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.


Introduction
China has built a large number of pioneering underground tunnel projects in recent years, driven by policies such as the Western Development Strategy, construction of the Guangdong Hong Kong Macao Greater Bay Area, and the rapid development of urban construction.These projects have long service lives, low resource consumption, and good concealment [1,2].The drilling and blasting method is widely used in the construction process of underground tunnel engineering owing to simple construction and low cost, which greatly improve labor production efficiency [3].Granite has high strength, strong deformation resistance, and low permeability, and is a common rock encountered in various underground engineering projects [4].Granite is a typical crystalline rock, and its internal mineral particle size, shape, mechanical properties, and bonding strength between the particles affect its macromechanical properties [5,6].The characteristics of granite under an impact load are significantly different from those under a static load, exhibiting nonlinear and high-strain-rate effects.This difference poses significant challenges to the dynamic response analysis of granite under impact load [7,8].Therefore, it is necessary to study the impact characteristics of granite.
The microscopic and macroscopic characteristics of granite are closely related to its mineral composition, structural characteristics, grain size, and rock morphology.In previous studies, rocks were often equivalent to continuous media, resulting in similar impact effects, but they were unable to 1331 (2024) 012019 IOP Publishing doi:10.1088/1755-1315/1331/1/012019 2 accurately analyze the initiation and propagation laws of new cracks in the rock.Conventional macro analysis cannot fully explain the formation mechanism of rock failure, cracking and fragmentation.Meso-structural factors control the damage evolution behavior, such as rock cracking and expansion, and meso-information, such as crystal fracture form and fracture morphology left by rock fracture, is an intrinsic reflection of macro-failure [9,10].Consequently, an analysis of the mineral's crystal scales is necessary.Because of technological limitations in the past, research was primarily conducted from a macro perspective.However, the technology advancement in recent years has made it feasible to analyze the impact mechanical properties and fracture mechanism of rocks from a micro perspective.With recent developments in computer hardware, computer tomography (CT), nuclear magnetic resonance (NMR), and digital image processing have become essential tools in modern science and technology [11].They were first applied in the fields of medicine and biology and later introduced into the microscopic research of rock and soil [12,13], achieving the use of digital methods to present the internal microstructure of rocks without damage, which greatly promoted the study of rock mesostructure and fracture development laws.Therefore, a grain-based model (GBM) that considers the mechanical properties of minerals inside rocks has been developed and has become an extremely effective simulation method for the mineral crystal scale [14,15].Many researchers have refined the GBM and used it to validate various laboratory tests and in the analysis of related mechanisms.Hu et al. [16] used the GBM to examine the influence of rock mesostructure on the creep characteristics of granite.Li et al. [17] used PFC discrete element numerical software to establish a mineral crystal model of granite and investigated the influence of mesostructural heterogeneity on the macroscopic mechanics and crack propagation law of fractured rocks.
In summary, researchers have investigated rock crack propagation and failure mechanisms using GBM, but studies on rock impact characteristics using GBM are scarce.Therefore, a GBM sample of granite was set up by CT scanning, and the crack characteristics of granite at different impact velocities were investigated at the mineral scale.

The microstructure of granite
The granite used in this study was obtained from the Xiamen Haicang port channel.Figure 1 shows a polarized microscopic image of its internal structure, which shows that the primary mineral components are quartz, feldspar, and mica.Figure 2 shows the CT scanned images of granite.The 3D granite samples were reconstructed using Avizo software, and different minerals were divided by the interactive threshold value.The proportions of quartz and mica in the granite were 76%, 19%, and 5%, respectively.

Modeling process
In the simulation, the crack characteristics of granite under an impact load were examined, and the GBM was used to establish the granite model.The granite sample was a standard cylindrical sample with dimensions of 50 mm × 100 mm.For ease of computation, a two-dimensional model measuring 50 mm in width and 100 mm in height was set up in the simulation.The GBM construction process includes the following four steps: (1) generation of corresponding circular particles based on statistical data of mineral size and proportion and division of the system into multiple polygonal regions through closed contact chains; (2) generation of new crystalline grid structures; (3) classification of crystal lattice structures to characterize different minerals; and (4) filling the crystalline grid structure with smaller particles and assigning bonding properties to the particles inside and at the boundaries, as shown in figure 3.

Microscopic parameter calibration
Currently, a trial-and-error method is widely used to calibrate the microscopic parameters of discrete element simulation specimens.The main calibration process is to first determine the approximate range of the mechanical properties of the main minerals inside the rock based on experience and reference literature.Subsequently, it is calibrated by comparing it with macroscopic parameters such as uniaxial compression, tensile strength, and elastic modulus obtained from indoor experiments.In this GBM model, a parallel bond contact model (PBM) was used between the particles inside the crystal, whereas a smooth joint contact model (SJM) was used for the crystal boundary.Table 1 shows the microscopic parameters of the GBM, categorized into three groups (basic particle, mineral particle, and mineral boundary) based on the characteristics of each parameter.In this model, the mineral boundary's SJM can be modified based on the properties of the mineral particles surrounding the boundary.By combining it with the SJM coefficient of the mineral boundary group, different SJM parameters can be assigned to different boundaries.A trial-and-error method was adopted to calibrate the microscopic parameters of the sample, and the results are listed in table 2.
Table 1.Microscopic parameters of GBM model.

Model validation
A comparison of the test and simulation results under uniaxial compression when the loading strain rate of the sample was 0.005 is shown in figure 4. Figure 4 (a) shows that the stress-strain simulation curve of the sample is relatively similar to that of the test, including the initial compaction, linear elastic deformation, stable microcrack propagation, and accelerated microcrack propagation stages.The peak stress in the test was 212.74 MPa, while in the simulation it was 201.26 MPa, with a minor difference between the two.This can be observed in figure 4 (b), the macro-failure modes of the rock in the test and simulation were similar, showing typical splitting failure with oblique fractures forming from the end to the bottom.The numerical simulation demonstrates a high level of reliability.

Evolution law of granite impact crack
To analyze the evolution law of the impact cracks of granite, an impact velocity of 10 m/s was applied to the top of the GBM model to simulate the impact failure of the sample.Figure 5 shows the failure process of the granite sample during impact.Figure 5 (a) shows that the crack first appears at the end of the sample where the impact load is applied, and then spreads from the top to the lower end, extending to the bottom of the sample at 2000 μs.Subsequently, the specimen expanded laterally and cracked, as shown in figures 5 (e) and (f). Figure 6 shows the progression of the total number of cracks, including tensile, and shear cracks in the sample.The evolution of cracks was categorized into three stages.Stage I corresponds to the rapid growth stage, characterized by a substantial increase in the number of cracks following the impact, while the rate of increase remained constant.Stage II represents a stage of decreasing growth rate, where the number of cracks in the sample continues to increases, but at a diminishing rate.Finally, Stage III is a relatively stable stage, during which the number of cracks in the sample remains stable, with only minor increases.Figure 7 shows the number of different types of cracks after impact.According to figure 7(a), there were 14522 tensile and 500 shear cracks, indicating that tensile failure was the main cause of the overall failure of the specimen during the impact process.As shown in figure 7(b), there were 13978 intrachrystalline and 1044 intergranular cracks, indicating that the impact failure of the sample was primarily intrachrystalline.Figure 7(c) shows that the intragranular cracks were further divided into 2844 quartz (20.84 %), 6688 feldspar (47.85 %), and 4446 mica cracks (31.31 %).In terms of the mineral composition, quartz accounted for 76%, but the total number of cracks in quartz was the lowest, which shows that quartz has superior deformation resistance.Mica accounted for 5% of the mineral composition, but cracks accounted for 31.31%,indicating that mica has weak mechanical properties.

Analysis of impact crack characteristics of granite with different impact velocities
To study the impact crack characteristics of granite at different impact velocities, impact velocities of 5 °, 10 °, 15 °, and 20 °were simulated.Figure 8 shows the total number of cracks in the samples at different impact velocities.The figure shows that as the impact velocity increased, the total number of cracks in the granite samples also increased, showing significant nonlinearity.Figure 9 depicts the curves of the tensile and shear cracks with the impact velocity.The graph shows that the shear cracks of granite increase with an increase in impact velocity, whereas tensile cracks do not necessarily increase with an increase in impact velocity, but show a trend of increasing first and then decreasing.Relationship between tensile and shear cracks and impact velocity.Figure 10 depicts the curves of the intrachrystalline and intergranular cracks with the impact velocity.The figure shows that the intergranular cracks of granite increase with an increase in the impact velocity, but the intrachrystalline cracks show a trend of first increasing and then decreasing.
Figure 11 shows the curve of the intrachrystalline cracks of different minerals with the impact velocity.The graph shows that the intrachrystalline cracks of different minerals all show a trend of first increasing and then decreasing with an increase in impact velocity, and the intrachrystalline cracks are the highest at 10 m/s.

Conclusion
(1) The evolution process of granite cracks under an impact load can be divided into three stages: rapid growth, decreasing growth, and gradually stable stages.
(2) The impact failure cracks in the sample were primarily tensile and intragranular cracks.There were more feldspar and quartz in the intrachrystalline and fewer in the quartz cracks.
(3) The total number of cracks, including shear and intergranular cracks, in the granite increased with the impact velocity.
(4) The tensile and intragranular cracks of granite initially increased and then decreased with an increase in the impact velocity.

Figure 1 .
Figure 1.Micro-structure of granite.Figure2shows the CT scanned images of granite.The 3D granite samples were reconstructed using Avizo software, and different minerals were divided by the interactive threshold value.The proportions of quartz and mica in the granite were 76%, 19%, and 5%, respectively.

Figure 2 .
Figure 2. Three-dimensional reconstruction of granite using CT scan.

5
(a) Stress-strain curve (b) Macroscopic failure characteristics Figure 4. Comparison of uniaxial compression test and simulation results.

Figure 6 .
Figure 6.Crack evolution process.Figure7shows the number of different types of cracks after impact.According to figure 7(a), there were 14522 tensile and 500 shear cracks, indicating that tensile failure was the main cause of the overall failure of the specimen during the impact process.As shown in figure 7(b), there were 13978 intrachrystalline and 1044 intergranular cracks, indicating that the impact failure of the sample was primarily intrachrystalline.Figure7(c) shows that the intragranular cracks were further divided into 2844 quartz (20.84 %), 6688 feldspar (47.85 %), and 4446 mica cracks (31.31 %).In terms of the mineral composition, quartz accounted for 76%, but the total number of cracks in quartz was the lowest, which shows that quartz has superior deformation resistance.Mica accounted for 5% of the mineral composition, but cracks accounted for 31.31%,indicating that mica has weak mechanical properties.

Figure 7 .
Figure 7. Number of cracks of different types.

Figure 8 .
Figure 8. Relationship between total number of cracks and impact velocity.

Figure 9 .
Figure9.Relationship between tensile and shear cracks and impact velocity.Figure10depicts the curves of the intrachrystalline and intergranular cracks with the impact velocity.The figure shows that the intergranular cracks of granite increase with an increase in the impact velocity, but the intrachrystalline cracks show a trend of first increasing and then decreasing.Figure11shows the curve of the intrachrystalline cracks of different minerals with the impact velocity.The graph shows that the intrachrystalline cracks of different minerals all show a trend of first increasing and then decreasing with an increase in impact velocity, and the intrachrystalline cracks are the highest at 10 m/s.

Figure 10 .
Figure 10.Relationship between intrachrystalline and intergranular cracks and impact velocity.

Figure 11 .
Figure 11.Relationship between the intragranular crack of different minerals and impact velocity.

Table 2 .
Micro-parameters of the numerical model.