Shield tunnel longitudinal stress calculation method and system considering inter-ring joint nonlinearity

Abstract

The application provides a shield tunnel longitudinal stress calculation method and system considering inter-ring joint nonlinearity, and relates to the technical field of underground engineering. The method comprises the following steps: obtaining parameter information of a shield tunnel, wherein the parameter information comprises structural design parameters, material parameters and stratum parameters; establishing a finite element model of the shield tunnel according to the initial stiffness of the inter-ring joint and the parameter information, and solving the finite element model based on a preset load to obtain first information, wherein the first information comprises the bending moment, shear force and longitudinal axial force of each inter-ring joint of the shield tunnel; constructing a stiffness three-dimensional surface of the inter-ring joint, calculating the stiffness information of the inter-ring joint according to the stiffness three-dimensional surface and the first information; updating the finite element model according to the stiffness information, and obtaining the longitudinal structural stress result of the shield tunnel through the updated finite element model. The application solves the problem that the existing beam-spring model ignores the changes of the bending stiffness and shear stiffness with the load when simulating the nonlinear behavior of the inter-ring joint.

Description

Technical Field

[0001] This invention relates to the field of underground engineering technology, and more specifically, to a method and system for calculating the longitudinal stress of shield tunnels considering the nonlinearity of ring-to-ring joints. Background Technology

[0002] The bending and shear stiffness of shield tunnel joints have been extensively studied. Although the longitudinal beam-spring model is widely used in the structural design and mechanical performance research of shield tunnels, existing methods typically treat the bending stiffness of the joint as a constant value, neglecting its nonlinear characteristics. In reality, the bending stiffness of the joint dynamically adjusts with changes in external loads, constraints, and deformation patterns, and existing models cannot reflect this dynamic process. Therefore, traditional methods based on constant stiffness values ​​cannot accurately simulate the mechanical response of shield tunnels under actual working conditions, leading to calculation results that deviate from reality.

[0003] Furthermore, existing longitudinal beam-spring models do not consider the shear stiffness of the inter-ring joints, making them unable to effectively simulate the misalignment deformation that may occur between rings during the longitudinal deformation of shield tunnels. This deficiency limits the applicability of the model under complex working conditions and prevents it from fully reflecting the true mechanical behavior of shield tunnel structures.

[0004] Therefore, existing longitudinal mechanical response analysis models for shield tunnels fail to fully consider the nonlinear characteristics of the stiffness of the inter-ring joints as a function of load, and also fail to simulate the deformation of the misalignment between the rings. This indicates that simply taking the stiffness of the inter-ring joints as a constant value is unreasonable. There is an interrelationship between the stiffness of the inter-ring joints and the internal forces of the segment lining structure, and the stiffness value must be updated gradually to approximate the true mechanical state under actual working conditions. Summary of the Invention

[0005] The purpose of this invention is to provide a method and system for calculating the longitudinal stress of shield tunnels considering the nonlinearity of ring-to-ring joints, in order to improve the aforementioned problems. To achieve the above objective, the technical solution adopted by this invention is as follows:

[0006] Firstly, this application provides a method for calculating the longitudinal stress of a shield tunnel considering the nonlinearity of ring-to-ring joints, including:

[0007] Obtain parameter information of the shield tunnel, including structural design parameters, material parameters, and geological parameters;

[0008] A finite element model of the shield tunnel is established based on the initial stiffness and parameter information of the ring joints, and the finite element model is solved based on the preset load to obtain the first information, which includes the bending moment, shear force and longitudinal axial force of each ring joint of the shield tunnel.

[0009] Construct a three-dimensional stiffness surface for the ring joint, and calculate the stiffness information of the ring joint based on the three-dimensional stiffness surface and the first information.

[0010] The finite element model is updated based on stiffness information, and the longitudinal structural stress results of the shield tunnel are obtained through the updated finite element model. The longitudinal structural stress results include longitudinal internal forces and displacements.

[0011] Secondly, this application also provides a system for calculating the longitudinal force of a shield tunnel considering the nonlinearity of ring-to-ring joints, including:

[0012] The acquisition unit is used to acquire parameter information of the shield tunnel, including structural design parameters, material parameters, and geological parameters.

[0013] The first calculation unit is used to establish a finite element model of the shield tunnel based on the initial stiffness and parameter information of the ring joints, and solve the finite element model based on the preset load to obtain the first information, which includes the bending moment, shear force and longitudinal axial force of each ring joint of the shield tunnel.

[0014] The second calculation unit is used to construct the stiffness three-dimensional surface of the ring joint and calculate the stiffness information of the ring joint based on the stiffness three-dimensional surface and the first information.

[0015] The update unit is used to update the finite element model based on stiffness information and obtain the longitudinal structural stress results of the shield tunnel through the updated finite element model. The longitudinal structural stress results include longitudinal internal forces and displacements.

[0016] The beneficial effects of this invention are as follows: By progressively updating the stiffness of the ring joint and dynamically adjusting the stiffness information based on the internal forces (bending moment, shear force, and longitudinal axial force) of the ring joint, this invention can accurately simulate the mechanical response of tunnel structures under actual working conditions. Compared with traditional methods, this invention can more closely approximate the actual loading state, ensuring the accuracy of the calculation results. Simultaneously, it can accurately determine whether the stiffness change after each calculation meets the set precision, and uses a gradient update method to optimize the stiffness adjustment process, ensuring that each calculation gradually approaches the true value. This not only guarantees high-precision calculation results but also improves the stability and reliability of the calculation.

[0017] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing embodiments of the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and drawings. Attached Figure Description

[0018] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a schematic diagram of the process for calculating the longitudinal force of a shield tunnel considering the nonlinearity of ring joints, as described in an embodiment of the present invention.

[0020] Figure 2 This is a schematic diagram of the shield tunnel described in an embodiment of the present invention;

[0021] Figure 3 This is a schematic diagram showing the bending moment results of the shield tunnel under different iteration numbers in an embodiment of the present invention;

[0022] Figure 4 This is a schematic diagram showing the bending moment results of shield tunnels under different conditions in an embodiment of the present invention. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0024] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this invention, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0025] Example 1:

[0026] This embodiment provides a method for calculating the longitudinal force of a shield tunnel that considers the nonlinearity of the ring joint.

[0027] See Figure 1 The figure shows that the method includes steps S1, S2, S3, and S4.

[0028] In this embodiment, as Figure 2 As shown, in the stress analysis of shield tunnels, multiple n segment rings and n-1 inter-ring joints are usually regarded as a whole, simplified into a continuous mechanical model. The connection between two segment rings is called an inter-ring joint, and the longitudinal bolts are an important component of the inter-ring joint. The segment ring is composed of multiple segments.

[0029] Step S1: Obtain parameter information of the shield tunnel, including structural design parameters, material parameters, and geological parameters;

[0030] In this embodiment, the structural design parameters of the shield tunnel include the outer diameter of the tunnel segments, the thickness of the tunnel segments, the width of the tunnel segments, and the number of bolts used for inter-segment joints. Material parameters include concrete grade and bolt strength. Different concrete grades have different mechanical properties, including compressive strength, tensile strength, and modulus of elasticity. This concrete grade refers to the strength grade of the concrete used to construct the shield tunnel segments, and different bolt strengths also have different mechanical properties. Soil parameters include the subgrade coefficient, which reflects the stiffness characteristics of the soil and is used to represent the interaction between the shield tunnel and the surrounding soil.

[0031] Step S2: Establish a finite element model of the shield tunnel based on the initial stiffness and parameter information of the ring joints, and solve the finite element model based on the preset load to obtain the first information, which includes the bending moment, shear force and longitudinal axial force of each ring joint of the shield tunnel.

[0032] In this embodiment, a preset load is applied to the finite element model and numerical calculations are performed to obtain the mechanical response of the shield tunnel, namely the bending moment, shear force and longitudinal axial force of each ring joint.

[0033] In step S2, the steps for constructing the finite element model are as follows:

[0034] Step S21: Construct the geometric model of the shield tunnel based on the structural design parameters;

[0035] Step S22: In the geometric model, beam elements are used to simulate the segment rings, spring elements with tensile, compressive, rotational and shear stiffness are used to simulate the ring joints, and formation spring elements are used to simulate the interaction between the segments and the formation.

[0036] In this embodiment, an improved longitudinal beam-spring model, namely a nonlinear beam-spring model, is used for simulation. The segment ring is simulated using beam elements, and the stiffness of the segment ring is based on the stiffness of the segment concrete. Figure 2 middle, and These represent the compressive stiffness and bending stiffness of the segment ring, respectively.

[0037] The ring joints are simulated using spring units with tensile, compressive, rotational, and shear stiffnesses, such as... Figure 2 As shown, rotational springs, axial springs, and shear springs are used to simulate... , and Furthermore, the stiffness of the ring joint is nonlinear, where, Indicates shear stiffness. Indicates bending stiffness. Indicates axial stiffness.

[0038] Step S23: Assign material properties to the segment rings and inter-ring joints in the geometric model according to the material parameters;

[0039] Step S24: Assign spring stiffness properties between the shield tunnel and the surrounding strata in the geometric model according to the stratum parameters;

[0040] Step S25: Set the initial stiffness of each ring joint in the geometric model to obtain the finite element model of the shield tunnel. The initial stiffness includes the initial bending stiffness and the initial shear stiffness.

[0041] Step S3: Construct the three-dimensional stiffness surface of the ring joint, and calculate the stiffness information of the ring joint based on the three-dimensional stiffness surface and the first information;

[0042] In this embodiment, the stiffness three-dimensional surface of the ring joint is obtained through numerical calculation.

[0043] In step S3, the calculation steps for the stiffness three-dimensional surface are as follows:

[0044] Step A1: Construct a detailed numerical model of the entity connecting the loops;

[0045] In this embodiment, the constructed detailed numerical model of the loop joint is actually a three-dimensional detailed numerical calculation model.

[0046] Step A2: Apply longitudinal axial force and bending moment to the solid refined numerical model to obtain the opening angle of the ring joint under different longitudinal axial forces and different bending moments;

[0047] In this embodiment, a longitudinal axial force is applied to the refined numerical model of the entity according to a certain loading scheme. and bending moment This causes the ring joint to open and deform, resulting in the opening angle of the ring joint, denoted as . During the loading process, the opening deformation of the ring joint is recorded in real time, that is, different longitudinal axial forces are recorded. Down, open the angle With bending moment The changing curve.

[0048] Step A3: Calculate the bending stiffness of the ring joint by the opening angle, and generate the first three-dimensional surface about the bending stiffness, bending moment and longitudinal axial force;

[0049] In this embodiment, based on the formula for calculating bending stiffness and the curve of the opening angle, the longitudinal axial force for different lengths is calculated. The bending stiffness of the lower ring joint is calculated using the following formula:

[0050] ;

[0051] In the formula, Indicates bending moment, Indicates the opening angle. It represents the bending stiffness.

[0052] By calculating multiple longitudinal axial forces After determining the bending stiffness of the lower ring joint, it will be related to the corresponding bending moment. The data was organized and analyzed to produce the first three-dimensional surface concerning bending stiffness, bending moment, and longitudinal axial force.

[0053] Step A4: Apply longitudinal axial force and shear force to the solid refined numerical model to obtain the misalignment displacement of the ring joint under different longitudinal axial forces and different shear forces;

[0054] In this embodiment, a longitudinal axial force is applied to the refined numerical model of the entity according to a specific loading scheme. and shear force The loading process is controlled to cause a misalignment displacement at the ring joint, denoted as... .

[0055] Monitor the misalignment deformation of the ring joint during loading and record the misalignment displacement. With shear force The changing data is recorded along with the corresponding longitudinal axial force. Different longitudinal axial forces were obtained. Below, misalignment With shear force The changing curve.

[0056] Step A5: Calculate the shear stiffness of the ring joint by the misalignment displacement, and generate a second three-dimensional surface about shear stiffness, shear force and longitudinal axial force;

[0057] In this embodiment, based on the shear stiffness calculation formula and the variation curve of the misalignment displacement, different longitudinal axial forces are calculated. The shear stiffness of the lower ring joint is calculated using the following formula:

[0058] ;

[0059] In the formula, Indicates misalignment displacement. Indicates shear force. It represents shear stiffness.

[0060] By calculating multiple longitudinal axial forces After determining the shear stiffness of the lower ring joint, it will be related to the corresponding shear force. The data was organized and analyzed to develop a second three-dimensional surface relating to shear stiffness, shear force, and longitudinal axial force.

[0061] Step A6: Use the first three-dimensional surface and the second three-dimensional surface as the stiffness three-dimensional surface of the ring joint.

[0062] In step S3, the calculation steps for the stiffness information are as follows:

[0063] Step B1: Discretize the three-dimensional stiffness surface into a bending stiffness-bending moment-longitudinal axial force stiffness matrix and a shear stiffness-shear force-longitudinal axial force stiffness matrix;

[0064] Step B2: Substitute the bending moment and longitudinal axial force of each ring joint into the bending stiffness-bending moment-longitudinal axial force stiffness matrix and perform linear difference calculation to obtain the bending stiffness of each ring joint.

[0065] Step B3: Substitute the shear force and longitudinal axial force of each ring joint into the shear stiffness-shear force-longitudinal axial force stiffness matrix to perform linear difference calculation to obtain the shear stiffness of each ring joint;

[0066] Step B4: Use the bending stiffness and shear stiffness as the stiffness information for each ring joint.

[0067] Step S4: Update the finite element model based on the stiffness information, and obtain the longitudinal structural stress results of the shield tunnel through the updated finite element model. The longitudinal structural stress results include longitudinal internal forces and displacements.

[0068] In step S4, the steps for obtaining the stress results of the longitudinal structure are as follows:

[0069] Step S41: Calculate the convergence result of each loop joint using stiffness information and convergence criteria;

[0070] In this embodiment, the absolute value of the difference in bending stiffness between two adjacent iterations of each ring joint is calculated as the first calculated value, and the absolute value of the difference in shear stiffness between two adjacent iterations of each ring joint is calculated as the second calculated value.

[0071] Determine whether the first calculated value is less than the first preset threshold. If so, it means that the convergence result of the ring joint in terms of bending stiffness is non-convergent. Determine whether the second calculated value is less than the second preset threshold. If so, it means that the convergence result of the ring joint in terms of shear stiffness is non-convergent.

[0072] Step S42: If at least one loop joint fails to converge, then update the stiffness information of all loop joints to obtain the updated stiffness information.

[0073] In this embodiment, if any one of the bending stiffness and shear stiffness of each ring joint is non-convergent, then the convergence result of that ring joint is non-convergent.

[0074] In step S42, obtaining the updated stiffness information includes:

[0075] Step S421: Set the rate of change for stiffness update;

[0076] In this embodiment, the rate of change controls the convergence speed. Here, the rate of change is set to 0.5, which represents the step size for each update.

[0077] Step S422: Construct the gradient calculation formula, which is constructed using the current stiffness information and the stiffness information obtained in the previous iteration;

[0078] In this embodiment, two objective functions are constructed: a bending stiffness objective function and a shear stiffness objective function. Specifically, an objective function is constructed regarding the longitudinal axial force. and bending moment Objective function for bending stiffness of ring joint And construct information about longitudinal axial force and shear force Objective function for shear stiffness of the ring joint .

[0079] The gradient is a vector that points in the direction in which the objective function changes the most rapidly at that point. In this step, the gradient is simplified to half the difference in stiffness information between two adjacent iterations at the loop junction.

[0080] Therefore, the gradient calculation formula includes the formula for calculating the bending stiffness gradient and the formula for calculating the shear stiffness gradient, specifically:

[0081] ;

[0082] ;

[0083] In the formula, Indicates the gradient of bending stiffness. Indicates the shear stiffness gradient. Indicates bending moment, Indicates shear force. Indicates longitudinal axial force. Indicates the first The bending stiffness obtained in the next iteration. Indicates the first The bending stiffness obtained in the next iteration. Indicates the first The shear stiffness obtained in the next iteration. Indicates the first The shear stiffness obtained from the next iteration.

[0084] Step S423: Calculate the stiffness gradient of each ring joint using the gradient calculation formula;

[0085] Step S424: Update the stiffness information of all loop joints by the rate of change, stiffness gradient, and descent direction of the stiffness gradient to obtain the updated stiffness information.

[0086] In this embodiment, the stiffness information of the loop joints is updated according to the stiffness gradient. Specifically, the parameters are moved in the opposite direction of the stiffness gradient (i.e., the decreasing direction), because the stiffness gradient points to the direction of the fastest increase in function value. Since the goal in this embodiment is to find the minimum value, the formula for updating the stiffness information of each loop joint is:

[0087] ;

[0088] ;

[0089] In the formula, This indicates the updated bending stiffness. This indicates the updated shear stiffness. This indicates the bending stiffness before the update. Shear stiffness before update This represents the flexural stiffness gradient before the update. This represents the shear stiffness gradient before the update. Indicates the rate of change.

[0090] Step S43: Use the updated stiffness information as the initial stiffness of the finite element model, and iterate the stiffness information again through the updated finite element model until the convergence results of all ring joints are converged. Then, obtain the longitudinal structural stress results of the shield tunnel through the current finite element model.

[0091] In this embodiment, if the convergence condition is not met, the stiffness gradient and updated stiffness information are repeatedly calculated and then used as the initial stiffness input to the finite element model to update the bending moment, shear force, and longitudinal axial force of the ring joint. The stiffness information is then obtained by interpolation through the three-dimensional stiffness surface until a certain convergence condition is met. The stiffness information obtained in the last iteration is then input into the finite element model to obtain the overall stress state of the shield tunnel in the longitudinal direction, i.e., the longitudinal structural stress result. The longitudinal structural stress result includes longitudinal internal forces and displacements. The longitudinal internal forces include longitudinal axial force, shear force, and bending moment, while the displacements include longitudinal displacement, rotation angle, and settlement.

[0092] like Figure 3 As shown, this is for applying additional loads. Bed coefficient The diagram below illustrates the bending moment results of the shield tunnel under different iteration numbers. The refined model results are obtained using a more complex finite element model, considering the actual geometry of the segment rings, the nonlinear contact between ring joints, the nonlinear reaction force of the foundation, and the actual distribution of earth pressure. However, this method is computationally expensive, time-consuming, and complex. The final calculation, however, is the result of multiple iterations of the nonlinear beam-spring model proposed in this invention. This model considers the nonlinear behavior of the ring joints while offering faster calculation speed, higher accuracy, and easier use by designers.

[0093] like Figure 4 As shown, to apply the same additional load Below, different bed coefficients A schematic diagram of the bending moment results for a shield tunnel is shown, where the calculated values ​​from the beam-spring model are the results of multiple iterations using the nonlinear beam-spring model as described in this invention. Figure 4 It can be seen that the inflection point is closely related to the additional load. Under different subgrade coefficients, the calculation results of the method of this invention are in high agreement with the calculation results of the refined model, thus confirming the correctness and reliability of the method proposed in this invention.

[0094] In summary, this invention accurately simulates the longitudinal stress of a shield tunnel by progressively updating the bending and shear stiffness of the ring joints. Furthermore, by constructing a three-dimensional stiffness surface to store the nonlinear relationships between the bending stiffness, bending moment, and longitudinal axial force of the ring joints, as well as between the shear stiffness, longitudinal axial force, and shear force, it achieves interpolation to solve for stiffness information. Finally, through convergence judgment and gradient update algorithms, the convergence of the calculation results is assessed, and the stiffness information is adjusted using gradient descent to ensure calculation accuracy.

[0095] Example 2:

[0096] This embodiment provides a longitudinal force calculation system for shield tunnels that considers the nonlinearity of ring-to-ring joints. The system includes:

[0097] The acquisition unit is used to acquire parameter information of the shield tunnel, including structural design parameters, material parameters, and geological parameters.

[0098] The first calculation unit is used to establish a finite element model of the shield tunnel based on the initial stiffness and parameter information of the ring joints, and solve the finite element model based on the preset load to obtain the first information, which includes the bending moment, shear force and longitudinal axial force of each ring joint of the shield tunnel.

[0099] The second calculation unit is used to construct the stiffness three-dimensional surface of the ring joint and calculate the stiffness information of the ring joint based on the stiffness three-dimensional surface and the first information.

[0100] The update unit is used to update the finite element model based on stiffness information and obtain the longitudinal structural stress results of the shield tunnel through the updated finite element model. The longitudinal structural stress results include longitudinal internal forces and displacements.

[0101] The first computing unit includes:

[0102] Construct sub-units to build the geometric model of the shield tunnel based on the structural design parameters;

[0103] The simulation sub-element is used in the geometric model to simulate segment rings using beam elements, inter-ring joints using spring elements with tensile, compressive, rotational and shear stiffness, and the interaction between segments and the formation using formation spring elements.

[0104] The first assignment sub-unit is used to assign material properties to the segment rings and ring-to-ring joints in the geometric model according to the material parameters;

[0105] The second sub-unit is used to assign the spring stiffness property between the shield tunnel and the surrounding strata in the geometric model according to the strata parameters.

[0106] Sub-elements are set to set the initial stiffness of each ring joint in the geometric model to obtain the finite element model of the shield tunnel. The initial stiffness includes the initial bending stiffness and the initial shear stiffness.

[0107] The second computing unit includes:

[0108] Discrete sub-elements are used to discretize the stiffness three-dimensional surface into bending stiffness-bending moment-longitudinal axial force stiffness matrices and shear stiffness-shear force-longitudinal axial force stiffness matrices.

[0109] The first calculation subunit is used to substitute the bending moment and longitudinal axial force of each ring joint into the bending stiffness-bending moment-longitudinal axial force stiffness matrix for linear difference calculation to obtain the bending stiffness of each ring joint.

[0110] The second calculation subunit is used to substitute the shear force and longitudinal axial force of each ring joint into the shear stiffness-shear force-longitudinal axial force stiffness matrix for linear difference calculation to obtain the shear stiffness of each ring joint.

[0111] The third calculation sub-unit is used to use the bending stiffness and shear stiffness as stiffness information for each ring joint.

[0112] The update unit includes:

[0113] The fourth computational subunit is used to calculate the convergence result of each loop joint using stiffness information and convergence criteria;

[0114] The first update sub-unit is used to update the stiffness information of all loop joints if the convergence result of at least one loop joint is non-convergence, so as to obtain the updated stiffness information.

[0115] The second update sub-unit is used to take the updated stiffness information as the initial stiffness of the finite element model and iterate the stiffness information through the updated finite element model until the convergence results of all ring joints are converged. Then, the longitudinal structural stress results of the shield tunnel are obtained through the current finite element model.

[0116] It should be noted that the specific methods by which each module performs operations in the system described in the above embodiments have been described in detail in the embodiments related to the method, and will not be elaborated here.

[0117] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0118] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for calculating the longitudinal force of a shield tunnel considering the nonlinearity of ring-to-ring joints, characterized in that, include: Obtain parameter information of the shield tunnel, including structural design parameters, material parameters, and geological parameters; A finite element model of the shield tunnel is established based on the initial stiffness and parameter information of the ring joints, and the finite element model is solved based on the preset load to obtain the first information, which includes the bending moment, shear force and longitudinal axial force of each ring joint of the shield tunnel. Construct a three-dimensional stiffness surface for the ring joint, and calculate the stiffness information of the ring joint based on the three-dimensional stiffness surface and the first information. The finite element model is updated based on stiffness information, and the longitudinal structural stress results of the shield tunnel are obtained through the updated finite element model. The longitudinal structural stress results include longitudinal internal forces and displacements. The calculation steps for the stiffness of the three-dimensional curved surface are as follows: Construct a refined numerical model of the entity with loop joints; By applying longitudinal axial force and bending moment to the solid refined numerical model, the opening angle of the ring joint under different longitudinal axial forces and bending moments is obtained; The bending stiffness of the ring joint is calculated by opening angle, and a first three-dimensional surface about bending stiffness, bending moment and longitudinal axial force is generated. By applying longitudinal axial force and shear force to the solid refined numerical model, the misalignment displacement of the ring joint under different longitudinal axial force and different shear force is obtained; The shear stiffness of the ring joint is calculated by the misalignment displacement, and a second three-dimensional surface is generated about the shear stiffness, shear force and longitudinal axial force. The first and second three-dimensional surfaces are used as the stiffness three-dimensional surfaces of the ring joint; The calculation steps for the stiffness information are as follows: The stiffness three-dimensional surface is discretized into a bending stiffness-bending moment-longitudinal axial force stiffness matrix and a shear stiffness-shear force-longitudinal axial force stiffness matrix. Substitute the bending moment and longitudinal axial force of each ring joint into the bending stiffness-bending moment-longitudinal axial force stiffness matrix and perform linear difference solution to obtain the bending stiffness of each ring joint. The shear force and longitudinal axial force of each ring joint are substituted into the shear stiffness-shear force-longitudinal axial force stiffness matrix for linear difference calculation to obtain the shear stiffness of each ring joint. Bending stiffness and shear stiffness are used as stiffness information for each ring joint.

2. The method for calculating the longitudinal force of a shield tunnel considering the nonlinearity of ring joints as described in claim 1, characterized in that... The steps for constructing the finite element model are as follows: Construct a geometric model of the shield tunnel based on the structural design parameters; In the geometric model, beam elements are used to simulate the segment rings, spring elements with tensile, compressive, rotational and shear stiffness are used to simulate the ring joints, and formation spring elements are used to simulate the interaction between the segments and the formation. The material properties of the segment rings and the joints between the rings in the geometric model are assigned according to the material parameters. The spring stiffness property between the shield tunnel and the surrounding strata is assigned to the geometric model based on the stratum parameters. By setting the initial stiffness of each ring joint in the geometric model, a finite element model of the shield tunnel is obtained. The initial stiffness includes the initial bending stiffness and the initial shear stiffness.

3. The method for calculating the longitudinal force of a shield tunnel considering the nonlinearity of ring joints as described in claim 1, characterized in that... The steps for obtaining the stress results of the longitudinal structure are as follows: The convergence result of each loop joint is calculated using stiffness information and convergence criteria; If at least one loop joint fails to converge, then the stiffness information of all loop joints is updated to obtain the updated stiffness information. The updated stiffness information is used as the initial stiffness of the finite element model. The next iteration of stiffness information is performed using the updated finite element model until the convergence results of all ring joints are converged. Then, the longitudinal structural stress results of the shield tunnel are obtained through the current finite element model.

4. The method for calculating the longitudinal force of a shield tunnel considering the nonlinearity of ring joints as described in claim 3, characterized in that... The obtained updated stiffness information includes: Set the rate of change for stiffness updates; A gradient calculation formula is constructed using the current stiffness information and the stiffness information obtained in the previous iteration. The stiffness gradient of each ring joint is calculated using the gradient calculation formula. The stiffness information of all loop joints is updated by updating the rate of change, stiffness gradient, and descent direction of the stiffness gradient, thus obtaining the updated stiffness information.

5. A system for calculating the longitudinal force of a shield tunnel considering the nonlinearity of ring-to-ring joints, characterized in that, include: The acquisition unit is used to acquire parameter information of the shield tunnel, including structural design parameters, material parameters, and geological parameters. The first calculation unit is used to establish a finite element model of the shield tunnel based on the initial stiffness and parameter information of the ring joints, and solve the finite element model based on the preset load to obtain the first information, which includes the bending moment, shear force and longitudinal axial force of each ring joint of the shield tunnel. The second calculation unit is used to construct the stiffness three-dimensional surface of the ring joint and calculate the stiffness information of the ring joint based on the stiffness three-dimensional surface and the first information. The update unit is used to update the finite element model according to the stiffness information, and to obtain the longitudinal structural stress results of the shield tunnel through the updated finite element model. The longitudinal structural stress results include longitudinal internal forces and displacements. The calculation steps for the stiffness of the three-dimensional curved surface are as follows: Construct a refined numerical model of the entity with loop joints; By applying longitudinal axial force and bending moment to the solid refined numerical model, the opening angle of the ring joint under different longitudinal axial forces and bending moments is obtained; The bending stiffness of the ring joint is calculated by opening angle, and a first three-dimensional surface about bending stiffness, bending moment and longitudinal axial force is generated. By applying longitudinal axial force and shear force to the solid refined numerical model, the misalignment displacement of the ring joint under different longitudinal axial force and different shear force is obtained; The shear stiffness of the ring joint is calculated by the misalignment displacement, and a second three-dimensional surface is generated about the shear stiffness, shear force and longitudinal axial force. The first and second three-dimensional surfaces are used as the stiffness three-dimensional surfaces of the ring joint; The second computing unit includes: Discrete sub-elements are used to discretize the stiffness three-dimensional surface into bending stiffness-bending moment-longitudinal axial force stiffness matrices and shear stiffness-shear force-longitudinal axial force stiffness matrices. The first calculation subunit is used to substitute the bending moment and longitudinal axial force of each ring joint into the bending stiffness-bending moment-longitudinal axial force stiffness matrix for linear difference calculation to obtain the bending stiffness of each ring joint. The second calculation subunit is used to substitute the shear force and longitudinal axial force of each ring joint into the shear stiffness-shear force-longitudinal axial force stiffness matrix for linear difference calculation to obtain the shear stiffness of each ring joint. The third calculation sub-unit is used to use the bending stiffness and shear stiffness as stiffness information for each ring joint.

6. The shield tunnel longitudinal force calculation system considering the nonlinearity of ring joints according to claim 5, characterized in that, The first computing unit includes: Construct sub-units to build the geometric model of the shield tunnel based on the structural design parameters; The simulation sub-element is used in the geometric model to simulate segment rings using beam elements, inter-ring joints using spring elements with tensile, compressive, rotational and shear stiffness, and the interaction between segments and the formation using formation spring elements. The first assignment sub-unit is used to assign material properties to the segment rings and ring-to-ring joints in the geometric model according to the material parameters; The second sub-unit is used to assign the spring stiffness property between the shield tunnel and the surrounding strata in the geometric model according to the strata parameters. Sub-elements are set to set the initial stiffness of each ring joint in the geometric model to obtain the finite element model of the shield tunnel. The initial stiffness includes the initial bending stiffness and the initial shear stiffness.

7. The shield tunnel longitudinal force calculation system considering the nonlinearity of ring joints according to claim 5, characterized in that, The update unit includes: The fourth computational subunit is used to calculate the convergence result of each loop joint using stiffness information and convergence criteria; The first update sub-unit is used to update the stiffness information of all loop joints if the convergence result of at least one loop joint is non-convergence, so as to obtain the updated stiffness information. The second update sub-unit is used to take the updated stiffness information as the initial stiffness of the finite element model and iterate the stiffness information through the updated finite element model until the convergence results of all ring joints are converged. Then, the longitudinal structural stress results of the shield tunnel are obtained through the current finite element model.

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