Design method of waterproof rubber sealing gasket for shield tunnel

Abstract

The invention provides a design method of a waterproof rubber sealing gasket for a shield tunnel. The design method comprises the following steps: acquiring a plurality of material parameters and a plurality of boundary conditions of the rubber sealing gasket; on the basis of a pre-established working condition numerical analysis model, according to the multiple material parameters and the multiple boundary conditions of the rubber sealing gasket, experimental design parameters of the rubber sealing gasket are determined; verifying the experimental design parameters of the rubber sealing gasket based on a preset experimental scheme, and determining the design parameters of the rubber sealing gasket according to the verification result of the experimental design parameters of the rubber sealing gasket. According to the method, the experimental design parameters can be determined at least through the pre-established working condition numerical analysis model, the experimental design parameters are verified according to actual experiments, the design parameters of the rubber sealing gasket are determined, and the reliability of actual engineering application of the shield tunnel sealing gasket is improved.

Description

Technical Field

[0001] The present application relates to the technical field of shield tunnel design, and in particular to a design method for a rubber sealing pad used for waterproofing a shield tunnel. Background Art

[0002] Shield tunnels are widely used in infrastructure such as subways, highways, and water conservancy projects, and their long-term, stable operation is of great significance to socioeconomic development. Tunnel waterproofing performance is directly related to the lifespan and safety of the structure. Rubber gaskets, as key waterproofing components in tunnel segment joints, play a central role in preventing groundwater seepage and maintaining tunnel structural safety. By closely contacting the segment sealing grooves, the gaskets form a physical barrier to withstand high water pressure shocks in complex geological conditions. However, the combined effects of construction, opening, offset, and water pressure can significantly affect the gasket's waterproofing performance.

[0003] Current research on shield tunnel gaskets focuses on idealized waterproofing performance evaluation under a single operating condition, lacking a systematic analysis of the coupled effects of multiple factors, including opening, misalignment, and water pressure. Traditional experimental methods, due to limited simulation conditions, struggle to accurately quantify the stress distribution and deformation patterns of gaskets under complex operating conditions. This results in a lack of scientific basis for gasket optimization design, limiting their reliability in practical engineering applications. Summary of the Invention

[0004] In view of this, the purpose of this application is to provide a design method for rubber sealing pads for shield tunnel waterproofing, which can at least determine the experimental design parameters through a pre-established working condition numerical analysis model, and verify the experimental design parameters based on actual experiments to determine the design parameters of the rubber sealing pads, thereby improving the reliability of the actual engineering application of shield tunnel sealing pads.

[0005] The present application provides a method for designing a rubber sealing pad for waterproofing a shield tunnel, comprising: Acquiring multiple material parameters and multiple boundary conditions of the rubber sealing gasket; Determining experimental design parameters of the rubber sealing gasket based on a pre-established working condition numerical analysis model and according to multiple material parameters and multiple boundary conditions of the rubber sealing gasket; The experimental design parameters of the rubber sealing gasket are verified based on a pre-set experimental scheme, and the design parameters of the rubber sealing gasket are determined according to the experimental design parameter verification results of the rubber sealing gasket.

[0006] Optionally, a numerical analysis model of the working condition is established by the following steps: The segment joint is simplified into a two-dimensional plane strain model and modeled according to the actual size of the longitudinal joint; Determining a plurality of material parameters of the rubber sealing gasket, wherein the plurality of material parameters of the rubber sealing gasket are defined based on a Mooney-Rivlin model; Based on the pre-acquired test data, the material parameters are fitted and the elastic modulus and shear modulus are determined; Define the rigid-flexible contact relationship between the sealing groove and the sealing gasket, and the soft-flexible contact relationship between the sealing gaskets.

[0007] Optionally, the experimental design parameters of the rubber sealing gasket are determined according to multiple material parameters and multiple boundary conditions of the rubber sealing gasket, including: Load different opening amounts, misalignment amounts, and water pressures; Extract contact stress distribution; Analyze gasket deformation and stress changes; Summarize the influencing rules and design optimization plans.

[0008] Optionally, the experimental design parameters of the rubber sealing gasket are verified by the following steps: According to the pre-established working conditions, multiple test seam openings and multiple test misalignments are set, and multiple test water pressures are applied to record the stress distribution and deformation state of the gasket during compression; According to the stress distribution and deformation state of the gasket during compression, the contact stress distribution at the bottom of the gasket teeth and the stress distribution curve between the gaskets are extracted; Define the contact stress greater than or equal to the target pressure as the effective contact stress, and calculate the proportion of the effective contact stress; The deformation of rubber sealing gasket is divided into elastic stage, instability stage and compaction stage, and the stress changes and hole closure characteristics of each stage are analyzed.

[0009] Optionally, the method further includes: Compare the effects of the effective contact stress ratio at different openings on the waterproof performance of the gasket, and determine the recommended design range of the opening based on the effects of the effective contact stress ratio at different openings on the waterproof performance of the gasket; Determine the effect of misalignment on the gasket comb teeth deformation and contact stress, and determine misalignment design recommendations based on the effect of misalignment on the gasket comb teeth deformation and contact stress; Determine the effect of water pressure on the deformation and waterproof performance of the gasket, and determine the degree of improvement of the self-sealing effect of the gasket based on the effect of water pressure on the deformation and waterproof performance of the gasket.

[0010] Optionally, the rubber sealing gasket includes a plurality of comb teeth, and when the comb teeth are laterally bent, the contact area and contact stress distribution are increased to improve the waterproof performance; The method further comprises: Increase the design thickness of the gasket comb teeth and adjust the hole arrangement; increase the contact area of ​​the water-facing surface and optimize the closing characteristics of the holes; Make optimized sealing gasket samples, conduct physical compression tests and water pressure tests to verify their waterproof performance; compare the contact stress, effective contact area and leakage before and after optimization.

[0011] In a second aspect, the present application further provides a design device for a rubber sealing pad for waterproofing a shield tunnel, the device comprising: A parameter acquisition module, configured to acquire a plurality of material parameters and a plurality of boundary conditions of the rubber sealing gasket; An experimental design parameter determination module is used to determine the experimental design parameters of the rubber sealing gasket based on a pre-established working condition numerical analysis model and according to multiple material parameters and multiple boundary conditions of the rubber sealing gasket; The design parameter determination module is used to verify the experimental design parameters of the rubber sealing gasket based on a preset experimental plan, and determine the design parameters of the rubber sealing gasket according to the experimental design parameter verification results of the rubber sealing gasket.

[0012] In a third aspect, the present application further provides a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the following steps are implemented: Acquiring multiple material parameters and multiple boundary conditions of the rubber sealing gasket; Determining experimental design parameters of the rubber sealing gasket based on a pre-established working condition numerical analysis model and according to multiple material parameters and multiple boundary conditions of the rubber sealing gasket; The experimental design parameters of the rubber sealing gasket are verified based on a pre-set experimental scheme, and the design parameters of the rubber sealing gasket are determined according to the experimental design parameter verification results of the rubber sealing gasket.

[0013] In a fourth aspect, the present application further provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the following steps: Acquiring multiple material parameters and multiple boundary conditions of the rubber sealing gasket; Determining experimental design parameters of the rubber sealing gasket based on a pre-established working condition numerical analysis model and according to multiple material parameters and multiple boundary conditions of the rubber sealing gasket; The experimental design parameters of the rubber sealing gasket are verified based on a pre-set experimental scheme, and the design parameters of the rubber sealing gasket are determined according to the experimental design parameter verification results of the rubber sealing gasket.

[0014] In a fifth aspect, the present application further provides a computer program product, comprising a computer program, which, when executed by a processor, implements the following steps: Acquiring multiple material parameters and multiple boundary conditions of the rubber sealing gasket; Determining experimental design parameters of the rubber sealing gasket based on a pre-established working condition numerical analysis model and according to multiple material parameters and multiple boundary conditions of the rubber sealing gasket; The experimental design parameters of the rubber sealing gasket are verified based on a pre-set experimental scheme, and the design parameters of the rubber sealing gasket are determined according to the experimental design parameter verification results of the rubber sealing gasket.

[0015] The design method for rubber sealing pads for shield tunnel waterproofing provided in the embodiment of the present application can at least determine the experimental design parameters through a pre-established working condition numerical analysis model, and verify the experimental design parameters based on actual experiments to determine the design parameters of the rubber sealing pads, thereby improving the reliability of the actual engineering application of the shield tunnel sealing pads.

[0016] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, preferred embodiments are given below and described in detail with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following is a brief introduction to the drawings required for use in the embodiments. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without creative work.

[0018] Figure 1 A schematic flow chart of a method for designing a rubber sealing pad for shield tunnel waterproofing provided in an embodiment of the present application; Figure 2 A schematic diagram of a segment joint model provided in an embodiment of the present application; Figure 3 A schematic diagram of a rubber sealing pad for a shield tunnel provided in an embodiment of the present application; Figure 4 A schematic diagram of various parts of a shield tunnel rubber sealing pad provided in an embodiment of the present application; Figure 5 A schematic diagram of the interaction between the sealing gaskets provided in the embodiments of the present application; Figure 6 A schematic diagram of the water pressure application point provided in an embodiment of the present application; Figure 7 Schematic diagram of the cross section of the sealing gasket at different compression stages provided by the embodiment of the present application; Figure 8 A schematic diagram of the sealing gasket stress provided in an embodiment of the present application; Figure 9 A schematic diagram of the contact stress of the sealing gasket provided in an embodiment of the present application; Figure 10 A schematic diagram of a contact stress extraction path along the contact surface between outer sealing gaskets provided in an embodiment of the present application; Figure 11 A schematic diagram of a contact stress distribution curve along the contact surface between outer sealing gaskets provided in an embodiment of the present application; Figure 12 A schematic diagram of a contact stress extraction path along the contact surface at the bottom of the comb teeth of the sealing gasket provided in an embodiment of the present application; Figure 13 A schematic diagram of the stress distribution along the contact surface at the bottom of the outer sealing gasket comb teeth provided in an embodiment of the present application; Figure 14 Schematic diagram of contact stress of 0 and contact stress mutation provided in the embodiment of the present application; Figure 15 A schematic diagram of the stress of the sealing gasket provided in an embodiment of the present application at different opening amounts; Figure 16 A schematic diagram of the contact stress distribution curves along the contact surface between the sealing gaskets at different opening amounts provided in the embodiment of the present application; Figure 17 Schematic diagram of the contact stress distribution curve along the contact surface of the bottom of the sealing gasket comb teeth at different opening amounts provided in the embodiment of the present application; Figure 18 A bar chart showing the calculation results of different contact stress paths with different opening amounts provided in the embodiments of the present application; Figure 19 A schematic diagram of the sealing gasket stress under different misalignment amounts provided in the embodiment of the present application; Figure 20 Schematic diagram of the contact stress distribution curve along the contact surface of the bottom of the comb teeth of the sealing gasket under different misalignment amounts provided in the embodiment of the present application; Figure 21 Schematic diagram of the contact stress distribution curve along the contact surface of the bottom of the comb teeth of the sealing gasket under different misalignment amounts provided in the embodiment of the present application; Figure 22 A bar chart showing the calculation results of different contact stress paths with the same misalignment amount provided in the embodiment of the present application; Figure 23 A schematic diagram of the contact stress distribution curves along the contact surface between the sealing gaskets under different water pressures provided in the embodiment of the present application; Figure 24Schematic diagram of contact stress distribution curves along the contact surface of the bottom of the comb teeth of the sealing gasket under different water pressures provided in an embodiment of the present application; Figure 25 A bar chart showing the calculation results of different contact stress paths under different water pressures provided in the embodiments of the present application; Figure 26 A schematic diagram of the deformation of the bottom of the comb teeth of the sealing gasket provided in an embodiment of the present application; Figure 27 A schematic diagram of the contact stress extraction path of the sealing gasket comb teeth along the contact surface provided in an embodiment of the present application; Figure 28 Schematic diagram of the contact stress distribution curve along the contact surface between the comb teeth of the sealing gasket and the sealing groove with different misalignment amounts provided in the embodiment of the present application; Figure 29 A structural block diagram of a device for designing a rubber sealing pad for waterproofing a shield tunnel according to one embodiment; Figure 30 FIG. 1 is a diagram showing the internal structure of a computer device in one embodiment. DETAILED DESCRIPTION

[0019] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all of the embodiments. The components of the embodiments of the present application generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the application for which protection is claimed, but merely represents the selected embodiments of the present application. Based on the embodiments of the present application, each other embodiment obtained by those skilled in the art without making creative work falls within the scope of protection of the present application.

[0020] First, the application scenarios to which this application is applicable are introduced. This application can be applied in the field of shield tunnel design technology.

[0021] Shield tunnels are widely used in infrastructure such as subways, highways, and water conservancy projects, and their long-term, stable operation is of great significance to socioeconomic development. Tunnel waterproofing performance is directly related to the lifespan and safety of the structure. Rubber gaskets, as key waterproofing components in tunnel segment joints, play a central role in preventing groundwater seepage and maintaining tunnel structural safety. By closely contacting the segment sealing grooves, the gaskets form a physical barrier to withstand high water pressure shocks in complex geological conditions. However, the combined effects of construction, opening, offset, and water pressure can significantly affect the gasket's waterproofing performance.

[0022] Current research on shield tunnel gaskets focuses on idealized waterproofing performance evaluation under a single operating condition, lacking a systematic analysis of the coupled effects of multiple factors, such as opening, misalignment, and water pressure. Furthermore, as a hyperelastic body, the deformation behavior of gaskets is complex. The specific impact of factors such as contact stress distribution, pore closure characteristics, and comb deformation on waterproofing performance under different operating conditions has yet to be fully understood. Traditional experimental methods, due to their limited simulation conditions, struggle to accurately quantify the stress distribution and deformation patterns of gaskets under complex operating conditions. This results in a lack of scientific basis for gasket optimization design, limiting their reliability in practical engineering applications.

[0023] Taking into account the complex working conditions that may arise during shield tunnel construction, establishing a scientific testing method for the waterproof performance of gaskets and conducting an in-depth analysis of the impact of factors such as joint opening, misalignment, and water pressure on gasket contact stress and waterproofing effectiveness has important engineering significance and theoretical value. By combining numerical simulation with experimental verification, not only can the deformation mechanism and failure mode of gaskets be revealed, but also a quantitative basis for optimizing gasket design can be provided, thereby improving the overall waterproofing capability of shield tunnels and extending the service life of the structure. This research will fill a gap in existing technology and provide technical support for related engineering practices.

[0024] Based on this, an embodiment of the present application provides a design method for a rubber sealing pad for shield tunnel waterproofing, which can at least determine the experimental design parameters through a pre-established working condition numerical analysis model, and verify the experimental design parameters based on actual experiments to determine the design parameters of the rubber sealing pad, thereby improving the reliability of the actual engineering application of the shield tunnel sealing pad.

[0025] In particular, this study provides a scientific and effective method for testing and optimizing the waterproof performance of rubber gaskets at segment joints in shield tunnels. By quantitatively studying the impact of complex operating conditions, such as opening, misalignment, and water pressure, on gasket performance, the study reveals the contact stress distribution, deformation characteristics, and failure mechanisms of gaskets under different operating conditions. This approach aims to comprehensively enhance the gasket's waterproofing capabilities under complex operating conditions, providing a theoretical basis and technical support for the construction and operation of shield tunnels.

[0026] By establishing an analytical system that combines numerical simulation with experimental verification, the team focused on studying the deformation patterns and contact stress distribution of gaskets under complex operating conditions. By simulating the combined effects of different variables (such as opening, misalignment, and water pressure), the team evaluated the comprehensive impact of operating conditions on the gasket's waterproof performance. The accuracy of the numerical simulations was verified using experimental data, providing a scientific basis for optimizing gasket performance.

[0027] By studying the failure modes and watertightness impacts of gaskets under complex operating conditions, a targeted gasket structural optimization design scheme is proposed. By adjusting the gasket's material properties, geometric parameters, and contact interface mechanical characteristics, the gasket's watertightness performance under complex operating conditions is further improved, thereby reducing engineering risks caused by leakage, extending the service life of shield tunnels, and providing economic benefits and social value for engineering construction and maintenance.

[0028] See also Figure 1 , Figure 1 This is a flow chart of a design method for a rubber sealing pad for shield tunnel waterproofing provided in an embodiment of the present application. Figure 1 As shown in , the design method of the rubber sealing pad for shield tunnel waterproofing provided by the embodiment of the present application includes: S101. Acquire multiple material parameters and multiple boundary conditions of the rubber sealing gasket.

[0029] As an example, boundary conditions can be set: the boundary of the right segment constrains the displacement in the X / Y directions, the opening amount is adjusted by controlling the displacement in the X direction of the left segment, and the misalignment amount is adjusted by the displacement in the Y direction.

[0030] S102 : Based on a pre-established working condition numerical analysis model, and in accordance with a plurality of material parameters and a plurality of boundary conditions of the rubber sealing gasket, determining experimental design parameters of the rubber sealing gasket.

[0031] Specifically, the working condition numerical analysis model is established through the following steps: simplifying the pipe segment joint into a two-dimensional plane strain model and modeling it according to the actual size of the longitudinal seam joint; determining multiple material parameters of the rubber sealing gasket, and the multiple material parameters of the rubber sealing gasket are defined based on the Mooney-Rivlin model; based on pre-acquired test data, fitting the material parameters and determining the elastic modulus and shear modulus; defining the rigid-flexible contact relationship between the sealing groove and the sealing gasket and the soft-flexible contact relationship between the sealing gaskets.

[0032] Here, EPDM rubber can be used as the research object. Its material properties are defined based on the Mooney-Rivlin model. Using relevant experimental data, the material parameters C10 and C01 are fitted, and the elastic modulus and shear modulus are calculated. A rigid-flexible contact relationship (between the sealing groove and the gasket) and a flexible-flexible contact relationship (between the gaskets) are defined. Using the ABAQUS finite element analysis tool, the contact friction coefficient between the gasket and the sealing groove is set to 0.5, and self-contact is set for the internal holes and edges of the gasket.

[0033] Among them, according to the multiple material parameters and multiple boundary conditions of the rubber sealing gasket, the experimental design parameters of the rubber sealing gasket are determined, including: loading different opening amounts, misalignment amounts, and water pressures; extracting the contact stress distribution; analyzing the deformation and stress changes of the sealing gasket; summarizing the influencing rules and designing an optimization plan.

[0034] Here, the seam opening can be set to 2 mm, 4 mm, 6 mm, 8 mm, etc., and the misalignment can be divided into 5 mm, 10 mm, 15 mm, 20 mm and other working conditions; apply a water pressure of 1 MPa to 1.5 MPa, and record the stress distribution and deformation state of the sealing gasket during compression.

[0035] Then, the contact stress distribution at the bottom of the gasket comb teeth and the stress distribution curve between the gaskets are extracted; the contact stress greater than or equal to 1 MPa is defined as the effective contact stress, and the proportion of the effective contact stress is calculated.

[0036] In this way, the deformation of the rubber sealing gasket can be divided into the elastic stage, the instability stage, and the compression stage, and the stress changes and hole closure characteristics of each stage can be analyzed.

[0037] S103 , verifying the experimental design parameters of the rubber sealing gasket based on a pre-set experimental scheme, and determining the design parameters of the rubber sealing gasket according to the verification result of the experimental design parameters of the rubber sealing gasket.

[0038] Specifically, the experimental design parameters of the rubber sealing gasket are verified through the following steps: according to the pre-established working conditions, multiple test joint opening amounts and multiple test misalignment amounts are set, and multiple test water pressures are applied to record the stress distribution and deformation state of the sealing gasket during compression; according to the stress distribution and deformation state of the sealing gasket during compression, the contact stress distribution at the bottom of the sealing gasket comb teeth and the stress distribution curve between the sealing gaskets are extracted; the contact stress greater than or equal to the target pressure is defined as the effective contact stress, and the proportion of the effective contact stress is calculated; the deformation of the rubber sealing gasket is divided into the elastic stage, the instability stage, and the compression stage, and the stress changes and hole closure characteristics of each stage are analyzed.

[0039] Optionally, the method also includes: comparing the influence of the effective contact stress ratio under different opening amounts on the waterproof performance of the sealing gasket, and determining the recommended design range of the opening amount based on the influence of the effective contact stress ratio under different opening amounts on the waterproof performance of the sealing gasket; determining the influence of the misalignment on the deformation and contact stress of the comb teeth of the sealing gasket, and determining the misalignment design recommendation based on the influence of the misalignment on the deformation and contact stress of the comb teeth of the sealing gasket; determining the influence of water pressure on the deformation and waterproof performance of the sealing gasket, and determining the degree of improvement of the self-sealing effect of the sealing gasket based on the influence of water pressure on the deformation and waterproof performance of the sealing gasket.

[0040] Wherein, the rubber sealing gasket includes a plurality of comb teeth, and when the comb teeth are laterally bent, the contact area and contact stress distribution are increased to improve the waterproof performance.

[0041] The method further comprises: Increase the design thickness of the gasket comb teeth and adjust the hole arrangement; increase the contact area of ​​the water-facing surface and optimize the closing characteristics of the holes; Make optimized sealing gasket samples, conduct physical compression tests and water pressure tests to verify their waterproof performance; compare the contact stress, effective contact area and leakage before and after optimization.

[0042] The effective contact stress ratios at different openings were compared to analyze their impact on the gasket's waterproof performance. Excessive or insufficient openings can reduce waterproof performance; a range of 4 mm to 6 mm is recommended.

[0043] Among them, see Figure 6 , studied the influence of misalignment on the deformation and contact stress of the gasket comb teeth, and put forward optimization design suggestions.

[0044] Among them, see Figure 7 , study the effect of water pressure on the deformation and waterproof performance of the gasket, and quantify the improvement of the self-sealing effect of the gasket.

[0045] Here, when the comb teeth bend laterally, the contact area increases, the contact stress distribution is optimized, and the waterproof performance is improved.

[0046] The design thickness of the gasket teeth can be increased and the hole arrangement adjusted; the contact area on the water-facing surface can be increased, and the hole closure characteristics can be optimized. Optimized gasket samples can then be manufactured and subjected to physical compression and water pressure tests to verify their waterproof performance. The contact stress, effective contact area, and leakage before and after optimization can be compared.

[0047] It should be noted that the joints of shield tunnel segments are divided into transverse joints and longitudinal joints. At the transverse joints of the tunnel, the jack thrust constraint and the concave-convex tongue-and-groove constraint between the pipe rings reduce the opening and misalignment, which is relatively safe. Therefore, only the waterproof performance and main influencing factors of the rubber sealing gasket at the longitudinal joints of the segments are analyzed.

[0048] For example, in the research process, the segment joint is simplified into a two-dimensional plane strain model. The boundary of the right segment is constrained to displace in the X and Y directions. The segment opening is controlled by controlling the displacement of the left segment in the X direction, and the segment joint misalignment is controlled by the displacement in the Y direction. Figure 2 As shown, the rubber gasket under study is discretely calculated using a plane strain hybrid element (CPE4H). The gasket joint form is as follows: Figure 2 As shown, the rubber seal is as Figure 3 shown.

[0049] In numerical simulations of the waterproofing capacity of sealing gaskets, the concrete sealing groove is simulated as a rigid body to simplify the calculations, given that its stiffness is much greater than that of rubber. The rubber sealing gasket is simulated using plane strain elements. In numerical simulations, the gasket is generally considered to be a hyperelastic body with reversible deformation and incompressibility. Regarding the choice of rubber constitutive models, the Mooney-Rivlin model and the Yeoh model are widely used.

[0050] Among them, EPDM rubber is usually regarded as an isotropic incompressible hyperelastic material. The nonlinear constitutive relationship of stress and strain of hyperelastic materials is mainly defined by the strain energy function. The commonly used Mooney-Rivlin two-parameter model will be used in the calculation, and its strain energy function expression is: U = C 10 ( I 1-3)+ C 01 ( I 2-3); Among them, U is strain energy; C10 and C01 are material parameters; I1 and I2 are the first and second invariants respectively.

[0051] Gent proposed a simplified calculation method for C10 and C01 based on fitting and linear regression of rubber test data. Assuming that the initial shear modulus (Gg) of the rubber gasket material is equal to twice the sum of the calculation model parameters, and the elastic modulus (Eg) of the rubber gasket material is equal to three times the initial shear modulus, it can be obtained: G g = 2( C 10 + C 01 ); E g =3 G g； Among them, the relationship between the hardness (Shore) and elastic modulus (Eg) of rubber materials is expressed as: ; In the rubber gasket studied, the hardness of EPDM rubber is 67 Shore A. After confirming the hardness of the gasket rubber, we used previous experimental data and the above calculation formula to determine the constitutive parameters of the gasket, as shown in Table 1. In the table, C10, C01, and D1 are the material parameters.

[0052] Table 1: Constitutive parameters of hyperelastic body

[0053] The contact generated during the compression process of shield gaskets can be classified into two types according to their properties: rigid-flexible contact and soft-flexible contact. The shield segments are made of concrete, and their rigidity is much greater than the gaskets nested in their grooves, so the contact between the segments and the gaskets is rigid-flexible contact; after the gaskets are compressed, contact will occur between the upper and lower gaskets, the outer contour of the gasket itself, and the closed hole, and this type of contact is soft-flexible contact. ABAQUS is used to simulate the above interactions. Based on the characteristics of shield gaskets, ABAQUS software uses contact pairs to achieve contact simulation between segments and gaskets, and between gaskets. As for the contact generated after the internal holes of the gaskets are compressed, and the contact of the outer contour of the gasket itself after compression, ABAQUS software simulates it by setting self-contact.

[0054] There are four types of contact between the segment and the gasket: left groove-left gasket, left groove-right gasket, right groove-left gasket, and right groove-right gasket. Figure 4 The left groove-left pad and right groove-right pad have been mentioned in previous literature, while the left groove-right pad and right groove-left pad are rarely mentioned. Under normal compression conditions, contact between the left groove-right pad and the right groove-left pad is unlikely to occur. However, under adverse working conditions, such as when the segments are misaligned, contact between the left groove-right pad and the right groove-left pad may occur.

[0055] In the process of establishing the finite element model, the contact between the rubber gasket model and the sealing groove of the pipe segment joint is relatively complex. When selecting the slave surface of the pipe segment-seal gasket contact pair, the principle of using the surface of the component with greater material stiffness as the master surface should be followed. The sealing groove surface is used as the master surface, and the outer contour surface of the gasket is used as the slave surface. Figure 5 As shown, each interaction is described separately: For the interaction between the side of the sealing gasket and the side of the sealing groove: Since the side of the rubber sealing gasket and the side of the bottom hole are not in contact with the side of the sealing groove in the initial compression state, in order to avoid the unit penetration of the sealing gasket during the compression simulation, the surface-surface friction contact interaction is set between the side of the sealing gasket and the side of the sealing groove. In the normal direction, "hard" contact is used to simulate the normal contact behavior between the side of the sealing gasket and the side of the sealing groove. In the tangential direction, the Coulomb friction model is used to simulate the friction and sliding behavior between the contact surfaces. The friction coefficient between the contact surfaces is taken as 0.5, as shown Figure 5 As shown in Figure (a); for the self-contact interaction of the gasket hole: during the deformation of the gasket section, the internal hole and the bottom hole are closed, so the self-contact interaction is set for the gasket hole, and the friction coefficient between the contact surfaces is taken as 0.57, as shown in Figure 5As shown in Figure (b) in the figure; for the gasket edge-gasket edge interaction: the gasket-gasket contact surface is the main channel for gasket water seepage, so the contact surface is set to surface-surface friction contact interaction, and "hard" contact is used to simulate the interaction between gaskets in the normal direction. The Coulomb friction model is used to simulate the friction and sliding behavior between the contact surfaces in the tangential direction. The friction coefficient between the contact surfaces is taken as 0.57, as shown in Figure 5 As shown in Figure (c).

[0056] Finite element software was used to analyze the stress and displacement response of the gasket after compression loading. Due to space limitations, the waterproof performance of the gasket was studied using a gasket with an opening of 8 mm, a stagger of 0 mm, and an applied water pressure of 1 MPa as an example.

[0057] The outer gasket section height is 25mm, the sealing groove depth is 15mm, and the compression of the double-sided gasket model is 20mm when fully closed. The compression analysis of the joint gasket is achieved by gradually loading the displacement on the left segment and applying water pressure. The water pressure is applied at the position shown in the figure. Figure 6 As shown, the cross-sections at different compression stages are shown in Figure 7 , the compression stage can be divided into Figure 7 There are four stages (a), (b), (c) and (d).

[0058] like Figure 7 As shown in the first (AB) stage (Figure a to Figure b): In this stage, the load value increases linearly with the increase of the compression deformation value of the sealing gasket, so the AB stage can be referred to as the "elastic stage". Figure 7 Figure (a) shows the cross section of the gasket before compression. When the gasket is compressed to B, the elastic stage ends. Figure 7 Figure (b) shows the cross-sectional shape of the gasket at the end of the compression elastic stage. It can be seen from the figure that at this stage, the sealing gasket closing hole begins to deform under the action of pressure, and the closing compression force of the gasket increases with the increase of compression. The second (BC) stage: In this stage, the closing compression force of the gasket does not increase with the increase of compression, but shows the characteristic that the closing compression force is basically stable even though the compression increases. Figure 7 Figure (c) shows the cross section of the gasket at the end of the BC stage of compression. This is because the closed pores become unstable under pressure, reducing their area. However, the closing compression force is maintained at the level of instability to maintain this state. Therefore, BC can be referred to as the "instability stage." The third stage (CD): In this stage, the load value increases exponentially with the increase in the gasket compression deformation value, as shown in Figure 2. Figure 7Figure (d) shows the cross section of the gasket when it is fully closed. At the beginning of this stage, the closed pores continue to be compressed, and by the end, they are almost completely closed. Simultaneously, the open pores begin to deform under the pressure. Since rubber has the characteristic of superelasticity—incompressibility—the closing compression force increases sharply with the amount of compression, so this stage can be called the "compression stage."

[0059] See also Figure 8 , Figure 8 Figure (a) and Figure 8 Figure (b) shows the contact stress contours after compression and water pressure application. It can be seen that when no water pressure is applied, the maximum stress reaches 3.781 MPa, located at the circular hole in the lower part of the outer gasket. When a water pressure of 1 MPa is applied, the maximum stress reaches 6.543 MPa, located at the fan-shaped hole in the upper right part of the outer gasket.

[0060] See also Figure 9 , Figure 9 Figure (a) and Figure 9 Figure (b) shows the contact stress contours after compression and water pressure application. It can be seen that when no water pressure is applied, the maximum stress is 8.512 MPa, located at the bottom of the upper comb teeth in the right gasket. When a water pressure of 1 MPa is applied, the maximum stress is 6.732 MPa, located at the intersection of the lower right portion of the outer gasket and the segment.

[0061] Observing the deformation morphology cloud diagrams of the gaskets under the two conditions reveals that: after considering the effect of water pressure, the gasket deforms significantly toward the water-repellent side, with the upper and lower gaskets squeezing each other more intensely. The squeezed right gasket, after compression, has already experienced a concave center, with a tendency to deform upward and downward. Under the action of water pressure, the entire gasket deforms downward, with the upper legs of the left and right gaskets completely disconnected from the sealing groove. The water-repellent side of the gasket is disconnected from the sealing groove, and the gasket legs are warped, with only the edges of the legs in contact with the sealing groove, resulting in contact stress concentration between the gasket and the sealing groove.

[0062] See also Figure 10 ,according to Figure 10 Extract the contact stress between the outer gaskets and press Figure 12 Extract the contact stress at the bottom of the inner and outer gasket comb teeth, and the results are as follows: Figure 11 、 Figure 13 and Figure 14 shown.

[0063] from Figure 11 and Figure 13It can be seen that the contact stress at the bottom of the gasket comb teeth is generally greater than the contact stress between the gaskets. As can be seen from the figure, the contact pressure curves between the outer and inner gaskets show a double "W" distribution when no water pressure is applied, and the stress at the corners is higher. This is because with the addition of the displacement in the X direction, the gasket is squeezed, resulting in stress concentration at the corners of the gasket. The water pressure calculated in this numerical simulation is 1MPa, so the contact stress greater than or equal to 1MPa is defined as the effective contact stress. After considering the effect of water pressure, the average contact stress of the gasket is increased, and the effective contact stress distribution is more concentrated. This is because after being affected by water pressure, the internal pores of the gasket gradually decrease, and the degree of squeezing at the corners of the upper and lower gaskets is more intense. This change in the contact stress distribution makes the contact stress at most points between the gaskets greater than 1MPa, but there are still some points where the contact stress is far less than 1MPa, which does not meet the waterproof requirements. After considering the effect of water pressure, the gasket deforms toward the backwater side as a whole, and the water-facing side of the gasket is out of contact with the sealing groove, which is consistent with the water pressure. Figure 13 Figure (a) and Figure 13 At the same time, under the action of water pressure, the contact stress between the gaskets and the effective contact stress at the bottom of the gasket comb teeth are more concentrated, and a sudden change occurs, such as Figure 14 As shown, this may lead to instability in the waterproofing ability of the gasket.

[0064] Therefore, the effective contact stress is defined as contact stress greater than or equal to 1MPa. The effective stress ratio of the gasket contact surface is shown in Table 2 below. It can be seen from the table that the effective stress ratio between the gaskets is higher than the effective stress ratio at the bottom of the gasket comb teeth. This is because under the action of water pressure, the torsional interaction on the contact surface between the gaskets can increase the effective stress ratio on the contact surface, thereby improving the waterproof performance of the gasket, and the generated effective stress ratio is also larger. In addition, the distribution of the effective stress of the two is also different. The effective stress distribution between the gaskets is parabolic with an opening upward, high at the corner end and low near the middle of the contact surface. This is because the deformation at the two ends is much greater than that in the middle. The effective stress at the bottom of the gasket comb teeth is mainly concentrated in the two bottom parts near the inside of the gasket. This is because the two bottom parts on the outside of the gasket are almost unable to bear the load due to excessive deformation, and the effective stress is concentrated in the two corners on the inside. Therefore, more consideration should be given to the situation of water leakage between the gasket and the groove, and protection in this regard should be strengthened.

[0065] Table 2: Effective stress ratio of gasket contact surface

[0066] Specifically, for the deformation of the gasket under different opening amounts, the shield tunnel segment joints are divided into transverse joints and longitudinal joints. Since the transverse joints are constrained by the thrust of the jack and the concave and convex grooves between the pipe rings, the opening and misalignment are small and safer. Therefore, the deformation and stress cloud diagrams of the cross section of the longitudinal seam of the gasket are extracted when the joint opening amount is 2mm, 4mm, 6mm, 8mm, etc. Figure 15 As shown. In the case of no misalignment: when the opening is 8mm, the closed holes near the comb teeth of the sealing gasket are compressed, and the bottom of the comb teeth in the upper middle part produce a large tilt deformation; when the opening is 6mm, the closed holes near the bottom of the comb teeth of the sealing gasket are further compressed, and the bottom of the comb teeth in the upper middle part produce a large tilt deformation; when the opening is 4mm, the shape of the sealing gasket is roughly the same as that of the 6mm, but the closed holes are basically completely closed, and the bottom of the upper comb teeth of the upper sealing gasket produce a large tilt deformation, which greatly reduces the open hole area; when the opening is 2mm, the closed holes are basically completely closed, the bottom of the upper comb teeth of the upper sealing gasket produce a large tilt deformation, and the open holes are almost filled with the sealing gasket.

[0067] (2) Contact stress under different opening amounts Draw the contact stress distribution curves along the actual distance of the contact surface between the gaskets under different opening amounts. Figure 16 As shown in the figure, the contact stress distribution curves of the bottom of the gasket comb teeth along the actual distance of the contact surface under different opening amounts are as follows: Figure 17 shown.

[0068] As can be seen from the figure: when there is no error: Figure 17 Figure (a) in Figure 17 As shown in Figure (b), stress concentration occurs on both sides of the bottom of the gasket teeth, and the contact stress at the foot on the side of the inclination direction after the bottom of the comb teeth deforms is greater. The contact stress at the bottom of the two middle comb teeth is greater, and the contact stress increases as the opening decreases. The contact stress between the gasket and the sidewall of the sealing groove also shows the characteristic of stress concentration at the boundary. Figure 16It can be seen that the contact stress between the gaskets is not uniformly distributed along the path. This is because the elastic rubber gasket contains a certain number of closed pores. During compression, the closed pores near the top surface are compressed and deformed, reducing the pore area and causing stress release. Therefore, the contact stress near the pores is relatively low. However, the rubber between adjacent closed pores cannot be compressed due to its material properties, resulting in higher contact stress near these locations. When the opening is 8mm, the contact stress distribution curve between the gaskets has four stress peaks and three stress valleys, corresponding to the four adjacent and three distant closed pores below the top of the gasket. When the opening is 2mm, the gasket is squeezed too much, causing the closed pores within the gasket to almost fit together before the water pressure is applied, resulting in a small internal space. After the water pressure is applied, the gasket only deforms along the longitudinal channel of the segment on the upstream and downstream sides. The center of the gasket, which has less deformation space to begin with, deforms less than the corners. This results in higher stress at the corners and lower stress in the center, resulting in an overall "W"-shaped stress curve.

[0069] For the comparison of average contact stress and peak stress at different opening amounts, the calculation results of average contact stress and peak stress of main water seepage path of gasket numerical model at different opening amounts are compared. The results are as follows: Figure 18 shown.

[0070] Depend on Figure 18It can be seen that when the opening amounts are 2mm, 4mm, 6mm and 8mm respectively, the peak contact stresses corresponding to the left sealing gasket and the bottom of the comb teeth are 8.08MPa, 7.98MPa, 7.73MPa and 4.53MPa respectively, and the average contact stresses are 1.04MPa, 1.45MPa, 1.67MPa and 1.07MPa respectively; the peak contact stresses corresponding to the sealing gaskets are 3.13MPa, 2.26MPa, 2.17MPa and 1.87MPa respectively, and the average contact stresses are 1.28MPa, 1.48MPa, 1.31MPa and 1.03MPa respectively; the peak contact stresses corresponding to the bottom of the comb teeth of the right sealing gasket are 5.22MPa, 9.82MPa, 7.03MPa and 4.77MPa respectively, and the average contact stresses are 0.58MPa, 1.35MPa, 1.29MPa and 0.92MPa respectively. When the opening is 2mm, the peak contact stress between the gaskets is the largest. As the opening gradually increases, the peak contact stress gradually decreases. There is a certain linear relationship between the two. However, from the perspective of average contact stress, as the opening increases, the average contact stress first increases and then decreases. This is because compared with the opening of 4mm, the opening of 2mm causes the compression of the gasket to be too large, the remaining pores are too small, and the deformation of the gasket is limited by the pipe segment. Under the action of water pressure, although the contact stress increases, due to the small deformable space, the contact stress is also smaller than the contact stress of the opening of 4mm. When the opening is 6mm compared to the opening of 4mm, although the pipe segment restriction is smaller and the deformation space is larger, the average contact stress is also relatively small because the compression of the gasket is relatively small. The same is true for the opening of 8mm. As shown in the following example, Figure 18 Figure (b) in Figure 18 Figure (c) shows that the contact stress at the base of the gasket teeth shows no clear linear trend with increasing opening, and the average contact stress on the left gasket is higher than on the right. This is because during compression, the top of the left gasket convexes and the corners concave, while the top of the right gasket concavely and the corners convex, resulting in the bases of the top and bottom teeth tightly contacting the segment. However, as compression increases, the bases of the two middle teeth on the right gasket gradually lose contact with the segment, and stress concentration occurs. Due to the reduced effective contact area between the right gasket and the segment, the average contact stress is also lower than that on the left gasket. Due to the stress concentration between the base of the right gasket teeth and the segment, the peak contact stress is higher at an opening of 4 mm than on the left.

[0071] In order to determine the effect of different opening amounts on the effective stress ratio, the contact stresses extracted from different contact paths were statistically analyzed, and the effective contact stress was taken as 1 MPa or greater. The results are shown in Table 3 below. As can be seen from the table, the effective contact stress ratio between the gaskets is generally higher than that at the bottom of the gasket teeth. Among them, when the opening amount is 2 mm, the effective contact stress ratio between the gaskets is the highest, at 93.10%; the ratio at the bottom of the gasket teeth is also the highest, at 52.33%. Moreover, when the opening amount is greater than or equal to 4 mm, as the opening amount increases, the effective contact stress ratio between the gaskets and the effective contact stress ratio at the bottom of the gasket teeth gradually decrease. At this time, there is a certain linear relationship between the effective contact stress ratio and the opening amount. In contrast, when the opening amount is 2 mm, the effective contact stress ratio is the lowest, whether between the gaskets or at the bottom of the gasket teeth. The main reason is that the opening amount is too small. After the pores inside the gasket are compressed, the pores in the pipe groove are too small. The gasket on the water side cannot deform toward the pores in the pipe groove. The gasket on the water-facing side bears most of the water pressure. During the load transfer process, the rest of the gasket also bears part of the load, but most of it is less than the effective contact stress.

[0072] Table 3: Effective stress ratio of gasket contact surface

[0073] According to the deformation of the gasket under different misalignment, the deformation and stress cloud diagrams of the longitudinal seam cross section of the gasket are extracted when the joint misalignment is 5mm, 10mm, 15mm, 20mm, etc. Figure 19 shown.

[0074] Depend on Figure 19 It can be seen that when the misalignment is 15mm and 20mm, the bottom of the outer gasket comb teeth detach from the sealing groove, while when the misalignment is 5mm and 10mm, the structure and shape of the bottom gasket comb teeth remain well and do not detach from the groove bottom surface. Analysis shows that this is because when the misalignment is small (5mm and 10mm), the force range of the gasket top surface is larger during compression, and the force on the bottom gasket comb teeth is more uniform. When the misalignment continues to increase (15mm), the misalignment of the pipe segment causes the uncontacted portion of the gasket top surface to warp during compression, causing the bottom comb teeth to detach from the bottom surface of the sealing groove. As the misalignment further increases (20mm), the uncontacted portion of the gasket top surface warps even more, causing the bottom comb teeth to detach from the bottom surface of the sealing groove, and the detachment range increases.

[0075] For the contact stress under different misalignment, the contact stress distribution curves along the actual distance of the contact surface between the gaskets under different misalignment are drawn as follows: Figure 20 As shown in the figure, the contact stress distribution curves of the bottom of the gasket comb teeth along the actual distance of the contact surface under different misalignment are as follows: Figure 21 shown.

[0076] like Figure 21 As shown in the figure, under different misalignment, the contact stress concentration phenomenon exists at the bottom of the comb teeth of the sealing gasket. The location of the stress concentration is located at the comb foot on the side of the comb teeth in the direction of the comb teeth's tilt deformation. In particular, the stress concentration phenomenon is obvious at the turning point of the sealing groove. The contact stress on the side of the sealing gasket that is more squeezed is greater. Figure 20 As shown in the figure, when the misalignment is 15 mm, the contact stress between the sealing gasket and the edge of the top surface of the opposite side sealing gasket is relatively large. There is an air surface in the middle of the sealing gasket, and the contact stress at the edge of the air surface is relatively large.

[0077] For the comparison of average contact stress and peak stress at different misalignments, the average contact stress and peak stress calculation results of the main water seepage path of the sealing gasket numerical model when the opening amount is 8mm are compared. The results are as follows: Figure 22 shown.

[0078] Depend on Figure 22 It can be seen that when the misalignment is 5mm, 10mm, 15mm and 20mm respectively, the peak contact stresses corresponding to the bottom of the left sealing gasket comb teeth are 5.66MPa, 6.39MPa, 8.53MPa and 7.78MPa respectively, and the average contact stresses are 1.04MPa, 1.08MPa, 1.02MPa and 1.11MPa respectively; the peak contact stresses corresponding to the gaskets are 1.94MPa, 2.27MPa, 1.76MPa and 1.89MPa respectively, and the average contact stresses are 1.05MPa, 1.05MPa, 1.01MPa and 0.93MPa respectively; the peak contact stresses corresponding to the bottom of the right sealing gasket comb teeth are 6.59MPa, 6.73MPa, 8.05MPa and 12.37MPa respectively, and the average contact stresses are 1.05MPa, 1.07MPa, 1.20MPa and 1.55MPa respectively. Generally speaking, because the contact area between the gasket and the sealing groove, and the bottom of the gasket teeth and the tube segment is smaller, the peak contact stress between the gasket and the sealing groove is greater than that between the gaskets. However, the difference in average contact stress between the two is not significant, and both are lower than the effective contact stress of 1.3 MPa.

[0079] Taking the peak contact stress and average contact stress on the main water seepage path as the research objects, the peak contact stress between the sealing gaskets does not show an obvious changing trend with the increase of the misalignment, which is mainly affected by the differences in the deformation morphology and contact state of the sealing gaskets under different misalignments; the average contact stress between the sealing gaskets basically shows a decreasing trend with the increase of the misalignment, and decreases to the lowest level when the misalignment is 20mm. This is because when the misalignment is 20mm, the phenomenon of the bottom of the sealing gasket detaching from the groove surface after deformation is more significant. The changing trends of the peak contact stress and the average contact stress at the bottom of the gasket comb teeth are also different. First, during the compression process, the right gasket is squeezed by the left gasket, the top of the gasket is concave, and the two corners are convex, and the height is higher than that of the corners of the left gasket. During the application of water pressure, the top is concave, and the right gasket with convex corners and the top are protruding. The left gasket with concave corners is compressed more tightly, and the top of the left gasket is more protruding, and the top of the right gasket is more concave. The top of the left gasket is wrapped by the right gasket, and the deformation space is smaller, so that after the offset is completed, along the contact surface between the gaskets, the deformation of the left gasket is smaller, and the average contact stress decreases slightly, while the deformation of the right gasket is larger, and the average contact stress increases slightly.

[0080] Regarding the influence of different misalignment amounts on the effective stress ratio, the specific effective stress ratios are shown in Table 4 below. It can be seen from the table that under the dual effects of opening and misalignment, the effective contact stress between the gaskets is the highest, at 62.07%, but the effective stress ratio at the bottom of the gasket comb teeth is the lowest, at 36.05%. On the contrary, under the working condition of 20mm with the largest misalignment, the effective stress ratio at the bottom of the gasket comb teeth is the largest, at 45.35%. Moreover, there is no absolute linear relationship between the peak contact stress and the amount of misalignment between the gaskets or at the bottom of the gasket comb teeth. Factors such as the deformation morphology of the gasket and the working state of the gasket and the pipe segment surface have an important influence on the contact stress. From the perspective of engineering practice, the best waterproofing effect is achieved under the combined effect of opening and misalignment.

[0081] Table 4: Effective stress ratio of gasket contact surface

[0082] For the contact stress under different water pressures, the contact stress distribution curves along the actual distance of the contact surface between the sealing gaskets under different water pressures are drawn respectively when the opening amount is 8mm and the misalignment amount is 0mm. Figure 23 As shown in the figure, the contact stress distribution curves of the bottom of the gasket comb teeth along the actual distance of the contact surface under different misalignment are as follows: Figure 24 shown.

[0083] like Figure 23As shown in the figure, under the working conditions of 8mm opening and 0mm misalignment, the contact stress curve between the gaskets has an obvious "four convex and three concave" shape, which corresponds to the holes in the gasket itself and the contact stress curves under different openings. The magnitude of the contact stress at different positions generally shows an obvious linear relationship with the magnitude of the water pressure. It can be seen that the pore position of the gasket itself has a great influence on the stress concentration phenomenon. Figure 24 As shown in the figure, the contact stress curves of the bottom of the gasket comb teeth show roughly the same corresponding relationship at the bottom of the upper and lower comb teeth of the gasket, but there is no such relationship at the bottom of the two middle comb teeth. The reason is that the bottoms of the two outer comb teeth are close to the pipe segment after compression, but the bottoms of the two middle comb teeth have more pores around them and a larger remaining deformable space. After water pressure is applied, the deformable space is also larger. Therefore, the contact stress at the bottom of the two middle comb teeth fluctuates greatly, and stress concentration occurs at both ends of the comb tooth bottom.

[0084] For the comparison of average contact stress and peak stress under different water pressure, the calculation results of average contact stress and peak stress of main water seepage path of gasket numerical model under different water pressure conditions are compared. The results are as follows: Figure 25 shown.

[0085] When water pressure is applied to the water-facing surface of the gasket, it initially acts on the upper side. As the water pressure increases, the gasket as a whole sags to the left, expanding the area affected by the water pressure and causing the contact surface at the upper end of the gasket's top surface to separate. As the water pressure continues to increase, the bottoms of the two comb teeth on the gasket gradually lose contact with the pipe segment over a large area.

[0086] When the water pressure reaches 1.50 MPa, most of the contact surface on the top of the gasket has already separated. A comparison of the contact stress distribution curves between the gaskets shows that when the water pressure is between 0.5 and 1 MPa, the area of ​​the gasket top surface affected by the water pressure is small, resulting in only a small gap at the bottom. The contact stress at the waterproof point where the gap is closed is greater than the current water pressure. However, the self-sealing effect of the gasket generated by the water pressure causes the contact stress at each point along the contact path to increase with increasing water pressure. However, when the water pressure approaches 1.3 MPa, due to excessive deformation at the bottom of the gasket teeth, the contact stress between the gaskets decreases as the compressed porosity decreases. At 1.5 MPa, the internal porosity is largely compressed. As the water pressure increases, the gasket is squeezed tighter. Furthermore, the deformation at the bottom of the lower teeth of the right gasket also blocks the channel between the segments, preventing the gasket from further deforming into the channel. This enhances the gasket's self-sealing effect, increasing both the average and peak contact stresses.

[0087] When the comb-shaped gasket is compressed to a certain extent, the comb teeth will buckle, and the bottom side of the comb teeth will contact the pipe segment. This indirectly increases the contact area between the gasket and the sealing groove, and to a certain extent improves the gasket's waterproofing ability, provided that the effective contact stress is greater than the design water pressure. To clarify the impact of lateral buckling at the bottom of the comb teeth on the gasket's waterproofing performance, the effect of lateral deformation at the bottom of the comb teeth on the gasket's waterproofing performance was evaluated under four operating conditions: an opening of 8mm and a water pressure of 1MPa, and considering misalignments of 5mm, 10mm, 15mm, and 20mm.

[0088] In view of the lateral deformation characteristics of the gasket comb teeth, here we take the gasket opening amount 8mm, the offset amount 20mm, and the applied water pressure 1MPa as an example working condition to analyze the lateral deformation characteristics of the gasket comb teeth under the action of compression-water load. Figure 26 As shown, under the dual effects of compression-water load and segment misalignment, the gasket comb teeth 1-8 all deformed to varying degrees. Deformation was particularly pronounced on comb teeth 1, 2, and 5, with their bases completely losing contact with the segment. Under the dual effects of load and displacement, the sides of comb teeth 1 and 2 came into contact with the segment, with the contact range larger than the original contact range between the bottom and the segment. Comb tooth 5 deformed away from the segment, completely losing contact with it. This excessive deformation affected comb tooth 6, causing its base to "warp upward," reducing its contact area with the segment and leaving its sides partially in contact. Under the influence of the deformation of comb tooth 2, comb tooth 3 also experienced a similar "warping" deformation as the base of comb tooth 6, with the majority of its base losing contact with the segment, while its sides remained partially in contact. Since comb teeth No. 4, 7, and 8 are relatively far away from the load and are less affected, the degree of deformation is relatively small, and the bottom of the comb teeth still maintains good contact with the pipe segment.

[0089] For the contact stress analysis of the gasket comb teeth under lateral deformation, Figure 27 The contact stress between the outer sealing gasket comb teeth and the sealing groove is extracted as shown, and the statistical results are plotted in the following Table 5.

[0090] Table 5: Stress ratio of the contact surface between the gasket comb teeth and the sealing groove

[0091] Since the water pressure in this operating condition is set at 1 MPa, the effective contact stress is assumed to be greater than or equal to 1 MPa. This yields the effective stress ratio between the gasket and the sealing groove, as shown in Table 5. The points where the contact stress between the gasket and the sealing groove is greater than 0 are counted, thereby determining the contact stress range. The table shows that before deformation, the contact range between the gasket and the sealing groove along the contact surface is the base of the four comb teeth. After deformation, some comb tooth bases are largely or completely out of contact with the segment. Under the combined influence of water pressure and segment misalignment, the comb teeth undergo lateral deformation along the segment groove. The statistical results in the table show that before deformation, the contact range between the left and right sides of the gasket and the segment is 35%, the length of the four comb tooth bases. After deformation, the two comb teeth near the starting point of the contact path on the left gasket undergo severe deformation. The comb tooth bases are completely out of contact with the segment, while a large portion of the comb tooth sides are in contact with the segment. This significantly increases the contact stress range of the left gasket, significantly improving its waterproofing capability by approximately 68.73%. The first comb tooth near the start of the contact path on the right gasket completely lost contact with the segment, and the bottom of the second comb tooth also largely lost contact with the segment. This resulted in a smaller contact stress range for the right gasket, statistically 30.99%, and a decrease in waterproofing capability of approximately 11.46%, which is consistent with the deformation behavior. It can also be seen that the waterproofing capability of the gasket is relatively weaker on the side with greater segment misalignment. The extracted contact stress values ​​were filtered and counted for points greater than or equal to 1 MPa. The effective contact stress percentages shown in the table are obtained, with the effective contact stress percentages for the left gasket being 53.33% and for the right being 57.58%.

[0092] According to the contact stress analysis and effective contact stress ratio of the comb teeth of the sealing gasket under different misalignment amounts, Figure 28 The contact stress extraction path of the sealing gasket after deformation is shown in the figure. The contact stress between the outer sealing gasket comb teeth and the sealing groove under four working conditions of opening amount 8mm, water pressure 1MPa, misalignment amount 5mm, 10mm, 15mm and 20mm are extracted respectively. The results are shown in the figure. Figure 28 The contact stress range and effective contact stress ratio of the extracted data are shown in Table 6 below.

[0093] Table 6 below also shows that the contact stress range on the right side of the gasket is generally smaller than that on the left side, which is consistent with the trend that the contact stress range is smaller on the side with greater segment misalignment. It is worth noting that the contact stress range of the right gasket does not necessarily decrease under the dual effects of water load and segment misalignment. For misalignment of 5mm and 10mm, the contact stress ranges of the right gasket are 43.95% and 44.41%, respectively, representing increases of 25.57% and 26.90%, respectively. The effective contact stress ratio does not follow a linear pattern like the contact stress range. When the misalignment is 5mm, 10mm, and 20mm, the effective contact stress of the left gasket is smaller than that of the right one. However, when the misalignment is 15mm, the effective contact stress of the left gasket is greater than that of the right one. The reason is that compared with the misalignment of 5mm, 10mm, and 15mm, the pores inside the gasket on the right side are increasing under the influence of the misalignment of the pipe segment, and the inner part of the gasket moves toward the pipe groove, and the corresponding part of the left gasket is squeezed and blocks the pipe groove, causing the left gasket to no longer be able to deform in the direction of the pipe groove. It is in a state of being surrounded by the pipe segment, the right gasket, the pipe groove, and the water pressure. The effective contact stress ratio is higher. When the misalignment is 20mm, the pipe segment moves, and the pipe groove creates space for the gasket to move, but if Figure 28 As shown in the figure, the right gasket is pulled downward, blocking the pipe groove again. At this point, the right gasket has more internal pores, but due to the excessive deformation, the effective contact stress generated is also higher. Overall, under the dual effects of misalignment and water load, the gasket's self-sealing effect is improved to a certain extent. After the comb teeth undergo lateral deformation, both the contact stress range and the effective contact stress are increased to a certain extent, which significantly improves the gasket's waterproof ability.

[0094] Table 6 Stress ratio of the contact surface between the gasket comb teeth and the sealing groove

[0095] This application studies the waterproof performance of sealing gaskets at the longitudinal joints of shield tunnels and its influencing factors. Under the action of water pressure, the torsional interaction between the sealing gaskets and the contact surfaces of the sealing gaskets can increase the effective stress ratio on the contact surface, thereby improving the waterproof performance of the sealing gaskets. Under normal compression conditions, the effective contact stress ratio between the sealing gaskets is higher than the effective contact stress ratio at the bottom of the sealing gasket comb teeth. More consideration should be given to the situation where water leaks between the sealing gasket comb teeth and the grooves, and protection in this regard should be strengthened. There is no absolute linear relationship between the peak contact stress, the effective contact stress ratio and the amount of misalignment. Factors such as the deformation form of the sealing gasket, the working state of the sealing gasket and the pipe segment surface are connected. The magnitude of contact stress plays an important role; when the opening amount and the misalignment act together on the gasket, we cannot only consider one factor and blindly optimize the defects of one aspect, but we need to consider the final effect after the two factors act together; the pores inside the gasket have a great influence on the magnitude of the contact stress on the gasket, and the staggered arrangement of holes of different shapes and sizes also has an alternating effect on the contact stress on the gasket, and the same is true for the stress concentration phenomenon; after the gasket comb teeth undergo lateral deformation, the contact stress range and effective contact stress are both improved to a certain extent, which has a certain improvement on the waterproof ability of the gasket.

[0096] It should be understood that, although the various steps in the flowcharts involved in the various embodiments described above are displayed in sequence according to the instructions of the arrows, these steps are not necessarily executed in sequence in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order restriction on the execution of these steps, and these steps can be executed in other orders. Moreover, at least a portion of the steps in the flowcharts involved in the various embodiments described above can include multiple steps or multiple stages, and these steps or stages are not necessarily executed and completed at the same time, but can be executed at different times, and the execution order of these steps or stages is not necessarily to be carried out in sequence, but can be executed in turn or alternately with other steps or at least a portion of steps or stages in other steps.

[0097] Based on the same inventive concept, the embodiments of the present application also provide a design device for a rubber sealing pad for shield tunnel waterproofing, which is used to implement the above-mentioned design method for a rubber sealing pad for shield tunnel waterproofing. The solution provided by this device is similar to the solution described in the above-mentioned method. Therefore, the specific limitations of one or more embodiments of the design device for a rubber sealing pad for shield tunnel waterproofing provided below can be found in the above-mentioned limitations of the design method for a rubber sealing pad for shield tunnel waterproofing, and will not be repeated here.

[0098] Please refer to Figure 29In an exemplary embodiment, a design device for a rubber sealing gasket for shield tunnel waterproofing is provided, comprising: a parameter acquisition module 20 for acquiring multiple material parameters and multiple boundary conditions of the rubber sealing gasket; an experimental design parameter determination module 30 for determining the experimental design parameters of the rubber sealing gasket based on the multiple material parameters and multiple boundary conditions of the rubber sealing gasket based on a pre-established working condition numerical analysis model; and a design parameter determination module 40 for verifying the experimental design parameters of the rubber sealing gasket based on a pre-set experimental scheme, and determining the design parameters of the rubber sealing gasket based on the experimental design parameter verification results of the rubber sealing gasket.

[0099] Each module in the aforementioned device for designing a rubber sealing pad for shield tunnel waterproofing can be implemented in whole or in part through software, hardware, or a combination thereof. Each module can be embedded in or independent of a processor in a computer device in the form of hardware, or can be stored in a memory in the computer device in the form of software, so that the processor can call and execute the corresponding operations of each module.

[0100] In an exemplary embodiment, a computer device is provided, which may be a terminal. The computer device includes a processor, memory, an input / output interface, a communication interface, a display unit, and an input device. The processor, memory, and input / output interface are connected via a system bus, and the communication interface, display unit, and input device are connected to the system bus via the input / output interface. The processor of the computer device provides computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and computer program stored in the non-volatile storage medium. The input / output interface of the computer device is used to exchange information between the processor and external devices. The communication interface of the computer device is used to communicate with external terminals via wired or wireless communication, which may be achieved via Wi-Fi, a mobile cellular network, near-field communication (NFC), or other technologies. When executed by the processor, the computer program implements a method for designing a rubber sealing pad for waterproofing a shield tunnel. The display unit of the computer device is used to produce a visual image and may be a display screen, a projection device, or a virtual reality imaging device. The display screen can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer device can be a touch layer covering the display screen, or a button, trackball or touchpad set on the computer device casing, or an external keyboard, touchpad or mouse.

[0101] Those skilled in the art will understand that Figure 30The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than shown in the figure, or combine certain components, or have a different component arrangement.

[0102] In an exemplary embodiment, a computer device is provided, including a memory and a processor, wherein a computer program is stored in the memory, and when the processor executes the computer program, the following steps are implemented: Acquiring multiple material parameters and multiple boundary conditions of the rubber sealing gasket; Determining experimental design parameters of the rubber sealing gasket based on a pre-established working condition numerical analysis model and according to multiple material parameters and multiple boundary conditions of the rubber sealing gasket; The experimental design parameters of the rubber sealing gasket are verified based on a pre-set experimental scheme, and the design parameters of the rubber sealing gasket are determined according to the experimental design parameter verification results of the rubber sealing gasket.

[0103] In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the following steps are implemented: Acquiring multiple material parameters and multiple boundary conditions of the rubber sealing gasket; Determining experimental design parameters of the rubber sealing gasket based on a pre-established working condition numerical analysis model and according to multiple material parameters and multiple boundary conditions of the rubber sealing gasket; The experimental design parameters of the rubber sealing gasket are verified based on a pre-set experimental scheme, and the design parameters of the rubber sealing gasket are determined according to the experimental design parameter verification results of the rubber sealing gasket.

[0104] In one embodiment, a computer program product is provided, comprising a computer program, which, when executed by a processor, implements the following steps: Acquiring multiple material parameters and multiple boundary conditions of the rubber sealing gasket; Determining experimental design parameters of the rubber sealing gasket based on a pre-established working condition numerical analysis model and according to multiple material parameters and multiple boundary conditions of the rubber sealing gasket; The experimental design parameters of the rubber sealing gasket are verified based on a pre-set experimental scheme, and the design parameters of the rubber sealing gasket are determined according to the experimental design parameter verification results of the rubber sealing gasket.

[0105] Those skilled in the art will understand that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. In particular, any reference to memory, database, or other media used in the embodiments provided in this application can include at least one of non-volatile memory and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM). The databases involved in the various embodiments provided herein may include at least one of a relational database and a non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the various embodiments provided herein may be, but are not limited to, general-purpose processors, central processing units (CPUs), graphics processing units (GPUs), digital signal processors (DSPs), programmable logic devices (PLDs), quantum computing-based data processing logic devices, artificial intelligence (AI) processors, and the like.

[0106] The technical features of the above embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this application.

[0107] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present application. It should be noted that a person of ordinary skill in the art may make various modifications and improvements without departing from the spirit of the present application, and these modifications and improvements fall within the scope of protection of the present application. Therefore, the scope of protection of the present application shall be determined by the appended claims.

[0108] It should be understood that, although the various steps in the flowcharts involved in the various embodiments described above are displayed in sequence according to the instructions of the arrows, these steps are not necessarily executed in sequence in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order restriction on the execution of these steps, and these steps can be executed in other orders. Moreover, at least a portion of the steps in the flowcharts involved in the various embodiments described above can include multiple steps or multiple stages, and these steps or stages are not necessarily executed and completed at the same time, but can be executed at different times, and the execution order of these steps or stages is not necessarily to be carried out in sequence, but can be executed in turn or alternately with other steps or at least a portion of steps or stages in other steps.

[0109] Those skilled in the art will understand that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. In particular, any reference to memory, database, or other media used in the embodiments provided in this application can include at least one of non-volatile memory and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM). The databases involved in the various embodiments provided herein may include at least one of a relational database and a non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the various embodiments provided herein may be, but are not limited to, general-purpose processors, central processing units (CPUs), graphics processing units (GPUs), digital signal processors (DSPs), programmable logic devices (PLDs), quantum computing-based data processing logic devices, artificial intelligence (AI) processors, and the like.

[0110] The technical features of the above embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this application.

[0111] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present application. It should be noted that a person of ordinary skill in the art may make various modifications and improvements without departing from the spirit of the present application, and these modifications and improvements fall within the scope of protection of the present application. Therefore, the scope of protection of the present application shall be determined by the appended claims.

Claims

1. A design method for a rubber sealing pad for shield tunnel waterproofing, characterized in that: include: Acquiring multiple material parameters and multiple boundary conditions of the rubber sealing gasket; Determining experimental design parameters of the rubber sealing gasket based on a pre-established working condition numerical analysis model and according to multiple material parameters and multiple boundary conditions of the rubber sealing gasket; The experimental design parameters of the rubber sealing gasket are verified based on a pre-set experimental scheme, and the design parameters of the rubber sealing gasket are determined according to the experimental design parameter verification results of the rubber sealing gasket.

2. The method according to claim 1, characterized in that The numerical analysis model of the working condition is established through the following steps: The segment joint is simplified into a two-dimensional plane strain model and modeled according to the actual size of the longitudinal joint; Determining a plurality of material parameters of the rubber sealing gasket, wherein the plurality of material parameters of the rubber sealing gasket are defined based on a Mooney-Rivlin model; Based on the pre-acquired test data, the material parameters are fitted and the elastic modulus and shear modulus are determined; Define the rigid-flexible contact relationship between the sealing groove and the sealing gasket, and the soft-flexible contact relationship between the sealing gaskets.

3. The method according to claim 1, characterized in that According to the multiple material parameters and multiple boundary conditions of the rubber sealing gasket, the experimental design parameters of the rubber sealing gasket are determined, including: Load different opening amounts, misalignment amounts, and water pressures; Extract contact stress distribution; Analyze gasket deformation and stress changes; Summarize the influencing rules and design optimization plans.

4. The method according to claim 1, wherein The experimental design parameters of the rubber sealing gasket are verified by the following steps: According to the pre-established working conditions, multiple test seam openings and multiple test misalignments are set, and multiple test water pressures are applied to record the stress distribution and deformation state of the gasket during compression; According to the stress distribution and deformation state of the gasket during compression, the contact stress distribution at the bottom of the gasket teeth and the stress distribution curve between the gaskets are extracted; Define the contact stress greater than or equal to the target pressure as the effective contact stress, and calculate the proportion of the effective contact stress; The deformation of rubber sealing gasket is divided into elastic stage, instability stage and compaction stage, and the stress changes and hole closure characteristics of each stage are analyzed.

5. The method according to claim 1, wherein The method further comprises: Compare the effects of the effective contact stress ratio at different openings on the waterproof performance of the gasket, and determine the recommended design range of the opening based on the effects of the effective contact stress ratio at different openings on the waterproof performance of the gasket; Determine the effect of misalignment on the gasket comb teeth deformation and contact stress, and determine misalignment design recommendations based on the effect of misalignment on the gasket comb teeth deformation and contact stress; Determine the effect of water pressure on the deformation and waterproof performance of the gasket, and determine the degree of improvement of the self-sealing effect of the gasket based on the effect of water pressure on the deformation and waterproof performance of the gasket.

6. The method according to claim 1, characterized in that The rubber sealing gasket includes a plurality of comb teeth, which, when the comb teeth are laterally bent, increase the contact area and contact stress distribution to improve the waterproof performance; The method further comprises: Increase the design thickness of the gasket comb teeth and adjust the hole arrangement; increase the contact area of ​​the water-facing surface and optimize the closing characteristics of the holes; Make optimized sealing gasket samples, conduct physical compression tests and water pressure tests to verify their waterproof performance; compare the contact stress, effective contact area and leakage before and after optimization.

7. A design device for a rubber sealing pad for shield tunnel waterproofing, characterized in that: The device comprises: A parameter acquisition module, configured to acquire a plurality of material parameters and a plurality of boundary conditions of the rubber sealing gasket; An experimental design parameter determination module is used to determine the experimental design parameters of the rubber sealing gasket based on a pre-established working condition numerical analysis model and according to multiple material parameters and multiple boundary conditions of the rubber sealing gasket; The design parameter determination module is used to verify the experimental design parameters of the rubber sealing gasket based on a preset experimental plan, and determine the design parameters of the rubber sealing gasket according to the experimental design parameter verification results of the rubber sealing gasket.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 6 are implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

10. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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