Method for determining instability load transfer characteristics of single coal pillar in coal pillar group-roof system

Abstract

The invention belongs to the technical field of coal mine room and pillar mining, and particularly relates to a single coal pillar instability load transfer characteristic determination method in a coal pillar group-roof system, which comprises the following steps of: a, constructing a coal pillar group-roof system two-dimensional mechanical model, constructing a room type goaf coal pillar group-roof system, and simplifying the room type goaf coal pillar group-roof system into a multi-span continuous beam mechanical model; the coal pillars are sequentially simplified into supports A, B, C, D and E from left to right, it is assumed that the whole structure bears the uniform overlying rock load q, and the distance between the supports is set to be l; b, calculating load transfer characteristics of the left single coal pillar B after instability; c, calculating load transfer characteristics after the middle single coal pillar is unstable; and d, calculating a load transfer rule after the instability of the right single coal pillar. By means of the method, the load transfer rule can be accurately mastered, the chain reaction caused by coal pillar instability can be effectively predicted, and important theoretical support and technical means are provided for safe production of the adjacent stopes of the room type goaf.

Description

Technical Field

[0001] The present invention belongs to the technical field of coal mining in room-and-pillar method, and particularly relates to a method for determining the load transfer characteristics of a single coal pillar instability in a coal pillar group-roof system. Background Art

[0002] After the formation of the room goaf, a large number of remaining coal pillars exist densely to form a coal pillar group, and the coal pillar group and the roof constitute a coal pillar group-roof system. In the coal pillar group-roof system, not only do the coal pillars and the roof coexist, and both jointly affect the overall failure of the system, but there are also connections between the coal pillars. The failure of any coal pillar or the roof may trigger the overall instability of the system. However, most of the existing literature regards all coal pillars as support bodies of the same nature to study the stress characteristics of the coal pillars and judge their stability. When a certain coal pillar loses stability, that is, after losing its supporting ability, its load will inevitably be transferred to other surrounding coal pillars. At this time, if the uniform stress method is used to calculate the stress and stability of the surrounding coal pillars, it will surely be inaccurate. That is, the existing technology lacks the study on the load transfer law after the instability of a certain coal pillar. Summary of the Invention

[0003] To solve the above technical problems, the present invention proposes a method for determining the load transfer characteristics of a single coal pillar instability in a coal pillar group-roof system, including the following steps:

[0004] S1: Construct a two-dimensional mechanical model of the coal pillar group-roof system

[0005] Construct a coal pillar group-roof system of the room goaf and simplify it into a multi-span continuous beam mechanical model; each coal pillar is successively simplified into supports A, B, C, D, and E from left to right. Assume that the overall structure bears a uniform overlying rock load q, and the distance between each support is set to l;

[0006] S2: Calculate the load transfer characteristics after the instability of the single coal pillar B on the left

[0007]

[0008] The reaction forces of the two adjacent coal pillars of coal pillar B are both linearly negatively correlated with the reaction force F of coal pillar B B When the reaction force F of support B B decays to the minimum value of 0, the reaction force F of coal pillar A A and the reaction force F of coal pillar C C reach the maximum value.

[0009] Preferably, it further includes S3: Calculate the load transfer characteristics after the instability of the single coal pillar in the middle

[0010]

[0011] The reaction forces of the two adjacent coal pillars of coal pillar C are both related to the reaction force F of coal pillar CC There is a linear negative correlation. When the reaction force F of support C C attenuates to the minimum value of 0, the reaction force F of coal pillar B B and the reaction force F of coal pillar D D reach the maximum value.

[0012] Preferably, it further includes S4: calculating the load transfer law after the instability of a single coal pillar on the right side

[0013]

[0014] The reaction forces of the two adjacent coal pillars of coal pillar D are both linearly negatively correlated with the reaction force F of coal pillar D D When the reaction force F of support D D attenuates to the minimum value of 0, the reaction force F of coal pillar C C and the reaction force F of coal pillar E E reach the maximum value.

[0015] Beneficial technical effects: There are differences in the physical and mechanical properties of each coal pillar in the room-and-pillar goaf area, the overlying strata loads and disturbance loads it receives, the degree of weathering or water erosion, etc. Coal pillars at different positions may all be the first to become unstable, and the resulting load transfer laws are different. Through the method for determining the load transfer characteristics of a single coal pillar instability in the coal pillar group-roof system of the present invention, the load transfer law can be accurately grasped, the chain reaction caused by coal pillar instability can be effectively predicted, providing important theoretical support and technical means for the safe production of adjacent stope in the room-and-pillar goaf area, providing guarantee for the healthy development of the mining area ecological environment, and having significant engineering application value and social and economic benefits. Description of the Drawings

[0016] Figure 1 It is a partial schematic diagram of a uniformly distributed coal pillar group-roof system;

[0017] Figure 2 It is a hyperstatic mechanical model of an equidistant coal pillar group-roof system;

[0018] Figure 3 It is a statically determinate mechanical model of an equidistant coal pillar group-roof system;

[0019] Figure 4 It is the basic structure of the force method replacing the single support on the left;

[0020] Figure 5 It is the structural moment diagram replacing the single support on the left;

[0021] Figure 6 It is the basic structure of the force method replacing the single support in the middle;

[0022] Figure 7 It is the structural moment diagram replacing the single support in the middle;

[0023] Figure 8 The basic structure of the force method to replace the single support on the right side;

[0024] Figure 9 The structural bending moment diagram to replace the single support on the right side. Specific implementation mode

[0025] The following introduces the specific implementation mode of the present invention in conjunction with the accompanying drawings.

[0026] The method for determining the load transfer characteristics of the instability of a single coal pillar in the coal pillar group-roof system proposed by the present invention includes:

[0027] The first step: constructing a two-dimensional mechanical model of the coal pillar group-roof system

[0028] A partial schematic diagram of the remaining coal pillar group-roof system in the room-and-pillar goaf is as shown in Figure 1 shown. Each coal pillar is numbered A, B, C, D, E from left to right, and it is simplified into a multi-span continuous beam mechanical model as shown in Figure 2 shown; among them, the roof is simplified into a continuous beam, and each coal pillar is successively simplified into supports A, B, C, D, E from left to right, and the vertical center line of each support coincides with the corresponding coal pillar; it is assumed that the overall structure bears a uniform overlying rock load q, and the distance between each support is set to l. Figure 2 The multi-span continuous beam in Figure 3 is a statically indeterminate structure, and its existence of redundant additional constraints makes the structure complex and not conducive to solving. According to the basic idea of the force method in structural mechanics, the statically indeterminate structure needs to be transformed into a statically determinate structure for solution. As shown in

[0029] shown, the redundant additional constraints of supports B, C, D in the statically indeterminate structure are removed and replaced by the unknown forces X1, X2, X3 of the redundant constraints respectively;

[0030] The second step: the load transfer characteristics after the instability of the single coal pillar on the left Figure 4 As shown in B shown, according to the basic principle of the force method, use the reaction force F B to replace support B in the statically determinate mechanical model of the coal pillar group-roof system, and study the influence of the change of the bearing of the single coal pillar on the left during the instability process on the bearing of adjacent coal pillars by analyzing the change of F

[0031]

[0032] In the formula: δ ij is the flexibility coefficient, indicating the displacement of the basic structure along the X j direction caused by the single action of X i =1, where i represents the direction of displacement and j represents the cause of displacement; X nThe unknown force that replaces the redundant constraint of the nth support; Δ nP Is the free term, representing the displacement of the basic structure caused by the known load in the X n direction;

[0033] Draw the bending moment diagrams of X2, X3, q, and F B acting alone to replace the basic structure of the left single support force method as shown in Figure 5 the figure; The values of each coefficient in equation (1) can be obtained successively by the graphical multiplication method, as shown below:

[0034]

[0035] In the formula: E is the elastic modulus; I is the interface moment of inertia; EI is the flexural rigidity;

[0036] Substitute the above coefficients into the typical force method equation (1), and the unknown forces of the redundant constraints of supports C and D can be obtained as:

[0037]

[0038] Use the superposition method to successively obtain the relationship between the reaction forces of adjacent supports and F B as:

[0039]

[0040] In summary, it can be obtained that:

[0041]

[0042] As can be seen from formula (10), the bearing of adjacent coal pillars is related to the bearing of the known coal pillar, the overlying rock load q, and the coal pillar spacing l. The reaction forces of the two adjacent supports of support B are both linearly negatively correlated with F B Although due to the different boundary conditions of supports A and C, the change values of their reaction forces are different, but as F B gradually decreases, the reaction forces F A and F C of adjacent coal pillars A and C both increase linearly. When F B decays to the minimum value of 0, F A and F C reach the maximum value.

[0043] Step 3: Load transfer characteristics after the instability of the middle single coal pillar

[0044] As Figure 6 shown, use the reaction force F C to replace support C in the middle of the model. By analyzing F CTo study the influence of the bearing change of the single coal pillar in the middle on the bearing of its adjacent coal pillars during the instability process of the single coal pillar in the middle through the change of C The typical equations of the force method to replace the basic structure of the single support in the middle are listed as follows:

[0045]

[0046] Draw the bending moment diagrams of the basic structure when X1, X3, q, and F C act alone as shown in Figure 7 ; Use the graphical multiplication method to find the coefficients in equation (11) as follows:

[0047]

[0048] Substitute the above coefficients into equation (11) to obtain:

[0049]

[0050] Use the superposition method to find the reaction forces of the two adjacent supports of support C as:

[0051]

[0052] In summary, the reaction forces of each support are:

[0053]

[0054] According to formula (18), the evolution laws of the reaction forces of the two adjacent supports of support C with respect to F C are obtained. As F C gradually decreases, the reaction forces F B and F D of its adjacent supports both increase linearly; at the same time, since the built structural model is symmetric about support C and the geometric and mechanical parameters of the supports on the left and right sides are symmetric, the evolution laws of the reaction forces of the supports on the left and right sides of the built structure also show symmetric evolution characteristics.

[0055] Step 4: Load transfer law after the instability of the single coal pillar on the right

[0056] As Figure 8 shown, remove support D in the basic structure of the force method of the coal pillar group - roof and replace it with the reaction force F D to analyze the influence of the instability of the single coal pillar on the right on the bearing of its adjacent coal pillars by reducing the value of F D ;

[0057] List the typical equations of the basic structure of the force method of the coal pillar group - roof to replace the single coal pillar on the right as follows:

[0058]

[0059] Draw X1, X2, q, and F D When acting alone, the bending moment diagram of the basic structure is as follows Figure 9 shown; using the moment distribution method, the coefficients in the typical force method equation (19) are obtained as follows:

[0060]

[0061]

[0062] Substitute the above coefficients into the typical force method equation (19) to obtain:

[0063]

[0064] Using the superposition method, the reaction forces of each support are obtained as:

[0065]

[0066] Finally, the reaction forces of each support are obtained as:

[0067]

[0068] Similarly, according to formula (28), the reaction forces of the adjacent supports of support D vary with F D The decreasing law, and the evolution laws presented by the reaction forces are consistent with the previous research conclusions, all increasing gradually with the decrease of the bearing capacity of the unstable support; at the same time, due to the symmetry of the established mechanical model, the bearing evolution characteristics of the remaining corresponding supports when replacing the basic structure of the single support force method on the right and the left are also symmetric left and right.

[0069] The present invention is not limited to the above best implementation mode. Anyone can obtain other various forms of methods under the inspiration of the present invention. However, as long as the technical solutions are the same as or similar to those of the present application, they all fall within the protection scope of the present invention.

Claims

1. A method for determining the instability load transfer characteristics of a single coal pillar in a coal pillar group-roof system, characterized in that: The steps include: S1: Constructing a two-dimensional mechanical model of the coal pillar group-roof system A coal pillar group-roof system in a room-type goaf is constructed and simplified into a multi-span continuous beam mechanical model; each coal pillar is simplified into supports A, B, C, D, and E from left to right, assuming that the entire structure bears a uniform overburden load q, and the distance between each support is set to l; S2: Calculate the load transfer characteristics after the left single coal pillar B becomes unstable The support reaction forces of the two adjacent coal pillars of coal pillar B are equal to the support reaction force F of coal pillar B. B There is a linear negative correlation. When the support reaction F of support B B When the reaction force F of the coal pillar A decays to the minimum value 0, A and the reaction force F of the coal pillar C C Reached maximum value.

2. The method for determining the instability load transfer characteristics of a single coal pillar according to claim 1, characterized in that: It also includes the calculation of the load transfer characteristics after the instability of a single coal pillar in the middle The support reaction forces of the two adjacent coal pillars of coal pillar C are equal to the support reaction force F of coal pillar C. C There is a linear negative correlation. When the support reaction F of support C C When the minimum value is 0, the reaction force F of the coal pillar B is B and the reaction force F of the coal pillar D D Reached maximum value.

3. The method for determining the instability load transfer characteristics of a single coal pillar according to claim 1 or 2, characterized in that: It also includes the calculation of the load transfer law after the right single coal pillar becomes unstable The support reaction forces of the two adjacent coal pillars of coal pillar D are equal to the support reaction force F of coal pillar D. D There is a linear negative correlation. When the support reaction F of the support D D When the minimum value is 0, the reaction force F of the coal pillar C is C and the reaction force F of the coal pillar E E Reached maximum value.

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