of Confining Pressure on the Macro- and Microscopic Mechanisms of Diorite under Triaxial Unloading Conditions

In this study, the response mechanism between macro- and microscales of deep hard-rock diorite is investigated under loading and unloading conditions. Moreover, the statistical theory is combined with particle flow code simulations to establish a correlation between unloading rates observed in laboratory experiments and numerical simulations. Subsequent numerical tests under varying confining pressures are conducted to examine the macroscopic mechanical properties and the evolution of particle velocity, displacement, contact force chain failures, and microcracks in both axial and radial directions of the numerical rock samples during the loading and unloading phases. The findings indicate that the confining pressure strength curve displays an instantaneous fluctuation response during unloading, which intensifies with higher initial confining pressures. This suggests that rock sample damage progresses in multiple stages of expansion and penetration. The study also reveals that with increased initial confining pressure, there is a decrease in particle velocity along the unloading direction and an increase in particle displacement and the number of contact force chain failures, indicating more severe radial expansion of the rock sample. Furthermore, microcracks predominantly accumulate near the unloading surface, and their total number escalates with rising confining pressure, suggesting that higher confining pressures promote the development and expansion of internal microcracks.

Failure Behavior and Fracture Evolution Mechanism of Coal with Fissures around Holes.

The fracture of coal is the main channel of gas flow and an important factor affecting the stability and efficiency of gas drainage boreholes. The coal structure, the development of hole cracks, and the degree of deformation are different. It affects the strength and mechanical deformation characteristics of coal to a great extent. In order to investigate the law of fracture evolution around the borehole of fractured coal, uniaxial and triaxial compression tests of raw coal samples have been carried out. The stress field evolution characteristics of fractured coal under compression were analyzed by Particle Flow Code (PFC2D). The strength, deformation, and fracture evolution behavior of fractured coal around boreholes under different confining pressures were studied. The results show that the compressive strength and fracture morphology evolution characteristics of coal around the hole are obviously related to the confining pressure and fracture occurrence of raw coal. The borehole structure itself has an important influence on the distribution location of the shear failure zone of the fracture around the hole, and its influence degree increases with the decrease of borehole confining pressure. During the deformation of coal with cracks around the hole, the initiation, propagation, and union behavior of cracks are related to the crack angle β. The cracks with β 0 and 180° are most easily closed during compression and the cracks with β 90° have little effect on the crack propagation zone. When the crack angle β is 45°, it is most easy to sprout and expand at the end; when the coal is compressed to the ultimate strength, the increase rate of the tensile crack increases, and the polymerization and combination behavior of the crack is more obvious. The evolution cloud map of the stress field can better reflect the evolution characteristics of fracture development, expansion, and fracture in the process of coal loading. Studying the failure behavior and fracture evolution mechanism of the coal around the hole can better predict and control the gas migration and extraction effect, which is of great significance to prevent the occurrence of gas accidents.

Dynamic impact of unsupported sleepers on railway infrastructure with a coupled MBD-DEM-FDM model

This paper introduced a numerical simulation model of vehicle-track-substructure system, which combines the multi-body dynamics method (MBD), the discrete element method (DEM) and the finite difference method (FDM). In this model, rail, fastener, sleeper and ballast particles were built based on the DEM by using Particle Flow Code (PFC) software, substructure (including subgrade and foundation) was built based on the FDM by using Fast Lagrangian Analysis of Continuum (FLAC) software, and the vehicle was built based on the MBD by self-programming. Here, two-way coupling calculation is implemented to satisfy the force equilibrium and displacement compatibility between railway components established by different method. And then, this coupled MBD-DEM-FDM model was validated by comparing the results with those from the classical vehicle-track dynamic model (VTCD model) and field test results. Afterward, the influence of unsupported sleepers on meso and macro dynamic behaviour of railway infrastructure was investigated. The coupled MBD-DEM-FDM model possesses the capability to accurately simulate the interaction between trains and tracks, analyze the meso mechanical responses of railway infrastructure, and capture significant subgrade deformations. Consequently, the proposed model offers a comprehensive understanding of the deterioration processes within railway infrastructure.

Discrete element analysis on impact failure mechanism of “Zhengzhou 7.20” catastrophic flood for coal gangue railway subgrade

Limited research has been conducted on the failure mechanism of coal gangue railway subgrade structures during catastrophic flood disasters, including the impact of varying flood impact heights and load sizes. This study investigates the process and mechanism of coal gangue railway subgrade failure in the coal mining subsidence area, in conjunction with the “7.20” catastrophic flood in Zhengzhou. First, various factors such as impact forms, impact height, flow velocity, water depth, and wave height are considered, and a wave-water flow coupling calculation method is proposed to determine the catastrophic flood load acting on inclined slopes. The maximum impact load calculated is then applied to simulate the impact process of the catastrophic flood using Particle Flow Code 2D. As the flood-related parameters increase, the maximum impact load on the subgrade slope also increases, leading to the breakdown of the subgrade and causing fatal damage. Finally, the failure process of the coal gangue railway subgrade under the impact and scour of a catastrophic flood is divided into three stages: erosion weakening, potential failure surface formation, and overall failure. The main failure mechanisms of each stage are revealed. These research result findings offer valuable insights for the design of railway subgrade reinforcement under catastrophic flood conditions.

Excavation compensation and bolt support for a deep mine drift

To overcome large deformation of deep phosphate rock roadways and pillar damage, a new type of constant-resistance large-deformation negative Poisson's ratio (NPR) bolt that can withstand a high pre-stress of at least 130 KN was developed. In the conducted tests, the amount of deformation was 200–2000 mm, the breaking force reached 350 KN, and a high constant-resistance pre-stress was maintained during the deformation process. A stress compensation theory of phosphate rock excavation based on NPR bolts is proposed together with a balance system for bolt compensation of the time-space effect and high NPR pre-stress. Traditional split-set rock bolts are unable to maintain the stability of roadway roofs and pillars. To verify the support effect of the proposed bolt, field tests were conducted using both the proposed NPR bolts and split-set rock bolts as support systems on the same mining face. In addition, the stress compensation mechanism of roadway mining was simulated using the particle flow code in three dimensions (PFC3D)-fast Lagrangian analysis of continua (FLAC3D) particle-flow coupling numerical model. On-site monitoring and numerical simulations showed that the NPR excavation compensation support scheme effectively improves the stress state of the bolts and reduces the deformation of the surrounding rock. Compared to the original support scheme, the final deformation of the surrounding rock was reduced by approximately 70%. These results significantly contribute to domestic and foreign research on phosphate-rock NPR compensation support technology, theoretical systems, and engineering practices, and further promote technological innovation in the phosphate rock mining industry.

A meso‐damage‐based constitutive model for yellow sandstone under dry–wet cycles

AbstractThe mechanical properties of rocks weaken under dry–wet cycles. This weakening may significantly modify the safety reserve of underground caverns or reservoir bank slopes. However, meso‐damage has not been carefully studied based on micromechanical observations and analyses. Therefore, in this study, meso‐damage of a yellow sandstone is investigated and a meso‐damage‐based constitutive model for dry–wet cycles is proposed. First, computed tomography scanning and uniaxial compression tests were conducted on yellow sandstones under different dry–wet cycles. Second, the evolution of rock mesostructures and the damage mechanism subjected to dry–wet cycles were simulated using the discrete element method with Particle Flow Code in 2 Dimensions (PFC2D) software. Third, a constitutive model was proposed based on the meso‐statistical theory and damage mechanics. Finally, this constitutive model was verified with the experimental results to check its prediction capability. It is found that the radius and number of pore throats in the sandstone increase gradually with the number of dry–wet cycles, and the pore structure connectivity is also improved. The contact force of sandstone interparticle cementation decreases approximately linearly and the continuity of the particle contact network is continuously broken. The meso‐deformation and strength parameters show similar declining patterns to the modulus of elasticity and peak strength of the rock sample, respectively. This meso‐damage‐based constitutive model can describe well the rock deformation in the initial pressure density stage and the damage stage under the coupling effect of dry–wet cycles and loads.

An numerical investigation of the three dimensional multi-level force chain network of the sample with a single fissure under uniaxial compression

A novel three-dimensional grain-based model based on Particle Flow Code is proposed. Within this model, both quantitative calculations and multi-level classifications of force chain networks are achieved. A batch of numerical samples with a single pre-existing fissure with different inclination angle αs is constructed and then applied to the uniaxial compression. The result shows that the general force chains (GF) are approximately uniformly distributed in each orientation. The number of high-strength force chains (HF) reaches its maximum at the peak load moment, and the main orientation is consistent with the loading direction. The average value of the force chain in the tip regions of the fissure at any characteristic moment is the highest. In the whole region and the upper and lower regions of the fissure, the level of the force chain network rises as αs increases. Conversely, within the tip regions of the fissure, both the average value and sum value of GF decrease. The fracture resistance of intragranular structures is the highest, surpassing that of both all structures and intergranular structures. The fracture resistance within the tip regions of the fissure is the lowest compared to the entire region and the upper and lower regions of the fissure.

Study on mechanical properties of interbedded rock masses with microcrack based on thermal-mechanical coupling.

The mechanical properties of deep rock masses are significantly influenced by temperature and other factors. The effect of temperature on the strength of deep rock masses will pose a serious challenge to deep resource exploitation and engineering construction. In this paper, the thermal-mechanical coupling calculation model is established by particle flow code (PFC2D) to study the uniaxial compression response of rock masses with microcracks after temperature load. The strength of failure, microcracks, and strain was analyzed. The results show that: (i) When the soft rock thickness ratio Hs/H < 0.5, the displacement caused by the applied temperature is concentrated at the structural plane, and the contact force is concentrated at the end of the initial microcrack. When Hs/H ≥ 0.5, the displacement caused by the applied temperature is concentrated on both sides of the initial microcrack, and the contact force is concentrated in the hard rock area. (ii) The number of microcracks decreases with the increase of soft rock thickness under different working conditions. When the soft rock thickness ratio Hs/H < 0.5, the relationship curve between the number of microcracks and the vertical strain shows two stages of change. When Hs/H ≥ 0.5, the relationship curve between the number of cracks and the vertical strain changes shows three stages of change. (iii) When the soft rock thickness ratio Hs/H < 0.5, the failure strength decreases with the increase of soft rock thickness ratio at T = 100°C and 200°C. When T = 300°C and 400°C, the failure strength decreased first and then increased. When Hs/H ≥ 0.5, the failure strength increases with the increase of soft rock thickness at T = 200°C, 300°C, and 400°C. At T = 100°C, the failure strength decreases with the increase of soft rock thickness.

Study on the Impact Law of V-Shaped Gully Debris Avalanches on Double-Column Piers

The concrete piers in steep mountain areas are highly susceptible to damage disasters due to the impact of debris avalanches, which pose a serious threat to the safe operation of bridge structures. In order to investigate the impact load characteristics of debris avalanches on bridge pier structures in V-shaped valley mountain areas, Particle Flow Code 3D (PFC3D) models based on a discrete element method were applied in this study to establish a full-scale three-dimensional model of a debris avalanche in a V-shaped valley. By installing double-column piers in the influence zone of the debris avalanche, the impact force, accumulation morphology, motion characteristics of debris particles, internal force response of the double-column piers, and impact energy indicators were investigated. In addition, parameters such as the layout position of the piers and the impact angle of the debris were studied. The results showed that the particles at the front edge of the debris avalanche have a significant impact on the magnitude and distribution of the impact force on the piers. It is important to consider the layout position of the piers and the impact angle of the debris when designing bridge pier structures in high, steep mountain areas. There was a significant difference in the movement patterns between the particles at the front and rear edges of the landslide. The particles at the front edge had a higher velocity and stronger impact, while the particles at the rear edge had a slower velocity and were more likely to be obstructed by bridge piers, leading to accumulation. The obstruction effect of the piers on the debris particles was closely related to their positioning and the impact angle. Piers that were closer to the center of the valley and had a larger impact angle have a more significant obstruction effect, and the topography of the valley had a significant focusing effect on the debris avalanche, resulting in a greater impact force and energy on the piers located closer to the center of the valley. The impact force amplitude and duration of landslide debris on bridge piers showed a significant difference between the bottom and upper piers, as well as between the piers on the upstream and downstream sides. These research findings can provide valuable references for the design and disaster assessment of bridge piers for impact prevention in steep slopes and mountainous areas with deep ravines.

Evaluation of FACTS Contributions Using Branch Flow Model and Newton–Raphson Algorithm

Flexible alternating current transmission systems (FACTSs) have been widely incorporated in electric power systems in order to control system parameters. This paper proposes the modeling of four FACTS devices, using the Branch Flow Model (BF) as an optimization problem to reduce the complexity of the Newton–Raphson (NR) load flow code with FACTS devices. The devices are represented as variable impedances, as a function of a firing angle, and as voltage source converters (VSCs) located on the buses and transmission lines. This proposed model solves the problem associated with the selection of appropriate initial conditions of the parameters of each device that guarantee convergence. The model is validated by evaluating its percentage deviation with respect to the NR method, using the standard test systems, IEEE 5-bus, IEEE 14-bus, IEEE 30-bus, and IEEE 57-bus systems.

A Novel Approach for Determining Cutting Geometry for TBM Using Full-scale Laboratory Linear Rock Cutting and PFC3D-Based Numerical Simulations

Efficient rock excavation requires an optimal s-p ratio, where adjacent cuts interact to completely plane the rock surface. Traditionally, the specific energy (SE) methodology has been used to determine this ratio, but its U-shaped curve is sometimes incomplete or absent, making it difficult to find the optimal s-p ratio. In this research, an alternative methodology is proposed. This methodology relies on the morphology of the excavated rock surface, specifically, the amounts of overbreaks. To evaluate the proposed methodology, full-scale rock cutting experiments were conducted in the laboratory. Numerical simulations were also conducted in 3D particle flow code (PFC3D) and the results were validated by the full-scale laboratory rock cutting experimental data. The study also involved conducting sensitivity analyses to evaluate the effectiveness of downscaling and upscaling the PFC3D-based model to obtain results for full-scale applications. Following the excavation, laser profilometry was employed to characterize the excavated rock surfaces, and the resulting profiles were used to calculate the volume of overbreaks. Plots of these volumes against the s-p ratio were generated to identify the optimal s-p ratio. The findings indicated the presence of a noticeable optimal s-p ratio in both the PFC3D-based simulations and full-scale laboratory experiments, which was not evident when the specific energy methodology was employed. This proposed methodology exhibits considerable potential and can prove beneficial in determining cutting geometry that is optimal for site-specifc and TBM-specific, as well as in the design and production of tunnel boring machines.

Force chains evolution and crack characteristics of multiple coal-rock sandwich composite structure by using particle flow code

The stability of residual coal pillars and surrounding rock structures in composite residual coal mining areas is crucial for the safe and efficient mining of residual coal resources. To explore the force chains evolution and crack propagation characteristics of multiple coal-rock sandwich composite structures, uniaxial compression tests with four types of multiple coal-rock sandwich composite structures were conducted using particle flow numerical simulations. The results showed that the characteristics of the force chain evolution and crack propagation characteristics of multiple coal-rock sandwich composite structures during the loading process were almost identical. The evolution of the internal contact force chains of the rock elements and the propagation of micro-cracks lagged relatively, induced mainly by the initial fracture of the coal elements. Moreover, the coal elements were instability hazard factors in multiple coal-rock sandwich composite structures. The energy released by the coal and rock elements affects each other, resulting in the destruction of the entire composite structure. This study provides a basis for the instability prevention and control of coal-rock bearing structures in composite residual coal mining areas.

Mechanical properties and failure mechanism of rock-like specimens with arc-shaped flaws under freeze–thaw cycles

To investigate the failure characteristics of jointed rock masses in cold regions after freeze–thaw (F-T) cycles, uniaxial compressive tests are conducted on rock-like specimens (a type of cement mortar) with prefabricated arc-shape flaws subjected to 0, 25, 50 and 100F-T cycles to determine their mechanical properties. Test results reveal that F-T cycles greatly affect the uniaxial compressive strengths (UCS) of the specimens, and the relationship between the peak strength and the number of freeze–thaw cycles is exponentially fitted. Notably, the initial 50 cycles have a more pronounced effect on UCS reduction compared to the subsequent 50 cycles, indicating that early F-T cycles are more detrimental to UCS. To further investigate the failure mechanism of the specimens, two-dimensional particle flow code (PFC2D) is utilized to simulate the F-T cycle process of the specimens. The mechanical properties and failure mechanism of specimens can be obtained after F-T cycles under uniaxial compression through numerical simulations. The findings indicate that F-T cycles can obviously deteriorate the ductility of the specimens, and to some extent, they also affect crack propagation during specimen failures. Through crack classification statistics and stress contour analysis of the simulated specimens, it reveals that different prefabricated flaw morphologies lead to distinct stress distributions, subsequently affecting crack propagation and specimen failure. It is also worth mentioning that the large curvature and inclination angle of the flaws may generate additional tensile and shear stress zones at the top of the flaw vault, which in turn may contribute to the development of crack propagation. The relevant experimental and numerical results are useful for investigating mechanical properties and failure mechanisms of rock masses in cold regions subjected to F-T cycles.

A novel bi-modular elastic algorithm in particle Flow Code for thermal cracking modeling of rock

Experimental studies indicated that most rocks exhibit distinct elastic moduli under compressive and tensile loading, leading to intricate stress conditions in rock mass under thermal–mechanical coupling. It is an urgent demand for advanced numerical methods that can simultaneously consider the bi-modular elasticity of rock, thermal–mechanical coupling effects, and thermal cracking behaviors to improve understanding of geological science. The Balanced Interface Method (BIM), a novel bi-modular elastic algorithm is proposed in Particle Flow Code to investigate the thermal–mechanical behavior of bi-modular elastic materials. Firstly, this study introduces the calculation principle of BIM and presents the calibration procedure for bi-modular elastic materials, which is further validated through two case exercises. Subsequently, the thermal–mechanical coupling algorithm is improved by utilizing the Flat-Joint Model (FJM), and a correction method for the position of the compression-tension interface based on BIM for the thermal–mechanical coupling process is introduced, which is then verified by a comprehensive transient heat conduction case with different elastic assumptions. Lastly, a cracking example induced by thermal–mechanical coupling is simulated. The numerical results demonstrate consistency with previous studies and reveal a significant improvement in the thermal cracking behavior of rock, proving the developed algorithm’s necessity in investigating the coupled thermal–mechanical problem.

Investigations into size dependence on the behavior of rocks with a “V” notch and hole under uniaxial compression

This study employed a combination of experimental analysis and numerical simulations using the Particle Flow Code (PFC2D) to investigate the impact of interaction between porosity and V-shaped notch on the breakage behavior of gypsum-based rock-like samples. Also, the influence of scale effect on the notch-hole interaction has been investigated while the “<” notches were positioned at three different orientations (0°, 45°, and 90°) relative to the X-axis. Parallel to the experimental phase, nine samples with analogous “<” shape notches, as well as nine additional models featuring different “>” shape notches, were generated and assessed through numerical simulations. The findings indicate that crack propagation was primarily governed by the notch shape, asymmetric line angle, and model dimensions. Notably, the rock bridge located between the “<” shape notch and the hole exhibited significantly greater breakage compared to other notch configurations (i.e., “>” shape notch). Moreover, the volume of damage increased with the inclination of the asymmetric line and the model's dimensions. Both the angle of the asymmetric line and the model's size contributed to enhanced sample strength. Elevating the asymmetric line angle, simulation size, and V-shaped notch led to the creation of more fractures, consequently resulting in a heightened occurrence of failure events in rock-like materials. Delay failure occurred in models containing “>” shaped notch while abrupt failure occurred in models containing “<” shaped notch. The experimental results affirm that PFC2D faithfully replicated the sample's failure pattern and strength. This study is useful for rock engineering design when delay failure and or abrupt failure threaten the stability of rock engineering structures.