A method for constructing a maximum bulk density model of a tailings aggregate

Abstract

The application discloses a construction method of a maximum packing density model of a tailings and gravel mixed aggregate, and belongs to the technical field of mining. The method determines the change rule of the packing density of the mixed aggregate by analyzing the packing characteristics of the tailings and gravel mixed aggregate in a unit volume and combining the boundary conditions, establishes the packing density models of the tailings and gravel mixed aggregate respectively, classifies and discusses the maximum packing density conditions of the two mixed materials, constructs the maximum packing density model of the tailings and gravel mixed aggregate, and determines the maximum adding proportion of the gravel. The model constructed by the application is scientific and reasonable, can quickly and accurately calculate the packing density of the tailings and gravel under any mixing condition, and simultaneously designs the maximum packing density for mine filling, so that the designed filling body strength is achieved, the cement consumption is greatly reduced, the cost is reduced, and a decision basis is provided for the rational utilization of the tunneling waste rock for mine filling.

Description

Technical Field

[0001] This invention belongs to the field of mining technology, specifically relating to a method for constructing a maximum packing density model for crushed stone and tailings mixed aggregate. Background Technology

[0002] Backfilling, as a crucial means of comprehensive utilization of solid waste in mines, not only compensates for the core deficiencies of traditional mining concepts, reduces environmental disturbance, coordinates the separation of mineral resource development and environmental governance, protects prospective resources, and eliminates safety hazards caused by mining subsidence areas, but also plays an irreplaceable role given the increasing normalization of deep resource development and utilization. The backfilling aggregates required for backfilling processes generally consist of waste rock and tailings. Since tailings do not require special processing, they are generally the first choice as backfilling aggregate. While this maximizes the utilization of tailings and reduces tailings emissions, waste rock is not fully utilized. Furthermore, because tailings are finer, have lower density, and a larger specific surface area, achieving the designed strength of the backfill body in the cemented backfilling process requires a significant amount of cement, resulting in high backfilling costs.

[0003] Waste rock is processed into crushed stone and mixed with tailings. Ideally, the crushed stone forms a supporting skeleton, and the tailings fully fill the pores of the crushed stone, thereby reducing the porosity of the material system and increasing its density. From the perspective of strength and mechanical properties, the filling body formed by crushed stone and tailings is essentially a low-grade concrete. Under the same cement dosage, it can greatly improve the strength of the filling body. It plays a positive role in reducing cement usage, lowering the cost of the filling body, and making full use of mine waste rock to reduce surface emissions.

[0004] How to mix crushed stone and tailings aggregate to achieve the ideal maximum bulk density? Too much tailings will cause the crushed stone to separate, resulting in a loosening effect and preventing it from forming a supporting skeleton, thus compromising the strength of the backfill. Insufficient tailings will not adequately fill the pores of the crushed stone, resulting in a still large pore volume and low density, requiring excessive cement to reach the design strength. Therefore, constructing a scientifically sound model for the maximum bulk density of crushed stone and tailings aggregate mixture, and accurately designing the mixing ratio of crushed stone and tailings, is crucial to meeting the trends and needs of backfill technology development and has significant application value. Summary of the Invention

[0005] To address the shortcomings of the existing technologies, this invention provides a method for constructing a maximum bulk density model for crushed stone and tailings mixed aggregates. This method can accurately calculate the bulk density of crushed stone and tailings under arbitrary mixing conditions. During mine backfilling, it can greatly reduce the analytical and experimental work required to determine the density of the two aggregate mixtures.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A method for constructing a maximum bulk density model for crushed stone and tailings mixed aggregate includes the following steps:

[0008] (1) Based on boundary conditions one and two of the tailings-based mixed aggregate, a model of the bulk density of the tailings-based mixed aggregate is established.

[0009] (2) Based on boundary conditions one and two of the crushed stone-based mixed aggregate, a compaction model of the crushed stone-based mixed aggregate is established.

[0010] (3) Based on the bulk density model of tailings-based mixed aggregate and the bulk density model of crushed stone-based mixed aggregate, establish the maximum bulk density model of crushed stone and tailings mixed aggregate, and calculate the maximum proportion of crushed stone added in the aggregate when the crushed stone and tailings mixed aggregate reaches the maximum bulk density.

[0011] In a preferred embodiment of the present invention, when the tailings-dominant mixed aggregate is a mixture of crushed stone and tailings, the tailings dominate the mixed aggregate. The packing characteristics of the tailings-dominant mixed aggregate are: the crushed stones are separated from each other and do not contact each other; the crushed stones are distributed within the tailings in the mixed aggregate. At this time, there are two boundary conditions for the mixed aggregate:

[0012] The boundary condition for a mixture primarily composed of tailings aggregate is that the entire unit volume consists of tailings aggregate with no crushed stone, expressed by the following formula:

[0013] M s1 =0 (1);

[0014] M s1 It is mainly composed of tailings, and refers to the mass of crushed stone in the crushed stone tailings mixed aggregate per unit volume.

[0015] The second boundary condition for tailings-dominated aggregate mixtures is that the crushed stones are in perfect contact with each other within a unit volume, expressed by the following formula:

[0016] M s1 =φ s ρ s1 (2);

[0017] φ s ρ represents the density of the crushed stone. s1 The apparent density of the crushed stone.

[0018] In aggregates primarily composed of tailings, the amount of crushed stone added falls between the two boundary conditions mentioned above. The amount of crushed stone added to the aggregates should satisfy the following:

[0019] 0≤M s1 ≤φ s ρ s1 (3).

[0020] In a preferred embodiment of the present invention, in step (1), in the main mixed aggregate containing tailings, the volume of the two aggregates per unit volume is equal to the sum of the volume of tailings and the apparent volume of crushed stone in the mixed aggregate, which can be expressed by the following formula:

[0021]

[0022] M w1 ρ is the mass of tailings in the tailings-dominant mixed aggregate per unit volume; w The bulk density of the tailings.

[0023] In a preferred embodiment of the present invention, in step (1), in the main mixed aggregate containing tailings, the bulk volume of the two aggregates per unit volume is equal to the sum of the apparent volume of tailings, the pore volume of tailings, and the apparent volume of crushed stone in the mixed aggregate, which can be expressed by the following formula:

[0024]

[0025] ρ w1 ε represents the apparent density of the tailings; w The porosity is the value of the tailings.

[0026] In a preferred embodiment of the present invention, in the tailings-dominated mixed aggregate, the bulk density of the two aggregates per unit volume is the ratio of the sum of the apparent volumes of the tailings and the crushed stone to the unit volume. Considering boundary conditions one and two, the bulk density of the tailings-dominated mixed aggregate is expressed by the following formula:

[0027]

[0028] φ ws The density of the mixed aggregate, mainly composed of tailings.

[0029] From equation (4), we can obtain:

[0030]

[0031] From equation (5), we can obtain:

[0032]

[0033] Substituting equation (7) into equation (8), we get:

[0034]

[0035] Substituting equation (9) into equation (6), the bulk density model of tailings-based mixed aggregate is expressed by the following equation:

[0036]

[0037] In a preferred embodiment of the present invention, when the crushed stone-based mixed aggregate is a mixture of crushed stone and tailings, crushed stone dominates the mixed aggregate. The packing characteristics of the crushed stone-based mixed aggregate are: the crushed stones are in contact with each other, and the tailings fill the pores of the crushed stones. At this time, there are two boundary conditions for the mixed aggregate:

[0038] The boundary condition for a mixed aggregate primarily composed of crushed stone is that the entire unit volume consists of crushed stone with no tailings, expressed by the following formula:

[0039] M w2 =0 (11);

[0040] M w2 It refers to the mass of tailings in a mixed aggregate mainly composed of crushed stone per unit volume.

[0041] The second boundary condition for a mixed aggregate primarily composed of crushed stone is that the voids in the crushed stone per unit volume are completely filled with tailings, expressed by the following formula:

[0042] M w2 =ε s ρ w (12);

[0043] ε s The porosity is the value of the crushed stone.

[0044] In aggregates primarily composed of crushed stone, the amount of tailings added falls between the two boundary conditions mentioned above. The amount of tailings added to the aggregates should satisfy the following:

[0045] 0≤M w2 ≤ε s ρ w (13).

[0046] In a preferred embodiment of the present invention, in step (2), since the tailings are only present in the pores of the crushed stone, the accumulated volume of the crushed stone and tailings is equal to the accumulated volume of the crushed stone, expressed by the following formula:

[0047]

[0048] M s2 ρ is the mass of crushed stone in a mixed aggregate primarily composed of crushed stone per unit volume. s It refers to the density of the accumulated gravel.

[0049] In a preferred embodiment of the present invention, in the crushed stone-based mixed aggregate, the packing density per unit volume of the two aggregates is the ratio of the sum of the apparent volumes of tailings and crushed stone to the unit volume. Considering boundary conditions one and two, the packing density model of the crushed stone-based mixed aggregate is as follows:

[0050]

[0051] in:

[0052]

[0053] Substituting equation (16) into equation (15), the bulk density φ of the aggregate mainly composed of crushed stone is... sw The model is represented by the following formula:

[0054]

[0055] As a preferred embodiment of the present invention, the establishment of the maximum bulk density model of the crushed stone and tailings mixed aggregate in step (3) specifically includes:

[0056] S1: For tailings-based aggregate mixtures, when adding crushed stone per unit volume of tailings, no more crushed stone can be added once the crushed stone in the aggregate mixture comes into contact with each other, and the density of the crushed stone and tailings aggregate mixture reaches its maximum. At this point, the amount of crushed stone added is:

[0057] M s1 =φ s ρ s1 (2).

[0058] S2: Substituting equation (2) into equation (10), we can obtain the maximum density of the tailings-based aggregate mixture as follows:

[0059] φ wsmax =1-(1-φ) s )ε w (18);

[0060] φ wsmax This represents the maximum bulk density of the tailings-based mixed aggregate.

[0061] S3: For aggregates mainly composed of crushed stone, tailings are added to fill the voids in the crushed stone per unit volume. When the tailings completely fill the voids in the crushed stone, no more tailings can be added, and the density of the crushed stone and tailings aggregate reaches its maximum. At this point, the amount of tailings added is:

[0062] M w2 =ε s ρ w (12).

[0063] S4: Substituting equation (12) into equation (17), we can obtain the maximum density of the aggregate mainly composed of crushed stone as follows:

[0064]

[0065] in:

[0066]

[0067] φ w This refers to the density of the tailings.

[0068] Substituting equation (20) into equation (19), we obtain the maximum density φ of the aggregate mainly composed of crushed stone. swmax for:

[0069] φ swmax =φ s +ε s φ w (twenty one).

[0070] S5: In essence, regardless of whether the main aggregate is tailings or crushed stone, when the two aggregates are mixed to achieve maximum density, the material packing in the mixed aggregate is consistent. That is, the crushed stone contacts each other to form a supporting skeleton, and the tailings fills the gaps in the crushed stone pores, increasing the packing density of the mixed aggregate. Therefore, equation (18) is equivalent to equation (21), and the maximum density φ of the crushed stone and tailings mixed aggregate is... max Represented as:

[0071] φ max =1-(1-φ) s )ε w =φ s +ε s φ w (twenty two).

[0072] In a preferred embodiment of the present invention, in step (3), according to equations (2) and (12), the maximum proportion λ of crushed stone in the aggregate when the crushed stone and tailings mixed aggregate reaches the maximum bulk density is calculated as follows:

[0073]

[0074] in:

[0075] φ s ρ s1 =ρ s (twenty four);

[0076] Substituting equation (24) into equation (23), we obtain the maximum proportion λ of crushed stone in the aggregate when the crushed stone and tailings mixed aggregate reaches its maximum bulk density:

[0077]

[0078] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0079] (1) The maximum bulk density model of crushed stone and tailings mixed aggregate constructed in this invention is scientific and reasonable. It can quickly and accurately calculate the bulk density of crushed stone and tailings under arbitrary mixing conditions. In the process of mine backfilling, it can greatly reduce the analysis and experimental work of determining the density of the two aggregates. Furthermore, it provides a decision-making basis for the rational use of tunneling waste rock for mine backfilling, which can greatly reduce the surface stockpiling of mine waste rock and is of great significance for protecting the surface environment.

[0080] (2) The maximum bulk density of the crushed stone and tailings mixed aggregate designed in this invention can be used for mine backfilling to achieve the designed backfill strength. Compared with using tailings or crushed stone alone for backfilling, it can greatly reduce the amount of cement used and reduce the backfilling cost. Attached Figure Description

[0081] Figure 1 This is an optimized flow chart of the optimal mix ratio of crushed stone tailings cemented backfill material based on the present invention.

[0082] Figure 2 This is a diagram showing the stockpiling state of the mixed aggregate, which is mainly composed of tailings.

[0083] Figure 3 This is a diagram showing the stockpiling state of a mixed aggregate primarily composed of crushed stone.

[0084] Figure 4 This is a diagram showing the maximum bulk density of the crushed stone and tailings mixed aggregate.

[0085] Figure 5 The diagram shows the bulk density distribution curve of the tailings-based mixed aggregate in Example 1.

[0086] Figure 6 The image shows the bulk density distribution curve of the crushed stone-based mixed aggregate in Example 1.

[0087] Figure 7 The curve shows the density distribution of the crushed stone and tailings mixed aggregate in Example 1.

[0088] Figure 8 This is a test block of cemented backfill material of crushed tailings from a copper mine in Example 1. Detailed Implementation

[0089] To better illustrate the purpose, technical solution, and advantages of the present invention, the present invention will be further described below in conjunction with specific embodiments.

[0090] Example 1

[0091] The engineering background of this embodiment 1 is a copper mine ore body that is gently dipping with significant variations in shape and dip angle. The ore body and surrounding rock are moderately stable with well-developed bedding. The design adopts a point-pillar type upward horizontal layered backfilling mining method for mining, with a layered roof control height of 5m. After the layered mining is completed, backfilling is carried out in two stages. The bottom layer uses non-cemented backfill with a backfill height of 2.7m; the surface layer uses tailings cemented backfill with a backfill height of 0.6m. The backfill strength is required to reach 2.0MPa after 7 days. The backfill mix ratio and backfill cost are shown in Table 1.

[0092] Table 1. Mix proportions and costs of cemented backfill material in a copper mine.

[0093]

[0094]

[0095] The mine has an annual tailings cemented backfill volume of 120,000 m³. 3 The annual backfilling cost is 17.8704 million yuan. Due to its low stiffness, the cemented tailings backfill is prone to large deformations during the ore body mining process, and the backfilling cost is too high. Therefore, the mine decided to adopt a crushed stone and tailings cemented backfilling process to improve the stiffness of the backfill and reduce the backfilling cost. The basic physical and mechanical parameters of the crushed stone and tailings in this copper mine are shown in Table 2.

[0096] Table 2 Basic physical and mechanical parameters of crushed stone and tailings from a copper mine

[0097]

[0098] The method for constructing the maximum bulk density model of crushed stone and tailings mixed aggregate according to the present invention includes the following steps:

[0099] (1) Based on the basic physical and mechanical parameters of the copper mine crushed stone and tailings shown in Table 2, the bulk density of the tailings as the main mixed aggregate is calculated using formula (10).

[0100] In the tailings-based aggregate mixture, the amount of crushed stone added is:

[0101] 0≤M s1 ≤1748 (26).

[0102] The expression for the bulk density of tailings-based aggregate mixture is:

[0103]

[0104] The calculated bulk density of the tailings-based aggregate mixture is shown in Equation (28), and the distribution results are as follows: Figure 5 As shown.

[0105] 50.64%≤φ ws ≤81.29% (28).

[0106] (2) Based on the basic physical and mechanical parameters of the copper mine crushed stone and tailings shown in Table 2, the bulk density of the mixed aggregate with crushed stone as the main component is calculated using formula (17).

[0107] In the aggregate mixture with crushed stone as the main component, the amount of tailings added is:

[0108] 0≤M w2 ≤556 (29).

[0109] The expression for the bulk density of a mixed aggregate mainly composed of crushed stone is:

[0110]

[0111] The calculated bulk density of the aggregate mainly composed of crushed stone is shown in Equation (31), and the distribution results are as follows: Figure 6 As shown.

[0112] 62.10%≤φ sw ≤81.29% (31).

[0113] (3) Based on the calculation results of equations (28) and (31), the bulk density of the aggregate under arbitrary mixing conditions of crushed stone and tailings can be obtained, as shown in the figure. Figure 7 As shown.

[0114] S1: When crushed stone and tailings are mixed, regardless of whether tailings or crushed stone are dominant, the maximum density is achieved when crushed stone contacts each other to form a supporting framework, and tailings completely fills the pores of the crushed stone. Based on the basic physical and mechanical parameters of the crushed stone and tailings in the copper mine shown in Table 2, the maximum density is calculated using equation (22), and the results are as follows:

[0115] φ max =1-(1-62.10%)×49.36%=62.10%+37.90%×50.64%=81.29% (32).

[0116] S2: The maximum proportion of crushed stone in the crushed stone tailings mixed aggregate when the maximum bulk density is achieved is calculated using formula (25). The results are as follows:

[0117]

[0118] (4) Based on the maximum bulk density of the crushed stone tailings mixed aggregate and the maximum addition ratio of crushed stone determined by formulas (32) and (33), the copper mine carried out a crushed stone tailings cemented backfill strength test. Combined with the backfill strength requirements, the optimal mix ratio with the lowest cost was finally determined, as shown in Table 3.

[0119] Table 3 Optimal mix proportions for cemented backfilling of crushed stone and tailings in a copper mine

[0120]

[0121]

[0122] According to Table 3, the cemented backfill prepared with the optimal mix proportions features a uniform alternating distribution of crushed stone and tailings. The crushed stone forms a supporting skeleton through mutual contact, while the tailings fully fill the pores between the crushed stone, maximizing the bulk density of the mixed aggregate. Figure 8 As shown. Compared with the original backfill mix ratio in the mine, using crushed stone and tailings backfill, although increasing the amount of crushed stone, significantly reduces the amount of cement used, resulting in a cost reduction of 21.75 yuan per cubic meter for the backfill body. This is based on an annual backfill volume of 120,000 cubic meters in the mine. 3 Calculations show that the annual filling cost is reduced by 2.61 million yuan, resulting in significant economic benefits.

[0123] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the essence and scope of the technical solutions of the present invention.

Claims

1. A method for constructing a maximum bulk density model for crushed stone and tailings mixed aggregate, characterized in that, Includes the following steps: (1) Based on the boundary conditions of tailings as the main aggregate, the first boundary condition is that the unit volume is all tailings and there is no crushed stone, and the second boundary condition is that the crushed stone is in contact with each other within the unit volume, a model of the bulk density of tailings as the main aggregate is established. (2) Based on the boundary conditions of the crushed stone-based mixed aggregate, the first boundary condition is that the unit volume is entirely composed of crushed stone with no tailings and the second boundary condition is that the pores of the crushed stone in the unit volume are completely filled by tailings, a compaction model of the crushed stone-based mixed aggregate is established. (3) Based on the bulk density models of tailings-based mixed aggregates and crushed stone-based mixed aggregates, a maximum bulk density model for crushed stone and tailings mixed aggregates is established, and the maximum proportion of crushed stone added to the aggregate is calculated when the crushed stone and tailings mixed aggregates reach the maximum bulk density. Specifically, it includes: S1: According to boundary condition two for tailings-dominated aggregate, the bulk density of the crushed stone and tailings-dominated aggregate reaches its maximum. At this point, the mass of crushed stone in the tailings-dominated aggregate per unit volume is... for: （2）； The density of the crushed stone; The apparent density of the crushed stone; S2: Based on S1 Model of bulk density of aggregate mainly composed of tailings, and maximum bulk density of aggregate mainly composed of tailings. for: （18）； The porosity of the tailings; S3: According to boundary condition two for the crushed stone-based aggregate mixture, the bulk density of the crushed stone and tailings aggregate mixture reaches its maximum. At this point, the mass of tailings in the crushed stone-based aggregate mixture per unit volume is... for: （12）； The porosity of the crushed stone; The bulk density of the tailings; S4: Based on S3 Using the compaction model of aggregates mainly composed of crushed stone, the maximum compaction of the aggregates mainly composed of crushed stone was obtained. for: （21）； This refers to the density of the tailings. , The apparent density of the tailings; S5: Equivalent to Equation (18) and Equation (21), the maximum bulk density of crushed stone tailings mixed aggregate. Represented as: （22）； S6: Based on equations (2) and (12), calculate the maximum proportion of crushed stone in the aggregate when the crushed stone and tailings mixed aggregate reaches the maximum bulk density. .

2. The method for constructing the maximum bulk density model of crushed stone and tailings mixed aggregate as described in claim 1, characterized in that, In step (1), the boundary condition for the main mixed aggregate, tailings, is expressed by the following formula: （1）； The mass of crushed stone in the tailings-main mixed aggregate per unit volume; The boundary condition for the tailings-based mixed aggregate is expressed by equation (2).

3. The method for constructing the maximum bulk density model of crushed stone and tailings mixed aggregate as described in claim 1, characterized in that, The tailings-based mixed aggregate is a mixture of crushed stones that are separated from each other and do not come into contact with each other, with the crushed stones distributed within the tailings. The amount of crushed stones added meets the following requirements: （3）。 4. The method for constructing the maximum bulk density model of crushed stone and tailings mixed aggregate as described in claim 2, characterized in that, In step (1), based on boundary conditions one and two for the tailings-based mixed aggregate, the bulk density model for the tailings-based mixed aggregate is as follows: （10）； The bulk density of the aggregate mainly composed of tailings; The mass of tailings in the main mixed aggregate per unit volume.

5. The method for constructing the maximum bulk density model of crushed stone and tailings mixed aggregate as described in claim 1, characterized in that, In step (2), the boundary condition for the aggregate mainly composed of crushed stone is expressed by the following formula: （11）； The boundary condition for the mixed aggregate with crushed stone as the main component is expressed by equation (12).

6. The method for constructing the maximum bulk density model of crushed stone and tailings mixed aggregate as described in claim 1, characterized in that, The main aggregate, crushed stone, is a mixed aggregate in which crushed stones are in contact with each other, and tailings fill the pores of the crushed stones. The amount of tailings added satisfies the following conditions: （13）。 7. The method for constructing the maximum bulk density model of crushed stone and tailings mixed aggregate as described in claim 5, characterized in that, In step (2), based on boundary conditions one and two for the crushed stone-based mixed aggregate, the bulk density model for the crushed stone-based mixed aggregate is as follows: （17）； The bulk density of the aggregate mixture with crushed stone as the main component; It refers to the mass of crushed stone in a mixed aggregate with crushed stone as the main component per unit volume.

8. The method for constructing the maximum bulk density model of crushed stone and tailings mixed aggregate as described in claim 1, characterized in that, In step (3), according to equations (2) and (12), the maximum proportion of crushed stone added to the aggregate is calculated when the crushed stone and tailings mixed aggregate reaches the maximum bulk density. for: （23）； in So, when the crushed stone and tailings aggregate reaches its maximum bulk density, what is the maximum proportion of crushed stone added to the aggregate? for: （25）； This represents the bulk density of the gravel.

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