Method for determining splayed stope span under roof filling body

Abstract

The invention belongs to the field of phosphorite bed mining design, and particularly relates to a method for determining the span of a splayed stope under a roof filling body. Comprising the following steps: constructing a splayed stope roof filling body structural mechanical model, simplifying two-end constraint into fixed constraint, and bearing an overlying rock load and two-end horizontal acting force; determining the total potential energy of the splayed stope roof filling body structure, wherein the total potential energy is the sum of the bending deformation energy of the roof filling body and the external potential energy change amount caused by the overlying rock load and the horizontal stress; analyzing a splayed stope top plate filling body structure by adopting a sharp point mutation theory; determining the top span of the splayed stope under the roof filling body; and calculating the bottom span of the splayed stope by adopting an FLAC numerical calculation method. The stoping method of the splayed stope under the filling body is provided, the structural mechanical model of the roof filling body is established, the mechanical mechanism of instability of the roof filling body is analyzed by applying the sharp point mutation theory, the stope arrangement mode and the determined parameters can effectively control the stope roof filling body to be stable, and stoping safety is ensured.

Description

Technical Field

[0001] The present invention belongs to the field of mining design of phosphate deposits, and particularly relates to a method for determining the span of an inverted V-shaped stope under a roof filling body. Background Art

[0002] In cemented filling mining method, the safe and efficient mining of thick and massive ore bodies under cemented filling bodies is the main problem faced by resource recovery under filling bodies in metal and non-metal mines. The Weng'an Daxin Beidoushan Phosphate Mine adopts an upward sublevel open stoping and subsequent filling mining mode of simultaneously mining two adjacent middle levels up and down to mine the steeply inclined thick and massive phosphate ore bodies in the mining area. Among them, the upper middle level and the lower middle level are both divided into three sublevels, and a bottom pillar (bottom pillar for the upper middle level and top pillar for the lower middle level) is left between the upper and lower middle levels; in each sublevel, "mining one and leaving one" is adopted along the strike for mining and filling. For example, odd ore rooms are first mined and filled, leaving even ore rooms as ore pillars, and then even ore rooms are mined and filled. The ore room is 15 m long along the strike, with a height equal to the height of the entire sublevel and a thickness equal to the thickness of the entire thick and massive ore body.

[0003] After the mining and filling of the bottom sublevel of the upper middle level and the top sublevel of the lower middle level are completed and the filling body is stable, the recovery of the bottom pillar between the two middle levels is prepared. The height of the bottom pillar is approximately equal to the height of one sublevel. Therefore, the bottom pillar recovery is also divided into ore rooms, and the ore rooms are mined and filled (since the reserved ore pillars are not recovered, the ore rooms can be mined and filled in sequence, or mined and filled in the same "mining one and leaving one" manner as the sublevel). However, due to the low roughness of the interface between two adjacent cemented filling ore rooms in the bottom sublevel of the upper middle level, the large inclination angle of the contact surface, and the complex mechanical properties of the interface, the mining of the bottom pillar is likely to cause tensile-shear mixed failure of the filling bodies at the two interfaces, damaging the structural mechanical properties of the filling body. Therefore, it is proposed that the actual stope length of the ore room during the recovery of the bottom pillar is slightly less than the length of the cemented filling ore room in the bottom sublevel of the upper middle level, and is wider at the bottom and narrower at the top, forming an inverted V-shaped stope, that is, the ore room is not fully mined, and a "reverse quadrangular prism"-shaped ore pillar is formed between the two inverted V-shaped stopes of adjacent ore rooms as a permanent ore pillar and is not recovered.

[0004] Therefore, the ultimate span (the length at the top of the ore room) of the roof filling body and the length of the top and bottom of the ore pillar are the key to controlling the stability of the ore room mining under the roof filling body. Summary of the Invention

[0005] In order to solve the above technical problems, the present invention proposes a method for determining the span of an inverted V-shaped stope under a roof filling body, including the following steps:

[0006] S1: Construct a structural mechanics model of the roof filling body of the inverted V-shaped stope

[0007] The top span of the inverted V-shaped stope at the lower part of the roof filling body is a. The constraints at both ends are simplified as fixed constraints, which bear the overlying strata load q and the horizontal forces P at both ends.

[0008] S2: Determine the total potential energy of the roof filling body structure in the inverted V-shaped stope

[0009] The total potential energy V of the roof filling body structure in the inverted V-shaped stope is the sum of the bending deformation energy of the roof filling body and the change in external potential energy caused by the overlying strata load q and the horizontal stress P.

[0010] S3: Analyze the roof filling body structure in the inverted V-shaped stope by using the cusp catastrophe theory

[0011] S4: Determine the top span of the inverted V-shaped stope under the roof filling body

[0012]

[0013] In the formula, h is the height of the roof filling body, in m; E is the elastic modulus of the roof filling body, and u is the Poisson's ratio of the roof filling body.

[0014] Preferably, it further includes step S5: Calculate the bottom span L of the inverted V-shaped stope by using the FLAC numerical calculation method.

[0015] Preferably, in step S1, the roof filling body is regarded as a continuous, uniform and isotropic body; the horizontal forces P at both ends are regarded as uniformly distributed loads; the overlying strata load q is regarded as a uniformly distributed load.

[0016] Preferably, in step S1, P = 0.0301H0 + 4.363; in the formula: H0 is the burial depth of the roof filling body.

[0017] Preferably, in step S2,

[0018]

[0019] In the formula: D is the flexural rigidity of the roof filling body, in N·m 2 ; ω is a constant.

[0020] Preferably, in step S3, let And introduce dimensional parameters, including the state parameter z, the control variable m, m = ζψ -1 / 2 , Then

[0021] Take the first derivative of V and set it to 0 to obtain the equilibrium surface equation of the roof filling body structure in the inverted V-shaped stope:

[0022] V' = x 3 + mx + n = 0

[0023] The second derivative of the total potential energy V of the roof filling body structure in the eight-shaped stope is 0, that is

[0024] V" = 3x 2 + m = 0

[0025] Furthermore, the cross-set equation of the equilibrium surface is solved as: 4m 3 + 27n 2 = 0

[0026] When the control variable m crosses the crease, the roof filling body is in a critical instability state.

[0027] Beneficial technical effects: The phenomenon that the ore body is located under the filling body is common in mines using the filling mining method. To recover as much mineral resources under the filling body as possible, it is of great significance to reasonably determine the layout method of the stope under the filling body. Based on the analysis of the structural characteristics of the filling body, the present invention proposes a mining method for the eight-shaped stope under the filling body, establishes a mechanical model of the roof filling body structure in the eight-shaped stope, and applies the cusp catastrophe theory to analyze its instability mechanical mechanism. The stope layout method and the determined parameters of the present invention can effectively control the stability of the roof filling body in the stope and ensure the safety of the mining operation. Description of the Drawings

[0028] Figure 1 is the stope layout form (strike section) for the pillar mining under the roof filling body;

[0029] Figure 2 is the mechanical model of the roof filling body structure in the eight-shaped stope of the present invention;

[0030] Figure 3 is the cusp catastrophe model of the roof filling body structure in the eight-shaped stope of the present invention. Detailed Embodiments

[0031] Taking the Wengan Daxin Beidoushan Phosphate Mine as an example, combined with the attached Figure 1-2 , the present invention will be further described.

[0032] The Wengan Daxin Beidoushan Phosphate Mine adopts the upward sublevel open stoping and subsequent filling mining mode of simultaneously mining two adjacent upper and lower levels to mine the steeply inclined thick phosphate ore body in the mining area. Among them, both the upper level and the lower level are divided into three sublevels, and a bottom pillar (the bottom pillar for the upper level and the top pillar for the lower level) is reserved between the upper and lower levels; in each sublevel, "mining one and leaving one" is adopted along the strike for mining and filling. For example, first mine and fill the odd ore rooms and leave the even ore rooms as pillars, and then mine and fill the even ore rooms. The ore room is 15 m long along the strike, with a height equal to the entire sublevel height and a thickness equal to the entire thickness of the thick ore body.

[0033] As Figure 1As shown in the figure, after the mining and filling of the upper-middle section bottom sublevel and the lower-middle section top sublevel are completed and the filling body is stable, the pillar between the two middle sections is ready to be recovered. The height of the pillar is approximately the same as that of a sublevel. Therefore, the pillar recovery is also divided into ore rooms ( Figure 1 Three ore rooms with the same rectangular cross-section size are shown schematically in it), and the ore rooms are mined and filled (since the reserved pillars are not recovered, the ore rooms can be mined and filled in sequence, or mined and filled in the alternate mining method same as the sublevel). However, due to the low interface roughness, large contact surface dip angle, and complex interface mechanical properties between two adjacent cemented filling ore rooms in the upper-middle section bottom sublevel, the pillar mining is likely to cause tensile-shear mixed failure of the filling body at the two interfaces, damaging the structural mechanical properties of the filling body. Therefore, it is proposed that the actual stope length of the ore room is slightly less than the length of the cemented filling ore room in the upper-middle section bottom sublevel during the pillar recovery, and it is wider at the bottom and narrower at the top, forming an inverted-V-shaped stope, that is, the ore room is not fully mined, and a "reverse quadrangular prism" shaped pillar is formed between the two inverted-V-shaped stopes of adjacent ore rooms as a permanent pillar and is not recovered.

[0034] Therefore, the ultimate span of the roof filling body (the length at the top of the stope) and the top and bottom lengths of the pillar are the key to controlling the stability of the ore room mining under the roof filling body after the ore room is mined to form a goaf. Therefore, it is necessary to construct a mechanical model of the stope surrounding rock to determine the stope parameters of the ore room.

[0035] In view of the above problems, the present invention proposes a method for determining the span of an inverted-V-shaped stope under a roof filling body, which includes the following steps:

[0036] S1: Construct a structural mechanical model of the roof filling body of the inverted-V-shaped stope

[0037] Based on Figure 1 , the present invention constructs a structural mechanical model of the roof filling body of the inverted-V-shaped stope as shown in Figure 2 . In the figure, a is the length of the inverted-V-shaped stope along the ore body strike (the span of the stope at the roof filling body), and h is the height of the roof filling body; the stability of the roof filling body depends not only on the action of external loads (the overlying rock load q and the horizontal forces P at both ends of the roof filling body), but also on the material ratio of the filling body, the rheological properties of the filling slurry, the layered structure characteristics, and the stability control of the surrounding rock of the roadway driven in the filling body, etc. In order to simplify the analysis, the following assumptions are made:

[0038] ① The roof filling body is regarded as a continuous, homogeneous, and isotropic body;

[0039] ② The constraints at both ends of the roof filling body are simplified to fixed constraints, and the horizontal forces P at both ends of the roof filling body are regarded as uniformly distributed loads acting on both ends of the roof filling body;

[0040] According to the calculation results of the distribution law of deep water stress in different regions of the country by scholars such as Jing Feng, the maximum horizontal principal stress σ max and the minimum principal stress σmin The relational expression is as follows:

[0041]

[0042] In this article, the horizontal force P takes σ max , that is, P = 0.0301H0 + 4.363;

[0043] In the formula: H0 is the buried depth of the rock stratum, which refers to the buried depth of the roof filling body in this article, m;

[0044] ③ The overlying rock load q acting on the roof filling body is regarded as a uniformly distributed load;

[0045] The vertical load exerted by the overlying rock on the roof filling body mainly comes from the self-weight of the overlying rock mass. According to the unit weight of the rock mass and the buried depth of the roof filling body, the calculation expression of the overlying rock load q is:

[0046] q = γH0 (2)

[0047] In the formula: γ is the unit weight of the overlying rock stratum, N / m 3 .

[0048] S2: Determine the total potential energy of the eight-shaped stope roof filling body structure

[0049] The total potential energy V of the eight-shaped stope roof filling body structure is the sum of the bending deformation energy of the roof filling body and the change in external potential energy caused by the overlying rock load q and the horizontal stress P, that is:

[0050]

[0051] In the formula: U s — The bending deformation energy of the roof filling body, J; W q — The external potential energy caused by the overlying rock load q, J; W P — The external potential energy caused by the horizontal stress P, J; D is the flexural rigidity of the roof filling body, N·m 2 ; The width takes the unit width, and the width refers to the direction of the ore seam thickness. E is the elastic modulus of the roof filling body, N / m 2 , u is the Poisson's ratio of the roof filling body;

[0052] According to the elastic theory, the curvature of the deflection curve of the roof filling body at s can be expressed in terms of the arc length coordinate as:

[0053]

[0054] In the formula: k(s) is the curvature function of the roof filling body; f(s) is the deflection function of the roof filling body, and f(s) is expanded in a Fourier series as:

[0055]

[0056] In the formula: s is the length of any arc segment of the roof filling body, in m; n refers to the nth arc segment;

[0057] The roof filling body is a gel with low flexural strength and shear strength. Under the action of the overlying strata load, it undergoes bending deformation. The deflection curve of the roof filling body can be approximately expressed by Equation (6):

[0058]

[0059] In the formula: ω is a constant;

[0060] Therefore, the bending deformation energy U of the roof filling body s is:

[0061]

[0062] In the formula: M(s) is the bending moment of the roof filling body, in N·m;

[0063] The work done by the overlying strata load q is:

[0064]

[0065] Under the action of the horizontal ground stress P, assume that the displacements at both ends of the roof filling body are Δa, and perform Taylor expansion on it:

[0066]

[0067] The work done by the horizontal stress P on the roof filling body is:

[0068]

[0069] Substitute Equation (7), Equation (8), and Equation (10) into Equation (3) to obtain:

[0070]

[0071] S3: Analyze the roof filling body structure of the eight-shaped stope by using the cusp catastrophe theory (construct a cusp catastrophe model for the roof filling body structure of the eight-shaped stope)

[0072] After the ore room is mined, the roof filling body begins to accumulate elastic energy under the action of external loads. When the elastic energy accumulates to a certain extent, it is immediately released, causing the filling body to be damaged. This characteristic is obvious and sudden, corresponding to the jump property of the cusp catastrophe theory. Therefore, the cusp catastrophe theory is used for analysis;

[0073] Perform variable substitution on Equation (11): Assume And introduce the dimensional parameters (z, m, n), where, That is, Equation (11) can be expressed as:

[0074]

[0075] Where: z is the state parameter, and m and n are control variables.

[0076] Equation (12) is the standard potential function form of the cusp catastrophe theory, indicating that the mechanical model of the roof filling body structure in the figure-eight stope conforms to the cusp catastrophe theory type; taking the first derivative of V and setting it to 0, the equilibrium surface equation of the roof filling body structure in the figure-eight stope can be obtained:

[0077] V' = x 3 + mx + n = 0 (13)

[0078] The equilibrium surface of the mechanical model of the roof filling body structure in the figure-eight stope represented by Equation (13) is shown in Figure 3 , and the surface is composed of upper, middle, and lower leaves, indicating that the state parameter of the roof filling body changes with the control variables; when the roof filling body is in the lower leaf of the equilibrium surface, the roof filling body is in a stable state. As the control variable m increases, the equilibrium state of the roof filling body moves from the lower leaf to the upper leaf. When the equilibrium state of the roof filling body moves to the fold of the surface, the roof filling body is in the limit equilibrium state, that is, the second derivative of the total potential energy V of the system is 0, as shown in Equation (14);

[0079] V" = 3x 2 + m = 0 (14)

[0080] Combining Equation (13) and Equation (14), the cross-set equation of the equilibrium surface is solved as:

[0081] 4m 3 + 27n 2 = 0 (15)

[0082] When the control variable m crosses the fold, the roof filling body is in the critical instability state, corresponding to Figure 3 the upper leaf of the cusp catastrophe model;

[0083] S4: Determine the span of the lower figure-eight stope of the roof filling body

[0084] S41: Determine the necessary conditions for the instability of the roof filling body

[0085] From Figure 3 it can be seen that when the roof filling body is unstable, there must be m ≤ 0. The equilibrium point of the roof filling body has the condition to cross the cross-set, which in turn leads to the instability of the roof filling body structure. That is, m ≤ 0 is the necessary condition for the instability of the roof filling body. To ensure the stability of the roof filling body, m > 0 should be satisfied, that is:

[0086]

[0087] Through comprehensive derivation, the critical span of the roof filling body can be obtained. That is, the span \(a\) of the stope at the roof filling body is:

[0088]

[0089] S41: Determine the sufficient conditions for the instability of the roof filling body

[0090] According to the cusp catastrophe theory, when the roof filling body structure is unstable, the roof filling body structure of the inverted V-shaped stope must satisfy the cross-set equation. When the roof filling body structure is in the critical instability condition, let

[0091] ▽ = 4m 3 + 27n 2 (18)

[0092] When ▽ > 0, equation (18) has only one real root, that is, the roof filling body is in a stable state; when ▽ < 0, equation (18) has three real roots, but the stability of the roof filling body is located on the upper lobe of the cusp catastrophe surface, and the roof filling body is in an unstable state; when ▽ = 0, equation (18) has three real roots, the roof filling body has two stable states and one unstable state, and the roof filling body transitions from a stable state to an unstable state until it finally returns to a stable state. Therefore, to ensure that the roof filling body is in a stable state, it is necessary to ensure that ▽ > 0, that is

[0093]

[0094] Take the limit condition:

[0095]

[0096] Then the \(m_1\) that satisfies the sufficient condition satisfies:

[0097]

[0098] Let the span of the stope roof filling body that satisfies the sufficient condition be \(a_1\). However, in the necessary condition, \(m>0\) when the stope is stable, so \(m_1 < m\); from equation (17), its derivative \(m'(D 1 / 2 )>0\), that is, \(f(N z ) = m(D 1 / 2 ) is an increasing function. \(N z refers to the variable greater than all variable values of \(D 1 / 2 It can be obtained that \(a_1 < a\), that is, the necessary conditions for the instability of the stope roof filling body satisfy the sufficient conditions for the instability of the filling body roof. The ultimate spans of the stope roof filling body corresponding to the two conditions are:

[0099]

[0100] In addition, the lower span L of the inverted-V stope (the span of the stope at the roof) is also a key factor for the stability of the stope surrounding rock. It is necessary to determine the optimal lower span of the stope, and the FLAC numerical calculation method can be used to calculate the lower span of the stope.

[0101] The present invention is not limited to the above-mentioned best implementation manner. Any person can obtain various other forms of methods under the inspiration of the present invention. However, any technical solution that is the same as or similar to the present application falls within the protection scope of the present invention.

Claims

1. A method for determining the span of an inverted V-shaped stope under a roof filling body, characterized in that, It includes the following steps: S1: Construct a structural mechanics model of the inverted-V-shaped stope roof filling body The top span of the inverted-V-shaped stope at the lower part of the roof filling body is a, and the constraints at both ends are simplified to fixed constraints, which bear the overlying rock load q and the horizontal forces P at both ends; S2: Determine the total potential energy of the inverted-V-shaped stope roof filling body structure The total potential energy V of the inverted-V-shaped stope roof filling body structure is the sum of the bending deformation energy of the roof filling body and the change in external potential energy caused by the overlying rock load q and the horizontal stress P; S3: Analyze the inverted-V-shaped stope roof filling body structure using the cusp catastrophe theory S4: Determine the top span of the inverted-V-shaped stope under the roof filling body In the formula, h is the height of the roof filling body, in m; E is the elastic modulus of the roof filling body, and u is the Poisson's ratio of the roof filling body.

2. The method for determining the span of the inverted V-shaped stope under the roof filling body according to claim 1, wherein It also includes step S5: Calculate the bottom span L of the inverted-V-shaped stope using the FLAC numerical calculation method.

3. The method for determining the span of the inverted V-shaped stope under the roof filling body according to claim 1 or 2, characterized in that In step S1, the roof filling body is regarded as a continuous, uniform and isotropic body; the horizontal forces P at both ends are regarded as uniformly distributed loads; the overlying rock load q is regarded as a uniformly distributed load.

4. The method for determining the span of the inverted V-shaped stope under the roof filling body according to claim 3, characterized in that, In step S1, P = 0.0301H0 + 4.363; where: H0 is the burial depth of the roof filling body.

5. The method for determining the span of the inverted V-shaped stope under the roof filling body according to claim 1 or 2 or 4, characterized in that In step S2, where: D is the flexural rigidity of the roof filling body, N·m 2 ; ω is a constant.

6. The method for determining the span of the inverted V-shaped stope under the roof filling body according to claim 5, characterized in that In step S3, set and introduce dimensional parameters, including state parameter z, control variables m, n Then Take the first derivative of V and set it to 0 to obtain the equilibrium surface equation of the inverted-V-shaped stope roof filling body structure: V' = x 3 + mx + n = 0 The second derivative of the total potential energy V of the inverted-V-shaped stope roof filling body structure is 0, that is V" = 3x 2 + m = 0 Furthermore, the cross-set equation of the equilibrium surface is solved as: 4m 3 + 27n 2 = 0 When the control variable m crosses the fold, the roof filling body is in a critical instability state.

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