Rectangular shield tunnel longitudinal torsional rigidity effective rate calculation method and system and storage medium

Abstract

The invention discloses a method and system for calculating the longitudinal torsional rigidity effective rate of a rectangular shield tunnel under combined acting force and a storage medium. The method comprises the following steps that S1, the bending-pressing-twisting combined acting force on a calculation unit of the rectangular shield tunnel is obtained according to the stress condition of the rectangular shield tunnel; s2, the stress state of the shield lining structure is judged according to the relation between the bending moment and the axial force, and the stress state of the structure is divided into two different conditions according to the position of the neutral axis; s3, for different stress states, according to deformation coordination conditions and mechanical equilibrium conditions, calculating the distance between a neutral axle on the section and the center of the section; s4, according to the torque balance condition and further according to the two different conditions, the position of the torsion center and the anti-friction torque generated by the concrete in the pressed area are calculated; and S5, calculating a joint torsion angle and equivalent torsional rigidity, and further calculating the effective rate of the torsional rigidity. According to the method, the longitudinal torsional rigidity effective rate of the rectangular shield tunnel under the bending, pressing and twisting combined acting force can be quickly and accurately obtained, and a basis is provided for structural safety analysis of the rectangular shield tunnel.

Description

Technical Field

[0001] The invention belongs to the technical field of underground engineering, and in particular relates to an effective calculation method, system and storage medium for the longitudinal torsional stiffness of a rectangular shield tunnel. Background Art

[0002] Under external loads, tunnels are prone to longitudinal uneven deformation, which in turn leads to uneven settlement, joint opening, water leakage and other defects. For rectangular shield tunnels, due to the difference in force mode from circular tunnels, they are more likely to produce longitudinal uneven torsional deformation under external uneven loads. Therefore, it is necessary to study the effective longitudinal torsional stiffness of rectangular shield tunnels.

[0003] During the construction and operation of rectangular shield tunnels, they are often faced with various uneven loads such as excavation of surrounding soil, ground eccentric loading, and ground fissures, which in turn lead to uneven torsion. Excessive uneven torsion will cause large stress and deformation in the segments and bolts, and cause annular seam dislocation and track tilt, seriously affecting tunnel safety. However, the current engineering community still lacks awareness and attention to the problem of tunnel torsion. Existing research mainly focuses on the bending and shear performance of shield tunnels, and rarely involves the torsion performance of shield tunnels. For rectangular shield tunnels, although the torsion performance of the tunnel is an important factor in ensuring the safety of the rectangular tunnel structure, there is currently no research on the longitudinal torsion performance of rectangular shield tunnels. Summary of the invention

[0004] In view of this, an object of the present invention is to provide a method, system and storage medium for effectively calculating the longitudinal torsional stiffness of a rectangular shield tunnel, so as to solve the deficiencies in the prior art.

[0005] In order to achieve the above object, the present invention is achieved through the following technical solutions:

[0006] On the one hand, a method for calculating the effective rate of longitudinal torsional stiffness of a rectangular shield tunnel is provided, wherein the rectangular shield tunnel is composed of a lining ring and an annular joint, and the method comprises the following steps:

[0007] S1. Take two adjacent half-segment rings and annular seams of a rectangular shield tunnel as a calculation unit, and obtain the bending-compression-torsion combined force MNT on a calculation unit according to the stress condition of the rectangular shield tunnel;

[0008] S2. According to the relationship between the bending moment M and the axial force N, the stress state of the tunnel structure is determined, and the stress state of the tunnel structure is divided into two different situations according to the position of the neutral axis: when the neutral axis is inside the cross section, the annular joint is open, and one end of the concrete at the annular joint is under compression and the other end is under tension; when the neutral axis is outside the cross section, the annular joint is closed, and the concrete at the annular joint is under compression;

[0009] S3. According to the different stress states, the distance c between the neutral axis on the cross section and the cross section center is calculated according to the deformation coordination condition and the mechanical equilibrium condition;

[0010] S4. According to the torque balance condition, the position a of the torsion center and the anti-friction torque T generated by the concrete in the compression zone are further calculated according to the two different situations. c ;

[0011] S5. Calculate the joint torsion angle and equivalent torsional rigidity (GI) eq , and further calculate the effective torsional stiffness ξ.

[0012] As described in the effective calculation method of the longitudinal torsional stiffness of a rectangular shield tunnel, the determination criteria of the bending moment and the axial force are:

[0013] N lim =M*A s *h / I s ;

[0014] Where N lim is the limit axial force that closes the annular gap under bending moment M, A s is the cross-sectional area of ​​the segment, h is half of the segment height, I s is the segment moment of inertia. For a rectangular shield tunnel, I s =4h 2 t(b+h / 3), b is half of the segment width, t is the segment thickness;

[0015] When N<N lim When N≥N, the neutral axis is in the cross section, the annular joint is open, and the concrete at the annular joint is under compression at one end and tension at the other end; lim When , the neutral axis is outside the cross section, the annular joint is closed, and the concrete in the annular joint is under pressure.

[0016] As described in the effective calculation method of the longitudinal torsional stiffness of a rectangular shield tunnel, when the neutral axis is within the cross section, the deformation coordination condition is:

[0017]

[0018]

[0019] In the formula, ε c and ε t are the compressive strain and tensile strain at the top and bottom of the segment, respectively, l s is the segment width, δ j is the width of the segment opening, α is the rotation angle within the annular gap, and c is the distance between the neutral axis and the center of the section;

[0020] The mechanical equilibrium condition is:

[0021]

[0022]

[0023]

[0024] In the formula, E s is the elastic modulus of concrete, k rh is the bolt line stiffness, E b is the elastic modulus of the bolt.

[0025] As described in the effective calculation method of the longitudinal torsional stiffness of a rectangular shield tunnel, when the neutral axis is outside the cross section, the deformation coordination condition is:

[0026]

[0027] The mechanical equilibrium condition is:

[0028] are the maximum and minimum compressive strains of concrete at the joint.

[0029]

[0030] As described above, the effective calculation method of the longitudinal torsional stiffness of a rectangular shield tunnel, when the neutral axis is within the cross section, the distance a between the torsion center and the cross section center can be obtained by combining the following formulas:

[0031] F bx +F cx =0

[0032]

[0033]

[0034] T=T c +T b

[0035]

[0036]

[0037]

[0038] In the formula, F bx is the component of the bolt shear force in the x direction, F cx is the component of concrete shear force in the x direction, is the joint torsion angle, T c is the friction torque generated by the concrete compressive stress, T bis the torque generated by the bolt, K t is the average shear stiffness of the bolts in the annular joint.

[0039] As described above, the effective calculation method of the longitudinal torsional stiffness of a rectangular shield tunnel, when the neutral axis is outside the cross section, the distance a between the torsion center and the cross section center can be obtained by combining the following formulas:

[0040] F bx +F cx =0

[0041]

[0042]

[0043] T=T c +T b

[0044]

[0045]

[0046]

[0047] In the formula, σ c1 and σ c2 are the maximum and minimum compressive stresses of concrete at the joints, respectively.

[0048] As described in the effective calculation method of the longitudinal torsional stiffness of a rectangular shield tunnel, when the neutral axis is within the cross section, the friction torque T generated by the concrete in the compression zone is c satisfy:

[0049]

[0050] As described in the effective calculation method of the longitudinal torsional stiffness of a rectangular shield tunnel, when the neutral axis is outside the cross section, the friction torque T generated by the concrete in the compression zone is c satisfy:

[0051]

[0052] As described above, the effective calculation method of the longitudinal torsional stiffness of a rectangular shield tunnel is as follows: c When , the torsional stiffness efficiency ξ satisfies:

[0053]

[0054] When T≤T c When , the torsional stiffness effective rate ξ is 1.

[0055] On the other hand, the present invention provides a system for calculating the effectiveness of the longitudinal torsional stiffness of a rectangular shield tunnel, which includes a computer-readable storage medium and a processor, wherein the computer-readable storage medium is used to store executable instructions, and the processor is used to read the executable instructions stored in the computer-readable storage medium to execute any one of the methods for calculating the effectiveness of the longitudinal torsional stiffness of a rectangular shield tunnel.

[0056] In yet another aspect, the present invention provides a computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, implements any one of the methods for calculating the effective longitudinal torsional stiffness of a rectangular shield tunnel.

[0057] The beneficial effects of the technical solution of the present invention are:

[0058] 1. The effective calculation method of the longitudinal torsional stiffness of a rectangular shield tunnel of the present invention considers the bending-compression-torsion combined force MNT on a calculation unit of the rectangular shield tunnel, judges the deformation state of the annular seam of the rectangular shield according to its specific stress conditions, and calculates the two states of the annular seam opening and the annular seam closing respectively, calculates the distance c of the neutral axis from the center of the cross section on the cross section according to the deformation coordination condition and the mechanical balance condition, and further calculates the position a of the torsion center and the anti-friction torque T generated by the concrete in the compression zone according to the torque balance condition c , and finally the effective rate ξ of the longitudinal torsional stiffness of the rectangular shield tunnel is obtained; the method of the present invention realizes the calculation of the effective rate of the longitudinal torsional stiffness of the rectangular shield tunnel, which can better characterize the torsional performance of the rectangular shield tunnel and provide a basis for the torsional characteristics of the rectangular shield tunnel during construction and operation;

[0059] 2. The present invention provides a method for judging the stress state of a rectangular shield tunnel. According to the relationship between the bending moment M and the axial force N, the opening and closing states of the annular joint of the rectangular shield tunnel are judged. The friction torque T generated by the external torsional load T and the concrete in the compression zone is c The relationship between the ring seam and the deformation of the rectangular shield tunnel can be used to determine whether the annular joint of the rectangular shield tunnel has been twisted, which is convenient for the project to quickly determine the stress and deformation characteristics of the rectangular shield tunnel.

[0060] In summary, the present invention can quickly and accurately obtain the effective longitudinal torsional stiffness of a rectangular shield tunnel under the combined forces of bending, compression and torsion, and provide a basis for the structural safety analysis of the rectangular shield tunnel. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] To further illustrate the above-mentioned objectives, structural features and effects of the present invention, the present invention will be described in detail below with reference to the accompanying drawings.

[0062] Figure 1 A schematic diagram of an effective method for calculating the longitudinal torsional stiffness of a rectangular shield tunnel in a preferred embodiment of the present invention;

[0063] Figure 2 This is a flow chart of the effective calculation method of the longitudinal torsional stiffness of a rectangular shield tunnel in a preferred embodiment of the present invention;

[0064] Figure 3a This is a schematic diagram of the longitudinal torsion resistance of a tunnel according to a preferred embodiment of the present invention;

[0065] Figure 3b A schematic diagram of a torsion calculation unit in a preferred embodiment of the present invention;

[0066] Figure 3c This is a simplified schematic diagram of bolt deformation in a preferred embodiment of the present invention;

[0067] Figure 4 This is a torsional force distribution diagram of the joint in a preferred embodiment of the present invention;

[0068] Figure 5 This is a diagram showing the stress and deformation distribution in the annular seam under the combined action of bending, compression and torsion in a preferred embodiment of the present invention (the neutral axis is in the cross section);

[0069] Figure 6 This is a diagram showing the stress and deformation distribution in the annular seam under the combined action of bending, compression and torsion in a preferred embodiment of the present invention (the neutral axis is outside the cross section);

[0070] Figure 7 This is a schematic diagram of the cross-sectional dimensions of a rectangular shield in a preferred embodiment of the present invention;

[0071] Figure 8 This is a graph showing the change in the longitudinal torsional stiffness effectiveness of a rectangular shield as the axial force changes in a preferred embodiment of the present invention;

[0072] Fig. 9 This is a graph showing the change in the effective longitudinal torsional stiffness of a rectangular shield as the bending moment changes in a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0073] The terms "invention", "present invention" and "the present invention" used in this specification are intended to refer broadly to all subject matter of this specification and any patent claims below. Statements containing these terms should not be understood to limit the subject matter described herein or to limit the meaning or scope of any patent claim below. In addition, this specification does not attempt to describe or limit the subject matter covered by any claim of any specific component, paragraph, statement or figure of this application. The subject matter should be understood with reference to the entire specification, all drawings and any claims below. The present invention may have other embodiments and be practiced or implemented in other ways. Moreover, it should be understood that the words and terms used herein are for illustrative purposes and should not be considered as limiting.

[0074] The details of the present invention will now be discussed with reference to the accompanying drawings which illustrate the present invention by way of example only. In the accompanying drawings, similar features or components may be marked with the same reference numerals.

[0075] The use of "including," "having," and "comprising" and variations thereof herein is meant to encompass the items listed thereafter and their equivalents and additional items. Although reference may be made to directions such as above, below, upward, downward, rearward, bottom, top, front, rear, etc., in describing the drawings, for convenience, reference is made relative to the drawings. These directions are not intended to literally accept or limit the present invention in any form. In addition, terms such as "first," "second," "third," etc., are used herein for illustrative purposes and are not intended to indicate or imply importance or significance.

[0076] The main purpose of the present invention is to analyze the effective longitudinal torsional stiffness of a rectangular shield tunnel under the combined action of bending, compression and torsion, so as to provide a basis for the torsional performance analysis of the rectangular shield tunnel in actual engineering.

[0077] See also Figure 1 , Figure 2 As shown, in a preferred embodiment, the method for calculating the effective bending stiffness of a rectangular shield tunnel of the present invention mainly includes:

[0078] S1. Take two adjacent half-segment rings and annular seams of a rectangular shield tunnel as a calculation unit, and obtain the bending-compression-torsion combined force MNT on a calculation unit according to the stress condition or monitoring results of the rectangular shield tunnel. The deformation mode and stress distribution of the rectangular shield tunnel structure are as follows: Figure 3a , Figure 3b , Figure 3c and Figure 4 shown.

[0079] S2. According to the relationship between bending moment M and axial force N, the stress state of the tunnel structure is determined, and the stress state of the tunnel structure is divided into two different situations. When the neutral axis is inside the cross section, the annular joint is open, and one end of the concrete at the annular joint is under compression and the other end is under tension; when the neutral axis is outside the cross section, the annular joint is closed, and the concrete at the annular joint is under compression. The distribution diagram of the stress and deformation of the annular joint when the neutral axis is inside the cross section is shown in Figure 5 As shown in the figure, the stress and deformation distribution diagram of the annular crack outside the cross section of the neutral axis is as follows Figure 6 shown.

[0080] S3. According to the different stress conditions of the tunnel, the deformation coordination conditions and mechanical equilibrium conditions in this case are listed, and the distance c from the neutral axis on the section to the center of the section is calculated.

[0081] S4. According to the torque balance condition, the position a of the torsion center and the anti-friction torque T generated by the concrete in the compression zone are further calculated according to the two different situations. c.

[0082] S5. Calculate the joint torsion angle and equivalent torsional rigidity (GI) eq , and further calculate the effective torsional stiffness ξ.

[0083] Specifically, the bending moment M, axial force N and torque T on the calculation unit obtained in S1, like the cross-sectional design parameters and joint design parameters of the rectangular shield tunnel, are the initial conditions of this calculation method.

[0084] Specifically, in S2, the limit axial force N required to close the annular gap under the bending moment M is first calculated: lim :

[0085] N lim =M*A s *h / I s ;

[0086] Where N lim is the limit axial force that closes the annular gap under bending moment M, A s is the cross-sectional area of ​​the segment, h is half of the segment height, I s is the segment moment of inertia. For a rectangular shield tunnel, I s =4h 2 t(b+h / 3), b is half of the segment width, and t is the segment thickness.

[0087] According to N and N lim The relationship between N and N can be used to determine the stress state of the tunnel. lim When N≥N, the neutral axis is in the cross section, the annular joint is open, and the concrete at the annular joint is under compression at one end and tension at the other end; lim When , the neutral axis is outside the cross section, the annular joint is closed, and the concrete in the annular joint is under pressure.

[0088] Specifically, in S3-S4, according to the different stress states of the tunnel, different deformation coordination conditions and mechanical equilibrium conditions are listed to calculate the position c of the neutral axis, the position a of the torsion center, and the anti-friction torque T generated by the concrete in the compression zone. c .

[0089] When the neutral axis is within the cross section, the deformation coordination condition and mechanical equilibrium condition in S3 are:

[0090]

[0091]

[0092] In the formula, ε c and ε t are the compressive strain and tensile strain at the top and bottom of the segment, respectively, l s is the segment width, δj is the width of the segment opening, α is the rotation angle within the annular gap, c is the distance between the neutral axis and the center of the section, E s is the elastic modulus of concrete, k rh is the bolt line stiffness, E b is the elastic modulus of the bolt.

[0093] The joint solution shows that the position c of the neutral axis satisfies:

[0094]

[0095] Where K j is the total stiffness of the bolt.

[0096] The position c of the neutral axis can be obtained by iterative solution.

[0097] The longitudinal bending stiffness effectiveness η, the annular gap angle α and the maximum compressive stress σ of the concrete at the joint can be further calculated by the following formula: c :

[0098]

[0099] Similarly, when the neutral axis is within the cross section, in S4, the distance a from the torsion center to the cross section center can be obtained by combining the following formulas:

[0100]

[0101] In the formula, F bx is the component of the bolt shear force in the x direction, F cx is the component of concrete shear force in the x direction, is the joint torsion angle, T c is the friction torque generated by the concrete compressive stress, T b is the torque generated by the bolt, K t is the average shear stiffness of the annular joint, which can be calculated by the following formula:

[0102]

[0103] Where n is the total number of bolts on the section, K b is the equivalent shear stiffness, K b =κ b G b A b / (λl b ), κ b is the shear correction factor of the bolt, A b is the cross-sectional area of ​​the bolt, G b is the shear stiffness modulus of the bolt, l b is the bolt length, and λ is the bolt effective shear length coefficient.

[0104] The combined solution shows that the position a of the torsion center of the cross section satisfies:

[0105]

[0106] The anti-friction torque T generated by the concrete in the compression zone can then be calculated c :

[0107]

[0108] When the neutral axis is within the cross section, the deformation coordination condition and mechanical equilibrium condition in S3 are:

[0109]

[0110]

[0111] In the formula, ε c1 and ε c2 are the maximum compressive strain and minimum compressive strain of concrete at the joint, respectively. c1 and σ c2 are the maximum and minimum compressive stresses of concrete at the joints, respectively.

[0112] The joint solution shows that the position c of the neutral axis satisfies:

[0113]

[0114] The annular gap angle α of the rectangular shield and the maximum compressive strain ε of the concrete at the joint can be further calculated by the following formula: c1 and the minimum compressive strain ε c2 and the maximum compressive stress σ c1 and the minimum compressive stress σ c2 :

[0115]

[0116] Similarly, when the neutral axis is outside the cross section, in S4, the distance a from the torsion center to the cross section center can be obtained by combining the following formulas:

[0117]

[0118] The combined solution shows that the position a of the torsion center of the cross section satisfies:

[0119]

[0120] The anti-friction torque T generated by the concrete in the compression zone can then be calculated c :

[0121]

[0122] Specifically, in S5, when the external torsion load T>T c When , the effective torsional stiffness ξ can be calculated by the following formula:

[0123]

[0124] Where θ s is the relative torsion angle of the segment, (GI) eq is the equivalent torsional stiffness, (GI) s is the torsional stiffness of the tunnel segment.

[0125] In S5, when T≤T c When , the torsional stiffness effective rate ξ is 1.

[0126] In order to further explain the method of the present invention, in the embodiment of the present invention, a rectangular shield tunnel is used as an analysis object for specific analysis. Figure 7 As shown in the figure, the rectangular shield tunnel segments are made of C50 concrete, and the concrete elastic modulus E s Take 34500MPa, bolt length l b Take 0.6m, bolt diameter d take 30mm, bolt elastic modulus E b Take 200GPa, the bolt shear modulus G b Take 80GPa, the bolt effective shear length coefficient λ is 0.33, and the friction coefficient between concrete is f c Take 0.2, segment width l s Take 1.5m. Figure 8 The medium torque T is 2MN·m, the bending moment M is 2MN·m, and the axial force N changes from 0 to 3.2MN, that is, the compression-torque ratio changes from 0 to 1.6. Fig. 9 The medium torque T is 2MN·m, the axial force N is 2MN, and the bending moment M changes from 0 to 18MN·m, that is, the bending-torsion ratio changes from 0 to 9.

[0127] Figure 8 The figure shows the relationship between the effective torsional stiffness and the compression-torsion ratio. Figure 8 It can be seen that in the initial state, the equivalent torsional stiffness is about 0.238, and then increases with the increase of axial pressure; when the compression-torsion ratio N / T increases to 1.37m -1 When , the effective equivalent torsional stiffness is 1, and the annular seam no longer undergoes torsion. Fig. 9 The figure shows the relationship between the effective torsional stiffness and the bending-torsion ratio. Fig. 9 It can be seen that as the bending-torsion ratio increases from 0 to 9, the equivalent torsional stiffness effectively first decreases from 0.173 to 0.169, and then gradually increases to 1. When the bending-torsion ratio M / T exceeds 7.6, there is no torsion in the annular joint. The increase in the bending-torsion ratio will increase the pressure between the annular joints of the tunnel, thereby improving the torsional performance of the tunnel. Figure 8and Fig. 9 The analysis results show that the method of the present invention can effectively analyze the longitudinal torsional stiffness of a rectangular shield tunnel under the combined forces of bending, compression and torsion.

[0128] The present invention also provides a system for calculating the effectiveness of the longitudinal torsional stiffness of a rectangular shield tunnel, comprising a computer-readable storage medium and a processor, wherein the computer-readable storage medium is used to store executable instructions, and the processor is used to read the executable instructions stored in the computer-readable storage medium to execute the method for calculating the effectiveness of the longitudinal torsional stiffness of a rectangular shield tunnel in the above-mentioned embodiment.

[0129] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method for calculating the effective longitudinal torsional stiffness of a rectangular shield tunnel as in the above-mentioned embodiment.

[0130] The effective calculation method of the longitudinal torsional stiffness of a rectangular shield of the present invention considers the bending-compression-torsion combined force MNT on a calculation unit of a rectangular shield tunnel, judges the deformation state of the annular seam of the rectangular shield according to its specific stress conditions, and calculates the two states of the annular seam opening and the annular seam closing respectively, calculates the distance c of the neutral axis on the cross section from the cross section center according to the deformation coordination condition and the mechanical balance condition, and further calculates the position a of the torsion center and the anti-friction torque T generated by the concrete in the compression zone according to the torque balance condition. c , and finally the effective value ξ of the longitudinal torsional stiffness of the rectangular shield tunnel is obtained. The method of the present invention realizes the calculation of the effective value of the longitudinal torsional stiffness of the rectangular shield tunnel, which can better characterize the torsional performance of the rectangular shield tunnel and provide a basis for the torsional characteristics of the rectangular shield tunnel during construction and operation.

[0131] In the embodiment of the present invention, for the above-mentioned S2-S5, Matlab software is used to independently write a program to implement it. When the method of the present invention is actually applied, it only needs to obtain the corresponding parameters, including the cross-sectional design parameters of the rectangular shield tunnel, the joint design parameters, and the bending moment, pressure and torque acting on the calculation unit, and run the corresponding code to quickly obtain the effective longitudinal torsional stiffness of the calculation unit under the current working condition, without relying on any simulation platform. The method is simple and efficient and has strong versatility. The present invention can be applied to the design and operation of rectangular shield tunnels, and the results obtained can assist engineers in quickly judging the torsional performance of rectangular shield tunnels.

[0132] The above are only preferred embodiments of the present invention, and are not intended to limit the implementation methods and protection scope of the present invention. Those skilled in the art should be aware that all solutions obtained by equivalent substitutions and obvious changes made using the description and illustrations of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for calculating the effective longitudinal torsional stiffness of a rectangular shield tunnel, wherein the rectangular shield tunnel is composed of a lining ring and an annular joint, characterized in that: The following steps are involved: S1. Take two adjacent half-segment rings and annular seams of a rectangular shield tunnel as a calculation unit, and obtain the bending-compression-torsion combined force MNT on a calculation unit according to the stress condition of the rectangular shield tunnel; S2. According to the relationship between the bending moment M and the axial force N, the stress state of the tunnel structure is determined, and the stress state of the tunnel structure is divided into two different situations according to the position of the neutral axis: when the neutral axis is inside the cross section, the annular joint is open, and one end of the concrete at the annular joint is under compression and the other end is under tension; when the neutral axis is outside the cross section, the annular joint is closed, and the concrete at the annular joint is under compression; S3. According to the different stress states, the distance c between the neutral axis on the cross section and the cross section center is calculated according to the deformation coordination condition and the mechanical equilibrium condition; S4. According to the torque balance condition, the position a of the torsion center and the anti-friction torque T generated by the concrete in the compression zone are further calculated according to the two different situations. c ; S5. Calculate the joint torsion angle and equivalent torsional rigidity (GI) eq , and further calculate the effective torsional stiffness ξ.

2. The method for calculating the effective rate of longitudinal torsional stiffness of a rectangular shield tunnel according to claim 1 is characterized in that: The criteria for determining the bending moment and axial force are: N lim =M*A s *h / I s ; Where N lim is the limit axial force that closes the annular gap under bending moment M, A s is the cross-sectional area of ​​the segment, h is half of the segment height, I s is the segment moment of inertia. For a rectangular shield tunnel, I s =4h 2 t(b+h / 3), b is half of the segment width, t is the segment thickness; When N<N lim When N≥N, the neutral axis is in the cross section, the annular joint is open, and the concrete at the annular joint is under compression at one end and tension at the other end; lim When , the neutral axis is outside the cross section, the annular joint is closed, and the concrete in the annular joint is under pressure.

3. The method for calculating the effective rate of longitudinal torsional stiffness of a rectangular shield tunnel according to claim 2 is characterized in that: When the neutral axis is within the cross section, the deformation coordination condition is: In the formula, ε c and ε t are the compressive strain and tensile strain at the top and bottom of the segment, respectively, l s is the segment width, δ j is the width of the segment opening, α is the rotation angle within the annular gap, and c is the distance between the neutral axis and the center of the section; The mechanical equilibrium condition is: In the formula, E s is the elastic modulus of concrete, k rh is the bolt line stiffness, E b is the elastic modulus of the bolt.

4. The method for calculating the effective rate of longitudinal torsional stiffness of a rectangular shield tunnel according to claim 2 is characterized in that: When the neutral axis is outside the cross section, the deformation coordination condition is: The mechanical equilibrium condition is: In the formula, εc1 and εc2 are the maximum and minimum compressive strains of concrete at the joints, respectively.

5. The method for calculating the effective rate of longitudinal torsional stiffness of a rectangular shield tunnel according to claim 3 is characterized in that: When the neutral axis is within the cross section, the distance a between the torsion center and the cross section center can be obtained by combining the following formulas: F bx +F cx =0 T=T c +T b In the formula, F bx is the component of the bolt shear force in the x direction, F cx is the component of concrete shear force in the x direction, is the joint torsion angle, T c is the friction torque generated by the concrete compressive stress, T b is the torque generated by the bolt, K t is the average shear stiffness of the bolts in the annular joint.

6. The method for calculating the effective rate of longitudinal torsional stiffness of a rectangular shield tunnel according to claim 4 is characterized in that: When the neutral axis is outside the cross section, the distance a between the torsion center and the cross section center can be obtained by combining the following formulas: F bx +F cx =0 T=T c +T b In the formula, σc1 and σc2 are the maximum and minimum compressive stresses of concrete at the joints, respectively.

7. The method for calculating the effective rate of longitudinal torsional stiffness of a rectangular shield tunnel according to claim 5 is characterized in that: When the neutral axis is within the cross section, the anti-friction torque T generated by the concrete in the compression zone c satisfy:

8. The method for calculating the effective rate of longitudinal torsional stiffness of a rectangular shield tunnel according to claim 6 is characterized in that: When the neutral axis is outside the cross section, the anti-friction torque T generated by the concrete in the compression zone c satisfy:

9. The method for calculating the effective rate of longitudinal torsional stiffness of a rectangular shield tunnel according to claim 7 or 8, characterized in that: When the external torsion load T>T c When , the torsional stiffness efficiency ξ satisfies: When T≤T c When , the torsional stiffness effective rate ξ is 1.

10. A rectangular shield tunnel longitudinal torsional stiffness efficiency calculation system, characterized in that: It comprises a computer-readable storage medium and a processor, wherein the computer-readable storage medium is used to store executable instructions, and the processor is used to read the executable instructions stored in the computer-readable storage medium to execute the method for calculating the effective rate of longitudinal torsional stiffness of a rectangular shield tunnel as described in any one of claims 1 to 9.

11. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the method for calculating the effective longitudinal torsional stiffness of a rectangular shield tunnel as described in any one of claims 1 to 9 is implemented.

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