Metal mine surface subsidence range prediction method and system based on cellular automaton

Abstract

The application discloses a metal mine surface subsidence range prediction method and system based on a cellular automaton, and the method comprises the following steps: constructing a two-dimensional cellular automaton profile model and determining an initial cellular state matrix; updating the matrix according to mining conditions to obtain a cellular state matrix after goaf disturbance; updating the position of a granular body and calculating damage increment based on gravity bias neighborhood to obtain an evolved cellular state matrix; solving and correcting subsidence increment along a vertical column to generate a continuous surface subsidence curve; extracting subsidence characteristic parameters to construct a subsidence discrimination function, and performing cyclic iteration operation, and finally outputting a surface subsidence range prediction result. The application can improve the prediction precision of the surface subsidence range of a caving method metal mine. The application can be widely applied to the technical field of mine geological disaster prediction.

Description

Technical Field

[0001] This invention relates to the field of geological disaster prediction technology in mines, and in particular to a method and system for predicting the extent of surface subsidence in metal mines based on cellular automata. Background Technology

[0002] Due to its high production capacity, low mining costs, and high degree of mechanization, caving has become one of the dominant underground mining techniques in large-scale metal mines both domestically and internationally. This technique is characterized by ore extraction, continuous overburden caving, and gradual surface subsidence. The mining process easily causes large deformations, discontinuous movement, and even penetration of the overlying strata to the surface, forming subsidence pits and fissures. This poses a significant threat to slope stability, surface structures, spoil heaps, and personnel safety. Therefore, accurately predicting the extent and evolution of surface subsidence induced by caving mining is a crucial issue that urgently needs to be addressed in mine safety production and surface land use planning.

[0003] Currently, prediction methods for surface subsidence and collapse induced by caving (and general underground mining) mainly fall into four categories: empirical-semi-empirical methods, mechanical analytical methods, numerical simulation methods, and measurement-inversion methods. Among these, empirical-semi-empirical methods, represented by probability integral methods and typical curve methods, treat surface subsidence as a probabilistic superposition of the effects of mining units. While parameter calibration is simple, they are essentially geared towards gently dipping, continuous subsidence basins and struggle to characterize the steep slope collapses and abrupt failures unique to caving. Mechanical analytical methods, represented by elastic thin-plate theory, limit equilibrium and block theory, and critical granular column theory, provide analytical estimates of surface subsidence or collapse boundaries from the perspective of overburden bending, shearing, or tensile cracking failure. These are static or quasi-static criteria and are insufficient in characterizing the gradual evolution of overburden failure, local damage transmission, and irregular expansion of collapse boundaries. Numerical simulation methods, such as finite element method, finite difference method, and discrete element method, can reproduce stress field evolution, plastic zone expansion, and crack penetration process in detail. However, continuous medium numerical methods suffer from severe mesh distortion and high computational cost when simulating large displacement processes of overburden from continuous to discontinuous and from small deformation to overall collapse. Although the discrete element method can reflect discontinuous characteristics, its particle-level modeling scale is limited and parameter calibration is difficult, making it difficult to quickly predict the collapse range on an engineering scale. Measured-inversion methods, such as physical simulation of similar materials and in-situ monitoring inversion, are mostly used for pattern revelation and model verification, and are difficult to use alone for rapid prediction.

[0004] In summary, existing methods for predicting surface subsidence in metal mines using the caving method mostly focus on fitting results, lacking a description of the caving mechanism and exhibiting poor extrapolation. Very few methods start from the intrinsic mechanism and evolution of surface collapse caused by caving mining to establish a bottom-up prediction model that reflects the gradual expansion of subsidence, resulting in limited accuracy in predicting the extent of surface subsidence and its engineering applicability. Summary of the Invention

[0005] To address the aforementioned technical problems, the present invention aims to provide a method and system for predicting the extent of surface subsidence in metal mines based on cellular automata, which can improve the accuracy of predicting the extent of surface subsidence in metal mines using the caving method.

[0006] The first technical solution adopted in this invention is: a method for predicting the extent of surface subsidence in metal mines based on cellular automata, comprising the following steps: A two-dimensional cellular automaton profile model is constructed based on the dip angle of the ore body, the mining level, the caving boundary, and the topographic line of the caving method mine, and the initial cellular state matrix is ​​determined; the cellular states include intact cells, damaged cells, caving cells, and void cells. The mining front range is determined based on the mining sequence and ore extraction intensity, and a goaf disturbance term is generated. The goaf state is updated on the initial cell state matrix. The complete cells within the mining front range are converted into void cells according to the extraction probability to obtain the cell state matrix after goaf disturbance. Based on the gravity bias neighborhood, the cell state matrix after the goaf disturbance is updated to separate body position, the probability of candidate cells migrating to target void cells is calculated, the overburden damage increment is calculated and the cell damage and collapse state are updated to obtain the evolved cell state matrix. The settlement is calculated for the evolved cellular state matrix along the vertical columns at each horizontal position on the ground surface. The surface settlement increment is obtained by combining the void defect, caving compaction and damage accumulation. The surface settlement increment is corrected by the horizontal coordination term to obtain the continuous surface settlement curve. Subsidence characteristic parameters are extracted from continuous surface subsidence curves. A surface collapse discrimination function is constructed by combining the degree of surface cell damage to determine the scope of surface collapse influence. The process is repeated iteratively until the target number of mining steps is reached or the collapse range and subsidence curve stabilize, thus obtaining the final predicted result of the surface collapse range.

[0007] Furthermore, the step of constructing a two-dimensional cellular automaton profile model and determining the initial cellular state matrix specifically includes: Based on the two-dimensional cellular automata profile model, each cell is characterized by a quadruple consisting of sinking, stress and stability indices to obtain a set of multi-attribute states for a single cell. The appropriate neighborhood type is selected based on the degree of anisotropy of the rock mass, and the suitable neighborhood configuration is determined; the neighborhood type includes at least one of Moore neighborhood, Von Neumann neighborhood and extended Moore neighborhood; The cell space is initialized by combining the set of multi-attribute states of a single cell with the adapted neighborhood configuration, and the initial cell state matrix is ​​determined.

[0008] Furthermore, the neighborhood type specifically includes: When using Moore neighborhood, the effective range of the preset neighborhood radius is defined according to the relative position of the cells, and a two-dimensional 8-neighborhood set of the target cell is obtained. When using the extended Moore neighborhood, spatial partitioning is performed based on the relative position of the cell and the target cell, resulting in three types of partitioned neighborhoods: upper neighborhood, lateral neighborhood, and lower neighborhood. The upper neighborhood is used to control the downward compensation of voids in the ore and rock mass, the lateral neighborhood is used to control horizontal shear expansion, and the lower neighborhood is used to describe the upward movement of voids and local backfilling.

[0009] Furthermore, the step of converting complete cells within the mining front range into void cells according to the extraction probability to obtain the cell state matrix after the goaf disturbance specifically includes: Construct a two-dimensional cell local state transition matrix to obtain a cell full state transition probability framework; The state transition probability framework is assigned probability values ​​to determine six types of state transition probabilities: complete to damage, complete to collapse, complete to gap, damage to collapse, collapse to gap, and gap to collapse, resulting in a quantified set of state transition probabilities. By combining the extraction coefficient and the mining front range, the state transformation of complete cells within the range is performed according to the quantified state transition probability set, and the cell state matrix after the goaf disturbance is obtained.

[0010] Furthermore, the step of calculating the probability of a candidate cell migrating to the target gap cell specifically includes: Based on the spatial position of the candidate cell relative to the target void cell, a basic neighborhood weight matrix with gravity bias is obtained by assigning basic weights. By combining the dip angle of the ore body, the direction of the dominant joints, and the difference between the hanging wall and footwall, the basic neighborhood weight matrix is ​​anisotropically corrected to obtain the corrected neighborhood weight matrix. The set of probability values ​​for the migration of candidate cells to target gap cells is obtained by normalizing the calculation based on the corrected neighborhood weight matrix, the elevation difference between candidate cells and target gap cells, and the gravity bias coefficient.

[0011] Furthermore, the step of calculating the overburden damage increment and updating the cellular damage and collapse state specifically includes: The void exposure coefficient is obtained by statistically analyzing the proportion of void cells in the neighborhood to the total number of neighboring cells. By combining the neighborhood damage transmission weight, the local instability function, and the structural anisotropy influence term with the void exposure coefficient, the overburden damage increment is obtained. The incremental damage of the overburden is added to the original damage variable and the upper limit is truncated to update the cell damage and collapse status.

[0012] Furthermore, after the step of updating cell damage and fall status, the following steps are also included: The damage variable of the cell and the void exposure coefficient are compared with the corresponding critical thresholds to obtain the threshold determination results; When the threshold determination result satisfies the condition that the damage variable or the void exposure coefficient reaches the corresponding threshold, the intact cell or the damaged cell is transformed into a collapsed cell, and the updated collapsed cell state matrix is ​​obtained.

[0013] Furthermore, the step of calculating the settlement of the evolved cellular state matrix using vertical columns at various horizontal positions along the land surface, combining void defect, caving compaction, and damage accumulation to obtain the surface settlement increment, and then correcting the surface settlement increment using a horizontal coordination term to obtain a continuous surface settlement curve, specifically includes: By performing component statistics on the evolved cell state matrix along the vertical columns at various horizontal positions on the Earth's surface, three types of settlement components were obtained: void deficit, caving compaction, and damage settlement. The weighted summation of the three types of settlement components yields the surface settlement increment at each horizontal position. A horizontal coordination term is introduced to smooth the surface subsidence increment at each horizontal location, eliminating abrupt subsidence changes at adjacent points and obtaining a continuous surface subsidence curve.

[0014] Furthermore, the step of extracting subsidence characteristic parameters from continuous surface subsidence curves and constructing a surface collapse discriminant function in conjunction with the degree of surface cell damage to determine the scope of surface collapse influence specifically includes: Differential calculations were performed based on continuous surface subsidence curves to obtain three types of subsidence characteristic parameters: surface subsidence amount, surface subsidence gradient, and surface subsidence curvature. The three types of settlement characteristic parameters and surface cell damage values ​​were normalized to obtain four types of normalized judgment ratios. The maximum value among the four normalized judgment ratios is selected to construct the surface collapse discrimination function. When the value of the surface collapse discrimination function is not less than 1, the corresponding surface location is determined to be within the collapse influence range. The collapse boundary and collapse width of the current mining step are obtained, and the surface collapse influence range is determined.

[0015] The second technical solution adopted in this invention is: a cellular automata-based system for predicting the extent of surface subsidence in metal mines, comprising: The first module is used to construct a two-dimensional cellular automaton profile model based on the dip angle of the ore body, the mining level, the caving boundary and the topographic line of the caving method mine, and to determine the initial cellular state matrix; the cellular state includes intact cells, damaged cells, caving cells and void cells. The second module is used to determine the mining front range based on the mining sequence and ore extraction intensity and generate a goaf disturbance term. It updates the goaf state of the initial cell state matrix, converts the complete cells within the mining front range into void cells according to the extraction probability, and obtains the cell state matrix after goaf disturbance. The third module is used to update the granular position of the cell state matrix after the goaf disturbance based on the gravity bias neighborhood, calculate the probability of the candidate cell migrating to the target void cell, calculate the overburden damage increment and update the cell damage and collapse state to obtain the evolved cell state matrix. The fourth module is used to calculate the settlement of the evolved cell state matrix along the vertical columns at various horizontal positions on the ground surface. It combines the void deficit, caving compaction and damage accumulation to obtain the surface settlement increment. The surface settlement increment is corrected by the horizontal coordination term to obtain the continuous surface settlement curve. The fifth module is used to extract settlement characteristic parameters from the continuous surface settlement curve, construct a surface collapse discrimination function in combination with the degree of surface cell damage to determine the scope of surface collapse influence, and repeat the iteration until the target number of mining steps or the collapse range and settlement curve are stable, so as to obtain the final surface collapse range prediction result.

[0016] The beneficial effects of the method and system of this invention are as follows: This invention discretizes the ore and rock area of ​​the caving method into four cellular states: intact, damaged, collapsed, and void. It drives the global evolution with local rules and can reflect the internal mechanism of the gradual expansion of the caving front, the transmission of overlying damage, and the self-organized evolution of the collapse from bottom to top. It solves the problem that existing methods are difficult to characterize the steep slope collapse and abrupt damage unique to the caving method, and improves the accuracy and engineering applicability of predicting the surface collapse range of metal mines using the caving method. Attached Figure Description

[0017] Figure 1 This is a flowchart of the steps of the method for predicting the extent of surface subsidence in metal mines based on cellular automata in this invention. Figure 2 This is a structural block diagram of the metal mine surface subsidence range prediction system based on cellular automata of the present invention; Figure 3 This is a schematic diagram of the method for predicting the extent of surface subsidence in metal mines using the caving method, provided in a specific embodiment of the present invention. Figure 4 This is a schematic diagram of the cell space of the collapse method provided in a specific embodiment of the present invention; Figure 5 This is a schematic diagram of the cell state transition process provided in a specific embodiment of the present invention. Detailed Implementation

[0018] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments. The step numbers in the following embodiments are only for ease of explanation and do not limit the order of the steps. The execution order of each step in the embodiments can be adapted according to the understanding of those skilled in the art.

[0019] Reference Figure 1 This invention provides a method for predicting the extent of surface subsidence in metal mines based on cellular automata. The method includes the following steps: S100. Construct a two-dimensional cellular automaton profile model based on the dip angle of the ore body, mining level, caving boundary and topographic line of the caving method mine, and determine the initial cellular state matrix; the cellular state includes intact cells, damaged cells, caving cells and void cells. In this embodiment, a two-dimensional cellular automaton profile model is established based on the dip angle of the ore body, the mining level, the caving boundary, and the topographic line of the caving method mine, and the cell size is determined. , and time step And initialize the cell state matrix; the cell states include intact cells, damaged cells, collapsed cells and void cells.

[0020] S110. Based on the two-dimensional cellular automata profile model, each cell is characterized by a quadruple consisting of sinking, stress and stability indices to obtain a set of multi-attribute states of a single cell. S120. Select the corresponding neighborhood type according to the degree of rock mass anisotropy, and determine the suitable neighborhood configuration; the neighborhood type includes at least one of Moore neighborhood, Von Neumann neighborhood and extended Moore neighborhood; Specifically, when using Moore neighborhood, the effective range of the preset neighborhood radius is defined according to the relative position of the cells to obtain a two-dimensional 8-neighborhood set of the target cell; when using extended Moore neighborhood, spatial partitioning is performed according to the relative position of the cell and the target cell to obtain three types of partitioned neighborhoods: upper neighborhood, lateral neighborhood, and lower neighborhood; wherein, the upper neighborhood is used to control the downward compensation of voids in the ore and rock granules, the lateral neighborhood is used to control horizontal shear expansion, and the lower neighborhood is used to describe the upward movement of voids and local backfilling.

[0021] In this embodiment, the cells are also characterized by a quadruple consisting of subsidence, stress, and stability indices; the neighborhood type of the two-dimensional cellular automata profile model includes at least one of Moore neighborhood, Von Neumann neighborhood, and extended Moore neighborhood, which are respectively applicable to isotropic media, layered anisotropic rock masses, and deep-buried large collapse voids.

[0022] When using Moore neighborhood, the neighborhood radius is determined based on the relative positions of the cells. The target cell has a two-dimensional 8-neighborhood. When using the extended Moore neighborhood, the neighborhood is divided into upper neighborhood, lateral neighborhood and lower neighborhood according to the relative position of the cell and the target cell. The upper neighborhood is used to control the downward compensation of voids in the ore and rock granules, the lateral neighborhood is used to control the horizontal shear expansion, and the lower neighborhood is used to describe the upward movement of voids and local backfilling.

[0023] S130. Initialize the cell space by combining the set of multi-attribute states of a single cell with the adapted neighborhood configuration, and determine the initial cell state matrix.

[0024] A two-dimensional cellular automaton profile model was established based on the dip angle of the ore body, the mining level, the caving boundary, and the topographic line of the caving method mine, and the cell size was determined. , and time step And initialize the cell state matrix.

[0025] Specifically, in the context of caving in metal mines, cellular automata consist of cells (intact ore, ore fragments, or void units) and cellular spaces (caving ore regions, such as...). Figure 4 (as shown), neighbors (nearest cells) ), cell evolution rules (mineral and rock damage, migration state transformation functions) and cell states ( This embodiment employs a two-dimensional cellular automaton of ore and rock, facilitating comparison with other collapse prediction methods on a two-dimensional scale. The evolution rule is a dynamic function, i.e., a state transition function, that determines the next state of a cell based on its current state and the states of its neighbors. ; In the above formula, Represents the state transition function (evolution rule); express time The state of the cell; express time The state of a cell's neighboring cells. A mineral-rock cellular automaton can be generalized to a quadruple, namely: ; In the above formula, The subsidence amount is in meters (m). Stress (MPa); This is a stability indicator.

[0026] In this embodiment, the rock mass in the collapse zone is discretized into four cellular states: intact cells (s=0), damaged cells (s=1), collapse cells (s=2, mobile loose material), and porous cells (s=3). Surface subsidence is not considered an independent cellular state, but rather the subsidence range is determined by the surface subsidence discriminant function. Representation. The meaning of each state is shown in Table 1.

[0027] Table 1. Definition of Cell States ; Different neighborhood types are selected based on the degree of rock mass anisotropy: Moore neighborhood is suitable for isotropic media, Von Neumann neighborhood is suitable for layered anisotropic rock masses, and extended Moore neighborhood is suitable for deeply buried large collapse voids (with a large influence radius). The correspondence between cellular automata elements and physical properties is shown in Table 2.

[0028] Table 2. Correspondence between cellular automata elements and physical structures ; In this embodiment, the Moore neighborhood is used as the basic neighborhood for the caving method ore and rock region. At that time, cell The two-dimensional 8-neighborhood is: ; When a wider overlying disturbance zone or non-local damage transmission needs to be considered, an extended Moore neighborhood can be used: ; Based on the relative positions of the cell and the target cell, the neighborhood can be divided into the upper neighborhood. Lateral Neighborhood and lower neighbor : ; The upper neighborhood primarily controls the downward compensation of voids in the ore-rock mass, the lateral neighborhood primarily controls horizontal shear propagation, and the lower neighborhood is mainly used to describe the upward movement of voids and local backfilling. For the target void cell... The basic weight matrix of the candidate migrant cells can be expressed as: ; In the above formula, the first row of the matrix corresponds to the candidate cells above and diagonally above the target cell, the second row corresponds to the candidate cells in the same layer, and the third row corresponds to the candidate cells below and diagonally below the target cell. The weight is shifted vertically downwards; The weight is shifted diagonally downwards; For lateral expansion weights; This represents the weights for the reverse effect. This matrix reflects the characteristic of ore-rock mass preferentially migrating from the upper part to the lower voids under gravity. Considering the dip angle of the ore body, dominant joints, and the difference between the hanging wall and footwall, the basic weights are anisotropically corrected: ; In the above formula, The corrected neighborhood weights; Basic weights; as candidate cells Pointing to target cell The direction vector; The unit vector is the direction of the dominant structural surface; , and These are the structural plane, hanging wall offset, and fault influence coefficients, respectively, and their precise selection depends on experiments and experience. and These are the indication functions for the hanging wall direction and the fault influence, respectively.

[0029] S200. Determine the mining front range based on the mining sequence and ore extraction intensity and generate a goaf disturbance term. Update the goaf state of the initial cell state matrix. Convert the complete cells within the mining front range into void cells according to the extraction probability to obtain the cell state matrix after goaf disturbance. In this embodiment, the mining front range is determined based on the mining sequence and ore extraction intensity, a goaf disturbance term is generated, and the complete cells within the mining front range are converted into void cells according to the extraction probability.

[0030] S210. Construct a two-dimensional cell local state transition matrix to obtain a cell full state transition probability framework. S220. Assign probability values ​​to the state transition probability framework and determine the six types of state transition probabilities: complete to damage, complete to collapse, complete to gap, damage to collapse, collapse to gap, and gap to collapse, to obtain a quantified set of state transition probabilities. Specifically, the transition relationship between cell states is described by a two-dimensional cell local state transition matrix, which includes the probability of an intact cell transforming into a damaged cell, the probability of an intact cell transforming into a collapsed cell, the probability of an intact cell transforming into a gap cell, the probability of a damaged cell transforming into a collapsed cell, the probability of a collapsed cell transforming into a gap cell, and the probability of a gap cell transforming into a collapsed cell.

[0031] S230. Combining the extraction coefficient and the mining front range, the state transformation of complete cells within the range is performed according to the quantified state transition probability set to obtain the cell state matrix after the goaf disturbance.

[0032] In this embodiment, the "mining" rule is an externally driven rule: if a complete cell falls on the mining front... Inside, the probability of extraction is used. It becomes a gap (0→3). When When a cell is located within an ore extraction or caving mining area, the cell transforms into a void cell. The extraction probability is: ; In the above formula, The probability of a complete mineral-rock cell transforming into a void cell; This is the extraction coefficient, which is related to the segment height, ore extraction intensity, and mining step distance. In practice, it is usually taken as 70% to 90%.

[0033] The local state transition matrix of a two-dimensional cell is ; In the above formula, For completeness → probability of damage; For completeness → probability of falling; The probability of mining disturbance leading to integrity → void; Damage → probability of falling; The probability of a cell migrating out and forming a gap (migrating → gap); This represents the probability that a gap will be filled by a piece of loose material (gap → loose material). Column 1 indicates the destination of intact cells, column 2 indicates the destination of damaged cells, column 3 indicates the destination of loose cells, and column 4 indicates the destination of gap cells. All four columns conform to the normalization requirements of the Markov transition matrix. The cell state transition process is as follows: Figure 5 As shown.

[0034] S300. Based on the gravity bias neighborhood, the cell state matrix after the goaf disturbance is updated with the position of the loose material, the probability of the candidate cell migrating to the target void cell is calculated, the overburden damage increment is calculated and the cell damage and collapse state are updated to obtain the evolved cell state matrix. In this embodiment, based on the gravity bias neighborhood, the probability of candidate cells migrating to target void cells is calculated. The positional state of ore-rock granular cells and void cells is updated according to the migration probability. The overburden damage increment is calculated based on the neighborhood void exposure coefficient, neighborhood damage transmission weight, local instability function, and structural anisotropy influence, and the cell damage state is updated. When the damage variable or void exposure coefficient reaches the corresponding threshold, the intact cell or damaged cell is converted into a collapse cell.

[0035] S310. Calculate the probability of a candidate cell migrating to the target gap cell; Specifically, basic weights are assigned based on the spatial position of candidate cells relative to target void cells to obtain a basic neighborhood weight matrix for gravity bias; anisotropic correction is performed on the basic neighborhood weight matrix by combining the dip angle of the ore body, the direction of the dominant joint, and the difference between the hanging wall and footwall to obtain a corrected neighborhood weight matrix; normalization calculation is performed based on the corrected neighborhood weight matrix, the elevation difference between candidate cells and target void cells, and the gravity bias coefficient to obtain a set of probability values ​​for the migration of candidate cells to target void cells.

[0036] The probability of a candidate cell migrating to a target void cell is calculated based on the neighborhood weight of the candidate cell, the elevation difference between the candidate cell and the target void cell, and the gravity bias coefficient. The neighborhood weight is anisotropically corrected based on the dip angle of the ore body, the direction of the dominant joint, and the difference between the hanging wall and footwall.

[0037] In this embodiment, the probability of candidate cells migrating to target void cells is calculated based on the gravity bias neighborhood, and the positional state of the ore-rock granular cells and void cells is updated according to the migration probability.

[0038] The "migration" rule is a gravity-driven movement rule: if there is a falling cell (S=2) above a gap cell (S=3) (in the opposite direction of gravity), then the two cells move according to the gravity offset probability. Swap positions: The fall into the gap, the gap moves up one space ( Candidate cells (s=2) To the interstitial cell The probability of migration is: ; This rule can achieve equivalent simulation of the downward migration of ore and rock granules and the upward migration of voids in a two-dimensional profile.

[0039] In the above formula, and These are the elevations of the candidate cell and the target gap cell, respectively. The height of a single cell as specified in the model; This is the gravity offset coefficient; For candidate cells in The transferability probability at time step; This represents the position of the candidate cell in the physical space matrix.

[0040] The local state transition of a single cell can be written as: ; Expanding all cells within the two-dimensional profile in column-first or layer-first order yields the global state matrix: ; The two-dimensional global state evolution can be represented as: ; In the above formula, It is a sparse global transition matrix assembled from two-dimensional neighborhood transition relations; This refers to the external disturbances caused by mining progress, ore extraction, and boundary conditions.

[0041] S320. Calculate the overburden damage increment and update the cell damage and collapse status.

[0042] Specifically, the proportion of void cells in the neighborhood to the total number of neighboring cells is used to obtain the void exposure coefficient; the void exposure coefficient is then weighted and summed with the neighborhood damage transmission weight, the local instability function, and the structural anisotropy influence term to obtain the overburden damage increment; the overburden damage increment is then added to the original damage variable and truncated at the upper limit to update the cell damage and collapse status.

[0043] The overburden damage increment is calculated by weighting the void exposure coefficient, the neighborhood damage transmission term, the local instability function, and the structural anisotropy influence term; the void exposure coefficient is calculated based on the proportion of void cells in the neighborhood to the total number of neighborhood cells.

[0044] In this embodiment, the overburden damage increment is calculated based on the neighborhood void exposure coefficient, neighborhood damage propagation weight, local instability function, and structural anisotropy influence, and the cell damage state is updated; when the damage variable or void exposure coefficient reaches the corresponding threshold, the intact cell or damaged cell is converted into a collapse cell.

[0045] Specifically, the "damage-drop" rule includes: if the neighborhood void exposure E of an intact (S=0) cell reaches a threshold... And the damage accumulates under shear stress. Reaching the threshold If the rock mass cell is damaged but has not yet collapsed, and if the voids are not sufficiently exposed and there is a lack of space for movement, then it is transformed from a damaged cell into a collapsed cell (1→2). If a complete cell has voids / collapses in its neighborhood, but has not yet reached the collapse threshold ( or If a cell is "damaged" (0→1), then it is considered a damaged cell; if a complete cell has neither gaps nor collapses in its neighborhood, then it remains intact (S=0). Let... For rock mass cells in At time t, the damage factor changes as follows during the transition from intact to damaged: ; In the above formula, You can take the engineering experience value or the tensile strength reduction factor. The critical damage threshold is selected based on engineering experience.

[0046] The increment of overburden damage is jointly determined by void exposure, damage propagation from neighboring areas, local instability, and the influence of structural surfaces: ; In the above formula, This is the void exposure coefficient; Weights are assigned to transfer damage. It is a locally unstable function; This refers to the anisotropy effect term of the structural surfaces; , , and This represents the corresponding influence coefficient.

[0047] Porosity Exposure Coefficient ( The critical void exposure coefficient (selected based on engineering experience) is: ; In the above formula, This is an indicator function; it takes the value 1 if the condition within the parentheses is met, and 0 if the condition is not met. The number of neighboring cells.

[0048] S400, along the vertical columns at each horizontal position on the ground surface, calculate the settlement of the evolved cell state matrix, combine the void deficit, caving compaction and damage accumulation to obtain the surface settlement increment, and correct the surface settlement increment through the horizontal coordination term to obtain the continuous surface settlement curve. In this embodiment, the surface settlement increment is calculated based on void deficit, caving compaction and damage accumulation along vertical columns at various horizontal positions on the ground surface, and the surface settlement curve is updated in conjunction with the horizontal coordination term.

[0049] The surface subsidence increment is calculated by weighting three parts: void deficit subsidence corresponding to void cells within the vertical column, caving compaction subsidence corresponding to caving cells, and damage subsidence corresponding to damage accumulation.

[0050] S410. Along the vertical columns at various horizontal positions on the ground surface, the components of the evolved cell state matrix are statistically analyzed to obtain three types of settlement components: void deficit, caving compaction, and damage settlement. S420. The three types of settlement components are weighted and summed to obtain the surface settlement increment at each horizontal position. S430. A horizontal coordination term is introduced to smooth the surface subsidence increment at each horizontal location, eliminating abrupt subsidence changes at adjacent points and obtaining a continuous surface subsidence curve.

[0051] In this embodiment, the surface settlement increment is calculated based on void deficit, caving compaction and damage accumulation along vertical columns at various horizontal positions on the ground surface, and the surface settlement curve is updated in conjunction with the horizontal coordination term.

[0052] Specifically, in a two-dimensional profile, surface subsidence occurs along the surface line. Calculation. For horizontal position The increase in surface subsidence can be represented by the accumulation of voidage loss, caving compaction, and damage within the vertical column profile as follows: ; In the above formula, The void deficit settlement coefficient; The settlement coefficient for caving compaction; The damage settlement coefficient, Compaction / Residual Porosity Factor of Falling Cells (Characteristic of the remaining compressible space after the compaction of the fragmented and collapsed body).

[0053] To ensure the continuity of the surface settlement curve, a one-dimensional horizontal compatibility term is introduced: ; In the above formula, This is the settlement compatibility coefficient.

[0054] S500: Extract subsidence characteristic parameters from continuous surface subsidence curves, construct a surface collapse discrimination function in combination with the degree of surface cell damage to determine the scope of surface collapse influence, repeat the iteration until the target number of mining steps or the subsidence range and subsidence curve are stable, and obtain the final predicted result of surface collapse range.

[0055] In this embodiment, a surface subsidence discrimination function is constructed based on surface subsidence, subsidence gradient, subsidence curvature, and surface cell damage degree to determine the surface subsidence influence range and obtain the subsidence boundary and subsidence width. The steps are repeated until the target number of mining steps is reached, or the surface subsidence influence range and the surface subsidence curve tend to stabilize, to obtain the predicted result of the surface subsidence range of the caving method metal mine.

[0056] The surface collapse discrimination function is determined based on the maximum value among the following: the ratio of surface subsidence to critical subsidence, the ratio of surface subsidence gradient to critical subsidence gradient, the ratio of surface subsidence curvature to critical curvature, and the ratio of surface cell damage value to surface critical damage value. When the value of the surface collapse discrimination function is not less than 1, the corresponding surface location is determined to have entered the collapse influence range.

[0057] S510. Based on the continuous surface subsidence curve, differential calculations are performed to obtain three types of subsidence characteristic parameters: surface subsidence amount, surface subsidence gradient, and surface subsidence curvature. S520. Normalize the three types of settlement characteristic parameters and the surface cell damage values ​​respectively to obtain four types of normalized judgment ratios. S530. Select the maximum value among the four normalized judgment ratios to construct the surface collapse discrimination function. When the value of the surface collapse discrimination function is not less than 1, it is determined that the corresponding surface location has entered the collapse influence range, and the collapse boundary and collapse width of the current mining step are obtained to determine the surface collapse influence range.

[0058] In this embodiment, a surface subsidence discrimination function is constructed based on the amount of surface subsidence, subsidence gradient, subsidence curvature and the degree of damage to surface cells to determine the scope of surface subsidence influence and obtain the subsidence boundary and subsidence width.

[0059] Specifically, the surface subsidence gradient and curvature are as follows: ; The surface subsidence discrimination function is defined as: ; In the above formula, This is the critical settlement amount; The critical settlement gradient; The critical curvature; This represents the critical damage value for the surface. When... At that time, determine the location on the ground. Entering the area affected by the collapse. The extent of surface subsidence in the two-dimensional profile is as follows ; The corresponding horizontal length of the collapse is: ; If the collapse zone is a continuous interval, then its left and right boundaries can be represented as: ; In the above formula, and These represent the left and right boundaries of the area affected by the collapse in the two-dimensional profile. The width affected by the collapse.

[0060] Repeat the steps until the target number of mining steps is reached, or the area affected by surface subsidence and the surface settlement curve tend to stabilize, to obtain the predicted result of the surface subsidence range of the caving method metal mine.

[0061] like Figure 3 As shown, the specific implementation process of this embodiment is as follows: 1) Establish a two-dimensional xz profile model based on the ore body dip angle, mining level, caving boundary, and topographic line, and determine the size of a single cell. , and time step ; 2) Initialize the two-dimensional cell state, assigning attributes such as ore body, surrounding rock, surface, collapse void, fault, joint, and ore outlet to form an initial state matrix. ; 3) Determined based on mining sequence and ore extraction intensity Generate mining subsidence disturbance item This generates interstitial cells; 4) The probability of mineral-rock mass-void exchange is calculated using a two-dimensional gravity-biased Moore neighborhood, and the states of mineral-rock mass, voids and loosely filled cells are updated. 5) Calculate the overburden damage increment and update the damage state based on void exposure, neighborhood damage propagation, local instability function, and structural surface influence; 6) Calculate the surface settlement increment along the vertical column at each horizontal position, and update the surface settlement curve through a one-dimensional horizontal coordination term; 7) Calculate the surface settlement gradient, curvature, collapse discrimination function and collapse influence range to obtain the left and right boundaries and collapse width of the surface collapse in the two-dimensional profile; 8) Repeat steps 3) to 7) until the target number of mining steps is reached, or the collapse range and settlement curve tend to stabilize. This method can characterize the coupled process of goaf disturbance, void upward movement, overburden damage expansion, and surface subsidence development under caving mining conditions at the profile scale. It is suitable for two-dimensional profile prediction of the surface collapse range in metal mine caving mining. If a complete planar collapse boundary is required, the calculation should be repeated on multiple typical profiles, and boundary extrapolation should be performed in conjunction with engineering geological interpretation.

[0062] In summary, this invention establishes a two-dimensional cellular automaton profile model based on the ore body dip angle, mining level, caving boundary, and topographic lines. This model discretizes the caving-method ore-rock region into four states: intact cells, damaged cells, caving cells, and void cells. The mining front range is determined based on the mining sequence and ore extraction intensity. Intact cells within this range are then converted into void cells according to extraction probability. The probability of candidate cells migrating to target void cells is calculated based on gravity bias neighborhood, updating the positional states of the ore-rock bulk cells and void cells. Finally, based on neighborhood void bursts… The invention calculates the overburden damage increment using the exposure coefficient, neighborhood damage propagation weight, local instability function, and structural anisotropy influence to determine cellular damage and caving state transitions. It also calculates surface subsidence increments along vertical columns and updates the surface subsidence curve. A surface collapse discrimination function is constructed based on surface subsidence, subsidence gradient, subsidence curvature, and surface cellular damage degree to determine the surface collapse impact range. This process is repeated until the target number of mining steps is reached or the collapse range and subsidence curve stabilize, achieving dynamic numerical prediction of the surface collapse range in caving-method metal mines. This embodiment of the invention uses local rules to drive global evolution, reflecting the inherent mechanism of self-organized, step-by-step expansion of collapse. It solves the problem that existing methods struggle to characterize the steep slope collapse and abrupt damage unique to caving-method mining, improving the accuracy and engineering applicability of surface collapse range prediction in caving-method metal mines.

[0063] Therefore, compared with the prior art, the embodiments of the present invention have the following advantages: This embodiment discretizes the ore-rock region of the caving method into four cellular states: intact, damaged, collapsed, and void. Driven by local rules, it allows for global evolution, reflecting the underlying mechanisms of bottom-up expansion of the caving front, transmission of overburden damage, and self-organized subsidence evolution. Compared to empirical-semi-empirical methods, the method provided in this application can characterize the steep slope collapse and abrupt failure unique to the caving method. Compared to mechanical analytical methods, the method provided in this application can reflect the gradual evolution of overburden failure and the irregular expansion of the subsidence boundary. Compared to continuous medium numerical simulation methods and discrete element methods, the method provided in this embodiment has simple calculation rules, clear physical meaning of parameters, and high computational efficiency, facilitating multi-condition comparison and sensitivity analysis, thereby improving the accuracy and engineering applicability of predicting the surface subsidence range in caving-based metal mines.

[0064] Finally, the present invention will be explained and illustrated with reference to specific embodiments: Taking a magnetite mine as an engineering case, under the geometric conditions of 335m overburden thickness, 244m goaf span, and 55° ore body dip angle, the method provided in this embodiment was used to predict the surface subsidence range of the mine under caving mining conditions. The prediction results were compared with those of the probability integral method and the critical granular column theory. The results show that the method provided in this embodiment predicts the average subsidence width. The value is 340m, falling between the values ​​obtained by the probability integral method (631m) and the critical granular column theory (244m). It can reproduce the spoon-shaped asymmetric collapse morphology (higher in the north, lower in the south) observed in actual engineering projects, verifying the effectiveness of the method provided in this application. In the numerical implementation, the settlement coordination coefficient... A value of 0.1 satisfies the stability condition. The dual criteria combined with the rolling window can ensure iterative convergence, and the position exchange mechanism can guarantee the conservation of mass.

[0065] Reference Figure 2 A cellular automata-based system for predicting the extent of surface subsidence in metal mines includes: The first module 201 is used to construct a two-dimensional cellular automaton profile model based on the dip angle of the ore body, the mining level, the caving boundary and the topographic line of the caving method mine, and to determine the initial cellular state matrix; the cellular state includes intact cells, damaged cells, caving cells and void cells. The second module 202 is used to determine the mining front range based on the mining sequence and ore extraction intensity and generate a goaf disturbance term, update the goaf state of the initial cell state matrix, and convert the complete cells within the mining front range into void cells according to the extraction probability to obtain the cell state matrix after goaf disturbance. The third module 203 is used to update the granular position of the cell state matrix after the goaf disturbance based on the gravity bias neighborhood, calculate the probability of the candidate cell migrating to the target void cell, calculate the overburden damage increment and update the cell damage and collapse state to obtain the evolved cell state matrix. The fourth module 204 is used to calculate the settlement of the evolved cell state matrix along the vertical columns at various horizontal positions on the ground surface. The surface settlement increment is obtained by combining the void deficit, caving compaction and damage accumulation. The surface settlement increment is corrected by the horizontal coordination term to obtain the continuous surface settlement curve. The fifth module 205 is used to extract settlement characteristic parameters from the continuous surface settlement curve, construct a surface collapse discrimination function in combination with the degree of surface cell damage to determine the scope of surface collapse influence, and repeat the iteration until the target number of mining steps or the collapse range and settlement curve are stable, so as to obtain the final surface collapse range prediction result.

[0066] The content of the above method embodiments is applicable to this system embodiment. The specific functions implemented in this system embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0067] The preferred embodiments of the present application have been described above with reference to the accompanying drawings, but this is not intended to limit the scope of the embodiments of the present application. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and substance of the embodiments of the present application shall be within the scope of the embodiments of the present application.

Claims

1. A method for predicting the extent of surface subsidence in metal mines based on cellular automata, characterized in that, Includes the following steps: A two-dimensional cellular automaton profile model is constructed based on the dip angle of the ore body, the mining level, the caving boundary, and the topographic line of the caving method mine, and the initial cellular state matrix is ​​determined; the cellular states include intact cells, damaged cells, caving cells, and void cells. The mining front range is determined based on the mining sequence and ore extraction intensity, and a goaf disturbance term is generated. The goaf state is updated on the initial cell state matrix. The complete cells within the mining front range are converted into void cells according to the extraction probability to obtain the cell state matrix after goaf disturbance. Based on the gravity bias neighborhood, the cell state matrix after the goaf disturbance is updated to separate body position, the probability of candidate cells migrating to target void cells is calculated, the overburden damage increment is calculated and the cell damage and collapse state are updated to obtain the evolved cell state matrix. The settlement is calculated for the evolved cellular state matrix along the vertical columns at each horizontal position on the ground surface. The surface settlement increment is obtained by combining the void defect, caving compaction and damage accumulation. The surface settlement increment is corrected by the horizontal coordination term to obtain the continuous surface settlement curve. Subsidence characteristic parameters are extracted from continuous surface subsidence curves. A surface collapse discrimination function is constructed by combining the degree of surface cell damage to determine the scope of surface collapse influence. The process is repeated iteratively until the target number of mining steps is reached or the collapse range and subsidence curve stabilize, thus obtaining the final predicted result of the surface collapse range.

2. The method for predicting the extent of surface subsidence in metal mines based on cellular automata according to claim 1, characterized in that, The step of constructing a two-dimensional cellular automaton profile model and determining the initial cellular state matrix specifically includes: Based on the two-dimensional cellular automata profile model, each cell is characterized by a quadruple consisting of sinking, stress and stability indices to obtain a set of multi-attribute states for a single cell. The appropriate neighborhood type is selected based on the degree of anisotropy of the rock mass, and the suitable neighborhood configuration is determined; the neighborhood type includes at least one of Moore neighborhood, Von Neumann neighborhood and extended Moore neighborhood; The cell space is initialized by combining the set of multi-attribute states of a single cell with the adapted neighborhood configuration, and the initial cell state matrix is ​​determined.

3. The method for predicting the extent of surface subsidence in metal mines based on cellular automata according to claim 2, characterized in that, The neighborhood types specifically include: When using Moore neighborhood, the effective range of the preset neighborhood radius is defined according to the relative position of the cells, and a two-dimensional 8-neighborhood set of the target cell is obtained. When using the extended Moore neighborhood, spatial partitioning is performed based on the relative position of the cell and the target cell, resulting in three types of partitioned neighborhoods: upper neighborhood, lateral neighborhood, and lower neighborhood. The upper neighborhood is used to control the downward compensation of voids in the ore and rock mass, the lateral neighborhood is used to control horizontal shear expansion, and the lower neighborhood is used to describe the upward movement of voids and local backfilling.

4. The method for predicting the extent of surface subsidence in metal mines based on cellular automata according to claim 3, characterized in that, The step of converting complete cells within the mining front area into void cells according to the extraction probability to obtain the cell state matrix after goaf disturbance specifically includes: Construct a two-dimensional cell local state transition matrix to obtain a cell full state transition probability framework; The state transition probability framework is assigned probability values ​​to determine six types of state transition probabilities: complete to damage, complete to collapse, complete to gap, damage to collapse, collapse to gap, and gap to collapse, resulting in a quantified set of state transition probabilities. By combining the extraction coefficient and the mining front range, the state transformation of complete cells within the range is performed according to the quantified state transition probability set, and the cell state matrix after the goaf disturbance is obtained.

5. The method for predicting the extent of surface subsidence in metal mines based on cellular automata according to claim 4, characterized in that, The step of calculating the probability of a candidate cell migrating to the target gap cell specifically includes: Based on the spatial position of the candidate cell relative to the target void cell, a basic neighborhood weight matrix with gravity bias is obtained by assigning basic weights. By combining the dip angle of the ore body, the direction of the dominant joints, and the difference between the hanging wall and footwall, the basic neighborhood weight matrix is ​​anisotropically corrected to obtain the corrected neighborhood weight matrix. The set of probability values ​​for the migration of candidate cells to target gap cells is obtained by normalizing the calculation based on the corrected neighborhood weight matrix, the elevation difference between candidate cells and target gap cells, and the gravity bias coefficient.

6. The method for predicting the extent of surface subsidence in metal mines based on cellular automata according to claim 5, characterized in that, The step of calculating the overburden damage increment and updating the cellular damage and collapse status specifically includes: The void exposure coefficient is obtained by statistically analyzing the proportion of void cells in the neighborhood to the total number of neighboring cells. By combining the neighborhood damage transmission weight, the local instability function, and the structural anisotropy influence term with the void exposure coefficient, the overburden damage increment is obtained. The incremental damage of the overburden is added to the original damage variable and the upper limit is truncated to update the cell damage and collapse status.

7. The method for predicting the extent of surface subsidence in metal mines based on cellular automata according to claim 6, characterized in that, Following the step of updating cell damage and fall status, the following is also included: The damage variable of the cell and the void exposure coefficient are compared with the corresponding critical thresholds to obtain the threshold determination results; When the threshold determination result satisfies the condition that the damage variable or the void exposure coefficient reaches the corresponding threshold, the intact cell or the damaged cell is transformed into a collapsed cell, and the updated collapsed cell state matrix is ​​obtained.

8. The method for predicting the extent of surface subsidence in metal mines based on cellular automata according to claim 7, characterized in that, The step of calculating the settlement of the evolved cellular state matrix using vertical columns at various horizontal positions along the land surface, combining void defect, caving compaction, and damage accumulation to obtain the surface settlement increment, and correcting the surface settlement increment with a horizontal compatibility term to obtain a continuous surface settlement curve, specifically includes: By performing component statistics on the evolved cell state matrix along the vertical columns at various horizontal positions on the Earth's surface, three types of settlement components were obtained: void deficit, caving compaction, and damage settlement. The weighted summation of the three types of settlement components yields the surface settlement increment at each horizontal position. A horizontal coordination term is introduced to smooth the surface subsidence increment at each horizontal location, eliminating abrupt subsidence changes at adjacent points and obtaining a continuous surface subsidence curve.

9. The method for predicting the extent of surface subsidence in metal mines based on cellular automata according to claim 8, characterized in that, The step of extracting subsidence characteristic parameters from continuous surface subsidence curves and constructing a surface collapse discriminant function based on the degree of surface cell damage to determine the scope of surface collapse influence specifically includes: Differential calculations were performed based on continuous surface subsidence curves to obtain three types of subsidence characteristic parameters: surface subsidence amount, surface subsidence gradient, and surface subsidence curvature. The three types of settlement characteristic parameters and surface cell damage values ​​were normalized to obtain four types of normalized judgment ratios. The maximum value among the four normalized judgment ratios is selected to construct the surface collapse discrimination function. When the value of the surface collapse discrimination function is not less than 1, the corresponding surface location is determined to be within the collapse influence range. The collapse boundary and collapse width of the current mining step are obtained, and the surface collapse influence range is determined.

10. A system for predicting the extent of surface subsidence in metal mines based on cellular automata, characterized in that, Includes the following modules: The first module is used to construct a two-dimensional cellular automaton profile model based on the dip angle of the ore body, the mining level, the caving boundary and the topographic line of the caving method mine, and to determine the initial cellular state matrix; the cellular state includes intact cells, damaged cells, caving cells and void cells. The second module is used to determine the mining front range based on the mining sequence and ore extraction intensity and generate a goaf disturbance term. It updates the goaf state of the initial cell state matrix, converts the complete cells within the mining front range into void cells according to the extraction probability, and obtains the cell state matrix after goaf disturbance. The third module is used to update the granular position of the cell state matrix after the goaf disturbance based on the gravity bias neighborhood, calculate the probability of the candidate cell migrating to the target void cell, calculate the overburden damage increment and update the cell damage and collapse state to obtain the evolved cell state matrix. The fourth module is used to calculate the settlement of the evolved cell state matrix along the vertical columns at various horizontal positions on the ground surface. It combines the void deficit, caving compaction and damage accumulation to obtain the surface settlement increment. The surface settlement increment is corrected by the horizontal coordination term to obtain the continuous surface settlement curve. The fifth module is used to extract settlement characteristic parameters from the continuous surface settlement curve, construct a surface collapse discrimination function in combination with the degree of surface cell damage to determine the scope of surface collapse influence, and repeat the iteration until the target number of mining steps or the collapse range and settlement curve are stable, so as to obtain the final surface collapse range prediction result.

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