A semi-analytical calculation method and system for shield segment floating and internal force during construction

Abstract

The application relates to the technical field of tunnel engineering, and discloses a semi-analytical calculation method and system for the floating of a shield segment during construction and internal force, which comprises the following steps: S1, a numerical model is established by using finite element software to simulate the shield tunneling construction process; S2, the floating force is calculated according to engineering parameters; S3, a deformation differential equation is established based on the bending equation of a beam, and the solution of the deformation differential equation is composed of a particular solution of a non-homogeneous equation and a general solution of a homogeneous equation; S4, the general solution of the homogeneous equation is solved, an n-order polynomial is used to fit the change form of the floating force, and the particular solution of the non-homogeneous equation is solved by substituting the non-homogeneous equation; S5, the undetermined coefficients of the differential equation are determined in combination with boundary conditions and continuity conditions, and a calculation method for the instantaneous floating amount of the segment under the action of single grouting is established; S6, based on the calculation method for the instantaneous floating amount of the segment under the action of single grouting, a calculation method for the cumulative floating amount of the segment under the action of continuous grouting is derived; and S7, according to the calculation method for the cumulative floating amount, a calculation method for the shear force, bending moment and rotation angle of the segment is established.

Description

TECHNICAL FIELD

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

[0002] With the promotion of new urbanization strategy, urban road reconstruction has become an important measure to improve urban road traffic capacity, adapt to traffic growth and meet the demand of urban road. Shield method is widely used in engineering due to its high degree of mechanization and small construction disturbance, especially in cross-river tunnel and urban subway construction. However, during shield tunneling, due to the failure of slurry to solidify in time, uneven floating of segments occurs when the segments are separated from the shield tail, causing misalignment of the segments, which can cause bolt damage and concrete cracking, resulting in segment water seepage, which seriously affects the stability of the tunnel structure and poses a great risk to construction safety. However, in the existing calculation, the change form of the floating force is only assumed to be linear, which does not conform to the actual situation. In fact, the change of the floating force during slurry solidification is a complex process, not just a simple linear decrease. Reasonably calculating and determining the change form of the floating force is the most important thing to ensure the accuracy of the calculation of segment floating and mechanical behavior. Therefore, the existing calculation of floating force and internal force has the problem of poor calculation accuracy. SUMMARY

[0003] The present application provides a semi-analytical calculation method for shield segment floating and internal force during construction, comprising:

[0004] S1, a segment numerical model of shield tunneling construction process is established by using finite element software, and a change form of floating force based on normal distribution of floating force is established combined with simulation results and test data;

[0005] S2, engineering parameters are determined according to shield tunneling construction, and the engineering parameters are substituted into the floating force change form to calculate the floating force on the segment;

[0006] S3, the segment numerical model is placed on the Euler-Bernoulli beam of the Pasternak foundation, and a deformation differential equation is established based on the bending equation of the beam, and the solution of the deformation differential equation is composed of the particular solution of the non-homogeneous equation and the general solution of the homogeneous equation;

[0007] S4, the general solution of the homogeneous equation is solved, the change form of the floating force is fitted by using an n-th order polynomial, and the particular solution is solved by substituting the non-homogeneous equation;

[0008] S5, the undetermined coefficients of the differential equation are determined combined with the boundary conditions and continuity conditions, and a segment instantaneous floating amount calculation method under single grouting action is established based on the undetermined coefficients;

[0009] S6, based on the single grouting under the instantaneous uplift amount calculation method, deduce the cumulative uplift amount calculation method under the sustained grouting effect, and calculate the instantaneous uplift amount and the cumulative uplift amount as the pipe piece uplift amount data;

[0010] S7, according to the cumulative uplift amount calculation method, further establish the calculation method of the shear force, bending moment and rotation angle of the pipe piece, and calculate the shear force, bending moment and rotation angle of the pipe piece as the internal force data of the pipe piece.

[0011] Optionally, the step S1 of establishing the uplift force change form based on the uplift force normal distribution comprises:

[0012] A numerical model of the pipe piece in the shield tunneling construction process is constructed by using a finite element software, and a simulation result is obtained by simulating the numerical model of the pipe piece;

[0013] The pipe piece in the shield tunneling construction process is tested based on the uplift force to obtain test data;

[0014] According to the simulation result and the test data, the uplift force change form of the uplift force normal distribution is constructed

[0015] The uplift force change form satisfies the following formula:

[0016] ;

[0017] ;

[0018] In the formula, p 0、 p 静态 、 p 动态 、 p 重力 The uplift force, the static uplift force generated by the grout surrounding, the dynamic uplift force generated by the synchronous grouting, and the gravity of the unit length of the shield tail pipe piece are respectively, γ g 、 γ c The grout bulk density and the pipe piece bulk density are respectively, r 外 And r 内 The outer diameter and the inner diameter of the pipe piece are respectively, P The synchronous grouting pressure, a The angle between the grouting pressure and the vertical direction, L 1 is the length of the uplift section, Indicates the uplift force on the pipe piece, Indicates the distance from the shield tail, Indicates the natural logarithm;

[0019] The step S2 includes:

[0020] The engineering parameters and the segment parameters of the shield tunneling construction process are obtained, and the engineering parameters and the segment parameters are substituted into the floating force variation form to calculate the floating force of the segment.

[0021] Optionally, the bending equation of the beam in the step S3 is expressed in a matrix form and satisfies the following relationship:

[0022] ;

[0023] ;

[0024] ;

[0025] ;

[0026] ;

[0027] In the formula, [ A ] is a coefficient matrix, [ C ] is a floating parameter matrix, [ T ] is a boundary condition and continuity condition matrix, L 1+ L 2= L , L 2、 L is the non-floating segment length, and the total length is calculated, 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 all represent intermediate calculation parameters, represents an undetermined coefficient,、 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 amount at the initial setting point of grouting, represents the segment rotation angle at the initial setting point of grouting, The bending moment of the segment at the point of initial setting of the grouting, The shear force of the segment at the point of initial setting of the grouting.

[0028] Optionally, the step S3 of establishing the deformation differential equation based on the bending equation of the beam comprises:

[0029] The deformation differential equation is constructed based on the bending equation of the beam, the buoyancy of the segment calculated by the change form of the buoyancy, and the relevant parameters of the beam, wherein the relevant parameters of the beam include the elastic modulus of the Euler-Bernoulli beam, the sectional moment of inertia of the Euler-Bernoulli beam, the shear coefficient of the elastic foundation, and the stiffness coefficient of the elastic foundation.

[0030] The deformation differential equation satisfies the following relationship:

[0031] ;

[0032] ;

[0033] ;

[0034] ;

[0035] ;

[0036] In the formula, E E is the elastic modulus of the homogeneous Euler-Bernoulli beam, I I is the sectional moment of inertia of the homogeneous Euler-Bernoulli beam, w H is the buoyancy of the segment, E c 、 I c E' and I' are the elastic modulus and the moment of inertia of the segment concrete, l c B is the width of the segment, A c A is the area of the segment concrete in the cross section, n N is the number of bolts between two adjacent rings, k b K is the linear stiffness of the bolt, k b = E b A b / l b , E b E' is the elastic modulus of the bolt, A b A' is the sectional area of the bolt,l b L is the bolt length, E s E is the equivalent elastic modulus of stratum, h 1 is the thickness of the shear layer of the foundation, D D is the diameter of the tunnel, h H is the buried depth of the tunnel, μ v is the Poisson's ratio, k 1, k 2 is the stiffness coefficient of the two-part corresponding elastic foundation, G 1, G 2 is the shear coefficient of the two-part corresponding elastic foundation, G C is the shear coefficient of the elastic foundation, θ is the angle of the neutral axis, S is the distance from the shield tail to the segment, L 1 is the length of the floating section, r 外 , r 内 D1 and D2 are the outer diameter and the inner diameter of the segment respectively, γ g , γ c ρ1 and ρ2 are the bulk density of the slurry and the segment respectively, P P is the synchronous grouting pressure, and k is the stiffness coefficient of the elastic foundation.

[0037] Optionally, the solution of the differential equation is:

[0038] The general solution of the non-homogeneous equation is:

[0039] ;

[0040] The particular solution of the non-homogeneous equation is:

[0041] ;

[0042] In the formula, T (1) is the particular solution, x (2) is the general solution; R x α i , β i E is the elastic coefficient, a 0, a 1, a 2, a 3, a 4 are the fitting coefficients of the floating force change function, which are determined by the length of the floating section and the floating force, and when L 1≤ x , a 0, a 1,​​a 2、 a 3、 a 4 are 0, denote undetermined coefficients, denote undetermined coefficients, denote undetermined coefficients, denote undetermined coefficients, 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, and k represents the stiffness coefficient of the elastic foundation, D is the diameter of the tunnel, G denotes the shear coefficient of the elastic foundation, p 0 is the buoyant force per unit length on the tail segment.

[0043] Optionally, the boundary conditions in the step S5 include:

[0044] ;

[0045] wherein L is the total length of calculation, denotes the amount of floating of the floating segment, denotes the rotation angle of the floating segment, denotes the bending moment of the floating segment, denotes the shear force of the floating segment, denotes the amount of floating of the segment not subjected to the buoyant force, denotes the rotation angle of the segment not subjected to the buoyant force, denotes the bending moment of the segment not subjected to the buoyant force, denotes the shear force of the segment not subjected to the buoyant force.

[0046] Optionally, the step S5 includes establishing a method for calculating the instantaneous amount of floating of the segment under the action of single grouting.

[0047] The undetermined coefficients in the differential equation are solved according to the boundary conditions and the continuity conditions, and a method for calculating the instantaneous amount of floating of the segment under the action of single grouting is established based on the solved undetermined coefficients.

[0048] The method for calculating the instantaneous amount of floating of the segment under the action of single grouting satisfies the following relationship:

[0049] ;

[0050] The step S6 includes deriving a method for calculating the cumulative amount of floating of the segment under the action of continuous grouting.

[0051] The method for calculating the cumulative amount of floating of the segment under the action of continuous grouting is derived by accumulating the instantaneous amount of floating according to the method for calculating the instantaneous amount of floating of the segment under the action of single grouting.

[0052] The calculation method for the cumulative uplift of the tunnel segments under continuous grouting satisfies the following relationship:

[0053] ;

[0054] In the formula, Let i be the instantaneous upward displacement during the i-th grouting. Let i be the cumulative float of the i-th grouting. w 1( x ), w 2( x ) are the instantaneous buoyancy expressions for the buoyant and non-buoyant sections, respectively.

[0055] Optionally, the shear force, bending moment, and rotation angle in step S7 are calculated using the following formulas:

[0056] ;

[0057] In the formula, Q is the shear force, M is the bending moment, and φ is the rotation angle.

[0058] Optionally, the finite element software in step S1 is Abaqus, and the thickness of the foundation shear layer in the numerical model satisfies:

[0059] ;

[0060] In the formula, The thickness of the foundation shear layer, where D is the tunnel diameter.

[0061] Secondly, embodiments of this application provide a semi-analytical calculation system for the uplift and internal forces of tunnel segments during construction, including a processor and a memory;

[0062] Memory, used to store computer programs;

[0063] When a processor executes a program stored in memory, it implements any of the steps of the method described in the first aspect.

[0064] Beneficial effects:

[0065] The semi-analytical calculation method for shield tunnel segment uplift and internal forces provided by this invention analyzes the influence of shield burial depth, grouting pressure, ground elastic modulus, and grout setting time on segment uplift and internal forces. This invention considers a more reasonable form of uplift force variation, enabling more accurate calculation of shield tunnel segment uplift and internal forces during construction, and improving the accuracy of ultimate support pressure. At the same time, based on the constructed segment uplift model, the shear deformation of the soil is considered, making the calculation more accurate. Attached Figure Description

[0066] Figure 1The flow chart of the semi-analytical calculation method for the floating of the shield segment and the internal force during construction period is provided.

[0067] Figure 2 The stress model of the segment separated from the shield tail is provided.

[0068] Figure 3 The stress result of the segment in the numerical simulation is provided.

[0069] Figure 4 The stress result of the segment in the numerical simulation is provided.

[0070] Figure 5 The change form of the slurry in the existing test research is provided.

[0071] Figure 6 The calculation and the measured results are compared. DETAILED DESCRIPTION

[0072] The technical solutions of the present application will be described clearly and completely below, obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all the other embodiments obtained by those skilled in the art without creative labor belong to the protection scope of the present application.

[0073] Unless otherwise defined, the technical terms or scientific terms used in the present application should be understood as the general meanings understood by those skilled in the art in the field of the present application. The terms "first", "second" and similar terms used in the present application do not represent any order, number or importance, but are only used to distinguish different components. Similarly, the terms "one" or "a" and similar terms do not represent a number limitation, but represent the existence of at least one. The terms "connected" or "connected" and similar terms are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. The terms "up", "down", "left", "right" and the like are only used to represent relative positional relationships, when the absolute positions of the described objects are changed, the relative positional relationships are also changed accordingly.

[0074] Please refer to Figures 1-5 The embodiment of the present application provides a semi-analytical calculation method for the floating of the shield segment and the internal force during construction period, comprising:

[0075] Step 1: a numerical model is established by using Abaqus finite element software, the construction process: excavation-shield shell installation and removal-activation of slurry (initial setting), segment installation-slurry (final setting) is simulated, according to the floating force of the segment in the simulation result, and combining with the existing test results, the change form of the floating force based on the normal distribution of the floating force is established. According to the engineering parameters, the floating force and the stratum and shield tunneling related parameters are calculated.

[0076] Step two: The segment is regarded as an Euler-Bernoulli beam placed on a Pasternak foundation beam. According to the bending equation of the beam, as shown in Figure 1 , the differential equation of deformation is established. The solution of the established differential equation is composed of the particular solution of the non-homogeneous equation and the general solution of the homogeneous equation.

[0077] (1)

[0078] For the floating segment, considering the incomplete solidification of the slurry, it is assumed that k 1、 G 1The linear increase from the shield tail to the initial setting point, therefore, the elastic foundation parameters of the floating segment are taken as 1 / 2 of the non-floating segment elastic foundation parameters, G 2=2 G 1、 k 2=2 k 1.

[0079] (2)

[0080] (3)

[0081] Step three: Solve the general solution and particular solution of the differential equation, and solve the general solution of the homogeneous equation:

[0082] (4)

[0083] Fit the upper floating force to obtain the expression form of the upper floating force n quadratic polynomial:

[0084] (5)

[0085] Solve the non-homogeneous differential equation to obtain the particular solution expression:

[0086] (6)

[0087] Get the expression of the upper floating edge:

[0088] (7)

[0089] Step four: According to the boundary conditions and continuity conditions, solve the undetermined coefficients in the differential equation, and establish the calculation method of the instantaneous floating amount of the segment under the action of single grouting;

[0090] (8)

[0091] (9)

[0092] (10)

[0093] (11)

[0094] (12)

[0095] (13)

[0096] Step five: according to the calculation method of the instantaneous pipe piece floating amount under the single grouting action, the calculation method of the cumulative pipe piece floating amount under the continuous grouting action is established;

[0097] (14)

[0098] (15)

[0099] Step six: according to the calculation method of the cumulative pipe piece floating amount under the continuous grouting action, the calculation method of the shear force, bending moment and rotation angle is established.

[0100] (16)

[0101] Step seven: according to the calculation method of the application, the relationship function of the pipe piece floating and internal force and the buried depth, grouting pressure, stratum elastic modulus and slurry setting time can be established, and the change law of the pipe piece floating and internal force can be determined.

[0102] In order for those skilled in the art to better understand the application scheme, the technical solutions in the embodiments of the application will be described clearly and completely in conjunction with the drawings in the embodiments of the application. Obviously, the described embodiments are only a part of the embodiments of the application, not all the embodiments. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative labor should belong to the scope of protection of the application.

[0103] In the embodiments of the application, a certain shield tunnel of a certain section of coastal highway is taken as an example, and the tunnel 900 ring-1000 ring pipe piece is taken as an example, and the calculation parameters involved are listed as shown in Table 1.

[0104] Table 1

[0105]

[0106] The pipe piece floating force is:

[0107] (17)

[0108] (18)

[0109] (19)

[0110] (20)

[0111] (twenty one)

[0112] Fitting the buoyancy force has

[0113] (twenty two)

[0114] Establish the bending equation of the beam

[0115] (twenty three)

[0116] General solution of the differential equation for beam bending

[0117] (twenty four)

[0118] Particular solution of the differential equation for beam bending

[0119] (25)

[0120] Segment floating expression

[0121] (26)

[0122] Boundary conditions and continuity conditions:

[0123] (27)

[0124] Expressed in matrix form as follows:

[0125] (28)

[0126] (29)

[0127] (30)

[0128] (31)

[0129] (32)

[0130] Program and solve the problem, then plot a comparison graph of the calculated and measured results of this invention, such as... Figure 6 As shown, the final uplift of the tunnel segment calculated by the method of this invention is 54 mm, while the field monitoring data is 44-59 mm. The difference between the two is small, so it can be considered that the calculation method of this invention can predict the uplift of the shield tail segment during the construction period, providing a reference for the selection of shield tunnel construction parameters and the prediction and control of segment uplift.

[0131] This application also provides a semi-analytical calculation system for the uplift and internal forces of tunnel segments during construction, including a processor and a memory;

[0132] a memory for storing a computer program;

[0133] a processor for implementing the method steps of any one of the semi-analytical calculation methods of the shield segment floating and internal force during construction when executing the program stored on the memory.

[0134] The semi-analytical calculation system of the shield segment floating and internal force during construction described above can implement each embodiment of the semi-analytical calculation method of the shield segment floating and internal force during construction described above and achieve the same beneficial effects, and thus will not be described here in detail.

[0135] The preferred embodiments of the present application are described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and changes without requiring creative efforts based on the concept of the present application. Therefore, any technical solutions obtained by logical analysis, reasoning or limited experiments based on the prior art according to the concept of the present application shall be within the protection scope defined by the claims.

Claims

1. A semi-analytical method for calculating the floating and internal forces of a shield segment during construction, characterized in that, The method comprises the following steps: S1, establishing a segment numerical model of a shield tunneling construction process by using a finite element software, and establishing a floating force variation form based on a normal distribution of the floating force according to simulation results and test data; S2, determining engineering parameters according to the shield tunneling construction, and calculating the floating force acting on the segment by substituting the engineering parameters into the floating force variation form; S3, placing the segment numerical model on an Euler-Bernoulli beam on a Pasternak foundation, and 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 particular solution of a non-homogeneous equation and a general solution of a homogeneous equation; S4, solving the general solution of the homogeneous equation, fitting the variation form of the floating force by using an n-order polynomial, and substituting the n-order polynomial into the non-homogeneous equation to solve the particular solution; S5, determining the undetermined coefficients of the differential equation according to boundary conditions and continuity conditions, and establishing a segment instantaneous floating amount calculation method under single grouting action based on the undetermined coefficients; S6, deriving a segment cumulative floating amount calculation method under continuous grouting action based on the segment instantaneous floating amount calculation method under single grouting action, and calculating the instantaneous floating amount and the cumulative floating amount as the floating amount data of the segment; S7, further establishing a segment shear force, bending moment and rotation angle calculation method according to the cumulative floating amount calculation method, and calculating the segment shear force, bending moment and rotation angle as the internal force data of the segment; The step S1 of establishing the floating force variation form based on the normal distribution of the floating force comprises: constructing a segment numerical model in the shield tunneling construction process by using a finite element software, and obtaining simulation results by simulating the segment numerical model; conducting a test based on the floating force on the segment in the shield tunneling construction process to obtain test data; constructing the floating force variation form based on the normal distribution of the floating force according to the simulation results and the test data wherein the floating force variation form satisfies the following formula: ； ； wherein, p 0, p 静态 , p 动态 , p 重力 are the buoyancy force, the static buoyancy force caused by the slurry surrounding, the dynamic buoyancy force caused by simultaneous grouting, the gravity, respectively, γ g , γ c are the slurry bulk density, the segment bulk density, respectively, r 外 and r 内 are the outer diameter and the inner diameter of the segment, respectively, P is the simultaneous grouting pressure, a is the angle between the grouting pressure and the vertical direction, L 1is the length of the floating section, represents the buoyancy force of the segment, represents the distance from the tail of the shield, represents the natural logarithm; The step S2 of calculating the floating force acting on the segment comprises: obtaining engineering parameters and segment parameters of the shield tunneling construction process, and substituting the engineering parameters and the segment parameters into the floating force variation form to calculate the floating force acting on the segment.

2. The semi-analytical method for calculating the floating and internal forces of a shield segment during construction according to claim 1, wherein, The bending equation of the beam in the step S3 is expressed in a matrix form and satisfies the following relationship: ； ； ； ； ； In the formula, [Mathematical Formula 1] is a coefficient matrix, [Mathematical Formula 2] is an upwelling parameter matrix, [Mathematical Formula 3] is a boundary condition and continuity condition matrix, A C T L 1+ L 2= L , L 2、 L is a non-upwelling segment length, and the total length is calculated, 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 all represent intermediate calculation parameters, represents an undetermined coefficient, represents that the segment displacement at the tail of the shield is 0, represents that the segment shear force at the tail of the shield is 0, represents the segment upwelling 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.​​​ 3. The semi-analytical method for calculating the floating and internal forces of a shield segment during construction according to claim 1, wherein, The step S3 of establishing the deformation differential equation based on the bending equation of the beam comprises: The deformation differential equation is constructed based on the bending equation of the beam and the upward buoyant force borne by the segment and the related parameters of the beam, wherein the related parameters of the beam include: the elastic modulus of Euler Bernoulli beam, the shear coefficient of the elastic foundation and the stiffness coefficient of the elastic foundation Bernoulli beam the deformation differential equation satisfies the following relationship: ； ； ； ； ； wherein, E E is the elastic modulus of the homogeneous Euler Bernoulli beam, I E is the elastic modulus of the homogeneous Euler Bernoulli beam, w is the pipe segment floating amount, E c , I c E and I are the elastic modulus and the moment of inertia of the pipe segment concrete, l c is the pipe segment width, A c is the pipe segment cross-sectional concrete area, 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 bolt length, E s is the equivalent elastic modulus of the stratum, h 1is 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 2are the stiffness coefficients of the two-part corresponding elastic foundation, G 1, G 2are the shear coefficients of the two-part corresponding elastic foundation, G denotes the shear coefficient of the elastic foundation, denotes the neutral axis angle, denotes the distance from the pipe segment shield tail, L 1is the floating segment length, r 外 , r 内 are the pipe segment outer diameter and inner diameter, respectively, γ g , γ c are the slurry unit weight and the pipe segment unit weight, respectively, P is the synchronous grouting pressure, and k denotes the stiffness coefficient of the elastic foundation.

4. The semi-analytical method for calculating the jacking force and the internal force of a shield segment during construction according to claim 3, characterized in that, The solution of the differential equation is: the general solution of the non-homogeneous equation: ； the particular solution of the non-homogeneous equation: ； wherein, T x is the particular solution, R x is the general solution; α i β i is the elastic coefficient, a 0, a 1, a 2, a 3, a 4 is the fitting coefficient of the buoyancy variation function, which is determined by the length of the floating section and the buoyancy, and 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 cross-sectional moment of inertia of the homogeneous Euler Bernoulli beam, and k represents the stiffness coefficient of the elastic foundation, D is the diameter of the tunnel, G represents the shear coefficient of the elastic foundation, p 0 is the unit length of the shield tail segment that is subjected to the buoyancy.​​​ 5. The semi-analytical method for calculating the jacking force and the internal force of a shield segment during construction according to claim 1, wherein, The boundary conditions in the step S5 comprise: ； wherein L is the total length calculated, represents the amount of float of the float-up section, represents the angle of rotation of the float-up section, represents the bending moment of the float-up section, represents the shear force of the float-up section, represents the amount of float of the float-up section without the float-up force, represents the angle of rotation of the float-up section without the float-up force, represents the bending moment of the float-up section without the float-up force, represents the shear force of the float-up section without the float-up force.

6. The semi-analytical method for calculating the jacking force and the internal force of a shield segment during construction according to claim 1, wherein, The step S5 of establishing the segment instantaneous floating amount calculation method under single grouting action comprises: solving the undetermined coefficients in the differential equation according to the boundary conditions and the continuity conditions, and establishing the segment instantaneous floating amount calculation method under single grouting action based on the solved undetermined coefficients; the segment instantaneous floating amount calculation method under single grouting action satisfies the following relationship: ； The step S6 of deriving the segment cumulative floating amount calculation method under continuous grouting action comprises: accumulating the instantaneous floating amount according to the segment instantaneous floating amount calculation method under single grouting action to derive the segment cumulative floating amount calculation method under continuous grouting action; The accumulated pipe piece floating amount calculation method under the continuous grouting effect satisfies the following relationship: ； wherein, is the instantaneous uplift amount of the i-th grouting, is the cumulative uplift amount of the i-th grouting, w 1( x ) and 2( w 2( x ) are the instantaneous uplift amount expressions located at 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 to the tail shield.

7. The semi-analytical method for calculating the jacking force and the internal force of a shield segment during construction according to claim 1, wherein, The shear force, bending moment and rotation angle in the step S7 are calculated by the following formula: ； In the formula, Q is the shear force, M is the bending moment, and φ is the rotation angle.

8. The semi-analytical method for calculating the jacking force and the internal force of a shield segment during construction according to claim 1, wherein, The finite element software in the step S1 is Abaqus, and the thickness of the foundation shear layer in the numerical model satisfies: ； In the formula, Foundation shear layer thickness, D is the diameter of the tunnel.

9. A semi-analytical system for calculating the floating and internal force of a shield segment during construction, characterized in that, The processor, the memory; The memory is used for storing computer programs; The processor is used for executing the program stored on the memory, and the method steps of any one of claims 1-8 are realized.

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