Method for calculating rock burst critical stress based on tensile-shear composite fracture weighted fusion

Abstract

This invention provides a method for calculating the critical stress of rockburst based on a weighted fusion of tension-shear composite fracture, relating to the field of rockburst prevention and control technology. The method first simplifies the stress-strain relationship of coal-rock mass into a bilinear constitutive relationship, establishing a bilinear elastic damage constitutive model of coal-rock mass and corresponding three-dimensional damage evolution equations. Then, based on a circular roadway, a dual-zone rockburst mechanical model is constructed. Next, the basic equations of the circular roadway rockburst mechanical model are constructed, further determining the deformation system equations under two ideal assumptions: tension fracture only and shear fracture only. Finally, based on the deformation system equations under these two ideal assumptions, the critical stress for rockburst is determined. This method overcomes the biases that may arise from a single fracture assumption and can more effectively predict the rockburst risk in deep coal mines.

Description

Technical Field

[0001] This invention relates to the field of rockburst prevention and control technology in mining, and in particular to a method for calculating the critical stress of rockburst based on the weighted fusion of tension-shear composite fracture. Background Technology

[0002] Rockbursts are violent dynamic destructive phenomena caused by the sudden release of elastic deformation energy accumulated in the surrounding rock of underground roadways or working faces in coal mines. They are characterized by their suddenness, destructiveness, and difficulty in prediction, and are recognized as a world-class engineering challenge in mining engineering and rock mechanics. With increasing mining depth, the number of mines prone to rockbursts is rising annually, the frequency of disasters is increasing, and the severity of damage is intensifying. This not only seriously threatens the lives of miners and mining efficiency but also leads to significant economic losses, posing a severe challenge to safe coal mine production.

[0003] In deep coal mines, tunnel excavation or face mining reduces the radial stress of the surrounding rock, promoting the tensile propagation of existing fractures. At this time, the coal and rock mass near the tunnel wall is under stress similar to the high axial stress observed in indoor uniaxial compression tests, making it prone to splitting failure primarily characterized by tensile fracturing. Therefore, under the combined influence of high ground stress and strong unloading, the failure mechanism of deep coal and rock masses may shift from the traditional shear-dominated fracture mode to a fracture pattern involving both tensile and shear fracturing. Furthermore, since the tensile strength of rock is much lower than its compressive strength, this shift in fracture mechanism may lead to premature rockbursts occurring at stress levels below conventional thresholds.

[0004] The critical stress for rockburst is a key indicator characterizing the likelihood of rockburst occurring in a roadway or working face after disturbance under specific geostress conditions. It is also an important foundation for rockburst stress prevention and prediction. This indicator refers to the far-field stress level corresponding to the occurrence of rockburst. By combining field monitoring results with the calculated critical stress value, the probability of rockburst occurrence can be determined, providing a quantitative basis for rockburst prevention design and the evaluation of the effectiveness of protective measures.

[0005] However, existing methods for calculating the critical stress of rockbursts mostly focus on the case of shear failure alone. For example, the methods proposed in Chinese patents CN117252019A and CN116498386A are both based on the shear failure mechanism of coal and rock masses. These methods are mainly applicable to shallow rockburst analysis because, under shallow conditions, even after excavation and unloading, the radial stress remains at a high level, allowing for approximate consideration of only shear failure. Currently, systematic research on the combined effects of tension and shear failure on rockbursts in deep mining is insufficient, making it difficult for existing methods to effectively predict the occurrence of rockbursts in deep coal mines. Therefore, establishing a new critical stress calculation method suitable for rockbursts in deep mining has become an important issue urgently needing to be addressed in the mining field. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a method for calculating the critical stress of rockburst based on the weighted fusion of tensile-shear composite fracture, which addresses the shortcomings of the prior art and enables the calculation of the critical stress of rockburst in deep mining.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by this invention is: a method for calculating the critical stress of rockburst based on the weighted fusion of tensile-shear composite fracture, comprising:

[0008] The stress-strain relationship of coal-rock mass is simplified to a bilinear constitutive relationship, and a bilinear elastic damage constitutive model of coal-rock mass is established, along with the corresponding three-dimensional damage evolution equation of coal-rock mass; the bilinear elastic damage constitutive model of coal-rock mass includes elastic constitutive equations and damage constitutive equations;

[0009] Based on circular tunnels, a dual-zone rock pressure model of "elastic zone - softened zone" is constructed;

[0010] The basic equations of the rock pressure model of a circular tunnel are constructed, and the deformation system equations are determined under two ideal assumptions: tensile fracturing and shear fracturing of the surrounding rock of the tunnel.

[0011] Based on the deformation system equations under two ideal assumptions—that only tensile fracturing and only shear fracturing occur in the surrounding rock of the tunnel—the critical stress for rockburst is determined.

[0012] Furthermore, the specific method for establishing the bilinear elastic damage constitutive model of coal and rock mass is as follows:

[0013] The typical uniaxial tensile and uniaxial compressive stress-strain curves of coal and rock mass are simplified into bilinear relationships. The mechanical behavior of coal and rock mass before peak strength is set as linear elasticity, described by the elastic modulus E, and the mechanical behavior after peak strength is set as linear strain softening, described by the softening modulus λ. The impact tendency index of coal and rock mass is K = λ / E. Therefore, elastic damage constitutive models of coal and rock mass under tensile and compressive states are established, as follows:

[0014] ;

[0015] ;

[0016] In the formula, Uniaxial compressive strength, Uniaxial tensile strength, This represents the limit value of elastic tensile strain. This represents the limit value of elastic compressive strain. This represents the tensile strain limit value. This represents the compressive strain limit value. For three-dimensional tensile strain, It represents three-dimensional compressive strain; where, and Represents the elastic constitutive equation. and Representative damage constitutive equation;

[0017] Furthermore, based on the bilinear elastic damage constitutive model of coal and rock mass, the corresponding three-dimensional damage evolution equation for coal and rock mass is established as follows:

[0018] ;

[0019] ;

[0020] in, For tensile damage variables, For shear damage variables, the damage variables evolve linearly and isotropically, where Indicates a state where there is no tensile damage. Indicates different degrees of tensile damage. This indicates complete tensile fracture; Indicates a state free from shear damage. Indicates different degrees of shear damage. This indicates complete shear failure.

[0021] Furthermore, the basic equations of the circular tunnel rock pressure model include the equilibrium differential equations, geometric equations, and constitutive equations of the coal and rock mass;

[0022] The equilibrium differential equation for the coal and rock mass is:

[0023] ;

[0024] The geometric equation is:

[0025] ;

[0026] In the formula, r is the radius of the surrounding rock of the tunnel; σ θ σ r These represent the tangential and radial stresses in the elastic zone of the borehole surrounding rock, respectively; ε r ε represents the radial strain of the surrounding rock in the tunnel. θ denoted as circumferential strain of the surrounding rock of the tunnel, and u as radial displacement of the surrounding rock of the tunnel.

[0027] The constitutive equations are the elastic constitutive equations and damage constitutive equations in the bilinear elastic damage constitutive model of coal and rock mass.

[0028] Furthermore, the specific method for determining the deformation system equations under the ideal assumption that only tensile fracturing occurs in the surrounding rock of the roadway is as follows:

[0029] Combining formulas , and and boundary conditions and R represents the radial stress at infinity, where the stress is obtained in the elastic region. and tangential stress The analytical solution is:

[0030] ;

[0031] In the formula, The radius of the softened zone is given under the ideal assumption that only tensile fracturing occurs in the surrounding rock of the tunnel. The stress at the boundary between the elastic zone and the softened zone under the ideal assumption that only tensile fracturing occurs in the surrounding rock of the tunnel;

[0032] At the boundary between the elastic zone and the softened zone, the initial damage... The Griffith strength criterion is shown in the following formula:

[0033] ;

[0034] The formula Substitution In the process, the stress at the boundary between the elastic zone and the softened zone is obtained under the ideal assumption that only tensile fracturing occurs in the surrounding rock of the tunnel. As shown in the formula below:

[0035] ;

[0036] According to damage mechanics, the Griffith strength criterion describing tensile damage to rocks is written as:

[0037] ;

[0038] Using the geometric equations of coal and rock mass and the continuity condition at the boundary between the elastic and softened zones, the three-dimensional damage evolution equation of coal and rock is rewritten as a function of the radius of the softened zone. Related functions:

[0039] ;

[0040] Formula and Substitute into the formula The equilibrium differential equation of the coal and rock mass is further obtained, as shown in the following formula:

[0041] ;

[0042] Combined with boundary conditions Furthermore, by applying the continuity condition at the boundary between the elastic and softened zones, the deformation system equations under the ideal assumption that only tensile fracturing occurs in the surrounding rock of the roadway are obtained, as shown below:

[0043] ;

[0044] In the formula, Let e ​​be an intermediate variable, and let e be the base of the natural logarithm.

[0045] Furthermore, the specific method for determining the deformation system equations under the ideal assumption that only shear fracture occurs in the surrounding rock of the roadway is as follows:

[0046] Combining formulas , and and boundary conditions and The radial stress in the elastic region is obtained. and tangential stress The analytical solution is:

[0047] ;

[0048] In the formula, ρ c The radius of the softened zone is given under the ideal assumption that only shear fracture occurs in the surrounding rock of the tunnel. The stress at the boundary between the elastic and softened zones under the ideal assumption that only shear fracture occurs in the surrounding rock of the tunnel;

[0049] At the boundary between the elastic zone and the softened zone, the initial damage D c The Mohr-Coulomb strength criterion with a value of 0 is shown in the following formula:

[0050] ;

[0051] In the formula, φ is an intermediate variable, representing the internal friction angle of the coal and rock mass;

[0052] The formula Substitution In the ideal assumption that the surrounding rock of the roadway only undergoes shear fracture, the stress at the boundary between the elastic zone and the softened zone is obtained, as shown in the following formula:

[0053] ;

[0054] According to damage mechanics, the Mohr-Coulomb strength criterion describing tensile damage to rocks is:

[0055] ;

[0056] Using the geometric equations of the coal and rock mass and the continuity condition at the boundary between the elastic and softened zones, the three-dimensional damage evolution equation of the coal and rock mass is rewritten as a function of the radius ρ of the softened zone. c Related functions:

[0057] ;

[0058] Formula and Substitute into the formula The equilibrium differential equation of the coal and rock mass is obtained as shown in the following formula:

[0059] ;

[0060] Combined with boundary conditions Radial stress in the softened zone for:

[0061] ;

[0062] Applying the continuity condition to the boundary between the elastic and softened zones, we obtain the deformation system equations under the ideal assumption that only shear fracture occurs in the surrounding rock of the roadway, as shown below:

[0063] .

[0064] Furthermore, based on the deformation system equations under two ideal assumptions—tensile fracturing and shear fracturing only—the specific method for determining the critical stress for rockburst is as follows:

[0065] For each formula and Using the criterion for the extreme point of instability in the disturbance response, the theoretical formulas for the critical stress of rockburst under two ideal conditions—tensile fracturing and shear fracturing—are derived, as follows:

[0066] ;

[0067] ;

[0068] In the formula, , These represent the critical stresses for rockburst under two ideal conditions: tensile fracturing and shear fracturing of the surrounding rock in the tunnel. ρ is an intermediate variable. tcr Let be the radius of the critical softening zone under the assumption that only tensile fracturing occurs in the surrounding rock, denoted as . ;ρ ccr Let be the radius of the critical softening zone under the assumption that only shear fracture occurs, denoted as Without considering the support stress p s Under both assumptions, the expression for the radius of the critical softening zone is the same;

[0069] Introducing the tensile and shear fracture weighting factor ω and , By weighting the critical stresses for rockbursts under two ideal conditions, the actual expression for the critical stress is obtained as follows:

[0070] .

[0071] The beneficial effects of adopting the above technical solution are as follows: The method for calculating the critical stress of impact ground pressure based on the weighted fusion of tension-shear composite failure provided by this invention considers both tensile failure and shear failure modes simultaneously, and introduces weighting factors (ω and ω). By employing weighted fusion, a method for calculating the critical stress of rockburst was established that better reflects the actual failure characteristics of deep coal and rock formations where tension and shear fracturing coexist. This method overcomes the biases that may arise from a single fracturing assumption, and can more effectively predict the risk of rockburst in deep coal mines, thus helping to improve mine safety and reduce the probability of disasters.

[0072] Furthermore, the method of this invention possesses excellent adaptability and can be adjusted according to the specific geological and mining conditions of different mining areas, making it suitable for predicting rockburst risks in various complex environments. This is mainly due to the clear quantitative relationship between the critical stress theoretical formula and factors such as coal and rock fracture modes, mechanical parameters, roadway dimensions, and support stress, allowing the critical stress value to dynamically change with actual mine conditions, thereby providing more reliable theoretical support for mine safety. Attached Figure Description

[0073] Figure 1 A flowchart of the method for calculating the critical stress of rockburst based on the weighted fusion of tension-shear composite fracture provided in an embodiment of the present invention;

[0074] Figure 2 A schematic diagram of the tensile and shear constitutive relations of coal and rock mass and their simplified model provided in the embodiments of the present invention;

[0075] Figure 3 The diagram below is a schematic diagram of the rockburst pressure model of a circular tunnel provided in an embodiment of the present invention, wherein (a) is a diagram of the rockburst pressure model of a dual-zone rockburst with "elasticity + softening" and (b) is a diagram of the distribution of stress components.

[0076] Figure 4 This is a schematic diagram of the envelope of the coal and rock mass strength criterion provided in an embodiment of the present invention;

[0077] Figure 5 This is a schematic diagram comparing the critical stress calculation method of the present invention with a traditional method, as provided in an embodiment of the present invention. Detailed Implementation

[0078] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0079] In this embodiment, the critical stress calculation method for rockburst based on the weighted fusion of tensile-shear composite fracture is as follows: Figure 1As shown, firstly, the stress-strain relationship of the coal-rock mass is simplified to a bilinear constitutive relationship, including linear elasticity and linear strain softening, establishing an elastic damage constitutive model for the coal-rock mass. Secondly, a mechanical model of rockburst in a circular roadway is established, which can be divided into an elastic zone and a softening zone. By neglecting gravity and considering the unit width along the roadway axis, the mechanical analysis problem of rockburst is simplified to an axisymmetric plane strain problem under hydrostatic pressure. Secondly, based on the boundary conditions and the continuity of the boundary stresses in the softening and elastic zones, the basic equations of the roadway rockburst mechanical model are determined. Then, based on the load-maximum instability criterion, the theoretical formula for the critical stress of rockburst under the ideal assumption of only tensile fracturing in the roadway surrounding rock is solved. Then, based on the load-maximum instability criterion, the theoretical formula for the critical stress of rockburst under the ideal assumption of only shear fracturing in the roadway surrounding rock is solved. Finally, the tensile and shear fracturing weighting factors ω are introduced. (satisfy By weighting the critical stress theoretical formulas obtained under the two ideal assumptions mentioned above, a final theoretical formula for the critical stress of rockburst in actual roadways is obtained. This method makes the prediction of rockburst in deep coal mining more mathematically grounded and more reliable.

[0080] The method specifically includes the following steps:

[0081] Step 1: Simplify the stress-strain relationship of coal and rock mass into a bilinear constitutive relationship, establish a bilinear elastic damage constitutive model of coal and rock mass, and establish the corresponding three-dimensional damage evolution equation of coal and rock mass;

[0082] The typical uniaxial tensile and uniaxial compressive stress-strain curves of coal and rock masses are simplified into bilinear relationships, such as... Figure 2 As shown. Rock mechanical parameters include uniaxial compressive strength σ. c Uniaxial tensile strength σ t The elastic modulus E, softening modulus λ, and impact susceptibility index K are used. Damage caused by microcracks before reaching the peak strength of the coal-rock mass is negligible; therefore, the mechanical behavior of the coal-rock mass before peak strength is set as linear elasticity, described by the elastic modulus E. The mechanical behavior after peak strength is set as linear strain softening, described by the softening modulus λ. The impact susceptibility index K = λ / E. Based on the above simplified bilinear relationship of the stress-strain curves, the elastic damage constitutive models of the coal-rock mass under tension and compression are established as follows:

[0083] ;

[0084] ;

[0085] In the formula, This represents the limit value of elastic tensile strain. This represents the limit value of elastic compressive strain. This represents the tensile strain limit value. This represents the compressive strain limit value. For three-dimensional tensile strain, It represents three-dimensional compressive strain. Among them, and Represents the elastic constitutive equation. and This represents the damage constitutive equation. Additionally, it should be noted that coal and rock masses undergo shear damage under compression.

[0086] Based on the above elastic damage constitutive model of coal and rock mass, the corresponding three-dimensional damage evolution equation of coal and rock mass is established as follows:

[0087] ;

[0088] ;

[0089] in, For tensile damage variables, For shear damage variables, the damage variables evolve linearly and isotropically, where Indicates a state where there is no tensile damage. Indicates different degrees of tensile damage. This indicates complete tensile fracture. Indicates a state free from shear damage. Indicates different degrees of shear damage. This indicates complete shear failure.

[0090] Step 2: Establish a dynamic model of the rockburst pressure in a circular tunnel;

[0091] Statistical data shows that both roadways and working faces are at risk of rockbursts, but roadways are particularly prone to such events. For ease of theoretical analysis, this invention uses a circular roadway as a basis to construct a dual-zone rockburst geological model consisting of an "elastic zone" and a "softening zone," as follows: Figure 3 As shown in the figure. In the figure, ρ is the radius of the softened zone, a is the radius of the tunnel, P is the far-field stress, and p... s For the support stress, neglecting the influence of gravity and taking a unit width along the roadway axis, the mechanical analysis problem of rockburst is further simplified into an axisymmetric plane strain problem under hydrostatic pressure. For non-circular roadways, an approximate solution can be obtained simply by introducing the corresponding shape correction coefficient into the rockburst mechanical analysis.

[0092] The circular tunnel rock pressure model is a classical mechanical model describing the elastic-plastic zonal deformation and failure of the surrounding rock after excavation in the original rock stress field. The core assumptions are: the tunnel is a circular cross-section with radius a, deeply buried in a homogeneous and isotropic rock mass with a far-field stress of P, and the far-field stress is a uniform hydrostatic pressure (i.e., the initial radial and tangential stresses are both P); after the tunnel is excavated, the surrounding rock forms two zones from the inside out due to stress redistribution: a softening zone (plastic / damaged zone) and an elastic zone. The radius of the interface between the two zones is ρ. The solution domain of the model can be regarded as an infinite domain problem with R→∞.

[0093] Figure 3 In the middle, the tunnel (excavation space) is a circular cavity with radius a. The tunnel wall can be subjected to support stress ps (ps=0 when there is no support), which is the boundary between stress release and surrounding rock deformation.

[0094] Softening zone (blue area, a≤r≤ρ): The surrounding rock area adjacent to the roadway wall. After excavation, the radial stress decreases and the tangential stress increases. The stress of the surrounding rock exceeds its yield strength, resulting in plastic yielding and strength deterioration (strain softening behavior). The surrounding rock loses its complete bearing capacity, mainly manifested as plastic flow, crack propagation and damage evolution. The stress no longer satisfies the linear elastic relationship, and the tangential stress first rises and then falls in this area.

[0095] Elastic zone (red area, r≥ρ): The surrounding rock area outside the softened zone. The stress level does not exceed the yield strength of the rock mass. The rock mass is still in the linear elastic deformation stage. The stress distribution conforms to the thick-walled cylinder theory of elastic mechanics. The radial stress gradually approaches the far-field stress P as the radius increases, and the tangential stress gradually decreases and approaches the far-field stress P as the radius increases. There is no plastic deformation or damage.

[0096] Step 3: Construct the basic equations of the rockburst mechanical model of a circular tunnel, and combine the Griffith strength criterion and the Mohr-Coulomb strength criterion to determine the deformation system equations under two ideal assumptions: tensile fracturing and shear fracturing of the surrounding rock of the tunnel.

[0097] Step 3.1: Construct the basic equations of the rock pressure model for a circular tunnel, including the equilibrium differential equations, geometric equations, and constitutive equations of the coal and rock mass;

[0098] Tensile and shear fracturing of the surrounding rock damage unit in a roadway can be described by the Griffith strength criterion and the Mohr-Coulomb strength criterion, respectively. The Griffith strength criterion provides the lower strength limit for fracturing in the coal-rock mass damage unit, while the Mohr-Coulomb strength criterion provides the upper strength limit, indicating that tensile fracturing occurs preferentially over shear fracturing. The Griffith and Mohr-Coulomb strength criteria together define the tensile-shear combined fracturing envelope of the coal-rock mass, as shown below. Figure 4 As shown.

[0099] The stress in the elastic zone needs to be solved by combining the equilibrium differential equations, geometric equations, and elastic constitutive equations of the coal and rock mass. The stress field in the softened zone is independent of the stress field in the elastic zone and is driven only by the roadway boundary loads, not by the far-field stress distribution. The stress in the softened zone can be solved by combining the equilibrium differential equations, geometric equations, damage constitutive equations, and strength criteria.

[0100] The equilibrium differential equation for coal and rock mass is:

[0101] ;

[0102] The geometric equation is:

[0103] ;

[0104] In the formula, r is the radius of the surrounding rock of the tunnel, and different values ​​of r represent different locations of the surrounding rock; σ θ σ r These represent the tangential and radial stresses in the elastic zone of the borehole surrounding rock, respectively; ε r For the radial strain of the surrounding rock of the tunnel, ε θ denoted as circumferential strain of the surrounding rock in the tunnel, and u as radial displacement of the surrounding rock in the tunnel.

[0105] The constitutive equations are the elastic constitutive equations and damage constitutive equations in the bilinear elastic damage constitutive model of coal and rock mass.

[0106] Step 3.2: Based on the basic equations of the circular tunnel rock pressure model and the Griffith strength criterion, determine the deformation system equations under the ideal assumption that the surrounding rock of the tunnel only undergoes tensile fracturing;

[0107] Combining formulas , and and boundary conditions and R represents the radial stress at infinity, where the stress is obtained in the elastic region. and tangential stress The analytical solution is:

[0108] ;

[0109] In the formula, The radius of the softened zone is given under the ideal assumption that only tensile fracturing occurs in the surrounding rock of the tunnel. This refers to the stress at the boundary between the elastic and softened zones under the ideal assumption that only tensile fracturing occurs in the surrounding rock of the tunnel.

[0110] At the boundary between the elastic zone and the softened zone ( ), initial damage The Griffith strength criterion is shown in the following formula:

[0111] ;

[0112] The formula Substitution In the process, the stress at the boundary between the elastic zone and the softened zone is obtained under the ideal assumption that only tensile fracturing occurs in the surrounding rock of the tunnel. As shown in the formula below:

[0113] ;

[0114] For the softened zone, all damage elements within it are assumed to exhibit tensile damage. According to damage mechanics, the Griffith strength criterion describing tensile damage in rock can be written as:

[0115] ;

[0116] Using the geometric equations of coal and rock masses and the boundary between the elastic and softened zones (r = ρ) t The continuity condition at point ) rewrites the three-dimensional damage evolution equation of coal and rock as a function of the radius of the softened zone. Related functions:

[0117] ;

[0118] Formula and Substitute into the formula The equilibrium differential equation of the coal and rock mass is further obtained, as shown in the following formula:

[0119] ;

[0120] Combined with boundary conditions And the boundary between the elastic region and the softened region (r = ρ) t Using the continuity condition at point (), that is, making the right side of equation (9) equal to the right side of equation (12), we obtain the deformation system equation under the ideal assumption that only tensile fracturing occurs in the surrounding rock of the roadway, as shown below:

[0121] ;

[0122] In the formula, Let e ​​be an intermediate variable, and let e be the base of the natural logarithm.

[0123] Step 3.3: Based on the basic equations of the circular tunnel rock pressure model and the Mohr-Coulomb strength criterion, determine the deformation system equations under the ideal assumption that the surrounding rock of the tunnel only undergoes shear fracture;

[0124] Combining formulas , and and boundary conditions and The radial stress in the elastic region is obtained. and tangential stress The analytical solution is:

[0125] ;

[0126] In the formula, ρ c The radius of the softened zone is given under the ideal assumption that only shear fracture occurs in the surrounding rock of the tunnel. P represents the stress at the boundary between the elastic and softened zones under the ideal assumption that only shear fracture occurs in the surrounding rock of the tunnel, and P is the far-field stress.

[0127] At the boundary between the elastic region and the softening region (r = ρ) c ), initial damage D c The Mohr-Coulomb strength criterion with a value of 0 is shown in the following formula:

[0128] ;

[0129] In the formula, φ is an intermediate variable, representing the internal friction angle of the coal and rock mass.

[0130] The formula Substitution In the ideal assumption that the surrounding rock of the roadway only undergoes shear fracture, the stress at the boundary between the elastic zone and the softened zone is obtained, as shown in the following formula:

[0131] ;

[0132] For the softened zone, all damage elements within it are assumed to exhibit shear damage. According to damage mechanics, the Mohr-Coulomb strength criterion describing tensile damage in rocks can be written as:

[0133] ;

[0134] Using the geometric equations of coal and rock masses and the boundary between the elastic and softened zones (r = ρ) c The continuity condition at point ) allows the three-dimensional damage evolution equation of coal and rock to be rewritten as a function of the radius ρ of the softened zone. c Related functions:

[0135] ;

[0136] Formula and Substitute into the formula The equilibrium differential equation of the coal and rock mass is obtained as shown in the following formula:

[0137] ;

[0138] Combined with boundary conditions Radial stress in the softened zone It can be written as:

[0139] ;

[0140] The boundary between the elastic region and the softened region (r = ρ) c Use the continuity condition at point ), that is, let the formula The right side of the equal sign and the formula With the right-hand side of the equation equal, we obtain the deformation system equation under the ideal assumption that only shear fracture occurs in the surrounding rock of the tunnel, as shown below:

[0141] ;

[0142] Step 4: Determine the critical stress for rockburst occurrence based on the deformation system equations under two ideal assumptions: tensile fracturing and shear fracturing in the surrounding rock of the tunnel.

[0143] For each formula and Using the disturbance response instability extreme point discrimination criterion The theoretical formulas for the critical stress of rockburst under two ideal conditions—tensile fracturing and shear fracturing—are derived as follows:

[0144] ;

[0145] ;

[0146] In the formula, , These represent the critical stresses for rockburst under two ideal conditions: tensile fracturing and shear fracturing of the surrounding rock in the tunnel. ρ is an intermediate variable. tcr Let be the radius of the critical softening zone under the assumption that only tensile fracturing occurs in the surrounding rock, denoted as . ;ρ ccr Let be the radius of the critical softening zone under the assumption that only shear fracture occurs, denoted as Without considering the support stress p s Under both assumptions, the expression for the radius of the critical softening zone is consistent.

[0147] Considering that tensile and shear fracturing actually coexist in deep coal and rock masses, the critical stress of rockburst should fall between the values ​​obtained from the two theoretical assumptions mentioned above. Therefore, a weighting factor ω for tensile and shear fracturing is introduced. (satisfy By weighting the critical stresses for rockbursts under two ideal conditions, the actual expression for the critical stress is obtained as follows:

[0148] ;

[0149] In the formula, the tension and shear fracture weighting factors ω and Based on indoor acoustic emission or on-site microseismic monitoring data, moment tensor inversion can be used to identify and calculate tensile and shear fractures.

[0150] like Figure 5 As shown, under a set of given parameters, by comparing the critical stress value of rockburst calculated by the traditional method with the critical stress value of rockburst calculated by the deep rockburst critical stress calculation method based on the coexistence of tension and shear fracture mechanism of this invention, it can be found that, under the same coal and rock rock impact tendency index, the rockburst stress threshold of deep coal seam roadways is lower than the traditional rockburst judgment index. Therefore, the influence of tension fracture on the critical stress of rockburst cannot be ignored.

[0151] This embodiment is based on the method for calculating the critical stress of deep rockburst based on the coexistence of tension and shear fracture mechanism of the present invention. The program is written in MATLAB to calculate the numerical solution of the critical stress of rockburst in deep mining of a certain coal mine.

[0152] In this embodiment, the burial depth of the No. 12 coal seam W1208 working face in this coal mine is approximately 1070 m, and the coal seam thickness is approximately 3.5 m - 4.6 m. Above the coal seam is a thick, hard mudstone roof with a thickness of 14 m. Currently, the average in-situ stress of the main coal seam group in this working face is 29.94 MPa. Based on indoor tests and field monitoring, the impact tendency index of the coal and rock mass in this working face is 0.58, the uniaxial compressive strength is 6.50 MPa, the uniaxial tensile strength is 0.81 MPa, the elastic modulus is 2.58 GPa, the internal friction angle of coal and rock is 30°, the support stress is 0.4 MPa, the roadway radius is 2.37 m, the tension fracture weight factor is 0.27, and the shear fracture weight factor is 0.73. Based on the above physical and mechanical parameters of the coal and rock, the formula is used... Calculations showed that the critical stress for rockburst in deep mining of this coal mine was 31.5 MPa, and the maximum allowable disturbance stress was 1.56 MPa. The maximum allowable disturbance stress was very small. During the mining process, the face reached the critical stress for rockburst, resulting in this particular rockburst event.

[0153] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the present invention.

Claims

1. A method for calculating the critical stress of rockburst based on weighted fusion of tension-shear composite fracture, characterized in that, include: The stress-strain relationship of coal-rock mass is simplified to a bilinear constitutive relationship, and a bilinear elastic damage constitutive model of coal-rock mass is established, along with the corresponding three-dimensional damage evolution equation of coal-rock mass; the bilinear elastic damage constitutive model of coal-rock mass includes elastic constitutive equations and damage constitutive equations; Based on circular tunnels, a dual-zone rock pressure model of "elastic zone - softened zone" is constructed; The basic equations of the rock pressure model of a circular tunnel are constructed, and the deformation system equations are determined under two ideal assumptions: tensile fracturing and shear fracturing of the surrounding rock of the tunnel. Based on the deformation system equations under two ideal assumptions—that only tensile fracturing and only shear fracturing occur in the surrounding rock of the tunnel—the critical stress for rockburst is determined.

2. The method for calculating the critical stress of rockburst based on weighted fusion of tensile-shear composite fracture according to claim 1, characterized in that, The specific method for establishing the bilinear elastic damage constitutive model of coal and rock mass is as follows: The typical uniaxial tensile and uniaxial compressive stress-strain curves of coal and rock mass are simplified into bilinear relationships. The mechanical behavior of coal and rock mass before peak strength is set as linear elasticity, described by the elastic modulus E, and the mechanical behavior after peak strength is set as linear strain softening, described by the softening modulus λ. The impact tendency index of coal and rock mass is K = λ / E. Therefore, elastic damage constitutive models of coal and rock mass under tensile and compressive states are established, as follows: ； ； In the formula, Uniaxial compressive strength, Uniaxial tensile strength, This represents the limit value of elastic tensile strain. This represents the limit value of elastic compressive strain. This represents the tensile strain limit value. This represents the compressive strain limit value. For three-dimensional tensile strain, It represents three-dimensional compressive strain; where, and Represents the elastic constitutive equation. and Representative damage constitutive equation; Furthermore, based on the bilinear elastic damage constitutive model of coal and rock mass, the corresponding three-dimensional damage evolution equation for coal and rock mass is established as follows: ； ； in, For tensile damage variables, For shear damage variables, the damage variables evolve linearly and isotropically, where Indicates a state where there is no tensile damage. Indicates different degrees of tensile damage. This indicates complete tensile fracture; Indicates a state free from shear damage. Indicates different degrees of shear damage. This indicates complete shear failure.

3. The method for calculating the critical stress of rockburst based on weighted fusion of tensile-shear composite fracture according to claim 2, characterized in that, The basic equations of the circular tunnel rock pressure model include the equilibrium differential equations, geometric equations, and constitutive equations of the coal and rock mass. The equilibrium differential equation for the coal and rock mass is: ； The geometric equation is: ； In the formula, r is the radius of the surrounding rock of the tunnel; σ θ σ r These represent the tangential and radial stresses in the elastic zone of the borehole surrounding rock, respectively; ε r ε represents the radial strain of the surrounding rock in the tunnel. θ denoted as circumferential strain of the surrounding rock of the tunnel, and u as radial displacement of the surrounding rock of the tunnel. The constitutive equations are the elastic constitutive equations and damage constitutive equations in the bilinear elastic damage constitutive model of coal and rock mass.

4. The method for calculating the critical stress of rockburst based on weighted fusion of tensile-shear composite fracture according to claim 3, characterized in that, The specific method for determining the deformation system equations under the ideal assumption that only tensile fracturing occurs in the surrounding rock of the roadway is as follows: Combining formulas , and and boundary conditions and R represents the radial stress at infinity, where the stress is obtained in the elastic region. and tangential stress The analytical solution is: ； In the formula, The radius of the softened zone is given under the ideal assumption that only tensile fracturing occurs in the surrounding rock of the tunnel. The stress at the boundary between the elastic zone and the softened zone under the ideal assumption that only tensile fracturing occurs in the surrounding rock of the tunnel; At the boundary between the elastic zone and the softened zone, the initial damage... The Griffith strength criterion is shown in the following formula: ； The formula Substitution In the process, the stress at the boundary between the elastic zone and the softened zone is obtained under the ideal assumption that only tensile fracturing occurs in the surrounding rock of the tunnel. As shown in the formula below: ； According to damage mechanics, the Griffith strength criterion describing tensile damage to rocks is written as: ； Using the geometric equations of coal and rock mass and the continuity condition at the boundary between the elastic and softened zones, the three-dimensional damage evolution equation of coal and rock is rewritten as a function of the radius of the softened zone. Related functions: ； Formula and Substitute into the formula The equilibrium differential equation of the coal and rock mass is further obtained, as shown in the following formula: ； Combined with boundary conditions Furthermore, by applying the continuity condition at the boundary between the elastic and softened zones, the deformation system equations under the ideal assumption that only tensile fracturing occurs in the surrounding rock of the roadway are obtained, as shown below: ； In the formula, Let e ​​be an intermediate variable, and let e be the base of the natural logarithm.

5. The method for calculating the critical stress of rockburst based on weighted fusion of tensile-shear composite fracture according to claim 4, characterized in that, The specific method for determining the deformation system equations under the ideal assumption that only shear fracture occurs in the surrounding rock of the roadway is as follows: Combining formulas , and and boundary conditions and The radial stress in the elastic region is obtained. and tangential stress The analytical solution is: ； In the formula, ρ c The radius of the softened zone is given under the ideal assumption that only shear fracture occurs in the surrounding rock of the tunnel. The stress at the boundary between the elastic and softened zones under the ideal assumption that only shear fracture occurs in the surrounding rock of the tunnel; At the boundary between the elastic zone and the softened zone, the initial damage D c The Mohr-Coulomb strength criterion with a value of 0 is shown in the following formula: ； In the formula, φ is an intermediate variable, representing the internal friction angle of the coal and rock mass; The formula Substitution In the ideal assumption that the surrounding rock of the roadway only undergoes shear fracture, the stress at the boundary between the elastic zone and the softened zone is obtained, as shown in the following formula: ； According to damage mechanics, the Mohr-Coulomb strength criterion describing tensile damage to rocks is: ； Using the geometric equations of the coal and rock mass and the continuity condition at the boundary between the elastic and softened zones, the three-dimensional damage evolution equation of the coal and rock mass is rewritten as a function of the radius ρ of the softened zone. c Related functions: ； Formula and Substitute into the formula The equilibrium differential equation of the coal and rock mass is obtained as shown in the following formula: ； Combined with boundary conditions Radial stress in the softened zone for: ； Applying the continuity condition to the boundary between the elastic and softened zones, we obtain the deformation system equations under the ideal assumption that only shear fracture occurs in the surrounding rock of the roadway, as shown below: 。 6. The method for calculating the critical stress of rockburst based on weighted fusion of tensile-shear composite fracture according to claim 5, characterized in that, Based on the deformation system equations under two ideal assumptions—tensile fracturing and shear fracturing only—the specific method for determining the critical stress for rockburst is as follows: For each formula and Using the criterion for the extreme point of instability in the disturbance response, the theoretical formulas for the critical stress of rockburst under two ideal conditions—tensile fracturing and shear fracturing—are derived, as follows: ； ； In the formula, , These represent the critical stresses for rockburst under two ideal conditions: tensile fracturing and shear fracturing of the surrounding rock in the tunnel. ρ is an intermediate variable. tcr Let be the radius of the critical softening zone under the assumption that only tensile fracturing occurs in the surrounding rock, denoted as . ;ρ ccr Let be the radius of the critical softening zone under the assumption that only shear fracture occurs, denoted as Without considering the support stress p s Under both assumptions, the expression for the radius of the critical softening zone is the same; Introducing the tensile and shear fracture weighting factor ω and , By weighting the critical stresses for rockbursts under two ideal conditions, the actual expression for the critical stress is obtained as follows: 。

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