A deep stage cemented filling body strength calculation method considering mining and filling timing

Abstract

The application discloses a kind of deep stage cemented filling body strength calculation method considering mining and filling timing, comprising the following steps: S1, construct the three-dimensional finite element model of underground ore body mining and filling mining and filling timing process, numerical simulation calculation is carried out;S2, the displacement cusp mutation analysis function of typical measuring point is established by strength reduction method to determine the threshold value of total displacement and safety factor, and the rationality of threshold value is verified by the displacement nephogram and stress nephogram of finite element cemented filling body numerical model, qualitative analysis;S3, by column network discrete method, the three-dimensional analysis model of cemented filling body strength requirement is reconstructed, and the volume of cemented filling body fracture surface and failure area is determined according to the threshold value of total displacement and safety factor, and finally the strength required by cemented filling body is determined.The strength of filling body determined by the method is accurate and reasonable, effectively solves the problem of filling mining safety and economic balance, and is especially suitable for the strength requirement calculation of cemented filling body of deep stage open stope subsequent filling mining method.

Description

Technical Field

[0001] This invention relates to the field of metal mining technology, and in particular to a method for calculating the strength of cemented backfill in deep stages, taking into account the mining and backfilling sequence. Background Technology

[0002] Shallow resource extraction in my country is nearing depletion, and mining is gradually moving towards deeper levels. Underground goafs damage rock strata, leading to surface subsidence and impacting ecology and livelihoods. Properly managing goafs is crucial for controlling ground pressure, preventing ground pressure activity, and ensuring safe production. Post-goaf backfilling mining is an organic combination of backfilling and open-pit mining methods, offering advantages such as mature mining technology, high production efficiency, and minimal impact on rock deformation and surface mining. It is currently the preferred method for efficient and green development of metal mines. Cemented backfill, as the core load-bearing component of post-goaf backfilling stopes, suffers from insufficient strength, leading to backfill failure and severely affecting stope safety and production efficiency; conversely, excessive strength results in wasted cementing materials and increased backfilling costs. Determining the appropriate strength of the backfill is key to balancing safety and economy in backfilling mining. Ore deposit excavation and backfilling typically involve multiple steps, placing the backfill in a repeatedly loaded and unloaded stress environment. With increasing depth, nonlinear stress paths become more pronounced, leading to significant extrusion failure. Therefore, the strength calculation model for shallow backfill needs improvement. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a method for calculating the strength of cemented backfill in deep stages, taking into account the timing of mining, which can determine the reasonable strength of the backfill.

[0004] To solve the above-mentioned technical problems, the technical solution adopted by the present invention includes the following steps: S1, constructing a three-dimensional finite element model of the mining and backfilling sequence process of underground ore body, and performing numerical simulation calculations;

[0005] S2. By establishing a cusp displacement mutation analysis function for typical measuring points using the strength reduction method, the thresholds for total displacement and safety factor are determined. Qualitative analysis is then performed using displacement and stress cloud diagrams from the finite element cemented filling numerical model to verify the rationality of the thresholds.

[0006] S3. The three-dimensional analysis model of the strength requirement of cemented filling body is reconstructed by the column grid discretization method. The volume of the fracture surface and the failure area of ​​cemented filling body is determined based on the total displacement and the safety factor threshold, and the required strength of cemented filling body is finally determined.

[0007] Furthermore, in step S1: based on the strength of the cemented backfill, a three-dimensional finite element model of the mining and backfilling sequence process of the ore body is established according to the conditions of the surrounding rock and ore body, and numerical simulation calculations are performed; the mining and backfilling process consists of three consecutive adjacent ore blocks, and three-step mining and backfilling are carried out.

[0008] Furthermore, the three-step mining and filling process is as follows: the first step is mining the intermediate block, with the voids cemented and filled, and the filling body grid is a regular hexahedral grid; the second step is mining one side of the block, with the voids not cemented and filled; the third step is mining the other side of the block, with the voids not filled.

[0009] Furthermore, in step S2: a cemented backfill body parameter with a preliminary lime-sand ratio is selected for numerical simulation calculation in step S1. The total displacement of the center point of the exposed face of the cemented backfill body in the void area of ​​the mining block during the mining of the right block is selected as the analysis index. The strength reduction method is used to evaluate the cohesion C of the backfill body before reduction and the internal friction angle of the backfill body before reduction. Perform the reduction and repeat step S1 numerical simulation calculation, and extract the total displacement of the center point of the exposed surface after each calculation. With the reduction factor F, cusp catastrophe theory is used to construct... Cusp mutation model function of F The mutation characteristic value was obtained, the critical strength of the cemented filling body was initially determined, and the total displacement value of the mutation point and the safety factor were set as the safety threshold.

[0010] Furthermore, the cemented filler parameters C and Strength reduction is performed according to the following formulas (2.1) and (2.2):

[0011] (2.1);

[0012] (2.2);

[0013] In the formula, —Cohesion of the filling material after reduction; —Angle of friction within the filler after reduction; C —Cohesion of the filler before reduction; — Friction angle of the filling material before reduction; F — Reduction factor;

[0014] The cusp mutation model function Perform according to the following formula (2.3):

[0015] (2.3);

[0016] In the formula, a0, a1, a2, a3, and a4 are undetermined coefficients; let Then, the formula for the standard function V value of the cusp mutation can be transformed into the following equation (2.4):

[0017] (2.4);

[0018] In the formula, , ;

[0019] but It can be used as the distance between the evolutionary state and the critical state of cemented filling, and is called the mutation characteristic value.

[0020] Further, in step S3: extract the preliminary given cemented infill parameters and the numerical calculation data information of the reduced cemented infill, such as the unit number, node number, node displacement, and element stress field, import them into Matlab, connect the center of the element mesh in the vertical direction to form a combined column, reconstruct the information of the cemented infill mesh in Matlab, and perform information reconstruction on the cemented infill mesh based on the total displacement determined in step S2. The fracture surface is searched using the reduction factor F. A smooth surface is generated using the surf function in Matlab, and the volume of the fracture envelope is calculated. If the volume is greater than or equal to 30% of the total volume, the cemented filling body will become unstable.

[0021] Furthermore, the feature is that the displacement of the reconstructed mesh center is calculated based on the following formula:

[0022] To calculate the center displacement of each element, first take the displacement values ​​of the eight nodes of that element, then calculate their average value. This average value is the displacement at the element center. The vector U of the element center displacement has several components. It is the following formula (3.1):

[0023] (3.1);

[0024] In the formula:

[0025] —Representing the research unit node Displacement components in the direction;

[0026] The formula for calculating the total displacement U is as follows (3.2):

[0027] (3.2);

[0028] The safety factor of the reconstructed grid center is calculated according to the following formula (3.3):

[0029] (3.3);

[0030] In the formula:

[0031] —The cohesive force of the filling material;

[0032] —Normal stress on any slip surface within a cubic mesh;

[0033] —Internal friction angle of the filling material;

[0034] —Shear stress along the downward direction on any slip surface within the cube search grid;

[0035] in , These are the inherent physical parameters of the filling material; and Then it is necessary to calculate it according to the relevant formulas of stress vector in elastoplastic mechanics. The specific calculation formulas are shown in the following formulas (3.4)-(3.8).

[0036] (3.4);

[0037] (3.5);

[0038] in,

[0039] (3.6);

[0040] (3.7);

[0041] (3.8);

[0042] In the formula:

[0043] —The normal stress vector on a plane in any direction;

[0044] — The transpose of the following table —Indicates the normal direction of the plane in any direction;

[0045] —The normal vector of the plane in any direction;

[0046] —Shear stress vector along the sliding direction on an arbitrary plane;

[0047] — transpose, subscript This indicates the downward direction of the arbitrary plane;

[0048] —The downward direction vector of the arbitrary plane;

[0049] —The six stress components corresponding to the center of the cuboid mesh, that is, the stress state at the center point of the mesh;

[0050] The safety factor of the fracture surface is calculated according to the following formula (3.9):

[0051] (3.9);

[0052] In the formula:

[0053] —Safety factor of the fracture surface;

[0054] —The number of discrete calculation points on the fracture surface;

[0055] —The safety factor value of the i-th calculation point;

[0056] —The safety factor value of the i-th calculation point;

[0057] The volume of the broken bread is calculated according to the following formula (3.10):

[0058] (3.10);

[0059] In the formula:

[0060] —Height of the top surface of the target filling body;

[0061] —The most dangerous slip surface is at point . The height of the location;

[0062] It is the integration region defined in the x and y directions.

[0063] The beneficial effects of adopting the above technical solution are as follows: This invention considers the influence of mining stress on the stability of the backfill body during the mining and backfilling process, and the strength of the backfill body is accurately and reasonably determined, effectively solving the problem of balancing safety and economy in backfilling mining. It is particularly suitable for calculating the strength requirements of cemented backfill bodies in deep-stage open-stope backfilling mining methods. Attached Figure Description

[0064] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0065] Figure 1 This is a three-dimensional solid model diagram of the entire invention;

[0066] Figure 2 This is a three-dimensional solid model diagram of the ore body of this invention;

[0067] Figure 3 This is a three-dimensional mesh diagram of the entire invention;

[0068] Figure 4 This is a mesh diagram of the ore body model of the present invention;

[0069] Figure 5 This is a diagram showing the layout of the monitoring line for the cemented filling body in one step of the present invention;

[0070] Figure 6 This is a fitted curve of the total displacement δ of the center point of the exposed surface of the cemented filler of the present invention and the reduction coefficient;

[0071] Figure 7 This is a graph showing the variation of the mutation eigenvalues ​​of this invention with the reduction coefficient;

[0072] Figure 8 This is a total displacement cloud diagram of the cemented backfill body of the two-step mining block without reduction according to the present invention;

[0073] Figure 9 This is a total displacement cloud diagram of the cemented backfill body of the three-step mining block without reduction according to the present invention;

[0074] Figure 10 This is a total displacement curve of the cemented backfill body of the two-step mining block without reduction according to the present invention;

[0075] Figure 11 This is a total displacement curve of the cemented backfill body of the three-step mining block according to the present invention;

[0076] Figure 12 This is a cloud diagram showing the total displacement of the cemented backfill body in the two-step mining chamber during the reduction process of this invention;

[0077] Figure 13 This is a cloud diagram showing the total displacement of the cemented filling body in the three-step mining chamber during the reduction process of this invention;

[0078] Figure 14 This is a graph showing the total displacement of the cemented filling body in the two-step mining chamber during the reduction process of this invention.

[0079] Figure 15 This is a graph showing the total displacement of the cemented filling body in the three-step mining chamber during the reduction process of this invention;

[0080] Figure 16 This is a vertical stress cloud diagram of the cemented backfill body of the two-step mining chamber without reduction according to the present invention;

[0081] Figure 17 This is a vertical stress cloud diagram of the cemented filling body of the three-step mining chamber without reduction according to the present invention;

[0082] Figure 18 This is the vertical stress curve of the cemented filling body of the two-step mining chamber without reduction according to the present invention;

[0083] Figure 19 This is the vertical stress curve of the cemented filling body of the three-step mining chamber without reduction according to the present invention;

[0084] Figure 20 This is a vertical stress cloud diagram of the cemented filling body of the two-step mining chamber during the reduction process of this invention;

[0085] Figure 21 This is a vertical stress cloud diagram of the cemented filling body of the three-step mining chamber during the reduction process of this invention;

[0086] Figure 22 This is the vertical stress curve of the cemented filling body of the two-step mining chamber during the reduction process of this invention;

[0087] Figure 23 This is the vertical stress curve of the cemented filling body of the three-step mining chamber during the reduction process of this invention;

[0088] Figure 24 This is a reconstruction diagram of the cemented filling body column grid of the present invention;

[0089] Figure 25 This is a spatial position diagram of the sub-sliding surface inside the column of the present invention;

[0090] Figure 26 This is a diagram showing the formation of an arbitrary sliding surface within the cubic grid of this invention;

[0091] Figure 27 This is a schematic diagram illustrating the solution of the downward sliding direction vector on the sliding surface within the cubic mesh according to the present invention;

[0092] Figure 28 This is a schematic diagram of solving the downward sliding direction vector on the sliding surface within a cubic mesh in another direction of the present invention;

[0093] Figure 29 This invention is based on control conditions , The search yielded a three-dimensional spatial damage surface map during the two-step sampling process;

[0094] Figure 30 The search method of this invention is based on control conditions. , Obtain three-dimensional spatial damage surface maps during the three-step sampling process;

[0095] Figure 31 This is a schematic diagram of the method flow of the present invention.

[0096] In the diagram: 1. 0.5m unconnected area; 2. First-step mining block; 3. Second-step mining block; 4. Third-step mining block; 5. Bar; 6. Local sub-slip surface; 7. i-th search grid; 8. Sub-slip surface within the search grid; 9. Slide direction vector; 10. Slide direction vector; ① Slide direction vector of the slip surface; ② Slide direction vector of the slip surface; ③ Slide direction vector of the slip surface; ④ Slide direction vector of the slip surface; 11 represents monitoring line 1; 12 represents monitoring line 2; 13 represents monitoring line 3; 14 represents monitoring line 4; 15 represents monitoring line 5; 16 represents monitoring line 6; 17 represents monitoring line 7; 18 represents monitoring line 8; 19 represents monitoring line 9. Detailed Implementation

[0097] Example: Figure 31 As shown, the calculation method for the strength of cemented backfill in the deep stage considering the timing of mining is as follows.

[0098] S1. Construct a typical three-dimensional finite element model of the underground ore body mining and filling sequence, and perform numerical simulation calculations:

[0099] The calculation model rock mass was selected as a typical mineralized rock with ore and surrounding rock from a typical mine. The lateral pressure coefficient was set to 1, and the burial depth was set to 1000m. The cemented backfill material was set with a lime-sand ratio of 1:8, and the uncemented backfill material was set with a lime-sand ratio of 1:20. Stope parameters: Y-axis length 40m, X-axis length 20m, Z-axis length 60m. The mining was divided into three steps. The first step involved mining the first-step ore block 2 in the middle area, followed by a first-step cemented backfill, with the top 0.5m considered an un-cemented area. The second step involved mining the second-step ore block 3 on the right, followed by a second-step uncemented backfill, with the top 0.5m considered an un-cemented area. The third step involved mining the third-step ore block 4 on the left, with no backfilling in the empty area. Based on Saint-Venant's principle in elasticity, the model size should be 3 to 5 times the size of the stope, reflecting stress redistribution within the affected area and stresses close to the original rock stress outside. This model setup helps to more accurately analyze and assess the impact of mining on the surrounding rock mass. Model dimensions: 600m in the Y-axis direction, 600m in the X-axis direction, and 500m in the Z-axis direction. See the complete 3D solid model below. Figure 1 Excluding surrounding rock models, such as Figure 2 As shown.

[0100] The grid cell length for the first-step mining block area is 1m, the grid cell length for the second and third-step mining block areas is 5m, and the grid cell length for the surrounding rock of the stope is 40m, resulting in a total of 107,508 nodes and 79,876 cells. Figure 3 The grid dimensions for dividing the surrounding rock and ore body are shown below. Figure 4 The ore body grid is shown.

[0101] Fixed constraints were applied to the bottom of the model, displacement constraints were applied to the sides, load boundaries were applied to the sides according to the lateral pressure coefficient, and vertical loads were applied to the top according to the burial depth. The mechanical parameters of the ore, rock, and filling body are shown in Table 1.

[0102] Table 1: Mechanical parameters of ore, rock, and filling material in this embodiment

[0103] name <![CDATA[Unit weight / (KN / m 3 )]]> Elasticity model / MPa Poisson's ratio Compressive strength / MPa Cohesion / MPa <![CDATA[Internal friction angle / 0 > Surrounding rock 25.18 57500 0.23 89.83 11.44 32.6 Ore body 25.02 54200 0.20 118.05 19.40 33.2 1:8 filling body 20.61 231.10 0.19 2.11 0.171 38.7 1:20 filling body 12.91 36.61 0.24 0.58 0.062 31.27

[0104] After constructing the overall model based on the above information, numerical simulation is performed. The specific steps of the simulation scheme for the mining and filling sequence are as follows: First, activate all meshes, boundary conditions, and static loads; Second, mine one block; Third, cement and fill one block with an initial strength ash-sand weight ratio of 1:8; Fourth, mine the left block; Fifth, non-cemented fill the left block with an ash-sand weight ratio of 1:20; Sixth, mine the right block.

[0105] S2. Establish a cusp displacement mutation analysis function for typical measuring points using the strength reduction method, and determine the total displacement and safety factor threshold:

[0106] Using formulas (2.1) and (2.2), the strength parameters of the cemented infill are determined using the strength reduction method. and Simultaneously apply the reduction factor F to obtain the reduced parameters. and Then, numerical simulation of the mining and filling time sequence is performed.

[0107] The monitoring plan is as follows: Monitoring lines are set at key locations in the cemented backfill material obtained in the first step, such as... Figure 5 The monitoring lines 1 to 9 are shown in the attached figures 11 to 19. Based on the monitoring lines, cross-sections of the filling body along the X direction (x=290m, x=300m) and along the Y direction (y=20m) are drawn to conduct a qualitative analysis of the stability of the filling mining area.

[0108] The total displacement parameters of the center point of the exposed surface of the cemented backfill were calculated numerically. With intensity reduction factor The changing trend of displacement parameters was analyzed to construct a fourth-order polynomial regression model between the two. With reduction factor Substituting the model coefficients into the catastrophe theory equation, the displacement catastrophe characteristic parameters under different reduction conditions are calculated. The evolution law; the state of cemented filling is judged based on the magnitude of the mutation characteristic value. Cemented filling is stable when ∆>0, unstable when ∆<0, and in critical state when ∆=0.

[0109] Using formulas (2.3) and (2.4), the total displacement of the center point of the exposed surface is calculated. With reduction factor Evolutionary patterns and total displacement With reduction factor The fitted curve, such as Figure 6 The study investigated the three-step mining conditions. With reduction factor The evolutionary laws, such as Figure 7 When the reduction factor When = 1.9, u = -0.14808, v = 0.03621, =0.00942>0, while when the reduction factor When = 2, u = -0.14692, v = 0.02985, =-0.00231<0, the filling material is unstable. This can be considered... =1.9 is the critical reduction factor of the cemented filling, which is the safety factor of the 2.11MPa filling. Under this condition, the critical strength is 1.11MPa.

[0110] Qualitative analysis was performed on the displacement and stress contour plots of the finite element cemented infill numerical model.

[0111] Figures 8-11 Displacement cloud diagrams and curve changes after mining blocks in two-step and three-step mining operations when the cemented backfill body with a strength of 2.11 MPa is not reduced. Figure 8 The cemented filling body of the two-step mining chamber is shown in (A) as a three-dimensional view, (B) as a displacement cloud profile at y=20m, and (C) as a displacement cloud profile at x=300m. Figure 9 The image shows the cemented backfill of a three-stage mining chamber. (D) is a three-dimensional view; (E) is a displacement cloud profile at y=20m; (F) is a displacement cloud profile at x=300m; and (G) is a displacement cloud profile at x=290m. When the 2.11MPa cemented backfill was first exposed under unreduced conditions, the total displacement at profiles y=20m and x=300m varied between 1.04–35.14mm and 3.11–25.41mm, respectively. During the second exposure of the cemented backfill, the total displacement at profiles y=20m, x=300m, and x=290m varied between 4.18–86.41mm, 5.14–62.64mm, and 8.12–45.28mm, respectively. During the second mining stage, the overall deformation was mainly concentrated in the middle of the top surface of the exposed face, primarily due to its own weight. Figure 10 , 11Data from monitoring lines 7 and 9 show that the displacement is distributed in an arc shape along the height direction, with a bottom bulge observed at the bottom of the exposed face. During the three-step mining process, the displacement mainly occurred in the upper half of the first exposed face. This is because the second-step backfilling block uses a non-cemented backfill, which cannot provide sufficient lateral support, making the upper half of the first exposed face more prone to displacement. Overall, however, this does not affect the overall stability of the backfill. From... Figure 9 The mid-section (E) and monitoring lines show that the cemented filling body is mainly characterized by slip failure, and its overall stability is good.

[0112] Figures 12-15 Displacement cloud diagrams and curve changes of cemented backfill with a strength of 2.11 MPa after two-step and three-step mining blocks, with a reduction factor of 2.1. Figure 12 The cemented filling body of the two-step mining chamber is shown in (A) as a three-dimensional view, (B) as a displacement cloud profile at y=20m, and (C) as a displacement cloud profile at x=300m. Figure 13 The image shows the cemented backfill of a three-stage mining chamber. (D) is a three-dimensional view; (E) is a displacement cloud profile at y=20m; (F) is a displacement cloud profile at x=300m; and (G) is a displacement cloud profile at x=290m. Under a reduction factor of 2.1, when the 2.11MPa cemented backfill was first exposed, the total displacement at profiles y=20m and x=300m varied between 7.1–62.23 mm and 1.28–58.01 mm, respectively. During the second exposure of the cemented backfill, the total displacement at profiles y=20m, x=300m, and x=290m varied between 9.25–169.26 mm, 3.17–148.39 mm, and 4.15–88.74 mm, respectively. In the second-stage mining, slippage failure mainly occurred in the upper half of the exposed surface. During the three-step mining process, displacement was mainly concentrated in the lower half of the exposed surface and inside the filling material, while the upper half showed greater displacement overall. The maximum displacement reached 173 mm, and the area with displacement ranging from 104 mm to 173 mm accounted for 41.6%, at which point the filling material might experience overall instability. Figure 13 The mid-section E and monitoring lines show that the overall displacement of the cemented filling body exhibits a scissor-like shape, indicating that shear failure is the dominant factor. Furthermore, from... Figure 14 , 15 Data from monitoring line 2 indicates that the point at a height of 275 mm in the filling material may be the slippage point.

[0113] Figures 16-19 Vertical stress cloud diagrams and curve changes after two-step and three-step mining blocks when the cemented backfill body with a strength of 2.11 MPa is not reduced; Figure 16The cemented filling body of the two-step mining chamber is shown in (A) as a three-dimensional view, (B) as a displacement cloud profile at y=20m, and (C) as a displacement cloud profile at x=300m. Figure 17 The three-step mining chamber cemented backfill is shown in (D) as a three-dimensional view, (E) as a displacement cloud profile at y=20m, (F) as a displacement cloud profile at x=300m, and (G) as a displacement cloud profile at x=290m. When the 2.11MPa cemented backfill was first exposed under unreduced conditions, the vertical stresses at profiles y=20m and x=300m varied between 0.001~-0.654MPa and 0.002~-0.336MPa, respectively, with a maximum tensile stress of 0.046MPa. The overall stress variation range was within the compressive strength range of the backfill, and the stress at the bottom of the backfill showed an arc-shaped trend. During the second exposure of the cemented backfill, the vertical stresses at profiles y=20m, x=300m, and x=290m varied between 0.015~-1.022MPa, 0.005~-0.638MPa, and 0.002~-0.981MPa, respectively, with a maximum tensile stress of 0.019MPa. Tensile stress concentration areas appeared on the exposed surface, and the overall stress variation of the backfill was under compression. The cross-sectional diagram shows stress concentration in the central region at the bottom of the exposed surface. From the stress monitoring line changes, during the two-step mining, the overall stress change of the cemented backfill body was not significant, except for a non-linear increasing trend with depth in the middle and interior of the exposed surface. During the three-step mining, the backfill body exhibited a non-linear variation characteristic, with internal stress gradually increasing from top to bottom. The stress in the middle part was mainly due to the effect of self-weight, continuously increasing with depth. The stress in the backfill body at the contact point with the surrounding rock showed a pattern of first increasing and then decreasing, mainly due to the influence of surrounding rock constraint and lateral pressure. Furthermore, the stress redistribution caused by stope exposure resulted in more significant stress changes on the exposed surface.

[0114] Figures 20-23 Vertical stress cloud diagrams and curve variations after two-step and three-step mining of cemented backfill with a reduction factor of 2.11 MPa; Figure 20 The cemented filling body of the two-step mining chamber is shown in (A) as a three-dimensional view, (B) as a displacement cloud profile at y=20m, and (C) as a displacement cloud profile at x=300m. Figure 21The three-step mining chamber cemented backfill is shown in (D) as a three-dimensional view, (E) as a displacement cloud profile at y=20m, (F) as a displacement cloud profile at x=300m, and (G) as a displacement cloud profile at x=290m. When the 2.11MPa cemented backfill was first exposed, the vertical stresses at profiles y=20m and x=300m varied between 0.028 and -0.677MPa and 0.008 and -0.492MPa, respectively, with a maximum tensile stress of 0.096MPa. During the second exposure of the cemented backfill, the vertical stresses at profiles y=20m, x=300m, and x=290m varied between -0.027 and -1.303MPa, -0.032 and -0.756MPa, and 0.087 and -1.213MPa, respectively, with a maximum tensile stress of 0.121MPa. This tensile stress exceeded the maximum tensile stress of the backfill by 0.1MPa. Figure 21 The stress cloud diagram in section E also shows a clear shear stress trend, and there is continuity between the front and rear walls. Overall, the stress exceeds the stress that the current cemented backfill can withstand, and overall instability may have already been reached. From the monitoring lines, the overall stress also increased several times over during the transition from two-step to three-step mining.

[0115] S3. The three-dimensional analysis model of the strength requirement of cemented filling body is reconstructed by the column grid discretization method. Combined with the threshold obtained in step S2, the fracture surface and volume of the failure area of ​​cemented filling body are searched and determined, and the strength of cemented filling body is finally determined.

[0116] Extract the preliminary given cemented infill parameters and the numerical calculation data of the reduced cemented infill, including element number, node number, nodal displacement, and element stress field. Import this data into Matlab, and connect the center points of the vertical element meshes to form a composite column. Reconstruct the cemented infill mesh information in Matlab, such as... Figure 24 As shown, the safety factor corresponding to the center point of each element mesh is calculated using the column grid discretization method based on displacement and stress data. And displacement values, then search for dangerous damage points on each information extraction line, mark the coordinate information of potential damage points, and use a quadratic polynomial fitting method to smooth the surface to obtain the potential three-dimensional damage surface.

[0117] The criterion for potential mesh failure is the safety factor. and the total displacement value at the grid center When the permissible damage threshold is reached, the mesh is marked as a damaged mesh, as shown in the following two equations:

[0118] ;

[0119] ;

[0120] In the formula, —The safety factor value corresponding to the cube grid; —Permissible safety factor; —The total displacement value corresponding to the center point of the cube grid; —The allowable total displacement of the grid center point.

[0121] To calculate the center displacement of each element, first take the displacement values ​​of the element's eight nodes, then calculate their average value. This average value is the displacement at the element's center. The vector U of the element's center displacement has the following components. It is the following formula (3.1):

[0122] (3.1);

[0123] In the formula, —Representing the research unit node Displacement components in the direction.

[0124] The total displacement of the grid center point is calculated and then processed using the Euclidean norm. The Euclidean norm is the standard way to measure the length of a vector in geometric space. For a vector, the Euclidean norm is the distance from the origin to the endpoint of the vector. Therefore, the formula for calculating the total displacement U of the grid center point is as follows (3.2):

[0125] (3.2);

[0126] Solve using the following equation (3.3):

[0127] (3.3);

[0128] In the formula, —The cohesive force of the filling material; —Normal stress on any slip surface within a cubic mesh; —Internal friction angle of the filling material; —Shear stress along the sliding direction on any slip surface within the cube search mesh.

[0129] in, , These are the inherent physical parameters of the filling material. and The result needs to be calculated using the stress vector formulas in elastoplastic mechanics. The specific calculation formulas are shown in equations (3.4)-(3.8) below.

[0130] (3.4);

[0131] (3.5);

[0132] (3.6);

[0133] (3.7);

[0134] (3.8);

[0135] In the formula, —The normal stress vector on a plane in any direction; — The transpose of the following table —Indicates the normal direction of the plane in any direction; —The normal vector of the plane in any direction; —Shear stress vector along the sliding direction on an arbitrary plane; — transpose, subscript This indicates the downward direction of the arbitrary plane; —The downward direction vector of the arbitrary plane; —The six stress components corresponding to the center of the cuboid mesh, i.e., the stress state at the center point of the mesh.

[0136] To calculate and We still need to solve it first. and Within any spatial column, there will always exist a local sub-slip surface 6 formed by the intersection of the global slip surface and column 5. When the column mesh size is small, it can be assumed that the slip surface within the mesh is an approximate plane, and points M, N, P, and Q can be used to represent the intersection points of the slip surface and the four edges of the column along the z-axis. Any three of these points can determine the sub-slip surface. and ,like Figure 25 As shown.

[0137] Figure 25 , 26 As shown, several potential sub-slip surfaces 8 within the search grid are generated. The safety factor corresponding to each slip surface is calculated, and the most dangerous slip surface is further selected. In each search grid, any three non-collinear points can determine a potential sub-slip surface 8 within the search grid. The 12 edges of the i-th search grid 7 are divided into equally spaced segments, and the segmentation points formed on each edge are collected into a set. By selecting three non-collinear points D from this set... i1 D i2 D i3 Combine them to create any sliding surface within the mesh, such as Figure 26As shown. The plane formed by these points is the slip surface of the i-th search grid. The more segments there are, the more segmentation points are generated, and the more slip surfaces are formed, thus resulting in higher computational accuracy. Slip surface normal vector. The calculation formula is as follows:

[0138] ;

[0139] In the formula, —The normal vector of plane MNPQ; —The vector of the line segment formed by points M and N; —The vector of the line segment formed by points M and P.

[0140] like Figure 27 , 28 As shown, the sliding direction of the slip surface is variable. There are four possible scenarios for the calculation.

[0141] Case 1: When the z-coordinates of points M, N, and P are all equal, surface MNPQ is a plane perpendicular to the z-axis. Under the action of self-weight stress, the downward sliding direction vector is considered to be 0, i.e. =0, such as Figure 27 , 28 The sliding direction of the surface shown is the loss of momentum ①.

[0142] Case 2: When only the z-coordinates of points M and N are equal, surface MNPQ is simply an inclined plane with a slope along the y-axis. The downward sliding direction vector in this case... with vector Consistency, that is = ,like Figure 27 , 28 The sliding surface shown in Figure ② has a sliding direction vector, where the sliding direction vector 10 is... , .

[0143] Case 3: When only the z-coordinates of points N and P are equal, surface MNPQ is simply an inclined plane with a slope along the y-axis. The downward sliding direction vector in this case... with vector Consistency, that is = ,like Figure 27 , 28 The sliding surface shown in Figure ③ has a sliding direction vector, where the sliding direction vector 9 is... .

[0144] Case 4: When the z-coordinates of points M, N, and P are all unequal, surface MNPQ is a sloped plane with gradients in both the x and y directions. The downward sliding direction vector is then a superposition of Case 2 and Case 3, i.e. = ,like Figure 27 , 28 The sliding direction of the surface shown is the loss of momentum ④.

[0145] Multiple slip surfaces can be generated within each search grid. This is achieved through calculation... The safety factor corresponding to each slip surface is obtained. Using the minimum safety factor as the criterion, the most dangerous slip surface within that grid is identified, thus effectively determining the most dangerous slip surface within each search grid. If no search grid within a certain column satisfies the control conditions for slip surface search, it can be inferred that slippage will not occur within that column. Finally, based on the magnitude of the safety factor and its spatial location at each discrete point on the target filling body, a weighted average method is used to comprehensively calculate the overall safety factor, enabling a quantitative evaluation of the stability of the target filling body. The formula for calculating the weighted average overall safety factor is (3.9):

[0146] (3.9);

[0147] In the formula, —Safety factor of the fracture surface; —The number of discrete calculation points on the fracture surface; —The safety factor value of the i-th calculation point; —The safety factor value of the i-th calculation point.

[0148] The slip volume of the failure zone is the volume enclosed above the failure surface, which can be calculated using a double integral, as shown in equation (3.10):

[0149] (3.10);

[0150] In the formula, —Height of the top surface of the target filling body; —The most dangerous slip surface is at point . The height of the location; It is the integration region defined in the x and y directions.

[0151] If the set volume is greater than or equal to 30% of the total volume, the cemented filling will become unstable.

[0152] The numerical results obtained from the 2.11 MPa target filling body under a reduction factor of 2 were imported into a pre-written Matlab program for further analysis, yielding the fracture surfaces for two-step and three-step mining as shown below. Figure 29 , Figure 30As shown in the figure, when the target filling body was first exposed, the sliding failure direction of the three-dimensional spatial fracture surface obtained through the search was on one side of the two-step mining block. At this time, the safety factor of the sliding surface was 1.72, and the volume enclosed by the fracture surface of the filling body was 12158.08 m³. 3 It accounts for 25.32% of the total volume, and the total volume of the first-stage mining chamber is 48,000 m³. 3 The fracture surface extends 30m down from the top of the backfill at x=290m, connecting to the top of the exposed surface. Upon re-exposing the target backfill, the sliding failure direction of the fracture surface, obtained through a search, is along one side of the three-step mining block. At this point, the safety factor of the slip surface is 0.87, and the volume enclosed by the fracture surface is 19487.28m³. 3 This accounts for 40.5% of the total volume. At this point, the filling body has already experienced overall instability, which further verifies that the 2.11MPa target filling body will experience overall failure in the three-step mining chamber under the condition of a reduction factor of 2.

[0153] Based on the above analysis, the required strength of the cemented filling body is 2.16 MPa when the safety factor is 2. The recommended design strength values ​​of the filling body can be obtained by calculating the strength requirement iterative search model of the cemented filling body, as shown in Table 2.

[0154] Table 2: Recommended Design Strength Values ​​for Fillings

[0155] Operating conditions Initial strength / MPa Critical strength / MPa Take a safety factor of 2 / MPa Lateral pressure coefficient at a burial depth of 1000m is 1 2.11 1.08 2.16

Claims

1. A method for calculating the strength of deep-stage cemented infill bodies considering the timing of mining and filling, characterized in that, The process includes the following steps: S1. Constructing a three-dimensional finite element model of the mining and backfilling sequence of underground ore bodies and performing numerical simulation calculations; S2. By establishing a cusp displacement mutation analysis function for typical measuring points using the strength reduction method, the thresholds for total displacement and safety factor are determined. Qualitative analysis is then performed using displacement and stress cloud diagrams from the finite element cemented filling numerical model to verify the rationality of the thresholds. S3. The three-dimensional analysis model of the strength requirement of cemented filling body is reconstructed by the column grid discretization method. The volume of the fracture surface and the failure area of ​​cemented filling body is determined based on the total displacement and the safety factor threshold, and the required strength of cemented filling body is finally determined.

2. The method for calculating the strength of deep-stage cemented infill considering the mining sequence as described in claim 1, characterized in that, Step S1: Based on the strength of the cemented backfill, design the surrounding rock and ore body conditions of the mine, establish a three-dimensional finite element model of the mining and backfilling sequence process of the ore body, and perform numerical simulation calculations; the mining and backfilling process consists of three consecutive adjacent ore blocks, and three steps of mining and backfilling are carried out.

3. The method for calculating the strength of deep-stage cemented infill considering the mining sequence as described in claim 2, characterized in that, The three-step mining and filling process is as follows: the first step is to mine the middle block and fill the void with cemented filling, with the filling body grid being a regular hexahedral grid; the second step is to mine one side of the block and fill the void without cementing; the third step is to mine the other side of the block and not fill the void.

4. The method for calculating the strength of deep-stage cemented infill considering the mining sequence as described in claim 1, characterized in that, Step S2: Initially select a cemented backfill body parameter with a certain lime-sand ratio and perform numerical simulation calculations for step S1. Select the total displacement of the center point of the exposed face of the cemented backfill body in the void area of ​​the mining block during the mining of the right-side block as the analysis index. Use the strength reduction method to evaluate the cohesion C and internal friction angle of the cemented backfill body before reduction. Perform the reduction and repeat step S1 numerical simulation calculation, and extract the total displacement of the center point of the exposed surface after each calculation. With the reduction factor F, cusp catastrophe theory is used to construct Cusp mutation model function of F The mutation characteristic value was obtained, the critical strength of the cemented filling body was initially determined, and the total displacement value of the mutation point and the safety factor were set as the safety threshold.

5. The method for calculating the strength of deep-stage cemented infill considering the timing of mining and filling, as described in claim 4, is characterized in that: The cemented filler parameters C and Strength reduction is performed according to the following formulas (2.1) and (2.2): （2.1）； （2.2）； In the formula, —Cohesion of the filling material after reduction; —Angle of friction within the filler after reduction; C —Cohesion of the filler before reduction; — Friction angle of the filling material before reduction; F — Reduction factor; The cusp mutation model function Perform according to the following formula (2.3): （2.3）； In the formula, a0, a1, a2, a3, and a4 are undetermined coefficients; let Then, the formula for the standard function V value of the cusp mutation can be transformed into the following equation (2.4): （2.4）； In the formula, , ; but It can be used as the distance between the evolutionary state and the critical state of cemented filling, and is called the mutation characteristic value.

6. A method for calculating the strength of deep-stage cemented infill considering the timing of mining, as described in any one of claims 1-5, characterized in that, Step S3: Extract the preliminary given cemented infill parameters and the numerical calculation data of the reduced cemented infill, including element number, node number, node displacement, and element stress field. Import this data into Matlab. Connect the center points of the vertical element meshes to form a combined column. Reconstruct the cemented infill mesh in Matlab, based on the total displacement determined in step S2. The fracture surface is searched using the reduction factor F. A smooth surface is generated using the surf function in Matlab, and the volume of the fracture envelope is calculated. If the volume is greater than or equal to 30% of the total volume, the cemented filling body will become unstable.

7. The method for calculating the strength of deep-stage cemented infill considering the timing of mining and filling, as described in claim 6, is characterized in that... The displacement of the reconstructed mesh center is calculated using the following formula: To calculate the center displacement of each element, first take the displacement values ​​of the eight nodes of that element, then calculate their average value. This average value is the displacement at the element center. The vector U of the element center displacement has several components. It is the following formula (3.1): （3.1）； In the formula: —Representing the research unit node Displacement components in the direction; The formula for calculating the total displacement U is as follows (3.2): （3.2）； The safety factor of the reconstructed grid center is calculated according to the following formula (3.3): （3.3）； In the formula: —The cohesive force of the filling material; —Normal stress on any slip surface within a cubic mesh; —Internal friction angle of the filling material; —Shear stress along the downward direction on any slip surface within the cube search grid; in , These are the inherent physical parameters of the filling material; and Then it is necessary to calculate it according to the relevant formulas of stress vector in elastoplastic mechanics. The specific calculation formulas are shown in the following formulas (3.4)-(3.8). （3.4）； （3.5）； in, （3.6）； （3.7）； （3.8）； In the formula: —The normal stress vector on a plane in any direction; — The transpose of the following table —Indicates the normal direction of the plane in any direction; —The normal vector of the plane in any direction; —Shear stress vector along the sliding direction on an arbitrary plane; — transpose, subscript This indicates the downward direction of the arbitrary plane; —The downward direction vector of the arbitrary plane; —The six stress components corresponding to the center of the cuboid mesh, that is, the stress state at the center point of the mesh; The safety factor of the fracture surface is calculated according to the following formula (3.9): （3.9）； In the formula: —Safety factor of the fracture surface; —The number of discrete calculation points on the fracture surface; —The safety factor value of the i-th calculation point; —The safety factor value of the i-th calculation point; The volume of the broken bread is calculated according to the following formula (3.10): （3.10）； In the formula: —Height of the top surface of the target filling body; —The most dangerous slip surface is at point . The height of the location; It is the integration region defined in the x and y directions.

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