A method for analyzing the longitudinal stress of soft soil shield tunnel during construction.

Abstract

This invention discloses a method for analyzing the longitudinal stress of a shield tunnel during construction in soft soil, comprising the following steps: 1) obtaining relevant parameters required for calculation; 2) dividing the shield tunnel into a section where the grout has not solidified and a section where the grout has solidified; 3) determining whether the stratum where the shield tunnel is located is soft soil based on national standards and specifications; 4) calculating the additional loads during the construction period of the shield tunnel; 5) calculating the equivalent longitudinal bending stiffness and equivalent shear stiffness of the shield tunnel; 6) performing stress analysis on a micro-element of the shield tunnel and establishing the model's governing equations; 7) solving the numerical solution of the governing equations using the finite difference method. The advantages of this invention are: clear concept, simple solution, and it can be used as a reference for engineering design.

Description

Technical Field

[0001] This invention relates to a method for analyzing the longitudinal stress during the construction of a shield tunnel in soft soil. Background Technology

[0002] Shield tunneling is the primary construction method for urban subway tunnels. Compared to traditional open-cut tunneling, it offers advantages such as faster construction speed, higher mechanization, and less impact on the surrounding environment. However, due to the characteristics of the shield tunneling process, the segments of shield tunnels in soft soil inevitably float during construction, leading to increased internal forces in the tunnel structure and increased construction risks. Therefore, it is necessary to propose a longitudinal stress analysis method for the floating of shield tunnels in soft soil during construction. This method can quickly and accurately assess the stress state of the shield tunnel structure under specific floating conditions, providing guidance for shield tunnel construction safety and optimized shield tunnel structural design.

[0003] Currently, the theories for longitudinal stress analysis of shield tunnels mainly fall into two categories. One is the longitudinal equivalent continuous beam theory proposed by Yukio Shiba in 1988, and the other is the longitudinal beam-spring theory proposed by Jun Koizumi in 1998. Both theories are based on the load-structure method, simplifying the shield tunnel structure as a whole into beams or segments into beams, and joint bolts into springs for calculation. Among them, the longitudinal equivalent continuous beam theory has a clear concept, well-defined parameters, and simple calculations, making it easier to use. Many practitioners have established longitudinal stress analysis models for shield tunnels during construction based on the longitudinal equivalent continuous beam theory. However, existing models do not comprehensively consider the upward loads during shield tunnel construction. Most studies only consider the influence of static and dynamic upward forces on the upward stress of the shield tunnel structure, without considering the influence of ground rebound forces. Comprehensively considering the vertical external forces and time-varying characteristics of external forces during shield tunnel construction is of great significance for improving the accuracy of longitudinal stress analysis for shield tunnel structures during construction. Summary of the Invention

[0004] This invention aims to address the problem that existing longitudinal stress analysis models for shield tunnels during construction based on the longitudinal equivalent continuous beam theory fail to fully consider the time-varying characteristics of the upward load and external forces during shield tunnel construction, and provides a method for analyzing the longitudinal stress of shield tunnels during construction in soft soil.

[0005] This invention is based on the finite difference method, which treats the shield tunnel as a continuous homogeneous Timoshenko beam in the longitudinal direction, while considering the influence of the time-varying characteristics of external forces on the buoyancy load and the ground rebound force on the buoyancy force of the shield tunnel. The calculation method is conceptually clear and easy to solve, and can be used as a reference.

[0006] The method for analyzing the longitudinal stress of soft soil shield tunnels during construction includes the following steps:

[0007] 1) Obtain the relevant parameters required for the calculation. Obtain the relevant parameters required for the calculation based on the shield tunnel structural design data, geological exploration report, and shield construction and excavation records.

[0008] 2) The shield tunnel is divided into a section where the grout has not yet solidified and a section where the grout has solidified. The length of the section where the grout has not solidified is L1, and the length of the section where the grout has solidified is L2. The length L1 of the section where the grout has not solidified can be determined by considering the shield tunneling progress and the grout solidification rate, while the length L2 of the section where the grout has solidified is generally chosen to be the larger value. The total length of the shield tunnel is L = L1 + L2.

[0009] 3) Determine whether the soil beneath the shield tunnel is soft soil based on the national standard "Design Standard for Shield Tunnel Engineering" (GB / T51438-2021). If it can be classified as soft soil, use the Winkler elastic foundation model to simplify the soil beneath the shield tunnel, reducing it to several linear grounding springs connected to the shield tunnel. The stiffness of the grounding springs is related to the size of the finite difference element and the subgrade reaction coefficient of the soil beneath the shield tunnel, and the specific expression is as follows:

[0010] k v =k s s (1)

[0011] In equation (1), k v k is the foundation spring constant. s is the subgrade reaction coefficient, which can be obtained from the geological exploration report; s is the vertical projected area of ​​the volume occupied by the finite difference element within the tunnel range;

[0012] The Winkler elastic foundation model assumes that the reaction force of the underlying soil is proportional to the vertical displacement of the soil, specifically expressed as:

[0013] p = k v w(2)

[0014] In equation (2), p is the soil reaction force caused by the vertical displacement of the element; w is the vertical displacement of the finite difference element.

[0015] 4) Calculate the additional loads during shield tunnel construction. The additional loads include buoyancy and anti-buoyancy forces. The buoyancy force includes static buoyancy, dynamic buoyancy, and ground rebound force, specifically expressed as follows:

[0016]

[0017]

[0018]

[0019] In equation (6), q1 is the static buoyancy force; γ fThe bulk density of the mixture of slurry and groundwater; γ w q2 is the unit weight of groundwater. In equation (7), q2 is the dynamic buoyancy force. E4 = -f4; q j1 The pressure of the lower slurry bubble; q j2 α1 is the upper bubble pressure; α2 is the lower bubble angle; α3 is the upper bubble angle. In equation (8), q3 is the formation resilience. E6 = 2f5 / L1; γ m R2 is the equivalent unit weight of the stratum; H is the shield excavation radius; H is the distance from the top of the grouting layer to the ground surface; H1 is the height of any soil column at any point on the outer circumference of the grouting layer; H1 = H + R2(1cosα); K0 is the coefficient of earth pressure at rest.

[0020] The buoyancy resistance includes the self-weight of the tunnel segments and ancillary facilities and the overlying soil pressure, and its specific expression is as follows:

[0021]

[0022]

[0023] In equation (6), γ c R1 is the unit weight of the segment concrete; R1 is the outer radius of the tunnel; R0 is the inner radius of the tunnel; W t0 The total weight of trailers and other ancillary facilities; L t Let K be the length of the trailer. In equation (7), K... s This is the earth lateral pressure coefficient, which is generally taken as 1; c is the internal friction angle of the soil. s For soil cohesion; γ s For soil bulk density; h s q represents the soil layer height. c B is due to ground overload; s Width of the loosened area

[0024] The additional load q can be calculated according to equation (8):

[0025] q=q1+q2+q3+q4+q5 (8)

[0026] 5) Calculate the equivalent longitudinal bending stiffness and equivalent shear stiffness of the shield tunnel. The specific formula for calculating the equivalent longitudinal bending stiffness of the shield tunnel is as follows:

[0027]

[0028]

[0029] In equation (9), K is the longitudinal equivalent bending stiffness of the shield tunnel; E is the neutral axis angle. c The elastic modulus of concrete; I c Let n be the moment of inertia of the shield tunnel cross section. In equation (10), n is the number of longitudinal joint bolts; K r For the longitudinal joint bolt linear stiffness; A c l is the cross-sectional area of ​​the shield tunnel; s This represents the width of one ring segment.

[0030] The specific formula for calculating the longitudinal equivalent shear stiffness of a shield tunnel is as follows:

[0031]

[0032] In equation (11), C is the equivalent longitudinal shear stiffness of the shield tunnel; ξ is the segment contact relationship correction coefficient; κ b and κ c G represents the shear coefficients for the joint bolts and the segments, respectively, and is taken as 0.9 and 0.5; b and G c These are the shear moduli of the joint bolts and the pipe segments, respectively.

[0033] 6) Perform stress analysis on a micro-element of the shield tunnel and establish the model's governing equations. Assume the micro-element, under the action of an additional load q, experiences a vertical displacement w, and the elastic foundation reaction force is p. According to the force equilibrium condition, we can obtain:

[0034] Dpdx-qdx-dQ=0 (12)

[0035]

[0036] In equations (12) and (13), M is the tunnel bending moment, Q is the tunnel shear force, q is the additional load, p is the foundation reaction force, and D is the outer diameter of the shield tunnel.

[0037] The tunnel bending moment and shear force can be calculated using the following formula:

[0038]

[0039]

[0040] In equations (14) and (15), θ is the tunnel turning angle.

[0041] By combining equations (12) to (15), the model control equations can be obtained:

[0042]

[0043] 7) Solve the numerical solution of the governing equations using the finite difference method. Discretize the shield tunnel structure with a total length of L into n intervals, each interval having a length of Δh = L / n. Place two virtual nodes before and after the first and last nodes, for a total of n+5 nodes.

[0044] Based on the central difference formulas of orders 1 to 4, equation (16) can be transformed into:

[0045]

[0046] In equation (17),

[0047] The boundary conditions of the model can be expressed as:

[0048]

[0049] Combining equations (17) and (18), we can obtain n+5 algebraic equations. By solving the n+5 algebraic equations using the iterative method, we can obtain the vertical displacement, rotation angle, bending moment and shear force under the upward action during the shield tunnel construction period.

[0050] The working principle of this invention is as follows: based on the finite difference method, the shield tunnel is equivalent to a continuous homogeneous Timoshenko beam in the longitudinal direction, while considering the influence of the time-varying characteristics of external forces on the upward load and the elastic force of the stratum on the upward force of the shield tunnel.

[0051] The advantages of this invention are: clear concept, simple solution, and can be used as a reference for engineering design. Attached Figure Description

[0052] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0053] Various exemplary embodiments of the present invention will now be described in detail. This detailed description should not be considered as a limitation of the present invention, but rather as a more detailed description of certain aspects, features, and embodiments of the present invention.

[0054] It should be understood that the terminology used in this invention is merely for describing particular embodiments and is not intended to limit the invention. Furthermore, with respect to numerical ranges in this invention, it should be understood that each intermediate value between the upper and lower limits of the range is also specifically disclosed. Every smaller range between any stated value or intermediate value within a stated range, and any other stated value or intermediate value within said range, is also included in this invention. The upper and lower limits of these smaller ranges may be independently included or excluded from the range.

[0055] Unless otherwise stated, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art. While only preferred methods and materials have been described herein, any methods and materials similar or equivalent to those described herein may be used in the implementation or testing of this invention. All references to this specification are incorporated by way of citation to disclose and describe methods and / or materials associated with those references. In the event of any conflict with any incorporated reference, the content of this specification shall prevail.

[0056] Various modifications and variations can be made to the specific embodiments described in this specification without departing from the scope or spirit of the invention, as will be apparent to those skilled in the art. Other embodiments derived from this specification will also be readily apparent to those skilled in the art. This application specification and embodiments are merely exemplary.

[0057] The terms “include,” “including,” “have,” “contain,” etc., used in this article are all open-ended terms, meaning that they include but are not limited to.

[0058] Unless otherwise specified, the term "parts" in this invention refers to parts by weight.

[0059] The method for analyzing the longitudinal stress of soft soil shield tunnels during construction includes the following steps:

[0060] 1) Obtain the relevant parameters required for the calculation. Obtain the relevant parameters required for the calculation based on the shield tunnel structural design data, geological exploration report, and shield construction and excavation records.

[0061] 2) The shield tunnel is divided into a section where the grout has not yet solidified and a section where the grout has solidified. The length of the section where the grout has not solidified is L1, and the length of the section where the grout has solidified is L2. The length L1 of the section where the grout has not solidified can be determined by considering the shield tunneling progress and the grout solidification rate, while the length L2 of the section where the grout has solidified is generally chosen to be the larger value. The total length of the shield tunnel is L = L1 + L2.

[0062] 3) Determine whether the soil beneath the shield tunnel is soft soil based on the national standard "Design Standard for Shield Tunnel Engineering" (GB / T51438-2021). If it can be classified as soft soil, use the Winkler elastic foundation model to simplify the soil beneath the shield tunnel, reducing it to several linear grounding springs connected to the shield tunnel. The stiffness of the grounding springs is related to the size of the finite difference element and the subgrade reaction coefficient of the soil beneath the shield tunnel, and the specific expression is as follows:

[0063] k v =k s s (1)

[0064] In equation (1), k v k is the foundation spring constant.s is the subgrade reaction coefficient, which can be obtained from the geological exploration report; s is the vertical projected area of ​​the volume occupied by the finite difference element within the tunnel range;

[0065] The Winkler elastic foundation model assumes that the reaction force of the underlying soil is proportional to the vertical displacement of the soil, specifically expressed as:

[0066] p = k v w(2)

[0067] In equation (2), p is the soil reaction force caused by the vertical displacement of the element; w is the vertical displacement of the finite difference element.

[0068] 4) Calculate the additional loads during shield tunnel construction. The additional loads include buoyancy and anti-buoyancy forces. The buoyancy force includes static buoyancy, dynamic buoyancy, and ground rebound force, specifically expressed as follows:

[0069]

[0070]

[0071]

[0072] In equation (6), q1 is the static buoyancy force; γ f The bulk density of the mixture of slurry and groundwater; γ w q2 is the unit weight of groundwater. In equation (7), q2 is the dynamic buoyancy force. E4 = -f4; q j1 The pressure of the lower slurry bubble; q j2 α1 is the upper bubble pressure; α2 is the lower bubble angle; α3 is the upper bubble angle. In equation (8), q3 is the formation resilience. E6 = 2f5 / L1; γ m R2 is the equivalent unit weight of the stratum; H is the shield excavation radius; H is the distance from the top of the grouting layer to the ground surface; H1 is the height of any soil column at any point on the outer circumference of the grouting layer; H1 = H + R2(1cosα); K0 is the coefficient of earth pressure at rest.

[0073] The buoyancy resistance includes the self-weight of the tunnel segments and ancillary facilities and the overlying soil pressure, and its specific expression is as follows:

[0074]

[0075]

[0076] In equation (6), γ c R1 is the unit weight of the segment concrete; R1 is the outer radius of the tunnel; R0 is the inner radius of the tunnel; Wt0 The total weight of trailers and other ancillary facilities; L t Let K be the length of the trailer. In equation (7), K... s This is the earth lateral pressure coefficient, which is generally taken as 1; c is the internal friction angle of the soil. s For soil cohesion; γ s For soil bulk density; h s q represents the soil layer height. c B is due to ground overload; s Width of the loosened area

[0077] The additional load q can be calculated according to equation (8):

[0078] q=q1+q2+q3+q4+q5 (8)

[0079] 5) Calculate the equivalent longitudinal bending stiffness and equivalent shear stiffness of the shield tunnel. The specific formula for calculating the equivalent longitudinal bending stiffness of the shield tunnel is as follows:

[0080]

[0081]

[0082] In equation (9), K is the longitudinal equivalent bending stiffness of the shield tunnel; E is the neutral axis angle. c The elastic modulus of concrete; I c Let n be the moment of inertia of the shield tunnel cross section. In equation (10), n is the number of longitudinal joint bolts; K r For the longitudinal joint bolt linear stiffness; A c l is the cross-sectional area of ​​the shield tunnel; s This represents the width of one ring segment.

[0083] The specific formula for calculating the longitudinal equivalent shear stiffness of a shield tunnel is as follows:

[0084]

[0085] In equation (11), C is the equivalent longitudinal shear stiffness of the shield tunnel; ξ is the segment contact relationship correction coefficient; κ b and κ c G represents the shear coefficients for the joint bolts and the segments, respectively, and is taken as 0.9 and 0.5; b and G c These are the shear moduli of the joint bolts and the pipe segments, respectively.

[0086] 6) Perform stress analysis on a micro-element of the shield tunnel and establish the model's governing equations. Assume the micro-element, under the action of an additional load q, experiences a vertical displacement w, and the elastic foundation reaction force is p. According to the force equilibrium condition, we can obtain:

[0087] Dpdx-qdx-dQ=0 (12)

[0088]

[0089] In equations (12) and (13), M is the tunnel bending moment, Q is the tunnel shear force, q is the additional load, p is the foundation reaction force, and D is the outer diameter of the shield tunnel.

[0090] The tunnel bending moment and shear force can be calculated using the following formula:

[0091]

[0092]

[0093] In equations (14) and (15), θ is the tunnel turning angle.

[0094] By combining equations (12) to (15), the model control equations can be obtained:

[0095]

[0096] 7) Solve the numerical solution of the governing equations using the finite difference method. Discretize the shield tunnel structure with a total length of L into n intervals, each interval having a length of Δh = L / n. Place two virtual nodes before and after the first and last nodes, for a total of n+5 nodes.

[0097] Based on the central difference formulas of orders 1 to 4, equation (16) can be transformed into:

[0098]

[0099] In equation (17),

[0100] The boundary conditions of the model can be expressed as:

[0101]

[0102] Combining equations (17) and (18), we can obtain n+5 algebraic equations. By solving the n+5 algebraic equations using the iterative method, we can obtain the vertical displacement, rotation angle, bending moment and shear force under the upward action during the shield tunnel construction period.

[0103] It should be understood that those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

Claims

1. Analysis method for longitudinal stress during the construction of a shield tunnel in soft soil, including the following steps: 1) Obtain the relevant parameters required for the calculation; The relevant parameters required for calculation are obtained based on shield tunnel structural design data, geological exploration reports, and shield tunneling records. 2) Divide the shield tunnel into a section where the grout has not solidified and a section where the grout has solidified; the length of the section where the grout has not solidified is L1, and the length of the section where the grout has solidified is L2; ​​the total length of the shield tunnel is L = L1 + L2. 3) Based on the national standard and specification "Design Standard for Shield Tunnel Engineering" (GB / T51438-2021), determine whether the soil under the shield tunnel is soft soil; if it is classified as soft soil, use the Winkler elastic foundation model to simplify the soil under the shield tunnel, simplifying it into several linear grounding springs connected to the shield tunnel. 4) Calculate the additional loads during the shield tunnel construction period; 5) Calculate the equivalent longitudinal bending stiffness and equivalent shear stiffness of the shield tunnel; 6) Perform stress analysis on the micro-element of the shield tunnel and establish the model control equations; 7) Solve the numerical solution of the governing equations using the finite difference method; Step 3) specifically includes: The stiffness of the grounding spring is related to the size of the finite difference element and the subgrade reaction coefficient of the soil beneath the shield tunnel. The specific expression is as follows: k v =k s s (1) In equation (1), k v k is the foundation spring constant. s is the subgrade reaction coefficient, obtained from the geological exploration report; s is the vertical projected area of ​​the volume occupied by the finite difference element within the tunnel range; The Winkler elastic foundation model assumes that the reaction force of the underlying soil is proportional to the vertical displacement of the soil, specifically expressed as: p=k v w (2) In equation (2), p is the soil reaction force caused by the vertical displacement of the element; w is the vertical displacement of the finite difference element; Step 4); specifically includes: the additional load includes buoyancy force and anti-buoyancy force; wherein, the buoyancy force includes static buoyancy force, dynamic buoyancy force and formation rebound force, and the specific expression is: In equation (6), q1 is the static buoyancy force; γ f The bulk density of the mixture of slurry and groundwater; γ w q2 is the unit weight of groundwater; in equation (7), q2 is the dynamic buoyancy force. E4 = -f4; q j1 The pressure of the lower slurry bubble; q j2 α1 is the upper bubble pressure; α2 is the lower bubble angle; α3 is the upper bubble angle; in equation (8), q3 is the formation rebound force. E6 = -2f5 / L1; γ m R1 is the equivalent unit weight of the stratum; R2 is the shield excavation radius; H is the distance from the top of the grouting layer to the ground surface; H1 is the height of the soil column at any point on the outer circumference of the grouting layer; H1 = H + R2(1 - cosα); K0 is the coefficient of earth pressure at rest. The buoyancy resistance includes the self-weight of the tunnel segments and ancillary facilities and the overlying soil pressure, and its specific expression is as follows: In equation (6), γ c R1 is the unit weight of the segment concrete; R1 is the outer radius of the tunnel; R0 is the inner radius of the tunnel; W t0 The total weight of trailers and other ancillary facilities; L t K is the length of the trailer; in equation (7), K s This is the earth lateral pressure coefficient, which is generally taken as 1; c is the internal friction angle of the soil. s For soil cohesion; γ s For soil bulk density; h s q represents the soil layer height. c B is due to ground overload; s Width of the loosened area The additional load q is calculated according to formula (8): q=q1+q2+q3+q4+q5 (8).

2. The method for analyzing the longitudinal stress during the construction of a soft soil shield tunnel as described in claim 1, characterized in that, Step 5); specifically, the formula for calculating the longitudinal equivalent bending stiffness of a shield tunnel is as follows: In equation (9), K is the longitudinal equivalent bending stiffness of the shield tunnel; E is the neutral axis angle. c The elastic modulus of concrete; I c Let n be the moment of inertia of the shield tunnel cross section; in equation (10), n is the number of longitudinal joint bolts; K r For the longitudinal joint bolt linear stiffness; A c l is the cross-sectional area of ​​the shield tunnel; s The width of one ring segment; The specific formula for calculating the longitudinal equivalent shear stiffness of a shield tunnel is as follows: In equation (11), C is the equivalent longitudinal shear stiffness of the shield tunnel; ξ is the segment contact relationship correction coefficient; κ b and κ c G represents the shear coefficients for the joint bolts and the segments, respectively, and is taken as 0.9 and 0.5; b and G c These are the shear moduli of the joint bolts and the pipe segments, respectively.

3. The method for analyzing the longitudinal stress during the construction of a soft soil shield tunnel as described in claim 1, characterized in that, Step 6); specifically includes: assuming the infinitesimal element undergoes a vertical displacement w under the action of an additional load q, and the elastic foundation reaction force is p, then according to the force equilibrium condition, we can obtain: Dpdx-qdx-dQ=0 (12) In equations (12) and (13), M is the tunnel bending moment, Q is the tunnel shear force, q is the additional load, p is the foundation reaction force, and D is the outer diameter of the shield tunnel. The tunnel bending moment and shear force are calculated using the following formula: In equations (14) and (15), θ is the tunnel turning angle; Combining equations (12) to (15), we obtain the model governing equations:

4. The method for analyzing the longitudinal stress during the construction of a soft soil shield tunnel as described in claim 3, characterized in that, Step 7); specifically includes: discretizing the shield tunnel structure with a total length of L into n intervals, the length of each interval being Δh = L / n; and arranging two virtual nodes before and after the first and last nodes respectively, for a total of n+5 nodes; Based on the central difference formulas of orders 1 to 4, equation (16) can be transformed into: In equation (17), The boundary conditions of the model can be expressed as: Combining equations (17) and (18), we can obtain n+5 algebraic equations. By solving the n+5 algebraic equations using the iterative method, we can obtain the vertical displacement, rotation angle, bending moment, and shear force under the upward action during the shield tunnel construction period.

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