A method and system for determining the longitudinal equivalent bending stiffness and deformation of a double-circle shield tunnel.

Abstract

This invention provides a method and system for determining the longitudinal equivalent bending stiffness and deformation of a double-circular shield tunnel. The double-circular shield tunnel is an underground prefabricated composite slender cylindrical structure assembled from precast segments connected by high-strength bolts during the tunneling process of a tunnel boring machine. Its cross-section is formed by the joining of two large circular arcs. Based on the design parameters of the double-circular shield tunnel cross-section, the corresponding bolt average linear stiffness, neutral axis position, and neutral axis position angle can be determined. Then, based on the position of the neutral axis, the longitudinal equivalent bending stiffness of the double-circular shield tunnel can be calculated using the corresponding formula. The beneficial effects of this invention are: it improves the reliability and accuracy of the longitudinal equivalent bending stiffness of the double-circular shield tunnel, provides assistance for the longitudinal structural design of double-circular shield tunnels, is of great significance for assessing the impact of adjacent construction on the double-circular shield tunnel, and further obtains deformation and stress indicators, providing a reference for the deformation and stress safety monitoring of double-circular shield tunnels.

Description

Technical Field

[0001] This invention relates to the field of underground construction engineering technology, and in particular to a method and system for determining the longitudinal equivalent bending stiffness and deformation of a double-circular shield tunnel. Background Technology

[0002] With the development of urban underground rail transit, underground space resources are becoming increasingly scarce. To adapt to the need for tunneling beneath dense urban buildings and to improve the effective utilization rate of underground space, irregular-section shield tunnels, represented by double-circular shield tunnels, have emerged. The cross-section of a double-circular shield tunnel is formed by two overlapping single circles. After a single excavation, it can simultaneously accommodate the round-trip operation of trains. This effectively avoids the mutual interference between two construction phases, reduces the double disturbance to surface buildings and structures, and saves construction time and economic costs. Compared with two traditional circular tunnels, the excavation area of ​​a double-circular shield tunnel is reduced by 24%, and its total width is reduced by 14%, saving valuable underground space resources and improving the effective utilization rate of underground space resources. Given the above advantages of double-circular shield technology, the construction technology of double-circular shield tunnels has been successfully applied to the subway tunnel section between Huangxing Greenland Station and Kailu Road Station on Shanghai Metro Line M8. With further optimization of the double-circular shield construction method, it has broad application prospects in densely populated urban areas and will become one of the main construction methods for urban subway tunnels.

[0003] Similar to single-circle shield tunnels, double-circle shield tunnels are assembled from prefabricated segments connected by high-strength bolts during the tunneling process, forming an underground prefabricated composite slender cylindrical structure. Under the influence of adjacent external construction (such as sudden surface loading, new pipeline crossings, and unloading from side pits) and long-term train vibrations, these composite slender cylindrical structures are highly susceptible to uneven longitudinal displacement, leading to problems such as water leakage at lining joints, segment damage and cracking, and bolt breakage, threatening train operation safety. With future urban development, similar adjacent construction projects involving shield tunneling will undoubtedly increase, making the assessment of deformation and stress conditions of operational tunnels increasingly important. Longitudinal bending stiffness is an important mechanical parameter for predicting the longitudinal stress and deformation of shield tunnels. It is also an important theoretical basis for assessing the safety of double-circle shield tunnel structures under external loads. After obtaining the equivalent longitudinal bending stiffness of a double-circle shield tunnel, the deformation and stress of the double-circle shield tunnel under external bending moment can be theoretically calculated. Specific indicators include radius of curvature, tensile and compressive stress of concrete segments, circumferential joint opening, and longitudinal bolt tensile stress. Furthermore, the corresponding limit radius of curvature can be calculated based on the deformation and stress limit values ​​given by relevant safety specifications, which helps in the safety monitoring of double-circle shield tunnels.

[0004] Existing technologies have developed a theory for calculating the longitudinal equivalent bending stiffness of single-circular shield tunnels, and conducted in-depth research on their longitudinal bending performance, thus basically perfecting the theory of longitudinal bending stiffness for single-circular shield tunnels. However, double-circular shield tunnels are special irregular-section shield tunnels formed by splicing two large circular arcs, resulting in significant differences in their longitudinal bending performance compared to two independent single-circular shield tunnels. Their bending stiffness values ​​cannot be simply obtained by analogy and direct copying from single-circular or rectangular shield tunnels. Their structural characteristics should be fully considered, and a longitudinal equivalent bending stiffness model conforming to their cross-sectional characteristics should be constructed; otherwise, the accuracy of the obtained bending stiffness will be low.

[0005] In the existing technology, the research on the longitudinal bending performance of the lining design and parameter selection of double-circular shield tunnels is seriously lagging behind the actual engineering needs. This makes it difficult to theoretically evaluate and predict its longitudinal deformation characteristics under close external construction, and thus cannot provide a reliable basis for the longitudinal structural design of double-circular shield tunnels. Summary of the Invention

[0006] To address the aforementioned problems, this invention provides a method for determining the longitudinal equivalent bending stiffness and deformation of a double-circular shield tunnel. The double-circular shield tunnel is assembled from prefabricated segments connected by high-strength bolts during the tunneling process of a tunnel boring machine. It is an underground prefabricated composite slender cylindrical structure. A cross-section of the tunnel segment is taken, comprising two large circular arcs and a column segment, divided into three parts from top to bottom: an upper double arch, a waist section, and a lower double arch. The left and right sides are composed of two circular arcs of the same radius. The method includes the following steps:

[0007] S101: Take a section of the double-circle shield tunnel and obtain the section parameters and component design parameters of the double-circle shield tunnel. The section parameters include: arc radius R, distance r from the center to the bolt, column height, central angle β of the 1 / 2 arch arc, and segment thickness t. The component design parameters include: segment elastic modulus E. s , Total number of longitudinal bolts n, Cross-sectional area of ​​a single bolt A b Length of a single bolt l b and bolt elastic modulus E b ;

[0008] S102: The average linear stiffness k of the bolts in the double-circle shield tunnel is calculated using the following formula. r :

[0009]

[0010] Where, k b Let l be the elastic stiffness coefficient of a single longitudinal bolt, and l be the total length of the bolt distribution.

[0011] S103: Based on the average linear stiffness of the bolts in the double-circular shield tunnel, and according to the moment balance equation, the neutral axis position x and the corresponding neutral axis position angle of the double-circular shield tunnel are obtained. The neutral axis position x is the position of the neutral axis in the vertical direction relative to the centroidal axis of the double-circle shield tunnel. It is numerically equal to the vertical distance from the center of the circle to the neutral axis. When the neutral axis is below the centroidal axis, the defined neutral axis position x is a positive value, and when the neutral axis is above the centroidal axis, the defined neutral axis position x is a negative value.

[0012] Neutral axis position x and neutral axis position angle The relationship is

[0013] When the neutral axis is located at the waist of the cross section, according to the equation The neutral axis position angle of the double-circle shield tunnel is obtained.

[0014] When the neutral axis is located in the lower part of the double arch section, according to the equation The neutral axis position angle of the double-circle shield tunnel can be obtained by solving the equation.

[0015] Among them, l s It is the distance between the annular wall of the two tunnel segments and their respective centerlines;

[0016] S104: The longitudinal equivalent bending stiffness of the double-circular shield tunnel is calculated based on the neutral axis position angle of the double-circular shield tunnel.

[0017] When the neutral axis is located at the waist of the cross section, the neutral axis position angle satisfy At this point, the longitudinal equivalent bending stiffness (EI) of the double-circular shield tunnel is... eq for:

[0018] (EI) eq =E s t(A3-A4+ψ(A5-A6))

[0019] in,

[0020]

[0021]

[0022]

[0023]

[0024]

[0025] When the neutral axis is located in the lower part of the double arch of the cross section, the neutral axis position angle satisfy At this point, the longitudinal equivalent bending stiffness (EI) of the double-circular shield tunnel is... eq for:

[0026] (EI) eq =E s t(B3+ψ(-B4+B5+B6))

[0027] in,

[0028]

[0029]

[0030]

[0031]

[0032] S105: Based on the obtained longitudinal equivalent bending stiffness of the double-circular shield tunnel, the tunnel deformation stress index is obtained, and then the deformation of the double-circular shield tunnel is determined; the tunnel deformation stress index includes the radius of curvature ρ and the maximum tensile stress σ of the concrete. t Maximum compressive stress σ in concrete c The circumferential joint opening δ and bolt tensile stress σ furthest from the neutral axis b ;

[0033]

[0034]

[0035]

[0036]

[0037]

[0038] Where J1′=tB3, J2′=t(-B4+B5+B6), M represents the bending moment experienced by the segment, and ε c ε represents the maximum compressive strain at the segment joint. t This indicates the maximum tensile strain of the segment joint.

[0039] Furthermore, there are two possible distributions of the neutral axis position: the neutral axis is located at the waist of the section and the neutral axis is located at the lower part of the section in a double arch configuration;

[0040] When the neutral axis is located at the waist of the cross section, the neutral axis position angle satisfy

[0041] When the neutral axis is located in the lower part of the double arch of the cross section, the neutral axis position angle satisfy

[0042] A system for determining the longitudinal equivalent bending stiffness and deformation of a double-circular shield tunnel includes:

[0043] The parameter acquisition module captures a cross-section of the double-circle shield tunnel to obtain its cross-sectional parameters and component design parameters. The cross-sectional parameters include: arc radius R, distance r from the center to the bolt, column height, central angle β of the half-arch arc, and segment thickness t. The component design parameters include: segment elastic modulus E. s , Total number of longitudinal bolts n, Cross-sectional area of ​​a single bolt A b Length of a single bolt l b and bolt elastic modulus E b ;

[0044] The module for obtaining the average linear stiffness of tunnel bolts calculates the average linear stiffness k of the bolts in the double-circular shield tunnel using the following formula. r :

[0045]

[0046] Where: k r The average linear stiffness of the bolts is n, where n is the total number of bolts in the longitudinal direction of the cross section, and k is k. b E is the elastic stiffness coefficient of a single longitudinal bolt, l is the total length of the bolt distribution, and E b It is the elastic modulus of the bolt, l b It is the length of a single bolt, A b β is the cross-sectional area of ​​a single bolt, β is the central angle of half the arch arc, and r is the distance from the center of the circle to the bolt;

[0047] The neutral axis position and neutral axis position angle acquisition module, combined with the average linear stiffness of the bolts in the double-circular shield tunnel, obtains the neutral axis position x and the corresponding neutral axis position angle of the double-circular shield tunnel according to the moment balance equation.

[0048] Neutral axis position x and neutral axis position angle The relationship is

[0049] When the neutral axis is located at the waist of the cross section, according to the equation The neutral axis position angle of the double-circle shield tunnel is obtained.

[0050] When the neutral axis is located in the lower part of the double arch section, according to the equation The neutral axis position angle of the double-circle shield tunnel can be obtained by solving the equation.

[0051] Among them, l sIt is the distance between the annular wall of the two tunnel segments and their respective centerlines;

[0052] The longitudinal equivalent bending stiffness acquisition module calculates the longitudinal equivalent bending stiffness of the double-circular shield tunnel based on the neutral axis position angle of the double-circular shield tunnel.

[0053] When the neutral axis is located at the waist of the cross section, the neutral axis position angle satisfy At this point, the longitudinal equivalent bending stiffness (EI) of the double-circular shield tunnel is... eq for:

[0054] (EI) eq =E s t(A3-A4+ψ(A5-A6))

[0055] in,

[0056]

[0057]

[0058]

[0059]

[0060]

[0061] When the neutral axis is located in the lower part of the double arch of the cross section, the neutral axis position angle satisfy At this point, the longitudinal equivalent bending stiffness (EI) of the double-circular shield tunnel is... eq for:

[0062] (EI) eq =E s t(B3+ψ(-B4+B5+B6))

[0063] in,

[0064]

[0065]

[0066]

[0067]

[0068] The tunnel deformation stress index acquisition module is used to obtain the tunnel deformation stress index based on the calculated longitudinal equivalent bending stiffness of the double-circular shield tunnel, thereby determining the deformation status of the double-circular shield tunnel. The tunnel deformation stress index includes the radius of curvature ρ and the maximum tensile stress σ in the concrete. tMaximum compressive stress σ in concrete c The circumferential joint opening δ and bolt tensile stress σ furthest from the neutral axis b ;

[0069]

[0070]

[0071]

[0072]

[0073]

[0074] Where J1′=tB3, J2′=t(-B4+B5+B6), M represents the bending moment experienced by the segment, and ε c ε represents the maximum compressive strain at the segment joint. t This indicates the maximum tensile strain of the segment joint.

[0075] The beneficial effects of the technical solution provided by this invention are: it improves the reliability and accuracy of the longitudinal equivalent bending stiffness of the double-circular shield tunnel, provides assistance for the longitudinal structural design of the double-circular shield tunnel, is of great significance for assessing the impact of adjacent construction on the double-circular shield tunnel, and determines the tunnel deformation through the obtained deformation and stress index, providing a reference for the deformation and stress safety monitoring of the double-circular shield tunnel. Attached Figure Description

[0076] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings:

[0077] Figure 1 This is a flowchart of the method for determining the longitudinal equivalent bending stiffness of a double-circular shield tunnel in an embodiment of the present invention;

[0078] Figure 2 This is a cross-sectional schematic diagram of the double-circle shield tunnel established in an embodiment of the present invention;

[0079] Figure 3 This is a schematic diagram of the bending deformation of the pipe segment in an embodiment of the present invention;

[0080] Figure 4 This is a schematic diagram of the neutral axis being located at the waist of the cross section in an embodiment of the present invention;

[0081] Figure 5 This is a schematic diagram of the double arch at the bottom of the cross section in an embodiment of the present invention;

[0082] Figure 6 This is a schematic diagram illustrating the variation of tensile and compressive stresses in concrete segments with radius of curvature in an embodiment of the present invention.

[0083] Figure 7 This is a schematic diagram illustrating the variation of the circumferential seam opening and longitudinal bolt tensile stress with the radius of curvature in an embodiment of the present invention.

[0084] Figure 2 In the diagram, 1 represents a double-circular shield tunnel, 2 represents the interface of the double-circular shield tunnel, 3 represents the track, and 4 represents the train. Detailed Implementation

[0085] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0086] The embodiments of the present invention provide a method and system for determining the longitudinal equivalent bending stiffness and deformation of a double-circular shield tunnel.

[0087] Please refer to Figure 1 , Figure 1 This is a flowchart illustrating a method for determining the longitudinal equivalent bending stiffness and deformation of a double-circular shield tunnel according to an embodiment of the present invention. The double-circular shield tunnel is an underground prefabricated composite slender cylindrical structure assembled from precast segments connected by high-strength bolts during the tunneling process of a shield machine. Figure 2 This is a schematic diagram of a double-circle shield tunnel. Figure 2 In the diagram, 1 represents a double-circular shield tunnel, 2 represents the interface of the double-circular shield tunnel, 3 represents the track, and 4 represents the train; the establishment of the longitudinal equivalent continuous model of the double-circular shield tunnel is based on... Figure 3 The tunnel segment shown is a unit. Figure 3 This is a schematic diagram of the bending deformation of the tunnel segment in an embodiment of the present invention. The distance l between the annular wall of two adjacent tunnel segments and their respective centerlines is taken as the distance between them. s As a computational unit, when a segment is subjected to a bending moment M, the segment element will deform and rotate, resulting in a rotation angle of θ; the final segment cross-section of the longitudinal equivalent continuous model of the double-circular shield tunnel is as follows. Figure 5 As shown, Figure 5 This is a schematic diagram of the cross-section of a double circular tunnel segment in an embodiment of the present invention. In this embodiment, it is assumed that the tunnel cross-section remains planar after deformation, and the amount of deformation at each point on the cross-section is proportional to the distance to the neutral axis. The planar cross-section is assumed to conform to the Saint-Venant principle. Figure 1 As shown, a method for determining the longitudinal equivalent bending stiffness and deformation of a double-circular shield tunnel includes the following steps:

[0088] S101: Based on the construction of the double-circular shield tunnel 1, determine the cross-sectional parameters and component design parameters of the double-circular shield tunnel 1. The specific meaning of each parameter is as follows: Figure 4 and Figure 5 As shown;

[0089] The cross-sectional parameters include: arc radius R, distance r from the center to the bolt, column height h, central angle β of the half-arch arc, and segment thickness t; the component design parameters include: segment elastic modulus E. s The number of longitudinal bolts n in the cross section, and the cross-sectional area A of a single bolt. b Bolt length l b Bolt elastic modulus E b ; Figure 4 and Figure 5 In this context, dα is the central angle corresponding to the arc of any differential unit on the segment ring. The neutral axis position angle is the angle between the line connecting the intersection of the neutral axis and the center line of the segment and the center of the circle, and the vertical line containing the center of the circle. α is the angle between the line connecting the differential unit and the center of the arc and the vertical direction.

[0090] Please refer to Figure 2 , Figure 2 This is a schematic diagram of a double-circular shield tunnel in an embodiment of the present invention, which determines the cross-sectional parameters and component design parameters of the double-circular shield tunnel. The specific meaning of each parameter is as follows: Figure 3 and Figure 4 As shown, in this embodiment, the selected double-circular shield tunnel has a total tunnel width of 10.9m, an arc radius of 3.15m, a distance of 3m from the center to the bolt position, a column height of 3.5m, a central angle of 54.3° for the half-arch arc, a segment thickness of 0.3m, and a segment width of 1.2m. The segment elastic modulus is 3.45 × 10⁻⁶. 4 MPa, total number of bolts: 46, individual bolt diameter: 30mm, individual bolt length: 370mm, bolt elastic modulus: 2.06×10⁻⁶. 5 MPa; The cross-sectional area A of a single bolt can be calculated from the bolt diameter. b ;

[0091] S102: Determine the average linear stiffness of the bolts in the double-circular shield tunnel based on the cross-sectional parameters and component design parameters; the bolt distribution in the circumferential direction is considered as a continuous and uniform distribution. The average linear stiffness of the bolts refers to the ability to resist tensile force per unit length of the circumference of the double-circular shield tunnel; the average linear stiffness of the bolts in the double-circular shield tunnel can be calculated by formula (1):

[0092]

[0093] Where: k r The average linear stiffness of the bolts is n, where n is the total number of bolts in the longitudinal direction of the cross section, and k is k. b E is the elastic stiffness coefficient of a single longitudinal bolt, l is the total length of the bolt distribution, and E b It is the elastic modulus of the bolt, l b It is the bolt length, Ab It is the cross-sectional area of ​​a single bolt, and β is 1 / 2 the central angle of the arch arc;

[0094] In this embodiment, by Figure 3 and Figure 4 The average linear stiffness of the bolts in the double-circle shield tunnel is calculated by substituting the values ​​of the parameters shown into the data.

[0095] S103: Based on the calculated average linear stiffness of the bolts in the double-circle shield tunnel, combined with the cross-sectional parameters and component design parameters of the double-circle shield tunnel, a moment balance equation is derived to obtain the neutral axis position and corresponding neutral axis position angle of the double-circle shield tunnel. The neutral axis position x of the double-circle shield tunnel is the vertical position of the neutral axis relative to the centroidal axis of the double-circle shield tunnel, numerically equal to the vertical distance from the center of the circle to the neutral axis. When the neutral axis is below the centroidal axis, the defined neutral axis position x is positive; when the neutral axis is above the centroidal axis, the defined neutral axis position x is negative. There are two distribution scenarios for the neutral axis position: the neutral axis is located at the waist of the cross-section and the neutral axis is located at the lower part of the double arch cross-section. When the neutral axis is located at the waist of the cross-section, the neutral axis position angle... satisfy When the neutral axis is located in the lower part of the double arch section, the neutral axis position angle is... satisfy Regardless of whether the neutral axis is located at the waist of the double-circle section or at the lower double arch, the neutral axis position x and the neutral axis position angle The relationship has always been

[0096] Based on the different positions of the neutral axis, corresponding deformation compatibility equations, force equilibrium equations, and moment equilibrium equations are listed. These can be combined to obtain an equation with only the neutral axis position angle as the unknown. During calculation, the position of the neutral axis is first assumed, and different equations are used to solve for the magnitude of the neutral axis position angle. If the assumption is satisfied, the obtained neutral axis position angle is the true neutral axis position angle; if the assumption is not satisfied, another equation is used to solve for it, such as... Figure 4 As shown, when the neutral axis is located at the waist of the double-circular section, the equation is used. Solve this problem; for example Figure 5 As shown, when the neutral axis is located at the lower part of the double arch in the double circular section, the corresponding equation is used. The neutral axis position angle of the double-circle shield tunnel can be obtained by solving; the neutral axis position can be determined from the obtained neutral axis position angle, and the relationship between the neutral axis position and the neutral axis position angle is as follows: in:

[0097]

[0098]

[0099]

[0100]

[0101] k r It is the average linear stiffness of the bolt, l s It is the distance between the centerlines of the two segment rings, E s Here, t is the elastic modulus of the tunnel segment, r is the distance from the center of the circle to the bolt, and β is the central angle of half the arch radius. The neutral axis position angle.

[0102] When the neutral axis is located in the lower part of the double arch of the cross section, the position angle of the neutral axis satisfies The corresponding neutral axis position angle is obtained by solving formula (2):

[0103]

[0104] in,

[0105]

[0106]

[0107] Solving If the previous assumptions are satisfied, then the neutral axis is indeed located at the lower part of the double arch of the double circular section, and the obtained neutral axis position angle is the true neutral axis position angle.

[0108] S104: Based on the neutral axis position angle of the double-circular shield tunnel, the longitudinal equivalent bending stiffness of the double-circular shield tunnel is calculated using the corresponding formula.

[0109] Neutral axis position angle satisfy When the neutral axis is located at the waist of the cross section, the longitudinal equivalent bending stiffness of the double-circular shield tunnel is calculated according to formula (3) as follows:

[0110] (EI) eq =E s (J1+ψJ2)(3)

[0111] Among them, (EI) eq For the equivalent bending stiffness of the double-circular shield tunnel, J1 = t(A3 - A4), J2 = t(A5 - A6).

[0112]

[0113]

[0114]

[0115]

[0116]

[0117] Neutral axis position angle satisfy When the neutral axis is located at the lower part of the double arch section, the longitudinal equivalent bending stiffness of the double-circular shield tunnel is calculated according to formula (4):

[0118] (EI) eq =E s (J1′+ψJ2′) (4)

[0119] in,

[0120] J1′=tB3,

[0121] J2′=t(-B4+B5+B6),

[0122]

[0123]

[0124]

[0125]

[0126] For example, in this embodiment, the neutral axis position angle satisfy At this point, the neutral axis is located at the lower part of the double arch in the double circular section. Substituting the relevant parameter values, the following calculation is obtained:

[0127]

[0128]

[0129]

[0130]

[0131]

[0132] J1′=tB3=0.3×2.193=0.6579,

[0133] J2′=t(-B4+B5+B6)=0.3×(-0.279+47.469+270.953)=95.4429

[0134] The final calculated longitudinal equivalent bending stiffness of the double-circular shield tunnel is:

[0135] (EI) eq=3.45×10 4 ×(0.6579+0.0533×95.4429)≈0.19819×10 9 kN·m·rad -1 ;

[0136] In this embodiment, the neutral axis is located at the lower part of the double arch section. Based on the derived expression for the longitudinal equivalent bending stiffness of the double-circular shield tunnel, the tunnel deformation stress indexes can be further obtained: radius of curvature ρ, concrete tensile stress σ. t σ compressive stress in concrete c Circumferential joint opening δ and bolt tensile stress σ b The calculation formula is as follows:

[0137]

[0138]

[0139]

[0140]

[0141]

[0142] Please refer to Figure 6 , Figure 7 , Figure 6 This is a schematic diagram illustrating the variation of tensile and compressive stresses in concrete segments with radius of curvature in an embodiment of the present invention. Figure 7 This is a schematic diagram illustrating the variation of the circumferential seam opening and longitudinal bolt tensile stress with the radius of curvature in an embodiment of the present invention. Figure 6 and Figure 7 [σ] t ] = 2.64 MPa, δ = 1 mm, [σ b =640MPa is the safety limit value for the deformation stress index.

[0143] A system for determining the longitudinal equivalent bending stiffness and deformation of a double-circular shield tunnel includes:

[0144] The parameter acquisition module captures the cross-section of the double-circle shield tunnel and obtains the cross-sectional parameters and component design parameters of the double-circle shield tunnel.

[0145] The module for obtaining the average linear stiffness of tunnel bolts calculates the average linear stiffness k of the bolts in the double-circular shield tunnel using the following formula. r :

[0146]

[0147] The neutral axis position and neutral axis position angle acquisition module, combined with the average linear stiffness of the bolts in the double-circular shield tunnel, obtains the neutral axis position x and the corresponding neutral axis position angle of the double-circular shield tunnel according to the moment balance equation.

[0148] The longitudinal equivalent bending stiffness acquisition module calculates the longitudinal equivalent bending stiffness of the double-circular shield tunnel based on the neutral axis position angle of the double-circular shield tunnel.

[0149] The tunnel deformation stress index acquisition module is used to obtain the tunnel deformation stress index based on the calculated longitudinal equivalent bending stiffness of the double-circular shield tunnel, thereby determining the deformation status of the double-circular shield tunnel; the tunnel deformation stress index includes the radius of curvature ρ and the concrete tensile stress σ. t σ compressive stress in concrete c Circumferential joint opening δ and bolt tensile stress σ b ;

[0150]

[0151]

[0152]

[0153]

[0154]

[0155] Where J1′=tB3, J2′=t(-B4+B5+B6), M represents the bending moment experienced by the segment, and ε c ε represents the maximum compressive strain at the segment joint. t This indicates the maximum tensile strain of the segment joint.

[0156] The beneficial effects of the technical solution provided by this invention are: it improves the reliability and accuracy of the longitudinal equivalent bending stiffness of the double-circular shield tunnel, provides assistance for the longitudinal structural design of the double-circular shield tunnel, is of great significance for assessing the impact of adjacent construction on the double-circular shield tunnel, and the derived formula for calculating the deformation stress index provides a reference for the deformation stress safety monitoring of the double-circular shield tunnel.

[0157] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for determining the longitudinal equivalent bending stiffness and deformation of a double-circle shield tunnel, comprising the following steps: S101: Take a section of the double-circle shield tunnel to obtain the section parameters and component design parameters of the double-circle shield tunnel. The section parameters include: arc radius R, distance r from the center to the bolt, central angle β of the half-arch arc, and segment thickness t. The component design parameters include: segment elastic modulus E. s , Total number of longitudinal bolts n, Cross-sectional area of ​​a single bolt A b Length of a single bolt l b and bolt elastic modulus E b ; S102: The average linear stiffness k of the bolts in the double-circle shield tunnel is calculated using the following formula. r : Where, k b Let l be the elastic stiffness coefficient of a single longitudinal bolt, and l be the total length of the bolt distribution. S103: Based on the average linear stiffness of the bolts in the double-circular shield tunnel, and according to the moment balance equation, the neutral axis position x and the corresponding neutral axis position angle of the double-circular shield tunnel are obtained. S104: The longitudinal equivalent bending stiffness of the double-circular shield tunnel is calculated based on the neutral axis position angle of the double-circular shield tunnel. When the neutral axis is located in the lower part of the double arch of the cross section, the neutral axis position angle satisfy At this point, the longitudinal equivalent bending stiffness (EI) of the double-circular shield tunnel is... eq for: (EI) eq =E s t(B3+ψ(-B4+B5+B6)) in, l s This indicates the distance between the annular wall of two tunnel segments and their respective centerlines; S105: Based on the obtained longitudinal equivalent bending stiffness of the double-circular shield tunnel, the tunnel deformation stress index is obtained, and then the deformation of the double-circular shield tunnel is determined; the tunnel deformation stress index includes the radius of curvature ρ and the maximum tensile stress σ of the concrete. t Maximum compressive stress σ in concrete c The circumferential joint opening δ and bolt tensile stress σ furthest from the neutral axis b ; When the neutral axis is located at the lower part of the double arch in the cross section, Where J1' = tB3, J2' = t(-B4 + B5 + B6), M represents the bending moment experienced by the segment, and ε c ε represents the maximum compressive strain at the segment joint. t This indicates the maximum tensile strain of the segment joint.

2. The method for determining the longitudinal equivalent bending stiffness of a double-circular shield tunnel and its deformation as described in claim 1, characterized in that: When the neutral axis is located at the waist of the cross section, the neutral axis position angle satisfy When the neutral axis is located in the lower part of the double arch of the cross section, the neutral axis position angle satisfy 3. The method for determining the longitudinal equivalent bending stiffness of a double-circular shield tunnel and its deformation as described in claim 1, characterized in that: The neutral axis position x is the position of the neutral axis in the vertical direction relative to the centroidal axis of the double-circle shield tunnel. It is numerically equal to the vertical distance from the center of the circle to the neutral axis. When the neutral axis is below the centroidal axis, the defined neutral axis position x is a positive value, and when the neutral axis is above the centroidal axis, the defined neutral axis position x is a negative value. Neutral axis position x and neutral axis position angle The relationship is When the neutral axis is located at the waist of the cross section, according to the equation The neutral axis position angle of the double-circle shield tunnel is obtained. When the neutral axis is located in the lower part of the double arch section, according to the equation The neutral axis position angle of the double-circle shield tunnel can be obtained by solving the equation. Among them, l s It is the distance between the two segment annular walls and their respective centerlines.

4. The method for determining the longitudinal equivalent bending stiffness of a double-circular shield tunnel and its deformation as described in claim 1, characterized in that: When the neutral axis is located at the waist of the cross section, the neutral axis position angle satisfy At this point, the longitudinal equivalent bending stiffness (EI) of the double-circular shield tunnel is... eq for: (IT) eq =E s t(A3-A4+ψ(A5-A6)) in, 5. A system for determining the longitudinal equivalent bending stiffness of a double-circular shield tunnel and its deformation, implemented based on the method for determining the longitudinal equivalent bending stiffness of a double-circular shield tunnel and its deformation obtained in any one of claims 1-4, characterized in that: include: The parameter acquisition module captures a cross-section of the double-circle shield tunnel to obtain its cross-sectional parameters and component design parameters. The cross-sectional parameters include: arc radius R, distance r from the center to the bolt, column height, central angle β of the half-arch arc, and segment thickness t. The component design parameters include: segment elastic modulus E. s , Total number of longitudinal bolts n, Cross-sectional area of ​​a single bolt A b Length of a single bolt l b and bolt elastic modulus E b ; The module for obtaining the average linear stiffness of tunnel bolts calculates the average linear stiffness k of the bolts in the double-circular shield tunnel using the following formula. r : Where: k r The average linear stiffness of the bolts is n, where n is the total number of bolts in the longitudinal direction of the cross section, and k is the average linear stiffness of the bolts. b E is the elastic stiffness coefficient of a single longitudinal bolt, l is the total length of the bolt distribution, and E b It is the elastic modulus of the bolt, l b It is the length of a single bolt, A b β is the cross-sectional area of ​​a single bolt, β is the central angle of half the arch arc, and r is the distance from the center of the circle to the bolt; The neutral axis position and neutral axis position angle acquisition module, combined with the average linear stiffness of the bolts in the double-circular shield tunnel, obtains the neutral axis position x and the corresponding neutral axis position angle of the double-circular shield tunnel according to the moment balance equation. Neutral axis position x and neutral axis position angle The relationship is When the neutral axis is located at the waist of the cross section, according to the equation The neutral axis position angle of the double-circle shield tunnel is obtained. When the neutral axis is located in the lower part of the double arch section, according to the equation The neutral axis position angle of the double-circle shield tunnel can be obtained by solving the equation. Among them, l s It is the distance between the annular wall of the two tunnel segments and their respective centerlines; The longitudinal equivalent bending stiffness acquisition module calculates the longitudinal equivalent bending stiffness of the double-circular shield tunnel based on the neutral axis position angle of the double-circular shield tunnel. When the neutral axis is located at the waist of the cross section, the neutral axis position angle satisfy At this point, the longitudinal equivalent bending stiffness (EI) of the double-circular shield tunnel is... eq for: (IT) eq =E s t(A3-A4+ψ(A5-A6)) in, When the neutral axis is located in the lower part of the double arch of the cross section, the neutral axis position angle satisfy At this point, the longitudinal equivalent bending stiffness (EI) of the double-circular shield tunnel is... eq for: (EI) eq =E s t(B3+ψ(-B4+B5+B6)) in, The tunnel deformation stress index acquisition module obtains the tunnel deformation stress index based on the calculated longitudinal equivalent bending stiffness of the double-circular shield tunnel, thereby determining the deformation status of the double-circular shield tunnel. The tunnel deformation stress index includes the radius of curvature ρ and the maximum tensile stress σ in the concrete. t Maximum compressive stress σ in concrete c The circumferential joint opening δ and bolt tensile stress σ furthest from the neutral axis b ; When the neutral axis is located at the lower part of the double arch in the cross section, Where J1' = tB3, J2' = t(-B4 + B5 + B6), M represents the bending moment experienced by the segment, and ε c ε represents the maximum compressive strain at the segment joint. t This indicates the maximum tensile strain of the segment joint.

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