Method for determining sealing extrusion amount of underwater joint

Abstract

The invention discloses a method for determining the sealing extrusion amount of an underwater joint, and the method comprises the following steps: (1) building a joint finite element calculation model: obtaining the contact pressure distribution of a contact interface of a rubber sealing gasket under different sealing extrusion amounts, and determining a dangerous section; (2) establishing a leakage rate-extrusion rate relation model: fitting a curve of sealing extrusion rate x-joint leakage rate Q, and determining the minimum extrusion rate meeting the sealing requirement as the lower limit xmin of the sealing extrusion rate; (3) establishing a service life-extrusion amount relation model: predicting the service life of the rubber sealing gasket, obtaining a relation curve between the extrusion amount and the service life, and ensuring that the maximum extrusion amount required by the rubber service life is used as a sealing extrusion amount upper limit xmax; and (4) determining an optimal extrusion amount range: selecting an optimal value between the extrusion amount lower limit xmin and the extrusion amount upper limit xmax, and determining a final design extrusion amount x. While the waterproof reliability is ensured, the service life of the sealing material is maximized.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater tunnel sealing, and in particular to a method for determining the sealing extrusion amount of an underwater joint. Background Art

[0002] With the rapid development of cross-sea tunnel construction, the sealing reliability of underwater tunnel pipe joints has become critical to project safety. As a core component of the tunnel joint sealing system, the performance of rubber gaskets directly affects the operational safety and service life of the entire tunnel. Currently, underwater tunnels generally use rubber gaskets to achieve joint sealing through extrusion and deformation. However, existing design methods have the following technical bottlenecks:

[0003] The determination of seal extrusion volume lacks systematic theoretical guidance and mainly relies on engineering experience or simplified calculations, making it difficult to accurately match the actual working conditions under different water depths and geological conditions.

[0004] Traditional design methods fail to comprehensively consider the synergistic relationship between waterproof performance and material durability, which can easily lead to initial leakage or sealing failure after long-term service;

[0005] In complex marine environments, affected by the coupling of multiple factors such as tidal loads, ground subsidence and seismic effects, existing design standards are difficult to meet the performance assurance requirements throughout the entire life cycle.

[0006] For the special application scenario of underwater tunnels, there is an urgent need to establish a sealing extrusion design method based on multi-parameter coupling analysis to maximize the service life of the sealing material while ensuring waterproof reliability. Summary of the Invention

[0007] The purpose of the present invention is to overcome the shortcomings of the above-mentioned prior art and provide a method for determining the sealing extrusion amount of underwater joints. By establishing the relationship between the extrusion amount of rubber sealing gaskets, leakage amount and service life, the lower limit of the extrusion amount x is determined within the allowable range of leakage amount. min The upper limit of extrusion volume x is determined by the service life requirement max , scientifically determine the optimal extrusion volume range.

[0008] In order to achieve the above object, the present invention adopts the following technical solutions:

[0009] A method for determining the sealing extrusion amount of an underwater joint comprises the following steps:

[0010] (1) Establishing the finite element calculation model of the joint:

[0011] A simplified model of the rubber seal of an underwater tunnel joint during extrusion was established using ABAQUS. The constitutive relationship of the rubber material was determined, and the underwater tunnel seal installation process was simulated. The contact pressure distribution at the rubber seal interface under different seal extrusion amounts was obtained, and the dangerous section was determined.

[0012] (2) Establish a leakage-extrusion relationship model:

[0013] Based on the magnification contact model, the seal extrusion amount x-joint leakage amount Q curve is fitted, the influence of the rubber seal deformation on the joint leakage is discussed, and the minimum extrusion amount that meets the sealing requirements is determined as the lower limit of the seal extrusion amount x min ;

[0014] (3) Establishing a life-extrusion relationship model:

[0015] Based on fracture mechanics, the life of rubber sealing gaskets is predicted, the maximum strain and crack initiation position are extracted, the crack growth rate equation and tearing energy theory are used to establish a life integral model, the number of fatigue cycles is calculated, the service life of rubber sealing gaskets is predicted, and the relationship curve between extrusion volume and life is obtained. The maximum extrusion volume required to ensure the service life of the rubber is determined as the upper limit of the sealing extrusion volume x max ;

[0016] (4) Determine the optimal extrusion range:

[0017] At the lower limit of extrusion amount x min and the upper limit of extrusion amount x max Select the optimal value between them, comprehensively consider the safety factor and working conditions, and determine the final design extrusion amount x.

[0018] The calculation process of the joint leakage Q is as follows: the joint finite element model is established using ABAQUS software. Taking into account the surface roughness of the tunnel section, the entire sealing contact area is divided into regular quadrilateral calculation units. The sealing interface contact area ratio A(ξ) / A0 is 0.4 as the criterion for determining the critical magnification factor. The average height of the leakage channel when the magnification factor is ξ is obtained. The unit leakage rate Q0 is calculated using the seepage theory, and finally the total leakage volume Q is calculated.

[0019] The entire contact area is defined as an area L x ×L y The rectangle is divided into L y / L x A regular quadrilateral with a side length of L x , when the critical magnification ξ is reached c When there is a path running through the entire contact area, the cross section of the path with the minimum width is called the critical channel of the path. The channel is simplified to a rectangular hole, and its height is defined as u1(ξ c), the pressure difference Δp appears at the critical magnification ξ c When , the unit quadrilateral fluid leakage rate Q0 can be calculated by formula (1):

[0020]

[0021] Where μ is the viscosity, α is the correction factor considering the influence of shrinkage cavity morphology at higher magnification. Since the critical shrinkage cavity is simplified to a rectangular hole, the true shape of the shrinkage cavity cannot be obtained, and α = 1.

[0022] When the magnification is ξ, the contact area ratio A(ξ) / A0 can be obtained by formula (2):

[0023]

[0024] Where p0 is the applied pressure, is the contact pressure when the magnification factor ξ is 1, erf is the error function, and G represents the effective stiffness of the surface roughness, which can be expressed as:

[0025]

[0026] Among them, q is the wave vector, q0 is the reference wave vector, E * is the equivalent elastic modulus, which can be obtained by formula (4), C(q) is the isotropic surface roughness PSD, which can be obtained by the one-dimensional PSD function C 1-D (q) is obtained by formula (5),

[0027]

[0028] Where υ is Poisson's ratio, E1 and E2 are the elastic moduli of the contact bodies,

[0029]

[0030] The height of the critical permeation path u1(ξ) is the separation height of the two contact surfaces when the first permeation path through the contact area appears. u1(ξ) can be obtained by formula (6):

[0031]

[0032] in, is the overall average height of the two surfaces at magnification ξ, u'(ξ) and A'(ξ) are the derivatives of u(ξ) and the contact area A(ξ) with respect to ξ, respectively. It can be obtained from formula (7) to formula (9),

[0033]

[0034] Among them, q0 is the reference wave vector, q1 is the maximum wave vector, w(q) is a weight function related to the surface roughness power spectrum C(q), p(ξ) is the nominal pressure at the current magnification, w(q,ξ) is a function related to the local contact stiffness, s(q,ξ) is a function related to the local pressure and elastic deformation, and s(q,ξ)=w(q,ξ) / E * , P(q,p,ξ) is an error function, which represents the influence of local contact pressure p on elastic contact probability under specific magnification ξ and wave vector q, γ0 is the correction factor, and γ0 is taken as 0.4.

[0035] For the top (bottom) of the gasket, the average contact pressure of each regular quadrilateral calculation unit in the region is similar, and the pressure difference Δp is the same. It is assumed that the leakage of the calculation units at the top (bottom) is approximately the same. The average leakage multiplied by the number of units is the leakage of the top (bottom) Q1 (Q2). For both sides of the gasket, since each calculation unit is at different water depths, its contact pressure and pressure difference are different. The leakage of all units needs to be calculated separately, and the sum of the values ​​multiplied by 2 is the leakage of both sides Q3. The total leakage of the flexible joint of the immersed tube tunnel can be calculated by formula (10).

[0036] Q=Q1+Q2+Q3 (10)

[0037] The calculation process of the expected service life T is as follows: establish the joint finite element model through ABAQUS software to obtain the maximum strain ε0, obtain σ(ε) through rubber compression test, calculate the strain energy density ω0, obtain the number of cycles N and estimate the service life T.

[0038] The fatigue crack growth rate of rubber material is expressed by formula (11):

[0039]

[0040] Where a is the crack length, N is the number of cycles, J is the maximum tearing energy in a single cycle, B is the material constant, and β is the crack growth constant.

[0041] The tearing form of the seal is described by single-sided incision stretching, and the crack growth rate can be expressed by formula (12):

[0042]

[0043] Where λ is the elongation ratio, λ = 1 + ε; ε is the rubber strain, and ω0 is the strain energy density, which is a function of ε:

[0044]

[0045] Here, σ(ε) is obtained from the rubber compression test.

[0046] By integrating the crack growth rate equation, we can obtain the fatigue life prediction formula:

[0047]

[0048] When the rubber gasket breaks and fails, a is visible macroscopically, a0 is at the micron level, and a0 represents the initial crack length. If a is much larger than a0, then:

[0049]

[0050] The service life T can be estimated by the number of cycles N, as shown in formula (16):

[0051]

[0052] Where n is the number of cycles per day and f is the number of working days per year.

[0053] The beneficial effect of the present invention is that by establishing the relationship between the extrusion amount, leakage amount and service life of the rubber sealing gasket, the lower limit of the extrusion amount x is determined within the allowable range of leakage amount. min The upper limit of extrusion volume x is determined by the service life requirement max , scientifically determine the optimal extrusion range to maximize the service life of the sealing material while ensuring waterproof reliability. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 This is the cross-sectional layout of the tunnel section.

[0055] Figure 2 This is a cross-sectional view of a rubber gasket.

[0056] Figure 3 This is the finite element model diagram of the underwater joint.

[0057] Figure 4 This is the contact pressure diagram of the rubber sealing gasket under 70mm extrusion.

[0058] Figure 5 Flowchart for calculating leakage using amplification contact theory.

[0059] Figure 6 The diagram for the division of the sealing interface regular quadrilateral calculation unit.

[0060] Figure 7 Select a diagram for the seal interface contact pressure path.

[0061] Figure 8 The contact pressure distribution diagram of the rubber sealing gasket under 70mm extrusion volume.

[0062] Figure 9 This is the surface morphology of the tunnel section.

[0063] Figure 10 Schematic diagram of the surface roughness power spectral density function.

[0064] Figure 11 It is the relationship diagram between the sealing extrusion amount x and the joint leakage amount Q.

[0065] Figure 12 Flowchart for predicting seal service life based on fracture mechanics.

[0066] Figure 13 This is the relationship diagram between seal extrusion amount x and service life T. DETAILED DESCRIPTION

[0067] The present invention will be further described below with reference to the accompanying drawings and specific embodiments:

[0068] like Figures 1-13 As shown, this embodiment discloses a method for determining the sealing extrusion amount of an underwater joint, comprising the following steps:

[0069] (1) Establishing the finite element calculation model of the joint:

[0070] A simplified model of the rubber sealing gasket extrusion of underwater tunnel joints was established using ABAQUS. The constitutive relationship of the rubber material was determined, and the underwater tunnel seal installation process was simulated. The contact pressure distribution of the rubber sealing gasket contact interface under different seal extrusion amounts was obtained, and the dangerous section was determined.

[0071] (2) Establish a leakage-extrusion relationship model:

[0072] Based on the magnification contact model, a method for calculating joint leakage is proposed. The sealing extrusion amount x-joint leakage amount Q curve is fitted, the influence of the rubber gasket deformation on joint leakage is discussed, and the minimum extrusion amount that meets the sealing requirements is determined as the lower limit of the sealing extrusion amount x min .

[0073] (3) Establishing a life-extrusion relationship model:

[0074] Based on fracture mechanics, the life of rubber sealing gaskets is predicted, the maximum strain and crack initiation position are extracted, the crack growth rate equation and tearing energy theory are used to establish a life integral model, the number of fatigue cycles is calculated, the service life of rubber sealing gaskets is predicted, and the relationship curve between extrusion volume and life is obtained. The maximum extrusion volume required to ensure the service life of the rubber is determined as the upper limit of the sealing extrusion volume x max .

[0075] (4) Determine the optimal extrusion range:

[0076] At the lower limit of extrusion amount x min and the upper limit of extrusion amount xmax Select the optimal value between them, comprehensively consider the safety factor and working conditions, and determine the final design extrusion amount x.

[0077] Establish the finite element model of underwater tunnel joint, refer to Figure 1 The total height of the concrete tunnel section is 10m and the width is 30m. In order to ensure the watertightness of the pipe joints, rubber gaskets are set along the top, bottom and both sides of the outer edge of the cross section. The inner ring size of the rubber gasket model is set to 29.4m*9.3m, and the outer ring size is 29.7m*9.6m, that is, the width of the rubber gasket is 150mm, the thickness of the rubber gasket is 200mm, and the cross-sectional dimensions are as follows: Figure 2 .

[0078] The rubber gasket is made from natural rubber, a hyperelastic material with nonlinear stress-strain characteristics. In the simulation, the normal contact relationship between the tunnel section and the rubber gasket is defined as "hard" contact. To account for the potential for slip friction between the tube section and the rubber, the tangential contact relationship is defined as a "penalty" function. Because the tunnel section is much stiffer than the rubber, the tunnel section is configured as a rigid body, with the section as the primary contact surface and the gasket as the secondary contact surface.

[0079] The rubber gasket is put into use only after the hydraulic pressure seal is completed. Therefore, the simulation is divided into two analysis steps: the first step is to set the concrete tunnel sections on both sides to be constrained as a single degree of freedom, and apply equal and opposite displacement loads to squeeze the gasket to complete the hydraulic pressure seal; the second step is to apply external water pressure to the rubber gasket according to the actual water depth of the project. Figure 3 , through ABAQUS software, simulate the rubber seal extrusion process, calculate its stress deformation under different extrusion amounts, when the rubber seal extrusion amount is 70mm (the thickness is squeezed 70mm), its contact pressure cloud diagram is as follows Figure 4 .

[0080] The proposed joint leakage calculation method based on the magnification model must consider not only the contact state between two surfaces but also fluid seepage theory. For leakage prediction, the magnification contact model is commonly used for seals between two stationary surfaces. Assuming the leakage pressure differential occurs at the critical path, the contact model is combined with seepage theory to determine the characteristics of the critical path and then calculate the leakage.

[0081] In the magnification contact theory, the entire contact area is defined as a region with an area of ​​L x ×L y The rectangle can be divided into L y / L x A regular quadrilateral with a side length of L x , area A0=Lx 2 . The magnification factor ξ is a key parameter in the theory, describing the scale at which the contact area is observed. The actual contact area is A(ξ), which varies with the magnification factor ξ. At the minimum magnification (ξ=1), the two surfaces are assumed to be in nominal full contact, i.e. A(1)=A0. As the magnification increases, details of the surface roughness become apparent. Some areas become non-contact (blank areas) and the actual contact area A(ξ) decreases. In the percolation theory, the critical magnification factor ξ c It is defined as the magnification at which the percolation path first appears, spanning the entire contact area. When the critical magnification ξ is reached c When , there is a path that runs through the entire contact area. The cross section with the minimum width is called the critical channel of the path. The channel is simplified to a rectangular hole, and its height is defined as u1(ξ c ), which is the distance between the rubber sealing pad and the concrete tunnel section.

[0082] Assuming that all leakage occurs from the seepage path, the pressure difference Δp appears at the critical amplification factor, and the unit square (L x ×L x )The fluid transmission velocity (leakage) Q0 can be calculated by formula (1).

[0083]

[0084] Where μ is the viscosity, α is the correction factor to consider the influence of shrinkage morphology at higher magnification. Since the critical shrinkage cavity is simplified to a rectangular hole, the true shape of the shrinkage cavity cannot be obtained, so α = 1. On the entire contact surface, the length direction is L y , then the number of regular quadrilaterals on the contact surface is L y / L x The total leakage rate can be obtained by Q = L y / L x Q0 calculation.

[0085] At this point, the key to solving the leakage is to find the critical amplification factor ξ when the penetration path appears c Define the non-contact area ratio of the regular quadrilateral as P c-n =1-A(ξ) / A0, as the magnification increases, the contact area A(ξ) decreases, and the non-contact area ratio P c-n According to the percolation theory, for the surface of isotropic materials, when the non-contact area is greater than P c-n When it reaches about 0.6, there is a channel connecting the two ends of the contact area. At this time, the corresponding contact area ratio A(ξ) / A0 is 0.4, which is used as the criterion for determining the critical magnification factor.

[0086] When the magnification is ξ, the contact area ratio A(ξ) / A0 can be obtained by formula (2).

[0087]

[0088] Where p0 is the applied pressure, is the contact pressure when the magnification factor ξ is 1, erf is the error function, and G represents the effective stiffness of the surface roughness, which can be expressed as:

[0089]

[0090] Where q is the wave vector, q0 is the reference wave vector, d is the integral symbol, E * is the equivalent elastic modulus, which can be obtained by formula (4), C(q) is the isotropic surface roughness PSD (power spectral density), which can be obtained by the one-dimensional PSD function C 1-D (q) is obtained by formula (5).

[0091]

[0092] Where υ is Poisson’s ratio, E1 and E2 are the elastic moduli of the contact bodies (i.e., rubber sealing pad and concrete tunnel section), respectively.

[0093]

[0094] The height of the critical penetration path u1(ξ) is the separation height of the two contact surfaces when the first penetration path through the contact area appears, that is, u1(ξ) is the height of the tunnel section and the rubber sealing pad surface. u1(ξ) can be obtained by formula (6).

[0095]

[0096] in, is the overall average height of the two surfaces at magnification ξ, u'(ξ) and A'(ξ) are the derivatives of u(ξ) and the contact area A(ξ) with respect to ξ, respectively. It can be obtained by formula (7)-formula (9).

[0097]

[0098] Among them, q0 is the reference wave vector, q1 is the maximum wave vector, w(q) is a weight function related to the surface roughness power spectrum C(q), p(ξ) is the nominal pressure at the current magnification,

[0099] w(q,ξ) is a function related to the local contact stiffness, s(q,ξ) is a function related to the local pressure and elastic deformation, and s(q,ξ)=w(q,ξ) / E *P(q,p,ξ) is an error function that represents the effect of the local contact pressure p on the elastic contact probability for a specific magnification factor ξ and wave vector q. Because the elastic energy stored in the contact area is less than the elastic energy in the full contact area, a correction factor γ0 is introduced. γ0 is less than 1 and is set to 0.4 in this example.

[0100] The entire leakage calculation process is summarized as follows: Figure 5 The contact pressure distribution is obtained by establishing a finite element model of the joint using ABAQUS software. Taking into account the surface roughness of the tunnel section, the entire sealing contact area is divided into regular quadrilateral calculation units. The sealing interface contact area ratio A(ξ) / A0 is 0.4 as the criterion for determining the critical magnification factor, and the average height of the leakage channel when the magnification factor is ξ is obtained. The unit leakage rate Q0 is calculated by the seepage theory, and the total leakage Q is finally calculated. The critical parameters include: critical magnification ξ c , average distance of infiltration path And the critical shrinkage height u1. After obtaining the shrinkage height, the unit leakage can be calculated using the seepage theory formula (1).

[0101] This method characterizes the contact state through the contact pressure of the sealing interface. The following is the form and method of extracting the contact pressure.

[0102] Since each calculation unit has different working conditions, its leakage is slightly different. In order to obtain accurate calculation results, when calculating the total leakage, it is necessary to divide the contact interface into several regular quadrilateral calculation units. The sealing width of the rubber gasket is 150mm, so it is divided into 150*150mm regular quadrilateral calculation units. According to the cross-sectional size of the gasket, the division results are as follows Figure 6 There are no seepage channels on both sides, and the inside and outside are not connected, that is, Figure 6 The four corners are not included in the calculation, and are considered to be leak-free. The long side is divided into 29400 / 150 = 196 computational units, numbered 1 to 196 from left to right, and the short side is divided into 9300 / 150 = 62 computational units, numbered 1 to 62 from top to bottom.

[0103] Determining the contact state of the contact surface is crucial for leakage calculations. A path is selected along the seal width, passing through the midpoint of each regular quadrilateral. This path is connected by several nodes. Ideally, the force applied to the gasket area at the same water depth should be the same, so the average contact pressure of the top and bottom regular quadrilaterals can be assumed to be similar. However, as the water depth increases, the water pressure acting on the outer side of the gasket increases, so the average contact pressure of the regular quadrilaterals on both sides of the gasket changes with water depth.

[0104] The selection of paths is the key to characterizing the contact state of the sealing interface. For the top (bottom) area of ​​the gasket, three paths are evenly selected, numbered 1 to 3 from left to right, and the contact pressure on the paths is extracted; for both sides of the gasket, each calculation unit selects a path, numbered 1 to 62, and the contact pressure on the path is extracted. The path distribution is as follows Figure 7 . Figure 8 The actual distance-contact pressure diagram of the rubber sealing gasket under 70mm extrusion volume. The three figures are the distance-contact pressure diagrams of the top, two sides, and bottom respectively.

[0105] To calculate the leakage, it is necessary to obtain the power spectrum density of the contact surface roughness. Since the surface roughness of the tunnel pipe section is much greater than that of the rubber gasket, the rubber gasket surface can be considered smooth and the concrete pipe section surface can be considered rough. The surface roughness of the tunnel pipe section is determined based on factors such as material properties and construction technology. The surface roughness is represented in the form of power spectrum density. The root mean square (RMS) of the roughness is set to 0.8, and the roughness data of the concrete is artificially generated to simulate the surface morphology of the sealing interface, such as Figure 9 The surface roughness distribution on the center line is extracted from the surface map, and the power spectrum density function of the concrete surface is generated by combining the sealing width of 150 mm, as shown in the figure. Figure 10 .

[0106] The long side of the rubber gasket is divided into 196 regular quadrilateral computational units, and the short side is divided into 62 regular quadrilateral computational units. At the top (bottom) of the gasket, the average contact pressures of the regular quadrilateral computational units within the region are similar, and the pressure differential Δp is the same. Therefore, the leakage of the computational units at the top (bottom) is assumed to be approximately the same. The average leakage is calculated using three regular quadrilateral units, and the average leakage is multiplied by 196 to obtain the leakage at the top (bottom) Q1 (Q2). For both sides of the gasket, since each computational unit is at different water depths, its contact pressure and pressure differential are different. Therefore, the leakage of 62 computational units must be calculated separately, and the sum of the values ​​multiplied by 2 is the leakage on both sides, Q3. The total leakage of the immersed tube tunnel flexible joint can then be calculated using Equation (10).

[0107] Q=Q1+Q2+Q3 (10)

[0108] Similarly, using ABAQUS finite element calculation software, the extrusion amount of the rubber seal is changed to obtain the contact pressure under different extrusion amounts, and the leakage amount can be calculated. In order to establish a quantitative relationship between the extrusion amount x and the leakage amount Q, the calculation results are mathematically analyzed, and the image and empirical formula of the extrusion amount x-leakage amount Q are obtained through curve fitting, as shown in the following example: Figure 11 The fitting results show that there is a significant exponential function relationship between the leakage volume Q and the extrusion volume x.

[0109] According to the actual project and the requirements of the specification, the leakage volume Q requirement can be determined. Using the empirical formula for leakage prediction, the lower limit of the sealing extrusion volume x that meets the maximum allowable leakage volume can be determined by inverse calculation. min .

[0110] This paper proposes a method for predicting the fatigue life of sealing rubber based on fracture mechanics. The core of the method is to establish a quantitative relationship between the crack growth rate and the strain energy release rate. The fatigue crack growth rate of rubber material is expressed by formula (11):

[0111]

[0112] Where a is the crack length, N is the number of cycles, J is the maximum tearing energy in a single cycle, B is the material constant, and β is the crack growth constant.

[0113] The tearing form of the seal is described by single-sided incision stretching, and the crack growth rate can be expressed by formula (12):

[0114]

[0115] Where λ is the elongation ratio, λ = 1 + ε; ε is the rubber strain, and ω0 is the strain energy density, which is a function of ε:

[0116]

[0117] Where σ(ε) is obtained from the rubber compression test. By integrating the crack growth rate equation, the fatigue life prediction formula can be obtained:

[0118]

[0119] When the rubber gasket breaks and fails, a is visible macroscopically, a0 is at the micron level, and a0 represents the initial crack length. If a is much larger than a0, then:

[0120]

[0121] The service life T can be estimated by the number of cycles N, as shown in formula (16):

[0122]

[0123] Where n is the number of cycles per day and f is the number of working days per year.

[0124] It can be found that the life of rubber gaskets is related to the rubber type, initial crack length and strain at the crack. When the rubber material is determined, its life is only related to the strain of the rubber: the greater the strain, the shorter the life, that is, the greater the extrusion of the rubber gasket, the shorter the life. Therefore, it is necessary to determine the upper limit of the seal extrusion x within a reasonable life requirement range. max, in order to better ensure the sealing effect.

[0125] Assuming that the initial cracks in the rubber are evenly distributed inside, the life span depends on the maximum strain. The extrusion volume affects the contact state of the sealing structure surface and the internal stress distribution, which has a great impact on the service life of the seal. In order to ensure that the seal maintains a good sealing effect within the designed service life, the ABAQUS finite element calculation software is used to change the extrusion volume of the rubber seal to obtain the contact pressure under different extrusion volumes, and its fatigue life is calculated based on the fracture mechanics method. The finite element model is the same as above, and the calculation process is as follows Figure 12 The finite element model of the joint was established using ABAQUS software to obtain the maximum strain ε0, where ε0 is the maximum strain of the rubber seal. σ(ε) was obtained through the rubber compression test, and the strain energy density ω0 was calculated. The number of cycles N was obtained and the service life T was estimated.

[0126] According to the finite element calculation results, it can be found that the maximum strain occurs at the corner of the rectangular gasket. Through iterative calculation, the expected service life T of the rubber gasket under different extrusion amounts is determined. The life prediction values ​​under different extrusion amounts are summarized and analyzed to obtain the relationship curve between extrusion amount and life, as shown in Figure 13 Then, according to the design service life required by the specification, determine the maximum extrusion required to ensure the service life of the rubber sealing gasket as the upper limit of the sealing extrusion amount x max .

[0127] Taking safety performance, working conditions and manufacturing feasibility into consideration, the lower limit of extrusion volume x is determined by the leakage of the joint. min , the service life of the seal determines the upper limit of the extrusion volume x max , and finally determine the optimal design extrusion amount x. This value is selected when x is satisfied. min <x<x max At the same time, it achieves the best balance among safety factor, adaptability to working conditions and economy.

[0128] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for determining the sealing extrusion amount of an underwater joint, characterized in that: The following steps are involved: (1) Establishing the finite element calculation model of the joint: A simplified model of the rubber seal of an underwater tunnel joint during extrusion was established using ABAQUS. The constitutive relationship of the rubber material was determined, and the underwater tunnel seal installation process was simulated. The contact pressure distribution at the rubber seal interface under different seal extrusion amounts was obtained, and the dangerous section was determined. (2) Establish a leakage-extrusion relationship model: Based on the magnification contact model, the seal extrusion amount x-joint leakage amount Q curve is fitted, the influence of the rubber seal deformation on the joint leakage is discussed, and the minimum extrusion amount that meets the sealing requirements is determined as the lower limit of the seal extrusion amount x min ; (3) Establishing a life-extrusion relationship model: Based on fracture mechanics, the life of rubber sealing gaskets is predicted, the maximum strain and crack initiation position are extracted, the crack growth rate equation and tearing energy theory are used to establish a life integral model, the number of fatigue cycles is calculated, the service life of rubber sealing gaskets is predicted, and the relationship curve between extrusion volume and life is obtained. The maximum extrusion volume required to ensure the service life of the rubber is determined as the upper limit of the sealing extrusion volume x max ; (4) Determine the optimal extrusion range: At the lower limit of extrusion amount x min and the upper limit of extrusion amount x max Select the optimal value between them, comprehensively consider the safety factor and working conditions, and determine the final design extrusion amount x.

2. A method for determining the sealing extrusion amount of an underwater joint according to claim 1, characterized in that: The calculation process of the joint leakage Q is as follows: the finite element model of the joint is established by ABAQUS software. Taking into account the surface roughness of the tunnel section, the entire sealing contact area is divided into regular quadrilateral calculation units. The sealing interface contact area ratio A(ξ) / A0 is 0.4 as the criterion for determining the critical magnification factor. The leakage when the magnification factor is ξ is obtained. Average height of leakage channel The unit leakage rate Q0 is calculated using the seepage theory, and finally the total leakage volume Q is calculated.

3. A method for determining the sealing extrusion amount of an underwater joint according to claim 2, characterized in that: The entire contact area is defined as an area L x ×L y The rectangle is divided into L y / L x A regular quadrilateral with a side length of L x , when the critical magnification ξ is reached c When there is a path running through the entire contact area, the cross section of the path with the minimum width is called the critical channel of the path. The channel is simplified to a rectangular hole, and its height is defined as u1(ξ c ), the pressure difference Δp appears at the critical magnification ξ c When , the unit quadrilateral fluid leakage rate Q0 can be calculated by formula (1): Where μ is the viscosity, α is the correction factor considering the influence of shrinkage cavity morphology at higher magnification. Since the critical shrinkage cavity is simplified to a rectangular hole, the true shape of the shrinkage cavity cannot be obtained, and α = 1.

4. A method for determining the sealing extrusion amount of an underwater joint as claimed in claim 2, characterized in that: When the magnification is ξ, the contact area ratio A(ξ) / A0 can be obtained by formula (2): Where p0 is the applied pressure, is the contact pressure when the magnification factor ξ is 1, erf is the error function, and G represents the effective stiffness of the surface roughness, which can be expressed as: Among them, q is the wave vector, q0 is the reference wave vector, E * is the equivalent elastic modulus, which can be obtained by formula (4), C(q) is the isotropic surface roughness PSD, which can be obtained by the one-dimensional PSD function C 1-D (q) is obtained by formula (5), Where υ is Poisson's ratio, E1 and E2 are the elastic moduli of the contact bodies, 5. A method for determining the sealing extrusion amount of an underwater joint as claimed in claim 2, characterized in that: The height of the critical permeation path u1(ξ) is the separation height of the two contact surfaces when the first permeation path through the contact area appears. u1(ξ) can be obtained by formula (6): in, is the overall average height of the two surfaces at magnification ξ, u'(ξ) and A'(ξ) are the derivatives of u(ξ) and the contact area A(ξ) with respect to ξ, respectively. It can be obtained from formula (7) to formula (9), Among them, q0 is the reference wave vector, q1 is the maximum wave vector, w(q) is a weight function related to the surface roughness power spectrum C(q), p(ξ) is the nominal pressure at the current magnification, w(q,ξ) is a function related to the local contact stiffness, s(q,ξ) is a function related to the local pressure and elastic deformation, and s(q,ξ)=w(q,ξ) / E * , P(q,p,ξ) is an error function, which represents the influence of local contact pressure p on elastic contact probability under specific magnification ξ and wave vector q, γ0 is the correction factor, and γ0 is taken as 0.

4.

6. A method for determining the sealing extrusion amount of an underwater joint as claimed in claim 2, characterized in that: For the top or bottom of the gasket, the average contact pressure of each regular quadrilateral calculation unit in the area is similar, and the pressure difference Δp is the same. It is assumed that the leakage of the calculation units at the top or bottom is approximately the same. The average leakage multiplied by the number of units is the leakage of the top or bottom Q1 or Q2. For both sides of the gasket, since each calculation unit is at different water depths, its contact pressure and pressure difference are different. The leakage of all units needs to be calculated separately, and the sum of the values ​​multiplied by 2 is the leakage of both sides Q3. The total leakage of the flexible joint of the immersed tube tunnel can be calculated by formula (10): Q=Q1+Q2+Q3 (10) 7. A method for determining the sealing extrusion amount of an underwater joint according to claim 1, characterized in that: The calculation process of the expected service life T is as follows: establish the joint finite element model through ABAQUS software to obtain the maximum strain ε0, obtain σ(ε) through rubber compression test, calculate the strain energy density ω0, obtain the number of cycles N and estimate the service life T.

8. A method for determining the sealing extrusion amount of an underwater joint according to claim 7, characterized in that: The fatigue crack growth rate of rubber material is expressed by formula (11): Where a is the crack length, N is the number of cycles, J is the maximum tearing energy in a single cycle, B is the material constant, and β is the crack growth constant.

9. A method for determining the sealing extrusion amount of an underwater joint according to claim 8, characterized in that: The tearing form of the seal is described by single-sided incision stretching, and the crack growth rate can be expressed by formula (12): Where λ is the elongation ratio, λ = 1 + ε; ε is the rubber strain, and ω0 is the strain energy density, which is a function of ε: Here, σ(ε) is obtained from the rubber compression test.

10. A method for determining the sealing extrusion amount of an underwater joint according to claim 9, characterized in that: By integrating the crack growth rate equation, we can obtain the fatigue life prediction formula: When the rubber gasket breaks and fails, a is visible macroscopically, a0 is at the micron level, and a0 represents the initial crack length. If a is much larger than a0, then: The service life T can be estimated by the number of cycles N, as shown in formula (16): Where n is the number of cycles per day and f is the number of working days per year.

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