Method for calculating gap opening and bending bearing capacity at shield tunnel lining joints

Abstract

The present invention provides a method for calculating the gap opening and bending bearing capacity at the joints of the shield tunnel lining, including assuming the initial elongation of the bolts at the joints to determine the stress state of the lining; obtaining various mechanical parameters in the current state according to the static equilibrium equation; and obtaining a curve of the change of the section bending moment with the gap opening by gradually increasing the elongation of the bolts, and obtaining the critical bending bearing capacity, critical gap opening and ultimate bending bearing capacity. The present invention is based on the actual deformation behavior of the shield tunnel lining under external loads, and fully considers the influence of stress environment, material properties and geometric parameters on the gap opening and bending bearing capacity. Compared with the prior art, the present invention has clear principles, simple operation and accurate results, and can be applied to the calculation of the gap opening and bending bearing capacity at the joints of shield tunnels under various environments.

Description

Technical Field

[0001] The present invention relates to the calculation and evaluation of the bearing capacity at the joints of shield tunnel lining, and in particular to a method for calculating the gap opening and bending bearing capacity at the joints of shield tunnel lining. Background Technology

[0002] With the continuous development of urbanization, the volume and number of infrastructure buildings such as subway tunnels have achieved unprecedented development. Due to its convenient construction, high degree of mechanization and high construction safety, shield tunnels are currently the commonly used form of urban subway tunnels. Shield tunnels are composed of multiple segments connected by bolts. The joints connected by transverse bolts are the weak links in the cross-section of the shield tunnel. Scientific calculation of the gap opening and bending bearing capacity at the joints is of great significance for guiding the design of shield tunnels. The joints of shield tunnels have complex structures, variable force modes, and are affected by factors such as stress environment, geometric dimensions, gap width and bolt grade. At present, there is still a lack of scientific and effective methods to calculate their gap opening and bending bearing capacity.

[0003] Patent CN117454485A mentions a method for calculating the bending bearing capacity of the transverse joints of shield tunnels. The lining stress states II and III in this method are somewhat different from the actual lining stress states, that is, it is difficult for the lining joints to have an ideal plane section rotation, but the lining joints rotate with the outer edge of the core area concrete as the center. Although the bending bearing capacity calculated by this method is not much different from the test value, the angle at the joint calculated by this method is significantly different from the actual value. Therefore, this method only gives the calculated value of the ultimate bending bearing capacity, and does not give the angle at the joint or the gap opening. In actual engineering, the gap opening is more intuitive, which makes it easier for engineering designers to understand and judge the stress state of the lining during construction, and is widely used in the seepage design of shield tunnels. SUMMARY OF THE INVENTION

[0004] The purpose of the present invention is to facilitate the engineering design of shield tunnels, and to propose a method for calculating the gap opening and bending bearing capacity at the lining joints of shield tunnels. In order to achieve the above purpose, the present invention adopts the following technical solutions:

[0005] S1. Determine the stress environment of the shield tunnel according to the engineering design data, and calculate the axial force level N in the lining based on the principle of mechanics. Usually, the modified conventional method or finite element numerical simulation can be used;

[0006] S2. Determine the geometric parameters and material properties of the lining joints, including the concrete yield strength f c , bolt cross-sectional area A s , bolt pre-tension stress σ sp , bolt yield strength fs The elastic modulus E of the bolt s The length l of the bolt s The lining thickness h tot The crack depth t 1 The crack width ω, the gasket thickness t 2 The height h of the concrete in the core area eff The distances from the bolt center to the upper and lower edges of the concrete in the core area and The specific meanings of the physical quantities can be referred to Figure 1 .

[0007] S3. Give the bolt elongation Δl s A relatively small initial value, and it is recommended that the initial value be less than 10 -7 mm, and gradually increase the value of Δl s . At each step, judge the stress state of the lining. In the present invention, the lining has 4 states, 1 initial state where Δl s =0, and 3 stress states. Since Δl s >0 during the calculation, only the 3 stress states need to be discriminated. The discrimination condition for stress state I is The discrimination condition for stress state II is and F N1 >0, and the discrimination condition for stress state III is F N1 =0, where F N1 is the axial force of the compressed zone of the concrete in the core area.

[0008] When the lining belongs to stress state I, the section moment M can be calculated by formula (1).

[0009]

[0010] where, F N1 =N + F s , and F N1 ≤A c f c , and F s ≤f s A s , A c is the equivalent compression area of the concrete in the core area.

[0011] The crack opening amount can be calculated by formula (2).

[0012]

[0013] And calculate the maximum value of F N1 in this state, briefly recorded as F N1,max .

[0014] The lining is in stress state Ⅱ, and the axial force of the concrete compression zone in the core area is F N1 , and the axial force of the concrete compression zone at the outer edge is F N2 . The section moment M can be calculated by formula (3).

[0015]

[0016] Among them, F N2 = N + F s - F N1 , and F s ≤ f s A s , F N1,max is the maximum value of F N1 , L is the influence depth of the concrete compression in the core area, Δ is the local compression deformation of the concrete in the core area, it is recommended to take L = 0.5m, A c = 0.01m 2 .

[0017] The crack opening width can be calculated by formula (4).

[0018]

[0019] When the lining is in stress state Ⅲ, the axial force of the concrete compression zone at the outer edge is F N2 , and the section moment M can be calculated by formula (5).

[0020]

[0021] Among them, F N2 = N + F s , and F s ≤ f s A s .

[0022] The crack opening width can be calculated by formula (6).

[0023]

[0024] S4. Continuously increase the bolt elongation Δl s , calculate the section moment M corresponding to each crack opening width ω o , draw the variation curve of M with ω o , and determine the critical flexural bearing capacity M o at the joint, the ultimate flexural bearing capacity M cr and the critical opening width ω u . The critical flexural bearing capacity M cr . The critical flexural bearing capacity M crFor M—ω o The value at the turning point between the first flat stage and the second rising stage in the curve, and the ultimate flexural bearing capacity M u For M—ω o The maximum value in the curve, and the opening amount corresponding to M cr is ω cr .

[0025] The beneficial effects of the present invention are as follows: For the convenience of engineering design, based on the deformation law of the actual shield tunnel joints under external loads, a mechanical calculation diagram of the joints is given. In this method, the edge of the core area at the joints is taken as the local compression area, and the lining rotates around this area, which is more in line with the engineering practice. Two new parameters, the equivalent compression area A c of the core area concrete and the influence depth L of the core area concrete under compression, are proposed, and the recommended values are given through optimization. A method for calculating the opening amount of the gap and the section moment is proposed based on the mechanical principle, and the values of the critical flexural bearing capacity, the ultimate flexural bearing capacity, and the critical opening amount of the gap are determined. By comparing with the results of model tests and numerical simulations, the technology of the present invention has high accuracy and can meet the needs of engineering design. Description of the Drawings

[0026] Figure 1 is the schematic diagram of the present invention and each physical quantity.

[0027] Figure 2 is the mechanical calculation diagram of the shield tunnel joints.

[0028] Figure 3 is the M—ω o curve calculated by using the method of the present invention and the comparison with other methods.

[0029] Figure 4 is the numerical model of the lining joints established by using the ABAQUS finite element software. Detailed Embodiment

[0030] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments.

[0031] Tongji University carried out a prototype test on the flexural bearing capacity of a certain shield tunnel lining joint. Patent CN117454485A also takes this case as an example. To verify the effectiveness of the method of the present invention, the specific implementation manner of the method of the present invention is also described by taking the parameters of this test shield tunnel as an example, and the results are compared with the test results and the numerical simulation results.

[0032] A method for calculating the opening amount of the gap and the flexural bearing capacity of the shield tunnel lining joints includes the following steps:

[0033] S1. According to the data in the above two materials, the axial force level N = 500 kN.

[0034] S2. According to the actual situation of the project and the two reference materials, the concrete yield strength f c = 43.3 MPa, the bolt cross-sectional area A s = 0.0014 m 2 , the bolt pre-tension stress σ sp = 0, the bolt yield strength f s = 480 MPa, the bolt elastic modulus E s = 210000 MPa, the bolt length l s = 0.48 m, the lining thickness h tot = 0.35 m, the gap depth t 1 = 0.037 m, the gap width ω = 0.004 m, the gasket thickness t 2 = 0.043 m, the height of the concrete in the core area h eff = 0.19 m, the distances from the bolt center to the upper and lower edges of the concrete in the core area 149 m and

[0035] S3. Assign a small initial value to the bolt elongation Δl s , and select the initial value as 10 -7 m in the implementation, and gradually increase the value of Δl s . At each step, judge the stress state of the lining.

[0036] In the present invention, the lining has 4 states, 1 initial state where Δl s = 0, and 3 stress states. Since Δl s > 0 during the calculation, only the 3 stress states need to be discriminated.

[0037] Stress state Ⅰ: The gap in the compression zone is not closed, and the discrimination condition is

[0038] Stress state Ⅱ: The gap in the compression zone is closed, and the concrete in the core area is under compression. The discrimination condition is and F N1 > 0,

[0039] Stress state Ⅲ: The gap in the compression zone is closed, and the pressure of the concrete in the core area is 0. The discrimination condition is F N1 = 0, where F N1 is the axial force in the compression zone of the concrete in the core area. The schematic diagrams of the stress states of the lining are shown in Figure 2 .

[0040] When the lining is in stress state Ⅰ, the sectional bending moment M can be calculated by formula (1).

[0041]

[0042] Among them, F N1 = N + F s , and F N1 ≤ A c f c , and F s ≤ f s A s A c is the equivalent compressive area of the core zone concrete.

[0043] The crack opening amount can be calculated by formula (2).

[0044]

[0045] And calculate the maximum value of F N1 in this state, briefly recorded as F N1,max .

[0046] When the lining is in stress state Ⅱ, the axial force of the compressive zone of the core zone concrete is F N1 , the axial force of the compressive zone of the outer edge concrete is F N2 , and the sectional bending moment M can be calculated by formula (3).

[0047]

[0048] Among them, F N2 = N + F s - F N1 , and F s ≤ f s A s F N1,max is the maximum value of F N1 , L is the influence depth of the compressive stress of the core zone concrete, Δ is the local compressive deformation of the core zone concrete, it is recommended to take L = 0.5m, A c = 0.01m 2 .

[0049] The crack opening amount can be calculated by formula (4).

[0050]

[0051] When the lining is in stress state Ⅲ, the axial force of the compressive zone of the outer edge concrete is F N2 , and the sectional bending moment M can be calculated by formula (5).

[0052]

[0053] Among them, F N2 = N + F s ,

[0054] The crack opening amount can be calculated by formula (6).

[0055]

[0056] S4. Continuously increase the bolt elongation Δl s , calculate the sectional bending moment M corresponding to each crack opening amount ω o , draw the variation curve of M with ω o , and determine the critical flexural bearing capacity M o at the joint, the ultimate flexural bearing capacity M cr , and the critical opening amount ω u . The critical flexural bearing capacity M cr is the value at the turning point between the first flat stage and the second lifting stage in the M-ω cr curve. The ultimate flexural bearing capacity M o is the maximum value in the M-ω u curve. The opening amount corresponding to M o is ω cr . The calculation results of this case can be seen in cr . Figure 3 .

[0057] It is known from Figure 3 that the critical flexural capacity value of this case is 144.5 kN·m, and the experimental value obtained by Tongji University is 148 kN·m. The error between the two is about 2.5%, which is closer than the value in Patent CN117454485A.

[0058] To further verify the effectiveness of this method, a numerical model consistent with the model test was established based on the commercial finite element software ABAQUS, as shown in Figure 4 , and the data of sectional bending moment and opening amount were extracted. The comparison is shown in Figure 3 . It is known from Figure 3 that the critical opening amount ω cr calculated by this method is 8.75 mm, which is relatively close to both the model test value and the numerical simulation value. This is the main advantage of this method compared with Patent CN117454485A. The difference between the ultimate moment calculated by this method and Patent CN117454485A is not large. Therefore, this method not only gives the critical moment and ultimate moment with relatively high precision, but also gives the critical opening amount at the joint that is more convenient for engineers to use, and is more likely to meet the needs of engineering practice.

[0059] As described above, it is only the preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. For example, the method of applying load with negative bending moment can be adopted for implementation, and the same good effect can be achieved. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution and inventive concept of the present invention, making equivalent replacements or changes, shall be covered by the protection scope of the present invention.

Claims

1. A method for calculating the gap opening and bending bearing capacity at the lining joint of a shield tunnel, characterized in that: The following steps are involved: S1. Assume that the elongation of the bolt is Δl s , giving Δl s A small initial value and gradually increase Δl s The value of is used to determine the stress state of the lining at each step. The stress state is divided into: Initial state: Δl s =0; Stress state I: the gap in the compression zone is not closed; Stress state II: The gaps in the compression zone are closed, and the concrete in the core zone is under compression; Stress state III: The gap in the compression zone is closed, and the concrete pressure in the core zone is 0; S2. Solve the gap opening ω in each state according to static equilibrium o and section bending moment M; geometric parameters and material properties at the lining joint include concrete yield strength f c , bolt cross-sectional area A s , bolt pre-tension stress σ sp , bolt yield strength f s , bolt elastic modulus E s , bolt length l s , lining thickness h tot , gap depth t1, gap width ω, sealing pad thickness t2, core area concrete height h eff , distance from the center of the bolt to the upper and lower edges of the core area concrete and When the lining is in stress state I, the axial force in the compression zone of the core concrete is F N1 , the section bending moment M can be calculated by formula (1); Among them, F N1 =N+F s , and F N1 ≤A c f c , And F s ≤f s A s , A c is the equivalent compressive area of ​​concrete in the core area, and N is the axial force level in the lining; Gap opening ω o Calculated by formula (2); When the lining is in stress state II, the axial force in the compression zone of the core concrete is F N1 , the axial force in the compression zone of the outer edge concrete is F N2 , the section bending moment M can be calculated by formula (3); in, F N2 =N+F s -F N1 , And F s ≤f s A s , F N1,max F N1 The maximum value of , L is the depth of concrete compression in the core area, Δ is the local compression deformation of concrete in the core area; The gap opening can be calculated by formula (4); When the lining is in stress state III, the axial force in the outer edge concrete compression zone is F N2 , the section bending moment M can be calculated by formula (5); Among them, F N2 =N+F s , And F s ≤f s A s ; The gap opening can be calculated by formula (6); S3, continue to increase the bolt elongation Δl s , calculate the opening amount ω of each gap o The corresponding section bending moment M is plotted against ω. o The change curve of M-ω o The critical bending bearing capacity M at the joint is determined by the curve cr , Ultimate bending bearing capacity M u and critical gap opening ω cr .

2. The method for calculating the gap opening and bending bearing capacity at the joint of the shield tunnel lining according to claim 1 is characterized in that: S2 F N1,max F is calculated when the lining is in stress state I N1 The maximum value of .

3. The method for calculating the gap opening and bending bearing capacity at the joints of the shield tunnel lining according to claim 1 is characterized in that: The core area concrete compression influence depth L and the core area concrete compression area equivalent area A c The recommended value is L = 0.5m, A c =0.01m 2 .

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