A method for calculating discontinuous deformation of bolt joints in shield tunnels

Abstract

The present invention discloses a method for calculating the discontinuous deformation of bolt joints in a shield tunnel, including: establishing a Dirac Delta function of a shield tunnel bolt longitudinal joint and calculating the first-order derivative and the second-order derivative; calculating the shear dislocation virtual distribution pressure when the shield tunnel bolt longitudinal joint is shear dislocated; calculating the bending rotation virtual distribution pressure when the shield tunnel bolt longitudinal joint is bent and rotated; establishing a control differential equation at the shield tunnel bolt movable joint, and calculating the discontinuous deformation parameters of the shield tunnel bolt joint. The present invention not only predicts the deflection of the pipeline, but also predicts the deformation joint and bolt joint dislocation and rotation of the shield tunnel, solving the problem that the existing algorithm cannot simulate the opening and dislocation of the joint, and cannot predict the discontinuous deformation and internal force of the shield tunnel, and is reasonable, convenient and comprehensive for estimating the discontinuous deformation of the existing shield tunnel longitudinal joint.

Description

Technical Field

[0001] The invention relates to the field of intelligent measurement and control technology, and in particular to a method for calculating discontinuous deformation of a shield tunnel bolt joint. Background Art

[0002] In recent years, underground space technology has developed rapidly around the world. A large number of tunnels are being built deeper and deeper, inevitably passing under existing underground structures such as tunnels, pipelines, and subway stations. Shield tunnels have become an important part of today's urban underground transportation construction. It can be seen that tunnel-soil interaction (TSI) is of great significance to ensure the safety and applicability of existing structures. Therefore, the differential deformation of the longitudinal joints during the construction and operation of shield tunnels has received increasing attention from all walks of life. During the construction and operation of shield tunnels, the front thrust of the shield during advancement and the additional stress of the surrounding soil caused by the friction between the shield and the soil cannot be ignored. The influence on the deformation of the shield tunnel and the safe construction and operation of the shield tunnel cannot be ignored.

[0003] There are two deformation modes of the segment links, the opening between the segment links, such as Figure 9a As shown; the misalignment between the segments, such as Figure 9b In fact, the third deformation mode is a combination of the opening and dislocation modes, as shown in Fig.9c As shown. The beam-spring model and the longitudinal continuous model are usually used to study the TSI problem considering the longitudinal joint. The beam-spring model regards the standard structural segment as a beam and the weak joint as an elastic spring to model the bending moment, axial force and shear force. The longitudinal continuous model regards the existing shield tunnel as a homogeneous continuous beam with stiffness reduction at the weak joint. In the traditional research method, the existing shield tunnel is regarded as an Euler-Bernoulli beam (EB) or Timoshenko beam (TB), located on an elastic foundation composed of the Winkler model, the two-parameter Pasternak model and the three-parameter Kerr model. This foundation beam model that combines the beam model and the foundation model is used to simulate the mechanical behavior of the new tunnel passing under the existing shield tunnel. Although the choice of model is essentially indifferent, some models assume that the deformation of the shield tunnel is continuous, and cannot simulate the opening and dislocation of the joints, and cannot predict the discontinuous deformation and internal force of the shield tunnel.

[0004] Therefore, there is an urgent need for a method that can timely monitor the additional stress generated in the soil around the longitudinal joints during the construction and operation of the shield tunnel, and can accurately predict the relative displacement and relative rotation angle generated at the longitudinal joints of the shield tunnel bolts. Summary of the invention

[0005] The present invention provides a method for calculating discontinuous deformation of shield tunnel bolt joints to overcome the above technical problems.

[0006] In order to achieve the above object, the technical solution of the present invention is:

[0007] A method for calculating discontinuous deformation of bolt joints in a shield tunnel comprises the following steps:

[0008] S1: Establishing the Dirac Delta function of the longitudinal joint of the shield tunnel bolt, and respectively calculating the first-order derivative and the second-order derivative of the Dirac Delta function, so as to obtain the shear dislocation calculation model of the longitudinal joint of the shield tunnel bolt and the bending rotation calculation model of the shield tunnel bolt joint;

[0009] S2: According to the shear dislocation calculation model of the shield tunnel bolt longitudinal joint, the shear dislocation virtual distributed pressure when the shield tunnel bolt longitudinal joint is shear dislocated is calculated:

[0010] S3: Calculate the bending and rotation virtual distributed pressure when the shield tunnel bolt longitudinal joint is bent and rotated according to the shield tunnel bolt joint bending and rotation calculation model;

[0011] S4: Establish a control differential equation at the active joint of the shield tunnel bolt, and calculate the discontinuous deformation parameters of the shield tunnel bolt joint according to the shear dislocation virtual distributed pressure and the bending rotation virtual distributed pressure, that is, the relative displacement generated at the longitudinal joint of the shield tunnel bolt and the relative rotation angle generated at the longitudinal joint of the shield tunnel bolt.

[0012] Beneficial effect: The method for calculating the discontinuous deformation of bolt joints in a shield tunnel of the present invention obtains a shear dislocation calculation model for longitudinal bolt joints in the shield tunnel and a bending and rotation calculation model for bolt joints in the shield tunnel based on the first-order derivative and the second-order derivative of the DiracDelta function. It can not only predict the deflection of the pipeline, but also predict the deformation joints and dislocation and rotation of bolt joints in the shield tunnel. It solves the problem that the existing algorithm assumes that the deformation of the shield tunnel is continuous, cannot simulate the opening and dislocation of the joints, and cannot predict the discontinuous deformation and internal force of the shield tunnel. It is reasonable, convenient and comprehensive for estimating the discontinuous deformation of the existing longitudinal joints of the shield tunnel. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0014] Figure 1 It is a flow chart of the method for calculating discontinuous deformation of shield tunnel bolt joints of the present invention;

[0015] Figure 2 is a schematic diagram of a step function in an embodiment of the present invention;

[0016] Figure 3 Schematic diagram of the Dirac delta function in an embodiment of the present invention;

[0017] Figure 4 Schematic diagram of the first-order derivative of the Dirac Delta function in an embodiment of the present invention;

[0018] Figure 5 Schematic diagram of joint shear misalignment caused by shear misalignment virtual distribution pressure in an embodiment of the present invention;

[0019] Figure 6 Schematic diagram of the second-order derivative of the Dirac Delta function in an embodiment of the present invention;

[0020] Figure 7 Schematic diagram of the bending and rotation of the joint caused by the bending and rotation virtual distribution pressure in an embodiment of the present invention;

[0021] Figure 8 Schematic diagram of calculation model of shield tunnel with longitudinal joints in an embodiment of the present invention

[0022] Figure 9a It is a schematic diagram of the deformation of the pipe segment of the present invention;

[0023] Figure 9b It is a schematic diagram of the dislocation deformation of the pipe segment of the present invention;

[0024] Fig.9c It is a schematic diagram of the combined deformation of the pipe segment of the present invention;

[0025] Fig.10 is a flow chart of a calculation method in an embodiment of the present invention. DETAILED DESCRIPTION

[0026] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0027] This embodiment provides a method for calculating discontinuous deformation of bolt joints in a shield tunnel, comprising the following steps: Figure 1 Shown and Fig.10 As shown,

[0028] S1: Establish the Dirac Delta function of the shield tunnel bolt longitudinal joint to obtain the shear dislocation calculation model of the shield tunnel bolt longitudinal joint and the bending rotation calculation model of the shield tunnel bolt joint;

[0029] The method for establishing the Dirac Delta function of the longitudinal joint of the shield tunnel bolt in S1 is as follows:

[0030] The Heaviside step function at the active part of the bolt joint in the shield tunnel is established as shown in the attached figure. Figure 2 As shown:

[0031]

[0032] Where: x j represents the coordinates of the jth longitudinal joint; x represents the variable of the longitudinal joint position; j represents the number of the longitudinal joint;

[0033] The Dirac Delta function is defined as a step function H(xx j ) in x j The derivative at Figure 3 As shown; then the difference method is used to calculate the function δ according to formula (1): h (xx j ) expression:

[0034]

[0035] Where: h (xx j ) represents the Dirac Delta function of the longitudinal joint of the shield tunnel bolt; h is the intermediate parameter;

[0036] When h→0, δ h (xx j )=δ(xx j )

[0037] Therefore, the calculation model of shear misalignment of the longitudinal joint of the shield tunnel bolt, i.e., the first-order derivative of the Dirac Delta function, is calculated as follows:

[0038]

[0039] Among them, △x represents the difference between the coordinates of the i-th longitudinal joint location and the longitudinal joint position variable;

[0040] The calculation model of shield tunnel bolt joint bending rotation, that is, the second-order derivative of Dirac Delta function, is calculated as follows:

[0041]

[0042] S2: According to the shear dislocation calculation model of the shield tunnel bolt longitudinal joint, the shear dislocation virtual distributed pressure when the shield tunnel bolt longitudinal joint is shear dislocated is calculated:

[0043] As attached Figure 4 As shown, it is a schematic diagram of the first-order derivative of the Dirac Delta function; Figure 5 Shown is a schematic diagram of joint shear misalignment caused by virtual distributed pressure of shear misalignment;

[0044] Calculate the shear force Q0 of equal magnitude and opposite direction caused by the virtual distribution pressure of shear dislocation; Assume e1(x) = C1δ'(x-xj); then

[0045] Specifically, by δ h '(xx j ) indicates that the virtual distributed pressure e1(x) caused by shear misalignment is two equal and opposite concentrated forces F0. F0 is the concentrated force assumed to act on the segment. In the shear misalignment deformation stage, it is equal to the shear force Q0, and in the bending deformation stage, it is the bending moment M0 multiplied by the lever arm.

[0046]

[0047] Where: F0 represents the concentrated force acting on the segment. When shear dislocation occurs in the longitudinal joint of the shield tunnel bolt, the concentrated force is equal to the shear force Q0. C1 represents the proportional constant of the reaction shear dislocation mode, that is, the virtual distribution pressure of the reaction shear dislocation is proportional to δ′(xx j ) is a constant of the proportional relationship between

[0048] Due to the shear force Q0, the longitudinal joint of the shield tunnel bolt produces a relative displacement Δδ. The virtual distribution pressure of the shear dislocation does not affect the balance of the system. Therefore, when Δδ is infinitely small at 2h, we can get:

[0049]

[0050] Where: Δδ represents the relative displacement generated at the longitudinal joint of the shield tunnel bolt; G represents the shear modulus; A represents the cross-sectional area; GA is the shear stiffness;

[0051] Specifically, it is defined that if the left section of the shield tunnel bolt longitudinal joint is higher than the right section, Δδ is positive. Otherwise, Δδ is negative; therefore, C1 = GAΔδ;

[0052] Therefore, the virtual distribution pressure e1(x) of shear dislocation is obtained as follows:

[0053] e1(x)=GA(△δ)δ′(xx j ) (7).

[0054] S3: Calculate the bending and rotation virtual distributed pressure when the shield tunnel bolt longitudinal joint is bent and rotated according to the shield tunnel bolt joint bending and rotation calculation model;

[0055] As attached Figure 6 As shown, it is a schematic diagram of the second-order derivative of the Dirac Delta function; Figure 7 The figure shows the bending and rotation of the joint caused by the virtual distributed pressure of the bending and rotation;

[0056] Calculate a pair of moments M0 caused by the virtual distributed pressure of bending and rotation. Specifically, when the longitudinal joint of the shield tunnel bolt is bent and rotated, the generated concentrated force F0 is equal to 1 / 2 of the force at the joint and opposite to the force at the joint; Assume that the virtual distributed pressure of bending and rotation e2(x)=C2δ"(xx j ),but

[0057]

[0058]

[0059] Where: C2 represents the proportional constant of the reaction bending mode, that is, the virtual distribution pressure of the reaction bending rotation and δ h ”(xx j ) is a constant of the proportional relationship between

[0060] Due to the action of the moment M0, a relative rotation angle Δθ is generated at the longitudinal joint of the shield tunnel bolt. The bending rotation virtual distribution pressure does not affect the balance of the system. Therefore, when Δθ is infinite at 2h, it can be obtained:

[0061]

[0062] Where: Δθ represents the relative rotation angle generated at the longitudinal joint of the shield tunnel bolt; E represents the elastic modulus; I represents the moment of inertia; EI represents the bending stiffness;

[0063] Specifically, when the longitudinal joint is deformed into a concave shape, Δθ is positive. On the contrary, Δθ is negative. Therefore, the constant C2 = EIΔθ.

[0064] Therefore, the bending rotation virtual distribution pressure e2(x) is obtained as:

[0065] e2(x)=EI△θδ″(xx j ) (11).

[0066] S4: According to the intelligent monitoring system set at the longitudinal joint of the shield tunnel bolt, the additional pressure acting on the longitudinal joint of the shield tunnel bolt is obtained;

[0067] Specifically, the intelligent measurement and control system in this embodiment is a conventional measurement and control system with data processing and computing capabilities in the field, and at least includes a monitoring device, a data processing system, and a human-computer interaction system; the monitoring device is specifically a plurality of sensors arranged at the longitudinal joints of the shield tunnel bolts, and the additional pressure acting on the shield tunnel bolt joints is monitored in real time through the monitoring device, and the monitoring data is transmitted to the data processing system through a transmission line. The calculation program of the discontinuous deformation of the shield tunnel bolt joints in this embodiment is implanted in the processing system, and the calculation results are visualized in real time through the human-computer interaction system, so that the monitoring personnel can grasp the deformation information of the tunnel in time, and the longitudinal joints of the shield tunnel bolts are monitored online and automatically 7*24 hours a day through the monitoring device, and the data is returned in real time, so as to avoid the problem that the surveying personnel need to rely on the skylight time to enter the railway tunnel for measurement in the traditional operation mode.

[0068] S5: Establish the governing differential equation of the Timoshenko beam based on the Winkler foundation model, and use it to represent the governing differential equation at the active joint of the shield tunnel bolts. According to the additional pressure, the shear dislocation virtual distributed pressure and the bending rotation virtual distributed pressure, calculate the relative displacement generated at the longitudinal joint of the shield tunnel bolts and the relative rotation generated at the longitudinal joint of the shield tunnel bolts.

[0069] The shield tunnel is composed of prefabricated reinforced concrete segments connected by longitudinal and circumferential joints; each ring of the shield tunnel is regarded as a short and thick beam. In this embodiment, the Timoshenko beam model is used to simulate the shield tunnel model;

[0070] In order to accurately calculate the discontinuous deformation of the shield tunnel, in this embodiment, the longitudinal joints of the existing shield tunnel are regarded as Timoshenko beams based on the Winkler foundation model (TBWM). Figure 8 The calculation model of TBWM is shown. The results are obtained by using the bending stiffness EI and the shear stiffness G of the segment links, as well as the reduced stiffness of the longitudinal joints.

[0071] The governing differential equation of TBWM is expressed as:

[0072]

[0073] Where: w(x) represents the deflection of the neutral axis of the beam; k represents the foundation reaction coefficient; q(x) represents the additional pressure acting on the beam;

[0074] The bending moment and shear force of the segment can be obtained by formula (13):

[0075]

[0076] Where M(x) is the function representing the moment; Q(x) is the function representing the shear force;

[0077] In order to express the reduced stiffness of the longitudinal joint, the ratio of the shear stiffness (bending stiffness) of the joint to the shear stiffness (bending stiffness) of the link is named the shear stiffness (bending stiffness) reduction coefficient α (β). The segment link means that each ring of the tunnel is called a segment link, and the shear stiffness and bending stiffness of the longitudinal joint are αGA and βE1 respectively.

[0078] The internal force of the longitudinal joint is:

[0079]

[0080] Where: M j (x j ) represents the bending moment of the jth longitudinal joint; β represents the bending stiffness reduction factor; Q j (x j ) represents the shear force of the jth longitudinal joint; α represents the shear stiffness reduction coefficient;

[0081] When α=1 and β=1, there are no longitudinal joints on the shield tunnel; the shear stiffness and bending stiffness of the longitudinal joints are evenly distributed along the existing tunnel; the shield tunnel is regarded as a continuous Timoshenko beam, and the longitudinal joints are not considered. j (x j )=M(x j ), Q j (x j )=Q(x j ). Among them, M(x j ) represents the bending moment when the longitudinal joint is not considered; Q(x j ) represents the shear force without considering the longitudinal joint;

[0082] When α = 0 and β = 0, the longitudinal joint is regarded as a hinge point; the bending stiffness and shear stiffness of the longitudinal joint are both zero. j The longitudinal joint bending moment M j (x j ) is equal to the internal force M(x j ) minus the bending moment M reduced by shear misalignment e (x j ), longitudinal joint shear force Q j (x j ) is equal to the internal force Q(x j ) minus the internal force Q reduced by the bending rotation e (x j ),

[0083] The shear misalignment virtual distributed pressure e1(x) and the bending rotation virtual distributed pressure e2(x) are applied at the longitudinal joint to obtain the bending moment M reduced by the shear misalignment. e (x j ) and the shear force Q reduced by the bending rotation e (x j )as follows:

[0084]

[0085] Substituting equation (15) into equations (13) and (14), Me(xj) and Qe(xj) can be written as:

[0086]

[0087] According to formula (6) and formula (10), we can get

[0088]

[0089] Substituting formula (17) into formula (16), we get

[0090]

[0091] Where: △θ j represents the relative rotation angle generated at the j-th bolt longitudinal joint of the shield tunnel;

[0092] △δ j represents the relative displacement generated at the jth bolt longitudinal joint of the shield tunnel;

[0093] Substituting formula (18) into formula (7) and formula (11), we get

[0094]

[0095] Where: e1(x j ) is the virtual distributed pressure of the shear misalignment of the jth longitudinal joint; e2(x j ) is the virtual distributed pressure of the bending rotation of the jth longitudinal joint;

[0096] Using the finite difference method, the shield tunnel is divided into n+5 units, and the length of each unit is l=2h.

[0097] According to formula (3) and formula (4), the shear misalignment virtual distributed pressure e1(x) and the bending rotation virtual distributed pressure e2(x) are substituted into formula (12), and we get

[0098]

[0099] Since e1(x) and e2(x) are x=x j is a constant at . Therefore, the second-order derivatives of e1(x) and e2(x) are both zero.

[0100] Simplifying formula (20), we get:

[0101]

[0102] Formula (21) is expressed in matrix-vector form as follows:

[0103]

[0104] Where: [M1] is the displacement stiffness matrix of the tunnel when the foundation effect is not considered; [M2] is the displacement stiffness matrix when the foundation shear stiffness is considered; [M3] is the displacement stiffness matrix when the foundation bending stiffness is considered; [E 11 ] is the modified stiffness matrix caused by the virtual distributed pressure of shear misalignment; [E 21 ] is the modified stiffness matrix caused by the virtual distributed pressure of bending rotation; [E 12 ] is the modified stiffness matrix caused by the virtual distributed pressure of shear misalignment when considering the foundation bending stiffness; [E 22 ] is the modified stiffness matrix caused by the virtual distributed pressure of bending rotation when considering the bending stiffness of the foundation; {w} is the displacement vector of the existing tunnel; {Q1} is the applied additional stress vector; {Q2} is the modified additional stress vector generated by the virtual distributed pressure of shear displacement; {Q3} is the modified additional stress vector generated by the connection of adjacent joints under the action of shear force; {Q4} is the supplementary vector; [P1] is the stress matrix caused by {Q1}; [P2] is the stress matrix caused by {Q3}; [QE1] is the modified stiffness matrix of additional stress caused by virtual distributed pressure of shear displacement; [QE2] is the modified stiffness matrix of additional stress caused by virtual distributed pressure of bending rotation; where:

[0105]

[0106] Among them, n is a variable representing the dimension of the matrix;

[0107]

[0108] in,

[0109]

[0110]

[0111]

[0112]

[0113] Among them, w n Represents the variable at the nth microelement;

[0114]

[0115] Among them, q n represents the additional pressure at the nth microelement;

[0116]

[0117]

[0118]

[0119]

[0120] The discontinuous deflection of the existing shield tunnel, i.e., the displacement vector {w}, is solved by equation (20).

[0121] According to formulas (23) and (24), the discontinuous bending moment and shear force of the existing shield tunnel can be obtained respectively:

[0122]

[0123]

[0124] According to formula (25), the relative rotation angle and relative displacement of the longitudinal joint are obtained:

[0125]

[0126] In this embodiment, if there are multiple longitudinal joints in the existing structure, [D11], [D12], [D13], [D21], and [D22] describe the stiffness matrix of the longitudinal joints. The diagonals of matrices [E11], [E12], [QE1], [E21], [E22], and [QE2] contain multiple [D11], [D12], [D13], [D21], and [D22] matrices, respectively.

[0127] According to the relative rotation angle and relative displacement of the longitudinal joint, the deformation condition generated at the j-th bolt longitudinal joint of the shield tunnel can be obtained.

[0128] The shield tunnel bolt joint discontinuous deformation calculation method of this embodiment can simulate the opening and dislocation of the joints and predict the discontinuous deformation and internal force of the shield tunnel. At the same time, the longitudinal continuous model fully considers the weak joints through the shear stiffness and bending stiffness of the longitudinal joints, and can accurately calculate the deformation of the shield tunnel.

[0129] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating discontinuous deformation of bolt joints in shield tunnels, characterized in that: The steps include: S1: Establishing the Dirac Delta function of the longitudinal joint of the shield tunnel bolt, and respectively calculating the first-order derivative and the second-order derivative of the Dirac Delta function, so as to obtain the shear dislocation calculation model of the longitudinal joint of the shield tunnel bolt and the bending rotation calculation model of the shield tunnel bolt joint; S2: According to the shear dislocation calculation model of the shield tunnel bolt longitudinal joint, the shear dislocation virtual distributed pressure when the shield tunnel bolt longitudinal joint is shear dislocated is calculated: S3: Calculate the bending and rotation virtual distributed pressure when the shield tunnel bolt longitudinal joint is bent and rotated according to the shield tunnel bolt joint bending and rotation calculation model; S4: According to the intelligent monitoring system set at the longitudinal joint of the shield tunnel bolt, the additional pressure acting on the longitudinal joint of the shield tunnel bolt is obtained; S5: establishing a control differential equation at the active joint of the shield tunnel bolt, and calculating the discontinuous deformation parameters of the shield tunnel bolt joint according to the additional pressure, the shear dislocation virtual distributed pressure and the bending rotation virtual distributed pressure, that is, the relative displacement generated at the longitudinal joint of the shield tunnel bolt and the relative rotation angle generated at the longitudinal joint of the shield tunnel bolt; The relative rotation angle and dislocation of the longitudinal joint are obtained as follows: Where: △θ j represents the relative rotation angle generated at the jth bolt longitudinal joint of the shield tunnel; △δ j represents the relative displacement of the jth bolt longitudinal joint of the shield tunnel; β represents the bending stiffness reduction factor; α represents the shear stiffness reduction factor; l represents the length of each unit of the shield tunnel; x j represents the coordinates of the jth longitudinal joint; x represents the variable of the longitudinal joint position; j represents the number of the longitudinal joint; w(x j ) represents the deflection of the neutral axis of the beam at the jth longitudinal joint; k represents the foundation reaction coefficient; q(x j ) represents the additional pressure acting on the beam at the jth longitudinal joint; G represents the shear modulus; A represents the cross-sectional area; GA is the shear stiffness; E represents the elastic modulus; I represents the moment of inertia; and EI represents the bending stiffness.

2. A method for calculating discontinuous deformation of bolt joints in a shield tunnel according to claim 1, characterized in that: The method for establishing the Dirac Delta function of the longitudinal joint of the shield tunnel bolt in S1 is as follows: Establish a step function for the active part of the bolt joint in the shield tunnel: Where: x j represents the coordinates of the jth longitudinal joint; x represents the variable of the longitudinal joint position; j represents the number of the longitudinal joint; The Dirac Delta function is defined as a step function H(xx j ) in x j The derivative at , so: Where: h (xx j ) represents the Dirac Delta function of the longitudinal joint of the shield tunnel bolt; h is the intermediate parameter; When h→0, δ h (xx j )=δ(xx j ) Therefore, the calculation model of shear dislocation of the longitudinal joint of the shield tunnel bolt is obtained as follows: Among them, △x represents the difference between the coordinates of the i-th longitudinal joint and the longitudinal joint position variable; the calculation model of the bending rotation of the shield tunnel bolt joint is obtained as follows:

3. A method for calculating discontinuous deformation of bolt joints in a shield tunnel according to claim 2, characterized in that: In S2, the shear dislocation virtual distribution pressure is calculated as follows: Calculate the shear force Q0 of equal magnitude and opposite direction caused by the virtual distribution pressure of shear dislocation; Assume e1(x) = C1δ'(x-xj); then Where: F0 represents the concentrated force acting on the segment link, which is equal to the shear force Q0 when shear dislocation occurs in the longitudinal joint of the shield tunnel bolt; C1 represents the proportional constant of the response shear dislocation mode; Where: Δδ represents the relative displacement generated at the longitudinal joint of the shield tunnel bolt; G represents the shear modulus; A represents the cross-sectional area; GA is the shear stiffness; Therefore, the virtual distribution pressure e1(x) of shear dislocation is obtained as follows: e1(x)=GA(△δ)δ′(x-x j ) (7)。 4. A method for calculating discontinuous deformation of bolt joints in a shield tunnel according to claim 3, characterized in that: In S3, the bending rotation virtual distribution pressure is calculated as follows: Calculate a pair of moments M0 caused by the virtual distributed pressure of bending rotation: Assume that the virtual distributed pressure of bending rotation e2(x)=C2δ”(xx j ),but Where: C2 represents the proportional constant of the reaction bending mode; Where: Δθ represents the relative rotation angle generated at the longitudinal joint of the shield tunnel bolt; E represents the elastic modulus; I represents the moment of inertia; EI represents the bending stiffness; Therefore, the bending rotation virtual distribution pressure e2(x) is obtained as: e2(x)=EI△θδ″(x-x j ) (11)。 5. A method for calculating discontinuous deformation of bolt joints in a shield tunnel according to claim 4, characterized in that: In S5, the relative displacement and the relative rotation angle generated at the longitudinal joint of the shield tunnel bolts are calculated as follows: The control differential equation of the bolt movable joint of the shield tunnel is established as: Where: w(x) represents the deflection of the neutral axis of the beam; k represents the foundation reaction coefficient; q(x) represents the additional pressure acting on the beam; The bending moment and shear force of the segment are obtained as follows: Where M(x) is the function representing the moment; Q(x) is the function representing the shear force; The internal force of the longitudinal joint is: Where: M j (x j ) represents the bending moment of the jth longitudinal joint; β represents the bending stiffness reduction factor; Q j (x j ) represents the shear force of the jth longitudinal joint; α represents the shear stiffness reduction coefficient; Obtain the bending moment M reduced by shear misalignment e (x j ) and the shear force Q reduced by the bending rotation e (x j )as follows: Substituting equation (15) into equations (13) and (14), Me(xj) and Qe(xj) can be written as: According to formula (6) and formula (10), we can get Substituting formula (17) into formula (16), we get Where: △θ j represents the relative rotation angle generated at the j-th bolt longitudinal joint of the shield tunnel; △δ j represents the relative displacement generated at the jth bolt longitudinal joint of the shield tunnel; Substituting formula (18) into formula (7) and formula (11), we get Where: e1(x j ) is the virtual distributed pressure of the shear misalignment of the jth longitudinal joint; e2(x j ) is the virtual distributed pressure of the bending rotation of the jth longitudinal joint; According to formula (3) and formula (4), the shear misalignment virtual distributed pressure e1(x) and the bending rotation virtual distributed pressure e2(x) are substituted into formula (12), and we get Simplifying formula (20), we get: Formula (21) is expressed in matrix-vector form as follows: Where: [M1] is the displacement stiffness matrix of the tunnel when the foundation effect is not considered; [M2] is the displacement stiffness matrix when the foundation shear stiffness is considered; [M3] is the displacement stiffness matrix when the foundation bending stiffness is considered; [E 11 ] is the modified stiffness matrix caused by the virtual distributed pressure of shear misalignment; [E 21 ] is the modified stiffness matrix caused by the virtual distributed pressure of bending rotation; [E 12 ] is the modified stiffness matrix caused by the virtual distributed pressure of shear misalignment when considering the foundation bending stiffness; [E 22 ] is the modified stiffness matrix caused by the virtual distributed pressure of bending rotation when considering the bending stiffness of the foundation; {w} is the displacement vector of the existing tunnel; {Q1} is the applied additional stress vector; {Q2} is the modified additional stress vector generated by the virtual distributed pressure of shear dislocation; {Q3} is the modified additional stress vector generated by the connection of adjacent joints under the action of shear force; {Q4} is the supplementary vector; [P1] is the stress matrix caused by {Q1}; [P2] is the stress matrix caused by {Q3}; [QE1] is the modified stiffness matrix of the additional stress caused by the virtual distributed pressure of shear dislocation; [QE2] is the modified stiffness matrix of the additional stress caused by the virtual distributed pressure of bending rotation; So we get: The relative rotation angle and dislocation of the longitudinal joint are obtained as follows:

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