Semi-analytical calculation method and system for floating and internal force of shield segment in construction period

Abstract

The invention relates to the technical field of tunnel engineering, and discloses a semi-analytical calculation method and system for floating and internal force of a shield segment in a construction period, and the method comprises the steps: S1, building a numerical model through finite element software, and simulating a shield tunneling construction process; s2, calculating upward buoyancy according to engineering parameters; s3, establishing a deformation differential equation based on the bending equation of the beam, wherein the solution of the deformation differential equation is composed of a special solution of a non-homogeneous equation and a general solution of a homogeneous equation; s4, solving a general solution of a homogeneous equation, fitting an upper buoyancy change form by adopting an n-order polynomial, and substituting the upper buoyancy change form into a non-homogeneous equation to solve a special solution; s5, determining an undetermined coefficient of a differential equation in combination with a boundary condition and a continuity condition, and establishing a calculation method for the instantaneous floating amount of the duct piece under the action of single-time grouting; s6, on the basis of an instantaneous floating amount calculation method under the action of single-time grouting, a segment accumulated floating amount calculation method under the action of continuous grouting is deduced; and S7, according to an accumulated floating amount calculation method, a calculation method of the shearing force, the bending moment and the corner of the duct piece is established.

Description

Technical Field

[0001] The present invention relates to the technical field of tunnel engineering, and particularly relates to a semi-analytical calculation method and system for the floating and internal force of shield segments during construction. Background Art

[0002] With the promotion of the new urbanization strategy, the reconstruction and expansion of urban roads have become an important measure to improve the traffic capacity of urban roads, adapt to the growth of traffic volume and meet the demand for urban roads. Due to its high degree of mechanization and small construction disturbance, the shield method is increasingly widely used in engineering, especially in the construction of cross-river tunnels and urban subways. However, during the shield tunneling process, due to the failure of the slurry to solidify in time, uneven floating occurs when the segment leaves the tail of the shield, resulting in misalignment of the segment. In severe cases, bolt damage and concrete cracking may occur, leading to water seepage in the segment, seriously affecting the stability of the tunnel structure and posing a great hidden danger to construction safety. However, in existing calculations, for the change form of the upward buoyancy force, it is only assumed to be linearly changing, which does not conform to the actual situation. In fact, the change of the upward buoyancy force during the slurry solidification process is a complex process, not just a simple linear decrease. Reasonably calculating and determining the change form of the upward buoyancy force is the top priority for ensuring the accuracy of calculating the floating and mechanical behavior of the segment. It can be seen that the existing calculations of the upward buoyancy force and internal force have problems with poor calculation accuracy. Summary of the Invention

[0003] The present invention provides a semi-analytical calculation method for the floating and internal force of shield segments during construction, including: S1. Establish a numerical model of the segment during the shield tunnel excavation construction process using finite element software, and establish a change form of the upward buoyancy force based on the normal distribution of the upward buoyancy force by combining the simulation results with the test data; S2. Determine the engineering parameters according to the shield tunnel excavation construction, and substitute the engineering parameters into the change form of the upward buoyancy force to calculate the upward buoyancy force received by the segment; S3. Place the segment numerical model on an Euler-Bernoulli beam on a Pasternak foundation, and establish a deformation differential equation based on the bending equation of the beam. The solution of the deformation differential equation consists of a particular solution of the non-homogeneous equation and a general solution of the homogeneous equation; S4. Solve the general solution of the homogeneous equation, fit the change form of the upward buoyancy force using an nth-degree polynomial, and substitute it into the non-homogeneous equation to solve for the particular solution; S5. Determine the undetermined coefficients of the differential equation by combining the boundary conditions and continuity conditions, and establish a calculation method for the instantaneous floating amount of the segment under the action of single grouting based on the undetermined coefficients; S6. Based on the calculation method for the instantaneous floating amount under the action of single grouting, derive a calculation method for the cumulative floating amount of the segment under the action of continuous grouting, and calculate the instantaneous floating amount and cumulative floating amount as the floating amount data of the segment; S7. According to the cumulative floating-up quantity calculation method, further establish the calculation methods for the shear force, bending moment and rotation angle of the segment, and calculate the shear force, bending moment and rotation angle of the segment as the internal force data of the segment.

[0004] Optionally, the establishment of the floating-up force variation form based on the normal distribution of the floating-up force in step S1 includes: Construct a segment numerical model during the shield tunneling construction process through finite element software, and simulate the segment numerical model to obtain the simulation results; Conduct an experiment on the segment during the shield tunneling construction process based on the floating-up force to obtain experimental data; Construct the floating-up force variation form of the normal distribution of the floating-up force according to the simulation results and the experimental data Among them, the floating-up force variation form satisfies the following formula: ; ; In the formula, p 0, p 静态 , p 动态 , p 重力 are respectively the floating-up force per unit length of the segment at the shield tail, the static floating-up force generated by the surrounding slurry, the dynamic floating-up force generated by the synchronous grouting, and the gravity, γ g , γ c are respectively the slurry specific weight and the segment specific weight, r 外 and r 内 are respectively the outer diameter and inner diameter of the segment, P is the synchronous grouting pressure, a is the angle between the grouting pressure and the vertical direction, L 1 is the length of the floating-up section, represents the floating-up force received by the segment, represents the distance from the shield tail, represents the natural logarithm; The calculation of the floating-up force received by the segment in step S2 includes: Obtain the engineering parameters and segment parameters during the shield tunneling construction process, and substitute the engineering parameters and the segment parameters into the floating-up force variation form to calculate the floating-up force received by the segment.

[0005] Optionally, the bending equation of the beam in step S3 is expressed in matrix form and satisfies the following relationship: ; ; ; ; ; In the formula, A is the coefficient matrix, C is the upward floating parameter matrix, T is the boundary condition and continuity condition matrix, L 1 + L 2 = L , L 2, L are the length of the non-upward floating section and the total calculation length, , , , , , , , , , , , , , , , , , , , , , all represent intermediate calculation parameters, represents undetermined coefficients, represents that the segment displacement at the shield tail is 0, represents that the segment shear force at the shield tail is 0, represents the segment upward floating amount at the initial setting point of grouting, represents the segment rotation angle at the initial setting point of grouting, represents the segment bending moment at the initial setting point of grouting, represents the segment shear force at the initial setting point of grouting.

[0006] Optionally, the establishment of the deformation differential equation based on the beam bending equation in step S3 includes: Constructing a deformation differential equation based on the beam bending equation, the buoyancy force on the segment calculated by the form of buoyancy force change, and the relevant parameters of the beam, where the relevant parameters of the beam include: the elastic modulus of the Euler-Bernoulli beam, the section moment of inertia of the Euler-Bernoulli beam, the shear coefficient of the elastic foundation, and the stiffness coefficient of the elastic foundation; Its deformation differential equation satisfies the following relationship: ; ; ; ; ; In the formula, E is the elastic modulus of the homogeneous Euler - Bernoulli beam, I is the moment of inertia of the cross - section of the homogeneous Euler - Bernoulli beam, w is the upward floating amount of the segment, E c 、 I c are the elastic modulus and moment of inertia of the segment concrete, l c is the width of the segment, A c is the area of the concrete on the cross - section of the segment, n is the number of bolts between two adjacent rings, k b is the linear stiffness of the bolt, k b = E b A b / l b , E b is the elastic modulus of the bolt, A b is the cross - sectional area of the bolt, l b is the length of the bolt, E s is the equivalent elastic modulus of the stratum, h 1 is the thickness of the foundation shear layer, D is the tunnel diameter, h is the tunnel burial depth, μ is the Poisson's ratio, k 1、 k 2 are the stiffness coefficients of the corresponding elastic foundations of the two parts, G 1、 G 2 are the shear coefficients of the corresponding elastic foundations of the two parts, G represents the shear coefficient of the elastic foundation, represents the neutral axis angle, represents the distance from the segment tail shield, L 1 is the length of the upward floating section, r 外 、 r 内 are the outer diameter and inner diameter of the segment respectively,γ g and γ c are the slurry unit weight and the segment unit weight respectively, P is the synchronous grouting pressure, and k represents the stiffness coefficient of the elastic foundation.

[0007] Optionally, the solution of the differential equation is: General solution of the non - homogeneous equation: ; Particular solution of the non - homogeneous equation: ; In the formula, T ( x ) is the particular solution, R ( x ) is the general solution; α i and β i are the elastic coefficients, a 0, a 1, a 2, a 3, a 4 are the fitting coefficients of the buoyancy change function, which are determined by the length of the floating section and the buoyancy. When L 1 ≤ x , a 0, a 1, a 2, a 3, a 4 are all 0, represents the undetermined coefficient, represents the undetermined coefficient, represents the undetermined coefficient, represents the undetermined coefficient, E is the elastic modulus of the homogeneous Euler - Bernoulli beam, I is the moment of inertia of the cross - section of the homogeneous Euler - Bernoulli beam, k represents the stiffness coefficient of the elastic foundation, D is the tunnel diameter, G represents the shear coefficient of the elastic foundation, p 0 is the buoyancy force per unit length of the segment at the shield tail.

[0008] Optionally, the boundary conditions in step S5 include: ; where L is the total calculation length, represents the floating amount of the floating section, represents the rotation angle of the floating section, represents the bending moment of the floating section, Denotes the shear force in the upward floating section, Denotes the upward floating amount in the section not subject to upward buoyancy force, Denotes the rotation angle in the section not subject to upward buoyancy force, Denotes the bending moment in the section not subject to upward buoyancy force, Denotes the shear force in the section not subject to upward buoyancy force.

[0009] Optionally, the method for calculating the instantaneous upward floating amount of the segment under single grouting in step S5 includes: Solving for the undetermined coefficients in the differential equation according to the boundary conditions and continuity conditions, and establishing a method for calculating the instantaneous upward floating amount of the segment under single grouting based on the solved undetermined coefficients; The method for calculating the instantaneous upward floating amount of the segment under single grouting satisfies the following relationship: ; The method for deriving the cumulative upward floating amount of the segment under continuous grouting in step S6 includes: According to the method for calculating the instantaneous upward floating amount of the segment under single grouting, accumulating the instantaneous upward floating amount to derive the method for calculating the cumulative upward floating amount of the segment under continuous grouting; The method for calculating the cumulative upward floating amount of the segment under continuous grouting satisfies the following relationship: ; In the formula, Is the instantaneous upward floating amount of the i-th grouting, Is the cumulative upward floating amount of the i-th grouting, w 1( x ) and w 2( x ) are the expressions of the instantaneous upward floating amount in the buoyant section and the non-buoyant section, respectively.

[0010] Optionally, the shear force, bending moment, and rotation angle in step S7 are calculated by the following formulas: ; In the formula, Q is the shear force, M is the bending moment, and φ is the rotation angle.

[0011] Optionally, the finite element software in step S1 is Abaqus, and the thickness of the foundation shear layer in the numerical model satisfies: ; In the formula, Is the thickness of the foundation shear layer, and D is the tunnel diameter.

[0012] In a second aspect, an embodiment of the present application provides a semi-analytical calculation system for the upward floating and internal forces of a shield segment during construction, including a processor and a memory; The memory is used to store a computer program; A processor, when executing a program stored in a memory, implements the method steps described in any one of the first aspects.

[0013] Beneficial effects: The semi-analytical calculation method for the floating and internal forces of shield segments during the construction period provided by the present invention analyzes the influence of shield burial depth, grouting pressure, formation elastic modulus, and slurry setting time on the floating and internal forces of segments. The present invention considers a more reasonable form of buoyancy change, can calculate the floating and internal forces of shield segments during the construction period more accurately, improves the accuracy of the ultimate support pressure. At the same time, based on the established segment floating model, considering the shear deformation of the soil makes the calculation more accurate. Description of the drawings

[0014] Figure 1 It is the calculation flow chart of the semi-analytical calculation method for the floating and internal forces of shield segments during the construction period; Figure 2 It is the force model of the segment when it detaches from the shield tail; Figure 3 It is the segment force result in the numerical simulation; Figure 4 It is the fitting of the segment force result in the numerical simulation; Figure 5 It is the change form of the slurry in the existing experimental research; Figure 6 It is the comparison between the calculation of the present invention and the measured results. Specific embodiments

[0015] The technical solutions of the present invention will be described clearly and completely below. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without making creative efforts belong to the scope of protection of the present invention.

[0016] Unless otherwise defined, the technical terms or scientific terms used in the present invention should have the ordinary meaning understood by those of ordinary skill in the art in the field to which the present invention belongs. The "first", "second" and similar terms used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. Similarly, the terms such as "a" or "one" do not indicate a quantity limit, but indicate that there is at least one. The terms such as "connected" or "coupled" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. The terms such as "up", "down", "left", "right" are only used to represent relative positional relationships. When the absolute position of the object being described changes, the relative positional relationship also changes accordingly.

[0017] Please refer to Figures 1-5, an embodiment of the present application provides a semi-analytical calculation method for the floating and internal forces of shield segments during construction, including: Step 1: Establish a numerical model using Abaqus finite element software to simulate the construction process: excavation - shield installation and removal - activation of slurry (initial setting), segment installation - slurry (final setting). Based on the buoyancy force on the segment in the simulation results and combined with existing test results, establish a buoyancy force variation form based on the normal distribution of the buoyancy force. Calculate the buoyancy force and related parameters of the formation and shield tunneling according to the engineering parameters; Step 2: Consider the segment as an Euler-Bernoulli beam placed on a Pasternak foundation beam, and establish a deformation differential equation according to the bending equation of the beam, as Figure 1 shown. The solution of the established differential equation consists of a particular solution of the non-homogeneous equation and a general solution of the homogeneous equation; (1) For the floating section, considering that the slurry is not completely solidified, assume k 1. G 1 increases linearly from the shield tail to the initial setting point. Therefore, the elastic foundation parameter of the buoyancy section is taken as 1 / 2 of the elastic foundation parameter of the non-buoyancy section, G 2 = 2 G 1. k 2 = 2 k 1.

[0018] (2) (3) Step 3: Solve the general solution and particular solution of the differential equation. Solve the general solution of the homogeneous equation: (4) Fit the buoyancy force to obtain the expression form of the buoyancy force n of the nth-degree polynomial: (5) Solve the non-homogeneous differential equation to obtain the particular solution expression: (6) Obtain the floating edge expression: (7) Step 4: Solve the undetermined coefficients in the differential equation according to the boundary conditions and continuity conditions, and establish a calculation method for the instantaneous floating amount of the segment under the action of single grouting; (8) (9) (10) (11) (12) (13) Step Five: According to the calculation method of the instantaneous floating amount of the segment under single grouting, establish the calculation method of the cumulative floating amount of the segment under continuous grouting; (14) (15) Step Six: According to the calculation method of the cumulative floating amount of the segment under continuous grouting, establish the calculation methods of shear force, bending moment and rotation angle.

[0019] (16) Step Seven: According to the calculation method of the present invention, the relationship functions between the segment floating and internal forces and the buried depth, grouting pressure, formation elastic modulus, and slurry setting time can be established, and the variation laws of the segment floating and internal forces can be determined.

[0020] In order to enable those skilled in the art to better understand the solution of the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative efforts shall fall within the protection scope of the present invention.

[0021] In the embodiment of the present invention, a certain shield tunnel on a coastal expressway is taken as an example. Taking the segments from ring 900 to ring 1000 of the tunnel as an example, the calculation parameters involved are listed in Table 1 as follows.

[0022] Table 1

[0023] The buoyancy force on the segment is: (17) (18) (19) (20) (21) Performing fitting on the buoyancy force gives (22) Establish the bending equation of the beam (23) The general solution of the differential equation of beam bending (24) Particular solution of the differential equation for beam bending (25) Expression for the floating up of segment (26) Boundary conditions and continuity conditions: (27) Expressed in the form of a matrix as follows: (28) (29) (30) (31) (32) Program and solve, draw the comparison diagram between the calculation of the present invention and the actual measurement, as Figure 6 shown. The final floating up amount of the segment obtained by the calculation method of the present invention is 54 mm, and the on-site monitoring data is 44 - 59 mm. The difference between the two is small. It can be considered that the calculation method of the present invention can predict the floating up amount of the shield tail segment during the construction period, and provide a reference for the selection of construction parameters of the shield tunnel and the prediction and control of the floating up of the segment.

[0024] The embodiment of the present application further provides a semi-analytical calculation system for the floating up and internal force of the shield segment during the construction period, including a processor and a memory; The memory is used to store a computer program; The processor, when executing the program stored on the memory, realizes any of the method steps in the semi-analytical calculation method for the floating up and internal force of the shield segment during the construction period.

[0025] The above semi-analytical calculation system for the floating up and internal force of the shield segment during the construction period can implement each embodiment of the above semi-analytical calculation method for the floating up and internal force of the shield segment during the construction period, and can achieve the same beneficial effects. Here, it will not be elaborated.

[0026] The preferred specific embodiments of the present invention have been described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and variations according to the concept of the present invention without creative efforts. Therefore, all technical solutions that can be obtained by those skilled in the art in the technical field based on the concept of the present invention through logical analysis, reasoning or limited experiments on the basis of the prior art should be within the protection scope determined by the claims.

Claims

1. A semi-analytical calculation method for the floating and internal forces of shield segments during construction period, characterized in that Including: S1. Establish a segment numerical model for the shield tunnel excavation construction process using finite element software, and establish the buoyancy change form based on the normal distribution of buoyancy by combining the simulation results with the test data; S2. Determine the engineering parameters according to the shield tunnel excavation construction, and substitute the engineering parameters into the buoyancy change form to calculate the buoyancy force on the segment; S3. Place the segment numerical model on the Euler-Bernoulli beam on the Pasternak foundation, and establish the deformation differential equation based on the bending equation of the beam. The solution of the deformation differential equation consists of the particular solution of the non-homogeneous equation and the general solution of the homogeneous equation; S4. Solve the general solution of the homogeneous equation, fit the change form of the buoyancy force with an n-degree polynomial, and substitute it into the non-homogeneous equation to solve the particular solution; S5. Determine the undetermined coefficients of the differential equation in combination with the boundary conditions and continuity conditions, and establish a calculation method for the instantaneous floating amount of the segment under single grouting based on the determined undetermined coefficients; S6. Based on the calculation method for the instantaneous floating amount under single grouting, deduce the calculation method for the cumulative floating amount of the segment under continuous grouting, and calculate the instantaneous floating amount and the cumulative floating amount as the floating amount data of the segment; S7. According to the calculation method for the cumulative floating amount, further establish the calculation methods for the shear force, bending moment and rotation angle of the segment, and calculate the shear force, bending moment and rotation angle of the segment as the internal force data of the segment.

2. The semi-analytical calculation method for the floating and internal forces of shield segments during construction according to claim 1, characterized in that The establishment of the buoyancy change form based on the normal distribution of buoyancy in step S1 includes: Construct a segment numerical model for the shield tunnel excavation construction process through finite element software, and perform simulation on the segment numerical model to obtain the simulation results; Conduct tests on the segments during the shield tunnel excavation construction process based on buoyancy to obtain test data; Construct the buoyancy change form of the normal distribution of buoyancy according to the simulation results and the test data Among them, the buoyancy change form satisfies the following formula: ； ； Wherein, p 0, p 静态 , p 动态 , p 重力 are respectively the upward buoyancy force per unit length of the segment at the shield tail, the static upward buoyancy force generated by the surrounding of the grout, the dynamic upward buoyancy force generated by the simultaneous grouting, and the gravity; γ g , γ c are respectively the unit weight of the grout and the unit weight of the segment; r 外 and r 内 are respectively the outer diameter and the inner diameter of the segment; P is the simultaneous grouting pressure; a is the angle between the grouting pressure and the vertical direction; L 1 is the length of the upward floating section; represents the upward buoyancy force on the segment; represents the distance from the shield tail; represents the natural logarithm; The calculation of the buoyancy force on the segment in step S2 includes: Obtain the engineering parameters and segment parameters during the shield tunnel excavation construction process, and substitute the engineering parameters and the segment parameters into the buoyancy change form to calculate the buoyancy force on the segment.

3. The semi-analytical calculation method for the floating and internal force of shield segments during the construction period according to claim 1, wherein The bending equation of the beam in step S3 is expressed in matrix form and satisfies the following relationship: ； ； ； ； ； In the formula, A is the coefficient matrix, C is the floating-up parameter matrix, T is the boundary condition and continuity condition matrix, L 1 + L 2 = L , L 2, L are the lengths of the non-floating-up section and the total calculation length, , , , , , , , , , , , , , , , , , , , , , all represent intermediate calculation parameters, represents undetermined coefficients, represents that the segment displacement at the shield tail is 0, represents that the segment shear force at the shield tail is 0, represents the segment floating-up amount at the initial setting point of grouting, represents the segment rotation angle at the initial setting point of grouting, represents the segment bending moment at the initial setting point of grouting, represents the segment shear force at the initial setting point of grouting.

4. The semi-analytical calculation method for the floating and internal force of shield segments during construction according to claim 1, wherein The establishment of the deformation differential equation based on the bending equation of the beam in step S3 includes: Construct a deformation differential equation based on the bending equation of the beam, the buoyancy force on the segment calculated through the buoyancy change form, and the relevant parameters of the beam. Among them, the relevant parameters of the beam include: the elastic modulus of the Euler-Bernoulli beam, the section moment of inertia of the Euler-Bernoulli beam, the shear coefficient of the elastic foundation, and the stiffness coefficient of the elastic foundation; Its deformation differential equation satisfies the following relationship: ； ； ； ； ； Wherein, E is the elastic modulus of the homogeneous Euler-Bernoulli beam, I is the moment of inertia of the cross-section of the homogeneous Euler-Bernoulli beam, w is the uplift of the segment, E c 、 I c are the elastic modulus and moment of inertia of the segment concrete, l c is the width of the segment, A c is the area of the concrete on the cross-section of the segment, n is the number of bolts between two adjacent rings, k b is the linear stiffness of the bolt, k b = E b A b / l b , E b is the elastic modulus of the bolt, A b is the cross-sectional area of the bolt, l b is the length of the bolt, E s is the equivalent elastic modulus of the formation, h 1 is the thickness of the foundation shear layer, D is the tunnel diameter, h is the tunnel burial depth, μ is the Poisson's ratio, k 1、 k 2 are the stiffness coefficients of the corresponding elastic foundations of the two parts, G 1、 G 2 are the shear coefficients of the corresponding elastic foundations of the two parts, G represents the shear coefficient of the elastic foundation, represents the neutral axis angle, represents the distance from the segment tail shield, L 1 is the length of the uplift section, r 外 、 r 内 are the outer diameter and inner diameter of the segment respectively, γ g 、 γ c are the slurry unit weight and segment unit weight respectively, P is the synchronous grouting pressure, and k represents the stiffness coefficient of the elastic foundation.

5. The semi-analytical calculation method for the floating and internal forces of shield segments during construction according to claim 4, characterized in that, The solution of the differential equation is: General solution of the non-homogeneous equation: ； Particular solution of the non-homogeneous equation: ； wherein, T ( x ) is a particular solution, R ( x ) is the general solution; α i and β i are elastic coefficients, a 0, a 1, a 2, a 3, a 4 are fitting coefficients of the buoyancy change function, which are determined by the length of the floating section and the buoyancy. When L 1 ≤ x , a 0, a 1, a 2, a 3, a 4 are all 0, represents an undetermined coefficient, represents an undetermined coefficient, represents an undetermined coefficient, represents an undetermined coefficient, E is the elastic modulus of the homogeneous Euler - Bernoulli beam, I is the cross - sectional moment of inertia of the homogeneous Euler - Bernoulli beam, k represents the stiffness coefficient of the elastic foundation, D is the tunnel diameter, G represents the shear coefficient of the elastic foundation, p 0 is the buoyancy force per unit length of the segment at the shield tail.

6. The semi-analytical calculation method for the floating and internal force of shield segments during construction according to claim 1, characterized in that, The boundary conditions in step S5 include: ； where, L is the total calculation length, represents the upward displacement of the upward floating section, represents the rotation angle of the upward floating section, represents the bending moment of the upward floating section, represents the shear force of the upward floating section, represents the upward displacement of the section not subject to upward buoyancy force, represents the rotation angle of the section not subject to upward buoyancy force, represents the bending moment of the section not subject to upward buoyancy force, represents the shear force of the section not subject to upward buoyancy force.

7. The semi-analytical calculation method for the floating and internal force of the shield segment during the construction period according to claim 1, characterized in that, The establishment of the calculation method for the instantaneous floating amount of the segment under single grouting in step S5 includes: Solve the undetermined coefficients in the differential equation according to the boundary conditions and continuity conditions, and establish a calculation method for the instantaneous floating amount of the segment under single grouting based on the solved undetermined coefficients; The calculation method for the instantaneous floating amount of the segment under a single grouting injection satisfies the following relational expression: ； The derivation of the calculation method for the cumulative floating amount of the segment under continuous grouting injection in step S6 includes: According to the calculation method for the instantaneous floating amount of the segment under a single grouting injection, accumulate the instantaneous floating amount to derive the calculation method for the cumulative floating amount of the segment under continuous grouting injection; The calculation method for the cumulative floating amount of the segment under continuous grouting injection satisfies the following relational expression: ； Wherein, is the instantaneous floating amount of the i-th grouting, is the cumulative floating amount of the i-th grouting, w 1( x ) and w 2( x ) are the expressions of the instantaneous floating amount located in the buoyant section and the non-buoyant section respectively, l c is the width of the segment, n is the number of bolts between two adjacent rings, represents the distance from the segment tail shield.

8. The semi-analytical calculation method for the floating and internal forces of shield segments during construction according to claim 1, characterized in that, The shear force, bending moment and rotation angle in step S7 are calculated by the following formulas: ； In the formula, Q is the shear force, M is the bending moment, and φ is the rotation angle.

9. The semi-analytical calculation method for the floating and internal force of shield segments during construction according to claim 1, characterized in that, The finite element software in step S1 is Abaqus, and the thickness of the foundation shear layer in the numerical model satisfies: ； wherein, the thickness of the foundation shear layer, and D is the tunnel diameter.

10. A semi-analytical calculation system for the floating and internal forces of shield segments during construction period, characterized in that, Comprising a processor and a memory; The memory is used for storing computer programs; The processor is used for implementing the method steps described in any one of claims 1-9 when executing the programs stored on the memory.

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