Calculation Method for Critical Conditions of Rockburst in Rectangular Roadways Based on Energy Criterion

Abstract

The calculation method for the critical conditions of rockburst in rectangular roadways based on the energy criterion includes the following steps: (1) simplifying the stress-strain relationship of coal and rock mass into a bilinear constitutive relationship and establishing a mechanical model for rockburst in rectangular roadways; (2) solving the parameters of the basic equations of the mechanical model for rockburst based on the deflection and stress continuity of the roof at the boundaries of the goaf, plastic softening zone, and elastic bearing zone; (3) solving the critical plastic zone length and critical load based on the stability energy criterion; (4) deriving the deformation energy accumulated in the elastic zone under the critical state based on the critical plastic zone length, and then predicting the magnitude; (5) identifying the risks caused by the mining depth based on the critical load under the critical state. The calculation method provided by this invention is more in line with engineering practice, and the solution result has smaller error. It can solve for the critical load of rockburst in roadways, as well as the critical plastic zone length, critical elastic deformation energy, critical mining depth, and safety factor.

Description

Technical Field

[0001] This invention belongs to the field of coal mine dynamic disaster prevention and control technology, specifically involving a method for calculating the critical conditions of rockburst in rectangular roadways based on energy criteria. Background Technology

[0002] In recent years, as coal mining has progressed to deeper levels, the conditions faced in mining have become increasingly complex, leading to a rise in the frequency and destructiveness of rockbursts. Quantitative research into the critical conditions for rockburst occurrence is fundamental and a prerequisite for rockburst prevention and control and ensuring safe coal mining.

[0003] Critical conditions for rockbursts include critical load and critical plastic zone length. Critical load refers to the overburden load borne by the surrounding rock above the coal seam during a rockburst. Critical plastic zone length refers to the length of the plastic zone within the coal seam during a rockburst. Combining field monitoring data with the critical plastic zone length and critical load, a preliminary prediction of whether a rockburst will occur can be made. The critical plastic zone length can also be used to calculate the deformation energy accumulated in the elastic zone, thereby estimating the magnitude of the rockburst; the critical load can be used to obtain the critical mining depth and safety factor of the mine, enabling mine safety assessment. Therefore, the calculation of critical conditions for roadway rockbursts has significant practical implications for assessing mine safety and predicting rockburst magnitudes. Studying the critical conditions for rockburst occurrence can lay the foundation for quantitative research on the mechanism and application of coal mine rockbursts. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a method for calculating the critical conditions for rockburst in rectangular roadways based on energy criteria. This method is scientifically sound, produces highly accurate data, and provides theoretical support for the safety of coal mining.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: a method for calculating the critical conditions of rockburst in rectangular tunnels based on energy criteria, comprising the following steps:

[0006] (1) The stress-strain relationship of coal and rock mass is simplified into a bilinear constitutive relationship, and a mechanical model of rockburst generation in rectangular roadways is established.

[0007] (2) Based on the continuity of the deflection and stress of the roof at the boundaries of the goaf, the plastic softening zone and the elastic bearing zone, the parameters of the basic equation of the mechanical model for rockburst generation are solved.

[0008] (3) Solve for the critical plastic zone length and critical load according to the stability energy criterion;

[0009] (4) The deformation energy accumulated in the elastic region under the critical state is derived from the length of the critical plastic region, and then the magnitude is predicted.

[0010] (5) Identify the risks arising from the mining depth based on the critical load under critical conditions.

[0011] Furthermore, the specific process of step (1) is as follows:

[0012] The area adjacent to the roadway in the coal seam is a plastic softening zone, and the governing equation is:

[0013]

[0014]

[0015] The deep coal seam is an elastic bearing zone, and the governing equation is:

[0016] σ x =v'σ z (4)

[0017]

[0018] In equations (1)-(6), h is the coal seam thickness, H is the roof thickness, K is the roof equivalent shear modulus, p is the supporting force of the coal seam on the roof strata, and q is the overburden load. w is the top plate deflection, λ is the softening modulus, and σ is the top plate deflection. x σ z Let f be the stress in the x and z directions, f be the interlaminar friction coefficient in the plastic zone, and σ be the stress in the x and z directions. c denoted as uniaxial compressive strength of the coal, E as elastic modulus, and v as Poisson's ratio;

[0019] The basic formulas for the simplified model are as follows:

[0020]

[0021] In the formula,

[0022] The basic formulas for the elastic bearing zone are:

[0023]

[0024] In the formula, These are all intermediate parameters and have no practical significance. Let Z be the elastic strain in the z-direction. It is the internal friction angle.

[0025] Furthermore, the specific process of step (2) is as follows:

[0026] At x = ∞, we have

[0027] At x = a, we have

[0028] At x = l, we have

[0029] a is 1 / 2 roadway width, l is the boundary between the plastic softening zone and the elastic bearing zone, and P is the support resistance;

[0030] The solution yields:

[0031]

[0032] In equations (15)-(18),

[0033]

[0034] A4=-(σ c +mP),

[0035]

[0036] In the formula, A1-A4 and B1-B4 are intermediate parameters and have no practical significance.

[0037] Furthermore, the specific process of step (3) is as follows:

[0038] Suppose that the coal-rock deformation system, under the action of surface force S and body force F, produces displacement u, stress σ, strain ε, and the size of the plastic softening zone V. s The remaining elastic region is V. e Suppose that under a certain equilibrium state, a small virtual displacement Δu is applied to the coal and rock mass, generating virtual stress Δσ and virtual strain Δε. If the virtual work done by the external force is greater than the increase in internal energy of the strain, then the coal and rock deformation system is unstable, i.e., the condition for rockburst is:

[0039]

[0040] The simplified critical condition for rockburst in a rectangular tunnel is as follows:

[0041]

[0042] In the formula,

[0043]

[0044] Solving equation (20) yields the critical plastic zone length l for rockburst in a rectangular tunnel. cr (l cr =la); when the length of the plastic zone of the coal seam reaches l cr A rockburst occurred;

[0045] Based on the vertical load continuity condition at the boundary between the elastic bearing zone and the plastic softening zone, we have: Then we have:

[0046]

[0047] The relationship between the overburden load q and the plastic zone length l is obtained by conversion:

[0048]

[0049] In the formula,

[0050]

[0051] Let l = l cr Substituting into equation (22), we obtain the critical load q for rockburst. cr When the overburden load reaches the critical load q cr At that time, a rockburst occurred.

[0052] Furthermore, the specific derivation process of step (4) is as follows:

[0053] The deformation of the elastic zone of the coal seam after tunnel excavation is divided into deformation caused by the original stress before excavation and deformation caused by excavation:

[0054] ε e =ε e '+ε e " (twenty three)

[0055] In the formula, ε e ε represents the strain induced by the original stress before excavation. e "Strain caused by excavation;"

[0056] If we approximate the deformation at the point l = ∞ in the coal seam as the deformation of the coal body caused by the original stress before excavation, then we have:

[0057]

[0058] The coal body strain caused by tunnel excavation is as follows:

[0059]

[0060] The strain energy in the elastic zone of the coal seam caused by tunnel excavation is:

[0061]

[0062] The result of the transformation is:

[0063]

[0064] Let l = l cr Substituting into equation (29), we obtain the deformation energy W accumulated in the elastic region under the critical state of rockburst. cr .

[0065] Furthermore, the specific process of step (5) is as follows:

[0066] Field monitoring indicates that each mine has a critical mining depth at which rockbursts occur; neglecting tectonic effects, assuming the unit weight of the overlying strata is γ, then under critical conditions, there is a critical load q. cr With critical mining depth H cr Relationship:

[0067]

[0068] In equation (30), g is the acceleration due to gravity; in addition, the critical load q for the roadway to experience rockburst is... cr The ratio of the stress to the actual overburden load q is defined as the stress safety factor S, which is used to evaluate the safety of the mine.

[0069]

[0070] The smaller the stress safety factor, the lower the safety level of the roadway and the higher the probability of rockburst. Conversely, the greater the critical stress of the roadway, the greater the safety factor, which means that the roadway is less likely to experience rockburst.

[0071] By adopting the above technical solution, the present invention has the following beneficial effects:

[0072] This invention substitutes the mechanical parameters of coal and rock mass, geometric parameters such as roadway dimensions, and support conditions obtained from field exploration into the mechanical model of rockburst generation in a rectangular roadway established by this invention. Using stability criteria, a system of equations is solved to obtain the critical rockburst load and critical plastic zone length of a certain mine roadway. Based on the subsequent calculation formulas of this invention, the critical elastic deformation energy, critical mining depth, and safety factor can also be further calculated.

[0073] Traditional methods for determining the critical conditions for rockbursts are mostly based on circular tunnel mechanical models. However, in actual engineering, tunnel cross-sections are predominantly rectangular, and the circular tunnel mechanical model is a simplified, idealized model. Furthermore, most solution methods rely on loads, resulting in relatively simplified formulas. Therefore, the calculation method provided in this invention is more aligned with engineering realities, leading to smaller errors in the solution results. Attached Figure Description

[0074] Figure 1 Schematic diagram of the mechanical model of rockburst generation in a rectangular tunnel.

[0075] Figure 2 Schematic diagram of the 3-1501 working face and roadway cross-section of Hongqinghe Coal Mine.

[0076] Figure 3Schematic diagram of the cross-section of the 3308 working face and roadway of Yangcheng Coal Mine.

[0077] Figure 4 Schematic diagram of the 1204 working face and roadway cross-section of Hongyang No. 3 Mine. Detailed Implementation

[0078] The method for calculating the critical conditions for rockburst in rectangular roadways based on the energy criterion includes the following steps:

[0079] (1) The stress-strain relationship of coal and rock mass is simplified into a bilinear constitutive relationship, and a mechanical model of rockburst generation in rectangular roadways is established.

[0080] (2) Based on the continuity of the deflection and stress of the roof at the boundaries of the goaf, the plastic softening zone and the elastic bearing zone, the parameters of the basic equation of the mechanical model for rockburst generation are solved.

[0081] (3) Solve for the critical plastic zone length and critical load according to the stability energy criterion;

[0082] (4) The deformation energy accumulated in the elastic region under the critical state is derived from the length of the critical plastic region, and then the magnitude is predicted.

[0083] (5) Identify the risks arising from the mining depth based on the critical load under critical conditions.

[0084] Furthermore, the specific process of step (1) is as follows:

[0085] The area adjacent to the roadway in the coal seam is a plastic softening zone, and the governing equation is:

[0086]

[0087] The deep coal seam is an elastic bearing zone, and the governing equation is:

[0088] σ x =v'σ z (4)

[0089]

[0090] In equations (1)-(6), h is the coal seam thickness, H is the roof thickness, K is the roof equivalent shear modulus, p is the supporting force of the coal seam on the roof strata, and q is the overburden load. w is the top plate deflection, λ is the softening modulus, and σ is the top plate deflection. x σ z Let f be the stress in the x and z directions, f be the interlaminar friction coefficient in the plastic zone, and σ be the stress in the x and z directions. c denoted as uniaxial compressive strength of the coal, E as elastic modulus, and v as Poisson's ratio;

[0091] The basic formulas for the simplified model are as follows:

[0092]

[0093] In the formula,

[0094] The basic formulas for the elastic bearing zone are:

[0095]

[0096] In the formula, These are all intermediate parameters and have no practical significance. Let Z be the elastic strain in the z-direction. It is the internal friction angle.

[0097] Furthermore, the specific process of step (2) is as follows:

[0098] At x = ∞, we have

[0099] At x = a, we have

[0100] At x = l, we have

[0101] a is 1 / 2 roadway width, l is the boundary between the plastic softening zone and the elastic bearing zone, and P is the support resistance;

[0102] The solution yields:

[0103]

[0104] In equations (15)-(18),

[0105]

[0106] A4=-(σ c +mP),

[0107]

[0108] In the formula, A1-A4 and B1-B4 are intermediate parameters and have no practical significance.

[0109] Furthermore, the specific process of step (3) is as follows:

[0110] Suppose that the coal-rock deformation system, under the action of surface force S and body force F, produces displacement u, stress σ, strain ε, and the size of the plastic softening zone V. s The remaining elastic region is V. eSuppose that under a certain equilibrium state, a small virtual displacement Δu is applied to the coal and rock mass, generating virtual stress Δσ and virtual strain Δε. If the virtual work done by the external force is greater than the increase in internal energy of the strain, then the coal and rock deformation system is unstable, i.e., the condition for rockburst is:

[0111]

[0112] The simplified critical condition for rockburst in a rectangular tunnel is as follows:

[0113]

[0114] In the formula,

[0115]

[0116] Solving equation (20) yields the critical plastic zone length l for rockburst in a rectangular tunnel. cr (l cr =la); when the length of the plastic zone of the coal seam reaches l cr A rockburst occurred;

[0117] Based on the vertical load continuity condition at the boundary between the elastic bearing zone and the plastic softening zone, we have: Then we have:

[0118]

[0119] The relationship between the overburden load q and the plastic zone length l is obtained by conversion:

[0120]

[0121] In the formula,

[0122]

[0123] Let l = l cr Substituting into equation (22), we obtain the critical load q for rockburst. cr When the overburden load reaches the critical load q cr At that time, a rockburst occurred.

[0124] Furthermore, the specific derivation process of step (4) is as follows:

[0125] The deformation of the elastic zone of the coal seam after tunnel excavation is divided into deformation caused by the original stress before excavation and deformation caused by excavation:

[0126] ε e =ε e '+ε e " (twenty three)

[0127] In the formula, ε eε represents the strain induced by the original stress before excavation. e "Strain caused by excavation;"

[0128] If we approximate the deformation at the point l = ∞ in the coal seam as the deformation of the coal body caused by the original stress before excavation, then we have:

[0129]

[0130] The coal body strain caused by tunnel excavation is as follows:

[0131]

[0132] The strain energy in the elastic zone of the coal seam caused by tunnel excavation is:

[0133]

[0134] The result of the transformation is:

[0135]

[0136] Let l = l cr Substituting into equation (29), we obtain the deformation energy W accumulated in the elastic region under the critical state of rockburst. cr .

[0137] Furthermore, the specific process of step (5) is as follows:

[0138] Field monitoring indicates that each mine has a critical mining depth at which rockbursts occur; neglecting tectonic effects, assuming the unit weight of the overlying strata is γ, then under critical conditions, there is a critical load q. cr With critical mining depth H cr Relationship:

[0139]

[0140] In equation (30), g is the acceleration due to gravity; in addition, the critical load q for the roadway to experience rockburst is... cr The ratio of the stress to the actual overburden load q is defined as the stress safety factor S, which is used to evaluate the safety of the mine.

[0141]

[0142] The smaller the stress safety factor, the lower the safety level of the roadway and the higher the probability of rockburst. Conversely, the greater the critical stress of the roadway, the greater the safety factor, which means that the roadway is less likely to experience rockburst.

[0143] The energy-based method for calculating the critical conditions for rockburst in rectangular roadways is applied in the following three coal mines:

[0144] Based on the method for solving the critical conditions of rockburst in rectangular tunnels described in this embodiment of the invention, a program was written to calculate the numerical solution. A schematic diagram of the mechanical model for rockburst in a rectangular tunnel is shown below. Figure 1 As shown.

[0145] Example Project 1: As Figure 2 As shown, the Hongqinghe Coal Mine is located in Inner Mongolia Autonomous Region, China. The main coal seam is 3-1, with an average burial depth of 718.60m and an average thickness of 6.23m. The overlying strata are mainly sandstone, while the floor consists of siltstone and sandy mudstone. Based on coal and rock impact tendency assessment, the coal seam, immediate roof, and floor strata all exhibit a weak impact tendency. The model parameters were determined using the auxiliary haulage roadway of the 3-1501 working face of the Hongqinghe Coal Mine. These parameters include: coal elastic modulus of 1.67 GPa, impact energy index of 7.73, Poisson's ratio of 0.29, internal friction angle of 30°, peak strength under uniaxial conditions of 24.27 MPa, roadway width of 5.8m, roadway height of 4.2m, and support strength of 0.4 MPa.

[0146] The solution yields a critical plastic zone length of 1.708m, a critical stress of 37.94MPa, a critical elastic energy of 3642300J, and a critical mining depth of 1517m for rockburst in the auxiliary haulage roadway of the 3-1501 working face of Hongqinghe Coal Mine.

[0147] Example Project 2: As Figure 3 As shown, Yangcheng Coal Mine is located in Shandong Province, China. The main coal seam is No. 3, with an average burial depth of 1200m and an average thickness of 7.5m. The roof consists of fine sandstone and siltstone, while the floor is mudstone. Based on coal and rock impact tendency assessment, both the coal seam and the roof and floor have a weak impact tendency. Parameters were determined using the track roadway of the 3308 working face of Yangcheng Coal Mine. These parameters include: coal elastic modulus of 0.93 GPa, impact energy index of 2.223, Poisson's ratio of 0.31, internal friction angle of 30°, peak strength under uniaxial conditions of 7.7 MPa, roadway width of 4.6m, height of 3.4m, and support strength of 0.4 MPa.

[0148] The solution yields the following critical plastic zone length for rockburst in the track roadway of the 3308 working face of Yangcheng Coal Mine: 2.816m; critical load: 29.372MPa; critical elastic energy: 7055500J; and critical mining depth: 1174m.

[0149] Example Project 3: As Figure 4As shown, Hongyang No. 3 Mine is located in Liaoning Province, China. Its main coal seam is Coal Seam No. 13, with an average burial depth of 850m and an average thickness of 2.6m. The roof consists of fine sandstone and mudstone, while the floor is siltstone. Based on coal and rock impact tendency assessment, both the coal seam and the roof and floor are weakly impact-prone. Parameters were determined using the return air roadway of the 1204 working face at Hongyang No. 3 Mine. These parameters include: coal elastic modulus of 0.89 GPa, impact energy index of 1.91, Poisson's ratio of 0.3, internal friction angle of 30°, peak strength under uniaxial conditions of 8.09 MPa, roadway width of 5.6m, height of 3.8m, and support strength of 0.2 MPa.

[0150] The solution yields the following critical plastic zone length for rockburst in the return air roadway of the 1204 working face of Hongyang No. 3 Mine: 0.911m; critical load: 32.431MPa; critical elastic deformation energy: 2228600J; and critical mining depth: 1300m.

[0151] This embodiment does not impose any limitation on the shape, material, structure, etc. of the present invention. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention shall fall within the protection scope of the technical solution of the present invention.

Claims

1. A method for calculating the critical condition of rock burst in rectangular roadway based on energy criterion, characterized in that: Comprising the following steps: (1) The stress-strain relationship of coal rock mass is simplified as a bilinear constitutive relation, and a mechanical model of rock burst in rectangular roadway is established; (2) According to the continuity of deflection and stress of the boundary roof of goaf, plastic softening zone and elastic bearing zone, the parameters of the basic equation of the mechanical model of rock burst are solved; (3) According to the stability energy criterion, the critical plastic zone length and critical load are solved; (4) According to the critical plastic zone length, the deformation energy accumulated in the elastic zone under the critical state is derived, and then the magnitude is predicted; (5) According to the critical load under the critical state, the risk caused by the mining depth of the mine is identified; The specific process of step (1) is: The coal seam near the roadway area is a plastic softening zone, and the control equation is: (1) (2) (3) The deep part of the coal seam is an elastic bearing zone, and the control equation is: (4) (5) (6) in formulas (1)-(6), h is a coal seam thickness, H is a roof thickness, K is an equivalent shear modulus of the roof, p is a support force of the coal seam to the roof stratum, q is an overburden load; ; ; w is a roof deflection, is a softening modulus, is a stress in the x, z direction, f is an interlayer friction coefficient of the plastic zone, is a uniaxial compressive strength of the coal body, E is an elastic modulus, v is a Poisson's ratio; The basic formula of the model is simplified, and the basic formula of the plastic softening zone is: (7) (8) (9) (10) In the formulae, , ; ; The basic formula of the elastic bearing zone is: (11) (12) (13) (14) wherein , ; , , , are intermediate variables without physical meaning; is the elastic strain in z direction, is the internal friction angle, is the plastic strain in z direction; The specific process of step (2) is: At place, there ; At x = 0.000101 a there is , ; At x = 0.000105 l there is , , ; a is 1 / 2 the roadway width, l is the boundary between the plastic zone of softening and the elastic zone of bearing, P is the support resistance, w e is the roof deflection of the elastic zone of bearing; w o is the roof deflection of the roadway zone, w p is the roof deflection of the plastic zone of softening; The solution is: (15) (16) (17) (18) In formula (15)-(18), , , , , , , , ； wherein , , , , , - are intermediate variables without physical meaning;​ The specific process of step (3) is: Let coal and rock deformation system under the action of surface force S and body force F , the displacement is u , the stress is σ , the strain is ε , and the size of the plastic softening zone is V s , and the size of the remaining elastic zone is V e ; let a small virtual displacement Δu be applied to the coal and rock body in a certain equilibrium state, resulting in a virtual stress Δσ , a virtual strain Δε , and Γ be the action area of surface force S. If the virtual work done by external force is greater than the increase of strain internal energy, the coal and rock deformation system is unstable, that is, the occurrence condition of rock burst is: (19) The critical condition of rock burst in rectangular roadway is simplified: (20) In the formula, ， ， ； Solving equation (20), the critical length of plastic zone of rectangular roadway is obtained l cr ( l cr = l-a );When the length of plastic zone reaches l cr , rock burst occurs According to the continuous condition of the vertical load at the junction of the elastic bearing area and the plastic softening area, there are then there are: (21) The conversion results in an overburden load q with the plastic zone length l relationship: (22) In the formula, ， ； Substituting equation (22) into equation (21) gives the critical load for rockburst occurrence l=l cr q cr ; rockburst occurs when the overburden load reaches the critical load q cr ;​ The specific derivation process of step (4) is: The deformation of the elastic zone of the coal seam after the excavation of the roadway is divided into the deformation caused by the original stress before the excavation and the deformation caused by the excavation: (23) wherein is the strain induced by the original stress before excavation, is the strain induced by the excavation; The coal seam The deformation at the coal seam is approximately the deformation of the coal body caused by the original stress before excavation, so that (24) (25) Then the coal body strain caused by the excavation of the roadway is: (26) (27) Then the strain energy of the coal seam elastic zone caused by the excavation of the roadway is: (28) The transformation is obtained: (29) Will l=l cr Substituting into equation (29), we obtain the deformation energy accumulated in the elastic region under the critical state of rockburst. W cr ; The specific process of step (5) is: Field monitoring shows that each mine has its critical mining depth of rock burst; without considering the tectonic effect, assuming the overburden rock density of coal seam is γ, there is a critical load q cr relationship with the critical mining depth H cr : (30) In formula (30), g is the acceleration of gravity; in addition, the critical load of the roadway when the rock burst occurs is defined as q cr The ratio of the actual overburden load q to the critical load is defined as the stress safety factor S , and the mine safety is evaluated: (31) The smaller the stress safety factor is, the lower the safety degree of the roadway is, and the probability of rock burst increases; on the contrary, the larger the critical stress of the roadway is, the larger the safety factor is, which means that the roadway is less likely to occur rock burst.

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