Distortion compensation method and system for coal and gas outburst physical simulation similarity criterion

Abstract

According to the distortion compensation method and system of the coal and gas outburst physical simulation similarity criterion, a gas-solid coupling control equation of coal and gas outburst physical simulation is selected, and a similarity ratio relational expression of key parameters is established; processing the similarity ratio relational expression to obtain a first similarity criterion; based on an effective stress theory and a thermodynamic theory, constructing a mechanical strength attenuation function of the porous medium material under the action of gas pressure; carrying out a mechanical test under different gas pressure conditions to measure material strength parameters of the prototype and the model; according to the material strength parameters, strength attenuation factors under different gas pressure conditions are calculated, and corresponding strength attenuation functions are obtained through fitting; combining the intensity attenuation function with a first similarity criterion, deducing to obtain a distortion compensation equation of the similarity criterion, and constructing a distortion compensation similarity criterion; and finally determining a distortion compensation value of each physical property parameter. According to the method, the correction and compensation of the physical simulation similarity relation under the action of the gas pressure can be realized, and the accuracy of the physical simulation result is improved.

Description

Technical Field

[0001] This invention relates to a distortion compensation method for simulating coal and gas outbursts, specifically a distortion compensation method and system for a similarity criterion in physical simulation of coal and gas outbursts, belonging to the field of gas-solid coupling engineering disaster similarity simulation technology. Background Technology

[0002] Coal and gas outbursts are a typical gas-solid coupled dynamic disaster, widely occurring in high-gas coal seams and deep coal mines. They are characterized by their suddenness and destructiveness, posing a serious threat to mine safety. Therefore, research on the mechanisms and prevention technologies of coal and gas outbursts is of great significance.

[0003] Coal and gas outbursts involve the coupling of multiple physical fields, including stress and gas fields. The disaster process is transient and unrepeatable, making it difficult to fully reveal its evolution mechanism solely through on-site monitoring or numerical simulation. Physical simulation experiments, capable of reproducing the disaster process under controllable conditions, have become an important tool for studying the mechanisms of coal and gas outbursts. To ensure the validity of physical simulation results, similarity criteria for stress, geometry, and gas pressure are typically established based on similarity theory. Existing physical simulation studies mostly derive similarity criteria based on classical similarity theory. However, under actual engineering conditions, gas pressure not only participates in effective stress regulation as pore pressure but also causes changes in the microstructure of the coal body through adsorption, desorption, and expansion, leading to a significant decrease in the mechanical strength of the coal with increasing gas pressure. Therefore, similarity criteria established based on the assumption of constant material parameters are difficult to meet strict similarity requirements under high gas pressure conditions.

[0004] Regarding the problem of coal strength degradation caused by gas pressure, no research has yet adjusted the similarity criteria through theoretical modeling. The original method is difficult to simultaneously characterize the strength evolution difference between the engineering prototype and the similar model under gas pressure, which limits the quantitative accuracy of the physical simulation results. Existing physical simulations of coal and gas outbursts do not fully consider the attenuation characteristics of coal mechanical strength under gas pressure, which leads to the failure of the similarity criteria under high gas pressure conditions. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a distortion compensation method and system for the similarity criterion of physical simulation of coal and gas outbursts, which can realize the correction and compensation of the similarity relationship of physical simulation under the action of gas pressure, and improve the accuracy and reliability of physical simulation results.

[0006] To achieve the above objectives, the present invention provides a distortion compensation method for a similarity criterion in physical simulation of coal and gas outbursts, comprising the following steps: Step 1: Select the gas-solid coupling control equation suitable for the physical simulation of coal and gas outbursts, determine the similarity ratio relationship of each physical quantity in the gas-solid coupling control equation, and establish the similarity ratio relationship of key parameters; Step Two: Based on The theorem is dimensionless to the similarity ratio relationship, and the first similarity criterion for physical simulation of coal and gas outburst is derived. Step 3: Based on the effective stress theory and thermodynamics theory, define the mechanical strength decay function of porous media materials under gas pressure. ,in Gas pressure, MPa; Atmospheric pressure, MPa; The strength of the material is expressed in MPa. Step 4: Conduct mechanical tests on the prototype coal sample and similar test model under different gas pressure conditions to measure the material strength parameters of the prototype coal sample and similar test model under gas pressure. Step 5: Based on the measured material strength parameters, calculate the strength attenuation factor under different gas pressure conditions, and perform function fitting on the strength attenuation factors of the prototype coal sample and the similar test model respectively to obtain the strength attenuation function of the prototype coal sample. Intensity decay function of similar experimental models ; Step Six: Apply the intensity decay function of the prototype coal sample Intensity decay function of similar experimental models Introducing the first similarity criterion from step two, we simultaneously derive the distortion compensation equation for the similarity criterion. And construct a similarity criterion for distortion compensation; Step 7: Based on the distortion compensation similarity criterion, determine the distortion compensation values ​​of each physical property parameter in the physical simulation of coal and gas outburst.

[0007] Preferably, step one is as follows: The gas-solid coupling control equations include: coal deformation control equations, damage and failure equations, and gas seepage control equations. Based on elastoplastic theory, the tensor expression of the equilibrium differential equations is as follows: In the formula, This is the tensor form of stress differential operations; It is the tensor form of the volume force components; Subscript The order of the second-order tensor; The tensor representation of geometric equations is as follows: In the formula, It is a second-order strain tensor; This is the tensor form for strain-displacement differential operations; The tensor expression of the constitutive relation of the elastic stage of coal-rock mass deformation is shown as: In the formula, Kronecker symbol; For stress tensor; Poisson's ratio; The elastic modulus is expressed in MPa. When considering the plastic state, the stress-strain relationship of gas-bearing coal can be obtained from the geometric relationship of the Mohr's circle: In the formula, Indicates the angle of internal friction, in °; Indicates uniaxial compressive strength, in MPa; and represents the minimum and maximum principal stresses, respectively, in MPa.

[0008] In outburst-prone coal seams, adsorbed gas diffuses through the pore system but does not transmit gas pressure, while free gas seeps through the fracture system and can transmit gas pressure. Assuming that the diffusion and seepage motions of adsorbed and free gas satisfy Fick's diffusion theorem and Darcy's seepage theorem, respectively, their respective second-order differential equations are expressed as: In the formula, Gas pressure, Pa; The diffusion time is in seconds. Let m be the coal seam diffusion coefficient. 2 / s; The gas content coefficient of the coal seam, m 3 / (m 3 ·Pa 1 / 2 ); The reference pressure (constant) for measuring gas content is generally taken as the atmospheric pressure under standard conditions, which is 101325 Pa. Let be the seepage time, in seconds; m is the permeability of the coal seam fracture system. 2 ; ρ is the gas dynamic viscosity, Pa·s.

[0009] Preferably, the first similarity criterion includes at least one of the stress similarity criterion, geometric similarity criterion, and gas pressure similarity criterion. The specific derivation process of the first similarity criterion is as follows: S21: Let the geometric similarity ratio be... The strain-displacement similarity ratio is The volume force similarity ratio is The stress similarity ratio is The strain similarity ratio is The similarity ratio of elastic modulus is The similarity ratio of the internal friction angle is The compressive strength similarity ratio is Then we can obtain: From the above formula, the following similarity criterion can be derived: Because of the similarity ratio of volume forces Similarity ratio to material density equal( ),parameter Since the number is dimensionless, the similarity ratio can be set to 1. The above similarity criteria can be further summarized as follows: S22: Diffusion and seepage are synchronous processes, so the time similarity ratio of the two processes is the same. The coal seam gas content coefficient β is related to the gas pressure. Functions: In the formula, W represents the gas content of the coal seam, m 3 / m 3 ; Let the dimensionless parameter coal seam gas content similarity ratio C W =1: From the above formula, it can be derived that Combining the above equations, we obtain the gas field similarity criterion: After conversion, the gas pressure similarity ratio can be obtained as follows: .

[0010] Preferably, the mechanical strength decay function of the porous medium material The function is monotonically decreasing, and the material strength under zero gas pressure conditions is used as the normalization benchmark. The specific derivation process of step three is as follows: Assume the gas intensity of the prototype coal sample is... The similar test model has a gas intensity of The gas pressure of the prototype coal sample was The gas pressure in the similar test model is Then the intensity function of the prototype coal sample can be expressed as: The strength function of the similar test model material is expressed as: .

[0011] Preferably, in step five, the function fitting employs any one of an exponential function, a linear function, or a power function: Exponential decay functions are applicable when gas adsorption is the dominant factor weakening the material's strength. Their expressions include, but are not limited to: The linear function type of attenuation function is applicable to the linear response of material strength under low pressure conditions, and its expression is: The power-law type decay function is applicable to the nonlinear response of material strength under high pressure conditions, and its expression is: In the formula, The gas attenuation coefficient is expressed in MPa⁻¹. This is the pressure sensitivity coefficient.

[0012] Preferably, the strength attenuation factor in step five is the ratio of the material's strength under a given gas pressure to its strength under zero gas pressure: .

[0013] Preferably, the distortion compensation equation in step six This is a ratio function of the intensity decay function of the prototype coal sample and the similar test model: The above formula describes the "similarity distortion" caused by the different coupling characteristics of materials and gas, which needs to be compensated for by adjusting material parameters to finally obtain the corrected effective strength similarity ratio. for: Preferably, the physical property parameters in step seven include at least one of elastic modulus, compressive strength, and cohesion: in, This is the distortion compensation value for the elastic modulus; This is the distortion compensation value for compressive strength; This is the distortion compensation value for cohesion.

[0014] This invention also provides a distortion compensation system for a similarity criterion in physical simulation of coal and gas outbursts, used for distortion compensation methods of the similarity criterion in physical simulation of coal and gas outbursts, comprising: (1) Physical testing device, which includes a gas pressure loading unit, a confining pressure loading unit and a mechanical parameter testing unit; (2) A calculation unit, connected to the physical test device, the distortion similarity criterion construction module, and the intensity attenuation modeling module respectively, is used for: a) Receive the material mechanical parameters under different gas pressure conditions obtained by the physical testing device; b) Calculate the strength attenuation factor of the material under different gas pressure conditions, and fit the strength attenuation function of the prototype coal sample respectively. Intensity decay function of similar experimental models And calculate the distortion compensation equation of the similarity criterion. ; c) Solve for the distortion compensation values ​​of each physical property parameter in the physical simulation of coal and gas outburst.

[0015] Compared with existing technologies, this invention, by selecting physical control equations applicable to coal and gas outbursts, can accurately characterize the core physical mechanism of outburst occurrence, avoid omitting key influencing factors during simulation, establish similarity ratios for key parameters, and based on... The theorem derives the similarity ratio relationship in a dimensionless manner, mapping the physical parameters of the prototype coal sample to the similar test coal sample model according to the similarity criterion. This ensures the consistency between the similar test coal sample model and the prototype coal sample in terms of physical laws, evolution trends, and dynamic responses. Through the dimensionless derivation, the influence of size effect on simulation results can be eliminated, allowing the experimental data of the similar test coal sample model to directly reflect the outburst laws of the prototype coal sample. This yields the first similarity criterion for the physical simulation of coal and gas outbursts, enabling a quantitative judgment on whether the model meets the similarity conditions and avoiding the subjectivity of empirical parameter selection in traditional simulations. Based on this, combining effective stress theory and thermodynamic theory, a strength attenuation function for porous media materials under gas pressure is constructed. This invention, by simultaneously incorporating the effective stress attenuation mechanism and the thermodynamic energy evolution mechanism, can accurately characterize the strength variation law in different gas pressure ranges. Simultaneously, the mechanical strength of prototype coal samples and similar experimental coal sample models under different gas pressure conditions is tested, and the strength attenuation factors of the prototype coal samples and similar experimental coal sample models under different gas pressure conditions are determined. These are then fitted to obtain the strength attenuation function of the prototype coal samples and the strength attenuation function of the similar experimental coal sample models. By comparing the evolution trends and parameter differences of the two types of functions, the rationality and similarity accuracy of the similar experimental coal sample models are verified, avoiding simulation distortion caused by model design deviations and improving the accuracy of the conversion from laboratory simulation to field engineering applications. Finally, the strength attenuation function of the prototype coal samples and the strength attenuation function of the similar experimental coal sample models are compared with the first similar... By combining the criteria, the distortion compensation equation of the similarity criterion is derived, which can solve the distortion problem of similarity experiments and improve the simulation accuracy. A distortion compensation similarity criterion is then constructed, and the distortion compensation values ​​of various physical property parameters in the physical simulation of coal and gas outbursts are determined accordingly. The distortion compensation similarity criterion allows for direct calculation of the distortion compensation values ​​of each physical property parameter, eliminating the need for extensive preliminary experiments to explore parameter correction schemes. This significantly reduces the difficulty of model material preparation and the precision requirements of experimental equipment, while also reducing the number of preliminary experiments and further controlling experimental costs. This invention addresses the problem that existing physical simulations of coal and gas outbursts do not fully consider the attenuation characteristics of coal mechanical strength under gas pressure, leading to the failure of similarity criteria under high gas pressure conditions. It proposes a distortion compensation method and system for the similarity criterion in physical simulation of coal and gas outbursts to correct and compensate for the similarity relationship in physical simulations under gas pressure, thereby improving the accuracy and reliability of the physical simulation results. Attached Figure Description

[0016] Figure 1 This is an overall flowchart of the present invention; Figure 2 This is a schematic diagram of the structure of a triaxial air-solid coupling mechanical loading device; Figure 3 It is the intensity decay function f of the prototype coal sample r The power function fitting curve of (p); Figure 4 It is the intensity decay function f of the similar test model m The power function fitting curve of (p); Figure 5 It is the ratio function of the three-dimensional decay function. picture. Detailed Implementation

[0017] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used by users of this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should be noted that the terminology used in this section is for the purpose of describing particular embodiments only and is not intended to limit the scope of protection according to the invention. The invention will now be further described in conjunction with the accompanying drawings.

[0018] Coal and gas outbursts are triggered by the coupling of multiple physical fields. The disaster process is transient and unrepeatable, and field monitoring and numerical simulation are insufficient to fully reveal its evolution mechanism. Therefore, physical simulation experiments under controllable conditions have become an important means of studying this mechanism. Existing studies are mostly based on classical similarity theory to derive similarity criteria such as stress, geometry, and gas pressure. However, gas pressure not only regulates effective stress through pore pressure, but also degrades the microstructure of coal and reduces mechanical strength through adsorption, desorption, and expansion. Similarity criteria based on constant material parameters cannot meet the strict similarity requirements under high gas pressure conditions. Currently, there is no research on adjusting similarity criteria through theoretical modeling to characterize the difference in strength evolution between the prototype and the model. The quantitative accuracy of physical simulation is limited. Therefore, it is necessary to calculate the error caused by the first similarity criterion for physical processes that cannot be effectively scaled down, and adjust it by introducing correction coefficients. like Figure 1 As shown, this invention provides a distortion compensation method for a similarity criterion in physical simulation of coal and gas outbursts, comprising the following steps: Step 1: Select the gas-solid coupling control equation suitable for the physical simulation of coal and gas outbursts, determine the similarity ratio relationship of each physical quantity in the gas-solid coupling control equation, and establish the similarity ratio relationship of key parameters; The gas-solid coupling control equations of this invention include: coal deformation control equations, damage and failure equations, and gas seepage control equations. Based on elastoplastic theory, the tensor expression of the equilibrium differential equations is as follows: In the formula, This is the tensor form of stress differential operations; It is the tensor form of the volume force components; Subscript The order of the second-order tensor; The tensor representation of geometric equations is as follows: In the formula, It is a second-order strain tensor; This is the tensor form for strain-displacement differential operations; The tensor expression of the constitutive relation of the elastic stage of coal-rock mass deformation is shown as: In the formula, Kronecker symbol; For stress tensor; Poisson's ratio; The elastic modulus is expressed in MPa. When considering the plastic state, the stress-strain relationship of gas-bearing coal is very complex. This paper uses the commonly used Mohr-Coulomb yield criterion to characterize this process. From the geometric relationship of the Mohr circle, we can obtain: In the formula, Indicates the angle of internal friction, in °; Indicates uniaxial compressive strength, in MPa; and represents the minimum and maximum principal stresses, respectively, in MPa.

[0019] In outburst-prone coal seams, adsorbed gas diffuses through the pore system but does not transmit gas pressure, while free gas seeps through the fracture system and can transmit gas pressure. Assuming that the diffusion and seepage motions of adsorbed and free gas satisfy Fick's diffusion theorem and Darcy's seepage theorem, respectively, their respective second-order differential equations are expressed as: In the formula, Gas pressure, Pa; The diffusion time is in seconds. Let m be the coal seam diffusion coefficient. 2 / s; The gas content coefficient of the coal seam, m 3 / (m 3 ·Pa 1 / 2 ); The reference pressure (constant) for measuring gas content is generally taken as the atmospheric pressure under standard conditions, which is 101325 Pa. Let be the seepage time, in seconds; m is the permeability of the coal seam fracture system. 2 ; ρ is the gas dynamic viscosity, Pa·s.

[0020] Step Two: Based on The theorem is dimensionless to the similarity ratio relationship, and the first similarity criterion for physical simulation of coal and gas outburst is derived. The first similarity criterion of this invention includes at least one of the stress similarity criterion, geometric similarity criterion, and gas pressure similarity criterion. The specific derivation process of the first similarity criterion is as follows: S21: Let the geometric similarity ratio be... The strain-displacement similarity ratio is The volume force similarity ratio is The stress similarity ratio is The strain similarity ratio is The similarity ratio of elastic modulus is The similarity ratio of the internal friction angle is The compressive strength similarity ratio is Then we can obtain: From the above four formulas, the following similarity criterion can be derived: Because of the similarity ratio of volume forces Similarity ratio to material density equal( ),parameter Since the number is dimensionless, the similarity ratio can be set to 1. The above similarity criteria can be further summarized as follows: S22: Diffusion and seepage are synchronous processes, so the time similarity ratio of the two processes is the same. The coal seam gas content coefficient β is related to the gas pressure. Functions: In the formula, W represents the gas content of the coal seam, m 3 / m 3 ; Let the dimensionless parameter coal seam gas content similarity ratio CW =1: From the above formula, it can be derived that Combining the above equations, we obtain the gas field similarity criterion: After conversion, the gas pressure similarity ratio can be obtained as follows: .

[0021] Step 3: Based on the effective stress theory and thermodynamics theory, define the mechanical strength decay function of porous media materials under gas pressure. ,in Gas pressure, MPa; Atmospheric pressure, MPa; The strength of the material is expressed in MPa. The mechanical strength attenuation function of the porous medium material The function is monotonically decreasing, and the material strength under zero gas pressure conditions is used as the normalization benchmark. The specific derivation process of step three is as follows: Assume the gas intensity of the prototype coal sample is... The similar test model has a gas intensity of The gas pressure of the prototype coal sample was The gas pressure in the similar test model is Then the intensity function of the prototype coal sample can be expressed as: The strength function of the similar test model material is expressed as: .

[0022] Step Four: Through Figure 2 The triaxial gas-solid coupling mechanical loading device shown sequentially measured the prototype coal sample and similar test model of the engineering disaster, and carried out mechanical tests under different gas pressure conditions to measure the material strength parameters of the prototype coal sample and similar test model under gas pressure. Fitting the intensity decay function f of the prototype coal sample r (p) and the intensity decay function f of similar experimental models m (p); Since power-law attenuation functions are applicable to the nonlinear response of material strength under high pressure, this invention employs a power-law function for function fitting to measure the specific f. r (p), f m (p) The function curves are shown as follows: Figure 3 , Figure 4 : Step 5: Based on the measured material strength parameters, calculate the strength attenuation factor under different gas pressure conditions, and perform function fitting on the strength attenuation factors of the prototype coal sample and the similar test model respectively to obtain the strength attenuation function of the prototype coal sample. Intensity decay function of similar experimental models ; The strength attenuation factor in step five is the ratio of the material's strength under a given gas pressure to its strength under zero gas pressure. definition The ratio function of the intensity attenuation function of the prototype coal sample and the similar test model is given, and the fitted curve is as follows: Figure 5 As shown; Step Six: Apply the intensity decay function of the prototype coal sample Intensity decay function of similar experimental models Introducing the first similarity criterion from step two, we simultaneously derive the distortion compensation equation for the similarity criterion. And construct a similarity criterion for distortion compensation; Distortion compensation equation in step six This is a ratio function of the intensity decay function of the prototype coal sample and the similar test model: The above formula describes the "similarity distortion" caused by the different coupling characteristics of materials and gas, which needs to be compensated for by adjusting material parameters to finally obtain the corrected effective strength similarity ratio. for: .

[0023] Step 7: Based on the distortion compensation similarity criterion, determine the distortion compensation values ​​for each physical property parameter in the physical simulation of coal and gas outburst; The physical property parameters in step seven include at least one of the following: elastic modulus, compressive strength, and cohesion. in, This is the distortion compensation value for the elastic modulus; This is the distortion compensation value for compressive strength; This is the distortion compensation value for cohesion.

[0024] With the prototype coal sample having a compressive strength of 20 MPa, the geometric similarity ratio C of the similarity test model is... l Taking the attenuation strength under a gas pressure of 1 MPa as an example, based on the distortion compensation similarity criterion, the compressive strength of the modified model is calculated as follows: Based on the geometric similarity ratio C between the prototype coal sample and the similar test model l Taking the attenuation strength of the prototype coal sample with a gas pressure of 1 MPa and the similar test model with a gas pressure of 0.8 MPa as an example, according to the distortion compensation similarity criterion, the compressive strength of the modified model is calculated as follows: .

[0025] A distortion compensation system for a physical simulation similarity criterion for coal and gas outbursts, used to implement a distortion compensation method for a physical simulation similarity criterion for coal and gas outbursts as described in any one of claims 1 to 8, comprising: (1) Physical testing device, the physical testing device includes a gas pressure loading unit, a confining pressure loading unit and a mechanical parameter testing unit; the gas pressure loading unit, confining pressure loading unit and mechanical parameter testing unit of the present invention are all conventional technical means in the field, and will not be described in detail here. The device structure is similar to that disclosed in patent 2015100556708. (2) The calculation unit is connected to the physical test device, the distortion similarity criterion construction module, and the intensity attenuation modeling module, respectively, and is used in conjunction with the formulas in the method of this invention for: a) Receive the material mechanical parameters under different gas pressure conditions obtained by the physical testing device; b) Calculate the strength attenuation factor of the material under different gas pressure conditions, and fit the strength attenuation function of the prototype coal sample respectively. Intensity decay function of similar experimental models And calculate the distortion compensation equation of the similarity criterion. ; c) Solve for the distortion compensation values ​​of each physical property parameter in the physical simulation of coal and gas outburst.

[0026] Finally, the following points should be noted: First, in the description of this application, it should be noted that, unless otherwise specified and limited, the terms "installation", "connection", and "linkage" should be interpreted broadly, and can be mechanical or electrical connections, or internal connections between two components, or direct connections. "Up", "down", "left", "right", etc. are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may change. Secondly: The accompanying drawings of the embodiments disclosed in this invention only involve structures relevant to the embodiments disclosed herein. Other structures can be referenced to common designs. Unless otherwise specified, the same and different embodiments of this invention can be combined with each other. In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A distortion compensation method for a similarity criterion in physical simulation of coal and gas outbursts, characterized in that, Includes the following steps: Step 1: Select the gas-solid coupling control equation suitable for the physical simulation of coal and gas outbursts, determine the similarity ratio relationship of each physical quantity in the gas-solid coupling control equation, and establish the similarity ratio relationship of key parameters; Step Two: Based on The theorem is dimensionless to the similarity ratio relationship, and the first similarity criterion for physical simulation of coal and gas outburst is derived. Step 3: Based on the effective stress theory and thermodynamics theory, define the mechanical strength decay function of porous media materials under gas pressure. ,in For gas pressure; Step 4: Conduct mechanical tests on the prototype coal sample and similar test model under different gas pressure conditions to measure the material strength parameters of the prototype coal sample and similar test model under gas pressure. Step 5: Based on the measured material strength parameters, calculate the strength attenuation factor under different gas pressure conditions, and perform function fitting on the strength attenuation factors of the prototype coal sample and the similar test model respectively to obtain the strength attenuation function of the prototype coal sample. Intensity decay function of similar experimental models ; Step Six: Apply the intensity attenuation function of the prototype coal sample Intensity decay function of similar experimental models Introducing the first similarity criterion from step two, we simultaneously derive the distortion compensation equation for the similarity criterion. And construct a similarity criterion for distortion compensation; Step 7: Based on the distortion compensation similarity criterion, determine the distortion compensation values ​​of each physical property parameter in the physical simulation of coal and gas outburst.

2. The distortion compensation method for a similarity criterion in physical simulation of coal and gas outbursts according to claim 1, characterized in that, The gas-solid coupling control equations include: coal deformation control equations, damage and failure equations, and gas seepage control equations. Based on elastoplastic theory, the tensor expression of the equilibrium differential equations is as follows: In the formula, This is the tensor form of stress differential operations; It is the tensor form of the volume force components; Subscript The order of the second-order tensor; The tensor representation of geometric equations is as follows: In the formula, It is a second-order strain tensor; This is the tensor form for strain-displacement differential operations; The tensor expression of the constitutive relation of the elastic stage of coal-rock mass deformation is shown as: In the formula, Kronecker symbol; For stress tensor; Poisson's ratio; The elastic modulus is expressed in MPa. When considering the plastic state, the stress-strain relationship of gas-bearing coal can be obtained from the geometric relationship of the Mohr's circle: In the formula, Indicates the angle of internal friction, in °; Indicates uniaxial compressive strength, in MPa; and These represent the minimum and maximum principal stresses, respectively, in MPa; In outburst-prone coal seams, adsorbed gas diffuses through the pore system but does not transmit gas pressure, while free gas seeps through the fracture system and can transmit gas pressure. Assuming that the diffusion and seepage motions of adsorbed and free gas satisfy Fick's diffusion theorem and Darcy's seepage theorem, respectively, their respective second-order differential equations are expressed as: In the formula, Gas pressure, Pa; The diffusion time is in seconds. Let m be the coal seam diffusion coefficient. 2 / s; The gas content coefficient of the coal seam, m 3 / (m 3 ·Pa 1 / 2 ); The reference pressure for measuring gas content is atmospheric pressure under standard conditions, 101325 Pa. The seepage time is in seconds. m is the permeability of the coal seam fracture system. 2 ; ρ is the gas dynamic viscosity, Pa·s.

3. The distortion compensation method for a similarity criterion in physical simulation of coal and gas outbursts according to claim 1, characterized in that, The first similarity criterion includes at least one of the stress similarity criterion, geometric similarity criterion, and gas pressure similarity criterion. The specific derivation process of the first similarity criterion is as follows: S21: Let the geometric similarity ratio be... The strain-displacement similarity ratio is The volume force similarity ratio is The stress similarity ratio is The strain similarity ratio is The similarity ratio of elastic modulus is The similarity ratio of the internal friction angle is The compressive strength similarity ratio is Then we can obtain: The following similarity criterion is derived from the above formula: Because of the similarity ratio of volume forces Similarity ratio to material density equal( ),parameter Since the number is dimensionless, the similarity ratio is set to 1. The above similarity criteria are further summarized as follows: S22: Diffusion and seepage are synchronous processes, so the time similarity ratio of the two processes is the same. The coal seam gas content coefficient β is related to the gas pressure. Functions: In the formula, W represents the gas content of the coal seam, m 3 / m 3 ; Let the dimensionless parameter coal seam gas content similarity ratio C W =1: From the above formula, Combining the above equations, we obtain the gas field similarity criterion: After conversion, the gas pressure similarity ratio is obtained as follows: 。 4. The distortion compensation method for a similarity criterion in physical simulation of coal and gas outbursts according to claim 1, characterized in that, The mechanical strength attenuation function of the porous medium material The function is monotonically decreasing, and the material strength under zero gas pressure conditions is used as the normalization benchmark. The specific derivation process of step three is as follows: Assume the gas intensity of the prototype coal sample is... The similar test model has a gas intensity of The gas pressure of the prototype coal sample was The gas pressure in the similar test model is Then the intensity function of the prototype coal sample is expressed as: The strength function of the similar test model material is expressed as: 。 5. The distortion compensation method for a similarity criterion in physical simulation of coal and gas outbursts according to claim 4, characterized in that, In step five, the function fitting employs any one of the following: an exponential function, a linear function, or a power function. Exponential decay functions, including but not limited to: The linear decay function is expressed as: The power-law decay function is expressed as: In the formula, The gas attenuation coefficient is expressed in MPa⁻¹. This is the pressure sensitivity coefficient.

6. The distortion compensation method for a similarity criterion in physical simulation of coal and gas outbursts according to claim 4, characterized in that, The strength attenuation factor in step five is the ratio of the material's strength under a given gas pressure to its strength under zero gas pressure. 。 7. The distortion compensation method for a similarity criterion in physical simulation of coal and gas outbursts according to claim 4, characterized in that, Distortion compensation equation in step six This is a ratio function of the intensity decay function of the prototype coal sample and the similar test model: The above formula describes the "similarity distortion" caused by the different coupling characteristics of materials and gas, which needs to be compensated for by adjusting material parameters to finally obtain the corrected effective strength similarity ratio. for: 。 8. The distortion compensation method for a similarity criterion in physical simulation of coal and gas outbursts according to claim 4, characterized in that, The physical property parameters in step seven include at least one of the following: elastic modulus, compressive strength, and cohesion. in, This is the distortion compensation value for the elastic modulus; This is the distortion compensation value for compressive strength; This is the distortion compensation value for cohesion.

9. A distortion compensation system for a similarity criterion in physical simulation of coal and gas outbursts, used to implement a distortion compensation method for a similarity criterion in physical simulation of coal and gas outbursts as described in any one of claims 1 to 8, characterized in that, include: (1) Physical testing device, which includes a gas pressure loading unit, a confining pressure loading unit and a mechanical parameter testing unit; (2) A calculation unit, connected to the physical test device, the distortion similarity criterion construction module, and the intensity attenuation modeling module respectively, is used for: a) Receive the material mechanical parameters under different gas pressure conditions obtained by the physical testing device; b) Calculate the strength attenuation factor of the material under different gas pressure conditions, and fit the strength attenuation function of the prototype coal sample respectively. Intensity decay function of similar experimental models And calculate the distortion compensation equation of the similarity criterion. ; c) Solve for the distortion compensation values ​​of each physical property parameter in the physical simulation of coal and gas outburst.

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