Rock burst tendency quantitative analysis method based on pore three-dimensional fractal dimension

Abstract

The invention relates to the technical field of geotechnical engineering, in particular to a rock burst tendency quantitative analysis method based on pore three-dimensional fractal dimensionalities, which comprises the following steps: preparing a rock sample, heating the sample to different high temperatures, treating the sample in three modes of natural cooling, water impact and liquid nitrogen cold impact, and combining a triaxial compression test with NMR (nuclear magnetic resonance), CT (computed tomography), XRD (X-Ray Diffraction), SEM (scanning electron microscope) and other microcosmic test means to obtain the rock burst tendency quantitative analysis method based on pore three-dimensional fractal dimensionalities. Analyzing the mechanical property, energy evolution and microstructure change, introducing four rockburst tendency evaluation indexes such as an energy impact index and a peak strength strain energy storage index, establishing a quantitative relationship between the pore three-dimensional fractal dimension and a rockburst tendency core index, selecting the peak strength strain energy storage index as a rockburst tendency core characterization index, and evaluating the rockburst tendency. And finally realizing quantitative grading and determination of the rock burst tendency.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering technology, specifically to a quantitative analysis method for rockburst tendency based on the three-dimensional fractal dimension of pores. Background Technology

[0002] Rockbursts are essentially brittle fracture processes caused by the sudden release of elastic strain energy due to high stress concentration in rock. Rockbursts are a significant geological hazard in deep engineering construction, posing a serious threat to equipment and personnel in underground spaces.

[0003] To overcome the problem of rockburst prevention, scholars both domestically and internationally have conducted extensive research and developed numerous rockburst prevention methods. For example, borehole water injection, decompression blasting, decompression drilling, and anchor-sprayed support are relatively mature technologies. Borehole water injection can alter the mechanical properties of rock, thereby reducing the risk of rockburst. Specifically, using water as a medium, uniaxial compression tests were conducted on granite samples with pre-drilled holes; water injection into the borehole significantly reduced the strength of the granite. Water can prevent excessive concentration of strain energy in sandstone, thus significantly improving its rockburst resistance. Simultaneously, drilling can effectively reduce the elastic strain energy of the rock, thereby reducing the tendency for rockburst. Furthermore, studies have shown that grout-reinforced samples have higher impact resistance than unreinforced rocks. However, with increasing underground excavation depth, traditional rockburst prevention methods have some limitations in solving complex rockburst problems. In application, both borehole water injection and decompression blasting face operational uncertainties. Borehole water injection parameters need to be determined based on the actual project, while the explosive quantity in decompression blasting is difficult to control. Decompression drilling and anchor bolt control also have shortcomings. While pressure-reducing boreholes can lower pressure, they can interfere with active support structures. In practical engineering, anchor bolts are prone to eccentricity, leading to poor rockburst control.

[0004] In summary, existing methods for evaluating rockburst tendency are mostly based on single lithological indicators or macroscopic mechanical parameters, which are insufficient to fully reflect the control effect of the heterogeneity and anisotropy of the internal microstructure of rocks on the rockburst triggering mechanism. Summary of the Invention

[0005] The purpose of this invention is to provide a quantitative analysis method for rockburst tendency based on the three-dimensional fractal dimension of pores. This method aims to address the shortcomings of existing rockburst control technologies by introducing a method that can accurately characterize the complexity of rock pore structure and fractal dimension. This extends the evaluation of rockburst tendency from traditional macroscopic mechanical experience to the level of quantitative characterization of microstructure, thereby overcoming the inherent defect of traditional methods that cannot quantify the relationship between pore structure characteristics and energy accumulation and dissipation. This enables a leap from qualitative description to precise and digital assessment of rockburst disaster risk.

[0006] To achieve the above objectives, this invention provides a method for quantitative analysis of rockburst tendency based on the three-dimensional fractal dimension of pores, comprising the following steps:

[0007] Step 1: Rock sample preparation and pretreatment;

[0008] Step 2: Conduct triaxial compression mechanics tests and microstructure characterization tests;

[0009] Step 3: Calculation and analysis of rockburst tendency evaluation index and pore three-dimensional fractal dimension index;

[0010] Step 4: Establish a quantitative relationship between the three-dimensional fractal dimension of pores and the core index of rockburst tendency, so as to realize the quantitative classification and judgment of rockburst tendency.

[0011] Optionally, the rock samples in step 1 must be homogeneous, with all samples taken from the same rock block. The execution process of step 1 includes the following steps:

[0012] Step 1.1: Sample preparation, selecting the basic physical parameters of the sample;

[0013] Step 1.2: Perform high-temperature heating treatment on the sample;

[0014] Step 1.3: Divide the heated samples into three groups for differentiated cold shock treatment;

[0015] Step 1.4: Sample drying completes the pretreatment.

[0016] Optionally, in step 2, the pretreated samples are subjected to X-ray diffraction testing, nuclear magnetic resonance testing, CT scanning and three-dimensional reconstruction, and scanning electron microscopy observation, respectively. The pretreated samples include samples that have not undergone triaxial compression mechanical testing and samples that have undergone triaxial compression mechanical testing.

[0017] Optionally, the execution process of step 3 includes the following steps:

[0018] Step 3.1: Calculation of rockburst tendency evaluation indicators, including energy impact index, peak strength strain energy storage index, residual elastic energy index, and improved brittleness index;

[0019] Step 3.2: Rock energy evolution calculation;

[0020] Step 3.3: Calculation of the three-dimensional fractal dimension of the pores.

[0021] Optionally, in step 4, a quantitative relationship between the three-dimensional fractal dimension of pores and the core index of rockburst tendency is established. Specifically, the peak strength strain energy storage index is selected as the core characterization index of rockburst tendency. The peak strength strain energy storage index value and the corresponding total pore fractal dimension and function relationship under different high temperature-cold shock conditions are established by curve fitting. The rockburst tendency classification standard is then combined to classify and determine the rockburst tendency.

[0022] The relationship equations between the fitted functions are as follows:

[0023]

[0024] Wherein represents the peak strength strain energy storage index, D represents the pore fractal dimension, and a, b, c, and d are constants determined for different high-temperature-cold shock conditions; High-temperature-natural cooling: a=1.193, b=117.167, c=344.119, d=1.4; High-temperature-water shock: a=1.618, b=386, c=1052.498, d=2.36; High-temperature-liquid nitrogen cold shock: a=10.126, b=94.34, c=272.643, d=1.685.

[0025] This invention provides a quantitative analysis method for rockburst tendency based on the three-dimensional fractal dimension of pores. By preparing rock samples, heating them to different high temperatures and treating them using three methods—natural cooling, water impact, and liquid nitrogen cold impact—combined with triaxial compression tests and microscopic testing techniques such as NMR, CT, XRD, and SEM, the mechanical properties, energy evolution, and microstructural changes are analyzed. Four rockburst tendency evaluation indicators are introduced, including the energy impact index and the peak strength strain energy storage index. A quantitative relationship is established between the three-dimensional fractal dimension of pores and the core indicators of rockburst tendency. The peak strength strain energy storage index is selected as the core characterization indicator of rockburst tendency, ultimately achieving quantitative classification and determination of rockburst tendency. Attached Figure Description

[0026] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 This is an experimental flowchart of a method for quantitative analysis of rockburst tendency based on the three-dimensional fractal dimension of pores according to the present invention.

[0028] Figure 2 This is a schematic diagram of the temperature-time curves of different high-temperature-cold shock schemes in the embodiments of the present invention.

[0029] Figure 3 This is a schematic diagram illustrating the changes in porosity of granodiorite under different high-temperature and cold-impact conditions in an embodiment of the present invention.

[0030] Figure 4 This is a schematic diagram of linear regression calculation of the fractal dimension of pores at 25°C-natural cooling in an embodiment of the present invention.

[0031] Figure 5 This is a schematic diagram of linear regression calculation of the fractal dimension of pores at 200°C-natural cooling in an embodiment of the present invention.

[0032] Figure 6 This is a schematic diagram of linear regression calculation of the fractal dimension of pores under 200°C water impact in an embodiment of the present invention.

[0033] Figure 7 This is a schematic diagram of linear regression calculation of the fractal dimension of pores under 200°C-liquid nitrogen cold impact in an embodiment of the present invention.

[0034] Figure 8 This is a schematic diagram of linear regression calculation of the fractal dimension of pores at 400°C-natural cooling in an embodiment of the present invention.

[0035] Figure 9 This is a schematic diagram of linear regression calculation of the fractal dimension of the pores in the 400°C water impact pores in an embodiment of the present invention.

[0036] Figure 10 This is a schematic diagram of the linear regression calculation of the fractal dimension of 400°C-liquid nitrogen cold shock in an embodiment of the present invention.

[0037] Figure 11 This is a schematic diagram of linear regression calculation of the fractal dimension of pores at 600°C-natural cooling in an embodiment of the present invention.

[0038] Figure 12 This is a schematic diagram of linear regression calculation of the fractal dimension of pores under 600°C water impact in an embodiment of the present invention.

[0039] Figure 13 This is a schematic diagram of linear regression calculation of the fractal dimension of pores under 600°C-liquid nitrogen cold impact in an embodiment of the present invention.

[0040] Figure 14 This is a schematic diagram of linear regression calculation of the fractal dimension of pores at 800°C-natural cooling in an embodiment of the present invention.

[0041] Figure 15 This is a schematic diagram of linear regression calculation of the fractal dimension of pores under 800°C water impact in an embodiment of the present invention.

[0042] Figure 16 This is a schematic diagram of linear regression calculation of the fractal dimension of pores under 800°C-liquid nitrogen cold impact in an embodiment of the present invention.

[0043] Figure 17 This is a flowchart of a three-dimensional reconstruction of a threshold-segmented image using the watershed algorithm in an embodiment of the present invention.

[0044] Figure 18 This is a schematic diagram of interlayer slicing and three-dimensional reconstruction modeling of high-temperature granodiorite under natural cooling at 25°C in an embodiment of the present invention.

[0045] Figure 19 This is a schematic diagram of interlayer slicing and three-dimensional reconstruction modeling of high-temperature granodiorite under natural cooling at 600°C in an embodiment of the present invention.

[0046] Figure 20 This is a schematic diagram of interlayer slicing and three-dimensional reconstruction modeling of high-temperature granodiorite under 600°C water impact in an embodiment of the present invention.

[0047] Figure 21 This is a schematic diagram of interlayer slicing and three-dimensional reconstruction modeling of high-temperature granodiorite under 600°C-liquid nitrogen cold shock in an embodiment of the present invention.

[0048] Figure 22 This is a schematic diagram of the porosity of granodiorite under natural cooling at 25°C in an embodiment of the present invention.

[0049] Figure 23 This is a schematic diagram of the porosity of granodiorite under natural cooling at 600°C in an embodiment of the present invention.

[0050] Figure 24 This is a schematic diagram of the porosity of granodiorite under water impact at 600°C in an embodiment of the present invention.

[0051] Figure 25 This is a schematic diagram of the porosity of granodiorite under 600°C-liquid nitrogen cold impact in an embodiment of the present invention.

[0052] Figure 26 This is a schematic diagram illustrating the relationship between the peak strength strain energy storage index of granodiorite and the three-dimensional fractal dimension of pores in an embodiment of the present invention. Detailed Implementation

[0053] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0054] This invention provides a method for quantitative analysis of rockburst tendency based on the three-dimensional fractal dimension of pores, comprising the following steps:

[0055] Step 1: Rock sample preparation and pretreatment;

[0056] Step 2: Conduct triaxial compression mechanics tests and microstructure characterization tests;

[0057] Step 3: Calculation and analysis of rockburst tendency evaluation index and pore three-dimensional fractal dimension index;

[0058] Step 4: Establish a quantitative relationship between the three-dimensional fractal dimension of pores and the core index of rockburst tendency, so as to realize the quantitative classification and judgment of rockburst tendency.

[0059] The following examples and specific execution steps provide further explanation:

[0060] The overall process of this test is as follows: Figure 1 As shown:

[0061] Step 1 involves sample preparation and pretreatment. In this embodiment, granodiorite from Fujian, China, was selected as the experimental material. All specimens were taken from a single large, dense granodiorite block to ensure homogeneity. First, the granodiorite was prepared into standard cylindrical specimens with a height of 100 mm and a diameter of 50 mm. At 25°C, the granodiorite specimens had an average density of 2775 kg / m³, an average uniaxial compressive strength of 154.97 MPa, and an average porosity of 0.81%.

[0062] In this experiment, steps 1.2 and 1.3 are collectively referred to as the high-temperature-cold shock pretreatment. A schematic diagram of the high-temperature-cold shock treatment is shown below. Figure 2As shown. An SX2-10-12NP muffle furnace was selected for experimental heating. Its rated maximum temperature is 1200°C, with nickel-chromium alloy wire heating elements, a working chamber size of 250 mm × 400 mm × 160 mm, and a temperature control accuracy of ±1°C. It is equipped with a microcomputer program that can integrate the setting of temperature, time, and heating rate. First, the granodiorite sample was heated to four different temperature levels (200°C, 400°C, 600°C, 800°C) in the muffle furnace, with a heating rate set to 5°C / min to prevent thermal shock caused by high heating rates during the heating process. After heating to the target temperature, the sample was kept in the muffle furnace for 3 hours to ensure that the sample was heated inside and out. Then, the heated granodiorite sample was treated with three different cooling methods to study the effects of different cooling rates on the rock's mechanical properties and microstructure. (I) Liquid nitrogen cold shock group: The preheated granodiorite sample was held in a crucible and immediately placed in a liquid nitrogen Dewar flask for rapid cooling for 5 minutes. (ii) The water impact test involved rapidly immersing the preheated granite in 20°C water for rapid cooling. To ensure consistency with the liquid nitrogen cold impact test in terms of time variation, the water impact reaction time was also set to 5 minutes. (iii) Natural cooling involved placing the preheated granodiorite at room temperature. After the above cooling process, all samples were placed in a drying oven at 105°C for at least 24 hours to prevent moisture from affecting the mechanical properties of the granodiorite.

[0063] Step 2: Nuclear magnetic resonance (NMR), X-ray diffraction (XRD), and CT scans were performed on the pretreated granodiorite. NMR was performed using a low-field NMR spectrometer with a magnetic field strength of 0.3 ± 0.05 T. The pretreated granodiorite sample was then placed in a vacuum water saturation apparatus for vacuum water saturation treatment. After treatment, the sample was removed, and the surface water was wiped off with a cloth. It was then quickly wrapped with plastic film to prevent moisture penetration and loss. XRD analysis was performed using a SmartLab high-resolution X-ray diffractometer with a Cu Kα radiation source, operating at 45 kV and 40 mA. Scans were performed at a speed of 10° / min within the 2θ range of 5° to 80°. CT scans were performed using a German YXLON FF85 CT scanner with a scanning voltage of 200 kV and an exposure time of 0.4 s. Triaxial mechanical tests were conducted on a fully automated triaxial rock testing platform. This instrument has a maximum axial load capacity of 2000 kN and can achieve confining pressures up to 60 MPa. After the specimen installation and sensor arrangement were completed, a pre-contact was first established at the top, and then confining pressure was applied at a rate of 1.5 MPa / min to achieve the preset confining pressures of 5 MPa, 15 MPa, and 25 MPa. The axial loading displacement was controlled at 0.2 mm / min until the specimen failed, at which point the loading process was terminated. After specimen failure, scanning electron microscopy (SEM) was performed using a Zeiss G300 SEM.

[0064] Step 3 selected four indicators: energy impact index (R), peak intensity strain energy storage index (... ), residual elasticity index ( The improved brittleness index (BIM) was used to evaluate rockburst tendency. The meanings and standards of the four rockburst tendency indices are shown in Table 1. Based on Table 1, the rockburst tendency and tendency discrimination results of granodiorite under different high-temperature cold shock conditions are shown in Table 2.

[0065] Table 1. Meaning of the Four Rockburst Proneness Indicators and Standards

[0066]

[0067] Table 2 Calculation results and rockburst tendency determination of granodiorite under different high-temperature cold shock conditions

[0068]

[0069] 1) The effect of temperature on rockburst tendency

[0070] Temperature is an important factor affecting the mechanical properties of rocks and their tendency to explode. As shown in Table 4, the R of room-temperature granodiorite is... , The BIM values ​​were 5.25, 4.79, 0.52, and 1.15 respectively, indicating a high tendency for rockbursts. The value of 4.79 (close to the critical value for high rockburst) indicates that granodiorite is brittle at room temperature and prone to rockburst. At temperatures ranging from 200℃ to 400℃, the mechanical properties of granodiorite subjected to the three cold impact methods gradually weaken, with R and... All indicators decreased, and the tendency for rockburst also weakened, but a certain degree of moderate rockburst tendency still exists. As the temperature further increases to 600℃, the mechanical properties of granodiorite continue to decrease, with R and... The rockburst tendency is significantly reduced, and the tendency to explode is further weakened. At this temperature, the inhibitory effect of liquid nitrogen shock on the rockburst tendency is particularly significant. It exhibits no tendency for rockbursts, while R exhibits a low tendency for rockburst. This phenomenon is attributed to the high temperature, which leads to an increase in internal fractures in the granodiorite. Liquid nitrogen cold impact further widens these internal fractures, resulting in decreased mechanical properties and increased energy dissipation, thus suppressing the rockburst tendency. When the temperature rises to 800°C, the rockburst tendency rating remains unchanged compared to the 600°C condition, indicating that the rockburst tendency of the granodiorite tends to stabilize in the temperature range of 600°C to 800°C.

[0071] 2) The effect of high-temperature-cold shock treatment on rockburst tendency

[0072] Different high-temperature-cold impact methods showed significant differences in their effectiveness in suppressing rockburst tendency. Natural cooling, being relatively slow, resulted in rockburst tendency in granodiorite at room temperature and 200°C. While the rockburst tendency decreased slightly above 400°C, the reduction was limited. On the other hand, water impact cooling was faster and more effective than natural cooling in suppressing rockburst tendency. For example, in granodiorite, at 400°C and 600°C, the R of naturally cooled granodiorite decreased by 7.05% and 54.48%, respectively, compared to room temperature; while the R of water-impacted granodiorite decreased by 53.33% and 58.67%, respectively, compared to room temperature. Among all cooling methods, liquid nitrogen impact showed the most significant suppressive effect. For instance, at 600°C, the R of granodiorite impacted by liquid nitrogen was 1.68, reducing the rockburst tendency from high at room temperature to low.

[0073] From the perspective of the rockburst tendency index, R is positively correlated with rockburst tendency; the higher the R value, the stronger the rockburst tendency. At room temperature, granodiorite has an R value of 5.25, indicating a high rockburst tendency. After being subjected to a 600℃ liquid nitrogen cold shock treatment, this value decreased to a minimum of 1.68, indicating a reduced rockburst tendency. and It is also positively correlated with the tendency of rockburst in granodiorite at room temperature. and The values ​​are 4.79 and 0.52 respectively, both indicating a high tendency for rockburst. (T400℃-liquid nitrogen cold-impact granodiorite) and The lowest values ​​were 1.4 (no rockburst tendency) and 0.11 (low rockburst tendency), respectively. The lower the BIM (Brittleness Index), the greater the rockburst risk. Room temperature granodiorite had a BIM of 1.15, indicating a high rockburst tendency. Under T400℃-liquid nitrogen cold shock conditions, the granodiorite had a BIM of 1.52, indicating a low rockburst tendency.

[0074] 3) Effects of high-temperature-cold shock treatment under different confining pressures on the tendency of granodiorite to burst.

[0075] To explore the effect of high-temperature-cold shock treatment on the rockburst tendency of granodiorite under different confining pressures, Table 3 lists the energy shock index R of untreated granodiorite and samples treated with different cooling methods at 600℃ under three confining pressure conditions (5 MPa, 15 MPa, and 25 MPa). The results show that high-temperature-cold shock treatment can significantly reduce the rockburst tendency of granodiorite, with liquid nitrogen cold shock having the most significant inhibitory effect.

[0076] Specifically, under a confining pressure of 15 MPa, the energy shock index of untreated granodiorite reached as high as 43.2, indicating its extreme susceptibility to rockburst. After 600℃-liquid nitrogen cold shock treatment, the index decreased to 2.05, approaching the critical value for low rockburst tendency (R=2). Under a confining pressure of 25 MPa, the R of the untreated sample was 14.74, indicating a high rockburst tendency. After liquid nitrogen cold shock treatment, the index decreased to 5, showing the best performance among the three cooling methods, further demonstrating that liquid nitrogen cold shock is an effective means of improving rockburst tendency. It is worth noting that as the confining pressure increased from 15 MPa to 25 MPa, the weakening effect of high-temperature cold shock on rockburst tendency decreased, and the improvement differences between different cooling methods also tended to narrow. This phenomenon reflects the inhibitory effect of confining pressure on thermal damage, providing lateral constraint to the rock and effectively suppressing the propagation and opening of microcracks during thermal shock. At the same time, in the initial loading stage, confining pressure has a certain "reinforcing" effect on the rock structure. Therefore, under 25 MPa conditions, although liquid nitrogen shock is still the best method, its advantages over water shock are not as significant as those under low confining pressure.

[0077] Table 3. Influence of cooling methods under different confining pressures on the energy index of granodiorite.

[0078]

[0079] Step 3 involved energy evolution analysis, the calculation principle of which is as follows:

[0080] Rocks deform and fracture under external forces, during which energy input, accumulation, dissipation, and release occur. Assuming no heat exchange occurs between the rock sample and its surroundings during loading, according to the first law of thermodynamics, the equation is:

[0081]

[0082] Where U is the total energy, Ue is the elastic energy, and Ud is the dissipated energy.

[0083] According to elasticity theory, the energy calculation formula under conventional triaxial loading can be expressed as follows:

[0084]

[0085]

[0086] Where E is the Young's modulus of the rock sample. Poisson's ratio of the rock sample It is the principal stress. Principal strains, i=1,2,3. Under conventional triaxial compression conditions, this can be simplified to:

[0087]

[0088] in and These are axial stress and confining pressure, respectively. and For axial strain and radial strain.

[0089] To further understand the energy evolution law, based on the principle of energy calculation, the relationship between the total energy, elastic energy, and dissipated energy of granodiorite samples under different high-temperature-cold shock conditions and strain was obtained. The energy evolution curves are divided into the following four stages:

[0090] (1) Initial Compaction Energy Dissipation Stage: In this stage, the rock is in a low-energy state. The compaction and closure of existing microcracks lead to significant internal energy dissipation, resulting in dissipated energy exceeding elastic energy. As axial strain continues to increase, the slope of the elastic energy curve gradually increases, indicating accelerated accumulation of elastic energy. In contrast, the dissipated energy curve remains stable with minimal change, indicating that energy dissipation has reached a steady state. This stage ends when the elastic energy curve exceeds and intersects with the dissipated energy curve. Notably, at 600°C, the intersection of water-impacted and liquid nitrogen-impacted granodiorite occurs later than that of naturally cooled granodiorite, indicating the presence of more initial microcracks in the water-impacted and liquid nitrogen-controlled rock.

[0091] (2) Linear energy storage stage: In this stage, the U and Ue curves rise rapidly, while the Ud curve remains stable, with Ue far exceeding Ud, and Ue gradually becoming dominant. The main reason is that Ud is the primary property of rock damage. In this stage, the rock mainly exhibits recoverable elastic deformation, without obvious crack development behavior, thus leading to the rapid accumulation of Ue, while the accumulation of Ud is slow. The total energy input in this stage is mainly stored in the form of elastic energy.

[0092] (3) Energy-consuming growth stage: As stress continues to increase, the U value of the sample further increases. Under the action of axial pressure, the internal damage of the sample gradually increases, and microcracks and pores begin to develop and permeate each other. During this process, Ue shows a rapid growth trend, while Ud gradually increases, but Ue still dominates, indicating that this process is still mainly driven by the energy stored in the rock.

[0093] (4) Post-peak energy release stage: In this stage, the rock bearing capacity reaches its limit, and the total energy accumulation reaches its peak. After damage, with the increase of strain, the accumulated Ue is continuously released, and the rate increases rapidly. Ud increases sharply, and the rate of increase is getting faster and faster. The rock strength decreases instantaneously, and the rock sample becomes unstable. After damage, the Ue curve of granodiorite subjected to 600℃-liquid nitrogen cold impact shows a step-like decrease, which indicates that the release of Ue is not continuous, but accompanied by multiple energy releases. This is because the microcracks formed inside the rock gradually expand during the damage process, resulting in the phased release of energy.

[0094] Furthermore, step 3 also involved calculating the three-dimensional fractal dimension of the pores, and performing microscopic analysis using NMR and CT scans respectively.

[0095] 1) NMR

[0096] In the study of water-saturated rock samples, the fluid relaxation mechanisms in the rock pores mainly include free relaxation, surface relaxation, and diffusion relaxation. When the rock contains only one type of fluid and is in a low-field environment, the transverse relaxation time of the free fluid and the transverse relaxation time caused by diffusion relaxation can be ignored. Therefore, the relaxation time T2 can be expressed as:

[0097]

[0098] in It is the transverse relaxation time of the fluid due to surface relaxation. Where S is the transverse surface relaxation strength, V is the pore surface area, Fs is the pore volume, and Fs is the form factor. It is the radius of the hole.

[0099] Different pores have different relaxation times T2. The horizontal relaxation time T2 reflects the size of the pore; the smaller the radius of the pore in the rock, the smaller the T2. The vertical signal intensity represents the number of pores of a specific size in the rock; the higher the value, the higher the number of pores of that size. T2 < 10 ms indicates micropores, 10 ms ≤ T2 ≤ 100 ms indicates mesopores, and T2 > 100 ms indicates macropores.

[0100] Porosity variation

[0101] By measuring the porosity of granodiorite samples under different temperatures and cooling methods, the evolution rate and extent of rock pore damage can be analyzed, such as... Figure 3 As shown.

[0102] The total porosity of the granodiorite sample at room temperature was 0.81%. The porosity of the granodiorite sample systematically increased with increasing temperature. The damage caused by liquid nitrogen cold shock was the greatest. Taking 600°C as an example, the effect of different cooling methods on the porosity of the granodiorite sample was analyzed. After heating at 600°C, the porosity of the granodiorite reached 3.43%, an increase of 323.46%. This is due to the increased crack length and connectivity within the granodiorite at 600°C. Quartz is one of the main rock-forming minerals of granodiorite, and its properties have a decisive influence on the thermodynamic response of the rock mass. At the critical temperature of 573°C, the cubic α-quartz in the granodiorite mass underwent a phase transformation to the hexagonal β-quartz, with a volume expansion of approximately 5%. After cooling to room temperature, β-quartz can completely revert to α-quartz, but the volume expansion generated in the first heating stage is irreversible. Temperatures above 573°C cause rapid crack propagation in granodiorite and a significant increase in porosity. Therefore, the significant increase in porosity from room temperature granodiorite to 600°C granodiorite is mainly due to the phase transformation of quartz. The porosity of the 600°C water-impacted granodiorite sample was 4.15%, a change of 412.35% compared to the untreated sample. There are two reasons for this: (1) Thermal damage to the room temperature granodiorite sample during the heating process. The thermal expansion coefficients of the minerals inside the granodiorite are different, and the expansion during the heating process is uneven; this uneven expansion generates thermal stress inside the granodiorite sample. When the thermal stress exceeds the ultimate strength between the minerals, it will generate microcracks or cause existing microcracks to expand inside the granodiorite. At high temperatures above 400°C, the high temperature provides more energy for the displacement phase transformation of minerals in the rock, further deteriorating the rock. (2) Thermal shock generated by the cooling of 600°C granodiorite by contact with water. When hot rocks are impacted by water, a significant temperature gradient is generated between their interior and exterior. When hot rocks come into contact with water, the exterior cools rapidly, at rates up to 100°C / min, while the interior of the sample, not in direct contact with water, remains at a much lower temperature than the exterior. This causes a severe thermal shock, inducing tensile stress on the exterior and forming tensile microcracks. Furthermore, tensile stress can connect these microcracks, further weakening the rock's properties. The porosity of granodiorite subjected to 600°C-liquid nitrogen cold impact was 4.88%, a further decrease compared to the porosity of granodiorite subjected to water impact. Liquid nitrogen cold impact also results in two-part damage, with the damage during the heating process consistent with that of granodiorite subjected to water impact. However, the damage to the granodiorite samples differs due to the different cooling media used. When liquid nitrogen is used in a standard atmospheric pressure environment at -196°C, the cooling rate differs significantly from that of test water at 20°C.The temperature difference between high-temperature granodiorite and liquid nitrogen is much greater than that between high-temperature granodiorite and water, resulting in higher tensile stress in the liquid nitrogen cold impact sample than in the water impact sample. Therefore, the liquid nitrogen cold impact on granodiorite is more severe.

[0103] fractal dimension

[0104] The complexity of rock pore structure mainly stems from the irregularity of pore shape and distribution. Fractal theory can effectively characterize the distribution of internal cracks in rocks; the lower the fractal dimension, the smaller the differences between pore structures and the higher the uniformity of pore distribution. High-temperature and cold-shock processes can damage the microstructure of rocks, primarily manifested in the dynamic changes of defects such as pores and cracks. According to fractal theory, the number of pores with a radius greater than r in granodiorite is defined as N, and the volume fraction of pores with a radius less than r can be expressed as follows:

[0105]

[0106] Taking the logarithm of both sides of the equation, we get:

[0107]

[0108] Where D is the fractal dimension.

[0109] The fractal dimensions Dmini, Dmeso, Dmacro, and Dtotal of micropores, mesopores, macropores, and total pores can be expressed as follows:

[0110]

[0111] Please see Figures 4 to 16In this embodiment, regression analysis was used to calculate the fractal dimension of granodiorite samples under various high-temperature cold shock conditions. The specific results are shown in Table 4. Generally, the fractal dimension of natural granodiorite is between 2 and 3. When the fractal dimension is close to 3, it indicates that the three-dimensional pore structure of the rock is very complex; when the fractal dimension is less than 2, it indicates that the pore structure of the rock is very uniform and has minimal complexity. As can be seen from the table, granodiorite only exhibits macroscopic pores under specific treatment conditions, resulting in poor fitting accuracy. The fractal dimension of granodiorite micropores at room temperature is 1.911, and the highest fractal dimension of micropores appears at 1.94 in granodiorite naturally cooled at T400°C. This indicates that micropores do not exhibit obvious fractal characteristics under both room temperature and high-temperature cold shock conditions. In contrast, the fractal dimension of mesopores ranges from 2.89 to 2.953, showing strong fractal characteristics. Under all test conditions, mesopores exhibited higher fitting accuracy and complexity in spatial distribution, with Dmeso exceeding Dmini, indicating a more complex mesopore structure than micropore structure. Furthermore, it was observed that the fractal dimension of mesopores in granodiorite was low at 25°C, increasing under high-temperature cold shock, suggesting that high temperatures enhance the complexity of the pore structure of granodiorite under temperature influence. Under 600°C-liquid nitrogen cold shock conditions and at 800°C, Dtotal was higher than under other test conditions, indicating that the complexity and irregularity of the overall pore structure of granodiorite were enhanced under these conditions.

[0112] Table 4. Fractal dimension of granodiorite samples under different high-temperature cold shock conditions

[0113]

[0114] 2) CT scan

[0115] During CT scanning, rock specimens are typically placed vertically on the scanning stage, and the CT detector uses a fan-beam scanning mode to acquire data from the specimen. Due to the limitations of the scanning geometry, fan-beam scanning results in a certain degree of data loss in the top and bottom slices of the specimen. To address this issue, a portion of the top and bottom slices can be removed to eliminate reconstruction errors caused by data loss during 3D reconstruction. CT detectors generate noise during imaging; to eliminate this effect and improve the quality of the digital image, "contour filtering" is applied to the original 2D slice images of the sample, effectively improving sharpness and contrast. In grayscale CT images, light-colored areas typically represent high-density materials, while dark-colored areas correspond to low-density materials; therefore, black areas represent pores in the rock. Thresholding segmentation is then performed on the denoised image. Thresholding segmentation divides the image into non-overlapping regions based on image grayscale, and then a watershed algorithm is used to perform 3D reconstruction on the thresholded segmented image. The flowchart is shown below. Figure 17As shown, the intermediate layer slices and three-dimensional reconstruction models of preheated granodiorite under different cooling methods are as follows: Figures 18 to 21 As shown.

[0116] Face gap change

[0117] Porosity reflects the proportion of pores in each layer of a sample to the total volume. To more clearly show the distribution of the pore structure inside the granodiorite sample, the porosity of granodiorite under three cooling conditions at 600℃ and at room temperature was analyzed. The results are as follows: Figures 22 to 25 As shown. It should be noted that the porosity measured by CT is an approximation and is mainly used for comparisons between different groups.

[0118] Figure 22 Analysis shows that the porosity of room-temperature granodiorite gradually increases from the middle to the top and bottom, with the peak porosity occurring in layer 24 at 1.5%. In contrast, the porosity of naturally cooled granodiorite at 600°C exhibits a high distribution at the upper end and a low distribution at the lower end. Figure 23 This is due to the structural design of the muffle furnace, where the thermal damage to the upper, overhanging portion of the sample is greater than that to the lower portion during heating. The regional porosity of the 600℃ water-impacted granodiorite and the 600℃ liquid nitrogen-impacted granodiorite shows a trend of high porosity at both ends and low porosity in the middle. Specifically, the average porosity of the 600℃ water-impacted granodiorite is 3.46%, with a faster increase in porosity at the upper end, peaking at layer 1483, where the porosity is 5.01%. Figure 24 The area porosity of the granodiorite subjected to 600℃-liquid nitrogen cold impact increases in layer 892, with peak porosity occurring in layer 1475, at 6.95%. Figure 25 Furthermore, in areas where the original porosity of granodiorite is relatively dense, the high-temperature-cold impact treatment causes more severe damage to the granodiorite. In particular, the granodiorite subjected to 600°C-liquid nitrogen cold impact exhibits the highest porosity curve, indicating the most severe damage.

[0119] Step 4 combines the peak strength strain energy storage index with the fractal dimension of rock porosity to study rockburst tendency from both macroscopic and microscopic perspectives. The criteria for judging rockburst tendency used in this invention are as follows:

[0120] Rockburst tendency is divided into three categories. When the peak strength strain storage index is greater than 5, it indicates that the rock has a high rockburst tendency; in the range of 2 to 5, it belongs to low rockburst tendency; less than 2 is considered to have no rockburst tendency.

[0121] Figure 26The relationship between the peak strength-strain storage index and the three-dimensional fractal dimension of granodiorite pores under high-temperature cold shock in this embodiment is shown. As shown in the figure, the equation relating the peak strength-strain storage index and the pore fractal dimension is as follows:

[0122]

[0123] in The peak strength strain energy storage index is represented by , D represents the pore fractal dimension, and a, b, c, and d are constants determined for different high-temperature-cold shock conditions. High-temperature-natural cooling: a=1.193, b=117.167, c=344.119, d=1.4; High-temperature-water shock: a=1.618, b=386, c=1052.498, d=2.36; High-temperature-liquid nitrogen cold shock: a=10.126, b=94.34, c=272.643, d=1.685.

[0124] Therefore, based on the established quantitative relationship model, the peak strength strain energy storage index can be directly calculated by measuring the three-dimensional fractal dimension D of rock pores. Combined with the rockburst tendency classification standard of the peak strength strain energy storage index, the quantitative classification and determination of rockburst tendency can be realized.

[0125] The above description discloses only one preferred embodiment of the present invention, and should not be construed as limiting the scope of the present invention. Those skilled in the art will understand that all or part of the processes of the above embodiments can be implemented, and equivalent changes made in accordance with the claims of the present invention are still within the scope of the invention.

Claims

1. A quantitative analysis method for rockburst tendency based on the three-dimensional fractal dimension of pores, characterized in that, Includes the following steps: Step 1: Rock sample preparation and pretreatment; Step 2: Conduct triaxial compression mechanics tests and microstructure characterization tests; Step 3: Calculation and analysis of rockburst tendency evaluation index and pore three-dimensional fractal dimension index; Step 4: Establish a quantitative relationship between the three-dimensional fractal dimension of pores and the core index of rockburst tendency, so as to realize the quantitative classification and judgment of rockburst tendency.

2. The method for quantitative analysis of rockburst tendency based on the three-dimensional fractal dimension of pores as described in claim 1, characterized in that, The rock samples in Step 1 must be homogeneous, and all samples must be taken from the same rock block. The execution process of Step 1 includes the following steps: Step 1.1: Sample preparation, selecting the basic physical parameters of the sample; Step 1.2: Perform high-temperature heating treatment on the sample; Step 1.3: Divide the heated samples into three groups for differentiated cold shock treatment; Step 1.4: Sample drying completes the pretreatment.

3. The method for quantitative analysis of rockburst tendency based on the three-dimensional fractal dimension of pores as described in claim 2, characterized in that, In step 2, the pretreated samples are subjected to X-ray diffraction, nuclear magnetic resonance, CT scan and three-dimensional reconstruction, and scanning electron microscopy observation, respectively. The pretreated samples include samples that have not undergone triaxial compression mechanical testing and samples that have undergone triaxial compression mechanical testing.

4. The method for quantitative analysis of rockburst tendency based on the three-dimensional fractal dimension of pores as described in claim 3, characterized in that, The execution process of step 3 includes the following steps: Step 3.1: Calculation of rockburst tendency evaluation indicators, including energy impact index, peak strength strain energy storage index, residual elastic energy index, and improved brittleness index; Step 3.2: Rock energy evolution calculation; Step 3.3: Calculation of the three-dimensional fractal dimension of the pores.

5. The method for quantitative analysis of rockburst tendency based on the three-dimensional fractal dimension of pores as described in claim 4, characterized in that, In step 4, a quantitative relationship between the three-dimensional fractal dimension of pores and the core index of rockburst tendency is established. Specifically, the peak strength strain energy storage index is selected as the core characterization index of rockburst tendency. The peak strength strain energy storage index value and the corresponding total pore fractal dimension and function relationship under different high temperature-cold shock conditions are established by curve fitting. The rockburst tendency classification standard is combined to classify and determine the rockburst tendency. The relationship equations between the fitted functions are as follows: in The peak strength strain energy storage index is represented by , D represents the pore fractal dimension, and a, b, c, and d are constants determined for different high-temperature-cold shock conditions; High-temperature-natural cooling: a=1.193, b=117.167, c=344.119, d=1.4; High-temperature-water shock: a=1.618, b=386, c=1052.498, d=2.36; High-temperature-liquid nitrogen cold shock: a=10.126, b=94.34, c=272.643, d=1.685.

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