A Multi-Objective Optimization Method for Filling Slurry Based on Response Surface Regression

Abstract

This invention provides a multi-objective optimization method for filling slurry based on response surface regression, comprising the following steps: determining the raw materials of the filling slurry; determining the range of the mass fraction ratio of waste rock to rod mill sand based on the maximum packing density of the aggregate; selecting a first preset quantity of the mass fraction ratio of waste rock to rod mill sand from the range as a first quantitative parameter; and inputting the first, second, third, and fourth quantitative parameters as slurry strength variables into a preset strength regression model to calculate the strength value of the filling slurry. This invention can solve the problems in the prior art where the contradiction between the "water requirement" of slurry transportation and the "hydrophobicity" of the filling body strength remains unresolved; and the problems that arise from the addition of tailings to waste rock coarse aggregate filling slurry, where the flocculation structure in the tailings and the adsorption of free water by fine particles weaken the fluidity of the filling slurry, increasing the difficulty of pipeline transportation.

Description

Technical Field

[0001] This invention relates to the field of slurry filling technology, and more specifically, to a multi-objective optimization method for filling slurries based on response surface regression. Background Technology

[0002] Cemented backfill slurry is generally prepared by mixing and stirring aggregates, binders, and water in a certain proportion. Its purpose is to control ground stress in the mining area using mine tailings, preventing surrounding rock deformation or surface subsidence, while relieving environmental pollution pressure from surface tailings accumulation. During the transportation of backfill slurry, high-concentration coarse aggregate backfill slurry has a large yield stress and viscosity coefficient. Long-distance pipeline transportation requires pumping to provide initial kinetic energy to overcome the frictional resistance from the pipe wall during transportation. As the mining depth increases, the coefficient of performance decreases, and some mines use gravity transportation instead of pumping to alleviate the high cost of pumping. Due to the large backfill volume, complex pipeline system, inconsistent backfill pipe diameter, poor controllability of the homogeneity of high-concentration slurry mixed with tailings, and unclear rheological and time-varying properties of the slurry during transportation, backfill pipeline blockage accidents are difficult to avoid. There are two main existing optimization design methods for cemented backfill slurry transportation. (1) Optimize the pipeline system: Improve the efficiency of slurry transportation by adjusting the pipeline layout, pipe diameter, pipeline material and environmental temperature and humidity; (2) Improve the slurry flow characteristics: Based on the results of physical test, optimize the slurry flow characteristics by adjusting the aggregate ratio and concentration of the slurry or adding external reagents. The characteristics of both methods are highly dependent on the results of engineering or physical tests. Whether adjusting the filling pipeline or carrying out flowability industrial tests, the operation and maintenance costs of mining enterprises are high in terms of time and manpower. After being filled into the goaf for a period of time, the slurry solidifies into a filling body. Its strength is the key factor that determines the filling quality and filling cost. There are two main existing methods for optimizing the strength of cemented filling bodies. (1) Improve the properties of the binder: Based on the principle of CSH gel generation by cement hydration reaction, develop a new type of cementitious material for optimizing the strength of tailings filling bodies; (2) Add admixtures: Increase the mass concentration of filling slurry by adding water-reducing agents or increase the early strength of filling bodies by adding early strength agents. Both methods are characterized by the fact that, as the hydration reaction proceeds, a structure with a certain strength is formed inside the cemented tailings backfill, filling the voids.

[0003] In summary, the current technology has the following drawbacks:

[0004] 1. The "mutual exclusion" between the cost of backfill materials and the strength of the backfill body. Based on the existing two methods for optimizing the strength of cemented backfill bodies, improving the curing strength of the backfill slurry requires the additional purchase of new cementitious materials, admixtures, or an increase in the amount of cement, which significantly increases the backfill cost. On the other hand, if the material cost is reduced to alleviate the pressure on mining companies, incomplete hydration reaction or even sedimentation and segregation of materials will cause a loss of backfill strength and affect the production process.

[0005] 2. The "singleness" of factors in the optimization process of backfill strength. In actual production, parameters such as slurry concentration and aggregate gradation all affect the strength of the backfill. The coupling effect between different parameters restricts the optimization and maximization of backfill strength. Considering only a single factor may affect other production processes. For example, only increasing the slurry concentration will inevitably affect the slurry's fluidity; only calculating material costs will inevitably affect the amount of binder used. In addition, the impact of gradation factors on the strength of backfill when using waste rock should not be underestimated.

[0006] 3. The contradiction between the "water requirement" of slurry transportation and the "hydrophobicity" of the filling body strength. After adding tailings to waste rock coarse aggregate filling slurry, the flocculation structure of the tailings and the adsorption of free water by fine particles weaken the slurry's fluidity, increasing its transportation difficulty. To eliminate these adverse effects, a technical measure based on material modification is needed to improve the workability of the filling slurry and reduce its transportation resistance. Currently, research on adapting various additives to high-concentration waste rock tailings filling slurry is relatively scarce. Especially after adding different types and quantities of modifying additives, although the slurry's fluidity properties are improved to some extent, the changes in the slurry's consolidation time and cementitious strength are unclear. Summary of the Invention

[0007] In view of the above problems, the purpose of this invention is to provide a multi-objective optimization method for filling slurry based on response surface regression, so as to solve the contradiction between the "water requirement" of slurry transportation and the "hydrophobicity" of filling body strength in the existing technology; and the problem that after adding tailings to waste rock coarse aggregate filling slurry, the flocculation structure in the tailings and the effect of fine particles adsorbing free water weaken the fluidity of the filling slurry and increase the difficulty of pipeline transportation.

[0008] This invention provides a multi-objective optimization method for filling slurry based on response surface regression, comprising the following steps:

[0009] S1. Determine the raw materials for the filling slurry, wherein the raw materials include aggregates, binders, water-reducing agents and water; wherein the aggregates include coarse aggregates composed of waste rock and rod mill sand and fine aggregates composed of tailings sand;

[0010] S2. Based on the maximum bulk density of the aggregate and the preset material mass fraction ratio of coarse aggregate to fine aggregate, determine the range of the mass fraction ratio of waste rock to rod mill sand.

[0011] S3. Select a first preset quantity of the mass fraction ratio of waste rock to the rod mill sand from the range as a first quantitative parameter, and select a second preset quantity of the mass fraction ratio of binder to aggregate from the preset range of mortar ratio as a second quantitative parameter, select a third preset quantity of the mass concentration of filling slurry from the preset range of filling slurry mass concentration as a third quantitative parameter, and select a fourth preset quantity of curing age as a fourth quantitative parameter. Input the first quantitative parameter, the second quantitative parameter, the third quantitative parameter, and the fourth quantitative parameter as slurry strength variables into a preset strength regression model to calculate the strength value of the filling slurry, and select the first quantitative parameter, the second quantitative parameter, and the third quantitative parameter that meet the preset strength requirements from the calculation results.

[0012] S4. The first quantitative parameter, the second quantitative parameter, and the third quantitative parameter that meet the preset strength requirements, along with the fifth preset amount of water-reducing agent selected from the preset range of water-reducing agent addition amount, are used as slurry rheological variables and input into the preset rheological regression model to calculate the rheological parameters of the filling slurry. The first quantitative parameter, the second quantitative parameter, the third quantitative parameter, and the amount of admixture that meet the preset rheological parameter requirements are selected from the calculation results and used as the first target variable, the second target variable, the third target variable, and the fourth target variable, respectively.

[0013] S5. Input the first target variable, the second target variable, the third target variable and the fourth target variable into the preset slurry cost model, and calculate the raw material ratio scheme of the filling slurry that meets both the strength requirements and the rheological requirements of the filling slurry with the lowest cost.

[0014] Furthermore, a preferred embodiment is that the density of the waste rock is 2.79–2.97 t·m³. -3 The bulk density is 1.60–1.76 t·m³. -3 The particle size distribution ranges from 0.1 to 15.0 mm, and the chemical composition contains 47.71% SiO2 and 16.39% CaO by mass; and / or,

[0015] The density of the rod-ground sand is 2.71–2.87 t·m³. -3 The bulk density is 1.49–1.63 t·m³. -3 The particle size distribution ranges from 0.1 to 15.0 mm, and the chemical composition contains 75.75% SiO2 and 10.95% Al2O3 by mass; and / or,

[0016] The density of the tailings is 2.74–2.82 t·m³. -3 The bulk density is 1.18–1.26 t·m³. -3 The particle size distribution ranges from 0.28 to 447.7 μm, and the mass percentage of SiO2 in the chemical composition is 42.20% and the mass percentage of MgO is 32.71%.

[0017] Furthermore, a preferred embodiment is that the binder is silicate cement; and / or, the water-reducing agent has a pH of 6.20 / 10 g·L. -1 Polycarboxylate superplasticizer.

[0018] Furthermore, a preferred embodiment is that the range for determining the mass fraction ratio of waste rock to rod mill sand based on the maximum bulk density of the aggregate and a preset material mass fraction ratio of coarse aggregate to fine aggregate includes:

[0019] Based on the cemented tailings backfill, the particle size distribution index of the aggregate is calculated using the Talbol gradation theory. By adjusting the mass fraction of the waste rock and the rod milled sand, the particle size composition of the aggregate is controlled, so that the particle size distribution index of the aggregate tends to the ideal value, thereby determining the preliminary range of the mass fraction ratio of the waste rock and the rod milled sand.

[0020] Based on the preliminary range, the maximum bulk density of the aggregate is calculated using a two-dimensional mixture bulk density model to reduce the proportion of binder in the filling slurry, and the range of the mass fraction ratio of waste rock to rod mill sand is obtained.

[0021] Furthermore, in a preferred embodiment, the formula for calculating the particle size distribution index of the aggregate using Talbol gradation theory is as follows:

[0022]

[0023] Where n is the Talbol particle size distribution index; D max D represents the maximum particle size in the aggregate test sample; D is the particle size index of the aggregate test sample; M is the mass of aggregate particles with a particle size not exceeding index D; M t The total mass of the aggregate test sample is given. The Talbol particle size distribution indices of waste rock and rod-ground sand are 0.687 and 0.335, respectively. The Talbol index of aggregate under ideal conditions is between the two.

[0024] Furthermore, a preferred embodiment is that the calculation formula for the two-dimensional mixture bulk density model is as follows:

[0025] in,

[0026] ρ1 is the density of waste rock; ρ2 is the density of rod mill sand; ρ is the mixed density of waste rock and rod mill sand; Φ1 is the bulk density of waste rock; Φ2 is the bulk density of rod mill sand; x is the proportion of waste rock in the total mass of aggregate, with a value range of 0 to 50%; based on the preset material mass fraction ratio of coarse aggregate to fine aggregate, the process of the change of aggregate bulk density with the mass ratio of waste rock to rod mill sand is calculated, and the range of the mass fraction ratio of waste rock to rod mill sand is obtained after solving.

[0027] Furthermore, a preferred embodiment includes, before calculating the strength value of the filling grout using the preset strength regression model, testing the accuracy of the preset strength regression model, including:

[0028] Select the test data set of the slurry strength variable, and input the test data set into the preset strength regression model to calculate the strength value of the filling slurry and obtain the calculation result data;

[0029] The error value is obtained by comparing the calculated data with the experimental data obtained by using the test data set as experimental data and conducting a composite test of the curing strength center of the filling slurry.

[0030] When the error value is less than the first preset error threshold, the preset strength regression model passes the accuracy test.

[0031] Furthermore, a preferred embodiment includes, before calculating the rheological parameters of the filling slurry using the preset rheological regression model, testing the accuracy of the preset rheological regression model, including:

[0032] Select the test data set of the slurry rheological variables, and input the test data set into the preset rheological regression model to calculate the rheological parameters of the filling slurry and obtain the calculation result data;

[0033] The error value is obtained by comparing the calculated data with the experimental data obtained by measuring the rheological properties of slurry at a constant shear rate using a rheometer with the test data set as the experimental data.

[0034] When the error value is less than the second preset error threshold, the preset rheological regression model passes the accuracy test.

[0035] Furthermore, in the preferred embodiment, the mass fraction ratio of the waste rock to the rod mill sand in the slurry strength variables is 3:7, 5:5, and 7:3; the mass fraction ratio of the binder to the aggregate is 1:6, 1:5, and 1:4; and the curing period of the filling slurry is 3 days, 7 days, and 28 days.

[0036] In the slurry rheological variables, there are 6 sets of data for the amount of water-reducing agent added, which are 0.00%, 0.10%, 0.20%, 0.30%, 0.40%, and 0.50% by mass concentration.

[0037] Furthermore, in a preferred embodiment, the calculation formula for the preset slurry cost model is as follows:

[0038] minf = [M j ]×j+[M f ]×f+[M b ]×b+[M q ]×q+[M w ]×w+[M pc ]×A

[0039] y1≥[C 3d ],y2≥[C 7d ],y3≥[C 28d ], 0≤A≤3.2×10 -3

[0040] j+f+b+q+w+A=m

[0041]

[0042]

[0043]

[0044]

[0045] z1≤[σ1]

[0046] z2≤[η1];

[0047] Where minf is the minimum cost of the filling slurry, [M j [M] represents the unit price of the binder. f [M] represents the unit price of waste rock. b [M] represents the unit price of rod grinding. q [M] represents the unit price of tailings. w [M] represents the unit price of the carrier. pc [C] represents the unit price of the admixture, j represents the mass of the binder, f represents the mass of the waste rock, b represents the mass of the rod mill sand, q represents the mass of the tailings, w represents the mass of the carrier, A represents the mass of the admixture, A = a * 1t, y1, y2, and y3 represent the strengths of the filling slurry output from the preset rheological regression model at curing ages of 3d, 7d, and 28d, respectively. 3d [C] 7d [C] 28d[σ1] represents the minimum strength of the filling slurry at curing ages of 3d, 7d, and 28d, respectively; m represents the total mass of the filling slurry; h represents the preset mass fraction ratio of coarse aggregate to fine aggregate; e and E represent the minimum and maximum mass fraction ratios of waste rock and rod mill sand, respectively; g and G represent the minimum and maximum mass fraction ratios of binder to aggregate, respectively; r and R represent the minimum and maximum mass concentrations of the filling slurry, respectively; z1 represents the yield stress of the filling slurry output by the preset rheological regression model; [σ1] represents the preset design value of yield stress; z2 represents the plastic viscosity of the filling slurry output by the preset rheological regression model; and [η1] represents the preset design value of plastic viscosity.

[0048] As can be seen from the above technical solution, the multi-objective optimization method for filling slurry based on response surface regression provided by this invention quantifies the response of the interaction between multiple factors by using the response surface regression calculation method to obtain the optimal solution of the multi-objective parameters; it fully considers the influence of aggregate gradation, mass fraction ratio of waste rock to rod mill sand, mass fraction ratio of binder to aggregate, and mass concentration of filling slurry on the curing strength of filling slurry, as well as the influence of the amount of water-reducing agent added on the rheological properties of filling slurry, to seek the balance point between "strength" and "flow" in the filling process of mine filling, and optimize the filling process in order to achieve the goal of "cost reduction and efficiency improvement" in mining; it effectively solves the contradiction between "water requirement" in slurry transportation and "hydrophobicity" of filling body strength that has not been solved in the prior art, as well as the problem that the increased fluidity of filling slurry leads to the difficulty of pipeline transportation.

[0049] To achieve the foregoing and related objectives, one or more aspects of the invention include the features that will be described in detail below. The following description and accompanying drawings illustrate certain exemplary aspects of the invention. However, these aspects indicate only a few of the various ways in which the principles of the invention can be used. Furthermore, the invention is intended to encompass all such aspects and their equivalents. Attached Figure Description

[0050] Other objects and results of the invention will become more apparent and readily understood with reference to the following description taken in conjunction with the accompanying drawings. In the drawings:

[0051] Figure 1 This is a flowchart of a multi-objective optimization method for filling slurry based on response surface regression according to an embodiment of the present invention;

[0052] Figure 2 This is a schematic diagram of a multi-objective optimization method for filling slurry based on response surface regression according to an embodiment of the present invention.

[0053] Figure 3 This is a graph showing the Talbol calculation results of the particle size of waste rock and rod mill sand in Example 1 of the present invention;

[0054] Figure 4 This is a graph showing the calculated bulk density of the mixed coarse aggregate of waste rock and rod mill sand in Example 1 of the present invention;

[0055] Figure 5 This is a bird's-eye view of the interaction of intensity response factors in Embodiment 1 of the present invention;

[0056] Figure 6 This is a graph showing the relative error between the calculation results and the actual results of the preset intensity regression model in Embodiment 1 of the present invention.

[0057] Figure 7 The rheological property curve of the slurry under the action of polycarboxylate superplasticizer in Example 1 of the present invention;

[0058] Figure 8 The image shows an electron microscope scan of the filling material in Example 1 of the present invention after curing for 28 days. (a) shows the filling material before optimization, (b) shows the maximum strength ratio, and (c) shows the ratio after response surface regression optimization.

[0059] In the accompanying drawings, the same reference numerals indicate similar or corresponding features or functions. Detailed Implementation

[0060] In the following description, numerous specific details are set forth for illustrative purposes and to provide a thorough understanding of one or more embodiments. However, it will be apparent that these embodiments may also be implemented without these specific details.

[0061] To address the unresolved contradiction between the "water requirement" for slurry transportation and the "hydrophobicity" of the filling body strength in the existing technologies mentioned above, and the fact that the addition of tailings to waste rock coarse aggregate filling slurry reduces the fluidity of the filling slurry and increases the difficulty of pipeline transportation due to the flocculation structure of the tailings and the adsorption of free water by fine particles, a multi-objective optimization method for filling slurry based on response surface regression is proposed.

[0062] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0063] To illustrate the multi-objective optimization method for filling slurry based on response surface regression provided by this invention, Figure 1 The flowchart of a multi-objective optimization method for filling slurry based on response surface regression according to an embodiment of the present invention is shown; Figure 2 The principle of a multi-objective optimization method for filling slurry based on response surface regression according to an embodiment of the present invention is illustrated; Figure 3 The Talbol calculation results for the particle size of waste rock and rod mill sand in Embodiment 1 of the present invention are shown; Figure 4 The calculation results of the bulk density of the mixed coarse aggregate of waste rock and rod mill sand in Embodiment 1 of the present invention are shown. Figure 5 The interaction of intensity response factors in Embodiment 1 of the present invention is illustrated; Figure 6 The relative error between the calculation results and the actual results of the preset intensity regression model in Embodiment 1 of the present invention is shown; Figure 7 The rheological properties of the slurry under the action of the polycarboxylate superplasticizer in Example 1 of the present invention are shown. Figure 8 The following is a scanning electron microscope image of the filling material in Example 1 of the present invention after curing for 28 days, wherein (a) is the filling material before optimization, (b) is the maximum strength ratio, and (c) is the ratio after response surface regression optimization.

[0064] like Figures 1 to 8 As shown in the figure, the multi-objective optimization method for filling slurry based on response surface regression provided by the present invention includes the following steps:

[0065] S1. Determine the raw materials for the filling slurry, which include aggregates, binders, water-reducing agents, and water; wherein, the aggregates include coarse aggregates composed of waste rock and rod mill sand and fine aggregates composed of tailings sand;

[0066] S2. Based on the maximum bulk density of the aggregate and the preset material mass fraction ratio of coarse aggregate to fine aggregate, determine the range of the mass fraction ratio of waste rock to rod mill sand.

[0067] S3. Select a first preset quantity of waste rock to rod mill sand mass fraction ratio as the first quantitative parameter from the range, and select a second preset quantity of binder to aggregate mass fraction ratio as the second quantitative parameter from the preset range of binder-mortar ratio, select a third preset quantity of filling slurry mass concentration as the third quantitative parameter from the preset range of filling slurry mass concentration, and select a fourth preset quantity of curing age as the fourth quantitative parameter. Input the first, second, third, and fourth quantitative parameters as slurry strength variables into the preset strength regression model to calculate the strength value of the filling slurry, and select the first, second, and third quantitative parameters that meet the preset strength requirements from the calculation results.

[0068] S4. Input the first, second, and third quantitative parameters that meet the preset strength requirements, along with the fifth preset amount of water-reducing agent selected from the preset range of water-reducing agent addition amount, as slurry rheological variables into the preset rheological regression model to calculate the rheological parameters of the filling slurry. From the calculation results, select the first, second, and third quantitative parameters and the amount of admixture that meet the preset rheological parameter requirements, and use them as the first, second, third, and fourth target variables, respectively.

[0069] S5. Input the first objective variable, the second objective variable, the third objective variable and the fourth objective variable into the preset slurry cost model, and calculate the raw material ratio scheme of the filling slurry that meets both the strength requirements and the rheological requirements of the filling slurry with the lowest cost.

[0070] By utilizing response surface regression to quantify the interaction between multiple factors, the optimal solution for multi-objective parameters is obtained. The study fully considers the influence of aggregate gradation, the mass ratio of waste rock to ground sand, the mass ratio of binder to aggregate, and the mass concentration of the filling slurry on the curing strength of the filling slurry, as well as the influence of the amount of water-reducing agent added on the rheological properties of the filling slurry. It seeks to find the balance between "strength" and "flow" in the backfilling process of mining, optimizing the backfilling process to achieve the goal of "cost reduction and efficiency improvement" in mining. It effectively solves the contradiction between the "water requirement" of slurry transportation and the "hydrophobicity" of the filling body strength, which were unresolved in existing technologies, as well as the difficulties in pipeline transportation caused by the increased fluidity of the filling slurry.

[0071] As a preferred embodiment of the present invention, the density of the waste rock is 2.79–2.97 t·m³. -3 The bulk density is 1.60–1.76 t·m³. -3 The particle size distribution ranges from 0.1 to 15.0 mm, and the chemical composition contains 47.71% SiO2 and 16.39% CaO by mass; and / or,

[0072] The density of the rod-ground abrasive is 2.71–2.87 t·m³. -3 The bulk density is 1.49–1.63 t·m³. -3 The particle size distribution ranges from 0.1 to 15.0 mm, and the chemical composition contains 75.75% SiO2 and 10.95% Al2O3 by mass; and / or,

[0073] The density of the tailings is 2.74–2.82 t·m³. -3 The bulk density is 1.18–1.26 t·m³. -3 The particle size distribution ranges from 0.28 to 447.7 μm, and the mass percentage of SiO2 in the chemical composition is 42.20%, while the mass percentage of MgO is 32.71%. Among them, d 10 =2.2μm, d 50 =16.9μm, d 90 =76.0μm; that is, the particle size of the material corresponding to the cumulative mass, such as d 10 This refers to arranging materials according to their particle size from smallest to largest. When the accumulated tailings mass is 10% of the total aggregate mass, the corresponding material particle size is 2.2 micrometers.

[0074] As a preferred embodiment of the present invention, the binder is silicate cement; preferably, it is ordinary silicate cement P·O42.5 conforming to GB 175-2007 standard, and / or, the water-reducing agent is pH 6.20 / 10g·L. -1 Polycarboxylate superplasticizers. Among them, CL - The mass fraction of the slurry is 0.06%, and the mass fraction of Na2SO4 is 2.60%. In this embodiment, water is used as the carrier for the filling slurry, preferably industrial water conforming to GB / T19923-2005, taken from a mine filling station.

[0075] As a preferred embodiment of the present invention, based on the maximum bulk density of the aggregate and a preset material mass fraction ratio of coarse aggregate to fine aggregate, the range of the mass fraction ratio of waste rock to rod mill sand includes:

[0076] Based on the cemented tailings backfill, the particle size distribution index of the aggregate is calculated using the Talbol gradation theory. By adjusting the mass fraction of waste rock and the rod milled sand, the particle size composition of the aggregate is controlled, so that the particle size distribution index of the aggregate tends to the ideal value, thereby determining the preliminary range of the mass fraction ratio of waste rock and the rod milled sand.

[0077] Based on the preliminary range, the maximum bulk density of the aggregate is calculated using a two-dimensional mixture bulk density model to reduce the proportion of binder in the filling slurry, and the range of the mass fraction ratio of waste rock to rod mill sand is obtained by solving.

[0078] Among them, the Talbol gradation theory states that if the calculated Talbol index of a certain component is higher than 0.5 under ideal conditions, it indicates that the mass fraction of the component is too large, and if it is lower than 0.5, it is too small. In this invention, it is used to optimize the gradation.

[0079] As a preferred embodiment of the present invention, the formula for calculating the aggregate particle size distribution index using Talbol gradation theory is as follows:

[0080]

[0081] Where n is the Talbol particle size distribution index; D max D represents the maximum particle size in the aggregate test sample; D is the particle size index of the aggregate test sample; M is the mass of aggregate particles with a particle size not exceeding index D; M t The total mass of the aggregate test sample is given. The Talbol particle size distribution indices of waste rock and rod-ground sand are 0.687 and 0.335, respectively. The Talbol index of aggregate under ideal conditions is between the two.

[0082] As a preferred embodiment of the present invention, the calculation formula for the two-dimensional mixture packing density model is as follows:

[0083] in,

[0084] ρ1 is the density of waste rock; ρ2 is the density of rod mill sand; ρ is the mixed density of waste rock and rod mill sand; Φ1 is the bulk density of waste rock; Φ2 is the bulk density of rod mill sand; x is the proportion of waste rock in the total mass of aggregate, with a value range of 0 to 50%; based on the preset material mass fraction ratio of coarse aggregate to fine aggregate, the process of the change of aggregate bulk density with the mass ratio of waste rock to rod mill sand is calculated, and the range of the mass fraction ratio of waste rock to rod mill sand is obtained after solving.

[0085] As a preferred embodiment of the present invention, before calculating the strength value of the filling grout using the preset strength regression model, the accuracy of the preset strength regression model is tested, including:

[0086] Select a set of test data for the slurry strength variable, and input the set of test data into a preset strength regression model to calculate the strength value of the filling slurry and obtain the calculation result data;

[0087] The error value is obtained by comparing the calculated data with the experimental data obtained by the composite test of the curing strength center of the filling slurry, which was previously used as the test data set;

[0088] When the error value is less than the first preset error threshold, the preset strength regression model passes the accuracy test.

[0089] As a preferred embodiment of the present invention, before calculating the rheological parameters of the filling slurry using a preset rheological regression model, the accuracy of the preset rheological regression model is tested, including:

[0090] Select a set of test data for the rheological variables of the slurry, and input the test data set into a preset rheological regression model to calculate the rheological parameters of the filling slurry and obtain the calculation results data;

[0091] The error value is obtained by comparing the calculated data with the experimental data obtained by measuring the rheological properties of slurry at a constant shear rate using a rheometer with the test data set as the experimental data.

[0092] When the error value is less than the second preset error threshold, the preset rheological regression model passes the accuracy test.

[0093] As a preferred embodiment of the present invention, in the slurry strength variable, the mass fraction ratio of waste rock to rod mill sand is 3:7, 5:5 and 7:3; the mass fraction ratio of binder to the aggregate is 1:6, 1:5 and 1:4; and the curing age of the filling slurry is 3 days, 7 days and 28 days.

[0094] In the slurry rheological variables, there are 6 sets of data for the amount of water-reducing agent added, with mass concentrations of 0.00%, 0.10%, 0.20%, 0.30%, 0.40%, and 0.50%.

[0095] As a preferred embodiment of the present invention, the calculation formula for the preset slurry cost model is as follows:

[0096] minf = [M j ]×j+[M f ]×f+[M b ]×b+[M q ]×q+[M w ]×w+[M pc ]×A

[0097] y1≥[C 3d ],y2≥[C 7d ],y3≥[C 28d ], 0≤A≤302×10 -3

[0098] j+f+b+q+w+A=m

[0099]

[0100]

[0101]

[0102]

[0103] z1≤[σ1]

[0104] z2≤[η1];

[0105] Where minf is the minimum cost of the filling slurry, [M j [M] represents the unit price of the binder. f [M] represents the unit price of waste rock. b [M] represents the unit price of rod grinding. q [M] represents the unit price of tailings. w [M] represents the unit price of the carrier. pc [C] represents the unit price of the admixture, j represents the mass of the binder, f represents the mass of the waste rock, b represents the mass of the rod mill sand, q represents the mass of the tailings, w represents the mass of the carrier, A represents the mass of the admixture, A = a * 1t, y1, y2, and y3 represent the strengths of the filling slurry output from the preset rheological regression model at curing ages of 3d, 7d, and 28d, respectively. 3d [C] 7d [C] 28d[σ1] represents the minimum strength of the filling slurry at curing ages of 3d, 7d, and 28d, respectively; m represents the total mass of the filling slurry; h represents the preset mass fraction ratio of coarse aggregate to fine aggregate; e and E represent the minimum and maximum mass fraction ratios of waste rock and rod mill sand, respectively; g and G represent the minimum and maximum mass fraction ratios of binder to aggregate, respectively; r and R represent the minimum and maximum mass concentrations of the filling slurry, respectively; z1 represents the yield stress of the filling slurry output by the preset rheological regression model; [σ1] represents the preset design value of yield stress; z2 represents the plastic viscosity of the filling slurry output by the preset rheological regression model; and [η1] represents the preset design value of plastic viscosity.

[0106] The following examples will further illustrate the present invention so that those skilled in the art can better understand its advantages and features.

[0107] Example 1:

[0108] like Figure 2 As shown, the multi-objective optimization design method for filling slurry based on response surface regression determines the raw materials of the aggregates in the filling slurry, and prepares various calculation methods and model evaluation schemes according to the design principle diagram. Specifically, it may include: formulating the aggregate gradation optimization calculation scheme, setting up a strength regression model, setting up a rheological regression model, evaluating the accuracy of the response surface regression model, and setting up a slurry cost model.

[0109] like Figure 3 As shown, the particle size distribution optimization process uses Talbol gradation theory to calculate the particle size composition of coarse aggregate. Talbol gradation theory calculates the mass M of aggregate with a particle size not exceeding the index D and the total mass M of the test sample. t The particle size distribution within this range is determined using the following formula:

[0110]

[0111] Where: n is the Talbol particle size distribution index; D max denoted as the maximum particle size in the test sample; D is the particle size index of the test sample; the Talbol particle size distribution indices of waste rock and rod milled sand are 0.687 and 0.335, respectively. Under ideal conditions, the Talbol index of coarse aggregate is 0.500, which is between the two. It is preferable to use a two-dimensional mixture packing density model to solve for the mass fraction of waste rock, rod milled sand and tailings.

[0112] like Figure 4 As shown. The bulk density of a single aggregate can be calculated using a two-dimensional mixture bulk density model to obtain the bulk density of the mixed aggregate. Using aggregate bulk density and density calculations, the bulk densities of waste rock, rod mill sand, and tailings are determined to be 0.684, 0.598, and 0.548, respectively. Further, according to the two-dimensional mixture bulk density model:

[0113]

[0114] Where: ρ1 and ρ2 are the densities of waste rock and rod mill sand, respectively, in t / m³. 3 ρ is the mixed density of waste rock and rod mill sand, t / m³ 3 Φ1 and Φ2 are the bulk density of waste rock and rod milled sand, respectively; x is the proportion of waste rock in the total solid mass, with a value range of 0 to 50%. The process of calculating the bulk density of mixed aggregate with the mass ratio of waste rock to rod milled sand coarse aggregate when the mass ratio of coarse and fine aggregate is 1 is calculated. Accordingly, the preferred mass fraction ratio of waste rock to rod milled sand (waste-to-rod ratio) is 3:7 to 7:3.

[0115] The optimal mass ratio of cement to aggregate (mortar ratio) is 1:6 to 1:4; the sum of the mass of aggregate and cement accounts for 75 to 77 wt% of the total mass of the slurry. At this point, the bleeding rate and diffusivity of the filling slurry meet the working conditions of the mixer and the conveying pipeline.

[0116] like Figure 5 As shown in Table 1, a composite algorithm was constructed using the cube tool of the Design-Export software. The slurry mass concentration, waste rod ratio, and mortar ratio were designed as three influencing factors on compressive strength, with the factor parameters represented by x1, x2, and x3, respectively. The compressive strength of the filling body at 3d, 7d, and 28d were used as response values, and the response results were represented by y1, y2, and y3, respectively. The influencing factors served as the input values ​​for the response surface regression model, and the response values ​​were the output values. The combinations of factor levels of -1, 0, and 1 represent the three levels of the three factors: slurry mass concentration, waste rod ratio, and mortar ratio, respectively. The regression models of the response surface calculation results y at 3d, 7d, and 28d ages with respect to the changes in factor levels are as follows:

[0117] y1=-86.6+201.1x1+2.7x2-15.5x3-112.3x1 2 -4.9e -3 x2 2 +0.1x3 2 -3.8x1x2+22.0x1x3+0.3x2x3(R 2 =0.982)

[0118] y2=-258.2+629.1x1+2.6x2-8.3x3-376.3x1 2 -0.01x2 2 -0.6x3 2 -3.8x1x2+16.4x1x3+0.4x2x3(R 2 =0.949)

[0119] y3=-471.4+1158.2x1+5.8x2-44.0x3-700.0x1 2 -0.03x2 2 -1.4x3 2 -8.4x1x2+66.0x1x3+1.2x2x3(R 2 =0.965)

[0120] Table 1 shows the results of the strength test (y) and the response surface regression calculation results (y') obtained from the preset strength regression model. See below:

[0121]

[0122]

[0123] Table 1

[0124] like Figure 6 As shown, analysis of variance is used to determine the sources of error in the parametric equations, and the F-values ​​of the equations are... min =705.09>F 0.95 (3,9) = 3.86, indicating strong significance of the regression results. The p-values ​​of the univariate terms (x1, x2, and x3) are all within the E range. -4 The magnitude is extremely high and the significance is very strong; among the interaction terms of factors, the interaction of maintenance age is the most significant; the accuracy assessment of the response surface parameters of the preset intensity regression model is shown in Table 2.

[0125]

[0126] Table 2

[0127] A three-dimensional error coordinate system was constructed, and the relative differences between the measured values ​​y and the calculated values ​​y' at curing ages of 3d, 7d, and 28d were plotted in the (x,y,z) coordinate system. The maximum relative error was calculated to be less than 10%, and this value was used as the error boundary to truncate the error space. Preferably, the relative error values ​​of the intensity at curing ages of 3d and 7d are all within 10%, and the relative error value at 28d is less than 6%, so that the calculated values ​​of the response surface parameter model are close to the actual values ​​of the intensity at curing ages of 3d, 7d, and 28d.

[0128] Preferably, the 3d compressive strength is characterized by a significance level of x1 > x3 > x2, with the interaction effect order being x1x2 > x1x3 > x2x3; the 7d compressive strength is characterized by a significance level of x1 > x2 > x3, with the interaction effect order being x1x2 > x1x3 > x2x3; and the 28d compressive strength is characterized by a significance level of x1 > x2 > x3, with the interaction effect order being x1x2 > x1x3 > x2x3.

[0129] like Figure 7As shown, with a mortar-to-mortar ratio of 1:6 to 1:4, a slurry mass concentration of 77%, and a waste rod ratio of 3:7, rheological experiments were designed with six levels of polycarboxylate superplasticizer mass concentration: 0.00%, 0.10%, 0.20%, 0.30%, 0.40%, and 0.50%. The experimental results are shown in Table 3. Regression equations were constructed with the superplasticizer mass fraction as the independent variable 'a' and the yield stress z1 and plastic viscosity z2 as the dependent variables:

[0130] z1 = 95.86 + 124 / (1 + (a / 0.21)) 1.52 ),(R 2 =0.9989),

[0131] z² = 0.97a + 1.51a 2 +0.94, (R 2 =0.8667)

[0132]

[0133] For waste rock tailings backfill slurry with a slurry concentration of 77%, the optimal solution for adding polycarboxylate superplasticizer is a polycarboxylate superplasticizer mass fraction of 0.32%. At this point, the yield stress of the backfill slurry is 139.57 Pa, the plastic viscosity is 0.78 Pa·s, and the workability improvement effect is maximized.

[0134] Based on the mine pressure data provided by the Jinchuan No. 2 mining area and the requirements of the artificial false roof for the strength of the backfill, the design strength of the backfill at 3d, 7d, and 28d is [C]. 3d MPa, [C 7d MPa and [C 28d According to the test results, the slurry rheological parameters, yield stress below [σ1] and plastic viscosity below [η1], are beneficial for conveying operations.

[0135] Optimize slurry mix proportions using goal programming: Based on the market price of materials, cement [M j Yuan / t, waste rock [M f Yuan / t, rod grinding sand [M] b Yuan / t, total tailings [M q Yuan / t, Industrial water [M w Yuan / t, Polycarboxylate superplasticizer [M] pc [Yuan / t] Calculate the material cost corresponding to the mass of cement j, waste rock f, rod mill sand b, total tailings q, industrial water w, and polycarboxylate superplasticizer a in 1t of slurry. Construct a target planning optimization model for slurry mix proportion considering the strength of the filling body, i.e., the preset slurry cost model.

[0136] minf = [M j ]×j+[Mf ]×f+[M b ]×b+[M q ]×q+[M w ]×w+[M pc ]×A

[0137] minf represents the lowest material cost while ensuring filling effect, expressed in yuan / m³. 3 The fgoalattain function in Matlab can be used to further optimize the slurry ratio to achieve the lowest cost.

[0138] For example: Based on the mine pressure data provided by the Jinchuan No. 2 mining area and the requirements of the artificial false roof for the strength of the backfill, the design strength of the backfill at 3d, 7d, and 28d is [C]. 3d ] = 1.5MPa, [C 7d ] = 2.5 MPa and [C 28d = 5MPa. The slurry mix ratio was optimized using goal programming. Based on the market prices of materials—cement 310 yuan / t, waste rock 21 yuan / t, rod mill sand 143 yuan / t, tailings 4 yuan / t, industrial water 3.2 yuan / t, and polycarboxylate superplasticizer 3000 yuan / t—the results were: slurry mass concentration 77%, waste rod ratio 2.33, mortar ratio 1:5, and polycarboxylate superplasticizer 0.22%. At this point, the strengths of the filling body at 3d, 7d, and 28d were 1.77MPa, 3.38MPa, and 5.7MPa, respectively; the slurry yield stress was 211.39Pa; and the plastic viscosity was 0.80Pa·s.

[0139] As can be seen from the above specific embodiments, the multi-objective optimization method for filling slurry based on response surface regression provided by the present invention quantifies the response of the interaction between multiple factors by using the response surface regression calculation method to obtain the optimal solution of multi-objective parameters; it fully considers the influence of aggregate gradation, mass fraction ratio of waste rock to rod mill sand, mass fraction ratio of binder to aggregate, and mass concentration of filling slurry on the curing strength of filling slurry, as well as the influence of the amount of water-reducing agent added on the rheological properties of filling slurry, seeking the balance point between "strength" and "flow" in the filling process of mine filling, optimizing the filling process to achieve the goal of "cost reduction and efficiency improvement" in mining; it effectively solves the contradiction between "water requirement" in slurry transportation and "hydrophobicity" of filling body strength that has not been solved in the prior art, as well as the problem of increased pipeline transportation difficulty caused by increased fluidity of filling slurry.

[0140] The multi-objective optimization method for filling slurry based on response surface regression proposed according to the present invention has been described above by way of example with reference to the accompanying drawings. However, those skilled in the art should understand that various modifications can be made to the multi-objective optimization method for filling slurry based on response surface regression proposed by the present invention without departing from the scope of the invention. Therefore, the scope of protection of the present invention should be determined by the content of the appended claims.

Claims

1. A multi-objective optimization method for filling slurry based on response surface regression, characterized in that, Includes the following steps: S1. Determine the raw materials for the filling slurry, wherein the raw materials include aggregates, binders, water-reducing agents and water; wherein the aggregates include coarse aggregates composed of waste rock and rod mill sand and fine aggregates composed of tailings sand; S2. Based on the maximum bulk density of the aggregate and the preset material mass fraction ratio of coarse aggregate to fine aggregate, determine the range of the mass fraction ratio of waste rock to rod mill sand; this includes: based on the cemented backfilling of tailings, calculating the particle size distribution index of the aggregate using Talbol gradation theory, adjusting the mass fraction of waste rock and rod mill sand to control the particle size composition of the aggregate, so that the particle size distribution index of the aggregate tends to an ideal value, thereby determining the preliminary range of the mass fraction ratio of waste rock to rod mill sand; Based on the preliminary range, the maximum bulk density of the aggregate is calculated using a two-dimensional mixture bulk density model to reduce the proportion of binder in the filling slurry, and the range of the mass fraction ratio of waste rock to the rod mill sand is obtained. S3. Select a first preset quantity of the mass fraction ratio of waste rock to the rod mill sand from the range as a first quantitative parameter, and select a second preset quantity of the mass fraction ratio of binder to aggregate from the preset range of mortar ratio as a second quantitative parameter, select a third preset quantity of the mass concentration of filling slurry from the preset range of filling slurry mass concentration as a third quantitative parameter, and select a fourth preset quantity of curing age as a fourth quantitative parameter. Input the first quantitative parameter, the second quantitative parameter, the third quantitative parameter, and the fourth quantitative parameter as slurry strength variables into a preset strength regression model to calculate the strength value of the filling slurry, and select the first quantitative parameter, the second quantitative parameter, and the third quantitative parameter that meet the preset strength requirements from the calculation results. S4. The first quantitative parameter, the second quantitative parameter, and the third quantitative parameter that meet the preset strength requirements, along with the fifth preset amount of water-reducing agent selected from the preset range of water-reducing agent addition amount, are used as slurry rheological variables and input into the preset rheological regression model to calculate the rheological parameters of the filling slurry. The first quantitative parameter, the second quantitative parameter, the third quantitative parameter, and the amount of admixture that meet the preset rheological parameter requirements are selected from the calculation results and used as the first target variable, the second target variable, the third target variable, and the fourth target variable, respectively. S5. Input the first target variable, the second target variable, the third target variable and the fourth target variable into the preset slurry cost model, and calculate the raw material ratio scheme of the filling slurry that meets both the strength requirements and the rheological requirements of the filling slurry with the lowest cost.

2. The multi-objective optimization method for filling slurry based on response surface regression according to claim 1, characterized in that, The density of the waste rock is 2.79–2.97 t·m³. -3 The bulk density is 1.60–1.76 t·m³. -3 The particle size distribution ranges from 0.1 to 15.0 mm, and the chemical composition contains 47.71% SiO2 and 16.39% CaO by mass; and / or, The density of the rod-ground sand is 2.71–2.87 t·m³. -3 The bulk density is 1.49–1.63 t·m³. -3 The particle size distribution ranges from 0.1 to 15.0 mm, and the chemical composition contains 75.75% SiO2 and 10.95% Al2O3 by mass; and / or, The density of the tailings is 2.74–2.82 t·m³. -3 The bulk density is 1.18–1.26 t·m³. -3 The particle size distribution ranges from 0.28 to 447.7 μm, and the mass percentage of SiO2 in the chemical composition is 42.20% and the mass percentage of MgO is 32.71%.

3. The multi-objective optimization method for filling slurry based on response surface regression according to claim 1, characterized in that, The binder is silicate cement; and / or, The water-reducing agent has a pH of 6.20 / 10 g·L. -1 Polycarboxylate superplasticizer.

4. The multi-objective optimization method for filling slurry based on response surface regression according to claim 1, characterized in that, The formula for calculating the particle size distribution index of the aggregate using Talbol gradation theory is as follows: Where n is the Talbol particle size distribution index; D max D represents the maximum particle size in the aggregate test sample; D is the particle size index of the aggregate test sample; M is the mass of aggregate particles with a particle size not exceeding index D; M t The total mass of the aggregate test sample is given. The Talbol particle size distribution indices of waste rock and rod-ground sand are 0.687 and 0.335, respectively. The Talbol index of aggregate under ideal conditions is between the two.

5. The multi-objective optimization method for filling slurry based on response surface regression according to claim 4, characterized in that, The calculation formula for the two-dimensional mixture bulk density model is as follows: in, ρ1 is the density of waste rock; ρ2 is the density of rod mill sand; ρ is the mixed density of waste rock and rod mill sand; Φ1 is the bulk density of waste rock; Φ2 is the bulk density of rod mill sand; x is the proportion of waste rock in the total mass of aggregate, with a value range of 0 to 50%; based on the preset material mass fraction ratio of coarse aggregate to fine aggregate, the process of the change of aggregate bulk density with the mass ratio of waste rock to rod mill sand is calculated, and the range of the mass fraction ratio of waste rock to rod mill sand is obtained after solving.

6. The multi-objective optimization method for filling slurry based on response surface regression according to claim 1, characterized in that, Before calculating the strength value of the filling grout using the preset strength regression model, the accuracy of the preset strength regression model is tested, including: Select the test data set of the slurry strength variable, and input the test data set into the preset strength regression model to calculate the strength value of the filling slurry and obtain the calculation result data; The error value is obtained by comparing the calculated data with the experimental data obtained by using the test data set as experimental data and conducting a composite test of the curing strength center of the filling slurry. When the error value is less than the first preset error threshold, the preset strength regression model passes the accuracy test.

7. The multi-objective optimization method for filling slurry based on response surface regression according to claim 1, characterized in that, Before calculating the rheological parameters of the filling slurry using the preset rheological regression model, the accuracy of the preset rheological regression model is tested, including: Select the test data set of the slurry rheological variables, and input the test data set into the preset rheological regression model to calculate the rheological parameters of the filling slurry and obtain the calculation result data; The error value is obtained by comparing the calculated data with the experimental data obtained by measuring the rheological properties of slurry at a constant shear rate using a rheometer with the test data set as the experimental data. When the error value is less than the second preset error threshold, the preset rheological regression model passes the accuracy test.

8. The multi-objective optimization method for filling slurry based on response surface regression according to claim 1, characterized in that, In the slurry strength variables, the mass fraction ratio of the waste rock to the rod mill sand is 3:7, 5:5, and 7:3; the mass fraction ratio of the binder to the aggregate is 1:6, 1:5, and 1:4; and the curing period of the filling slurry is 3 days, 7 days, and 28 days. In the slurry rheological variables, there are 6 sets of data for the amount of water-reducing agent added, which are 0.00%, 0.10%, 0.20%, 0.30%, 0.40%, and 0.50% by mass concentration.

9. The multi-objective optimization method for filling slurry based on response surface regression according to claim 8, characterized in that, The calculation formula for the preset slurry cost model is as follows: minf=[M j ]×j+[M f ]×f+[M b ]×b+[M q ]×q+[M w ]×w+[M pc ]×A y1≥[C 3d ],y2≥[C 7d ],y3≥[C 28d ],0≤A≤3.2×10 -3 j+f+b+q+w+A=m z1≤[σ1] z2≤[η1]; Where minf is the minimum cost of the filling slurry, [M j [M] represents the unit price of the binder. f [M] represents the unit price of waste rock. b [M] represents the unit price of rod grinding. q [M] represents the unit price of tailings. w [M] represents the unit price of the carrier. pc [C] represents the unit price of the admixture, j represents the mass of the binder, f represents the mass of the waste rock, b represents the mass of the rod mill sand, q represents the mass of the tailings, w represents the mass of the carrier, A represents the mass of the admixture, y1, y2, and y3 represent the strengths of the filling slurry output from the preset rheological regression model at curing ages of 3d, 7d, and 28d, respectively. 3d [C] 7d [C] 28d [σ1] represents the minimum strength of the filling slurry at curing ages of 3d, 7d, and 28d, respectively; m represents the total mass of the filling slurry; h represents the preset mass fraction ratio of coarse aggregate to fine aggregate; e and E represent the minimum and maximum mass fraction ratios of waste rock and rod mill sand, respectively; g and G represent the minimum and maximum mass fraction ratios of binder to aggregate, respectively; r and R represent the minimum and maximum mass concentrations of the filling slurry, respectively; z1 represents the yield stress of the filling slurry output by the preset rheological regression model; [σ1] represents the preset design value of yield stress; z2 represents the plastic viscosity of the filling slurry output by the preset rheological regression model; and [η1] represents the preset design value of plastic viscosity.

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