A rock brittleness determination method based on whole-process energy three-way integration and net energy release

Abstract

The application discloses a rock brittleness determination method based on whole-process energy three-way integration and net energy release, relates to the technical field of underground engineering safety evaluation, and obtains the whole-process three-way loading curve, three-way unloading curve and three-way stress-strain curve of a rock sample in the initial hydrostatic pressure loading and unloading stage, the pre-peak axial cyclic loading and unloading stage, the post-peak stage, the post-peak unloading stage and the hydrostatic pressure unloading stage. The three-way integration and accumulation are carried out on the curves in each stage, the pre-peak cumulative total net work, the elastic strain energy density of each level of cyclic loading and unloading process, the pre-peak effective jointing energy, the lateral expansion dissipation work, the elastic strain energy density of the post-peak axial stress valley bottom point, the hydrostatic background elastic strain energy release amount and the post-peak net jointing energy density and other whole-process energy components are quantified, and a normalized net energy release rate index is constructed to determine the rock brittleness. The rock brittleness determination precision is improved.

Description

Technical Field

[0001] This application relates to the field of underground engineering safety evaluation technology, and in particular to a method for determining rock brittleness based on the triaxial integral of energy throughout the entire process and net energy release. Background Technology

[0002] Rock brittleness is a key indicator for evaluating the stability of deep underground engineering, the compressibility of shale oil and gas reservoirs for fracturing, and the tendency for rockburst. More than eighty rock brittleness evaluation methods have been established, mainly covering five categories of evaluation systems: those based on mineral component weight calculations (such as the ratio of quartz, carbonate, and clay mineral content), those based on strength parameter ratios (such as the ratio of uniaxial compressive to tensile strength), those based on normalized combinations of elastic parameters (such as high Young's modulus and low Poisson's ratio), those based on the geometric characteristics of stress-strain curves (such as post-peak modulus and stress drop rate), and those based on energy evolution ratios (such as the ratio of elastic energy storage to dissipated energy).

[0003] However, the above methods have the following significant drawbacks: 1) They only reflect the static characteristics of a single stage and do not cover the entire rock fracturing process. The brittleness of rock is a comprehensive property determined by the accumulation and dissipation of energy before the peak, the self-fracture ability after the peak, and the energy release rate. Its evaluation should cover the entire process from loading to failure. Methods based on elastic parameters only use static deformation parameters such as Young's modulus and Poisson's ratio in the linear elastic stage before the peak as brittleness criteria, while methods based on the stress drop rate or the magnitude of irreversible strain after the peak only define a certain local geometric feature of the stress-strain curve. These methods essentially replace the comprehensive consideration of the entire rock fracturing process with static mechanical indicators of a single stage, and cannot reflect the influence of damage accumulation before the peak on the fracture mode after the peak, nor can they reflect the ability of rock to maintain fracture by relying on its own energy storage in the post-peak stage. 2) They are calibrated based on normal pressure or low hydrostatic pressure conditions and lack stress environment sensitivity. The strength, modulus, and other mechanical parameters of rock have a significant nonlinear response to hydrostatic pressure. The compressive strength increases with the increase of hydrostatic pressure, but the increase decreases as the hydrostatic pressure continues to increase. The strength parameter determination method, represented by the ratio of uniaxial compressive to tensile strength, and some indices based on empirical regression of rock density and strength, are all based on experimental data at normal or low hydrostatic pressure. In ultra-deep, high-stress environments, this standard of determination based on normal pressure calibration will lose its representativeness. 3) The work done by environmental resistance and ineffective energy consumption are not eliminated, leading to an overestimation of rock brittleness under high hydrostatic pressure. Under high hydrostatic pressure, post-peak fracture of rock requires overcoming hydrostatic pressure to undergo shear dilatation and expansion. This energy is consumed to maintain the structure or overcome friction, and is not the effective energy driving fracture. Plastic frictional heat generated by microcrack closure and slippage also exists in the pre-peak stage, which is dissipation that does not contribute to brittle fracture. The energy determination method based on the ratio of pre-peak elastic storage to total dissipated energy and the analysis method based on the ratio of post-peak fracture energy to replenished energy both include the above-mentioned ineffective losses in the fracture driving energy, leading to a serious overestimation of rock brittleness under high hydrostatic pressure. 4) Energy calculations are based on linear elastic assumptions and do not consider theoretical stress deviations caused by damage. Traditional energy calculations generally adopt... Simplified formula ( For stress, The elastic modulus is assumed to be ideally linearly elastic in the pre-peak stage. However, deep rocks undergo significant microcrack evolution before the peak, and the actual stress path deviates from the theoretical linear elastic value. If this damage effect is ignored, all energy classification methods based on the linear elastic assumption for calculating pre-peak elastic energy storage will produce systematic errors in their energy quantification results.

[0004] In summary, the aforementioned shortcomings ultimately lead to low accuracy in determining rock brittleness. Therefore, a method for determining rock brittleness based on the triaxial integration of energy throughout the entire process and net energy release is needed to address the problem of low accuracy in determining rock brittleness. Summary of the Invention

[0005] The purpose of this application is to provide a method for determining rock brittleness based on the triaxial integration of energy throughout the entire process and net energy release, so as to solve the problem of low accuracy in determining rock brittleness.

[0006] To achieve the above objectives, this application provides the following solution.

[0007] This application provides a method for determining rock brittleness based on the three-dimensional integral of energy throughout the entire process and net energy release, including: The triaxial unloading curves of the rock sample during the initial hydrostatic pressure loading and unloading stage were obtained. The triaxial unloading curves during the initial hydrostatic pressure loading and unloading stage were integrated and accumulated to obtain the initial hydrostatic elastic strain energy density. The triaxial unloading curves include: axial unloading curve, first radial unloading curve and second radial unloading curve. The triaxial loading curve, triaxial unloading curve, and acoustic emission signal data of the rock sample during the N-stage cyclic loading and unloading process before the peak were obtained; N is the preset number of stages, the first N-1 stages of the cyclic loading and unloading process include the loading process and the unloading process, and the N-stage cyclic loading and unloading process includes the loading process; the triaxial loading curves include: axial loading curve, first radial loading curve, and second radial loading curve; the acoustic emission signal data include the rise time, peak amplitude, ring count, and duration of the acoustic emission signal in multiple acoustic emission events; By integrating and summing the three-dimensional loading and unloading curves during the N-stage cyclic loading and unloading process, the total net power accumulated before the peak is obtained. The elastic strain energy density of the first N-1 stage cyclic loading and unloading process is obtained by integrating and summing the triaxial unloading curves. Regression analysis was performed on the axial stress and elastic strain energy density of the first N-1 stage cyclic loading and unloading process to establish the first fitting relationship. The peak value of the axial stress in the Nth stage cyclic loading and unloading process was substituted into the first fitting relationship to obtain the elastic strain energy density of the Nth stage cyclic loading and unloading process. The first fitting relationship is the fitting relationship between elastic strain energy density and axial stress in the axial cyclic loading and unloading stage before the peak. Based on acoustic emission signal data, cumulative net work before the peak, and elastic strain energy density of the Nth stage loading and unloading process, the effective crack-forming energy before the peak is determined. The triaxial stress-strain curves of the rock sample in the post-peak stage were obtained, and the triaxial stress-strain curves in the post-peak stage were integrated and accumulated to obtain the lateral expansion dissipation work. The triaxial stress-strain curves include: axial stress-strain curve, first radial stress-strain curve and second radial stress-strain curve. The triaxial unloading curves of the rock sample during the post-peak unloading stage were obtained, and the triaxial unloading curves during the post-peak unloading stage were integrated and accumulated to obtain the elastic strain energy density during the post-peak unloading stage. Regression analysis was performed on the elastic strain energy density during the post-peak unloading stage to establish a second fitting relationship. The axial stress valley point after the peak in the triaxial stress-strain curve was substituted into the second fitting relationship to obtain the elastic strain energy density at the axial stress valley point after the peak. The second fitting relationship is the fitting relationship between the elastic strain energy density and the axial stress during the post-peak unloading stage. The triaxial unloading curves of the rock sample during the hydrostatic unloading stage were obtained, and the residual hydrostatic elastic strain energy density was obtained by integrating and summing the triaxial unloading curves during the hydrostatic unloading stage. The difference between the initial hydrostatic elastic strain energy density and the residual hydrostatic elastic strain energy density is used to obtain the hydrostatic background elastic strain energy release. Based on the elastic strain energy density of the Nth cyclic loading and unloading process, the elastic strain energy density of the axial stress valley point after the peak, the elastic strain energy release in the still water background, and the lateral expansion dissipation work, the net crack-making energy density after the peak is determined. Based on the effective fracture energy before the peak, the net fracture energy density after the peak, the elastic strain energy density during the Nth stage loading and unloading process, and the initial hydrostatic elastic strain energy density, the normalized net energy release rate index of the rock sample is determined, thus completing the determination of the rock brittleness of the rock sample.

[0008] According to the specific embodiments provided in this application, the following technical effects are disclosed: This application discloses a method for determining rock brittleness based on the triaxial integration of energy and net energy release throughout the entire process. By acquiring triaxial stress-strain data of the rock sample during the initial hydrostatic loading / unloading stage, the pre-peak axial cyclic loading / unloading stage, the post-peak stage, the post-peak unloading stage, and the hydrostatic unloading stage, triaxial integration and summation are performed on the triaxial loading curve, triaxial unloading curve, and triaxial stress-strain curve for each stage. This accurately quantifies the total net work accumulated before the peak, the elastic strain energy density during each stage of cyclic loading / unloading, the lateral expansion dissipation work, and the elastic strain energy density at the post-peak axial stress trough. The system incorporates energy components throughout the entire process, including the release of elastic strain energy in the still water background and the effective fracture-forming energy before the peak. Based on these energy components, a normalized net energy release rate index is constructed. This ensures that the determination of rock brittleness covers the complete energy evolution path from pre-peak loading to post-peak failure. Furthermore, by processing triaxial stress integrals and acoustic emission signal data, the system eliminates the ineffective dissipation of radial expansion and the release of elastic strain energy in the still water background, thus avoiding the energy calculation errors caused by traditional methods that rely solely on a single-stage static index, fail to eliminate ineffective energy dissipation, and assume linear elasticity. This significantly improves the accuracy of rock brittleness determination. Attached Figure Description

[0009] To more clearly illustrate the technical solutions in the embodiments of this application or related technologies, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0010] Figure 1 This is a schematic flowchart of a method for determining rock brittleness based on the triaxial integration of energy throughout the entire process and net energy release, provided as an embodiment of this application. Detailed Implementation

[0011] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0012] The purpose of this application is to provide a method for determining rock brittleness based on the triaxial integration of energy throughout the entire process and net energy release, aiming to improve the accuracy of rock brittleness determination.

[0013] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0014] In one exemplary embodiment, such as Figure 1 As shown, a method for determining rock brittleness based on the triaxial integral of energy throughout the entire process and net energy release is provided, including the following steps.

[0015] Step 01: Obtain the triaxial unloading curve of the rock sample during the initial hydrostatic pressure loading and unloading stage. Integrate and sum the triaxial unloading curves during the initial hydrostatic pressure loading and unloading stage to obtain the initial hydrostatic elastic strain energy density.

[0016] The three-way unloading curves include: axial unloading curve, first radial unloading curve, and second radial unloading curve.

[0017] As an optional implementation, in step 01, the formula for calculating the initial hydrostatic elastic strain energy density is: ; in, This represents the initial hydrostatic elastic strain energy density. The axial strain at the unloading point during the initial hydrostatic pressure loading and unloading stage; The axial strain is the final unloading strain during the initial hydrostatic pressure loading and unloading phase. For axial stress; For axial strain; The first radial strain at the unloading point during the initial hydrostatic pressure loading and unloading stage; The first radial strain at the unloading endpoint during the initial hydrostatic pressure loading and unloading stage; Lateral stress; The first radial strain; The second radial strain at the unloading initiation point during the initial hydrostatic pressure loading and unloading stage; The second radial strain is the endpoint of unloading during the initial hydrostatic pressure loading and unloading stage. This represents the second radial strain.

[0018] Specifically, in the initial hydrostatic pressure loading and unloading stage, hydrostatic pressure is applied to the rock sample to the target value, that is, both axial stress and lateral stress are applied to the target value, so that the rock sample is in a hydrostatic pressure state, and at least one hydrostatic pressure loading and unloading cycle is performed.

[0019] Prior to step 01, experimental preparation and sensor arrangement were carried out: a high-stiffness electro-hydraulic servo rock mechanics testing machine was used. High-precision sensors for monitoring axial deformation, first radial deformation, and second radial strain were installed on the surface of the rock specimen. At the same time, acoustic emission sensors were symmetrically arranged on the surface of the rock specimen to synchronously monitor acoustic emission signal data during the loading process.

[0020] Step 02: Obtain the triaxial loading curve, triaxial unloading curve, and acoustic emission signal data of the rock sample during the N-stage cyclic loading and unloading process in the axial loading and unloading phase before the peak.

[0021] Wherein, N is the preset number of stages, the first N-1 stages of the cyclic loading and unloading process include the loading process and the unloading process, the Nth stage of the cyclic loading and unloading process includes the loading process; the three-dimensional loading curves include: the axial loading curve, the first radial loading curve and the second radial loading curve; the acoustic emission signal data include the rise time, peak amplitude, ring count and duration of the acoustic emission signal in multiple acoustic emission events.

[0022] Specifically, during the pre-peak axial cyclic loading and unloading phase, the lateral stress is kept constant, and axial stress is applied at a constant rate. Based on the estimated peak intensity, graded cyclic loading and unloading are performed at stress levels of approximately 40%, 60%, and 80%; if it is difficult to predict, a fixed increment of axial stress is used.

[0023] Step 03: Integrate and sum the three-dimensional loading curves and three-dimensional unloading curves in the N-stage cyclic loading and unloading process to obtain the total net power accumulated before the peak.

[0024] As an optional implementation, in step 03, the formula for calculating the total net power accumulated before the peak is: ; in, Accumulate total net work before the peak; Let be the axial strain corresponding to the peak point of axial stress during the i-th stage of cyclic loading and unloading; The axial strain at the loading start point during the i-th stage of the loading and unloading cycle; The first radial strain is the point corresponding to the peak axial stress during the i-th stage of cyclic loading and unloading. The first radial strain at the loading starting point during the i-th stage of cyclic loading and unloading; The second radial strain is the point corresponding to the peak axial stress during the i-th stage of cyclic loading and unloading. The second radial strain is the loading initiation point during the i-th stage cyclic loading and unloading process; Let be the axial strain at the end of the unloading process during the i-th stage of the loading and unloading cycle; The first radial strain at the unloading endpoint during the i-th stage of the loading and unloading process; The second radial strain is the endpoint of the unloading process during the i-th stage of the loading and unloading cycle. The axial strain is the axial strain corresponding to the peak point of axial stress during the Nth stage of loading and unloading. The axial strain at the loading start point during the Nth stage of the loading and unloading cycle; The first radial strain corresponds to the peak point of axial stress during the Nth stage of loading and unloading process; The first radial strain at the loading initiation point during the Nth stage of cyclic loading and unloading; The second radial strain corresponds to the peak point of axial stress during the Nth stage of loading and unloading process. The second radial strain is the starting point of the loading process during the Nth stage of the loading and unloading cycle.

[0025] Step 04: Integrate and sum the triaxial unloading curves of the first N-1 stage cyclic loading and unloading processes to obtain the elastic strain energy density of the first N-1 stage cyclic loading and unloading processes.

[0026] As an optional implementation, in step 04, the formula for calculating the elastic strain energy density of the i-th cyclic loading and unloading process during the first N-1 cyclic loading and unloading processes is: ; in, Let be the elastic strain energy density during the i-th stage cyclic loading and unloading process.

[0027] Step 05: Perform regression analysis on the axial stress value and elastic strain energy density of the first N-1 stage cyclic loading and unloading process, establish the first fitting relationship, and substitute the peak value of the axial stress of the Nth stage cyclic loading and unloading process into the first fitting relationship to obtain the elastic strain energy density of the Nth stage cyclic loading and unloading process.

[0028] Among them, the first fitting relationship is the fitting relationship between elastic strain energy density and axial stress during the pre-peak axial cyclic loading and unloading stage.

[0029] Step 06: Determine the effective crack-forming energy before the peak based on acoustic emission signal data, cumulative net power before the peak, and elastic strain energy density during the Nth stage loading and unloading process.

[0030] As an optional implementation, in step 06, the formula for calculating the effective pre-peak joint energy is: ; ; ; in, This provides effective seam creation energy before the peak; The coefficient representing the proportion of tensile cracks; The total energy dissipation density before the peak; The number of acoustic emission events judged as tensile cracks; This represents the total number of acoustic emission events in the acoustic emission signal data; The elastic strain energy density is the Nth stage loading and unloading process.

[0031] Specifically, The determination process includes: calculating each acoustic emission event in the acoustic emission signal data one by one. Value and The value is used to determine the crack type corresponding to each acoustic emission event based on the boundary line.

[0032] The value is defined as the ratio of the rise time to the peak amplitude of the acoustic emission signal. ; The AF value is defined as the ratio of the ring count of the acoustic emission signal to the duration of the acoustic emission signal. ; The physical basis of crack classification: The acoustic emission signals generated by different fracture mechanisms exhibit systematic differences in waveform characteristics. Tensile cracks, dominated by tensile stress, are characterized by rapid crack surface separation, producing signals rich in longitudinal waves (P-waves) and high-frequency components, resulting in low RA values ​​and high AF values. Shear cracks, dominated by frictional slip, produce signals dominated by transverse waves (S-waves) and low-frequency components, resulting in high RA values ​​and low AF values. Based on this physical law, quantitative differentiation of crack types can be achieved by establishing classification boundaries in the RA-AF coordinate system.

[0033] Establishing Crack Classification Criteria: Accurately determining the crack classification boundary is crucial for the RA-AF method. In the RA-AF scatter plot, data points for tensile cracks cluster in the upper left region (low RA, high AF), while data points for shear cracks cluster in the lower right region (high RA, low AF). The classification boundary is typically established using a linear equation. The form in which the slope and intercept The value of RA-AF varies depending on the rock type, test conditions, and acoustic emission system parameters, and needs to be determined through calibration tests. The ratio of AF to RA in the RA-AF boundary can differ by several orders of magnitude for different rocks. Therefore, for a specific test rock type, Brazilian splitting tests (calibrating pure tensile cracks) and shear tests (calibrating pure shear cracks) should be carried out to obtain the RA-AF data distribution and determine the classification boundary applicable to that rock.

[0034] Step 07: Obtain the triaxial stress-strain curve of the rock sample in the post-peak stage, and integrate and accumulate the triaxial stress-strain curve in the post-peak stage to obtain the lateral expansion dissipation work.

[0035] The triaxial stress-strain curves include: axial stress-strain curve, first radial stress-strain curve, and second radial stress-strain curve.

[0036] As an optional implementation, in step 07, the formula for calculating the lateral expansion dissipation work is: ; in, This is for lateral expansion to dissipate work; This represents the axial strain corresponding to the axial stress valley point in the post-peak stage. This represents the axial strain corresponding to the peak point of axial stress in the post-peak stage. This represents the first radial strain corresponding to the bottom point of the axial stress valley after the peak in the post-peak stage. This represents the first radial strain corresponding to the peak point of axial stress in the post-peak stage. This represents the second radial strain corresponding to the bottom point of the axial stress valley after the peak in the post-peak stage. This represents the second radial strain corresponding to the peak point of axial stress in the post-peak stage.

[0037] Step 08: Obtain the triaxial unloading curve of the rock sample in the post-peak unloading stage, and integrate and sum the triaxial unloading curves in the post-peak unloading stage to obtain the elastic strain energy density in the post-peak unloading stage.

[0038] As an optional implementation, in step 08, the formula for calculating the elastic strain energy density during the post-peak unloading stage is: ; in, This represents the elastic strain energy density during the post-peak unloading phase. This represents the axial strain corresponding to the unloading start point during the post-peak unloading stage. This represents the axial strain corresponding to the unloading endpoint during the post-peak unloading stage. This refers to the first radial strain corresponding to the unloading start point in the post-peak unloading stage. This refers to the first radial strain corresponding to the unloading endpoint in the post-peak unloading stage. This refers to the second radial strain corresponding to the unloading start point in the post-peak unloading stage. This represents the second radial strain corresponding to the unloading endpoint during the post-peak unloading phase.

[0039] Specifically, during the post-peak unloading phase, the unloading operation is performed.

[0040] Step 09: Perform regression analysis on the elastic strain energy density of the post-peak unloading stage, establish a second fitting relationship, and substitute the post-peak axial stress valley point in the triaxial stress-strain curve into the second fitting relationship to obtain the elastic strain energy density of the post-peak axial stress valley point.

[0041] The second fitting equation is the fitting relationship between elastic strain energy density and axial stress during the post-peak unloading stage.

[0042] Step 10: Obtain the triaxial unloading curve of the rock sample during the hydrostatic unloading stage, and integrate and accumulate the triaxial unloading curve during the hydrostatic unloading stage to obtain the residual hydrostatic elastic strain energy density.

[0043] As an optional implementation, in step 10, the formula for calculating the residual hydrostatic elastic strain energy density is: ; in, The residual hydrostatic elastic strain energy density; This represents the axial strain corresponding to the unloading start point during the hydrostatic unloading stage. This represents the axial strain corresponding to the end point of the hydrostatic unloading stage. The first radial strain corresponds to the unloading start point during the hydrostatic unloading stage; This represents the first radial strain corresponding to the end point of the hydrostatic unloading stage. This represents the second radial strain corresponding to the unloading start point during the hydrostatic unloading stage. This represents the second radial strain corresponding to the unloading endpoint of the hydrostatic unloading stage.

[0044] Specifically, during the hydrostatic pressure unloading phase, the hydrostatic pressure is gradually reduced to zero.

[0045] Step 11: Subtract the initial hydrostatic elastic strain energy density from the residual hydrostatic elastic strain energy density to obtain the hydrostatic background elastic strain energy release.

[0046] Specifically, the formula for calculating the release of elastic strain energy in a still water background is: .

[0047] in, This represents the amount of elastic strain energy released in a still water background.

[0048] Step 12: Determine the net crack-forming energy density after the peak based on the elastic strain energy density of the Nth-stage cyclic loading and unloading process, the elastic strain energy release amount in the still water background, and the lateral expansion dissipation work.

[0049] As an optional implementation, in step 12, the formula for calculating the net fracture energy density after the peak is: ; in, The net energy density of the fracture after the peak; The elastic strain energy density at the bottom of the axial stress valley after the peak; This represents the amount of elastic strain energy released in a still water background.

[0050] Step 13: Based on the effective fracture energy before the peak, the net fracture energy density after the peak, the elastic strain energy density of the Nth stage loading and unloading process, and the initial hydrostatic elastic strain energy density, determine the normalized net energy release rate index of the rock sample, and complete the determination of the rock brittleness of the rock sample.

[0051] As an optional implementation, in step 13, the formula for calculating the normalized net energy release rate index is: ; in, It is the normalized net energy release rate index.

[0052] Specifically, The higher the value, the higher the proportion of effective net energy release during the destruction process, and the more significant the rock brittleness.

[0053] Furthermore, a triaxial cyclic loading and unloading test was conducted on a standard cylindrical shale specimen (25 mm in diameter and 50 mm in height) at a certain depth using a high-rigidity rock mechanics testing system, with the hydrostatic pressure set at 40 MPa. The rock brittleness of this standard cylindrical shale specimen was also determined using the method described in this application, and the determination steps are as follows.

[0054] (1) During the initial hydrostatic pressure loading and unloading stage, a hydrostatic pressure of 40 MPa was applied to the rock sample, and the initial hydrostatic elastic strain energy density was determined. The initial hydrostatic elastic strain energy density was: .

[0055] (2) During the axial cyclic loading and unloading phase before the peak, the hydrostatic pressure is kept constant, and deviatoric stress is applied by axial displacement control. Loading and unloading cycles are performed at 40%, 60%, 80%, and 90% of the estimated peak strength (a total of 4 loading / unloading cycles + 1 destructive loading cycle). The total net cumulative work before the peak is determined as follows: The first fitting equation is: The peak axial stress of the specimen during the failure loading process was measured to be... MPa. (The rest of the text appears to be incomplete and requires further context.) Substituting MPa into the first fitted equation, extrapolation yields the elastic strain energy density at the peak moment (the elastic strain energy density during the failure loading process). The total energy dissipation density before the peak is Statistical analysis of tensile crack events during the pre-peak axial cyclic loading and unloading phase yielded a tensile crack proportion coefficient of 40. The effective crack formation energy pre-peak was calculated to be... .

[0056] (3) In the post-peak stage, determine the lateral expansion dissipation work, which is: .

[0057] (4) During the post-peak unloading stage, the elastic strain energy density at the bottom of the post-peak axial stress valley is: .

[0058] (5) Calculate the net fracture energy density after the peak. The net fracture energy density after the peak is: .

[0059] (6) Calculate the normalized net energy release rate index, which is: The normalized net energy release rate index quantifies the true net energy release efficiency of shale under a high hydrostatic pressure of 40 MPa, after deducting ineffective expansion dissipation and environmental background energy storage. The larger the value, the stronger the rock brittleness.

[0060] The beneficial effects of this application are: The physical significance is clear: This method explicitly deducts the ineffective expansion work consumed in overcoming hydrostatic pressure constraints during the post-peak expansion process, effectively correcting the overestimation of brittle characteristics by traditional evaluation methods based on elastic modulus or stress drop under high hydrostatic pressure conditions, making the evaluation results more consistent with the mechanical nature of deep rock mass failure. High computational accuracy: The full-process energy calculation abandons the simplified modulus calculation based on the linear elastic assumption, and adopts the direct integration method of the stress-strain curve to obtain the total work and elastic energy in three dimensions. This processing method can accurately capture the nonlinear deformation characteristics and hysteresis effect of rock during loading and unloading, significantly improving the accuracy of energy component calculation; Accurate identification of fracture mechanisms: Acoustic emission (RA-AF) parameter correlation analysis technology is introduced to decompose the pre-peak dissipation energy and quantify the proportion of tensile cracks in the overall damage. By only considering the effective tensile fracture-forming energy, the ineffective dissipation caused by pre-peak plastic flow and interparticle friction slip is eliminated, thus achieving accurate characterization of the brittle fracture nature of rocks. Wide applicability: By using the initial hydrostatic elastic energy as the normalized benchmark for background elastic energy storage capacity, the magnitude interference of different occurrence depths and hydrostatic pressure conditions on the absolute energy value is eliminated. This index can uniformly evaluate the evolution law of rocks from shallow low hydrostatic pressure brittle fracture to deep high hydrostatic pressure brittle-ductile transition, and has good engineering universality; The energy decomposition is comprehensive, enabling true tracking of "triaxial stress" throughout the entire process: Traditional energy methods often only consider the work done by axial stress, neglecting the elastic energy stored and released by lateral stress during lateral deformation. This method strictly executes triaxial stress-strain curve integration throughout the entire process, including pre-peak loading, post-peak drop, post-peak unloading, and hydrostatic unloading, achieving independent decoupling and synchronous tracking of axial and lateral energy. This approach can truly reflect the anisotropic characteristics of rock energy storage and release under triaxial stress, and is particularly suitable for explaining the complex energy migration behavior of deep rock masses under true triaxial stress conditions. Background: Physical separation of hydrostatic elastic properties: This method creatively stores energy during the initial hydrostatic pressure loading and unloading phase. As an independent background energy term, it participates in the normalization and release calculation throughout the entire process, achieving a physical separation between the energy stored under hydrostatic pressure constraint (background energy imparted by hydrostatic pressure) and the energy stored under deviatoric stress loading (crack propagation driving energy caused by shear). This treatment effectively avoids the influence of hydrostatic pressure amplitude on the calculation basis of brittleness index, so that the brittleness evaluation results only reflect the fracture tendency of the rock material itself, without being directly affected by the selection of the experimental hydrostatic pressure magnitude; This method considers both pre-peak damage accumulation and post-peak failure processes, creating a comprehensive evaluation system. Compared to single-stage evaluation methods that rely solely on pre-peak stress-strain curve characteristics (such as Young's modulus and Poisson's ratio) or post-peak stress drop rates, this method integrates pre-peak effective fracture-forming energy (characterizing damage development efficiency) and post-peak net fracture-forming energy (characterizing macroscopic failure intensity) into the numerator, and establishes a correlation between these two factors and the total energy storage background of the rock through normalized denominators. This method achieves a continuous characterization of the entire chain of rock brittleness, from microcrack initiation and propagation to macroscopic instability, resulting in evaluation conclusions with greater geomechanical significance.

[0061] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0062] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for determining rock brittleness based on the triaxial integral of energy throughout the entire process and net energy release, characterized in that, The method for determining rock brittleness includes: The triaxial unloading curves of the rock sample during the initial hydrostatic pressure loading and unloading stage were obtained. The triaxial unloading curves during the initial hydrostatic pressure loading and unloading stage were integrated and accumulated to obtain the initial hydrostatic elastic strain energy density. The triaxial unloading curves include: axial unloading curve, first radial unloading curve and second radial unloading curve. The triaxial loading curve, triaxial unloading curve, and acoustic emission signal data of the rock sample during the N-stage cyclic loading and unloading process before the peak were obtained; N is the preset number of stages, the first N-1 stages of the cyclic loading and unloading process include the loading process and the unloading process, and the N-stage cyclic loading and unloading process includes the loading process; the triaxial loading curves include: axial loading curve, first radial loading curve, and second radial loading curve; the acoustic emission signal data include the rise time, peak amplitude, ring count, and duration of the acoustic emission signal in multiple acoustic emission events; By integrating and summing the three-dimensional loading and unloading curves during the N-stage cyclic loading and unloading process, the total net power accumulated before the peak is obtained. The elastic strain energy density of the first N-1 stage cyclic loading and unloading process is obtained by integrating and summing the triaxial unloading curves. Regression analysis was performed on the axial stress and elastic strain energy density of the first N-1 stage cyclic loading and unloading process to establish the first fitting relationship. The peak value of the axial stress in the Nth stage cyclic loading and unloading process was substituted into the first fitting relationship to obtain the elastic strain energy density of the Nth stage cyclic loading and unloading process. The first fitting relationship is the fitting relationship between elastic strain energy density and axial stress in the axial cyclic loading and unloading stage before the peak. Based on acoustic emission signal data, cumulative net work before the peak, and elastic strain energy density of the Nth stage loading and unloading process, the effective crack-forming energy before the peak is determined. The triaxial stress-strain curves of the rock sample in the post-peak stage were obtained, and the triaxial stress-strain curves in the post-peak stage were integrated and accumulated to obtain the lateral expansion dissipation work. The triaxial stress-strain curves include: axial stress-strain curve, first radial stress-strain curve and second radial stress-strain curve. The triaxial unloading curves of the rock sample during the post-peak unloading stage were obtained, and the triaxial unloading curves during the post-peak unloading stage were integrated and accumulated to obtain the elastic strain energy density during the post-peak unloading stage. Regression analysis was performed on the elastic strain energy density during the post-peak unloading stage to establish a second fitting relationship. The axial stress valley point after the peak in the triaxial stress-strain curve was substituted into the second fitting relationship to obtain the elastic strain energy density at the axial stress valley point after the peak. The second fitting relationship is the fitting relationship between the elastic strain energy density and the axial stress during the post-peak unloading stage. The triaxial unloading curves of the rock sample during the hydrostatic unloading stage were obtained, and the residual hydrostatic elastic strain energy density was obtained by integrating and summing the triaxial unloading curves during the hydrostatic unloading stage. The difference between the initial hydrostatic elastic strain energy density and the residual hydrostatic elastic strain energy density is used to obtain the hydrostatic background elastic strain energy release. Based on the elastic strain energy density of the Nth cyclic loading and unloading process, the elastic strain energy density of the axial stress valley point after the peak, the elastic strain energy release in the still water background, and the lateral expansion dissipation work, the net crack-making energy density after the peak is determined. Based on the effective fracture energy before the peak, the net fracture energy density after the peak, the elastic strain energy density during the Nth stage loading and unloading process, and the initial hydrostatic elastic strain energy density, the normalized net energy release rate index of the rock sample is determined, thus completing the determination of the rock brittleness of the rock sample.

2. The method for determining rock brittleness based on the triaxial integral of energy throughout the entire process and net energy release as described in claim 1, characterized in that, The formula for calculating the initial hydrostatic elastic strain energy density is: ； in, This represents the initial hydrostatic elastic strain energy density. The axial strain at the unloading point during the initial hydrostatic pressure loading and unloading stage; The axial strain is the final unloading strain during the initial hydrostatic pressure loading and unloading phase. This is axial stress; For axial strain; The first radial strain at the unloading point during the initial hydrostatic pressure loading and unloading stage; The first radial strain at the unloading endpoint during the initial hydrostatic pressure loading and unloading stage; Lateral stress; The first radial strain; The second radial strain at the unloading initiation point during the initial hydrostatic pressure loading and unloading stage; The second radial strain is the endpoint of unloading during the initial hydrostatic pressure loading and unloading stage. This represents the second radial strain.

3. The method for determining rock brittleness based on the three-dimensional energy integral and net energy release throughout the entire process, as described in claim 2, is characterized in that... The formula for calculating the total net work accumulated before the peak is: ； in, Accumulate total net work before the peak; Let be the axial strain corresponding to the peak point of axial stress during the i-th stage of cyclic loading and unloading; The axial strain at the loading start point during the i-th stage of the loading and unloading cycle; The first radial strain is the point corresponding to the peak axial stress during the i-th stage of cyclic loading and unloading. The first radial strain at the loading starting point during the i-th stage of cyclic loading and unloading; The second radial strain is the point corresponding to the peak axial stress during the i-th stage of cyclic loading and unloading. The second radial strain is the loading initiation point during the i-th stage cyclic loading and unloading process; Let be the axial strain at the end of the unloading process during the i-th stage of the loading and unloading cycle; The first radial strain at the unloading endpoint during the i-th stage of the loading and unloading process; The second radial strain is the endpoint of the unloading process during the i-th stage of the loading and unloading cycle. The axial strain is the axial strain corresponding to the peak point of axial stress during the Nth stage of loading and unloading. The axial strain at the loading start point during the Nth stage of the loading and unloading cycle; The first radial strain corresponds to the peak point of axial stress during the Nth stage of loading and unloading process; The first radial strain at the loading initiation point during the Nth stage of cyclic loading and unloading; The second radial strain corresponds to the peak point of axial stress during the Nth stage of loading and unloading process. The second radial strain is the starting point of the loading process during the Nth stage of the loading and unloading cycle.

4. The method for determining rock brittleness based on the triaxial integral of energy throughout the entire process and net energy release according to claim 3, characterized in that, The formula for calculating the elastic strain energy density of the i-th stage of the loading and unloading process during the first N-1 stages of cyclic loading and unloading is: ； in, Let be the elastic strain energy density during the i-th stage cyclic loading and unloading process.

5. The method for determining rock brittleness based on the triaxial integral of energy throughout the entire process and net energy release according to claim 4, characterized in that, The formula for calculating the effective joint energy before the peak is: ； ； ； in, This provides effective seam creation energy before the peak; The coefficient representing the proportion of tensile cracks; The total energy dissipation density before the peak; The number of acoustic emission events judged as tensile cracks; This represents the total number of acoustic emission events in the acoustic emission signal data; The elastic strain energy density is the Nth stage loading and unloading process.

6. The method for determining rock brittleness based on the triaxial integral of energy throughout the entire process and net energy release as described in claim 5, characterized in that, The formula for calculating the work dissipated by lateral expansion is: ； in, This is for lateral expansion to dissipate work; This represents the axial strain corresponding to the axial stress valley point in the post-peak stage. This represents the axial strain corresponding to the peak point of axial stress in the post-peak stage. This represents the first radial strain corresponding to the bottom point of the axial stress valley after the peak in the post-peak stage. This represents the first radial strain corresponding to the peak point of axial stress in the post-peak stage. This represents the second radial strain corresponding to the bottom point of the axial stress valley after the peak in the post-peak stage. This represents the second radial strain corresponding to the peak point of axial stress in the post-peak stage.

7. The method for determining rock brittleness based on the triaxial integral of energy throughout the entire process and net energy release as described in claim 6, characterized in that, The formula for calculating the elastic strain energy density during the post-peak unloading stage is: ； in, This represents the elastic strain energy density during the post-peak unloading phase. This represents the axial strain corresponding to the unloading start point during the post-peak unloading stage. This represents the axial strain corresponding to the unloading endpoint during the post-peak unloading stage. This refers to the first radial strain corresponding to the unloading start point in the post-peak unloading stage. This refers to the first radial strain corresponding to the unloading endpoint in the post-peak unloading stage. This refers to the second radial strain corresponding to the unloading start point in the post-peak unloading stage. This represents the second radial strain corresponding to the unloading endpoint during the post-peak unloading phase.

8. The method for determining rock brittleness based on the triaxial integral of energy throughout the entire process and net energy release according to claim 7, characterized in that, The formula for calculating the residual hydrostatic elastic strain energy density is: ； in, The residual hydrostatic elastic strain energy density; This represents the axial strain corresponding to the unloading start point during the hydrostatic unloading stage. This represents the axial strain corresponding to the end point of the hydrostatic unloading stage. The first radial strain corresponds to the unloading start point during the hydrostatic unloading stage; This represents the first radial strain corresponding to the end point of the hydrostatic unloading stage. This represents the second radial strain corresponding to the unloading start point during the hydrostatic unloading stage. This represents the second radial strain corresponding to the unloading endpoint of the hydrostatic unloading stage.

9. The method for determining rock brittleness based on the triaxial integral of energy throughout the entire process and net energy release as described in claim 8, characterized in that, The formula for calculating the net joint energy density after the peak is: ； in, The net energy density of the fracture after the peak; The elastic strain energy density at the bottom of the axial stress valley after the peak; This represents the amount of elastic strain energy released in a still water background.

10. The method for determining rock brittleness based on the triaxial integral of energy throughout the entire process and net energy release according to claim 9, characterized in that, The formula for calculating the normalized net energy release rate index is: ； in, It is the normalized net energy release rate index.

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