Composite roof anchor rod pre-tightening force calculation method

Abstract

The invention belongs to the field of roadway surrounding rock control, and provides a composite roof anchor rod pre-tightening force calculation method which comprises the following steps: dividing each key layer and a roof rock layer moving synchronously with the key layer together as a separation layer control layer; assuming that k separation layer control layers are arranged from bottom to top; simplifying each separation layer control layer into a clamped beam to determine a deflection expression; the minimum pre-tightening force Pm provided by the composite top plate in unit area is equal to the acting force of the anchor rod on the anchoring layer and equal to the sum of the acting force applied by the anchor rod on the non-anchoring layer, and the anchoring layer of the anchor rod is the kth separation layer control layer on the uppermost portion; the non-anchoring layer is a separation layer control layer from the first layer to the (k-1) th layer; therefore, the minimum pre-tightening force provided by the roof rock stratum in unit area can be determined, and the anchor rod pre-tightening force can be determined according to the supporting area of each anchor rod. According to the method, the relation between the interlayer acting force and the ultimate tensile strength is considered, the influence of the interlayer acting force of the composite roof is considered when the anchor rod pretightening force is determined, and calculation of the anchor rod pretightening force better fits actual engineering.

Description

Technical Field

[0001] The invention belongs to the field of tunnel surrounding rock control, and proposes a method for calculating anchor rod preload when anchor rods are used to support the composite roof after tunnel excavation under composite roof conditions. The method is suitable for controlling deformation and delamination of the composite roof after tunnel excavation.

[0002] The composite roof mentioned in the present invention refers to a roof condition in which the number of roof rock layers is large and relatively thin. Background Art

[0003] Composite roofs are common geological structures in mining operations, accounting for over one-third of coal mine roadway roofs. Layered composite roofs exhibit significant transverse isotropy, but exhibit significant differences in physical and mechanical properties in the vertical direction. After roadway excavation, the lower portion of the composite roof becomes exposed to the air, and the rock layers within the composite roof begin to deform. As the deformation increases, the interlayer tensile stress gradually increases, eventually reaching the tensile strength of the interlayer structural plane, triggering rupture of the structural plane. Uneven deformation of the interlayer rock layers can cause delamination, a significant precursor to composite roof failure and instability.

[0004] Existing technologies lack systematic research on composite roof mechanical models that consider interlaminar forces. Therefore, establishing a composite roof mechanical model that considers interlaminar forces and proposing a reasonable calculation method for composite roof anchor preload are crucial for controlling composite roof edge and delamination, as well as for safe excavation of composite roof tunnels. Summary of the Invention

[0005] The present invention proposes a method for calculating the preload force of composite roof anchor rods, comprising the following steps:

[0006] S1. Classify each key layer in the roof and its upper synchronously moving roof rock layer as a separation control layer;

[0007] S2. Assume that there are k layers of separation control layers from bottom to top;

[0008] S3. Simplify each separation control layer into a fixed beam and determine the deflection expression;

[0009] S4. Minimum preload force P per unit area of composite roof m , which is equal to the force exerted by the anchor rod on the anchoring layer and the sum of the forces exerted by the anchor rod on the non-anchoring layer, where the anchoring layer of the anchor rod is the top k-th delamination control layer; the non-anchoring layer is the 1st to k-1th delamination control layers; then the minimum preload force that the roof rock layer should provide per unit area is

[0010]

[0011] In the formula, [σck-1 ] is the interlayer tensile strength between the kth layer separation control layer and the k-1th layer separation control layer; E k ′ is the overall elastic modulus of the kth separation layer control layer; h k ′ is the thickness of the kth separation control layer; E i ′ is the overall elastic modulus of the ith separation layer control layer; h i ′ is the thickness of the ith separation control layer; q k is the load borne by the key layer in the kth layer of separation control layer; q i is the load borne by the key layer in the ith separation control layer;

[0012] S5. Determine the anchor preload force based on the support area of each anchor.

[0013] Preferably, in step S1, the lowest roof rock layer is the first key layer.

[0014] Preferably, in step S5, the anchor preload force P is calculated using the following formula:

[0015] P≥P m ·L s ·L P

[0016] Where, L s is the anchor spacing, L P Anchor rod spacing.

[0017] Compared with the prior art, the present invention has the following beneficial effects:

[0018] (1) The composite roof mechanical model of the present invention takes into account the relationship between interlayer forces and ultimate tensile strength, making the separation position determination more accurate.

[0019] (2) The influence of the interlayer force of the composite roof is taken into account in the design calculation, making the calculation of the anchor preload more consistent with the actual project. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 This is a schematic diagram of the distribution of composite roof rock layers;

[0021] Figure 2 This is a schematic diagram of the division of the composite roof separation control layer;

[0022] Figure 3 This is a schematic diagram of the interlayer force calculation model when there are two layers of separation control layers;

[0023] Figure 4 Schematic diagram of the interlayer force calculation model when the number of delamination control layers is more than two;

[0024] Figure 5Schematic diagram of the composite roof anchor preload calculation model. DETAILED DESCRIPTION

[0025] The present invention will be further described below with reference to the accompanying drawings.

[0026] Example 1

[0027] like Figure 1-5 As shown, the present invention proposes a method for calculating the preload force of composite roof anchor rods, comprising the following steps:

[0028] S1. When the composite roof sinks, not all rock layers will produce delamination. Those rock layers with small thickness and low strength will move synchronously with the thick hard rock layer below them. This rock layer that controls the movement of the rock layer is called a key layer. First, the key layer theory is used to determine the position of the key layer in the composite roof. The rock layers between any adjacent key layers are controlled by the key layer at the lower part and delamination will occur below the key layer at the upper part. In order to facilitate the determination of the delamination position, the synchronously moving roof rock layers are divided together as a delamination control layer. The method for determining the key layer is a method known in the art and is briefly introduced below in this patent. The position of the key layer in the composite roof can be determined by formula (1) and formula (2).

[0029] (q n )1>(q n+1 )1 (1)

[0030]

[0031] In the formula, (q n )1 is the load generated when the nth roof rock layer affects the first roof rock layer, Pa; (q n+1 )1 is the load generated when the n+1th roof rock layer affects the first roof rock layer, Pa; γ i , γ1 are the bulk density of the i-th layer and the first layer of roof rock, kN·m -3 ;h i and h1 are the thickness of the i-th roof rock layer and the first roof rock layer, respectively, in m; E i and E1 are the elastic moduli of the i-th roof rock layer and the first roof rock layer, GPa;

[0032] like Figure 1-2 As shown, the mechanical parameters of the two adjacent rock layers in the composite roof are substituted into formula (2) from bottom to top, and formula (1) is used as the judgment standard. If formula (1) is satisfied, the nth layer and the n+1th layer in the composite roof have the prerequisite for separation. At this time, the n+1th layer of the roof rock layer is the key layer. It should be noted that the lowest roof rock layer (the first layer of the roof rock layer) can also be regarded as a key layer. Figure 1-2 As shown, roof rock layer 1 (the first roof rock layer) and roof rock layer n+1 (the n+1th roof rock layer) are key layers, controlling the second to nth roof rock layers and the n+2th roof rock layer respectively; roof rock layers 1 to n are a separation control layer, and roof rock layers n+1 to n+2 are a separation control layer, which are numbered and named from bottom to top, respectively, as separation control layer 1 and separation control layer 2, and the area between separation control layer 1 and separation control layer 2 is the separation generating position;

[0033] S2. Determine the stress form of the separation control layer, such as Figure 3-4 As shown in the figure, there are significant differences in the manifestation of interlayer forces between two-layer delamination control layers and multi-layer delamination control layers; assuming that there are k layers of delamination control layers from bottom to top;

[0034] When k=2, the force expression of each separation layer control layer is shown in formula (3):

[0035]

[0036] When k>2, the force expression of each separation layer control layer is shown in formula (4):

[0037]

[0038] Where Q i is the overall force on the control layer of the ith separation layer, Pa, Q i+1 is the overall force on the i+1th layer of separation control layer, Pa, q i is the load borne by the key layer in the ith separation control layer, Pa, q i+1 is the load borne by the key layer in the i+1th separation control layer, Pa, which can be obtained by formula (2); σ ci is the interlayer tensile stress between the i-th delamination control layer and the i+1-th delamination control layer, Pa; σ ci-1 is the interlayer tensile stress between the i-1th delamination control layer and the i-th delamination control layer, Pa;

[0039] S3. Simplify the composite roof (each separation control layer) into a fixed beam and obtain the deflection expression of the composite roof (each separation control layer)

[0040]

[0041]

[0042] Where, L is the span of each separation layer, that is, the width of the roadway, m; E i ' is the overall elastic modulus of the i-th separation layer control layer, GPa; I i ' is the moment of inertia of the control layer of the ith separation layer, m 4, the expression is shown in formula (6); h i ' is the thickness of the ith layer of separation control layer (along the roadway height direction), m; b i ' is the width of the ith separation control layer (along the roadway axis), m;

[0043] The purpose of anchor support is to prevent delamination between the composite roof rock layers, that is, to make the deflection and deformation of each delamination control layer equal; Substitute equation (3) or equation (4) into equation (5), make the deflection and deformation of each delamination control layer equal, and calculate the interlayer force σ of each delamination control layer ci ;

[0044] When the number of separation control layers k=2, the expression of the interlayer force of the separation control layers is:

[0045]

[0046] When the number of separation control layers k>2, the expression of the interlayer force of the separation control layers is:

[0047]

[0048] Where, E i+1 ' is the overall elastic modulus of the i+1th layer of separation control layer, GPa; I i+1 ' is the moment of inertia of the control layer of the i+1th separation layer, m 4 , the expression is shown in formula (6); h i+1 ' is the thickness of the i+1th layer separation control layer (along the roadway height direction), m; b i+1 ' is the width of the i+1th separation control layer (along the roadway axis), m;

[0049] S4. Figure 5 As shown, the minimum preload force P that the composite top plate should provide per unit area is m , which is equal to the force exerted by the anchor rod on the anchor layer and the sum of the forces exerted by the anchor rod on the non-anchor layer, where the anchor layer of the anchor rod is the top k-th separation control layer; the non-anchor layer is the 1st to k-1th separation control layers; that is, as follows

[0050]

[0051] Where, P k is the force exerted by the anchor on the kth delamination control layer, Pa; P i is the force exerted by the anchor on the ith delamination control layer, Pa;

[0052] For each non-anchored separation control layer below the anchoring layer:

[0053]

[0054] For the anchoring layer, i.e. the kth separation control layer:

[0055] Q i =q i +P i +σ ci-1 , i=k (11)

[0056] According to the ultimate tensile strength of the rock between each separation control layer and the principle of coordinated deformation of each separation control layer, the minimum preload force that the roof rock layer should provide per unit area can be determined by substituting equations (9), (10) and (11) into equation (5).

[0057]

[0058] In the formula, [σ ck-1 ] is the interlayer tensile strength between the kth layer separation control layer and the k-1th layer separation control layer, Pa; E k ′ is the overall elastic modulus of the kth separation control layer, GPa; h k ′ is the thickness of the kth layer of separation control layer, m; q k is the load borne by the key layer in the kth separation control layer, Pa;

[0059] S5. Calculate the anchor preload force P using the following formula

[0060] P≥P m ·A s (13)

[0061] A s =L s ·L P (14)

[0062] Where, P is the anchor preload, kN, A s is the support area, m 2 , L s is the anchor spacing, m, L P is the anchor rod spacing, m.

[0063] Example 2

[0064] Based on the first embodiment, a specific example is given as follows:

[0065] Through the study of geological data and mining data of a coal mine, it was found that the composite roof rock type of the 5# coal seam is mainly oil shale, with a thickness of 11.18m, an elastic modulus of 2.41GPa, and a bulk density of 24kN / m 2The roof rock layer is thin and obviously broken, and there are seven obvious stratifications, located at 0.52m, 1.18m, 1.99m, 3.02m, 3.94m, 5.14m, and 6.62m from the roadway roof. The ultimate tensile strength between the layers in the oil shale is 0kPa.

[0066] Substituting the layer parameters of the composite roof into formula (2) and distinguishing them through formula (1), the roof rock layers within the bolt support range are divided into separation control layer 1 (0.0-0.52m), separation control layer 2 (0.52-1.18m), separation control layer 3 (1.18-1.99m), and separation control layer 4 (1.99-3.94m). The loads on each separation control layer are 11.72kPa, 14.88kPa, 18.26kPa, and 25.66kPa, respectively.

[0067] q1=γ1h1=11.72kPa

[0068] q2=γ2h2=14.88kPa

[0069] q3=γ3h3=18.26kPa

[0070]

[0071] Determine the number of separation control layers to be 4, and take the unit width b i '=1m, determine the interlayer force of each separation layer control layer to meet the formula (8), determine the interlayer force σ of each separation layer control layer c1 , σ c2 , σ c3 The sizes are 10.52kPa, 22.95kPa and 36.91kPa respectively;

[0072]

[0073]

[0074]

[0075] Calculations show that the interlayer forces between each delamination control layer exceed the ultimate tensile strength between each delamination control layer. Therefore, it is determined that delamination has occurred between each control layer and preload needs to be applied for control.

[0076] Combined with the ultimate tensile strength of each roof rock layer, according to formula (12), the minimum preload force P that the roof per unit area should provide is: m Calculation formula, calculation can get P m It is 36.71kN. In actual support, determine the anchor spacing L s =1.2m, row spacing L P=1.2m, according to formula (13) and formula (14), determine the support area A S 1.44m 2 , then the anchor preload force P is not less than 52.86kN;

[0077]

[0078] A s =L s ·L P =1.44m 2

[0079] P≥P m ·A s =52.86kN.

[0080] The present invention is not limited to the above-mentioned optimal implementation mode. Anyone can derive other various forms of methods under the inspiration of the present invention. However, any technical solution that is the same or similar to that of the present application falls within the scope of protection of the present invention.

Claims

1. A method for calculating the preload force of composite roof anchor bolts, characterized in that: The steps include: S1. Classify each key layer in the roof and its upper synchronously moving roof rock layer as a separation control layer; S2. Assume that there are k layers of separation control layers from bottom to top; S3. Simplify each separation control layer into a fixed beam and determine the deflection expression; S4. Minimum preload force P per unit area of composite roof m , which is equal to the force exerted by the anchor rod on the anchoring layer and the sum of the forces exerted by the anchor rod on the non-anchoring layer, where the anchoring layer of the anchor rod is the top k-th delamination control layer; the non-anchoring layer is the 1st to k-1th delamination control layers; then the minimum preload force that the roof rock layer should provide per unit area is In the formula, [σ ck-1 ] is the interlayer tensile strength between the kth layer separation control layer and the k-1th layer separation control layer; E k ′ is the overall elastic modulus of the kth separation layer control layer; h k ′ is the thickness of the kth separation control layer; E i ′ is the overall elastic modulus of the ith separation layer control layer; h i ′ is the thickness of the ith separation control layer; q k is the load borne by the key layer in the kth layer of separation control layer; q i is the load borne by the key layer in the ith separation control layer; S5. Determine the anchor preload force based on the support area of each anchor.

2. The method for calculating the preload force of composite roof anchor bolts according to claim 1, characterized in that: In step S1, the lowest roof rock layer is the first key layer.

3. The method for calculating the preload force of composite roof anchor bolts according to claim 1, characterized in that: In step S5, the anchor preload force P is calculated using the following formula: P≥P m ·L s ·L P Where, L s is the anchor spacing, L P Anchor rod spacing.

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