A method and system for predicting the scope of surface subsidence after backfill mining

Abstract

The present invention belongs to the technical field of mining engineering data processing, and discloses a method and system for predicting the scope of surface subsidence after backfill mining. The method uses a material mechanics method to simplify the analysis of the top rock beam, and obtains a rock beam fracture mechanics model; establishes a separation criterion through the deflection relationship of adjacent rock beams, and then obtains a synchronously moving rock layer group; uses a material mechanics method to judge the initial fracture data; judges the periodic fracture of the rock beam through the periodic fracture data of the rock beam; uses a surface subsidence prediction method under backfill mining conditions to obtain a surface subsidence prediction calculation formula; and performs surface subsidence prediction. Based on the different failure mechanisms of the fracture zone and the slow subsidence zone, the present invention determines the fracture transmission law, obtains the surface subsidence prediction calculation formula, and thus achieves the purpose of predicting the subsidence range. It has the advantages of relatively simple mechanical analysis, relatively accurate prediction results, and is suitable for engineering applications.

Description

Technical Field

[0001] The invention belongs to the technical field of mining engineering data processing, and in particular relates to a method and a system for predicting the scope of surface subsidence after backfill mining. Background Art

[0002] Surface subsidence has significant impacts on the environment and human activities, including land resources, plant growth, water resources and surface buildings. For example, surface subsidence may lead to a decrease in land carrying capacity, affect plant growth, change the distribution of water resources, and even damage surface buildings.

[0003] The invention patent (publication number CN116822328A, publication date 2023.09.29) discloses a method for determining the predicted parameters of surface subsidence in a mine goaf, performing predicted parameter analysis using the probability integral method, obtaining the geological mining condition parameters of the mining face, and reassigning the optimized optimal parameters to the fuzzy neural network model. After training and simulation, the optimal predicted parameters of surface subsidence in a mine goaf are obtained.

[0004] The method commonly used in this type of research is to use elastic mechanics to solve the stress at any point on the beam. However, under backfill mining conditions, the reaction force provided by the backfill has a nonlinear distribution law along the direction of the goaf, which makes the elastic mechanics solution extremely complex and unsuitable for engineering applications. Compared with the elastic mechanics solution, the difference of the material mechanics method is that an additional term in the solution is ignored. The existence of the additional term will make the result more accurate, but when the height-to-span ratio of the beam is smaller, the additional term has less effect on the calculation accuracy of the stress in the beam model. Based on this, it is urgent to develop a method to predict the range of surface subsidence after backfill mining. Summary of the invention

[0005] In order to overcome the problems existing in the related art, the disclosed embodiment of the present invention provides a method and system for predicting the scope of surface subsidence after backfill mining. The present invention uses a material mechanics method to simplify the analysis of the roof rock beam, improves the feasibility of prediction, and expands the scope of application.

[0006] The technical solution is as follows: A method for predicting the scope of surface subsidence after backfill mining, comprising:

[0007] S1. Use material mechanics method to simplify the analysis of the top rock beam and obtain the fracture mechanics model of the rock beam;

[0008] S2. Based on the obtained rock beam fracture mechanics model, a separation criterion is established through the deflection relationship of adjacent rock beams to obtain a synchronously moving rock layer group;

[0009] S3. Based on the obtained synchronously moving rock formation group, before the roof rock beam has its first fracture, the boundary condition is simplified to a fixed-support beam, and the first fracture data is determined using the material mechanics method;

[0010] S4. Based on the initial fracture data, for the periodic fracture of the rock strata in the goaf area, under the same stress state of the rock beam, the periodic fracture of the rock beam is judged by the periodic fracture data of the rock beam to obtain the periodic fracture of the rock beam;

[0011] S5. According to the periodic fracture of the rock beam obtained, based on the different failure mechanisms of the fracture zone and the slow subsidence zone, the surface subsidence prediction method under backfill mining conditions is used to obtain the calculation formula for surface subsidence prediction;

[0012] S6. Surface subsidence prediction is carried out based on the obtained surface subsidence prediction calculation formula.

[0013] In step S1, a rock beam fracture mechanics model is obtained, including:

[0014] (1) The goaf is mined and filled simultaneously, and the interval time between coal seam mining and filling processes is negligible;

[0015] (2) The influence of internal joints and structural surfaces of the rock on the crack propagation path is negligible;

[0016] (3) According to the critical layer theory, the overburden load borne by the rock layer is given by formula (1):

[0017] (1);

[0018] In the formula, is the overburden load carried by the rock strata; is the elastic modulus of the first rock layer above the rock layer in the bedrock, is the elastic modulus of the second rock layer above the rock layer in the bedrock, The first layer above the bedrock The elastic modulus of the rock layer, in MPa; is the bulk density of the first rock layer above the bedrock layer, is the bulk density of the second rock layer above the rock layer in the bedrock. The first layer above the bedrock The unit of bulk density of the rock layer is kN / m 3 ; is the thickness of the first rock layer above the rock layer in the bedrock, is the thickness of the second rock layer above the rock layer in the bedrock, The first layer above the bedrock The thickness of the rock layer, in m;

[0019] (4) For the structural planes existing between all rock layers, the rock beam separation criterion for determining a group of synchronously moving rock layers is given by equation (2) based on the rock layer deflection function:

[0020] (2);

[0021] In the formula, In bedrock The deflection of the rock layer when it is not subjected to the reaction force of filling. From bottom to top in the bedrock The deflection of the rock layer, From bottom to top in the bedrock The maximum deflection of the rock layer when it is not subjected to the backfill reaction force. From bottom to top in the bedrock The maximum deflection of the rock layer; (5) According to the first strength criterion of rock mechanics, the fracture criterion of the rock beam is determined as formula (3):

[0022] (3);

[0023] In the formula, In bedrock The maximum tensile stress of the rock layer, in MPa; In bedrock The tensile strength of the rock layer, in MPa.

[0024] In step S2, a separation criterion is established based on the deflection relationship between adjacent rock beams, including:

[0025] Starting from the immediate top of the coal seam, the rock layers from bottom to top are the 1st to mth rock layers, and the maximum deflection of the rock beam under the condition of only its own gravity is calculated respectively; the deflection curve equation of the beam is formula (4):

[0026] (4);

[0027] In the formula, is the elastic modulus, is the moment of inertia, is the deflection, is the bending moment of the cross section;

[0028] The bending moment of the cross section is given by formula (5):

[0029] (5);

[0030] In the formula, is the maximum load on the upper part of the first layer of rock beam, is the maximum reaction force at the bottom of the first layer of rock beam, is the length of the first layer beam, is the distance from the support origin to the point;

[0031] Substituting equation (5) into equation (4), the maximum deflection value is obtained as equation (6):

[0032] (6);

[0033] In the formula, is the maximum deflection of the first rock layer above the rock layer in the bedrock, is the elastic modulus of the first rock layer above the rock layer in the bedrock, is the maximum load on the upper part of the rock beam, is the maximum reaction force at the bottom of the rock beam, is the length of the beam.

[0034] In step S2, a synchronously moving rock formation group is obtained, including:

[0035] According to formula (2), the position relationship of adjacent rock layers is calculated in sequence until , Layers of rock If there is separation between the layers of rock, Horizon A group of rock layers moving in synchrony.

[0036] In step S3, the initial fracture data is determined using a material mechanics method, including:

[0037] The first group of coordinated rock beam movement According to the key layer theory, the stress boundary condition of the rock beam is as follows:

[0038] (7);

[0039] In the formula, is the length of the first layer beam;

[0040] According to material mechanics, there is formula (8):

[0041] (8);

[0042] In the formula, is the normal stress on the cross section of a rectangular beam during bending deformation, is the bending moment of the cross section, is the distance from the point on the cross section to the neutral axis, is the moment of inertia of the cross section about the neutral axis, is the shear stress on the cross section, is the shear force on the cross section, is the static moment of the area below the horizontal line of the neutral axis on the cross section about the neutral axis, is the cross-section width;

[0043] The expression of the stress component at any point in the rock beam is as follows:

[0044] (9);

[0045] The principal tensile stress and principal compressive stress at any point in the rock beam are expressed as formula (10):

[0046] (10);

[0047] In the formula, is the maximum principal stress, is the minimum principal stress;

[0048] According to equations (9) and (10), the point with the maximum tensile stress inside the rock beam appears at The criterion for the initial fracture of the entire rock beam is expressed as formula (11):

[0049] (11);

[0050] In the formula, is the maximum tensile stress of the first group of rock beams, in MPa; is the tensile strength of the first rock layer in the bedrock, in MPa;

[0051] According to equations (9) to (11), the fracture step distance of the first layer of rock beam is obtained: ; Rock beam fracture angle It is expressed as formula (12):

[0052] (12);

[0053] Break Step Substituting into formula (12), we get the fracture angle of the first fracture of the first layer of rock beam: for:

[0054] (13);

[0055] The height of the fracture zone under this condition is expressed as formula (14):

[0056] (14);

[0057] In the formula, For the The height of the broken rock layer, The height of the fracture zone is developed for filling and mining.

[0058] In step S4, the periodic fracture situation of the rock beam is determined by judging the periodic fracture data of the rock beam, including:

[0059] The first group of synchronously moving rock strata above the goaf roof is taken as the first cantilever beam, and the beam height is , take the midpoint of the boundary close to the coal wall as the origin to establish the coordinate system;

[0060] The reaction force of filling gangue is expressed as formula (15):

[0061] (15);

[0062] The stress state at any point in the cantilever beam is expressed as (16):

[0063] (16);

[0064] In the formula, For the Length of layer beam;

[0065] The ultimate span of the first group of rock beams According to equations (11), (15) and (16), when the fracture criterion is met, the entire rock beam fractures;

[0066] Substituting the stress equation (16) at any point of the rock beam into equation (12), the fracture angle of the first group of rock beams during periodic fracture is obtained as equation (17):

[0067] (17);

[0068] In the formula, is the fracture angle of the first group of rock beams during periodic fracture.

[0069] In step S5, the method for predicting surface subsidence under filling mining conditions includes:

[0070] From a mechanical point of view, the movement process of the slow-sinking zone can be ideally divided into three stages: slip, cracking, and shearing. The lower rock layer slips at the edge, causing the rear edge of the loose layer on the surface to crack and expand downward. The shear stress of the middle rock layer gradually accumulates with the development of the slip section and the cracking section. When the rock layer in the slow-sinking zone is a non-homogeneous random particle, tensile shear failure occurs. The rock layer in the slow-sinking zone moves along the horizontal plane at an angle of 45°+ φ / 2, shear failure occurs, eventually forming a funnel-shaped settlement boundary curve in the settlement area.

[0071] In step S5, the surface subsidence prediction method under backfill mining conditions is used to obtain a surface subsidence prediction calculation formula, including:

[0072] Based on the different failure mechanisms of the fracture zone and the slow subsidence zone, the surface subsidence prediction method under backfill mining conditions is used to derive the surface subsidence prediction formula (18) when the key layer breaks:

[0073] (18);

[0074] In the formula, is the estimated length of surface subsidence, is the length of the goaf, is the initial fracture angle of the rock layer, is the fracture angle of the rock beam during periodic fracture, is the internal friction angle of the rock formation, is the rock layer thickness, is the number of co-moving rock layers in the fracture zone, The rock layer is located in layer, is the number of layers of the main key layer, The total number of rock layers.

[0075] Another object of the present invention is to provide a system for predicting the scope of surface subsidence after backfill mining, the system implements the method for predicting the scope of surface subsidence after backfill mining, the system comprising:

[0076] The basic model and hypothesis module is used to simplify the analysis of the roof rock beam using the material mechanics method to obtain the rock beam fracture mechanics model;

[0077] The layer transfer criterion module, based on the obtained rock beam fracture mechanics model, establishes the delamination criterion through the deflection relationship of adjacent rock beams to obtain the synchronously moving rock layer group.

[0078] The rock beam initial fracture data judgment module uses the material mechanics method to judge the initial fracture data based on the obtained synchronously moving rock layer group and the boundary conditions are simplified to a fixed-support beam before the roof rock beam first fractures;

[0079] The rock beam periodic fracture data judgment module, based on the initial fracture data, targets the periodic fracture of the rock strata in the goaf area, and determines the periodic fracture of the rock beam through the rock beam periodic fracture data under the same stress state of the rock beam;

[0080] The surface subsidence prediction module, based on the periodic fracture of the rock beam, the different failure mechanisms of the fracture zone and the slow subsidence zone, and the surface subsidence prediction method under backfill mining conditions, derives the calculation formula for surface subsidence prediction;

[0081] The surface subsidence prediction module is used to predict the surface subsidence according to the obtained surface subsidence prediction calculation formula.

[0082] Combining all the above technical solutions, the beneficial effects of the present invention are as follows: the present invention simplifies the analysis of the roof rock beam by material mechanics method, and establishes a rock beam fracture mechanics model based on the key layer theory. The layered transfer criterion, the initial fracture mechanism and the periodic fracture mechanism of the rock beam are analyzed. Combining the destruction mechanism of the fracture zone and the slow subsidence zone, a surface subsidence prediction model is proposed, and the surface subsidence range is predicted by a calculation formula. Finally, taking the T3292 working face of a mine as an example, the accuracy of the prediction model is verified, and the measured error is only 6.48%, indicating that the model can effectively predict the range of surface subsidence under filling mining conditions.

[0083] Under the assumption that the overall situation is not affected, the present invention establishes the separation criterion through the deflection relationship of adjacent rock beams, and then finds the rock layer group moving synchronously according to the formula; the boundary condition of the roof rock beam can be simplified to a fixed support beam, and the material mechanics method is used to judge the initial fracture data; then the rock layer in the goaf area will undergo periodic fractures every time it reaches a certain step distance, and the fracture situation of the rock layer can be obtained; based on the different failure mechanisms of the fracture zone and the slow subsidence zone, the fracture transmission law is determined, and the calculation formula for the surface subsidence prediction is obtained, thereby achieving the purpose of predicting the subsidence range. It has the advantages of relatively simple mechanical analysis, relatively accurate prediction results, and is suitable for engineering applications.

[0084] The present invention predicts the subsidence range of the ground after backfill mining in advance, evaluates the ground damage, greatly reduces the serious situation of economic losses and casualties, and has excellent economic benefits. The elastic mechanics method is used to solve the problem, which is a common method used in this type of research. However, the reaction force of the filling body has a nonlinear distribution law, which makes the elastic mechanics solution extremely complex and unsuitable for engineering applications. The present invention innovatively uses the material mechanics method to solve the problem, and can also obtain good predicted results. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] The accompanying drawings herein are incorporated in and constitute a part of the specification, illustrate embodiments consistent with the present disclosure, and together with the description, serve to explain the principles of the present disclosure;

[0086] Figure 1 is a flow chart of a method for predicting the scope of surface subsidence after backfill mining provided by an embodiment of the present invention;

[0087] Figure 2 It is a principle diagram of obtaining a rock beam fracture mechanics model provided by an embodiment of the present invention;

[0088] Figure 3 1 is a diagram of a fixed-support beam model of a rock beam with initial fracture provided by an embodiment of the present invention; wherein (a) is an engineering prototype diagram; (b) is a mechanical model diagram;

[0089] Figure 4 is a schematic diagram of the initial fracture angle of a rock beam provided by an embodiment of the present invention;

[0090] Figure 5 Schematic diagram of a cantilever beam model of a rock beam periodic fracture provided by an embodiment of the present invention; wherein (a) is an engineering prototype diagram; (b) is a mechanical model diagram;

[0091] Figure 6 is a schematic diagram of periodic fracture angle of a rock beam provided by an embodiment of the present invention;

[0092] Figure 7 There is no obvious settlement map in the surface subsidence type provided by the embodiment of the present invention;

[0093] Figure 8 The surface subsidence type provided by the embodiment of the present invention has an obvious subsidence map;

[0094] Fig. 9 It is a schematic diagram of calculating the range of surface subsidence provided by an embodiment of the present invention;

[0095] Fig.10 It is a fracture model diagram of an engineering example provided by an embodiment of the present invention;

[0096] Fig.11 It is a surface subsidence prediction effect diagram provided by an embodiment of the present invention;

[0097] Fig.12 Schematic diagram of a system for predicting the scope of surface subsidence after backfill mining provided by an embodiment of the present invention;

[0098] In the figure: 1. Basic model and hypothesis module; 2. Layered transfer criterion module; 3. Rock beam initial fracture data judgment module; 4. Rock beam periodic fracture data judgment module; 5. Surface subsidence prediction module; 6. Surface subsidence prediction module. DETAILED DESCRIPTION

[0099] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below in conjunction with the accompanying drawings. In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without violating the connotation of the present invention, so the present invention is not limited by the specific implementation disclosed below.

[0100] The innovation of the present invention is that it abandons the traditional elastic mechanics method of this type of research, and innovatively adopts the material mechanics method to obtain a calculation formula for surface subsidence prediction through inference and analysis of the rock formation model. The formula can quickly and accurately calculate the subsidence range based on the rock formation data. It is simpler, faster, more efficient and more accurate than previous methods.

[0101] Embodiment 1, as Figure 1As shown, the method for predicting the scope of surface subsidence after backfill mining provided by the embodiment of the present invention includes the following steps:

[0102] S1. Use material mechanics method to simplify the analysis of the top rock beam and obtain the fracture mechanics model of the rock beam;

[0103] S2. Based on the obtained rock beam fracture mechanics model, a separation criterion is established through the deflection relationship of adjacent rock beams to obtain a synchronously moving rock layer group;

[0104] S3. Based on the obtained synchronously moving rock formation group, before the roof rock beam has its first fracture, the boundary condition is simplified to a fixed-support beam, and the first fracture data is determined using the material mechanics method;

[0105] S4. Based on the initial fracture data, for the periodic fracture of the rock strata in the goaf area, under the same stress state of the rock beam, the periodic fracture of the rock beam is judged by the periodic fracture data of the rock beam to obtain the periodic fracture of the rock beam;

[0106] S5. According to the periodic fracture of the rock beam obtained, based on the different failure mechanisms of the fracture zone and the slow subsidence zone, the surface subsidence prediction method under backfill mining conditions is used to obtain the calculation formula for surface subsidence prediction;

[0107] S6. Surface subsidence prediction is carried out based on the obtained surface subsidence prediction calculation formula.

[0108] For example, in step S1, a rock beam fracture mechanics model is proposed, and the elastic mechanics method is used to solve the stress at any point on the beam. This is a method commonly used in this type of research. However, under backfill mining conditions, the reaction force provided by the backfill body has a nonlinear distribution law along the direction of the goaf, which makes the elastic mechanics solution extremely complex and unsuitable for engineering applications. Compared with the elastic mechanics solution, the difference of the material mechanics method is that an additional term in the solution is ignored. The existence of the additional term will make the result more accurate, but the smaller the height-to-span ratio of the beam, the smaller the influence of the additional term on the calculation accuracy of the stress in the beam model. Based on this, if Figure 2 As shown in the figure, the material mechanics method is used to simplify the analysis of the roof rock beam. This simplification should refer to the following assumptions:

[0109] (1) The goaf is mined and filled simultaneously, and the interval time between coal seam mining and filling processes is negligible;

[0110] (2) The influence of internal joints and structural surfaces of the rock on the crack propagation path is negligible;

[0111] (3) The load borne by the rock beam is calculated according to the key layer theory. According to the key layer theory, the overburden load borne by the rock layer is expressed as formula (1):

[0112] (1);

[0113] In the formula, is the overburden load carried by the rock strata; is the elastic modulus of the first rock layer above the rock layer in the bedrock, is the elastic modulus of the second rock layer above the rock layer in the bedrock, The first layer above the bedrock The elastic modulus of the rock layer, in MPa; is the bulk density of the first rock layer above the bedrock layer, is the bulk density of the second rock layer above the rock layer in the bedrock. The first layer above the bedrock The unit of bulk density of the rock layer is kN / m 3 ; is the thickness of the first rock layer above the rock layer in the bedrock, is the thickness of the second rock layer above the rock layer in the bedrock, The first layer above the bedrock The thickness of the rock layer, in m;

[0114] (4) When analyzing rock beams at different levels, whether the upper and lower rock beams are in contact is used as the basis for determining the stress boundary conditions. Assuming that there are structural planes between each rock layer, that is, the bending deformation of each rock layer is independent of each other, the rock beam separation criterion for determining a group of synchronously moving rock layers based on the rock layer deflection function is proposed as formula (2):

[0115] (2);

[0116] In the formula, In bedrock The deflection of the rock layer when it is not subjected to the reaction force of filling. From bottom to top in the bedrock The deflection of the rock layer, From bottom to top in the bedrock The maximum deflection of the rock layer when it is not subjected to the backfill reaction force. From bottom to top in the bedrock The maximum deflection of the rock layer; (5) The fracture of the rock beam meets the first strength criterion, and the failure mainly occurs in the direction perpendicular to the principal tensile stress. According to the first strength criterion of rock mechanics, the fracture criterion of the rock beam is determined as formula (3):

[0117] (3);

[0118] In the formula, In bedrock The maximum tensile stress of the rock layer, in MPa; In bedrock The tensile strength of the rock layer, in MPa.

[0119] Based on the above basic assumptions, a rock beam fracture mechanics model is proposed.

[0120] Exemplarily, in step S2, establishing the hierarchical transfer criteria includes:

[0121] The separation criterion is established through the deflection relationship of adjacent rock beams. Assuming that the rock layers are the 1st to mth rock layers from bottom to top starting from the direct top of the coal seam, the maximum deflection of the rock beam under the condition of only its own gravity is calculated respectively. The deflection curve equation of the beam is formula (4):

[0122] (4);

[0123] In the formula, is the elastic modulus, is the moment of inertia, is the deflection, is the bending moment of the cross section;

[0124] The bending moment of the cross section is given by formula (5):

[0125] (5);

[0126] In the formula, is the maximum load on the upper part of the first layer of rock beam, is the maximum reaction force at the bottom of the first layer of rock beam, is the length of the first layer beam, is the distance from the support origin to the point;

[0127] Substituting equation (5) into equation (4), the maximum deflection value is obtained as equation (6):

[0128] (6);

[0129] In the formula, is the maximum deflection of the first rock layer above the rock layer in the bedrock, is the elastic modulus of the first rock layer above the rock layer in the bedrock, is the maximum load on the upper part of the rock beam, is the maximum reaction force at the bottom of the rock beam, is the length of the beam.

[0130] Among them, the technical function of formula (6) is: it is used to calculate the extreme deflection and innovatively transforms a group of rock beams into an integrated rock layer group.

[0131] Then, according to the formula (2) in the basic assumption, the position relationship of adjacent rock layers is calculated in sequence until , Layers of rock If there is separation between the layers of rock, Horizon A group of rock layers moving in synchrony.

[0132] Exemplarily, in step S3, determining the initial fracture data of the rock beam includes:

[0133] When the goaf reaches a certain distance along the strike, the roof rock beam will undergo the initial fracture. Before the initial fracture, the boundary condition of the roof rock beam can be simplified to a fixed-support beam. Take the first group of synchronously moving rock layers directly above the top as the first rock beam, and take the midpoint of the boundary close to the opening hole as the origin to establish the coordinate system.

[0134] Assume that the first group of coordinated rock beams According to the key layer theory, the stress boundary condition of the rock beam is as follows:

[0135] (7);

[0136] In the formula, is the length of the first layer beam;

[0137] According to material mechanics, there is formula (8):

[0138] (8);

[0139] In the formula, is the normal stress on the cross section of a rectangular beam during bending deformation, is the bending moment of the cross section, is the distance from the point on the cross section to the neutral axis, is the moment of inertia of the cross section about the neutral axis, is the shear stress on the cross section, is the shear force on the cross section, is the static moment of the area below the horizontal line of the neutral axis on the cross section about the neutral axis, is the cross-section width;

[0140] The expression of the stress component at any point in the rock beam is as follows:

[0141] (9);

[0142] The principal tensile stress and principal compressive stress at any point in the rock beam are expressed as formula (10):

[0143] (10);

[0144] In the formula, is the maximum principal stress, is the minimum principal stress;

[0145] Since rock is a brittle material, it usually breaks in a direction perpendicular to the maximum tensile stress. According to the analysis of the failure process of the rock beam in the fault layer, the beam first cracks in the direction perpendicular to the maximum tensile stress at the upper corner. As the stress increases further, the compressive stress at the lower corner of the rock beam reaches the maximum compressive stress, so the rock beam will shear from the lower corner to the end of the upper crack.

[0146] According to equations (9) and (10), the point with the maximum tensile stress inside the rock beam appears at The criterion for the initial fracture of the entire rock beam is expressed as formula (11):

[0147] (11);

[0148] In the formula, is the maximum tensile stress of the first group of rock beams, in MPa; is the tensile strength of the first rock layer in the bedrock, in MPa;

[0149] According to equations (9) to (11), the fracture step distance of the first layer of rock beam is obtained: ; Rock beam fracture angle It is expressed as formula (12):

[0150] (12);

[0151] Break Step Substituting into formula (12), we get the fracture angle of the first fracture of the first layer of rock beam: for:

[0152] (13);

[0153] The height of the fracture zone under this condition is expressed as formula (14):

[0154] (14);

[0155] In the formula, For the The height of the broken rock layer, The height of the fracture zone is developed for filling and mining.

[0156] Among them, the fixed-support beam model of the initial fracture of the rock beam is as follows Figure 3 As shown, Figure 3 (a) is the engineering prototype, and (b) is the mechanical model; Figure 4 Schematic diagram of the initial fracture angle of the rock beam.

[0157] Exemplarily, in step S4, determining the rock beam periodic fracture data includes:

[0158] After the initial fracture, as the working face is mined, the rock strata in the goaf will fracture periodically after reaching a certain step distance, and the stress state of the rock beam before each fracture is basically the same. Therefore, for the rock beam periodic fracture model, the rock beam is simplified to a cantilever beam model for mechanical analysis. The first group of synchronously moving rock strata above the goaf roof is taken as the first cantilever beam, and the beam height is h 1. Take the midpoint of the boundary close to the coal wall as the origin to establish the coordinate system.

[0159] Obviously, the maximum deflection in the periodic fracture beam occurs on the air side of the model, so the reaction force of the filling gangue is expressed as formula (15):

[0160] (15);

[0161] The stress state at any point in the cantilever beam is expressed as (16):

[0162] (16);

[0163] In the formula, For the Length of layer beam;

[0164] Similarly, the ultimate span of the first group of rock beams is It can be obtained according to equations (11), (15), and (16). When the model meets the fracture criterion, the entire rock beam fractures.

[0165] Substituting the stress equation (16) at any point of the rock beam into equation (12), the fracture angle of the first group of rock beams during periodic fracture is obtained as equation (17):

[0166] (17);

[0167] In the formula, is the fracture angle of the first group of rock beams during periodic fracture.

[0168] Similar to the first group of rock beams, the fracture conditions of the upper synchronously moving rock layer can be continued to be calculated.

[0169] in, Figure 5 is the cantilever beam model of rock beam periodic fracture, Figure 5 Figure (a) is the engineering prototype. Figure 5 The middle (b) figure is the mechanical model; Figure 6 Schematic diagram of periodic fracture angle of rock beam.

[0170] Exemplarily, in step S5, the surface subsidence range model prediction method includes:

[0171] The scope of surface subsidence after coal mining is closely related to the development height of the fracture zone and the stratigraphic relationship of the key layer. When the fracture zone development height reaches above the key layer, the key layer is damaged, its control effect on the upper rock layer is significantly weakened, and the surface subsidence occurs significantly. On the contrary, when the fracture zone has not developed to the key layer, the complete key layer can effectively control the strata above it to the surface, and under this condition, the surface does not produce obvious subsidence.

[0172] The fracture law of rock beams in the fracture zone can be determined by calculating the corresponding fracture angle based on different rock beam models for initial fracture and periodic fracture, and determining the "broken line" fracture transmission law of rock beams in the fracture zone. The rock layers in the slow-sinking zone above the fracture zone usually have the characteristics of low strength and looseness, and different mechanical models are needed to determine their fracture transmission laws. According to existing work, the rock layers in the slow-sinking zone are usually assumed to be a series of inhomogeneous particles, and the random medium theory proposed in the existing technology is used for analysis, and the surface subsidence amount is deduced based on the random medium theory in the existing technology. w The horizontal movement U Calculation formula. According to the analysis of the rock stratum slow-sinking zone by existing technology, from the perspective of mechanics, the movement process of the slow-sinking zone is ideally divided into three stages: slip-crack-shear. That is, the lower rock layer slips at the edge, causing the rear edge of the loose layer on the surface to crack and expand downward, and the shear stress of the middle rock layer gradually accumulates with the development of the slip section and the crack section. It is assumed that the rock layer in the slow-sinking zone is a non-homogeneous random particle, which is prone to tensile shear failure. Due to the weak shear strength, the rock layer in the slow-sinking zone is easy to move along the horizontal plane at an angle of 45°+ φ / 2, shear failure occurs, eventually forming a funnel-shaped settlement boundary curve in the settlement area.

[0173] Therefore, based on the different failure mechanisms of the fracture zone and the slow-sinking zone, and using the surface subsidence prediction method under backfill mining conditions, it can be deduced that when the key layer breaks, the present invention innovatively proposes a calculation formula (18) for predicting surface subsidence.

[0174] (18);

[0175] In the formula, is the estimated length of surface subsidence, is the length of the goaf, is the initial fracture angle of the rock layer, is the fracture angle of the rock beam during periodic fracture, is the internal friction angle of the rock formation, is the rock layer thickness, is the number of co-moving rock layers in the fracture zone, The rock layer is located in layer, is the number of layers of the main key layer, The total number of rock layers.

[0176] in, Figure 7 There is no obvious settlement map in the surface subsidence type provided by the embodiment of the present invention; Figure 8 The surface subsidence type provided by the embodiment of the present invention has an obvious subsidence map; Fig. 9 Schematic diagram for calculating the scope of surface subsidence.

[0177] Exemplarily, in step S6, the surface subsidence prediction effect includes:

[0178] The T3292 working face of a mine adopts gangue filling mining, mining 9 coal seams, with an average coal thickness of 4m, an average mining depth of 729m, and mechanical calculation parameters of the overlying rock strata. The working face adopts the mining method of longwall comprehensive mining, and the gangue filling management roof in the goaf has a strike length of 1150m and a daily advance of 2m. The filling material uses coal gangue as aggregate, and cement and fly ash are added to the filling material. The 7d compressive strength is 4.8MPa.

[0179] First, according to the method in step S2, the synchronously moving rock formation group is determined.

[0180] Then, according to the beam model of each synchronously moving rock layer, the fracture boundary of each group of rock layers is calculated from bottom to top. According to the calculation method of the initial fracture angle and periodic fracture angle of the rock beam, the fracture conditions of the model fracture zone are calculated respectively.

[0181] The calculation of the fracture boundary of each group of rock formations includes: Substituting the data in Table 1 into formula (7), formula (9)-formula (11), the fracture step distance can be obtained ;

[0182] The calculation of the fracture conditions of the fracture zone in the model includes: Substituting into formula (13) (obtaining the initial fracture angle) and formula (17) (obtaining the periodic fracture angle), the calculated data are shown in Table 2.

[0183] According to the predicted results obtained by the model, the surface subsidence range of T3292 is calculated to be 1313m. According to the measured results of surface subsidence, the surface subsidence range of T3292 working face is 1404m, and the error predicted by the model is only 6.48%. Considering the uncertainty of the crack width in the actual fracture, the model can better predict the surface subsidence range under filling mining conditions.

[0184] The calculated surface subsidence range of T3292 is 1313 m, which includes: Substituting the results obtained in the above steps and the data in the table into formula (18) to obtain the result.

[0185] Example 2, taking a mine T3292 as an example, the working face adopts gangue filling mining, 9 coal seams are mined, the average coal thickness is 4m, the average mining depth is 729m, and the mechanical calculation parameters of the overlying rock strata are listed in Table 1. The working face adopts the mining method of longwall comprehensive mining, the goaf area gangue filling management roof, the strike length is 1150m, and the daily advance is 2m. The filling material is coal gangue as aggregate, cement and fly ash are added to the filling material, and the 7d compressive strength is 4.8MPa.

[0186] Table 1 Mechanical parameters of overlying rock formations

[0187]

[0188] First, according to the method in S2, the synchronously moving rock formation group is determined.

[0189] Then, according to the beam model of each synchronously moving rock layer, the fracture boundary of each group of rock layers is calculated from bottom to top. According to the calculation method of the initial fracture angle and periodic fracture angle of the rock beam, the fracture conditions of the model fracture zone are calculated respectively. The calculation data of each rock layer are listed in Table 2, and the schematic diagram is shown in Fig.10 shown.

[0190] Table 2 Calculation results of fracture angles of various rock layers

[0191]

[0192] According to the predicted results obtained by the model, the surface subsidence range of T3292 is calculated to be 1313m. According to the measured results of surface subsidence, the surface subsidence range of T3292 working face is 1404m, and the error of the model prediction is only 6.48%. Fig.11 Considering the uncertainty of the crack width in the actual fracture, the model can better predict the scope of surface subsidence under backfill mining conditions.

[0193] Embodiment 3, as Fig.12 As shown, the system for predicting the scope of surface subsidence after filling mining provided by the embodiment of the present invention includes:

[0194] Basic model and assumption module 1 is used to simplify the analysis of the top rock beam using material mechanics methods to obtain the rock beam fracture mechanics model;

[0195] Layer transfer criterion module 2, based on the obtained rock beam fracture mechanics model, establishes the delamination criterion through the deflection relationship of adjacent rock beams to obtain the synchronously moving rock layer group.

[0196] The rock beam initial fracture data judgment module 3, based on the obtained synchronously moving rock layer group, before the roof rock beam first fractures, the boundary condition is simplified to a fixed-support beam, and the initial fracture data is judged using the material mechanics method;

[0197] The rock beam periodic fracture data judgment module 4, based on the initial fracture data, for the periodic fracture of the rock strata in the goaf area, under the same stress state of the rock beam, judges the periodic fracture of the rock beam through the rock beam periodic fracture data to obtain the periodic fracture of the rock beam;

[0198] The surface subsidence prediction module 5 obtains the surface subsidence prediction formula according to the obtained rock beam periodic fracture situation, based on the different failure mechanisms of the fracture zone and the slow subsidence zone, and using the surface subsidence prediction method under the filling mining condition;

[0199] The surface subsidence prediction module 6 is used to predict the surface subsidence according to the obtained surface subsidence prediction calculation formula.

[0200] In the above embodiments, the description of each embodiment has its own emphasis. For parts that are not described or recorded in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0201] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with the technical field within the technical scope disclosed by the present invention and within the spirit and principles of the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for predicting the scope of surface subsidence after backfill mining, characterized in that: The method includes: S1. Use material mechanics method to simplify the analysis of the top rock beam and obtain the fracture mechanics model of the rock beam; S2. Based on the obtained rock beam fracture mechanics model, a separation criterion is established through the deflection relationship of adjacent rock beams to obtain a synchronously moving rock layer group; S3. Based on the obtained synchronously moving rock formation group, before the roof rock beam has its first fracture, the boundary condition is simplified to a fixed-support beam, and the first fracture data is determined using the material mechanics method; S4. Based on the initial fracture data, for the periodic fracture of the rock strata in the goaf area, under the same stress state of the rock beam, the periodic fracture of the rock beam is judged by the periodic fracture data of the rock beam to obtain the periodic fracture of the rock beam; S5. According to the periodic fracture of the rock beam obtained, based on the different failure mechanisms of the fracture zone and the slow subsidence zone, the surface subsidence prediction method under backfill mining conditions is used to obtain the calculation formula for surface subsidence prediction; S6. Calculate the surface subsidence according to the obtained surface subsidence prediction calculation formula; In step S5, the method for predicting surface subsidence under filling mining conditions includes: From a mechanical point of view, the movement process of the slow-sinking zone can be ideally divided into three stages: slip, cracking, and shearing. The lower rock layer slips at the edge, causing the rear edge of the loose layer on the surface to crack and expand downward. The shear stress of the middle rock layer gradually accumulates with the development of the slip section and the cracking section. When the rock layer in the slow-sinking zone is a non-homogeneous random particle, tensile shear failure occurs. The rock layer in the slow-sinking zone moves along the horizontal plane at an angle of 45°+ φ / The corner of 2 undergoes shear failure, eventually forming a funnel-shaped settlement boundary curve in the settlement area; In step S5, the surface subsidence prediction method under backfill mining conditions is used to obtain a surface subsidence prediction calculation formula, including: Based on the different failure mechanisms of the fracture zone and the slow subsidence zone, the surface subsidence prediction method under backfill mining conditions is used to derive the surface subsidence prediction formula (18) when the key layer breaks: ； In the formula, is the estimated length of surface subsidence, is the length of the goaf, is the initial fracture angle of the rock layer, is the fracture angle of the rock beam during periodic fracture, is the internal friction angle of the rock formation, is the rock layer thickness, is the number of co-moving rock layers in the fracture zone, The rock layer is located in layer, is the number of layers of the main key layer, The total number of rock layers.

2. The method for predicting the scope of surface subsidence after backfill mining according to claim 1 is characterized in that: In step S1, a rock beam fracture mechanics model is obtained, including: (1) The goaf is mined and filled simultaneously, and the interval between coal seam mining and filling is negligible; (2) The influence of internal joints and structural surfaces of the rock on the crack propagation path is negligible; (3) According to the critical layer theory, the overburden load borne by the rock layer is given by formula (1): ； In the formula, is the overburden load carried by the rock strata; is the elastic modulus of the first rock layer above the rock layer in the bedrock, is the elastic modulus of the second rock layer above the rock layer in the bedrock, The first layer above the bedrock The elastic modulus of the rock layer, in MPa; is the bulk density of the first rock layer above the bedrock layer, is the bulk density of the second rock layer above the rock layer in the bedrock. The first layer above the bedrock The unit of bulk density of the rock layer is kN / m 3 ; is the thickness of the first rock layer above the rock layer in the bedrock, is the thickness of the second rock layer above the rock layer in the bedrock, The first layer above the bedrock The thickness of the rock layer, in m; (4) For the structural planes existing between all rock layers, the rock beam separation criterion for determining a group of synchronously moving rock layers is given by equation (2) based on the rock layer deflection function: ； In the formula, In bedrock The deflection of the rock layer when it is not subjected to the reaction force of filling. From bottom to top in the bedrock The deflection of the rock layer, From bottom to top in the bedrock The maximum deflection of the rock layer when it is not subjected to the backfill reaction force. From bottom to top in the bedrock The maximum deflection of the rock layer; (5) According to the first strength criterion of rock mechanics, the fracture criterion of the rock beam is determined as formula (3): ； In the formula, In bedrock The maximum tensile stress of the rock layer, in MPa; In bedrock The tensile strength of the rock layer, in MPa.

3. The method for predicting the scope of surface subsidence after backfill mining according to claim 2 is characterized in that: In step S2, a separation criterion is established based on the deflection relationship between adjacent rock beams, including: Starting from the immediate top of the coal seam, the rock layers from bottom to top are the 1st to mth rock layers, and the maximum deflection of the rock beam under the condition of only its own gravity is calculated respectively; the deflection curve equation of the beam is formula (4): ； In the formula, is the elastic modulus, is the moment of inertia, is the deflection, is the bending moment of the cross section; The bending moment of the cross section is given by formula (5): ； In the formula, is the maximum load on the upper part of the first layer of rock beam, is the maximum reaction force at the bottom of the first layer of rock beam, is the length of the first layer beam, is the distance from the support origin to the point; Substituting equation (5) into equation (4), the maximum deflection value is obtained as equation (6): ； In the formula, is the maximum deflection of the first rock layer above the rock layer in the bedrock, is the elastic modulus of the first rock layer above the rock layer in the bedrock, is the maximum load on the upper part of the rock beam, is the maximum reaction force at the bottom of the rock beam, is the length of the beam.

4. The method for predicting the scope of surface subsidence after backfill mining according to claim 2 is characterized in that: In step S2, a synchronously moving rock formation group is obtained, including: According to formula (2), the position relationship of adjacent rock layers is calculated in sequence until , Layers of rock If there is separation between the layers of rock, Horizon A group of rock layers moving in synchrony.

5. The method for predicting the scope of surface subsidence after backfill mining according to claim 3 is characterized in that: In step S3, the initial fracture data is determined using a material mechanics method, including: The first group of coordinated rock beam movement According to the key layer theory, the stress boundary condition of the rock beam is as follows: ； In the formula, is the length of the first layer beam; According to material mechanics, there is formula (8): ； In the formula, is the normal stress on the cross section of a rectangular beam during bending deformation, is the bending moment of the cross section, is the distance from the point on the cross section to the neutral axis, is the moment of inertia of the cross section about the neutral axis, is the shear stress on the cross section, is the shear force on the cross section, is the static moment of the area below the horizontal line of the neutral axis on the cross section about the neutral axis, is the cross-section width; The expression of the stress component at any point in the rock beam is as follows: ； The principal tensile stress and principal compressive stress at any point in the rock beam are expressed as formula (10): ； In the formula, is the maximum principal stress, is the minimum principal stress; According to equations (9) and (10), the point with the maximum tensile stress inside the rock beam appears at The criterion for the initial fracture of the entire rock beam is expressed as formula (11): ； In the formula, is the maximum tensile stress of the first group of rock beams, in MPa; is the tensile strength of the first rock layer in the bedrock, in MPa; According to equations (9) to (11), the fracture step distance of the first layer of rock beam is obtained: ; Rock beam fracture angle It is expressed as formula (12): ； Break Step Substituting into formula (12), we get the fracture angle of the first fracture of the first layer of rock beam: for: ； The height of the fracture zone under this condition is expressed as formula (14): ； In the formula, For the The height of the broken rock layer, The height of the fracture zone is developed for filling and mining.

6. The method for predicting the scope of surface subsidence after backfill mining according to claim 5 is characterized in that: In step S4, the periodic fracture situation of the rock beam is determined by judging the periodic fracture data of the rock beam, including: The first group of synchronously moving rock layers above the goaf roof is taken as the first cantilever beam, and the beam height is , take the midpoint of the boundary close to the coal wall as the origin to establish the coordinate system; The reaction force of filling gangue is expressed as formula (15): ； The stress state at any point in the cantilever beam is expressed as (16): ； In the formula, for Length of layer beam; The ultimate span of the first group of rock beams According to equations (11), (15) and (16), when the fracture criterion is met, the entire rock beam fractures; Substituting the stress equation (16) at any point of the rock beam into equation (12), the fracture angle of the first group of rock beams during periodic fracture is obtained as equation (17): ； In the formula, is the fracture angle of the first group of rock beams during periodic fracture.

7. A system for predicting the scope of surface subsidence after backfill mining, characterized in that: The system implements the method for predicting the scope of surface subsidence after backfill mining as claimed in any one of claims 1 to 6, and the system comprises: The basic model and assumption module (1) is used to simplify the analysis of the roof rock beam using the material mechanics method to obtain the rock beam fracture mechanics model; The layer transfer criterion module (2) is based on the obtained rock beam fracture mechanics model, establishes the delamination criterion through the deflection relationship of adjacent rock beams, and obtains the rock layer group with synchronous movement. The rock beam initial fracture data judgment module (3) is based on the obtained synchronously moving rock layer group. Before the top rock beam first fractures, the boundary condition is simplified to a fixed-support beam, and the initial fracture data is judged using the material mechanics method; The rock beam periodic fracture data judgment module (4) determines the periodic fracture of the rock strata in the goaf area based on the initial fracture data and the periodic fracture of the rock beam under the same stress state of the rock beam by judging the periodic fracture data of the rock beam to obtain the periodic fracture of the rock beam; The surface subsidence prediction module (5) obtains a surface subsidence prediction formula based on the obtained rock beam periodic fracture conditions, the different failure mechanisms of the fracture zone and the slow subsidence zone, and the surface subsidence prediction method under backfill mining conditions; The surface subsidence prediction module (6) is used to predict the surface subsidence according to the obtained surface subsidence prediction calculation formula.

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