Shield tunnel longitudinal stress calculation method and system considering nonlinearity of joint between rings

Abstract

The invention provides a shield tunnel longitudinal stress calculation method and system considering nonlinearity of inter-ring joints, and relates to the technical field of underground engineering.The method comprises the steps that parameter information of a shield tunnel is obtained, and the parameter information comprises structural design parameters, material parameters and stratum parameters; a finite element model of the shield tunnel is established according to the initial rigidity and parameter information of the inter-ring joints, the finite element model is solved based on a preset load, first information is obtained, and the first information comprises bending moment, shearing force and longitudinal axial force of each inter-ring joint of the shield tunnel; constructing a rigidity three-dimensional curved surface of the inter-ring joint, and calculating rigidity information of the inter-ring joint according to the rigidity three-dimensional curved surface and the first information; the finite element model is updated according to the rigidity information, and the longitudinal structure stress result of the shield tunnel is obtained through the updated finite element model. The method solves the problem that when an existing beam-spring model simulates the nonlinear behavior of the joint between the rings, the change of the flexural rigidity and the shear rigidity along with the load is neglected.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of underground engineering, in particular to a shield tunnel longitudinal stress calculation method and system considering the nonlinearity of inter-ring joints. BACKGROUND

[0002] The bending stiffness and shear stiffness of the inter-ring joint of a shield tunnel have been widely studied. Although the longitudinal beam-spring model is widely used in the structural design and mechanical performance research of shield tunnels, the existing methods usually calculate the bending stiffness of the inter-ring joint as a constant value, which ignores the nonlinear characteristics of the bending stiffness of the inter-ring joint. In fact, the bending stiffness of the inter-ring joint dynamically adjusts with changes in external loads, constraint conditions, and deformation patterns, and the existing model cannot reflect this dynamic change process. Therefore, the traditional method based on a constant stiffness value cannot accurately simulate the mechanical response of a shield tunnel under actual working conditions, resulting in a deviation of the calculation results from the actual situation.

[0003] In addition, the existing longitudinal beam-spring model does not consider the shear stiffness of the inter-ring joint, which makes it unable to effectively simulate the misalignment deformation of the inter-ring joint that may occur during the longitudinal deformation of the shield tunnel. This defect limits the applicability of the model under complex working conditions and cannot fully reflect the true mechanical behavior of the shield tunnel structure.

[0004] Therefore, the existing longitudinal mechanical response analysis model of a shield tunnel does not fully consider the nonlinear characteristics of the stiffness of the inter-ring joint with changes in load, nor does it simulate the misalignment deformation of the inter-ring joint. This shows that it is unreasonable to simply take the stiffness of the inter-ring joint as a constant value. There is a mutual influence relationship between the stiffness of the inter-ring joint and the internal forces of the segment lining structure, and the stiffness value must be updated step by step to approximate the true mechanical state under actual working conditions. SUMMARY

[0005] The present application relates to the technical field of underground engineering, in particular to a shield tunnel longitudinal stress calculation method and system considering the nonlinearity of inter-ring joints. In order to achieve the above-mentioned purpose, the technical scheme adopted by the present application is as follows: A shield tunnel longitudinal stress calculation method considering the nonlinearity of inter-ring joints is provided, comprising: obtaining parameter information of the shield tunnel, the parameter information including 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 predetermined load to obtain first information, the first information including the bending moment, shear force, and longitudinal axial force of each inter-ring joint of the shield tunnel; update the finite element model according to 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 including longitudinal internal force and displacement.

[0006] In a second aspect, the application further provides a shield tunnel longitudinal stress calculation system considering inter-ring joint nonlinearity, comprising: An acquisition unit is configured to acquire parameter information of the shield tunnel, the parameter information including structural design parameters, material parameters and stratum parameters. A first calculation unit is configured to establish a finite element model of the shield tunnel according to initial stiffness of the inter-ring joint and the parameter information, and solve the finite element model based on a preset load to obtain first information, the first information including bending moment, shear force and longitudinal axial force of each inter-ring joint of the shield tunnel. A second calculation unit is configured to construct a stiffness three-dimensional surface of the inter-ring joint, and calculate stiffness information of the inter-ring joint according to the stiffness three-dimensional surface and the first information. An update unit is configured to update the finite element model according to 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 including longitudinal internal force and displacement.

[0007] The application has the following beneficial effects: the application can accurately simulate the mechanical response of the tunnel structure under actual working conditions by gradually updating the stiffness of the inter-ring joint and dynamically adjusting the stiffness information based on the internal force (bending moment, shear force and longitudinal axial force) of the inter-ring joint. Compared with the traditional method, the application can be closer to the actual load state, ensuring the accuracy of the calculation results. At the same time, it can accurately judge whether the stiffness change after each calculation meets the set precision, and optimize the stiffness adjustment process using the gradient update method, ensuring that each calculation gradually approaches the true value, not only ensuring high-precision calculation results, but also improving the stability and reliability of the calculation.

[0008] Other features and advantages of the application will be set forth in the following description, and in part will become apparent to those skilled in the art from the following, or can be learned by practice of the application as described in the written description and claims hereof. The objectives and other advantages of the application will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings. BRIEF DESCRIPTION OF DRAWINGS

[0009] In order to more clearly illustrate the technical solutions of the embodiments of the application, the following will briefly introduce the drawings needed to be used in the embodiments. It should be understood that the following drawings only show some of the embodiments of the application, and therefore should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can also be obtained without creative labor on the basis of these drawings.

[0010] Figure 1A flowchart of a shield tunnel longitudinal stress calculation method considering inter-ring joint nonlinearity is shown in the embodiment of the present application. Figure 2 A schematic diagram of a shield tunnel is shown in the embodiment of the present application. Figure 3 A schematic diagram of a shield tunnel is shown in the embodiment of the present application. Figure 4 A schematic diagram of a shield tunnel is shown in the embodiment of the present application. DETAILED DESCRIPTION

[0011] To make the objectives, technical solutions and advantages of the embodiments of the present application clearer, the following will be combined with the accompanying drawings of the embodiments of the present application to make a clear and complete description of the technical solutions in the embodiments of the present application. Obviously, the described embodiments are some of the embodiments of the present application, but not all the embodiments. The components of the embodiments of the present application described and shown in the accompanying drawings can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present application provided in the accompanying drawings is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the scope of protection of the present application.

[0012] It should be noted that: similar reference numerals and letters represent similar items in the following drawings, therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings. Meanwhile, in the description of the present application, the terms “first”, “second” and the like are only used for distinguishing description, and cannot be understood as indicating or implying relative importance.

[0013] Embodiment 1 The embodiment provides a shield tunnel longitudinal stress calculation method considering inter-ring joint nonlinearity.

[0014] Referring to Figure 1 , the method includes steps S1, S2, S3 and S4.

[0015] In the embodiment, as shown in Figure 2 , in the stress analysis of the shield tunnel, a plurality of n segment rings and n-1 inter-ring joints are usually regarded as a whole and simplified as a continuous mechanical model. The connection part between the two segment rings is called an inter-ring joint, a longitudinal bolt is an important component of the inter-ring joint, and a segment ring is composed of a plurality of segments.

[0016] Step S1: acquiring parameter information of the shield tunnel, the parameter information including structural design parameters, material parameters and stratum parameters; In this embodiment, the structural design parameters of the shield tunnel include the outer diameter of the segment, the thickness of the segment, the width of the segment, and the number of bolts of the inter-ring joint. The material parameters are the concrete grade and the bolt strength. Different concrete grades have different mechanical properties, including compressive strength, tensile strength, and elastic modulus. The concrete grade is the strength grade of the concrete used to construct the segment of the shield tunnel. Different bolt strengths also have different mechanical properties. The stratum parameters include the bed coefficient, which reflects the stiffness characteristics of the stratum and is used to represent the interaction between the shield tunnel and the surrounding stratum.

[0017] Step S2: establishing a finite element model of the shield tunnel according to the initial stiffness and parameter information of the inter-ring joint, and solving the finite element model based on a preset load to obtain first information, the first information including the bending moment, shear force, and longitudinal axial force of each inter-ring joint of the shield tunnel; In this embodiment, after the preset load is loaded into the finite element model, numerical calculation is performed to obtain the mechanical response of the shield tunnel, i.e., the bending moment, shear force, and longitudinal axial force of each inter-ring joint.

[0018] In step S2, the construction steps of the finite element model are as follows: Step S21: constructing a geometric model of the shield tunnel according to the structural design parameters; Step S22: in the geometric model, using beam elements to simulate the segment ring, using spring elements with tensile-compressive, rotational, and shear stiffness to simulate the inter-ring joint, and using stratum spring elements to simulate the interaction between the segment and the stratum; In this embodiment, a modified longitudinal beam-spring model is used for simulation, i.e., a nonlinear beam-spring model. The segment ring is simulated by beam elements, and the stiffness of the segment ring uses the stiffness of the segment concrete, as shown in Figure 2 , and represent the compressive stiffness and bending stiffness of the segment ring, respectively.

[0019] The inter-ring joint is simulated by spring elements with tensile-compressive, rotational, and shear stiffness, as shown in Figure 2 Rotational springs, axial springs, and shear springs are used to simulate , and , respectively, and the stiffness of the inter-ring joint is nonlinear, where represents the shear stiffness, represents the bending stiffness, represents the axial stiffness.

[0020] Step S23: assigning material properties to the segment ring and the inter-ring joint in the geometric model according to the material parameters; Step S24: according to the stratum parameters, a spring stiffness attribute between the shield tunnel and the surrounding stratum in the geometric model is given; Step S25: an initial stiffness of each inter-ring joint in the geometric model is set, and a finite element model of the shield tunnel is obtained, the initial stiffness including an initial bending stiffness and an initial shear stiffness.

[0021] Step S3: a stiffness three-dimensional surface of the inter-ring joint is constructed, and the stiffness information of the inter-ring joint is calculated according to the stiffness three-dimensional surface and the first information; In the embodiment, the stiffness three-dimensional surface of the inter-ring joint is obtained through numerical calculation.

[0022] In step S3, the calculation step of the stiffness three-dimensional surface is: Step A1: a solid refined numerical model of the inter-ring joint is constructed; In the embodiment, the solid refined numerical model of the inter-ring joint is actually a three-dimensional refined numerical calculation model.

[0023] Step A2: a longitudinal axial force and a bending moment are applied to the solid refined numerical model, and an opening angle of the inter-ring joint under different longitudinal axial forces and different bending moments is obtained; In the embodiment, the longitudinal axial force and the bending moment are applied to the solid refined numerical model according to a certain loading scheme , so that the inter-ring joint is deformed to open, and the opening angle of the inter-ring joint is obtained, denoted as . During the loading process, the opening deformation of the inter-ring joint is recorded in real time, that is, the change curve of the opening angle with the change of the longitudinal axial force and the bending moment is recorded.

[0024] Step A3: the bending stiffness of the inter-ring joint is calculated through the opening angle, and a first three-dimensional surface about the bending stiffness-bending moment-longitudinal axial force is generated; In the embodiment, according to the bending stiffness calculation formula and the change curve of the opening angle, the bending stiffness of the inter-ring joint under different longitudinal axial forces is calculated, wherein the bending stiffness calculation formula is: In the formula, M represents the bending moment, represents the opening angle, and represents the bending stiffness.

[0025] After the bending stiffness of the inter-ring joint under multiple longitudinal axial forces is calculated, the corresponding bending moment is obtained. ​​​​The data are collated and analyzed, and the first three-dimensional surface of bending stiffness-bending moment-longitudinal axial force is obtained.

[0026] Step A4: Apply longitudinal axial force and shear force to the entity refined numerical model to obtain the misalignment displacement of the inter-ring joint under different longitudinal axial forces and different shear forces; In this embodiment, a longitudinal axial force is applied to the entity refined numerical model according to a specific loading scheme. and shear force , control the loading process, so that the inter-ring joint produces a misalignment displacement, which is recorded as .

[0027] Monitor the misalignment deformation of the inter-ring joint during loading and record the misalignment displacement With shear force Changing data, while recording the corresponding longitudinal axial force , and obtain different longitudinal axial forces Next, the displacement With shear force The changing curve of change.

[0028] Step A5: Calculate the shear stiffness of the inter-ring joint through the misalignment displacement, and generate a second three-dimensional surface of shear stiffness-shear force-longitudinal axial force; In this embodiment, according to the shear stiffness calculation formula and the displacement curve, different longitudinal axial forces are calculated. The shear stiffness of the lower ring joint, where the shear stiffness calculation formula is: ; Where, Indicates the displacement of the platform, represents the shear force, Represents shear stiffness.

[0029] By calculating multiple longitudinal axial forces The shear stiffness of the lower ring joint will be compared with the corresponding shear force The data is collated and analyzed to form the second three-dimensional surface of shear stiffness-shear force-longitudinal axial force.

[0030] Step A6: Use the first three-dimensional curved surface and the second three-dimensional curved surface as the stiffness three-dimensional curved surfaces of the inter-ring joint.

[0031] In step S3, the stiffness information is calculated as follows: Step B1: Discrete the stiffness three-dimensional surface into a bending stiffness-bending moment-longitudinal axial force stiffness matrix and a shear stiffness-shear force-longitudinal axial force stiffness matrix; Step B2: linear difference is solved by substituting the bending moment and longitudinal axial force of each ring-to-ring joint into the bending stiffness-bending moment-longitudinal axial force stiffness matrix to obtain the bending stiffness of each ring-to-ring joint; Step B3: linear difference is solved by substituting the shear force and longitudinal axial force of each ring-to-ring joint into the shear stiffness-shear force-longitudinal axial force stiffness matrix to obtain the shear stiffness of each ring-to-ring joint; Step B4: the bending stiffness and the shear stiffness are taken as the stiffness information of each ring-to-ring joint.

[0032] Step S4: updating the finite element model according to the stiffness information, and obtaining the longitudinal structural stress results of the shield tunnel by the updated finite element model, the longitudinal structural stress results including longitudinal internal forces and displacements.

[0033] In step S4, the obtaining step of the longitudinal structural stress results is: Step S41: calculating the convergence results of each ring-to-ring joint by the stiffness information and the convergence criterion; In this embodiment, the absolute value of the difference between the bending stiffnesses of two adjacent iterations of each ring-to-ring joint is taken as the first calculation value, and the absolute value of the difference between the shear stiffnesses of two adjacent iterations of each ring-to-ring joint is taken as the second calculation value.

[0034] If the first calculation value is less than the first preset threshold, it means that the convergence result of the ring-to-ring joint in the bending stiffness is not convergent, and if the second calculation value is less than the second preset threshold, it means that the convergence result of the ring-to-ring joint in the shear stiffness is not convergent.

[0035] Step S42: if the convergence results of at least one ring-to-ring joint are not convergent, updating the stiffness information of all ring-to-ring joints to obtain updated stiffness information; In this embodiment, the convergence result of each ring-to-ring joint is not convergent as long as there is one of the bending stiffness and the shear stiffness that is not convergent.

[0036] In step S42, the updated stiffness information includes: Step S421: setting a change rate of stiffness updating; In this embodiment, the change rate controls the convergence speed, and the change rate is set to 0.5, which represents the step size of each update.

[0037] Step S422: constructing a gradient calculation formula, the gradient calculation formula being constructed by the current stiffness information and the stiffness information obtained in the last iteration; In this embodiment, two objective functions are constructed, which are the bending stiffness objective function and the shear stiffness objective function. Specifically, the bending stiffness objective function is constructed with respect to the longitudinal axial force and the bending moment The bending stiffness objective function of the inter-ring joint is , and construct about the longitudinal axial force and shear force The shear stiffness objective function of the inter-ring joint is .

[0038] The gradient is a vector pointing to the direction in which the objective function changes fastest at that point. In this step, the gradient is simplified to half the difference between the stiffness information of two adjacent iterations of the inter-loop joint.

[0039] Therefore, the gradient calculation formula includes the bending stiffness gradient calculation formula and the shear stiffness gradient calculation formula, specifically: ; ; Where, represents the bending stiffness gradient, represents the shear stiffness gradient, represents the bending moment, represents the shear force, represents the longitudinal axial force, Indicates the The bending stiffness obtained by the iteration is Indicates the The bending stiffness obtained by the iteration is Indicates the The shear stiffness obtained by the iteration is Indicates the The shear stiffness obtained by the iteration.

[0040] Step S423: Calculate the stiffness gradient of each inter-ring joint using a gradient calculation formula; Step S424: updating the stiffness information of all the inter-loop joints by using the change rate, stiffness gradient, and the descending direction of the stiffness gradient to obtain updated stiffness information.

[0041] In this embodiment, the stiffness information of the inter-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 descending direction). This is because the stiffness gradient points to the direction in which the function value increases fastest, and the goal in this embodiment is to find the minimum value. Therefore, the formula for updating the stiffness information of each inter-loop joint is: ; ; Where, represents the updated bending stiffness, represents the updated shear stiffness, represents the bending stiffness before updating, Shear stiffness before updating, represents the bending stiffness gradient before updating, represents the shear stiffness gradient before updating, Indicates the rate of change.

[0042] Step S43: Use the updated stiffness information as the initial stiffness of the finite element model, and iterate the stiffness information for the next time through the updated finite element model until the convergence results of all inter-ring joints are converged. Then, obtain the longitudinal structural force results of the shield tunnel through the current finite element model.

[0043] In this embodiment, if the convergence condition is not met, the stiffness gradient is repeatedly calculated and the stiffness information is updated, and then input into the finite element model as the initial stiffness to update the bending moment, shear force and longitudinal axial force of the inter-ring joint, and then the difference is performed through the stiffness three-dimensional surface to obtain iterative stiffness information until a certain convergence condition is met. The stiffness information obtained by the last iteration is input into the finite element model to obtain the finite element model to obtain the overall stress state of the shield tunnel in the longitudinal direction, that is, the longitudinal structural stress result, wherein the longitudinal structural stress result includes longitudinal internal force and displacement, the longitudinal internal force includes longitudinal axial force, shear force and bending moment, and the displacement includes longitudinal displacement, rotation angle and settlement.

[0044] like Figure 3 As shown, the additional load is applied , base bed coefficient Schematic diagram of the bending moment results of a shield tunnel at different iteration numbers. The refined model results are obtained using a more complex finite element model, taking into account the actual geometry of the segment rings, the nonlinear contact of the inter-ring joints, the nonlinear reaction of the foundation, the true distribution of earth pressure, etc. However, this method is computationally expensive, time-consuming, and complex. The final calculation is the result of multiple iterations of the nonlinear beam-spring model proposed in the method of this invention. This model takes into account the nonlinear behavior of the inter-ring joints while simulating faster and more accurate calculations, making it easier for designers to use.

[0045] like Figure 4 As shown, the same additional load is applied Under different base bed coefficients Schematic diagram of the bending moment results of the shield tunnel, where the beam-spring model calculation value is the result of multiple iterations of the nonlinear beam-spring model used in this invention. Figure 4 It can be seen that the inflection point position is closely related to the additional load. Under different base bed coefficients, the calculation results of the method of the present invention are highly consistent with the calculation results of the refined model, thus confirming the correctness and reliability of the method proposed by the present invention.

[0046] To sum up, the application simulates the longitudinal stress result of the shield tunnel by gradually updating the bending stiffness and shear stiffness of the inter-ring joint, and stores the nonlinear relationship between the bending stiffness, bending moment and longitudinal axial force of the inter-ring joint and the nonlinear relationship between the shear stiffness, longitudinal axial force and shear force by constructing a stiffness three-dimensional surface, so as to realize interpolation solving of the stiffness information. Finally, the convergence of the calculation result is judged by the convergence judgment and gradient updating algorithm, and the gradient descent method is used to adjust the stiffness information, so as to ensure the calculation accuracy.

[0047] Embodiment 2 The embodiment provides a shield tunnel longitudinal stress calculation system considering the nonlinearity of the inter-ring joint, and the system comprises: An acquisition unit is configured to acquire parameter information of the shield tunnel, wherein the parameter information comprises structural design parameters, material parameters and stratum parameters; A first calculation unit is configured to establish a finite element model of the shield tunnel according to the initial stiffness of the inter-ring joint and the parameter information, and solve the finite element model based on a preset load to obtain first information, wherein the first information comprises a bending moment, a shear force and a longitudinal axial force of each inter-ring joint of the shield tunnel; A second calculation unit is configured to construct a stiffness three-dimensional surface of the inter-ring joint, and calculate stiffness information of the inter-ring joint according to the stiffness three-dimensional surface and the first information; An updating unit is configured to update the finite element model according to the stiffness information, and acquire a longitudinal structural stress result of the shield tunnel through the updated finite element model, wherein the longitudinal structural stress result comprises a longitudinal internal force and a displacement.

[0048] The first calculation unit comprises: A construction subunit is configured to construct a geometric model of the shield tunnel according to the structural design parameters; A simulation subunit is configured to simulate, in the geometric model, a segment ring by using a beam element, simulate an inter-ring joint by using a spring element with tensile, compressive, rotational and shear stiffness, and simulate the interaction between the segment and the stratum by using a stratum spring element; A first assigning subunit is configured to assign material properties of the segment ring and the inter-ring joint in the geometric model according to the material parameters; A second assigning subunit is configured to assign spring stiffness properties between the shield tunnel and the surrounding stratum in the geometric model according to the stratum parameters; A setting subunit is configured to set an initial stiffness of each inter-ring joint in the geometric model to obtain the finite element model of the shield tunnel, wherein the initial stiffness comprises an initial bending stiffness and an initial shear stiffness.

[0049] The second calculation unit comprises: A discretization subunit is configured to discretize the stiffness three-dimensional surface into a bending stiffness-bending moment-longitudinal axial force stiffness matrix and a shear stiffness-shear force-longitudinal axial force stiffness matrix. The first calculation subunit is used to substitute the bending moment and longitudinal axial force of each inter-ring joint into the bending stiffness-bending moment-longitudinal axial force stiffness matrix to perform linear difference solution to obtain the bending stiffness of each inter-ring joint; The second calculation subunit is used to substitute the shear force and longitudinal axial force of each inter-ring joint into the shear stiffness-shear force-longitudinal axial force stiffness matrix to perform linear difference solution to obtain the shear stiffness of each inter-ring joint; The third calculation subunit is used to use the bending stiffness and the shear stiffness as stiffness information of each inter-ring joint.

[0050] The updating unit includes: a fourth calculation subunit, configured to calculate a convergence result of each inter-ring joint using stiffness information and a convergence criterion; A first updating subunit is configured to update stiffness information of all inter-loop joints to obtain updated stiffness information if the convergence result of at least one inter-loop joint is non-convergence; The second updating subunit is used to use the updated stiffness information as the initial stiffness of the finite element model, and to iterate the stiffness information for the next time through the updated finite element model until the convergence results of all the inter-ring joints are converged. Then, the longitudinal structural force results of the shield tunnel are obtained through the current finite element model.

[0051] It should be noted that, regarding the system in the above embodiment, the specific manner in which each module performs operations has been described in detail in the embodiment of the method, and will not be elaborated on here.

[0052] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

[0053] 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 modifications or substitutions that can be easily conceived by a person 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 based on the scope of protection of the claims.

Claims

1. A method for calculating the longitudinal forces of a shield tunnel considering the nonlinearity of the inter-ring joints, characterized in that: include: Acquiring parameter information of a shield tunnel, wherein the parameter information includes structural design parameters, material parameters, and formation parameters; Establishing a finite element model of the shield tunnel based on the initial stiffness and parameter information of the inter-ring joints, and solving the finite element model based on a preset load to obtain first information, wherein the first information includes a bending moment, a shear force, and a longitudinal axial force of each inter-ring joint of the shield tunnel; Constructing a stiffness three-dimensional surface of the inter-ring joint, and calculating stiffness information of the inter-ring joint according to the stiffness three-dimensional surface and the first information; The finite element model is updated according to the stiffness information, and the longitudinal structural stress results of the shield tunnel are obtained through the updated finite element model, wherein the longitudinal structural stress results include longitudinal internal force and displacement.

2. The method for calculating longitudinal forces in a shield tunnel considering the nonlinearity of inter-ring joints according to claim 1 is characterized in that: The steps for constructing the finite element model are: 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 tension, compression, rotation and shear stiffness are used to simulate the inter-ring joints, and formation spring elements are used to simulate the interaction between the segments and the formation. Assign material properties to the segment rings and inter-ring joints in the geometric model based on material parameters; The spring stiffness properties between the shield tunnel and the surrounding strata in the geometric model are assigned according to the stratum parameters; The initial stiffness of each inter-ring joint in the geometric model is set to obtain a finite element model of the shield tunnel, wherein the initial stiffness includes an initial bending stiffness and an initial shear stiffness.

3. The method for calculating longitudinal forces in a shield tunnel considering the nonlinearity of inter-ring joints according to claim 1 is characterized in that: The calculation steps of the stiffness three-dimensional surface are: Construct a detailed numerical model of the inter-ring joint; Apply longitudinal axial force and bending moment to the entity refined numerical model to obtain the opening angle of the inter-ring joint under different longitudinal axial forces and different bending moments; The bending stiffness of the inter-ring joint is calculated by the opening angle, and the first three-dimensional surface of bending stiffness-bending moment-longitudinal axial force is generated; Apply longitudinal axial force and shear force to the entity refined numerical model to obtain the misalignment displacement of the inter-ring joint under different longitudinal axial forces and different shear forces; The shear stiffness of the inter-ring joint is calculated by the misalignment displacement, and a second three-dimensional surface of shear stiffness-shear force-longitudinal axial force is generated; The first three-dimensional surface and the second three-dimensional surface are used as the stiffness three-dimensional surfaces of the joint between the rings.

4. The method for calculating longitudinal forces in a shield tunnel considering nonlinearity of inter-ring joints according to claim 1 is characterized in that: The calculation steps of the stiffness information are: Discrete the stiffness three-dimensional surface into bending stiffness-bending moment-longitudinal axial force stiffness matrix and shear stiffness-shear force-longitudinal axial force stiffness matrix; Substitute the bending moment and longitudinal axial force of each inter-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 inter-ring joint; Substitute the shear force and longitudinal axial force of each inter-ring joint into the shear stiffness-shear force-longitudinal axial force stiffness matrix and perform linear difference solution to obtain the shear stiffness of each inter-ring joint; The bending stiffness and shear stiffness are taken as the stiffness information of each inter-ring joint.

5. The method for calculating longitudinal forces of a shield tunnel considering nonlinearity of inter-ring joints according to claim 1 is characterized in that: The steps for obtaining the longitudinal structure stress results are: Calculate the convergence results of each inter-ring joint using stiffness information and convergence criteria; If the convergence result of at least one inter-ring joint is not converged, the stiffness information of all inter-ring joints is updated to obtain 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 through the updated finite element model until the convergence results of all inter-ring joints are converged. The longitudinal structural force results of the shield tunnel are obtained through the current finite element model.

6. The method for calculating longitudinal forces in a shield tunnel considering nonlinearity of inter-ring joints according to claim 5 is characterized in that: The updated stiffness information is obtained, including: Set the rate of change of stiffness update; Constructing a gradient calculation formula, wherein the gradient calculation formula is constructed by using the current stiffness information and the stiffness information obtained in the previous iteration; The stiffness gradient of each inter-ring joint is calculated using the gradient calculation formula; The stiffness information of all inter-ring joints is updated by the change rate, stiffness gradient and descending direction of the stiffness gradient to obtain the updated stiffness information.

7. A shield tunnel longitudinal force calculation system considering the nonlinearity of inter-ring joints, characterized by: include: an acquisition unit, configured to acquire parameter information of a shield tunnel, wherein the parameter information includes structural design parameters, material parameters, and formation parameters; a first calculation unit, configured to establish a finite element model of the shield tunnel based on the initial stiffness and parameter information of the inter-ring joints, and solve the finite element model based on a preset load to obtain first information, wherein the first information includes a bending moment, a shear force, and a longitudinal axial force of each inter-ring joint of the shield tunnel; a second calculation unit, configured to construct a stiffness three-dimensional surface of the inter-ring joint, and calculate stiffness information of the inter-ring joint according to the stiffness three-dimensional surface and the first information; The updating unit is used to update the finite element model according to the stiffness information, and obtain the longitudinal structural force results of the shield tunnel through the updated finite element model, wherein the longitudinal structural force results include longitudinal internal force and displacement.

8. The shield tunnel longitudinal force calculation system considering the nonlinearity of inter-ring joints according to claim 7 is characterized in that: The first computing unit includes: A construction subunit is used to construct a geometric model of the shield tunnel according to the structural design parameters; The simulation sub-unit is used to simulate the segment rings with beam elements, simulate the inter-ring joints with spring elements with tension, compression, rotation and shear stiffness, and simulate the interaction between the segment and the formation with formation spring elements in the geometric model; The first assigning subunit is used to assign material properties of the segment rings and the inter-ring joints in the geometric model according to the material parameters; The second assigning subunit is used to assign the spring stiffness properties between the shield tunnel and the surrounding strata in the geometric model according to the stratum parameters; A subunit is set to set the initial stiffness of each inter-ring joint in the geometric model to obtain a finite element model of the shield tunnel, wherein the initial stiffness includes an initial bending stiffness and an initial shear stiffness.

9. The shield tunnel longitudinal force calculation system considering the nonlinearity of inter-ring joints according to claim 7 is characterized in that: The second calculation unit includes: Discrete sub-units, used to discretize the stiffness three-dimensional surface into a bending stiffness-bending moment-longitudinal axial force stiffness matrix and a shear stiffness-shear force-longitudinal axial force stiffness matrix; The first calculation subunit is used to substitute the bending moment and longitudinal axial force of each inter-ring joint into the bending stiffness-bending moment-longitudinal axial force stiffness matrix to perform linear difference solution to obtain the bending stiffness of each inter-ring joint; The second calculation subunit is used to substitute the shear force and longitudinal axial force of each inter-ring joint into the shear stiffness-shear force-longitudinal axial force stiffness matrix to perform linear difference solution to obtain the shear stiffness of each inter-ring joint; The third calculation subunit is used to use the bending stiffness and the shear stiffness as stiffness information of each inter-ring joint.

10. The shield tunnel longitudinal force calculation system considering the nonlinearity of inter-ring joints according to claim 7 is characterized in that: The updating unit includes: a fourth calculation subunit, configured to calculate a convergence result of each inter-ring joint using stiffness information and a convergence criterion; A first updating subunit is configured to update stiffness information of all inter-loop joints to obtain updated stiffness information if the convergence result of at least one inter-loop joint is non-convergence; The second updating subunit is used to use the updated stiffness information as the initial stiffness of the finite element model, and to iterate the stiffness information for the next time through the updated finite element model until the convergence results of all the inter-ring joints are converged. Then, the longitudinal structural force results of the shield tunnel are obtained through the current finite element model.

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