Similarity criterion-based rock burst physical simulation method and system

Abstract

The invention discloses a rock burst physical simulation method and system based on a similarity criterion, and the simulation method comprises the following steps: selecting a suitable rock burst control equation, and obtaining a similarity ratio form of the rock burst control equation; according to a similarity ratio form of the rock burst control equation, a factor containing a parameter similarity ratio is extracted, a pi equation is obtained according to a similar second theorem and solved, and a similarity criterion is obtained; further deriving and simplifying under the similarity criterion established by the pi equation to obtain a rock burst preliminary similarity criterion; deducing a statics similarity criterion of the rock burst by combining the preliminary similarity criterion according to the fact that the acceleration similarity ratio is 1; according to the standard that the uniaxial compressive strength of the coal body in the dynamic state is larger than that in the static state and the damage time is smaller than that in the static state, the rock burst dynamic similarity criterion can be deduced; and deducing various parameter indexes of the model in the laboratory according to the established rock burst statics similarity criterion and dynamics similarity criterion.

Description

Technical Field

[0001] The present invention relates to the technical field of rock burst, and in particular to a rock burst physical simulation method and system based on similarity criteria. Background Art

[0002] Rock burst is a complex, catastrophic phenomenon caused by the superposition of dynamic and static loads, and its hazards are extremely severe. After long-term research, scholars have found that physical simulation experiments are an effective scientific research method for revealing the mechanisms of rock burst. Physical models are reproductions of real physical entities. Under the condition of satisfying the principle of similarity, they can objectively reflect the development process of rock burst construction and deformation and failure. Physical simulation plays an important role that other research methods cannot replace, for discovering new phenomena, exploring new laws, revealing new mechanisms, and verifying new theories. Therefore, physical similarity simulation methods are widely used by scholars due to their intuitive, accurate, and vivid characteristics.

[0003] In recent years, the physical simulation of rock burst has developed rapidly. Research institutions, such as universities and research institutes, have conducted large-scale simulation experiments, enriching the understanding of rock burst laws. Currently, there is little systematic research on similarity criteria for the physical simulation of rock burst. The rock burst simulation experiments conducted by scholars mainly draw on the research results of similarity criteria in solid mechanics and fluid mechanics. Most parameter similarity ratios are obtained only through dimensional analysis, lacking systematic derivation and verification, and thus lacking persuasiveness in reproducing rock burst phenomena. Simulation results often produce impact phenomena close to those in the field, and therefore this experimental method has been accepted by more and more scholars. However, the theoretical rationality and comprehensiveness of this method require the verification of similarity criteria. Therefore, it is very important to conduct research on similarity criteria for the physical simulation of rock burst. Summary of the Invention

[0004] In response to the problems and needs raised above, this solution proposes a method and system for simulating rock burst based on similarity criteria. By adopting the following technical features, it can achieve the above technical objectives and bring about many other technical effects.

[0005] An object of the present invention is to provide a method for simulating rock burst based on similarity criteria, comprising the following steps: S10: Deriving the rock burst similarity equation: After selecting the applicable rock burst control equation, extract the parameters within the equation and convert them into the form of similarity ratios. By substituting them into the original equation, the similarity ratio form of the rock burst control equation can be obtained; S20: Solve the π equation: Based on the similarity ratio form of the rock burst control equation, extract the factors containing the parameter similarity ratio, derive the π equation according to the second similarity theorem and solve it to obtain the similarity criterion under the π equation; S30: Establishing a preliminary similarity criterion for rock burst: Based on the similarity criterion established by the π equation, the mass M, size L, and time T system are introduced as eigenvalues to further deduce and simplify the similarity criterion, thereby obtaining a preliminary similarity criterion for rock burst; S40: Establish the static similarity criterion: The static similarity criterion satisfies the Froude criterion. Based on the acceleration similarity ratio of 1 and the preliminary similarity criterion, the static similarity criterion of rock burst is derived. S50: Establish the criteria for the dynamic similarity criterion: Based on the criterion that the uniaxial compressive strength of the coal mass in the dynamic state is greater than that in the static state, and the failure time is shorter than that in the static state, the dynamic similarity criterion of rock burst can be derived; S60: Derivation of model parameter indicators: Based on the established static similarity criteria and dynamic similarity criteria for rock burst, various parameter indicators of the laboratory model are derived, including: energy, uniaxial compressive strength, failure time and strain rate.

[0006] In addition, the rock burst physical simulation method and system based on similarity criteria according to the present invention may also have the following technical features: In one example of the present invention, in step S10, the rock burst control equation includes: a critical load theory equation, a rock burst stress control theory equation, a roadway limit equilibrium energy control equation, and a coal body damage and failure equation; wherein, The critical load theoretical equation for rock burst is expressed as follows: , Where, P cr is the impact critical load; s c is the uniaxial compressive strength; K is the impact tendency index; The expression of the rock burst stress control theoretical equation is: , In the formula s n,t is the relative stress of the coal body at point n at time t; Board n,t is the stress gradient; The expression of the tunnel limit equilibrium energy control equation is: , , , Where, Accumulate energy for static load in the ultimate equilibrium zone of the roadway; is the dynamic load energy obtained from the ultimate equilibrium zone of the roadway; The energy consumed by the coal body to be destroyed under the one-dimensional stress state; 、 、 are the first principal stress, the second principal stress, and the third principal stress respectively; m is Poisson's ratio; E is the elastic modulus; The damage and failure equation of coal body is expressed as: , Where: is the internal friction angle.

[0007] In one example of the present invention, the specific derivation process of step S20 is as follows: S21: Based on the transformation step of the second similarity theorem, define the impact critical load similarity ratio C Pcr , stress similarity ratio C σ , similarity ratio of internal friction angle , impact energy index similarity ratio C K , energy similarity ratio C Q , elastic modulus similarity ratio C E Similarity ratio with time C t The specific expression is as follows: , Where: P cr is the impact critical load; s is the principal stress; K is the impact tendency index; is the internal friction angle; Q is energy; t is time; the superscript “′” indicates the model; S22: Substituting the transformed similarity ratio into the prototype equation, we can obtain the model equation, which is expressed as follows: The model expression of the critical load theoretical equation for rock burst is: , The model expression of the damage and failure equation of coal body is: , The model expression of the tunnel limit equilibrium energy control equation is: , , The model expression of the rock burst stress control theoretical equation is: , S23: Based on the model, rock burst occurs and the conditions of the formula in step S22 are satisfied. Therefore, the rock burst dynamic similarity criterion can be derived according to the equation. The specific formulas for the similarity criterion of dynamic load, energy, elastic modulus, internal friction angle, impact energy index and Poisson's ratio are as follows: , Where, is the uniaxial compressive strength similarity ratio; is the Poisson's similarity ratio; is the similarity ratio of the relative stress of the coal body at point n at time t.

[0008] In an example of the present invention, step S30 specifically includes the following steps: S31: According to the similarity criterion, the mass M, size L, and time T system are used as basic dimensions to obtain the dynamic parameters π 1~ π Function criterion relationship of 7 , the π matrix expression of the dynamic parameters is obtained by analysis: , S32: Take mass M, size L, and time T as the basic quantities, where The specific expression of the dynamic similarity criterion is determined again as follows: ; ; Where, t is the impact time; T is time; L is the geometric length; v is the velocity; a is the acceleration; Q is the energy; is the strain rate; is the energy density; is the impact critical pressure; M is the mass; S33: The similarity criterion expression π The formula is transformed to get the following expression: ; S34: Substitute the similarity ratio of each parameter into the formula of step S33 to obtain the following expression: ; Where, is the speed similarity ratio; is the geometric similarity ratio; is the acceleration similarity ratio; is the temporal similarity ratio; is the impact time similarity ratio; is the strain rate similarity ratio; is the energy density similarity ratio; is the mass similarity ratio; is the energy similarity ratio; S35: Formula Substituting the above formula, we can obtain the preliminary similarity criterion of rock burst: ; Where, is the density similarity ratio.

[0009] In one example of the present invention, in step S40, the calculation expression of the speed similarity ratio in the Froude criterion is: , Where, Fr is the Froude number; v is the velocity; g is the acceleration of gravity; l is the length of the dynamic load transmission; is the speed similarity ratio; is the geometric similarity ratio; the superscript “′” is the model.

[0010] In one example of the present invention, in step S40, according to the velocity similarity criterion in the Froude criterion, the similarity ratio expressions of the static parameters of time, acceleration, energy, dynamic load strain rate, energy density and impact critical pressure and the impact tendency discrimination index are respectively: , Where, C t is the temporal similarity ratio; C a is the acceleration similarity ratio; C Q is the energy similarity ratio; C ρ is the density similarity ratio; is the strain rate similarity ratio; is the shock critical pressure similarity ratio; C σ is the stress similarity ratio; C l is the geometric similarity ratio; is the energy density similarity ratio.

[0011] In one example of the present invention, in step S50, when the dynamic load received by the coal body during impact damage is such that the propagation direction of the dynamic load is perpendicular to the coal seam and is consistent with the direction of gravity acceleration, the acceleration similarity ratio between the prototype and the model is , time similarity ratio between prototype and model , speed similarity ratio between prototype and model and stress similarity ratio between prototype and model They are: Acceleration similarity ratio between prototype and model The expression is: , Where, is the prototype dynamic load in the y direction; m is the prototype mass; is the prototype gravitational acceleration; is the dynamic load of the model in the y direction; m' is the mass of the model; is the model gravitational acceleration; Time similarity ratio between prototype and model The expression is: , Where, The acceleration applied to the prototype; the acceleration applied to the model; is the geometric similarity ratio; Speed similarity ratio between prototype and model The expression is: , Where, is the impact time similarity ratio; Stress similarity ratio between prototype and model The expression is: , Where, is the density similarity ratio.

[0012] In one example of the present invention, in step S50, when the dynamic load applied to the coal body during impact failure is such that there is a certain angle between the propagation direction of the main body of the dynamic load and the gravity acceleration of the coal seam, and when the dynamic load propagates in other directions, the acceleration similarity ratio, time similarity ratio, velocity similarity ratio, and stress similarity ratio of the prototype and the model are respectively: Similarity ratio of acceleration between prototype and model for: , Where, is the dynamic load of the prototype in the x direction; For prototype y Dynamic load in direction; i is the angle between the prototype dynamic load and gravity; is the dynamic load of the model in the x direction; For the model y Directional dynamic load; C l is the geometric similarity ratio; C ρ is the density similarity ratio; m is the prototype mass; m' is the model mass; is the prototype's gravitational acceleration; is the gravitational acceleration of the model; Dynamic loads borne by the prototype; is the dynamic load borne by the model; I will is the angle between the model dynamic load and gravity; Time similarity ratio between prototype and model for: , Speed similarity ratio between prototype and model for: , Stress similarity ratio between prototype and model for: .

[0013] Another object of the present invention is to provide a rock burst physical simulation system based on similarity criteria, comprising: A rock burst similarity equation module is configured to select an applicable rock burst control equation, extract parameters within the equation, and convert them into a similarity ratio form. By substituting the parameters into the original equation, the similarity ratio form of the rock burst control equation can be obtained. A π equation solving module is configured to extract a factor including a parameter similarity ratio based on a similarity ratio form of the rock burst control equation, derive the π equation based on the second similarity theorem, solve the equation, and obtain a similarity criterion under the π equation; A preliminary similarity criterion module for rock burst is established, which is configured to introduce the mass M, size L, and time T system as eigenvalues under the similarity criterion established by the π equation to further deduce and simplify the similarity criterion to obtain the preliminary similarity criterion for rock burst; A static similarity criterion judgment standard module is established, which is configured to ensure that the static similarity criterion meets the Froude criterion. The static similarity criterion of rock burst is derived based on the acceleration similarity ratio of 1 and the preliminary similarity criterion. A dynamic similarity criterion judgment standard module is established, which is configured to derive the rock burst dynamic similarity criterion based on the criterion that the uniaxial compressive strength of the coal body in the dynamic state is greater than that in the static state, and the failure time is shorter than that in the static state; The model parameter index derivation module is configured to derive various parameter indicators of the laboratory model based on the established static similarity criterion and dynamic similarity criterion of rock burst, wherein the parameter indicators include: energy, uniaxial compressive strength, failure time and strain rate.

[0014] In one example of the present invention, the rock burst control equation includes: a critical load theory equation, a rock burst stress control theory equation, a roadway limit equilibrium energy control equation, and a coal body damage and failure equation; wherein, The critical load theoretical equation for rock burst is expressed as follows: , Where: P cr is the impact critical load; s c is the uniaxial compressive strength; K is the impact tendency index; The expression of the rock burst stress control theoretical equation is: , In the formula s n,t is the relative stress of the coal body at point n at time t; Board n,t is the stress gradient; The expression of the tunnel limit equilibrium energy control equation is: , , , Where, Accumulate energy for static load in the ultimate equilibrium zone of the roadway; is the dynamic load energy obtained from the ultimate equilibrium zone of the roadway; The energy consumed by the coal body to be destroyed under the one-dimensional stress state; 、 、 are the first principal stress, the second principal stress, and the third principal stress respectively; m is Poisson's ratio; E is the elastic modulus; The damage and failure equation of coal body is expressed as: , Where: is the internal friction angle.

[0015] Compared with the prior art, the present invention has the following beneficial effects: The similarity criterion used in this simulation method is the theoretical basis for building a physical model of rock burst. It can improve the similarity between the physical model and the actual model, and provide an effective solution for cross-scale research on rock burst. Based on the similarity theory, it ensures that the experimental model and the actual project maintain a corresponding proportional relationship in terms of geometry, dynamics and material properties, so that the small-scale experimental results can be reasonably extrapolated to the actual coal mine environment.

[0016] This simulation method uses a rational stress loading method (such as the superposition of proportional static and dynamic loads) to more realistically reproduce the rock burst-induced environment in mines. When similarity criteria are met, the energy accumulation and release process, shock wave propagation characteristics, and coal fracture evolution patterns induced by rock burst are consistent with actual engineering practices. Furthermore, the experimentally measured impact kinetic energy, stress concentration areas, and failure thresholds can be used to predict rock burst risks under different coal seam conditions.

[0017] Coal mine dynamic hazards involve issues ranging from small-scale experiments (laboratory specimens) to large-scale projects (actual mines). Directly using measured mine data for research is difficult. The application of similarity criteria in this simulation method enables small-scale experiments to reveal large-scale coal dynamic characteristics, providing key parameters for field monitoring and numerical simulation. Numerical simulation is combined with physical model optimization: Based on the test data from the physical model, numerical simulation parameters can be calibrated to improve simulation accuracy and predict rock burst risks under different geological conditions.

[0018] This simulation method, based on physical model tests based on similarity criteria, can effectively simulate rock burst characteristics under different coal seam occurrence conditions. In engineering practice, physical models established using similarity criteria have been used to optimize coal mining plans, such as rationally arranging tunnel support structures and evaluating the impact of different mining processes on rock burst, providing a scientific basis for coal mine safety production.

[0019] Hereinafter, the best embodiment of the present invention will be described in more detail with reference to the accompanying drawings so that the features and advantages of the present invention can be easily understood. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings of the embodiments of the present invention. The drawings are only used to illustrate some embodiments of the present invention, but not to limit all embodiments of the present invention thereto.

[0021] Figure 1 Flowchart of a method for simulating rock burst physical pressure based on similarity criteria according to an embodiment of the present invention; Figure 2 Schematic diagram of two propagation directions of dynamic loads applied to coal during impact failure according to an embodiment of the present invention; Figure 3 Schematic diagram of the destruction of a dynamic model at different geometric similarity ratios according to an embodiment of the present invention; Figure 4 is a static uniaxial curve according to an embodiment of the present invention; Figure 5 is a dynamic uniaxial curve according to an embodiment of the present invention. DETAILED DESCRIPTION

[0022] In order to make the purpose, technical solution and advantages of the technical solution of the present invention clearer, the technical solution of the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings of specific embodiments of the present invention. The same figure marks in the drawings represent the same parts. It should be noted that the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the described embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0023] Unless otherwise defined, the technical or scientific terms used herein shall have the ordinary meaning understood by persons of ordinary skill in the field to which the invention belongs. The words "first", "second" and similar terms used in the patent application specification and claims of the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. Similarly, words such as "a" or "an" do not necessarily indicate a quantity limitation. Words such as "include" or "comprising" mean that the elements or objects preceding the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. Words such as "connected" or "connected" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the object being described changes, the relative positional relationship may also change accordingly.

[0024] According to a first aspect of the present invention, a rock burst physical simulation method based on similarity criteria is as follows: Figure 1 As shown, the following steps are included: S10: Deriving the rock burst similarity equation: After selecting the applicable rock burst control equation, extract the parameters within the equation and convert them into the form of similarity ratios. By substituting them into the original equation, the similarity ratio form of the rock burst control equation can be obtained; S20: Solve the π equation: Based on the similarity ratio form of the rock burst control equation, extract the factors containing the parameter similarity ratio, derive the π equation according to the second similarity theorem and solve it to obtain the similarity criterion under the π equation; S30: Establishing a preliminary similarity criterion for rock burst: Based on the similarity criterion established by the π equation, the mass M, size L, and time T system are introduced as eigenvalues to further deduce and simplify the similarity criterion, thereby obtaining a preliminary similarity criterion for rock burst; S40: Establish the static similarity criterion: The static similarity criterion satisfies the Froude criterion. Based on the acceleration similarity ratio of 1 and the preliminary similarity criterion, the static similarity criterion of rock burst is derived. S50: Establishing the criteria for determining the dynamic similarity criterion: The dynamic similarity criterion differs from the static similarity criterion. When a rockburst disaster occurs in a coal seam, it is affected not only by gravity but also by instantaneous dynamic loads, thus changing the acceleration similarity ratio. Based on the criterion that the uniaxial compressive strength of the coal mass in the dynamic state is greater than that in the static state, and the failure time is shorter than that in the static state, the dynamic similarity criterion for rockburst can be derived. S60: Derivation of model parameter indicators: Based on the established static similarity criteria and dynamic similarity criteria for rock burst, various parameter indicators of the laboratory model are derived, including: energy, uniaxial compressive strength, failure time and strain rate.

[0025] The similarity criterion used in this simulation method is the theoretical basis for building a physical model of rock burst. It can improve the similarity between the physical model and the actual model, and provide an effective solution for cross-scale research on rock burst. Based on the similarity theory, it ensures that the experimental model and the actual project maintain a corresponding proportional relationship in terms of geometry, dynamics and material properties, so that the small-scale experimental results can be reasonably extrapolated to the actual coal mine environment.

[0026] This simulation method uses a rational stress loading method (such as the superposition of proportional static and dynamic loads) to more realistically reproduce the rock burst-induced environment in mines. When similarity criteria are met, the energy accumulation and release process, shock wave propagation characteristics, and coal fracture evolution patterns induced by rock burst are consistent with actual engineering practices. Furthermore, the experimentally measured impact kinetic energy, stress concentration areas, and failure thresholds can be used to predict rock burst risks under different coal seam conditions.

[0027] Coal mine dynamic hazards involve issues ranging from small-scale experiments (laboratory specimens) to large-scale projects (actual mines). Directly using measured mine data for research is difficult. The application of similarity criteria in this simulation method enables small-scale experiments to reveal large-scale coal dynamic characteristics, providing key parameters for field monitoring and numerical simulation. Numerical simulation is combined with physical model optimization: Based on the test data from the physical model, numerical simulation parameters can be calibrated to improve simulation accuracy and predict rock burst risks under different geological conditions.

[0028] This simulation method, based on physical model tests based on similarity criteria, can effectively simulate rock burst characteristics under different coal seam occurrence conditions. In engineering practice, physical models established using similarity criteria have been used to optimize coal mining plans, such as rationally arranging tunnel support structures and evaluating the impact of different mining processes on rock burst, providing a scientific basis for coal mine safety production.

[0029] First, we select the governing equations that characterize the entire rockburst process. These equations describe the causes, conditions, mechanisms, and physical processes of rockburst. These equations must include physical parameters such as stress, energy, time, and strain rate. The internal parameters of the rockburst governing equations are converted into similarity ratios and substituted into the equations to describe the similarity between the model and the prototype. Using the second similarity theorem, we further derive and optimize the resulting similarity equations, yielding the π equation that describes the relationship between the internal parameters. Solving the π equation and introducing the mass M, size L, and time T system establishes a preliminary similarity criterion for rockburst.

[0030] Rock burst is a coal mine disaster caused by the superposition of static and dynamic loads. This is the result of the superposition of static loads in the coal and rock surrounding the mining area and dynamic loads from mine tremors. When the superimposed load exceeds the critical load for rock burst, the coal and rock experience instantaneous dynamic failure, resulting in rock burst. Therefore, through preliminary similarity criteria and further calculations and analysis, we have developed static and dynamic load similarity criteria that are consistent with the characteristics of rock burst.

[0031] The static similarity criterion for rock burst conforms to the Froude criterion in fluid mechanics. The Froude criterion characterizes the relationship between gravity and inertial force. From the Froude criterion, it can be deduced that the acceleration similarity ratio between the model and the prototype under the static state is 1. Substituting the acceleration similarity ratio = 1 into the preliminary similarity criterion, the static similarity criterion for the rock burst physical simulation test can be obtained.

[0032] The dynamic similarity criterion for rock burst does not conform to the Froude criterion. When a mine tremor generates a dynamic load, it is transmitted to the coal seam in the form of a stress wave, causing a rock burst disaster. The coal seam is affected by the original gravity and the dynamic load, so the similarity ratio acceleration in the impact area is ≠ 1. The specific range of acceleration values in the dynamic state is determined by the indicators that the uniaxial compressive strength of the coal sample in the dynamic state is greater than that in the static state, and the impact process time is less than that in the static state. Substituting the acceleration into the initial similarity criterion, the dynamic similarity criterion for the physical simulation test of rock burst can be obtained.

[0033] It is important to note that the governing equation for rock burst, which can also be considered the mechanism of rock burst, is the most important and fundamental component of rock burst research and the premise and theoretical foundation for rock burst disaster assessment, prediction, and prevention. The governing equation for rock burst encompasses the causes, conditions, mechanisms, and physical processes of rock burst. Numerous governing equations exist for rock burst. Table 1 lists the traditional and widely accepted rock burst equations in academia and engineering. When selecting these equations, key rock burst parameters such as stress, energy, and time should be included.

[0034]

[0035] In one example of the present invention, in step S10, the rock burst control equation includes: a critical load theory equation, a rock burst stress control theory equation, a roadway limit equilibrium energy control equation, and a coal body damage and failure equation; wherein the critical load theory equation for rock burst is expressed as: , Where: P cr is the impact critical load, MPa; s c is the uniaxial compressive strength, MPa; K is the impact tendency index; The expression of the rock burst stress control theoretical equation is: , Where, s n,t is the relative stress of the coal body at point n at time t, MPa; Board n,t is the stress gradient, MPa / s; The expression of the tunnel limit equilibrium energy control equation is: , , , Where, Accumulate energy for static load in the ultimate equilibrium zone of the roadway; is the dynamic load energy obtained from the ultimate equilibrium zone of the roadway; The energy consumed by the coal body to be destroyed under the one-dimensional stress state; 、 、 are the first principal stress, the second principal stress and the third principal stress, MPa; m is Poisson's ratio; E is the elastic modulus; The damage and failure equation of coal body is expressed as: , Where: is the internal friction angle, °.

[0036] In one example of the present invention, the specific derivation process of step S20 is as follows: S21: Based on the transformation step of the second similarity theorem, define the impact critical load similarity ratio C Pcr , stress similarity ratio C σ , similarity ratio of internal friction angle , impact energy index similarity ratio CK , energy similarity ratio C Q , elastic modulus similarity ratio C E Similarity ratio with time C t The specific expression is as follows: , Where: P cr is the impact critical load; s is the principal stress; K is the impact tendency index; is the internal friction angle; Q is energy; t is time; the superscript “′” indicates the model; S22: Substituting the transformed similarity ratio into the prototype equation, we can obtain the model equation, which is expressed as follows: The model expression of the critical load theoretical equation for rock burst is: , The model expression of the damage and failure equation of coal body is: , The model expression of the tunnel limit equilibrium energy control equation is: , , The model expression of the rock burst stress control theoretical equation is: , S23: Based on the model, rock burst occurs and the conditions of the formula in step S22 are satisfied. Therefore, the rock burst dynamic similarity criterion can be derived according to the equation. The specific formulas for the similarity criterion of dynamic load, energy, elastic modulus, internal friction angle, impact energy index and Poisson's ratio are as follows: , Where, is the uniaxial compressive strength similarity ratio; is the Poisson's similarity ratio; is the similarity ratio of the relative stress of the coal body at point n at time t.

[0037] The above formula expresses the similarity criterion involving dynamic load, energy, elastic modulus, internal friction angle, impact energy index, and Poisson's ratio. Further derivations involving energy density, impact velocity, acceleration, dynamic load strain rate, and acceleration can be derived from the above formula.

[0038] In an example of the present invention, step S30 specifically includes the following steps: S31: According to the similarity criterion, the mass M, size L, and time T system are used as basic dimensions to obtain the dynamic parameters π 1~ π Function criterion relationship of 7 , the π matrix expression of the dynamic parameters is obtained by analysis: , S32: Take mass M, size L, and time T as the basic quantities, where The specific expression of the dynamic similarity criterion is determined again as follows: ; ; Where, t is the impact time; T is time; L is the geometric length; v is the velocity; a is the acceleration; Q is the energy; is the strain rate; is the energy density; is the impact critical pressure; M is the mass; S33: The similarity criterion expression π The formula is transformed to get the following expression: ; S34: Substitute the similarity ratio of each parameter into the formula of step S33 to obtain the following expression: ; ; Where, is the speed similarity ratio; is the geometric similarity ratio; is the acceleration similarity ratio; is the temporal similarity ratio; is the impact time similarity ratio; is the strain rate similarity ratio; is the energy density similarity ratio; is the mass similarity ratio; is the energy similarity ratio; S35: Formula Substituting the above formula, we can obtain the preliminary similarity criterion of rock burst: ; Where, is the density similarity ratio.

[0039] In one example of the present invention, in step S40, the calculation expression of the speed similarity ratio in the Froude criterion is: , Where, Fr is the Froude number; v is the velocity; g is the acceleration of gravity; l is the length of the dynamic load transmission; is the speed similarity ratio; is the geometric similarity ratio; the superscript “′” is the model.

[0040] The static process of rock burst includes the static state before and after the impact. In the static state, the coal rock layer should comply with the Froude criterion. The core of this criterion is to keep the acceleration as a similar invariant, that is, The calculation of the velocity similarity ratio in the Froude criterion is shown in the above formula.

[0041] In one example of the present invention, in step S40, according to the velocity similarity criterion in the Froude criterion, the similarity ratio expressions of the static parameters of time, acceleration, energy, dynamic load strain rate, energy density and impact critical pressure and the impact tendency discrimination index are respectively: , Where, C t is the temporal similarity ratio; C a is the acceleration similarity ratio; C Q is the energy similarity ratio; C ρ is the density similarity ratio; is the strain rate similarity ratio; is the shock critical pressure similarity ratio; C σ is the stress similarity ratio; C l is the geometric similarity ratio; is the energy density similarity ratio.

[0042] That is, according to the velocity similarity criterion in Froude's criterion , the similarity ratio between the static parameters such as time, acceleration, energy, dynamic load strain rate, energy density and impact critical pressure and the impact tendency judgment index can be derived.

[0043] The difference between the dynamic similarity theory and the static similarity theory of rock burst is that the acceleration of the coal body changes at the moment of dynamic load release. In addition to the original gravitational acceleration of the coal body, it is also subjected to the instantaneous acceleration from the dynamic load, which causes the coal body to be instantly destroyed and forms a rock burst disaster. Therefore, the dynamic similarity theory of rock burst is discussed in depth in the acceleration part.

[0044] In one example of the present invention, in step S50, as Figure 2 As shown in the figure, when the dynamic load on the coal body during impact failure is perpendicular to the coal seam and consistent with the direction of gravity acceleration, the acceleration similarity ratio between the prototype and the model is , time similarity ratio between prototype and model , speed similarity ratio between prototype and model and stress similarity ratio between prototype and model They are: First, when the dynamic load and gravity acceleration are in the same direction, the resultant force on the coal body is: , The acceleration is: , Acceleration similarity ratio between prototype and model The expression is: , Where, is the prototype dynamic load in the y direction, N; m is the prototype mass, kg; is the acceleration due to gravity, m / s 2 ; is the dynamic load of the model in the y direction; m' is the mass of the model, kg; is the model gravity acceleration, m / s 2 ; Assume the acceleration of the dynamic load , then the similarity ratio of the overall acceleration and the similarity ratio of the dynamic load acceleration are: ; Thus, the temporal similarity ratio between the prototype and the model can be derived The expression is: , Where, C td is the kinetic time similarity ratio; is the acceleration applied to the prototype, m / s 2 ; Acceleration applied to the model, m / s 2 ; is the geometric similarity ratio; Speed similarity ratio between prototype and model The expression is: , Where, is the temporal similarity ratio; Stress similarity ratio between prototype and model The expression is: , Where, is the density similarity ratio.

[0045] In one example of the present invention, in step S50, as Figure 2 As shown, in step S50, when the dynamic load on the coal body during impact failure is such that there is a certain angle between the propagation direction of the main body of the dynamic load and the gravity acceleration of the coal seam, when the dynamic load propagates in other directions, the acceleration similarity ratio, time similarity ratio, velocity similarity ratio, and stress similarity ratio between the prototype and the model are respectively: The case of rock burst dynamics similarity theory is that the direction of dynamic load does not match the gravitational acceleration and there is an angle. At this time, the force on the coal body is: , The acceleration is: , Similarity ratio of acceleration between prototype and model for: , Where, is the dynamic load of the prototype in the x direction; For prototype y Directional dynamic load; i is the angle between the prototype dynamic load and gravity; is the dynamic load of the model in the x direction; For the model y Directional dynamic load; C l is the geometric similarity ratio; C ρ is the density similarity ratio; m is the prototype mass; m' is the model mass; is the prototype's gravitational acceleration; is the gravitational acceleration of the model; Dynamic loads borne by the prototype; is the dynamic load borne by the model; I will is the angle between the model dynamic load and gravity; Time similarity ratio between prototype and model for: , Speed similarity ratio between prototype and model for: , Stress similarity ratio between prototype and model for: .

[0046] According to a second aspect of the present invention, a rock burst physical simulation system based on similarity criteria includes: A rock burst similarity equation module is configured to select an applicable rock burst control equation, extract parameters within the equation, and convert them into a similarity ratio form. By substituting the parameters into the original equation, the similarity ratio form of the rock burst control equation can be obtained. A π equation solving module is configured to extract a factor including a parameter similarity ratio based on a similarity ratio form of the rock burst control equation, derive the π equation based on the second similarity theorem, solve the equation, and obtain a similarity criterion under the π equation; A preliminary similarity criterion module for rock burst is established, which is configured to introduce the mass M, size L, and time T system as eigenvalues under the similarity criterion established by the π equation to further deduce and simplify the similarity criterion to obtain the preliminary similarity criterion for rock burst; A static similarity criterion judgment standard module was established and configured to ensure that the static similarity criterion met the Froude criterion. The Froude criterion was based on an acceleration similarity ratio of 1 under a gravity field. Based on the acceleration similarity ratio of 1 and the preliminary similarity criterion, the static similarity criterion for rock burst was derived. A dynamic similarity criterion judgment standard module is established, which is configured to derive the rock burst dynamic similarity criterion based on the criterion that the uniaxial compressive strength of the coal body in the dynamic state is greater than that in the static state, and the failure time is shorter than that in the static state; The model parameter index derivation module is configured to derive various parameter indicators of the laboratory model based on the established static similarity criterion and dynamic similarity criterion of rock burst, wherein the parameter indicators include: energy, uniaxial compressive strength, failure time and strain rate.

[0047] The similarity criterion used in this simulation system is the theoretical basis for building a physical model of rock burst. It can improve the similarity between the physical model and the actual model, and provide an effective solution for cross-scale research on rock burst. Based on the similarity theory, it ensures that the experimental model and the actual project maintain a corresponding proportional relationship in terms of geometry, dynamics and material properties, so that the results of small-scale experiments can be reasonably extrapolated to the actual coal mine environment.

[0048] This simulation system uses a rational stress loading method (such as the superposition of proportional static and dynamic loads) to more realistically reproduce the rock burst-induced environment in mines. When similarity criteria are met, the energy accumulation and release process, shock wave propagation characteristics, and coal fracture evolution patterns induced by rock burst closely match those of actual projects. Furthermore, the experimentally measured impact kinetic energy, stress concentration areas, and failure thresholds can be used to predict rock burst risks under different coal seam conditions.

[0049] Coal mine dynamic hazards involve issues ranging from small-scale experiments (laboratory specimens) to large-scale engineering projects (actual mines). Directly using measured mine data for research is difficult. The application of similarity criteria in this simulation system enables small-scale experiments to reveal large-scale coal dynamic characteristics, providing key parameters for field monitoring and numerical simulation. Numerical simulation is combined with physical model optimization: Based on the test data from the physical model, numerical simulation parameters can be calibrated to improve simulation accuracy and predict rock burst risks under different geological conditions.

[0050] This simulation system, based on physical model tests based on similarity criteria, can effectively simulate rock burst characteristics under different coal seam occurrence conditions. In engineering practice, physical models established using similarity criteria have been used to optimize coal mining plans, such as rationally arranging tunnel support structures and evaluating the impact of different mining processes on rock burst, providing a scientific basis for coal mine safety production.

[0051] In one example of the present invention, the rock burst control equation includes: a critical load theory equation, a rock burst stress control theory equation, a roadway limit equilibrium energy control equation, and a coal body damage and failure equation; wherein the critical load theory equation for rock burst is expressed as: , Where: P cr is the impact critical load, MPa; s c is the uniaxial compressive strength, MPa; K is the impact tendency index; The expression of the rock burst stress control theoretical equation is: , In the formula s n,t is the relative stress of the coal body at point n at time t, MPa; Board n,t is the stress gradient, MPa / s; The expression of the tunnel limit equilibrium energy control equation is: , , , Where, is the static load accumulated energy in the ultimate equilibrium zone of the roadway, J / m 3 ; is the dynamic load energy obtained from the ultimate equilibrium zone of the roadway, J / m 3 ; The energy consumed by the coal body under one-dimensional stress state, J / m 3 ; 、 、 are the first principal stress, the second principal stress and the third principal stress, MPa; m is Poisson's ratio; E is the elastic modulus, MPa; The damage and failure equation of coal body is expressed as: , Where: is the internal friction angle, °.

[0052] specific case When simulating the scale of impacted coal samples, when the geometric similarity ratio is large, the model size and physical and mechanical properties are small, which is not meaningful for research. Therefore, the geometric similarity ratio of the model is set as 20 as the limit of the geometric similarity ratio, and the model simulation research is carried out using geometric similarity ratios of 2, 5, 10, and 20.

[0053] Similarity theory verification plan for impact coal samples: First, the physical and mechanical parameters and impact tendency indicators of the prototype are selected, and the size and static parameters of the model sample are reduced according to different geometric similarity ratios. Then, stress is applied to the samples of different sizes through uniaxial compression to obtain the dynamic and static mechanical parameters and impact tendency indicators under different sizes. The obtained parameters and indicators are then compared with the theoretical values to judge the correctness of the dynamic similarity theory and the beneficialness of the dynamic similarity criterion.

[0054] The impact coal sample selected for the prototype is a strong impact sample, and its specific parameters are shown in Table 2:

[0055] The geometric similarity ratios are selected as 2, 5, 10, and 20 because the geometric similarity ratio has a greater impact on the parameters, while the density similarity ratio has a consistent impact on the dynamic parameters. Therefore, in the simulation stage, the density similarity ratio is set to "1" and the density of the model is consistent with that of the prototype.

[0056] like Figure 3 The figure shows the fracture results of impacted coal samples tested under different geometric similarity ratios. As can be seen from the figure, as the geometric similarity ratio increases, the degree of internal fragmentation in the model gradually decreases, the degree of crack development in the model gradually decreases, the volume of the broken blocks increases, and the crack propagation trend is not obvious.

[0057] Figure 4 and Figure 5The static and dynamic stress-time curves of the model under different geometric similarity ratios are shown in the figure. It can be seen from the figure that the uniaxial compressive strength and failure time gradually decrease during the static simulation. During the dynamic simulation, the failure time under each similarity ratio is less than that of statics, and the uniaxial compressive strength is greater than that of statics, indicating that the simulation results are consistent with the theoretical derivation and can show the impact state of the coal sample.

[0058] Table 3 compares the theoretical and simulated values of the impact propensity index at different geometric similarity ratios. Under different geometric similarity ratios, the model's impact energy index is smaller than the theoretical value, but still exhibits a strong impact propensity. The model's uniaxial compressive strength is essentially consistent with the theoretical value. The overall failure time of the model varies significantly, but overall, the difference between the static similarity theory and the model is minimal. The dynamic failure time is shorter than the static failure time, and the uniaxial compressive strength is greater than the static uniaxial compressive strength. This also demonstrates that the dynamic similarity theory also conforms to the theoretical value range, further proving that the application of the dynamic similarity criterion can simulate the dynamic state of specimen failure.

[0059]

[0060] The exemplary implementation scheme of the impact ground pressure physical simulation method and system based on similarity criteria proposed in the present invention is described in detail above with reference to the preferred embodiments. However, those skilled in the art will understand that, without departing from the concept of the present invention, various modifications and variations can be made to the above-mentioned specific embodiments, and various technical features and structures proposed in the present invention can be combined in various ways without exceeding the scope of protection of the present invention, which is determined by the appended claims.

Claims

1. A method for simulating rock burst based on similarity criteria, characterized in that: The steps include: S10: Deriving the rock burst similarity equation: After selecting the applicable rock burst control equation, extract the parameters within the equation and convert them into the form of similarity ratios. By substituting them into the original equation, the similarity ratio form of the rock burst control equation can be obtained; S20: Solve the π equation: Based on the similarity ratio form of the rock burst control equation, extract the factors containing the parameter similarity ratio, derive the π equation according to the second similarity theorem and solve it to obtain the similarity criterion under the π equation; S30: Establishing a preliminary similarity criterion for rock burst: Based on the similarity criterion established by the π equation, the mass M, size L, and time T system are introduced as eigenvalues to further deduce and simplify the similarity criterion, thereby obtaining a preliminary similarity criterion for rock burst; S40: Establish the static similarity criterion: The static similarity criterion satisfies the Froude criterion. Based on the acceleration similarity ratio of 1 and the preliminary similarity criterion, the static similarity criterion of rock burst is derived. S50: Establish the criteria for the dynamic similarity criterion: Based on the criterion that the uniaxial compressive strength of the coal mass in the dynamic state is greater than that in the static state, and the failure time is shorter than that in the static state, the dynamic similarity criterion of rock burst can be derived; S60: Derivation of model parameter indicators: Based on the established static similarity criteria and dynamic similarity criteria for rock burst, various parameter indicators of the laboratory model are derived, including: energy, uniaxial compressive strength, failure time and strain rate.

2. The rock burst physical simulation method based on similarity criterion according to claim 1 is characterized in that: In step S10, the rock burst control equation includes: critical load theory equation, rock burst stress control theory equation, tunnel limit equilibrium energy control equation, and coal body damage and failure equation; wherein, The critical load theoretical equation for rock burst is expressed as follows: ， Where, P cr is the impact critical load; σ c is the uniaxial compressive strength; K is the impact tendency index; The expression of the rock burst stress control theoretical equation is: ， In the formula σ n,t is the relative stress of the coal body at point n at time t; Δσ n,t is the stress gradient; The expression of the tunnel limit equilibrium energy control equation is: ， ， ， Where, Accumulate energy for static load in the ultimate equilibrium zone of the roadway; is the dynamic load energy obtained from the ultimate equilibrium zone of the roadway; The energy consumed by the coal body to be destroyed under the one-dimensional stress state; 、 、 are the first principal stress, the second principal stress, and the third principal stress respectively; μ is Poisson's ratio; E is the elastic modulus; The damage and failure equation of coal body is expressed as: ， Where: is the internal friction angle.

3. The rock burst physical simulation method based on similarity criterion according to claim 1 is characterized in that: The specific derivation process of step S20 is as follows: S21: Based on the transformation step of the second similarity theorem, define the impact critical load similarity ratio C Pcr , stress similarity ratio C σ , similarity ratio of internal friction angle , impact energy index similarity ratio C K , energy similarity ratio C Q , elastic modulus similarity ratio C E Similarity ratio with time C t The specific expression is as follows: ， Where: P cr is the impact critical load; σ is the principal stress; K is the impact tendency index; is the internal friction angle; Q is energy; t is time; the superscript "′" indicates the model; S22: Substituting the transformed similarity ratio into the prototype equation, we can obtain the model equation, which is expressed as follows: The model expression of the critical load theoretical equation for rock burst is: ， The model expression of the damage and failure equation of coal body is: ， The model expression of the tunnel limit equilibrium energy control equation is: ， ， The model expression of the rock burst stress control theoretical equation is: ， S23: Based on the model, rock burst occurs and the conditions of the formula in step S22 are satisfied. Therefore, the rock burst dynamic similarity criterion can be derived according to the equation. The specific formulas for the similarity criterion of dynamic load, energy, elastic modulus, internal friction angle, impact energy index and Poisson's ratio are as follows: ， Where, is the uniaxial compressive strength similarity ratio; is the Poisson's similarity ratio; is the similarity ratio of the relative stress of the coal body at point n at time t.

4. The rock burst physical simulation method based on similarity criterion according to claim 1, characterized in that: The step S30 specifically includes the following steps: S31: According to the similarity criterion, the mass M, size L, and time T system are used as basic dimensions to obtain the dynamic parameters π 1~ π Function criterion relationship of 7 , the π matrix expression of the dynamic parameters is obtained by analysis: ， S32: Take mass M, size L, and time T as the basic quantities, where The specific expression of the dynamic similarity criterion is determined again as follows: ； ； Where, t is the impact time; T is time; L is the geometric length; v is the velocity; a is the acceleration; Q is the energy; is the strain rate; is the energy density; is the impact critical pressure; M is the mass; S33: The similarity criterion expression π The formula is transformed to get the following expression: ； S34: Substitute the similarity ratio of each parameter into the formula of step S33 to obtain the following expression: ； Where, is the speed similarity ratio; is the geometric similarity ratio; is the acceleration similarity ratio; is the temporal similarity ratio; is the impact time similarity ratio; is the strain rate similarity ratio; is the energy density similarity ratio; is the mass similarity ratio; is the energy similarity ratio; S35: Formula Substituting the above formula, we can obtain the preliminary similarity criterion of rock burst: ， Where, is the density similarity ratio.

5. The rock burst physical simulation method based on similarity criterion according to claim 1 is characterized in that: In step S40, the calculation expression of the velocity similarity ratio in the Froude criterion is: ， Where, Fr is the Froude number; v is the velocity; g is the acceleration of gravity; l is the length of the dynamic load transmission; is the speed similarity ratio; is the geometric similarity ratio; the superscript “′” indicates the model.

6. The rock burst physical simulation method based on similarity criterion according to claim 1, characterized in that: In step S40, according to the velocity similarity criterion in the Froude criterion, the similarity ratio expressions of the static parameters of time, acceleration, energy, dynamic load strain rate, energy density and impact critical pressure and the impact tendency discrimination index are respectively: ， Where, C t is the temporal similarity ratio; C a is the acceleration similarity ratio; C Q is the energy similarity ratio; C ρ is the density similarity ratio; is the strain rate similarity ratio; is the shock critical pressure similarity ratio; C σ is the stress similarity ratio; C l is the geometric similarity ratio; is the energy density similarity ratio.

7. The rock burst physical simulation method based on similarity criterion according to claim 1, characterized in that: In step S50, when the dynamic load on the coal body during impact damage is such that the propagation direction of the dynamic load is perpendicular to the coal seam and is consistent with the direction of gravity acceleration, the acceleration similarity ratio between the prototype and the model is , time similarity ratio between prototype and model , speed similarity ratio between prototype and model and stress similarity ratio between prototype and model They are: Acceleration similarity ratio between prototype and model The expression is: ， Where, is the prototype dynamic load in the y direction; m is the prototype mass; is the prototype gravitational acceleration; is the model dynamic load in the y direction; m' is the model mass; is the model gravitational acceleration; Time similarity ratio between prototype and model The expression is: ， Where, The acceleration applied to the prototype; the acceleration applied to the model; is the geometric similarity ratio; Speed similarity ratio between prototype and model The expression is: ， Where, is the impact time similarity ratio; Stress similarity ratio between prototype and model The expression is: ， Where, is the density similarity ratio.

8. The rock burst physical simulation method based on similarity criterion according to claim 1, characterized in that: In step S50, when the dynamic load on the coal body during impact failure is such that there is a certain angle between the propagation direction of the main dynamic load and the gravity acceleration of the coal seam, when the dynamic load propagates in other directions, the acceleration similarity ratio, time similarity ratio, velocity similarity ratio, and stress similarity ratio between the prototype and the model are respectively: Similarity ratio of acceleration between prototype and model for: ， Where, is the dynamic load of the prototype in the x direction; For prototype y Directional dynamic load; θ is the angle between the prototype dynamic load and gravity; is the dynamic load in the x-direction of the model; For the model y Directional dynamic load; C l is the geometric similarity ratio; C ρ is the density similarity ratio; m is the prototype mass; m' is the model mass; is the prototype's gravitational acceleration; is the gravitational acceleration of the model; Dynamic loads borne by the prototype; is the dynamic load borne by the model; θ' is the angle between the model dynamic load and gravity; Time similarity ratio between prototype and model for: ， Speed similarity ratio between prototype and model for: ， Stress similarity ratio between prototype and model for: 。 9. A rock burst physical simulation system based on similarity criteria, characterized in that: include: A rock burst similarity equation module is configured to select an applicable rock burst control equation, extract parameters within the equation, and convert them into a similarity ratio form. By substituting the parameters into the original equation, the similarity ratio form of the rock burst control equation can be obtained. A π equation solving module is configured to extract a factor including a parameter similarity ratio based on a similarity ratio form of the rock burst control equation, derive the π equation based on the second similarity theorem, solve the equation, and obtain a similarity criterion under the π equation; A preliminary similarity criterion module for rock burst is established, which is configured to introduce the mass M, size L, and time T system as eigenvalues under the similarity criterion established by the π equation to further deduce and simplify the similarity criterion to obtain the preliminary similarity criterion for rock burst; A static similarity criterion judgment standard module is established, which is configured to ensure that the static similarity criterion meets the Froude criterion. The static similarity criterion of rock burst is derived based on the acceleration similarity ratio of 1 and the preliminary similarity criterion. A dynamic similarity criterion judgment standard module is established, which is configured to derive the rock burst dynamic similarity criterion based on the criterion that the uniaxial compressive strength of the coal body in the dynamic state is greater than that in the static state, and the failure time is shorter than that in the static state; The model parameter index derivation module is configured to derive various parameter indicators of the laboratory model based on the established static similarity criterion and dynamic similarity criterion of rock burst, wherein the parameter indicators include: energy, uniaxial compressive strength, failure time and strain rate.

10. The rock burst physical simulation system based on similarity criterion according to claim 9, characterized in that: The rock burst control equations include: critical load theory equation, rock burst stress control theory equation, tunnel limit equilibrium energy control equation, and coal body damage and failure equation; The critical load theoretical equation for rock burst is expressed as follows: ， Where: P cr is the impact critical load; σ c is the uniaxial compressive strength; K is the impact tendency index; The expression of the rock burst stress control theoretical equation is: ， In the formula σ n,t is the relative stress of the coal body at point n at time t; Δσ n,t is the stress gradient; The expression of the tunnel limit equilibrium energy control equation is: ， ， ， Where, Accumulate energy for static load in the ultimate equilibrium zone of the roadway; is the dynamic load energy obtained from the ultimate equilibrium zone of the roadway; The energy consumed by the coal body to be destroyed under the one-dimensional stress state; 、 、 are the first principal stress, the second principal stress, and the third principal stress respectively; μ is Poisson's ratio; E is the elastic modulus; The damage and failure equation of coal body is expressed as: ， Where: is the internal friction angle.

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