Method and device for calculating influence of foundation settlement on immersed tunnel by considering differential distribution of soil springs and medium

Abstract

The invention discloses a method and device for calculating the influence of foundation settlement on an immersed tube tunnel by considering soil spring differential distribution and a medium, and relates to the technical field of civil engineering-immersed tube tunnels. The method comprises the steps that stress analysis is conducted on the axial direction of a pipe joint, and an infinitesimal body is taken; timoshenko beam model equilibrium analysis is carried out on the infinitesimal body; based on the equilibrium analysis result, dividing an equilibrium differential equation solution domain of the pipe joint to replace a continuous solution domain; and on the basis of an equilibrium differential equation solution domain of the divided pipe joints, a finite difference method is utilized to add boundary conditions to form a matrix for solution, and the influence of foundation settlement on the immersed tunnel is calculated. According to the method, the problem that the shearing effect generated in the deformation of the beam cannot be considered in the existing beam theory in the non-uniform foundation settlement of the immersed tube tunnel can be solved, and the influence of the foundation difference on the immersed tube tunnel is not considered by a theoretical calculation method at present; and mechanical responses of deflection, bending moment, shearing force and the like of the pipe joint influenced by the foundation cannot be calculated.

Description

Technical Field

[0001] The present invention relates to the technical field of civil engineering-immersed tube tunnels, and more specifically, to a method, device and medium for calculating the influence of foundation settlement on an immersed tube tunnel taking into account the differential distribution of soil springs. Background Art

[0002] Currently, there are no simplified analytical theories for predicting the mechanical response of immersed tube tunnels under uneven foundations. The main analytical theory used for underground pipeline corridors, pipelines, and tunnels is the spring-beam foundation model. This model simplifies the pipeline and tunnel into elastic beams, treats the soil as a Winkler foundation model, and interprets soil compression as spring compression. The soil-structure interaction is simplified to the interaction of a structural beam placed on a spring. Equilibrium is achieved by applying forces or soil displacements to the spring-beam foundation model. The equilibrium equations are analyzed to obtain analytical or semi-analytical solutions, which are then used to determine the mechanical response of the beam. Semi-analytical solutions of the spring-beam model have been successfully applied to shield tunnel prediction.

[0003] The current spring foundation beam model assumes that the soil is uniformly distributed and has consistent mechanical properties, so the same soil springs are used. However, in reality, pipelines and tunnels inevitably pass through different soil layers due to their large axial length. As a result, the soil mechanical properties cannot remain consistent, and the existing model cannot account for the differences in soil spring distribution. Summary of the Invention

[0004] In order to solve the above technical problems, the present invention provides a calculation method, device and medium for the influence of foundation settlement on an immersed tube tunnel taking into account the differential distribution of soil springs, so as to solve the problems that the existing spring foundation beam theory calculation method does not use the finite difference method to quickly and concisely solve the mechanical response of the immersed tube tunnel under foundation settlement, and the existing spring foundation beam theory cannot take into account the difference in foundation soil springs and cannot better capture the mechanical response of underground structures with large spans under different soil layers.

[0005] In a first aspect, the present invention provides a method for calculating the influence of foundation settlement on an immersed tube tunnel by considering the differential distribution of soil springs, the method comprising:

[0006] Conduct axial stress analysis on the pipe segment and obtain microelement;

[0007] Performing Timoshenko beam model equilibrium analysis on the microelement;

[0008] Based on the equilibrium analysis results, the equilibrium differential equation solution domain of the pipe segment is divided to replace the continuous solution domain;

[0009] Based on the divided solution domain of the equilibrium differential equation of the pipe segment, the finite difference method with additional boundary conditions is used to form a matrix solution to calculate the influence of foundation settlement on the immersed tube tunnel.

[0010] Furthermore, the axial stress analysis of the pipe segment is performed and the microelement is obtained, including:

[0011] An arbitrary unit with a length of dx is selected as a microelement for force and deformation analysis, and the roadbed reaction force is determined based on the Winkler bed coefficient and the longitudinal displacement of the pipeline;

[0012] Determine the thrust exerted by the soil on the micro-element based on the displacement caused by uneven foundation settlement;

[0013] Determining a vertical force equilibrium equation of the micro-element based on the roadbed reaction force and the thrust exerted by the soil on the micro-element;

[0014] Determining the bending moment equilibrium equation of the microelement;

[0015] Based on the vertical force balance equation and the bending moment balance equation of the micro-element, a simplified mechanical equation of the micro-element is obtained.

[0016] Furthermore, based on the Winkler bed coefficient and the longitudinal displacement of the pipeline, the roadbed reaction force is determined by the following formula:

[0017] s(x)=k b / u δ(x) (1)

[0018] Where s(x) is the roadbed reaction force, k b / u is the Winkler bed coefficient, δ(x) is the longitudinal displacement of the pipeline;

[0019] According to the displacement caused by uneven foundation settlement, the thrust exerted by the soil on the micro-element is determined by the following formula:

[0020] q(x)=k b / u u(x) (2)

[0021] Where q(x) is the thrust exerted by the soil on the microelement, and u(x) is the displacement caused by uneven foundation settlement.

[0022] Furthermore, the vertical force balance equation of the microelement is expressed as:

[0023] Q+q(x)dx=Q+dQ+s(x)dx (3)

[0024] Where Q is the cross-sectional shear force and dQ is the incremental shear force of the infinitesimal element.

[0025] The moment equilibrium equation of the microelement is expressed as:

[0026]

[0027] Where M is the bending moment, dM is the bending moment increment of the microelement;

[0028] The simplified mechanical equation of the microelement is expressed as:

[0029]

[0030] Furthermore, a Timoshenko beam model equilibrium analysis is performed on the microelement, including:

[0031] According to the deformed Timoshenko beam model, the relationship between shear force Q, bending moment M and deflection, rotation angle θ and shear angle γ is determined;

[0032] According to the relationship between the shear force Q, the bending moment M and the deflection, the rotation angle θ and the shear angle γ, the differential equilibrium equation of the pipe segment microelement is determined.

[0033] Furthermore, the relationship between the shear force Q, bending moment M and deflection, rotation angle θ and shear angle γ is expressed as:

[0034] δ=δ b +δ s (6)

[0035]

[0036] Where, δ b is the vertical deflection of the immersed tunnel segment due to bending, δ s is the vertical deflection of the pipe segment due to shear, E p I is the bending stiffness of the pipe segment, κ is the Timoshenko shear coefficient of the pipe segment, G is the shear modulus of the pipe segment, A r is the cross-sectional area of ​​the pipe segment;

[0037] The differential balance equation of the pipe segment microelement is expressed as

[0038]

[0039] Furthermore, based on the equilibrium analysis results, the equilibrium differential equation solution domain of the pipe segment is divided to replace the continuous solution domain, including:

[0040] The pipe segment is divided into n1 pipe segments according to the joints. Each pipe segment is discretized into n2 differential nodes with equal spacing along the longitudinal direction. Two virtual differential nodes are constructed at both ends of the joint to construct the differential equation of the joint node. Two virtual differential nodes are constructed at both ends of the pipe gallery to construct the differential equation of the endpoint. Using the standard finite difference principle, the finite difference forms of the first, second, third, and fourth order differential terms are obtained respectively, which are expressed as:

[0041]

[0042] In formulas (14) to (17), δ b(i) , δ b(i-1) , δ b(i+1) , δ b(i+2) and δ b(i-2) are the vertical displacements of the pipe segments due to bending at the ith, i-1th, i+1th, i+2th, and i-2th differential nodes, respectively; l is the distance between the differential nodes;

[0043] Based on the finite difference form of the first, second, third, and fourth order differential terms, the finite difference expression of the conventional differential node deflection differential equation of the pipe segment is obtained as follows:

[0044]

[0045] The bending moment M at the immersed tube joint j The expression is as follows:

[0046]

[0047] Where k θ is the joint torsional spring stiffness, and are the rotation angles of the nodes at both ends of the joint;

[0048] According to the bending moment continuity assumption, we get:

[0049]

[0050] Where, and are the bending moments at the nodes at both ends of the joint, expressed as:

[0051]

[0052] The differential expressions for determining virtual differential nodes j+1 and j-1 are:

[0053]

[0054] Where, is the virtual node at the right end of the joint, is the first virtual node on the left end of the joint, k θ is the rotational spring stiffness, is the right end node of the joint, is the left end node of the joint, δ b(j+1) is the first regular node on the right side of the joint, δ b(j-1) It is the first regular node on the left end of the joint;

[0055] The shear force at the joint node is determined by the following formula:

[0056]

[0057] Where, is the shear force at the left end of the joint, is the shear force at the right end of the joint, is the second virtual node on the right side of the joint, δ b(j-2) is the second regular node on the left end of the joint, δ b(j+2) It is the second regular node on the right side of the joint;

[0058] From the joint balance we get:

[0059]

[0060] Where k s is the joint shear spring stiffness, Q j is the joint shear force, is the bending deflection of the left end node of the joint, is the bending deflection of the right end node;

[0061] The differential expressions of the joint virtual differential nodes j+2 and j-2 are determined by the following formula:

[0062]

[0063] Sure δ b(j-1) , δ b(j+1) The differential expression of the four nodes is expressed as:

[0064]

[0065] Where u - is the node load at the left end of the joint, u + is the node load at the right end of the joint, u j-1 is the first normal node load at the left end of the joint, u j+1 is the first normal node load at the right end of the joint;

[0066] For both ends of the pipe segment, we can get the following assumptions:

[0067] M1=M n =0 (30)

[0068] Q1=Q n =0 (31)

[0069] Where M1 represents the bending moment of the first node at the left end of the pipeline, M n represents the bending moment at the last node of the rightmost end of the pipeline, Q1 represents the shear force at the first node of the leftmost end of the pipeline, and Q n Indicates the shear force at the rightmost end node of the pipeline;

[0070] The differential expression for determining the differential nodes at both ends is:

[0071]

[0072] Where u1, u2, u n and u n-1 are the first node load at the leftmost end of the pipeline, the second node load at the leftmost end of the pipeline, the last node load at the end of the pipeline, and the second to last load; δ b(n) is the bending deflection of the nth node;

[0073] Combining the previously obtained differential expressions to form a linear algebraic equation system, the matrix form of the differential nodes at both ends is determined as follows:

[0074] ([K1]-[K][K2]+[K][K3]){δ b}=[K][U]{u} (33)

[0075] Where K1 is the pipeline structure matrix, K2 is the shear coefficient matrix, K3 is the bending coefficient matrix, K is the soil spring distribution matrix, and U is the displacement coefficient matrix;

[0076] The total vertical settlement δ of the pipe segment is calculated using formula (7);

[0077] The pipe segment strain is calculated using the following formula:

[0078]

[0079] Where D is the transverse width of the tunnel;

[0080] Substituting formula (34) into formula (11) and sorting it out, we get:

[0081]

[0082] The bending moment of the joint is obtained by sorting:

[0083]

[0084] Where, is the node strain at the left end of the joint, is the node strain at the right end of the joint;

[0085] The strain matrix is ​​obtained by formulas (35) and (36):

[0086] {ε b}=[K][K4]{δ b} (37)

[0087] Where K4 is the gauge coefficient matrix.

[0088] Furthermore, based on the divided solution domain of the equilibrium differential equation of the pipe segment, the solution matrix composed of the additional boundary conditions using the finite difference method is:

[0089]

[0090]

[0091]

[0092]

[0093] Where n1n2 is the total number of nodes.

[0094] In a second aspect, the present invention provides a device for calculating the influence of foundation settlement on an immersed tube tunnel taking into account the differential distribution of soil springs, the device comprising:

[0095] The stress analysis module is configured to perform stress analysis on the axial direction of the pipe segment and obtain microelement bodies;

[0096] A balance analysis module is configured to perform a Timoshenko beam model balance analysis on the microelement;

[0097] A solution domain determination module is configured to divide the solution domain of the equilibrium differential equation of the pipe segment based on the equilibrium analysis result to replace the continuous solution domain;

[0098] The solution calculation module is configured to solve the equilibrium differential equation domain based on the divided pipe segments, and uses the finite difference method with additional boundary conditions to form a matrix solution to calculate the impact of foundation settlement on the immersed tube tunnel.

[0099] In a third aspect, the present invention provides a readable storage medium, wherein the readable storage medium stores one or more programs, and the one or more programs can be executed by one or more processors to implement the method as described above.

[0100] The present invention has at least the following beneficial effects:

[0101] The present invention considers the differences in mechanical properties of different soil layers, changes the soil springs at different pipe section positions, performs axial force analysis on the pipe sections, and performs deformation analysis of the Timoshenko beam model on microelements to obtain equilibrium equations. The obtained equilibrium equations are divided into solution domains to replace the continuous solution domains, and the additional boundary conditions are solved using the finite difference method to implement analytical theoretical solutions to the effects of uneven foundation settlement on immersed tube tunnels. This solves the problem that the existing Euler-Bernoulli beam theory cannot consider the shear effect generated by the beam during deformation in the uneven foundation settlement of immersed tube tunnels, and the problem that the theoretical calculation method has not yet considered the effects of foundation differences on immersed tube tunnels, and thus cannot calculate the mechanical responses of the pipe sections affected by the foundation, such as deflection, bending moment and shear force. BRIEF DESCRIPTION OF THE DRAWINGS

[0102] Figure 1 A flow chart of a method for calculating the influence of foundation settlement on an immersed tube tunnel taking into account differential distribution of soil springs according to an embodiment of the present invention is shown;

[0103] Figure 2 A bending moment calculation verification diagram according to an embodiment of the present invention is shown;

[0104] Figure 3 A diagram illustrating a verification diagram of a rotation angle calculation according to an embodiment of the present invention is shown;

[0105] Figure 4 A structural diagram of a device for calculating the influence of foundation settlement on an immersed tunnel taking into account differential distribution of soil springs according to an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0106] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention is described in detail below with reference to the accompanying drawings and specific embodiments. The embodiments of the present invention are further described in detail below with reference to the accompanying drawings and specific embodiments, but are not intended to limit the present invention. For the various steps described herein, if there is no necessity for a contextual relationship between each other, the order in which they are described as examples herein should not be regarded as limiting, and those skilled in the art should know that they can be adjusted in order as long as the logic between them is not destroyed, resulting in the inability to implement the entire process.

[0107] The embodiment of the present invention provides a calculation method for the influence of foundation settlement on immersed tube tunnel considering the differential distribution of soil spring. Figure 1 As shown in FIG, the calculation method for the influence of foundation settlement on the immersed tube tunnel considering the differential distribution of soil spring includes the following steps: Step 1 to Step 4.

[0108] Step 1: Analyze the axial force of the pipe segment and take the microelement.

[0109] Step 2: Perform Timoshenko beam model equilibrium analysis on the microelement.

[0110] Step 3: Divide the solution domain of the equilibrium differential equation of the pipe section to replace the continuous solution domain.

[0111] Step 4: Use the finite difference method to add boundary conditions to form a matrix for solution.

[0112] The specific calculation steps of Step 1 are:

[0113] Take any unit of length dx for force and deformation analysis. According to the definition of Winkler foundation model in spring foundation beam model, the deflection of the microelement has

[0114] s(x)=k b / u δ(x) (1)

[0115] In formula (1), s(x) is the roadbed reaction force, k b / u is the Winkler bed coefficient, and δ(x) is the longitudinal displacement of the pipeline.

[0116] For the forces exerted by soil on the structure, there are

[0117] q(x)=k b / u u(x) (2)

[0118] In formula (2), q(x) is the thrust exerted by the soil on the microelement, and u(x) is the displacement caused by uneven foundation settlement.

[0119] From the vertical force balance of the microelement, we can get:

[0120] Q+q(x)dx=Q+dQ+s(x)dx (3)

[0121] In formula (3), Q is the cross-sectional shear force, and dQ is the shear force increment of the infinitesimal element.

[0122] From the bending moment balance of the microelement, we can get:

[0123]

[0124] In formula (4), M is the bending moment, and dM is the bending moment increment of the microelement.

[0125] Simplifying the above formula and ignoring the higher-order traces, we can get

[0126]

[0127] The specific calculation steps of Step 2 are:

[0128] For the deformed Timoshenko beam model, the following relationships between the shear force Q, bending moment M, and deflection, rotation angle θ, and shear angle γ can be given:

[0129] δ=δ b +δ s (6)

[0130]

[0131] In formulas (6) to (12), δ b is the vertical deflection of the immersed tunnel segment due to bending, δ s is the vertical deflection of the pipe segment due to shear, E p I is the bending stiffness of the pipe segment, κ is the Timoshenko shear coefficient of the pipe segment, G is the shear modulus of the pipe segment, A r is the cross-sectional area of ​​the pipe segment;

[0132] Combining formulas (1) to (12), the differential equilibrium equation of the pipe segment can be obtained:

[0133]

[0134] Formula (13) is a differential equation related only to the vertical displacement δ.

[0135] The specific calculation steps of Step 3 are:

[0136] Using the finite difference method, the pipe section is divided into n1 pipe sections according to the joints. Each pipe section is discretized into n2 differential nodes with equal spacing along the longitudinal direction. Two virtual differential nodes are constructed at both ends of the joint to construct the differential equation of the joint node. In addition, two virtual differential nodes are constructed at both ends of the pipe corridor to construct the differential equation of the endpoints. Using the standard finite difference principle, the finite difference forms of the first, second, third, and fourth order differential terms can be obtained respectively as follows:

[0137]

[0138] In formulas (14) to (17), δ b(i) , δ b(i-1) , δ b(i+1) , δ b(i+2) and δ b(i-2) are the vertical displacements of the pipe segments due to bending at the ith, i-1th, i+1th, i+2th, and i-2th differential nodes, respectively; l is the distance between the differential nodes;

[0139] After sorting out, the finite difference expression of the conventional differential node deflection differential equation of the pipe segment can be obtained as follows:

[0140]

[0141] The bending moment at the immersed tube joint can be expressed as follows:

[0142]

[0143] In formula (19), k θ is the joint torsional spring stiffness, and are the rotation angles of the nodes at both ends of the joint.

[0144] According to the bending moment continuity assumption, we can get

[0145]

[0146] In formula (20), and are the bending moments at the nodes at both ends of the joint, and we can get

[0147]

[0148] Formula (21) is the differential equation expression of the bending moment at both ends of the joint.

[0149] Combining the formula and sorting it out, we can get

[0150]

[0151] In formula (22), is the virtual node at the right end of the joint, is the first virtual node on the left end of the joint, k θ is the rotational spring stiffness, is the right end node of the joint, is the left end node of the joint, δ b(j+1) is the first regular node on the right side of the joint, δ b(j-1) This is the first regular node at the left end of the connector.

[0152] Formula (22) is the differential expression of virtual differential nodes j+1 and j-1.

[0153] The shear force of the joint node can be obtained by sorting the formula

[0154]

[0155] In formula (23), is the shear force at the left end of the joint, is the shear force at the right end of the joint, is the second virtual node on the right side of the joint, δ b(j-2) is the second regular node on the left end of the joint, δ b(j+2) It is the second regular node at the right end of the connector.

[0156] From the joint balance, we can get

[0157]

[0158] In formula (24), k s is the joint shear spring stiffness, Q j is the joint shear force, is the bending deflection of the left end node of the joint, is the bending deflection of the right end node;

[0159]

[0160] Formula (25) is the differential expression of the joint virtual differential nodes j+2 and j-2;

[0161] In summary, we can get the equation

[0162]

[0163]

[0164] Where u - is the node load at the left end of the joint, u + is the node load at the right end of the joint, u j-1 is the first normal node load at the left end of the joint, u j+1 is the first normal nodal load at the right end of the connector.

[0165] Formulas (26), (27), (28), and (29) are δ b(j-1) , δ b(j+1) Differential expressions of four nodes;

[0166] For both ends of the pipe segment, we can get

[0167] M1=M n =0 (30)

[0168] Q1=Q n =0 (31)

[0169] Where M1 represents the bending moment of the first node at the left end of the pipeline, M n represents the bending moment at the last node of the rightmost end of the pipeline, Q1 represents the shear force at the first node of the leftmost end of the pipeline, and Q n Represents the shear force at the rightmost end node of the pipeline.

[0170] Rearranging the equations yields

[0171]

[0172] Where u1, u2, u n and u n-1are the first node load at the leftmost end of the pipeline, the second node load at the leftmost end of the pipeline, the last node load at the end of the pipeline, and the second to last load; δ b(n) is the bending deflection at the nth node.

[0173] Formula (32) is the differential node δ at both ends b(1) , δ b(2) , δ b(n-1) , δ b(n) The differential expression of , combined with the differential expression obtained previously, forms a linear algebraic equation system, which can be expressed in matrix form as follows:

[0174] ([K1]-[K][K2]+[K][K3]){δ b}=[K][U]{u} (33)

[0175] Where K1 is the pipe structure matrix, K2 is the shear coefficient matrix, K3 is the bending coefficient matrix, K is the soil spring distribution matrix, and U is the displacement coefficient matrix.

[0176] The total vertical settlement δ of the pipe segment can be calculated using formula (7).

[0177] The pipe joint strain can be calculated using the following formula:

[0178]

[0179] Where D is the transverse width of the tunnel.

[0180] Substituting into formula (11) and sorting it out, we can get:

[0181]

[0182] The bending moment of the joint can be obtained by sorting:

[0183]

[0184] Where, is the node strain at the left end of the joint, is the node strain at the right end of the joint.

[0185] By sorting (35) and (36), we can get the matrix of strain:

[0186] {ε b}=[K][K4]{δ b} (37)

[0187] Where K4 is the gauge coefficient matrix.

[0188] The specific calculation matrix of Step 4 is:

[0189] For formula (33), the expressions of each matrix are as follows:

[0190]

[0191]

[0192]

[0193] Where n1n2 is the total number of nodes.

[0194] This analytical method has been piloted for pipeline calculations to predict the effects of normal faults on pipe joints. It is important to note that previous studies have shown differences in the interaction forces between pipes and soil under normal faults, similar to the variations in bearing capacity of the foundation of immersed tunnels caused by different construction times. Furthermore, the structure of the pipe joints is similar to that of the immersed tunnels, resulting in weak points. Therefore, the effectiveness of the calculation method was evaluated by predicting the mechanical response of the pipes under normal faults.

[0195] rp is defined as the ratio of the distance from the left end of the pipeline to the fault trace to the length of a single section of pipeline.

[0196] The calculation results are as follows:

[0197] For bending moments, the results are as follows Figure 2 As shown, for the joint angle, the results are as follows Figure 3 As shown in the results, the analytical method can predict the bending moment strain of the pipeline and the rotation angle of the pipeline joint, which proves the effectiveness of the method. In addition, it can consider the influence of foundation differences on pipe joints in any case.

[0198] The embodiment of the present invention also provides a device for calculating the influence of foundation settlement on immersed tunnels taking into account the differential distribution of soil springs, such as Figure 4 As shown, the device includes:

[0199] The force analysis module 401 is configured to perform force analysis on the axial direction of the pipe segment and extract microelement bodies;

[0200] A balance analysis module 402 is configured to perform a Timoshenko beam model balance analysis on the microelement;

[0201] The solution domain determination module 403 is configured to divide the solution domain of the equilibrium differential equation of the pipe segment based on the equilibrium analysis result to replace the continuous solution domain;

[0202] The solution calculation module 404 is configured to solve the equilibrium differential equation of the divided pipe segment domain, use the finite difference method with additional boundary conditions to form a matrix solution, and calculate the influence of foundation settlement on the immersed tube tunnel.

[0203] It should be noted that the structures of the calculation devices for the impact of foundation settlement on immersed tube tunnels taking into account the differential distribution of soil springs described in this embodiment belong to the same technical concept as the calculation method for the impact of foundation settlement on immersed tube tunnels taking into account the differential distribution of soil springs described previously, and achieve the same beneficial effects through the same principles, which will not be repeated here.

[0204] An embodiment of the present invention further provides a readable storage medium, which stores one or more programs. The one or more programs can be executed by one or more processors to implement the method described in any of the above embodiments.

[0205] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions or improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for calculating the influence of foundation settlement on immersed tunnels taking into account the differential distribution of soil springs, characterized in that: The method comprises: Conduct axial stress analysis on the pipe segment and obtain microelement; Performing Timoshenko beam model equilibrium analysis on the microelement; Based on the equilibrium analysis results, the equilibrium differential equation solution domain of the pipe segment is divided to replace the continuous solution domain; Based on the divided solution domain of the equilibrium differential equation of the pipe segment, the finite difference method with additional boundary conditions is used to form a matrix solution to calculate the influence of foundation settlement on the immersed tube tunnel.

2. The calculation method for the influence of foundation settlement on immersed tunnels considering the differential distribution of soil spring according to claim 1 is characterized in that: Perform axial stress analysis on the pipe segment and extract microelement, including: An arbitrary unit with a length of dx is selected as a microelement for force and deformation analysis, and the roadbed reaction force is determined based on the Winkler bed coefficient and the longitudinal displacement of the pipeline; Determine the thrust exerted by the soil on the micro-element based on the displacement caused by uneven foundation settlement; Determining a vertical force equilibrium equation of the micro-element based on the roadbed reaction force and the thrust exerted by the soil on the micro-element; Determining the bending moment equilibrium equation of the microelement; Based on the vertical force balance equation and the bending moment balance equation of the micro-element, a simplified mechanical equation of the micro-element is obtained.

3. The calculation method for the influence of foundation settlement on immersed tunnels considering the differential distribution of soil springs according to claim 2 is characterized in that: Based on the Winkler bed coefficient and the longitudinal displacement of the pipeline, the roadbed reaction force is determined by the following formula s(x)=k b / u δ(x) (1) Where s(x) is the roadbed reaction force, k b / u is the Winkler bed coefficient, δ(x) is the longitudinal displacement of the pipeline; According to the displacement caused by uneven foundation settlement, the thrust exerted by the soil on the micro-element is determined by the following formula: q(x)=k b / u u(x) (2) Where q(x) is the thrust exerted by the soil on the microelement, and u(x) is the displacement caused by uneven foundation settlement.

4. The calculation method for the influence of foundation settlement on immersed tunnels considering the differential distribution of soil springs according to claim 3 is characterized in that: The vertical force balance equation of the microelement is expressed as: Q+q(x)dx=Q+dQ+s(x)dx (3) Where Q is the cross-sectional shear force and dQ is the incremental shear force of the infinitesimal element. The bending moment equilibrium equation of the microelement is expressed as: Where M is the bending moment, dM is the bending moment increment of the microelement; The simplified mechanical equation of the microelement is expressed as:

5. The calculation method for the influence of foundation settlement on immersed tunnels considering the differential distribution of soil spring according to claim 4 is characterized in that: Performing a Timoshenko beam model equilibrium analysis on the microelement includes: According to the deformed Timoshenko beam model, the relationship between shear force Q, bending moment M and deflection, rotation angle θ and shear angle γ is determined; According to the relationship between the shear force Q, the bending moment M and the deflection, the rotation angle θ and the shear angle γ, the differential equilibrium equation of the pipe segment microelement is determined.

6. The calculation method for the influence of foundation settlement on immersed tunnels considering the differential distribution of soil springs according to claim 5 is characterized in that: The relationship between the shear force Q, bending moment M and deflection, rotation angle θ and shear angle γ is expressed as follows: d=d b +d s (6) Where, δ b is the vertical deflection of the immersed tunnel segment due to bending, δ s is the vertical deflection of the pipe segment due to shear, E p I is the bending stiffness of the pipe segment, κ is the Timoshenko shear coefficient of the pipe segment, G is the shear modulus of the pipe segment, A r is the cross-sectional area of ​​the pipe segment; The differential balance equation of the pipe segment microelement is expressed as 7. The calculation method for the influence of foundation settlement on an immersed tube tunnel considering the differential distribution of soil spring according to claim 6 is characterized in that: Based on the equilibrium analysis results, the equilibrium differential equation solution domain of the pipe segment is divided to replace the continuous solution domain, including: The pipe segment is divided into n1 pipe segments according to the joints. Each pipe segment is discretized into n2 differential nodes with equal spacing along the longitudinal direction. Two virtual differential nodes are constructed at both ends of the joint to construct the differential equation of the joint node. Two virtual differential nodes are constructed at both ends of the pipe gallery to construct the differential equation of the endpoint. Using the standard finite difference principle, the finite difference forms of the first, second, third, and fourth order differential terms are obtained respectively, which are expressed as: In formulas (14) to (17), δ b(i) , δ b(i-1) , δ b(i+1) , δ b(i+2) and δ b(i-2) are the vertical displacements of the pipe segments due to bending at the ith, i-1th, i+1th, i+2th, and i-2th differential nodes, respectively; l is the distance between the differential nodes; Based on the finite difference form of the first, second, third, and fourth order differential terms, the finite difference expression of the conventional differential node deflection differential equation of the pipe segment is obtained as follows: The bending moment M at the immersed tube joint j The expression is as follows: Where k θ is the joint torsional spring stiffness, and are the rotation angles of the nodes at both ends of the joint; According to the bending moment continuity assumption, we get: Where, and are the bending moments at the nodes at both ends of the joint, expressed as: The differential expressions for determining virtual differential nodes j+1 and j-1 are: Where, is the virtual node at the right end of the joint, is the first virtual node on the left end of the joint, k θ is the rotational spring stiffness, is the right end node of the joint, is the left end node of the joint, δ b(j+1) is the first regular node on the right side of the joint, δ b(j-1) It is the first regular node on the left end of the joint; The shear force at the joint node is determined by the following formula: Where, is the shear force at the left end of the joint, is the shear force at the right end of the joint, is the second virtual node on the right side of the joint, δ b(j-2) is the second regular node on the left end of the joint, δ b(j+2) It is the second regular node on the right side of the joint; From the joint balance we get: Where k s is the joint shear spring stiffness, Q j is the joint shear force, is the bending deflection of the left end node of the joint, is the bending deflection of the right end node; The differential expressions of the joint virtual differential nodes j+2 and j-2 are determined by the following formula: Sure δ b(j-1) , δ b(j+1) The differential expression of the four nodes is expressed as: Where u - is the node load at the left end of the joint, u + is the node load at the right end of the joint, u j-1 is the first normal node load at the left end of the joint, u j+1 is the first normal node load at the right end of the joint; For both ends of the pipe segment, we can get the following assumptions: M1=M n =0 (30) Q1=Q n =0 (31) Where M1 represents the bending moment of the first node at the left end of the pipeline, M n represents the bending moment at the last node of the rightmost end of the pipeline, Q1 represents the shear force at the first node of the leftmost end of the pipeline, and Q n Indicates the shear force at the rightmost end node of the pipeline; The differential expression for determining the differential nodes at both ends is: Where u1, u2, u n and u n-1 are the first node load at the leftmost end of the pipeline, the second node load at the leftmost end of the pipeline, the last node load at the end of the pipeline, and the second to last load; δ b(n) is the bending deflection of the nth node; Combining the previously obtained differential expressions to form a linear algebraic equation system, the matrix form of the differential nodes at both ends is determined as follows: ([K1]-[K][K2]+[K][K3]){δ b }=[K][U]{u} (33) Where K1 is the pipeline structure matrix, K2 is the shear coefficient matrix, K3 is the bending coefficient matrix, K is the soil spring distribution matrix, and U is the displacement coefficient matrix; The total vertical settlement δ of the pipe segment is calculated using formula (7); The pipe segment strain is calculated using the following formula: Where D is the transverse width of the tunnel; Substituting formula (34) into formula (11) and sorting it out, we get: The bending moment of the joint is obtained by sorting: Where, is the node strain at the left end of the joint, is the node strain at the right end of the joint; The strain matrix is ​​obtained by formulas (35) and (36): {e} b }=[K][K4]{δ b } (37) Where K4 is the gauge coefficient matrix.

8. The calculation method for the influence of foundation settlement on immersed tube tunnel considering the differential distribution of soil spring according to claim 7 is characterized in that: Based on the divided solution domain of the equilibrium differential equation of the pipe segment, the solution matrix composed of the additional boundary conditions using the finite difference method is: Where n1n2 is the total number of nodes.

9. A device for calculating the influence of foundation settlement on immersed tunnels taking into account the differential distribution of soil springs, characterized in that: The device comprises: The stress analysis module is configured to perform stress analysis on the axial direction of the pipe segment and obtain microelement bodies; A balance analysis module is configured to perform a Timoshenko beam model balance analysis on the microelement; A solution domain determination module is configured to divide the solution domain of the equilibrium differential equation of the pipe segment based on the equilibrium analysis result to replace the continuous solution domain; The solution calculation module is configured to solve the equilibrium differential equation domain based on the divided pipe segments, and uses the finite difference method with additional boundary conditions to form a matrix solution to calculate the influence of foundation settlement on the immersed tube tunnel. 10 . A non-transitory computer-readable storage medium storing instructions, which, when executed by a processor, executes the method according to claim 1 .

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