A method for calculating the bending bearing capacity of a reinforced joint of a shield tunnel steel plate

Abstract

The present application relates to a kind of shield tunnel steel plate reinforced joint bending carrying capacity calculation method, comprising the following steps: 1) the virtual strain of the inner edge of joint surface is obtained when calculating steel plate reinforcement, and the critical compression zone height of bolt yielding and the critical compression zone height of steel plate yielding when section failure;2) assume that joint surface is in a certain failure state, based on the axial force balance equation under the failure state, corresponding steel plate reinforced joint joint surface compression zone height is obtained by trial;3) whether joint surface compression zone height meets the range requirement of current failure state, if yes, then execute step 4), if not, then replace another failure state, return to step 2);4) the steel plate reinforced joint joint surface compression zone height obtained in step 2) is substituted into the bending moment balance equation under the current failure state, and the limit bending moment is calculated and obtained.Compared with prior art, the present application has the advantages of effectively reducing workload, improving efficiency and the like.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of shield tunnel engineering structure reinforcement design, and relates to a structure bending resistance calculation, in particular to a shield tunnel steel plate reinforcement joint bending resistance calculation method. BACKGROUND

[0002] In recent years, with the continuous and rapid development of urban shield tunnel engineering, the safety performance problem of shield segment lining structure is becoming increasingly serious. The segment lining structure is a prefabricated assembly type concrete structure composed of multiple segments and bolts through multi-ring staggered joint connection, and is widely used in the field of urban underground shield tunnel engineering. In the process of tunnel shield construction and operation, the segment lining structure mainly bears external earth pressure, underground water pressure, ground overload and excavation dynamic working conditions and other external confining pressure. Therefore, as the external structural support system of the tunnel, the mechanical bearing performance and failure mode of the segment lining structure under external confining pressure are crucial to the overall safety of the tunnel. Therefore, effective repair and reinforcement measures must be taken for the shield tunnel segment ring with diseases to ensure the safe operation of the subway tunnel and meet the durability requirements.

[0003] At present, for shield tunnels with excessive transverse deformation, the reinforcement method of internal tension steel plates is often used to limit the further development of lining structure diseases. In the field of shield tunnel structure reinforcement design, numerical simulation calculation is often used to analyze the bending resistance of steel plate reinforcement joints, which requires the pre-establishment of a three-dimensional simulation model, and the workload is large, making it difficult to quickly determine the bending resistance of the steel plate reinforcement joint. SUMMARY

[0004] The purpose of the present application is to overcome the low efficiency of the existing numerical simulation and to provide a shield tunnel steel plate reinforcement joint bending resistance calculation method.

[0005] The purpose of the present application can be achieved by the following technical solutions:

[0006] A shield tunnel steel plate reinforcement joint bending resistance calculation method, comprising the following steps:

[0007] 1) Obtain the structural parameters, material parameters and joint surface mechanical parameters of the joint surface, and calculate the virtual strain of the inner edge of the joint surface when the steel plate is reinforced sp,0 , the critical compression zone height x cb1 of bolt yielding and the critical compression zone height x cb2 of steel plate yielding.

[0008] 2) Based on the data obtained in step 1), assume that the joint surface is in a certain failure state, and based on the axial force balance equation under the failure state, the corresponding joint surface compression zone height x c of the steel plate reinforcement joint is obtained by trial calculation.

[0009] 3) Determine the height x of the compression zone of the joint surface obtained in step 2) c whether the range requirement of x in the current failure state is met, if yes, execute step 4), if not, replace another failure state and return to step 2) until all failure states are traversed; c

[0010] 4) Substitute the height of the compression zone of the joint surface of the steel plate reinforced joint obtained in step 2) into the moment balance equation in the current failure state to calculate the ultimate moment.

[0011] Further, the construction parameters include: bolt-to-joint surface outer edge distance, joint surface height, joint surface width, joint surface outer edge height, outer edge compression zone height, waterproof zone height, core compression zone height, joint inner edge height, bolt cross-sectional area and steel plate cross-sectional area;

[0012] The material parameters include: concrete axial compressive strength design value, concrete yield strain, concrete ultimate compressive strain, bolt yield strain, steel plate yield strain, bolt yield stress, steel plate yield stress, bolt elastic modulus and steel plate elastic modulus;

[0013] The joint surface mechanical parameters are the axial force and the moment of the joint surface when the steel plate is reinforced.

[0014] Further, the virtual strain ε sp,0 is obtained according to the following formula:

[0015]

[0016] In the formula, ε c,0 is the concrete compressive strain of the joint surface outer edge when the steel plate is reinforced, x0 is the joint surface compression zone height when the steel plate is reinforced, and h is the joint surface height.

[0017] ε c,0 and x0 are obtained by simultaneously solving the following formulas:

[0018]

[0019]

[0020]

[0021]

[0022] In the formula, σ c is the concrete stress, ε c is the concrete strain, f c is the concrete axial compressive strength design value, and ε c0 ​is the yield strain of concrete, b is the width of joint surface, d1 is the outer edge of joint, d2 is the outer edge bearing area, d3 is the waterproof area, d4 is the core bearing area, d5 is the inner edge of joint, p is the integral variable, N0 is the axial force of joint surface when reinforced by steel plate, M0 is the bending moment of joint surface when reinforced by steel plate, σ m,0 is the bolt stress when reinforced by steel plate, A m is the cross-sectional area of bolt, E m is the elastic modulus of bolt.

[0023] Further, the critical bearing area height x cb1 at which the bolt yields when the cross section fails, and the critical bearing area height x cb2 at which the steel plate yields is obtained according to the following formula:

[0024]

[0025]

[0026] wherein ε cu is the ultimate compressive strain of concrete, f my is the yield stress of bolt, E m is the elastic modulus of bolt, d is the distance from bolt to the outer edge of joint surface, f spy is the yield stress of steel plate, E sp is the elastic modulus of steel plate, and h is the height of joint surface.

[0027] Further, the failure states include that the bolt yields and the steel plate does not yield S-a, the bolt and the steel plate both yield S-b, the bolt does not yield and the steel plate yields S-c, and the bolt and the steel plate both do not yield S-d;

[0028] The axial force equilibrium equation under each failure state is expressed as:

[0029] Failure state S-a:

[0030]

[0031] Failure state S-b:

[0032]

[0033] Failure state S-c:

[0034]

[0035] Failure state S-d:

[0036]

[0037] wherein σ sp is the steel plate stress when the cross section fails, and εsp σ is the steel plate strain at cross-section failure, σ m b is the bolt stress at cross-section failure, b is the joint surface width, p is the integral variable, σ c σ is the concrete stress, ε cu ε is the ultimate compressive strain of concrete, A m A is the bolt cross-sectional area, A sp A is the steel plate cross-sectional area, f my f is the yield stress of the bolt, f spy f is the yield stress of the steel plate, N i N is the cross-sectional axial force corresponding to each failure state, x ci x is the joint surface compression zone height corresponding to each failure state, i = 1, 2, 3, 4, d i d1 is the joint surface outer edge height, d2 is the outer edge compression zone height, d3 is the waterproof zone height, d4 is the core compression zone height, d5 is the joint inner edge height, n = number of joint surface area blocks - 1;

[0038] The bending moment equilibrium equation corresponding to each failure state is as follows:

[0039] Failure state S-a:

[0040]

[0041] Failure state S-b:

[0042]

[0043] Failure state S-c:

[0044]

[0045] Failure state S-d:

[0046]

[0047] In the formula, M i is the ultimate bending moment corresponding to each failure state, h is the joint surface height, and d is the distance from the bolt to the outer edge of the joint surface.

[0048] Further, in step 3), if the joint surface compression zone height x c is greater than the distance d from the bolt to the outer edge of the joint surface under failure state S-c or failure state S-d, then the σ m A m term in the axial force equilibrium equation is removed and the current failure state is returned to step 2);

[0049] In step 4), if the joint surface compression zone height x cIf the distance d between the bolt and the outer edge of the joint surface is greater than the distance d, then the σ in the bending moment balance equation is cancelled m A m The (h-d) term.

[0050] Further, in step 2), the integral calculation term in the axial force balance equation is replaced by an integral approximation formula to approximate the solution, and the integral approximation formula is represented as:

[0051]

[0052] In the formula, α and β are equivalent coefficients, and satisfy the following formula:

[0053]

[0054]

[0055] In the formula, f c is the design value of the axial compressive strength of concrete.

[0056] Further, in step 4), the integral calculation term in the bending moment balance equation is replaced by an integral approximation formula to approximate the solution, and the integral approximation formula is represented as:

[0057]

[0058] In the formula, f c is the design value of the axial compressive strength of concrete.

[0059] Further, the range requirement of x c for each of the failure states is as follows:

[0060] Failure state S-a: x cb2 <x c1 ≤x cb1 ;

[0061] Failure state S-b: x c2 ≤x cb1 and x c2 ≤x cb2 ;

[0062] Failure state S-c: x cb1 <x c3 ≤x cb2 ;

[0063] Failure state S-d: x c4 >x cb1 and x c4 >x cb2 .

[0064] The application also provides a computer readable storage medium comprising one or more programs for execution by one or more processors of an electronic device, the one or more programs comprising instructions for performing the method for calculating the bending resistance of a shield tunnel steel plate reinforced joint.

[0065] Compared with the prior art, the application has the following beneficial effects:

[0066] 1. The application obtains the bending resistance of the steel plate reinforced joint through a theoretical method based on the actually collected basic parameters of the joint surface to be calculated, without modeling, overcomes the low efficiency defect of numerical simulation calculation in determining the bending resistance of the steel plate reinforced joint, and can quickly determine the bending resistance of the steel plate reinforced joint, which has a reference significance for the steel plate reinforcement design of the shield tunnel.

[0067] 2. The application considers the concave-convex features of the joint surface, quickly determines the failure state through trial calculation of the axial force balance equation of multiple failure states, and thus determines the ultimate bending moment of the joint surface, thereby ensuring the accuracy and improving the calculation efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0068] Figure 1 is a schematic diagram of the structure of the joint surface;

[0069] Figure 2 is a schematic diagram of the stress distribution of the joint surface when the steel plate is reinforced;

[0070] Figure 3 is a schematic diagram of the stress distribution of the joint surface when the section fails;

[0071] Figure 4 is a bearing capacity calculation process. DETAILED DESCRIPTION

[0072] The application will be described in detail below in combination with the drawings and specific embodiments. The embodiments are implemented on the premise of the technical solution of the application, and detailed implementation modes and specific operation processes are given, but the protection scope of the application is not limited to the following embodiments.

[0073] As shown in Figure 4 , the application provides a method for calculating the bending resistance of a shield tunnel steel plate reinforced joint, comprising the following steps: 1) obtaining the structure parameters, material parameters and joint surface mechanical parameters of the joint surface, and calculating the virtual strain ε sp,0 of the inner edge of the joint surface when the steel plate is reinforced and the critical compression zone height x cb1 of the bolt yielding when the section fails and the critical compression zone height x cb2 of the steel plate yielding; 2) based on the data obtained in step 1), assuming that the joint surface is in a certain failure state, based on the axial force balance equation under the failure state, trial calculation is performed to obtain the corresponding joint surface compression zone height xc 3) Determine the height x of the pressure zone of the joint surface obtained in step 2). c Does the current failure state satisfy x? c If the range requirement is met, proceed to step 4); otherwise, replace with another failure state and return to step 2), until all failure states are traversed; 4) Substitute the height of the compression zone of the steel plate reinforced joint surface obtained in step 2) into the moment balance equation under the current failure state to calculate the ultimate bending moment.

[0074] To facilitate the use of the above method, the following assumptions are made before implementation: the bond between the steel plate and the concrete is good, and slippage and failure of the bond surface are not considered; the influence of the steel plate thickness is not considered; the deformation of the joint surface satisfies the plane section assumption; the influence of bolt preload on the bending capacity of the joint is not considered; the ultimate compressive strain of the concrete is taken as the failure criterion of the section; only the tensile properties of the bolts and the steel plate are considered; the deformation of the joint before reinforcement is moderate, that is, the core and outer edge concrete share the pressure.

[0075] The above method is explained in detail below:

[0076] I. Obtaining basic parameters of the joint surface

[0077] The joint surface construction is shown in the attached figure. Figure 1 As shown. The basic parameters include structural parameters, material parameters, and joint surface mechanical parameters. The structural parameters include: distance d from the bolt to the outer edge of the joint surface, joint surface height h, joint surface width b, outer edge height d1, outer bearing zone height d2, waterproof zone height d3, core bearing zone height d4, inner edge height d5, and bolt cross-sectional area A. m steel plate cross-sectional area A sp Material parameters include: design value of axial compressive strength f of concrete. c ε yield strain of concrete c0 ultimate compressive strain ε of concrete cu ε of the bolt my Yield strain ε of steel plate spy The yield stress f of the bolt my Yield stress f of steel plate spy The elastic modulus E of the bolt m The elastic modulus E of the steel plate sp The mechanical parameters of the joint surface include: axial force N0 and bending moment M0 at the joint surface when reinforced with steel plate. These data can be obtained from engineering design documents and on-site measured data.

[0078] The joint involves three materials: concrete, reinforcing bars, and steel plates. The concrete adopts a combination of parabolic and linear constitutive models, as shown in Equation (1); the bolts adopt a bilinear constitutive model, as shown in Equation (2); and the steel plates adopt a bilinear constitutive model, as shown in Equation (3).

[0079]

[0080]

[0081]

[0082] where σ c is the stress of concrete; f c is the design value of axial compressive strength of concrete; ε c is the strain of concrete; ε c0 is the yield strain of concrete, which can be taken as 0.002; ε cu is the ultimate compressive strain of concrete, which can be taken as 0.0033; σ m is the stress of bolt; σ sp is the stress of steel plate; ε m is the strain of bolt; ε sp is the strain of steel plate; ε my is the yield strain of bolt; ε spy is the yield strain of steel plate; f my is the yield stress of bolt; f spy is the yield stress of steel plate.

[0083] II. Determination of the virtual strain ε sp,0 of the inner edge of the joint surface when the steel plate is reinforced.

[0084] In order to ensure the reinforcement effect of the joint, the opening range of the joint surface before reinforcement should not be too large, the enhancement effect of the bolt tension on the contact surface stress can be ignored, and it is assumed that the concrete constitutive curve is only in the parabolic segment. The stress distribution of the joint surface when the steel plate is reinforced is shown in the attached Figure 2 figure. N0 is the axial force of the joint surface; M0 is the bending moment of the joint surface; ε c,0 is the compressive strain of the concrete at the outer edge of the joint surface; σ c,0 is the compressive stress of the concrete at the outer edge of the joint surface; x0 is the height of the compression zone of the joint surface. The axial force balance equation is established as formula (4), the bolt stress expression when reinforced is formula (5), and the bending moment balance equation is formula (6). The x0 and ε c，0 are obtained by simultaneously solving formulas (4), (5) and (6). The ε sp，0 is obtained by substituting formula (7).

[0085]

[0086]

[0087]

[0088]

[0089] In the formula, p is the integral variable; b is the width of the joint surface; d i and d i+1 The dimensions of each divided area on the joint surface.

[0090] III. Determine the height x of the boundary pressure zone of the joint. cb

[0091] x cb1 The critical compression zone height for bolt yielding at section failure is given by equation (8); x cb2 The critical compression zone height is the height at which the steel plate yields when the section fails, as shown in equation (9).

[0092]

[0093]

[0094] When the joint fails, the height of the pressure zone on the joint surface is less than x. cb1 When the bolt yields, it will yield; conversely, it will not yield. When the joint fails, the height of the compression zone on the joint surface is less than x. cb2 When the steel plate yields, it will yield; otherwise, it will not yield.

[0095] IV. Determination of Failure State of Joint Surface

[0096] Stress distribution on the joint surface when the section fails is as follows Figure 3 As shown in the figure. Based on whether the bolt and steel plate yield at the time of section failure, the failure states of steel plate reinforced joints are divided into four types: Sa, bolt yields but steel plate does not; Sb, both bolt and steel plate yield; Sc, bolt does not yield but steel plate yields; Sd, neither bolt nor steel plate yields. A schematic diagram of the strain and stress distribution at the joint surface failure is attached. Figure 3 As shown. For failure state Sa, the height of the pressure zone x c1 x must be satisfied cb2 <x c1 ≤x cb1 For failure state Sb, the height of the pressure zone x c2 x must be satisfied c2 ≤x cb1 And x c2 ≤x cb2 For failure state Sc, the height of the pressure zone x c3 x must be satisfied cb1 <x c3 ≤x cb2 For failure state Sd, the height of the pressure zone x c4 x must be satisfied c4 >x cb1 And x c4 >x cb2 .

[0097] V. Height of compression zone x for different failure modes of joint surface c and the formula of ultimate bending moment M.

[0098] 1. When failure mode S-a occurs, the axial force equilibrium equation is shown in equation (10) and the bending moment equilibrium equation is shown in equation (11). Given N1, equations (10) to (12) can be solved to obtain x c1 and M1.

[0099]

[0100]

[0101] σ sp = ε sp E sp = (ε cu h / x c1 - ε cu - ε sp,0 ) E sp (12)

[0102] In the equation, N1 is the axial force on the joint, A m is the cross-sectional area of the bolt, A sp is the cross-sectional area of the steel plate, and n has no physical meaning. Numerically, n = the number of blocks of the joint surface area - 1.

[0103] 2. When failure mode S-b occurs, the axial force equilibrium equation is shown in equation (13) and the bending moment equilibrium equation is shown in equation (14). Given N2, equations (13) to (14) can be solved to obtain x c2 and M2.

[0104]

[0105]

[0106] 3. When failure mode S-c occurs, the axial force equilibrium equation is shown in equation (15) and the bending moment equilibrium equation is shown in equation (16). Given N3, equations (15) to (17) can be solved to obtain x c3 and M3.

[0107]

[0108]

[0109]

[0110] 4. When failure mode S-d occurs, the axial force equilibrium equation is shown in equation (18) and the bending moment equilibrium equation is shown in equation (19). Given N4, equations (18) to (19) can be solved to obtain xc4 And M4.

[0111]

[0112]

[0113] The above calculation method does not consider the compressive strength of the bolts and steel plates. If the height of the compression zone at the joint surface is x c If the distance d from the bolt to the outer edge of the joint surface is greater than the distance d, then σ in equations (15) and (18) needs to be removed. m A m The terms, and σ in equations (16) and (19) m A m (hd) item.

[0114] The above method employs a trial-and-error approach, substituting the obtained parameters one by one into the axial force equilibrium equation corresponding to each failure state, and combining this with the integral approximation formula of the axial force equilibrium equation to obtain the height x of the compression zone of the cross section. c Determine whether it satisfies the selected axial force balance equation and integral approximation formula for x. c The range requirement must be met. If satisfied, the selected failure state is correct. After determining the failure state of the joint surface, substitute the corresponding moment equilibrium equation into the equation and use the integral approximation formula of the moment equilibrium equation to obtain the ultimate bending moment.

[0115] VI. Approximate solution methods for calculation formulas.

[0116] Since the above formula involves complex integral calculations, it is not convenient to quickly solve for the ultimate bending moment of the joint. To simplify the formula, in another embodiment, the stress distribution of the concrete at the joint surface can be converted into a rectangular distribution using an equivalent method. To ensure that the axial force and bending moment at the joint surface remain unchanged after the conversion, equations (20) and (21) must be satisfied.

[0117]

[0118]

[0119] In the formula, α and β are equivalent coefficients.

[0120] VII. Determine the approximate expression methods for the integral parts involved in formulas (10) to (19), as shown in Table 1.

[0121] Table 1. Approximate expressions for the integral part of the calculation model.

[0122]

[0123] If the above method is realized in the form of a software function unit and sold or used as an independent product, it can be stored in a computer readable storage medium. Based on this understanding, the technical solutions of the present application essentially or the parts that contribute to the prior art or parts of the technical solutions can be embodied in the form of a software product, which is stored in a storage medium, including a number of instructions to make a computer device (which can be a personal computer, server, or network device, etc.) execute all or part of the steps of the method described in various embodiments of the present application. The foregoing storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), magnetic disk or optical disk, and various media that can store program codes.

[0124] Embodiment

[0125] The above method is illustrated by a specific engineering case:

[0126] I. According to the engineering design data, the joint surface structure and material parameters are obtained as follows:

[0127] h is 350 mm, d is 200 mm, d1 is 5 mm, d2 is 35 mm, d3 is 74 mm, d4 is 211 mm, b is 1500 mm, f c is 25.3 MPa, f spy is 200 MPa, f my is 400 MPa, E sp is 210 GPa, E c is 35.5 GPa, E m is 206 GPa, N is 1000 kN, M0 is 156 kN·m, A m is 1413.5 mm 2 , A sp is 3000 mm 2 .

[0128] II. Substitute the above parameters into the corresponding formula to obtain the virtual strain ε sp,0 = 0.0015.

[0129] III. The critical compression zone height x of bolt yielding when the cross section fails is obtained as cb1 = 125.9 mm and the critical compression zone height x of steel plate yielding is obtained as cb2 = 200.8 mm.

[0130] IV. Substitute N = 1000 kN into the axial force balance equation corresponding to the failure state of each joint surface to determine x cThe joint surface failure state is S-c, i.e. the steel plate is yielded and the bolt is not yielded when the cross section is failed, and the bolt stress is 358.1 MPa.

[0131] V. Substituting x c = 145.7 mm into the bending moment balance equation corresponding to S-c, the limit bending moment M of the joint surface is 334.2 kN·m.

[0132] The above results are close to the results of numerical simulation, which shows that the above method has the effect of ensuring certain calculation precision and improving calculation efficiency.

[0133] The above detailed the preferred embodiments of the present application. It should be understood that those of ordinary skill in the art can make many modifications and variations without creative work based on the concept of the present application. Therefore, any technical solutions obtained by logical analysis, reasoning or limited experiments based on the prior art within the concept of the present application should be within the protection scope defined by the claims.

Claims

1. A method for calculating the flexural capacity of a reinforced joint of a shield tunnel steel plate, characterized in that, The method comprises the following steps: 1) Obtain the configuration parameters, material parameters and mechanical parameters of the joint surface, and calculate the virtual strain of the inner edge of the joint surface when the steel plate is reinforced And the critical compression zone height of bolt yielding when the section fails And the critical compression zone height of steel plate yielding ; 2) Based on the data obtained in step 1), assuming the joint surface is in a certain failure state, the corresponding compression zone height of the steel plate reinforced joint surface is obtained by trial calculation based on the axial force balance equation under the failure state ; 3) determining the height of the compression zone of the joint surface obtained in step 2) whether the current failure state meets the range requirement of if yes, then executing step 4), if no, then replacing another failure state and returning to step 2) until all failure states are traversed; 4) substituting the compressive zone height of the steel plate reinforced joint joint surface obtained in step 2) into the moment balance equation in the current failure state to calculate the ultimate moment; The failure states include bolt yielding and steel plate not yielding S-a, bolt and steel plate both yielding S-b, bolt not yielding and steel plate yielding S-c, and bolt and steel plate both not yielding S-d; The axial force balance equation in each failure state is expressed as: Failure state S-a: Failure state S-b: Failure state S-c: Failure state S-d: wherein, is the steel plate stress at cross-section failure, is the steel plate strain at cross-section failure, is the bolt stress at cross-section failure, is the joint surface width, is the integral variable, is the concrete stress, is the concrete ultimate compressive strain, is the bolt cross-sectional area, is the steel plate cross-sectional area, is the yield stress of the bolt, is the yield stress of the steel plate, is the cross-section axial force corresponding to each failure state, is the compressive zone height of the joint surface corresponding to each failure state, , wherein: is the joint surface outer edge height, is the outer edge compressive zone height, is the waterproof zone height, is the core compressive zone height, is the joint inner edge height, n = joint surface area block number - 1; The moment balance equation corresponding to each failure state is as follows: Failure state S-a: Failure state S-b: Failure state S-c: Failure state S-d: wherein Mlimis the limit bending moment for each failure mode, h is the height of the joint surface, d is the distance from the bolt to the outer edge of the joint surface.

2. The method of calculating the flexural capacity of a shield tunnel steel plate reinforced joint according to claim 1, characterized in that, The construction parameters include: bolt-to-joint surface outer edge distance, joint surface height, joint surface width, joint surface outer edge height, outer edge compressive zone height, waterproof zone height, core compressive zone height, joint inner edge height, bolt cross-sectional area, and steel plate cross-sectional area; The material parameters include concrete axial compressive strength design value, concrete yield strain, concrete ultimate compressive strain, bolt yield strain, steel plate yield strain, bolt yield stress, steel plate yield stress, bolt elastic modulus, and steel plate elastic modulus; The joint surface mechanical parameters are the axial force and moment of the joint surface when the steel plate is reinforced.

3. The method of calculating the flexural capacity of a shield tunnel steel plate reinforced joint according to claim 1, characterized in that, The virtual strain of the inner edge of the joint surface when the steel plate is reinforced This is obtained according to the following formula: In the formula, the compressive strain of the concrete at the outer edge of the joint surface when the steel plate is used for reinforcement, the height of the compression zone of the joint surface when the steel plate is used for reinforcement, the height of the joint surface; and By solving the following equations simultaneously: wherein, is the concrete stress, is the concrete strain, is the design value of the concrete axial compressive strength, is the concrete yield strain, is the joint surface width, is the joint outer edge, is the outer edge bearing area, is the waterproof area, is the core bearing area, is the joint inner edge, is the integral variable, is the joint surface axial force when reinforced with steel plates, is the joint surface bending moment when reinforced with steel plates, is the bolt stress when reinforced with steel plates, is the bolt cross-sectional area, is the bolt elastic modulus.

4. The method of calculating the flexural capacity of a shield tunnel steel plate reinforced joint according to claim 1, wherein, The critical height of the compressive zone at which the bolt yields at failure of the cross-section The critical height of the compressive zone at which the steel plate yields Is obtained according to the following formula: wherein is the ultimate compressive strain of concrete, is the yield stress of the bolt, is the elastic modulus of the bolt, is the distance from the bolt to the outer edge of the joint surface, is the yield stress of the steel plate, is the elastic modulus of the steel plate, is the height of the joint surface.

5. The method of calculating the flexural capacity of a shield tunnel steel plate reinforced joint according to claim 1, wherein, In step 3), if the joint face compression zone height is greater than the bolt to joint face outer edge distance in the failure state S-c or failure state S-d , then cancel the term in the axial force equilibrium equation and return to step 2) with the current failure state. ​ In Step 4), if the calculated height of the compression zone of the joint surface is greater than the distance from the bolt to the outer edge of the joint surface in the failure state S-c or the failure state S-d , then the term in the bending moment balance equation is cancelled. ​ 6. The method of calculating the flexural capacity of a shield tunnel steel plate reinforced joint according to claim 1, wherein, In step 2), the integral calculation term in the axial force balance equation is replaced with an integral approximation formula for approximate solution, and the integral approximation formula is expressed as: wherein , is an equivalent coefficient, satisfying the following equation: In the formula, is the design value of the axial compressive strength of concrete.

7. The method of calculating the flexural capacity of a shield tunnel steel plate reinforced joint according to claim 1, wherein, In step 4), the integral calculation term in the moment balance equation is replaced with an integral approximation formula for approximate solution, and the integral approximation formula is expressed as: In the formula, is the design value of the axial compressive strength of concrete.

8. The method of calculating the flexural capacity of a shield tunnel steel plate reinforced joint according to claim 1, wherein, each of the failure states The range requirement for each of the failure states is: Failure state S-a: ; Failure state S-b: and ; Failure state S-c: ; Failure state S-d: and .

9. A computer-readable storage medium, characterized in that, The method comprises one or more programs for one or more processors of an electronic device to execute, the one or more programs comprising instructions for performing the shield tunnel steel plate reinforced joint bending capacity calculation method according to any one of claims 1-8.

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