A critical criterion method for rock burst induced by breaking of thick and hard roof

Abstract

The application discloses a kind of thick hard roof breakage induced critical criterion method of rock burst, comprising: S1: establishing in-situ stress environment database;S2: establish roof energy storage model;S3: derive elastic energy density distribution analytical expression;S4: define equivalent crack propagation driving force and introduce non-local fracture criterion;S5: build dynamic evolution equation;S6: reveal mutation precursor signal;S7: define new expression of energy release rate mutation factor Λ;S8: establish peak energy release rate Gpeak Calculation model;S9: derive critical mutation threshold Λ c ;S10: propose modified critical condition;S11: field real-time calculation process and dynamic early warning rule;S12: verification and adaptive parameter adjustment method.The method quantitatively describes the dynamic process of energy release rate from "slow change" to "mutation" before and after roof breakage, and establishes a clear mathematical critical condition, so as to realize accurate and advanced discrimination of rock burst occurrence time, and improve the reliability and practicality of mine dynamic disaster prediction.

Description

Technical Field

[0001] This invention belongs to the field of mine safety and rock mechanics engineering technology, specifically relating to a critical criterion method for rockburst induced by the fracture of a thick, hard roof. Background Technology

[0002] Rockbursts are extremely destructive dynamic hazards in deep coal mining, and the sudden fracture of thick, hard roofs is one of the main triggers. Accurately determining when the thick, hard roof will fracture and whether its fracture is sufficient to trigger a rockburst is a core challenge in rock mass control and disaster prevention in mining areas.

[0003] Currently, research by scholars both domestically and internationally on criteria for fracture of thick, hard roof slabs mainly focuses on the following two technical approaches:

[0004] (1) Static criteria based on stress or deformation: An empirical threshold is set by monitoring the internal stress of the roof (e.g., borehole stress gauge) or the deformation of the rock strata (e.g., delamination gauge, multi-point displacement gauge). When the monitored value exceeds the threshold, it is judged as dangerous. For example, in the literature "Research on the relationship between mine pressure manifestation and rockburst in hard roof fracture" (Journal of Mining and Safety Engineering, 2018, 35(2):256-262), the ultimate overhang distance of the roof is used as the fracture criterion. However, such methods ignore the dynamic process and release rate of energy release at the moment of fracture, resulting in a lag in early warning and poor universality of the threshold.

[0005] (2) Energy accumulation criterion based on numerical simulation: The total amount of elastic energy accumulated in the roof is calculated using finite element or discrete element software (such as FLAC3D, UDEC). When the total energy exceeds a certain preset value, it is judged as dangerous. For example, patent CN104929664A "A method for predicting the risk of rockburst in a mining area" assesses the risk by simulating the flexural deformation energy of the roof. However, such methods are computationally complex, making it difficult to achieve real-time early warning, and they do not consider the key dynamic indicator of energy release rate (energy released per unit time or per unit fracture area), while the level of energy release rate is the direct factor determining the magnitude of the impact load.

[0006] In summary, the fundamental flaw in existing technologies lies in the lack of a method to quantify the "abrupt" characteristics of the energy release rate at the moment of fracture of a thick, rigid roof (i.e., the drastic transition from slow accumulation to instantaneous release) and to establish a critical criterion that can be analytically calculated. This results in either a delayed or inaccurate determination of whether the fracture induces an impact, failing to meet the need for immediate and reliable early warning on-site. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention aims to provide a critical criterion method for detecting rockbursts induced by the fracture of thick, hard roofs based on the abrupt change characteristics of energy release rate. This method can quantitatively describe the dynamic process of energy release rate changing from a "gradual change" to a "sudden change" before and after roof fracture, and establish clear mathematical critical conditions, thereby achieving accurate and advanced determination of the timing of rockburst occurrence and improving the reliability and practicality of mine dynamic disaster prediction.

[0008] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0009] A critical criterion method for determining whether thick, rigid roof fracture can induce rockburst, comprising the following steps:

[0010] S1: Collect key physical and mechanical parameters of thick and hard roof slabs and establish an in-situ stress environment database.

[0011] The essence of rockburst is a sudden process from steady-state energy accumulation to unstable release in the roof system. This process is highly dependent on the intrinsic physical properties of the roof rock mass and the geostress field in which it is located. Therefore, the first step must be to obtain a set of basic parameters that can characterize the energy storage limit, fracture toughness, and dynamic response of the rock mass through field exploration and laboratory tests. Unlike conventional methods, this step additionally requires the determination of the damage localization coefficient and the nonlocal influence radius. These two parameters will be used in the nonlocal damage gradient model in the subsequent step S2.

[0012] Define physical quantities and their symbols (all using the International System of Units):

[0013]

[0014] S2: Establish a roof energy storage model based on nonlocal damage gradients.

[0015] Classical linear elastic fracture mechanics assumes that the crack tip is a singularity, which cannot describe the damage process zone that exists in real rock. This invention introduces the nonlocal damage gradient theory, treating the thick, hard roof as a continuous medium containing diffuse cracks. Its damage variable D(x) depends not only on the strain at that point but also on the damage state of the neighborhood. The total energy stored in the roof consists of two parts: elastic strain energy and damage surface energy.

[0016] Total potential functional under nonlocal damage gradient

[0017]

[0018] In the formula: Ω represents the two-dimensional or three-dimensional continuous domain occupied by the top plate; σ ij Let ε be the stress tensor. ij For the strain tensor, satisfying the constitutive relation σ ij =C ijkl εkl C ijkl Let ε be the elastic stiffness tensor. kl , which is the component form of the second-order strain tensor; D(x) is the damage variable, with a value range of 0≤D≤1, where D=0 represents intact rock and D=1 represents complete failure; β is the gradient damage modulus (N), a material constant, which is determined by fitting the strain softening curve under uniaxial tension. The nonlocal influence radius (i.e., the parameter in step S1) controls the distance of nonlocal interactions of damage. The square of the damage field gradient represents the degree of spatial inhomogeneity of the damage. The energy dissipation function for local damage is usually taken as... (Linear softening) or (Secondary softening), among which This is a Type I fracture energy; the present invention employs a bilinear form to better match the brittle behavior of hard rock:

[0019]

[0020] This formula ensures that when D=1, the fracture energy dissipated per unit volume is The total fracture energy after integration is related to Consistent;

[0021] Γ t The portion on the boundary to which an external force is applied; T i For surface force components; u i For displacement components;

[0022] This potential energy functional is the first to combine gradient damage theory with the problem of roof fracture-induced rockburst, in which... The method can simulate the width effect of the damage zone at the crack tip, avoiding the stress singularity in classical linear elastic fracture mechanics, and providing a physical basis for subsequent calculations of the continuous evolution of energy release rate.

[0023] The output of step S2: the total potential energy Π of the top plate under any load condition and its relationship to the crack length. The variational derivative of the energy release rate will be used in step S5.

[0024] S3: Derive the analytical formula for the elastic energy density distribution inside the top plate under bending deformation.

[0025] Thick, rigid roofs undergo bending deformation under the load of overlying strata and horizontal tectonic stress. To accurately calculate the stored elastic energy, the stress state at any point within the roof is required. This invention employs the theory of elastic thin plates and considers bidirectional stress states, deriving the distribution function of energy density with respect to roof thickness h and overhang length L. Unlike the classic Kirchhoff assumption, this invention introduces an additional shear deformation correction factor to be applicable to rigid roofs with a large thickness-to-span ratio (h / L>0.1).

[0026] Consider the energy density function of shear deformation:

[0027] Assume the top plate is a rectangular plate fixed at both ends (take unit length in the width direction), with a uniformly distributed load q (MPa) on its upper surface, and a horizontal structural stress σ along the overhang direction. h and horizontal structural stress σ along the width direction h2 σ is usually taken h2 =λ h σ h , λ h The lateral pressure coefficient is used; the coordinate system is as follows: x is along the exposed direction, with the origin at the fixed end; z is vertically downward, with z=0 representing the mid-surface.

[0028] Stress components:

[0029]

[0030] Bending normal stress:

[0031]

[0032] in, For elastic modulus, The coordinates are the normal coordinates of the mid-plane. Let w(x) be the Poisson's ratio (dimensionless) and w(x) be the deflection function. For a fixed beam under uniformly distributed load, we approximate it as:

[0033]

[0034] In the formula: For surface load, This refers to the exposed length of the roof slab. The thickness of the top plate. Moment of inertia per unit width The cut correction term is the cut correction term;

[0035] Total normal stress:

[0036]

[0037]

[0038] Shear stress (caused by lateral load):

[0039]

[0040] In the formula: Shear force distribution;

[0041] Elastic energy density (energy stored per unit volume):

[0042]

[0043] In the formula: Shear modulus The normal stress is in the x-direction (exposed direction). The normal stress is in the y-direction (width direction). It is the square of the shear stress in the xz plane.

[0044] S4: Define the equivalent crack propagation driving force and introduce the nonlocal fracture criterion.

[0045] Primary or mining-induced fractures in the roof propagate under stress; classical fracture mechanics uses the stress intensity factor K. I With fracture toughness K IC The comparison is used as a crack initiation criterion, but this criterion cannot describe the energy dissipation history during crack propagation; this invention proposes an equivalent crack propagation driving force J. eq It is based on J-integral but performs nonlocal averaging to eliminate the influence of the sharp singular field;

[0046] Nonlocal equivalent driving force

[0047]

[0048] In the formula: The current main crack length is either half-length or full-length (depending on the geometric model), in meters (m); J( For the classical Rice-J integral, for a crack subjected to far-field stress under plane strain conditions, we have:

[0049]

[0050] In the formula: E′ is the plane strain equivalent elastic modulus. It is a Type I (opening) stress intensity factor. The main crack length is ν, where ν is Poisson's ratio and J is J. sh Contributes to the shear component;

[0051] The nonlocal influence radius of step S1 is used as the decay length of the exponential weighting function; The exponential weighting function assigns higher weights to areas closer to the current crack tip (smaller r), while the influence of areas further away decays exponentially; r is the integral variable, representing the offset distance from the current crack tip.

[0052] Physical meaning:

[0053] J eq This can be understood as the average energy release rate within a damage process zone in front of the crack tip, when J eq Achieving the nonlocal fracture toughness J of the material IC nl At that time, the crack begins to propagate in a steady state; where:

[0054]

[0055] In the formula, The initial crack size is represented by this correction term, which reflects the effect of small-scale yield or damage zones on improving fracture toughness.

[0056] Originality Note: Traditional J-integrals only satisfy path independence at the crack tip, but in real rock, due to the presence of the damage zone, the J value depends on the path. This invention introduces an exponentially weighted nonlocal average, which for the first time... The (non-local radius) is embedded in the definition of the driving force, which gives the criterion an inherent length scale, solves the grid dependency problem, and naturally leads to the subsequent energy release rate mutation analysis.

[0057] S5: Constructing the energy release rate G eff ( With crack length Dynamic evolution equations

[0058] The energy release rate G is defined as the system potential energy released per unit area of ​​crack propagation. In the nonlocal damage model, G is not an instantaneous local quantity, but a cumulative effect dependent on the crack propagation history. This invention derives the effective energy release rate G. eff ( The integral differential equation of ) contains both the elastic release part and the damage dissipation part;

[0059] Evolution equation of effective energy release rate

[0060]

[0061] In the formula: For the intermediate length of crack propagation, Let G0 be the weighting function. Let be the elastic nominal energy release rate, assumed to be given by elasticity when the material is undamaged; for a top plate subjected to bending and compression, the following is derived:

[0062]

[0063] In the formula: For horizontal structural stress, Y(L / ) is the crack closure influence coefficient. ) is a geometric correction factor for a finite-width plate. (Empirical fitting polynomial); For cumulative damage dissipation, it represents the crack length from its initial length. 0 extended The energy consumed in the damage process region during the process is expressed as:

[0064]

[0065] w(D) has been defined in step S2. This is the location of the crack tip. The thickness direction coordinates at the crack tip; For memory kernel function, The memory kernel function characterizes the impact of historical crack propagation on the current energy release rate; in this invention, it is chosen as:

[0066]

[0067] in, Let ξ be the length of the memory (taken as 0.5m, on the same order of magnitude as the thickness of the top plate), and ξ be the relative distance variable. ; 0 represents the initial crack length (measured or assumed to be 0.05m in step S1).

[0068] This equation shows that the true energy release rate G eff The value is less than the elastic solution G0 because some energy is dissipated by the damaged area; but more importantly, when crack propagation accelerates, the historical dissipation term affects the current G. eff The "hindrance" effect weakened, leading to G eff A jump occurs near the critical point; this is the theoretical source of the abrupt change in energy release rate.

[0069] Innovation: This step introduces the memory kernel function into the energy release rate evolution for the first time, borrowing the constitutive equation form from viscoelasticity and applying it to the fracture process. This enables the model to describe the historical dependence of crack propagation rate, providing a time (or path) cumulative effect for subsequent calculations of mutation factors.

[0070] S6: Calculate the second derivative of energy release rate with respect to crack length to reveal precursor signals of abrupt changes.

[0071] In classical catastrophe theory, the critical point of system instability corresponds to the third derivative of the potential energy function being zero or the first derivative of the state variables approaching infinity. This invention does not directly use potential energy, but instead analyzes the energy release rate G. eff ( ) as crack length The function; when the system approaches instability, dG eff / d It increases dramatically, while d 2 G eff / d 2 It will change from a negative value to a positive value, producing a characteristic "inflection point," which is a precursor signal of a sudden change;

[0072] Theoretical formula: First and second order sensitivity of energy release rate

[0073] First, regarding the evolution equation in step S5... Differentiate:

[0074]

[0075] In the formula, dG0 / d The growth rate of the elastic nominal energy release rate is obtained by explicitly differentiating G0 in step S5; using Leibniz's law, we get:

[0076]

[0077] in: This is a weighting coefficient representing the location of the crack tip itself.

[0078] Find the second derivative:

[0079]

[0080]

[0081] In the formula To remember the second derivative of the kernel function, ,in ;because (ξ) is an even function and takes its maximum value at ξ=0, ∂ (0) / ∂a=0; therefore, the above equation simplifies to:

[0082]

[0083] In the formula, The second-order rate of change of damage dissipation energy with respect to crack length is obtained through numerical difference.

[0084] Criteria for detecting precursors of mutation:

[0085] when When =0, it corresponds to G eff ( The inflection point of the curve; before this point, d 2 G eff / d 2 When d < 0, the curve is convex upwards, and the energy release rate increases more slowly; after this point, d 2 G eff / d 2 When the value is greater than 0, the curve dips downwards, the energy release rate increases rapidly, and the system enters the unstable propagation stage. The crack length corresponding to this inflection point is denoted as . .

[0086] Additional notes on symbols:

[0087]

[0088] S7: Define a new expression for the energy release rate mutation factor Λ (including higher-order gradient terms).

[0089] In existing technologies, the mutation factor is typically defined as the ratio of the peak value to the average value (as mentioned in the background section, λ=G). peak / G pre This definition ignores the abrupt change in the rate of change of energy release rate. This invention proposes a dimensionless abrupt change factor Λ, which simultaneously incorporates both the magnitude jump of the energy release rate and the step change in its rate of change, and introduces a nonlocal gradient term to reflect the severity of the spatial abrupt change;

[0090] Theoretical formula: Multiscale mutation factor Λ

[0091]

[0092] In the formula, G peak This is the peak effective energy release rate at the instant of crack instability propagation (fracture), which is not equal to the static fracture energy G. f Rather, it is the amplified value caused by dynamic effects, which will be specifically calculated in step S8; G pre The average energy release rate during the steady-state propagation stage before instability is taken as the crack length starting from 0.9. c to 0.99 c G within the interval eff The arithmetic mean of which c The critical crack length (satisfying J) eq ( c )=J IC nl); β1 is the amplitude jump sensitivity index, determined by lithology, and its value range is... Initially, β1 = 1.0 is set, and subsequently adjusted through adaptive learning in S12; dG eff / d Let be the derivative of energy release rate with respect to crack length. c − Indicates from less than c The direction is approaching, c + Indicates greater than c The direction approaches (because the crack length jumps instantaneously after fracture, this right derivative is undefined in the classical model, but this invention uses limit extrapolation); β2 is the rate-to-sensitivity index, with a value range of Typically, β² = 0.5 is taken. The Laplace operator for the energy release rate field is calculated near the crack tip; for a two-dimensional problem, Its value reflects G eff The degree of unevenness in spatial distribution; Let the magnitude be the energy release rate gradient. ;ℓ is the radius of nonlocal influence (same as step S1); third term This is called the spatial mutation enhancement factor; when a highly concentrated energy release rate gradient appears in front of the crack tip... A large positive value indicates that the factor is greater than 1, significantly increasing Λ;

[0093] Physical meaning:

[0094] Λ integrates mutation characteristics from three dimensions:

[0095] (1) A jump in energy amplitude;

[0096] (2) Reversal of the rate of change of energy release rate (because before instability dG / d >0 and increasing, the instant of instability is due to the crack jump, dG / d Theoretically, it tends towards infinity, so the ratio is extremely large.

[0097] (3) The singularity of the spatial gradient field is enhanced.

[0098] S8: Establish a peak energy release rate (Gpeak) calculation model that considers dynamic fracture velocity.

[0099] At the moment of top plate failure, the crack propagates at a high speed (up to 0.3-0.9 times the Rayleigh wave velocity of the material). At this time, the inertial effect causes the dynamic stress intensity factor to be significantly higher than the static value, thus releasing more energy than the static fracture energy. Based on Freund's formula in dynamic fracture mechanics, this invention proposes a dynamic amplification factor applicable to rock masses and introduces a method for estimating the crack propagation rate v.

[0100] Dynamic peak energy release rate

[0101]

[0102] In the formula: G static ( c (This refers to the time when the crack length reaches a critical value) c The static effective energy release rate at time, i.e., G eff ( c F(vcr) is the dynamic amplification factor, which is dimensionless. Based on Freund's analytical solution for semi-infinite cracks and modified for application to finite geometries, this invention proposes the following empirical-theoretical hybrid formula:

[0103]

[0104] In the formula, v is the crack propagation velocity (m / s); C R The Rayleigh wave velocity (m / s) is the velocity of the top rock layer. Where μ is the density (kg / m³) 3 ); γ is a material constant that reflects the brittleness of the rock mass; The dimensionless value is 1. For hard rock sandstone, γ is usually between 0.5 and 1.2.

[0105] Crack propagation rate v cr Estimate:

[0106] At the critical instability point, the crack propagation rate is determined by the balance between the energy release rate and the fracture energy; this invention uses the following energy balance equation to solve for v:

[0107]

[0108] In the formula, Let v be the longitudinal wave velocity, and the right side represent the dynamic fracture energy, taking into account the effects. This equation is a transcendental equation, which can be solved using numerical iteration methods (such as Newton's method). Substituting v into F(v) yields G. peak ;

[0109] Innovation: Traditional methods completely ignore the influence of crack propagation rate in quantitative prediction. This invention is the first to quantitatively introduce the amplification effect of dynamic fracture mechanics into the calculation of peak energy release rate, so that Λ has a real physical meaning.

[0110] S9: Derivation of the critical mutation threshold Λ based on the principle of minimum energy consumption c

[0111] Critical threshold Λ c This is the dividing line for determining whether a rockburst has occurred. Existing technologies mostly rely on empirical values ​​or statistical regression, lacking theoretical basis. This invention, based on the principle of minimum energy consumption in non-equilibrium thermodynamics, derives Λ c Explicit expressions for the basic parameters of the rock mass; the principle states that when a system becomes unstable, it always chooses the path with the highest energy release rate, and the critical state corresponds to zero energy consumption with respect to the second variation of the control parameters;

[0112] Theoretical expression of critical mutation factor

[0113]

[0114] In the formula: G f The fracture energy of the material (J / m2) is obtained from step S1; G0( 0) is the elastic nominal energy release rate at the initial crack length, calculated according to the formula in step S5; ratio G f / G0( 0) characterizes the abundance of a material's resistance to crack initiation relative to the current driving force. The larger this ratio, the higher the abrupt change factor required to trigger an impact. Therefore, Λ c Positively correlated with it; The radius of nonlocal influence (m); The increment by which the crack extends from its initial length to the critical length; ratio This reflects the importance of the damage process zone scale relative to the crack propagation distance, when A larger value indicates a wider damage area, requiring a greater energy release rate mutation to overcome dissipation; therefore, Λ c Increase; exp(σ) t / σ c The term σ is an exponential term derived from the Boltzmann factor in the derivation of the principle of minimum energy dissipation; its physical meaning is the tensile strength σ. t Relative to compressive strength σ c The larger the value of σ, the more brittle the rock becomes and the more prone it is to abrupt changes. Therefore, the exponential term is greater than 1 and increases with σ. t / σ c The expression is increased rapidly until its dimension is 1, and all parameters can be obtained experimentally through step S1;

[0115] Derivation points: Starting from the total potential energy Π of the system, considering the irreversibility of crack propagation, establish dissipation... The principle of minimum energy consumption requires It holds true at the critical point; after variational operations, and assuming that the damage evolution satisfies... The form ultimately yields the aforementioned Λ c Expression; Λ c It is a constant that depends solely on the intrinsic properties of the material, rather than an empirically fitted value.

[0116] S10: Propose modified critical conditions considering surrounding rock stiffness and support reaction force.

[0117] The thick, hard roof is not an isolated structure; it is supported by coal seams, immediate roof, and floor above and below it, and the mining area has supports. The stiffness of the surrounding rock (i.e., the restraining force of the surrounding rock mass when the roof bends) and the support reaction force absorb some energy, thus altering the abrupt change in energy release rate at the moment of fracture. Regarding Λ in step S9... c To make corrections, the surrounding rock stiffness coefficient K is introduced. surr Equivalent damping C of support supp ;

[0118] Revised Critical Mutation Factor (Initial Revised Version)

[0119]

[0120] Where: K plate The bending stiffness (N / m) of the top slab itself is given for cantilever or fixed slabs per unit width. (Stiffness at midpoint of fixed beam); K surr The equivalent stiffness of the surrounding rock (N / m) is obtained through in-situ plate pressure tests or numerical inversion; hard rock roof First correction factor ;

[0121] Physical meaning: The greater the stiffness of the surrounding rock, the "harder" the roof system as a whole, and the more concentrated the energy release. Therefore, the critical mutation factor should be reduced (i.e., it is easier to reach the critical point); however, note the factor less than 1 multiplied in the formula, which makes Λ c mod <Λ c C indicates that it is more likely to trigger an impact; supp The equivalent damping coefficient of the support system The pressure relief characteristics of the support and the flow rate of the column safety valve are determined, and can be obtained by integrating the force-contraction hysteresis curve of the hydraulic support; v is the critical crack propagation rate (calculated in step S8); the second correction factor An exponent term less than 1 indicates that the support system dissipates energy through damping, thus raising the critical threshold, because Λ cmod Smaller, and the actual required Λ is easier to achieve; the original criterion was Λ≥Λ. c Triggered impact; corrected Λ c mod A smaller value means that a smaller Λ is needed to trigger the impact, which seems to contradict the intuition that support improves safety; it should be revised to: support absorbs energy, requiring a larger mutation to induce an impact, therefore the criticality factor should be increased; for this purpose, the invention redefines...

[0122] The correct criterion after revision should be:

[0123]

[0124] Thus, the greater the stiffness of the surrounding rock (K) surr (large), Λ c mod Increase; the greater the support damping, the greater Λ c mod The increase also means that a stronger energy release rate mutation is needed to induce an impact, which is consistent with physical reality;

[0125] Final critical condition:

[0126] ;

[0127] Innovation: This step is the first to embed the surrounding rock stiffness and support damping into the critical criteria in an exponential and linear form, making the method adaptable to different geological conditions and support parameters in different mining areas, and has a high degree of engineering adaptability.

[0128] S11: On-site Real-time Calculation Process and Dynamic Early Warning Rules

[0129] Transforming the above theory into an operational field early warning system requires clarifying the timing sequence of data acquisition, parameter updates, Λ calculation, and comparison with the correction threshold. This step designs a five-level early warning mechanism and provides a simplified calculation process to reduce the real-time computing burden.

[0130] S11.1 Data Acquisition and Preprocessing (every 30 minutes)

[0131] Microseismic events within the roof slab were located using a microseismic monitoring system, and crack clusters were identified using a clustering algorithm to estimate the current equivalent crack length. ;

[0132] The exposed length L of the roof is obtained through a mine pressure monitoring system;

[0133] Horizontal structural stress σ is obtained using a borehole stress gauge. h ;

[0134] S11.2 Parameter Update

[0135] Based on the current L, Call G0 in step S5 ( )formula;

[0136] Call dG in step S6 eff / d and d 2 G eff / d 2 (Using the finite difference approximation, there is no need to solve the integral equation in real time; different equations can be pre-calculated.) (Derivative table under / L).

[0137] Call the Λ formula in step S7, where G pre Take G in the past 24 hours eff The moving average (window length 5 sampling points);

[0138] S11.3 Calculate the corrected critical value

[0139] Calculate Λ based on the intrinsic parameters determined in step S1. c (One-time offline calculation);

[0140] Based on the current support status of the mining area (damping C) supp (Dynamic assessment based on stent pressure monitoring) to calculate Λ c mod ;

[0141] S11.4 Warning Level Determination

[0142] Let the ratio be ;

[0143]

[0144] S11.5 Dynamic Feedback Correction

[0145] Each time the roof slab fractures (regardless of whether an impact was induced), record the Λ at the actual fracture point. 实际 The sensitivity indices β1, β2, etc. are updated by Kalman filtering (see step S12) to achieve adaptive learning.

[0146] S12: Verification and Adaptive Parameter Tuning Methods

[0147] In the theoretical model, β1, β2, γ, In the initial stage, empirical or semi-empirical parameters are used; however, as the field progresses and multiple roof collapse events are recorded, adaptive corrections can be made through Bayesian inversion or recursive least squares method to improve forecast accuracy; this step provides a specific online parameter update algorithm.

[0148] S12.1 Definition of the objective function

[0149] For the k-th roof failure event (k=1,2,...), let the critical mutation factor predicted by the model be Λ. c (k) (Theoretical value), Λ at the actual trigger impact 实际 (k) (Obtained from the measured data in step S11); Error defined:

[0150]

[0151] S12.2 Parameter vector to be corrected

[0152]

[0153] Initial values ​​for each parameter: β1(0) = 1.0; β2(0) = 0.5; γ(0) = 0.8 (typical sandstone); ;

[0154] S12.3 Recursive Least Squares Update Formula

[0155] Update parameters each time new event data is obtained:

[0156]

[0157] In the formula: Let be the vector of parameters to be estimated after the k-th step update. The parameter estimates are for the (k-1)th step. Let the observation residual be the one observed at step k. , where is the sensitivity vector, which can be calculated using finite difference, where This is the rupture threshold intensity function; P is the transpose of the sensitivity vector; k For the covariance matrix, update formula initial value ; This is the initial value vector; the recursive formula can adjust the parameters online in real time without storing all historical data.

[0158] S12.4 Convergence Criterion

[0159] After three consecutive events, the parameter change At that point, the parameters are considered to have converged and can be fixed for subsequent predictions;

[0160] S12.5 Verification Test Protocol

[0161] On a laboratory scale, three-point bending or uniformly distributed loading tests were conducted using similar material models (cement, gypsum, and mica powder to simulate the roof slab); acoustic emission probes were deployed to monitor the crack propagation process, and load-displacement curves were measured simultaneously to calculate the experimental G. eff And Λ, compared with theoretical predictions; for field verification, two working faces with similar geological conditions were selected, one of which was used for early warning based on this criterion and risk mitigation measures were taken, and the other was used as a control to count the occurrence rate of rockburst.

[0162] Compared with existing technologies, the critical criterion method for determining rockburst induced by the fracture of a thick, hard roof proposed in this invention has the following technical advantages:

[0163] 1) The physical mechanism is clear and the scientific nature is stronger: This invention no longer simply relies on empirical thresholds of stress or deformation, but starts from the essence of the impact induced by the fracture of a thick and hard top plate - the sudden change in energy release rate - and establishes a rigorous mathematical model based on fracture mechanics to reveal the mechanical mechanism of the impact.

[0164] 2) High predictability and accuracy of early warning: This method monitors the energy release rate during the stable propagation phase of a fracture and can make a judgment before the mutation factor exceeds the critical value at the moment of fracture, thus realizing the transformation from "post-event monitoring" to "pre-event early warning". At the same time, it quantifies the dynamic enhancement effect, avoiding false alarms and missed alarms.

[0165] 3) The parameters have clear physical meaning and strong adaptability: The parameters in the critical criterion λc can all be obtained through standard rock mechanics tests and have clear physical meaning. The differences in roof conditions in different mining areas are directly reflected in the parameter values, making this criterion method have good geological adaptability and promotion value.

[0166] 4) Simple calculation and easy to implement on site: This invention provides analytical calculation formulas. On-site technicians only need to input a few key parameters (roof thickness, overhang length, rock strength, etc.) to quickly calculate the λ value and compare it with λc. There is no need for complex and time-consuming numerical simulation, which makes it easy to develop into portable calculation software or integrate it into the mine safety monitoring system.

[0167] 5) Effective guidance for engineering practice: This criterion method can not only provide early warning, but also guide the evaluation of the effectiveness of pressure relief measures. For example, after blasting to cut the roof, the effective exposed length L of the roof plate is reduced, and the calculated λ value will drop significantly. When it drops below λc, the hazard relief measures can be considered effective, thus forming a closed-loop control of "monitoring-early warning-hazard relief-verification". Detailed Implementation

[0168] The technical solution of the present invention will be further described below with reference to the embodiments.

[0169] The following examples illustrate the specific engineering application of this invention in the Hongqinghe Coal Mine, a deep mine prone to rockbursts. The main coal seams in the Hongqinghe Coal Mine are generally buried at depths exceeding 700 m. Their basic roof is primarily composed of thick, medium- to coarse sandstone from the Middle Jurassic Zhiluo Formation. This structure exhibits strong integrity and high uniaxial compressive strength, representing a typical deep, thick, and hard roof structure. It is highly susceptible to accumulating enormous elastic energy during mining operations, potentially triggering high-energy fracture-type rockbursts.

[0170] In this embodiment, the 3-1103 ultra-long fully mechanized longwall face in the third panel area of ​​the Hongqinghe Coal Mine, which was the first to be mined, was selected as the monitoring object. The average burial depth of this longwall face is H = 740 m, and the basic roof thickness is h = 25.5 m. Core samples were taken from geological boreholes in the transport roadway and return airway, and standard rock mechanics tests were conducted in the laboratory to obtain key physical and mechanical parameters of the thick and hard roof, and an in-situ stress environment database was established. Combined with the intrinsic properties of the brittle medium sandstone in the Hongqinghe Coal Mine, the parameters obtained through indoor uniaxial compression and three-point bending tests and digital image correlation (DIC) observation are shown in Table 1.

[0171] Table 1: Intrinsic Parameter Database of Roof Strata in Hongqinghe Coal Mine 3-1103 Working Face

[0172]

[0173] The collected stiffness tensor and nonlocal influence radius are used to... Substituting 1.2 m into the nonlocal damage gradient model, the thick sandstone roof is considered as a continuous medium containing dispersed mining-induced fractures; its total potential functional... It includes elastic strain energy and damage field gradient dependent energy. The surface energy is utilized, thereby eliminating the stress singularity at the crack tip.

[0174] In response to the large roof thickness-to-span ratio of Hongqinghe Coal Mine ( Due to the characteristics of [the structure / features], the classical Kirchhoff thin-plate theory is no longer applicable. This embodiment introduces a shear deformation correction factor to derive the elastic bending energy density function considering bidirectional tectonic stress. :

[0175]

[0176] By analyzing the deflection function Applying a shear correction term can precisely lock the high-density elastic energy enrichment region on the symmetry plane of the fixed end edge and the center line of the plate, providing accurate data input for the subsequent continuous variation of energy release rate.

[0177] During the continuous advancement of the working face, the primary fractures initiate and accelerate forward under the bending load of mining. This embodiment introduces a non-locally averaged Rice J-integral, setting the attenuation length as... = 1.2 m, thus obtaining the equivalent crack propagation driving force. .

[0178] By analyzing the effective energy release rate An integral-differential equation is established, and a kernel function reflecting the dissipative memory effect of historical damage is introduced. (Here, the characteristic memory length of the Hongqinghe sandstone is taken) In real-time monitoring, the system... Regarding the equivalent crack length Find the second derivative:

[0179]

[0180] When discovered The value changes from negative (curve convex, energy release is hindered by damage) to positive (curve concave, energy release is accelerated), and its second derivative is exactly zero. This means that the physical "inflection point" of the massive roof fracture at the Hongqinghe Coal Mine was precisely captured. This point is the core precursor signal for the energy release rate to change from a "gradual change" to a "sudden change".

[0181] Using the captured critical crack length Calculate the amplitude jump, rate step, and spatial Laplace operator at the moment of instability. This forms a dimensionless mutation factor that comprehensively reflects the multidimensional characteristics of time and space. .

[0182] Meanwhile, based on the principle of minimum energy consumption in nonequilibrium thermodynamics, the theoretical critical abrupt change threshold of the sandstone in the Hongqing River was calculated. Because the working face uses hydraulic supports with high working resistance, the equivalent stiffness of the surrounding rock must be considered. The equivalent damping coefficient of the support The interception effect on energy release. The dynamically adjusted correction criterion formula is defined as:

[0183]

[0184] Based on the in-situ pressure plate test at the 3-1103 working face of Hongqinghe Coal Mine and the real-time monitoring of the working resistance of the hydraulic support, the corrected critical threshold was obtained through calculation. .

[0185] This embodiment introduces the SOS microseismic monitoring system configured at Hongqinghe Coal Mine for multi-dimensional joint verification. The system performs data acquisition and inversion every 30 minutes, and uses the clustering radius of microseismic spatial location event groups and energy dissipation model to estimate the equivalent crack length within the basic roof in real time. .

[0186] During a complete roof pressure cycle as the 3-1103 working face advances to 420 m to 465 m, microseismic data and abrupt change index R( The real-time evolution comparison of ) is shown in Table 2:

[0187] Table 2: Measured data on the evolution of microseismic characteristic parameters and abrupt change indices during the periodic pressure on the working face.

[0188] T+1 420.0 <![CDATA[2.3×10 3 ]]> 12 0.45 0.22 0.12 Green (Safe) T+3 432.5 <![CDATA[4.5×10 4 ]]> 28 1.20 0.58 0.32 Green (Safe) T+5 445.0 <![CDATA[1.8×10 5 ]]> 65 2.65 1.15 0.63 Yellow (Caution) T+7 452.0 <![CDATA[8.9×10 5 ]]> 114 4.10 1.58 0.87 Orange (Warning) T+8 458.5 <![CDATA[3.4×10 6 ]]> 185 5.85 1.76 0.97 Red (critical) T+9 462.0 <![CDATA[1.2×10 7 ]]> 242 7.20 1.95 1.07 Black (Instant)

[0189] Microseismic evolution process and critical criterion verification analysis:

[0190] Steady-state expansion stage (T+1 to T+5): As the working face advances, the massively thick roof begins to be exposed, microseismic events are scattered, and the energy remains below 105 J. The calculated warning index R < 0.6. The system determines that the basic roof is in the steady-state energy storage stage.

[0191] Unsteady-state accelerated evolution (T+7 to T+8): After advancing to 452 m, microseismic events exhibited a highly localized clustering in space (epidermis densely converging towards the fixed supports), with a frequency exceeding 100. At this point, the system detected an inflection point signal where da2d2Geff approached 0, and Λ rapidly increased. At T+8, the R index reached 0.97, triggering a red alert, indicating that the main crack inside the roof had entered an unstable propagation stage, and a sudden change was imminent.

[0192] On-site response and pressure relief inspection: After the red alert was triggered, the mine immediately activated the emergency response plan, stopped the advance of the working face, and quickly carried out deep-hole advance blasting to cut the roof and relieve the danger in the advance roadway.

[0193] Adaptive correction feedback (corresponding to step S12): After the blasting, the equivalent exposed length L of the roof was forcibly shortened from 55m to 28m. In the subsequent roof fracture manifestation, due to the premature release of energy, no large-energy impact disaster occurred on site. The system entered the actual fracture value Λactual = 1.95 into the database and automatically corrected the rate sensitivity index β2 using the recursive least squares (RLS) method, improving the accuracy of subsequent predictions by 8.4%.

[0194] This embodiment powerfully demonstrates that the method can overcome the lag of traditional static stress monitoring. By dynamically fusing the characteristics of sudden changes in energy release rate with microseismic data, it achieves advanced, high-precision, and real-time early warning of deep, thick, and hard roof fracture-type rockburst in the Hongqing River.

[0195] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A critical criterion method for determining rockburst induced by the fracture of a thick, hard roof slab, characterized in that, The critical criterion method includes the following steps: S1: Collect key physical and mechanical parameters of thick and hard roof slabs and establish an in-situ stress environment database. Through field detection and indoor tests, a set of basic parameters that can characterize the energy storage limit, fracture toughness and dynamic response of rock mass were obtained; at the same time, the damage localization coefficient and nonlocal influence radius were determined. These two parameters will be used in the nonlocal damage gradient model in the next step. S2: Establish a roof energy storage model based on nonlocal damage gradients. This step introduces the nonlocal damage gradient theory, treating the thick, hard top plate as a continuous medium containing dispersed cracks, whose damage variables... It depends not only on the strain at that point, but also on the damage state of the surrounding area; the total energy stored in the top plate consists of two parts: elastic strain energy and damage surface energy. Total potential functional under nonlocal damage gradient In the formula: Ω represents the two-dimensional or three-dimensional continuous domain occupied by the top plate; For stress tensor, For the strain tensor, satisfying the constitutive relation ,in Let be the elastic stiffness tensor. It is the component form of the second-order strain tensor; For damage variables, the range of values ​​is... D=1 represents intact rock, and D=1 represents complete destruction. β is the gradient damage modulus , is a material constant, determined by fitting the strain softening curve under uniaxial tension; The radius of nonlocal influence controls the distance of nonlocal interactions between damage. The square of the damage field gradient represents the degree of spatial inhomogeneity of the damage. The energy dissipation function for local damage is usually taken as... (Linear softening) or (Secondary softening), among which for Type fracture energy; this step employs a bilinear form to better match the brittle behavior of hard rock: This formula ensures that when D=1, the fracture energy dissipated per unit volume is The total fracture energy after integration is related to Consistent; The portion on the boundary to which an external force is applied; T i For surface force components; For displacement components; S2 output: Total potential energy of the top plate under any load condition. and its effect on crack length The variational derivative; S3: Derive the analytical formula for the elastic energy density distribution inside the top plate under bending deformation. Thick, hard topslabs undergo bending deformation under the load of overlying strata and horizontal tectonic stress. To accurately calculate the stored elastic energy, it is necessary to obtain the stress state at any point within the plate. This step employs the theory of elastic thin plates and considers the bidirectional stress state to derive the energy density as a function of plate thickness. and hanging length The distribution function was derived and a shear deformation correction factor was introduced to apply it to rigid roofs with large thickness-to-span ratios. ; Consider the energy density function of shear deformation: Assume the top plate is a rectangular plate fixed at both ends, with its upper surface subjected to a uniformly distributed load. Simultaneously, there exists horizontal tectonic stress along the exposed direction. and horizontal structural stress along the width direction ,Pick , The lateral pressure coefficient; coordinates: Along the direction of exposure, the origin is at the fixed support end; Vertically downwards, For the middle surface; Stress components: Bending normal stress: in, For elastic modulus, The coordinates are the normal coordinates of the mid-plane. Poisson's ratio (dimensionless). For a fixed beam under uniformly distributed load, the deflection function is approximately taken as: In the formula: For surface load, This refers to the exposed length of the roof slab. The thickness of the top plate. Moment of inertia per unit width This is a cut correction term; Total normal stress: Shear stress (caused by lateral load): In the formula: Shear force distribution; Elastic energy density (energy stored per unit volume): In the formula: Shear modulus for Directional (exposed direction) normal stress, for Directional (width direction) normal stress, for In-plane shear stress S4: Define the equivalent crack propagation driving force and introduce the nonlocal fracture criterion. Primary or mining-induced fractures in the roof propagate under stress; classical fracture mechanics uses the stress intensity factor. With fracture toughness The comparison is used as a crack initiation criterion, but this criterion cannot describe the energy dissipation history during crack propagation; this step proposes an equivalent crack propagation driving force. It is based on The integral was performed but a nonlocal average was applied to eliminate the effects of the apex singular field; Nonlocal equivalent driving force In the formula: The current main crack length is either half-length or full-length, in units of... ; For classic Integrating, for a crack subjected to far-field stress under plane strain conditions, we have: In the formula: The equivalent elastic modulus of plane strain. for Type (opening type) stress intensity factor, The main crack length It is the square of Poisson's ratio. Contributes to the shear component; For steps The nonlocal influence radius is used as the decay length of the exponential weighting function; The exponential weighting function assigns higher weights to areas closer to the current crack tip, while the influence at a distance decays exponentially. This is the integral variable, representing the offset distance from the current crack tip; This can be understood as the average energy release rate within a damage process zone in front of the crack tip. Achieving non-local fracture toughness of materials At that time, the crack begins to propagate in a steady state; where: In the formula, The initial crack size is represented by this correction term, which reflects the effect of small-scale yield or damage zones on improving fracture toughness. S5: Constructing Energy Release Rate With crack length Dynamic evolution equations Energy release rate Defined as the system potential energy released per unit area of ​​crack propagation, in nonlocal damage models... It is not an instantaneous local quantity, but a cumulative effect dependent on the crack propagation history; this step derives the effective energy release rate. The integral differential equation contains both the elastic release part and the damage dissipation part. Evolution equation of effective energy release rate In the formula: For the intermediate length of crack propagation, For the weight function, Let be the elastic nominal energy release rate, assumed to be given by elasticity when the material is undamaged; for the top plate subjected to bending and compression, the derivation is as follows: Mode For horizontal structural stress, The crack closure influence coefficient is... For a finite-width plate, the geometric correction factor is... ; For cumulative damage dissipation, it represents the crack length from its initial length. Extended to The energy consumed in the damage zone during the process is expressed as follows: in, Already in steps The definition in the Chinese text is as follows: This is the location of the crack tip. The thickness direction coordinates at the crack tip; Let be the memory kernel function, representing the impact of historical crack propagation on the current energy release rate; it is taken as: in, For memory length, For relative distance variables, ; The initial crack length; This equation shows the true energy release rate. Less than the elastic solution This is because some energy is dissipated by the damaged area; but more importantly, as crack propagation accelerates, the historical dissipation term has a greater impact on the current... The hindering effect weakens, leading to A jump occurs near the critical point; this is the theoretical source of the abrupt change in energy release rate. S6: Calculate the second derivative of energy release rate with respect to crack length to reveal precursor signals of abrupt changes. This step does not use potential energy directly, but rather analyzes the energy release rate. Crack length The function; when the system approaches instability, It increased dramatically, and It will change from a negative value to a positive value, producing a characteristic inflection point, which is the precursor signal of a sudden change; First, regarding the steps The evolution equations in Differentiate: In the formula, The growth rate of the elastic nominal energy release rate is determined by the steps. middle Explicit differentiation; using Leibniz's rule, we obtain: in: This is a weighting coefficient representing the location of the crack tip itself. Find the second derivative: In the formula, To remember the second derivative of the kernel function, ,in ;because It is an even function and in Take the maximum value at that point. Therefore, the above formula simplifies to: In the formula, The second-order rate of change of damage dissipation energy with respect to crack length is determined by numerical difference. Precursor criterion for mutation: when When, corresponding The inflection point of the curve; before that point, The curve is convex upwards, indicating a slowdown in the energy release rate; after this point, The curve dips downwards, the energy release rate increases rapidly, and the system enters the unstable propagation stage. The crack length corresponding to this inflection point is denoted as... ; S7: Define the energy release rate mutation factor New expression The mutation factor is usually defined as the ratio of the peak value to the average value. This definition ignores the abrupt changes in the rate of energy release. This step proposes a dimensionless mutation factor. It simultaneously includes both the magnitude jump of the energy release rate and the step jump of its rate of change, and introduces a nonlocal gradient term to reflect the drastic spatial abruptness. Multiscale mutation factors In the formula, The peak effective energy release rate during crack instability propagation is not equal to the static fracture energy. It is not the amplification value caused by dynamic effects; The average energy release rate during the steady-state propagation stage before instability is taken as the crack length starting from 0.

9. to 0.99 Within the range The arithmetic mean of which The critical crack length; The amplitude jump sensitivity index is determined by lithology, and its value range is [not specified]. ; Let be the derivative of energy release rate with respect to crack length. Indicates from less than The direction is approaching, + Indicates greater than The direction is approaching; The rate-to-sensitivity index has a range of values. ; The Laplace operator for the energy release rate field is calculated near the crack tip; for a two-dimensional problem, Its value reflects The degree of unevenness in spatial distribution; Let the magnitude be the energy release rate gradient. ; The third term represents the radius of nonlocal influence. This is called the spatial mutation enhancement factor; when a highly concentrated energy release rate gradient appears in front of the crack tip... A large positive value indicates that the factor is greater than 1, significantly improving performance. ; S8: Establish the peak energy release rate considering dynamic fracture velocity. Computational model At the moment of top plate fracture, the crack propagates at high speed. At this moment, the inertial effect causes the dynamic stress intensity factor to be significantly higher than the static value, thus releasing more energy than the static fracture energy. This step is based on dynamic fracture mechanics. The formula proposes a dynamic amplification factor applicable to rock masses and introduces crack propagation rate. The estimation method; Dynamic peak energy release rate In the formula: To reach the critical value of crack length The static effective energy release rate at that time, i.e. ; This is the dynamic amplification factor, dimensionless; according to For the analytical solution of the semi-infinite crack, and modified to apply to finite geometries, this step proposes the following empirical-theoretical hybrid formula: In the formula, The crack propagation rate is (m / s). The Rayleigh wave velocity (m / s) is the velocity of the top rock layer. ,in Density (kg / m³) 3 ); This is a material constant that reflects the degree of brittleness of the rock mass; Dimensionless, for hard rock sandstone, It is usually between 0.5 and 1.2; Crack propagation rate Estimate: At the critical instability point, the crack propagation rate is determined by the balance between the energy release rate and the fracture energy; this step uses the following energy balance equation for solution. : In the formula, The right side represents the longitudinal wave velocity, and the right side represents the dynamic fracture energy, taking into account the effects. This equation is a transcendental equation and can be solved using numerical iteration methods (such as Newton's method). Substitute Get ; S9: Derivation of the critical mutation threshold based on the principle of minimum energy consumption Based on the principle of minimum energy consumption in non-equilibrium thermodynamics, the following is derived: Explicit expressions for the basic parameters of the rock mass; the principle states that when a system becomes unstable, it always chooses the path with the highest energy release rate, and the critical state corresponds to zero energy consumption with respect to the second variation of the control parameters; Theoretical expression of critical mutation factor In the formula: fracture energy of materials This is obtained from step S1; The elastic nominal energy release rate at the initial crack length is calculated according to the formula in step S5; ratio This ratio characterizes the material's ability to resist crack initiation relative to the current driving force; the larger this ratio, the higher the abrupt change factor required to trigger the impact. Positively correlated with it; nonlocal influence radius ; The increment by which the crack extends from its initial length to the critical length; ratio This reflects the importance of the damage process zone scale relative to the crack propagation distance, when Compared to A larger value indicates a wider damage area, requiring a greater abrupt change in the energy release rate to overcome dissipation. Increase; The term is an exponential term, derived from the Boltzmann factor in the derivation of the principle of minimum energy consumption; S10: Propose modified critical conditions considering surrounding rock stiffness and support reaction force. The thick, hard roof is not an isolated structure; it is supported by coal seams, immediate roof, and floor above and below it, and the mining area has supports. The stiffness of the surrounding rock and the reaction force of the supports absorb some energy, thus altering the abrupt change in energy release rate at the moment of fracture. This relates to step S9. To make corrections, the surrounding rock stiffness coefficient is introduced. Equivalent damping of support Calculate the critical mutation factor . S11: On-site Real-time Calculation Process and Dynamic Early Warning Rules Transforming the above theory into an operational field early warning system requires clarifying the timing sequence of data acquisition, parameter updating, Λ calculation, and comparison with the correction threshold. This step designs an early warning mechanism and provides a simplified calculation process to reduce the real-time computing burden. S11.1 Data Acquisition and Preprocessing Microseismic events within the roof slab were located using a microseismic monitoring system, and crack clusters were identified using a clustering algorithm to estimate the current equivalent crack length. ; The length of the exposed roof is obtained through the mine pressure monitoring system. ; Horizontal structural stress was obtained using a borehole stress gauge. ; S11.2 Parameter Update According to the current , Call step S5 formula; Call step S6 and ; Call step S7 Formula, where Take the past 24 hours The moving average; S11.3 Calculate the corrected critical value Based on the intrinsic parameters measured by S1, calculate ; Based on the current support status of the mining area, damping Dynamic assessment based on stent pressure monitoring, calculation ; S11.4 Warning Level Determination Let the ratio be ; S11.5 Dynamic Feedback Correction Each time the roof slab breaks, record the actual time of breakage. Updated via Kalman filtering , Sensitivity index enables adaptive learning; S12: Verification and Adaptive Parameter Tuning Methods In the theoretical model Empirical or semi-empirical parameters are initially adopted using empirical values; however, as the field progresses and multiple roof collapse events are recorded, adaptive corrections are made through Bayesian inversion or recursive least squares method to improve forecast accuracy; this step provides a specific online parameter update algorithm. S12.1 Definition of Objective Function For the k-th roof failure event (k=1,2,...), let the critical mutation factor predicted by the model be... When the actual impact is triggered ; Define error: S12.2 Parameter vector to be corrected ； S12.3 Recursive Least Squares Update Formula Update parameters each time new event data is obtained: In the formula: Let be the vector of parameters to be estimated after the k-th step update. For the first The parameter estimates of the step, Let the observation residual be the one observed at step k. , where is the sensitivity vector, which can be calculated using finite difference; where , This is the rupture threshold intensity function; This is the transpose of the sensitivity vector; For the covariance matrix, update formula initial value ; This is the initial value vector; the recursive formula can adjust the parameters online in real time without storing all historical data. S12.4 Convergence Criterion After three consecutive events, the parameter change At that point, the parameters are considered to have converged and can be fixed for subsequent predictions; S12.5 Verification Test Protocol On a laboratory scale, three-point bending or uniformly distributed loading tests were conducted using similar material models; acoustic emission probes were deployed to monitor the crack propagation process, while load-displacement curves were measured, and experimental calculations were performed. and The results were compared with theoretical predictions; for field verification, two working faces with similar geological conditions were selected. One face was used for early warning based on this criterion and risk mitigation measures were taken, while the other face was used as a control to statistically analyze the occurrence rate of rockburst.

2. The critical criterion method for determining rockburst induced by the fracture of a thick, hard roof slab according to claim 1, characterized in that, In step S9, the derivation process is as follows: from the total potential energy of the system... Starting from the irreversibility of crack propagation, we establish dissipation... ; The principle of minimum energy consumption requires It holds true at the critical point; after variational operations, and assuming that the damage evolution satisfies... The form ultimately yields the above. expression; It is a constant that depends solely on the intrinsic properties of the material, rather than an empirically fitted value.

3. The critical criterion method for determining rockburst induced by the fracture of a thick, hard roof plate according to claim 1, characterized in that, In step S10, the critical mutation factor is calculated. The steps are as follows: Revised Critical Mutation Factor (Initial Revised Version) In the formula: The bending stiffness (N / m) of the top slab itself is given for cantilever or fixed slabs per unit width. (Stiffness at midpoint of the fixed beam); The equivalent stiffness of the surrounding rock (N / m) is obtained through in-situ plate pressure tests or numerical inversion; hard rock roof First correction factor ; The greater the stiffness of the surrounding rock, the harder the overall roof system, and the more concentrated the energy release; therefore, the critical mutation factor should be reduced. However, note that the factor multiplied by less than 1 in the formula should be used to ensure that... This indicates that it is more likely to trigger an impact; The equivalent damping coefficient of the support system The pressure relief characteristics of the support and the flow rate of the column safety valve are determined by the pressure relief characteristics of the support and can be obtained by integrating the force-contraction hysteresis curve of the hydraulic support. Crack critical propagation rate; second correction factor An exponent term less than 1 indicates that the support system dissipates energy through damping, thus raising the critical threshold; after correction... To become smaller means to be even smaller. This can be triggered immediately, which seems to contradict the intuition that support improves safety; it should be revised to: support absorbs energy, requiring a larger mutation to induce impact, therefore the critical factor should be increased; for this reason, this step is redefined. The correct criterion after revision should be: Thus, the greater the stiffness of the surrounding rock ( big), Increase; the greater the support damping, The increase also means that a stronger energy release rate mutation is needed to induce an impact, which is consistent with physical reality; Final critical condition: 。

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