A method for predicting the long-term waterproof performance and leakage rate of shield tunnel joints

Abstract

The present invention relates to the research field of the waterproof performance of shield tunnel joints under the action of sealing gaskets, and proposes a method for predicting the long-term waterproof performance and leakage rate of shield tunnel joints, the steps of which include: conducting an assembly force test on the sealing gasket to obtain a nonlinear relationship between the compression strain of the sealing gasket and the equivalent compression modulus; performing a morphological scan on the sealing gasket contact surface through an AFM test to obtain the surface morphology parameters of the sealing gasket rubber; utilizing multi-scale contact theory and percolation theory to obtain the percolation pressure considering long-term aging behavior; combining the self-sealing effect of the sealing gasket to obtain the critical leakage water pressure of the joint; obtaining the critical hydraulic opening under the contact of the sealing gasket based on the Persson model, and predicting the leakage rate of the sealing gasket at each stage under different joint opening and dislocation forms and the influence of long-term rubber aging based on the cubic law. The present invention can improve the existing shield tunnel joint waterproof design method and provide guidance for the waterproof performance of the sealing gasket under the influence of long-term aging.

Description

Technical Field

[0001] The invention relates to the research field of waterproof performance of shield tunnel joints under the action of sealing pads. Background Art

[0002] Water leakage is a common problem in shield tunnels during long-term operation, with the majority occurring at joints. Localized leakage can also induce significant deformation and cracking in the lining. Joint leakage is primarily driven by the gaskets embedded in the joint grooves, which are affected by the joint's opening and misalignment, as well as the gasket's performance. Therefore, understanding and predicting the gasket's waterproofing mechanism is crucial for long-term tunnel operation safety.

[0003] Theoretically, leakage in rubber waterproofing contacts, such as gaskets, is a typical percolation behavior, characterized by gradual leakage and a certain contact pressure at the critical leakage point. However, existing theories of gasket waterproofing generally oversimplify this complex contact relationship, equating the critical leakage water pressure to the gasket contact pressure at the critical leakage point. This also ignores the long-term aging of the gasket. Furthermore, there are few predictive methods for calculating gasket leakage, and existing theories mostly rely on fitting experimental data, lacking theoretical validity and universality.

[0004] To avoid water leakage during tunnel operation and the resulting structural damage caused by insufficient consideration of joint hydraulic degradation, it is necessary to accurately assess and predict joint leakage behavior during the design phase. This requires a more universal joint waterproofing performance prediction method that considers the long-term aging behavior of gaskets. By embedding aging-related parameters into the computational model, researchers can further analyze the impact of each parameter on joint waterproofing and seepage rate, thereby improving the design method of joint waterproofing systems. Summary of the Invention

[0005] In view of the above problems, the present invention proposes a method for predicting the long-term waterproof performance and leakage rate of shield tunnel joints.

[0006] The technical solutions of the present invention are as follows:

[0007] A method for predicting the long-term waterproof performance and leakage rate of shield tunnel joints comprises the following steps:

[0008] Step 1: Through the gasket assembly force loading test, the nonlinear relationship between the compressive strain and the equivalent compression modulus of the gasket in the groove is obtained;

[0009] Step 2: Scan the surface morphology of the gasket contact surface at different aging levels through AFM testing to obtain the surface morphology parameters of the gasket rubber surface. Perform an equivalent transformation on the contact between the two gaskets to obtain the equivalent contact surface elastic modulus and the roughness power spectrum of the rigid substrate.

[0010] Step 3: Calculate the percolation pressure of the gasket contact surface considering long-term aging behavior using multi-scale contact theory and percolation theory;

[0011] Step 4: Combine the self-sealing effect of the sealing gasket and modify the contact pressure relationship under the critical leakage state based on the percolation pressure to obtain the critical leakage water pressure of the joint;

[0012] Step 5: Based on the Persson model, the hydraulic opening of the gasket contact surface is obtained. Based on the cubic law, the leakage rate of the gasket at each stage under different joint opening and misalignment forms and the influence of long-term rubber aging is calculated.

[0013] Beneficial effects of the present invention:

[0014] The present invention analyzes the influence of rubber aging on leakage behavior (including waterproof performance and leakage rate) based on the surface morphology characteristics of the sealing gasket, and combines the waterproof mechanism of the sealing gasket to provide guidance for the long-term waterproof design of actual shield tunnel joints. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 Schematic diagram of the process of the present invention.

[0016] Figure 2 Schematic diagram of the simplified model of the seam seal contact.

[0017] Figure 3 Schematic diagram of gasket percolation pressure calculation.

[0018] Figure 4 Schematic diagram of the relationship between the critical leakage water pressure of the sealing gasket and the total contact pressure.

[0019] Figure 5 A graph showing the critical leakage water pressure of the sealing gasket before and after aging versus the opening amount in the embodiment.

[0020] Figure 6 A graph showing the leakage rate of the sealing gasket before and after aging versus external water pressure in the embodiment. DETAILED DESCRIPTION

[0021] The technical solution provided by this application will be further described below in conjunction with specific embodiments and accompanying drawings. The advantages and features of this application will become more apparent with reference to the following description.

[0022] This paper proposes a method for predicting the long-term waterproof performance and leakage rate of shield tunnel joints. Based on the surface morphology of the sealing gasket, the influence of rubber aging on the leakage behavior (including waterproof performance and leakage rate) is analyzed. Combined with the waterproof mechanism of the sealing gasket, it provides guidance for the long-term waterproof design of actual shield tunnel joints. The implementation process of this method is as follows: Figure 1 shown.

[0023] Step 1: Obtain the compressive strain ε and equivalent compression modulus E of the gasket in the groove through the gasket assembly force loading test g nonlinear relationship.

[0024] Specifically include:

[0025] Step 1.1: Set a sealing gasket groove similar to the joint structure in the loading mold, and vertically load the sealing gasket through the testing machine to obtain a series of vertical external loads and corresponding compression displacements of the sealing gasket, forming multiple sets of vertical external load-compression displacement data.

[0026] Step 1.2 Convert the data in the vertical external load-compression displacement data set: convert the compression displacement into the sealing gasket compression strain ε, and convert the obtained vertical external load F N And the compression strain ε is converted into the equivalent compression modulus E of the sealing gasket g , thereby obtaining the sealing gasket compressive strain-equivalent compression modulus data set.

[0027]

[0028] Where, F N is the vertical external load per linear meter, w g is the top width of the gasket.

[0029] Step 1.3, the converted test results (seal gasket compression strain ε-seal gasket equivalent compression modulus E g The data set) is fitted to obtain the empirical formula of the equivalent compression modulus of the sealing gasket. For example, the empirical formula shown in the following formula (2) can be used for fitting:

[0030] E g =E0+bexp(cε) (2)

[0031] Where E0, b and c are fitting constants.

[0032] Step 2: Scan the surface morphology of the gasket contact surface at different aging levels using AFM testing to obtain the gasket rubber surface morphology parameters, including surface roughness power spectrum, roughness coefficient, and RMS (root-mean-square) roughness peak height and slope. Additionally, perform an equivalent transformation of the contact surface elastic modulus and the roughness power spectrum of the rigid substrate.

[0033] The specific steps include:

[0034] Step 2.1 Scan the surface morphology of the gasket at different aging degrees through AFM test, and obtain the surface roughness power spectrum C through formula (3) g (q):

[0035]

[0036] Where q is the morphological wave number at the current observation scale, H is the roughness coefficient (Haus index), <h 2 > is the square value of the surface profile height, <h 2 > Take h rms is the rms roughness peak height, and q0 is the minimum morphological wave number.

[0037] The rms slope ξ is obtained by equation (4):

[0038]

[0039] Where q1 is the maximum morphological wave number.

[0040] Step 2.2: The contact problem between two gaskets is equivalent to the contact problem between a rigid rough substrate and an elastic body, as shown in Figure 2 As shown. The equivalent contact surface elastic modulus E * Calculated by formula (5):

[0041]

[0042] Where E1 and E2 are the Young's moduli of the solids on both sides of the contact surface; v1 and v2 are their respective Poisson's ratios; v eff is the equivalent Poisson's ratio of the sealing gasket, and the empirical value is 0.3 to 0.5.

[0043] The roughness power spectrum C(q) of the equivalent rigid matrix can be calculated by formula (6):

[0044] C(q)=C1(q)+C2(q)=2C g (q) (6)

[0045] Where C1(q) and C2(q) are the roughness power spectra of the solids on both sides of the contact surface, C g (q) is the power spectrum of the surface roughness of the sealing gasket.

[0046] Step 3: Based on the percolation theory in a two-dimensional framework, derive the percolation pressure P of the gasket contact surface perc .

[0047] Based on the percolation theory in a two-dimensional framework, whether the leakage condition is met is determined by the relative contact area A(ζ) / A0 between the gaskets. The relationship between the relative contact area A(ζ) / A0 and the nominal contact pressure p can be given by formula (7):

[0048]

[0049] Where A and A0 are the true contact area and nominal contact area, respectively, ζ is the observation scale, p is the nominal contact pressure, erf is the error function, and G can be calculated by formula (8):

[0050]

[0051] The effective pressure of the contact surface at the critical leakage state is defined as the percolation pressure. The percolation pressure comprehensively reflects the influence of the contact morphology characteristics and nonlinear compressive mechanical properties of the sealing gasket on the leakage of the sealing gasket. The concept of percolation pressure of the waterproof sealing gasket contact is given in the literature "Persson, BNJ, 2022. Fluid Leakage in Static Rubber Seals" for "O" ring waterproofing. The present invention modifies it and introduces it into the field of joint sealing gasket seepage, and E * Consider the equivalent elastic modulus that changes with compressive strain to accommodate the pore characteristics of the gasket, as described in step 2.2.

[0052] Furthermore, the percolation pressure P is defined as perc is the average contact pressure of the sealing gasket when the relative contact area A(ζ) / A0 reaches the leakage condition, which can be calculated by formula (9):

[0053]

[0054] Where erfinv is the inverse error function.

[0055] Preferably, when the relative contact area A(ζ) / A0 reaches 0.4, the contact surface begins to leak, and the percolation pressure P perc It can be calculated by formula (9′), as Figure 3 As shown:

[0056]

[0057] Step 4: Considering the self-sealing effect and sealing coefficient κ under lateral water pressure, the contact pressure relationship of the sealing gasket is corrected by the percolation pressure to obtain the critical leakage water pressure P of the sealing gasket under different joint forms. wc Critical leakage water pressure P wc Total contact pressure P c , percolation pressure P perc Relationships such as Figure 4 As shown. In the critical leakage state (leakage just started), the critical leakage water pressure P wc and percolation pressure P perc The sum of the total contact stress P c When the staggered effect is considered, the sealing coefficient k is used to correct the critical leakage water pressure.

[0058] Step 4.1 Determine the slope k0 of the self-sealing effect using the equivalent Poisson's ratio or empirical formula.

[0059] The equivalent Poisson's ratio v can be obtained from formula (10) eff k0 is calculated. When the nonlinear self-sealing effect that varies with the compressive strain is considered, k0 can also be obtained by an empirical formula with ε as the variable, as shown in formula (11), and the corresponding equivalent Poisson's ratio v is obtained at the same time. eff :

[0060]

[0061] k0=aε 2 (11)

[0062] Where a is the correction coefficient of the empirical formula.

[0063] According to the sealing mechanism of the gasket, k0 should be close to 1 when the seam is in a fully closed state.

[0064] Step 4.2 Calculate the sealing coefficient κ considering the staggered seam using formula (12).

[0065]

[0066] Where, β is the correction coefficient of the sealing coefficient, s is the amount of gasket stagger, w g is the top width of the gasket.

[0067] Step 4.3 Calculate the critical leakage water pressure P corrected by percolation pressure using formula (13) wc .

[0068] Based on the conceptual formula given in the literature "Gong CJ et al., 2019. Failure mechanism of joint waterproofing inprecast segmental tunnel linings", this formula was modified to take into account the influence of the percolation pressure at the contact surface:

[0069]

[0070] Step 5: Based on the Persson model, the critical hydraulic opening of the gasket contact surface is obtained. Based on the cubic law, the leakage rate of the gasket at each stage under different joint opening and misalignment forms and the influence of long-term rubber aging is calculated.

[0071] Specifically include:

[0072] Step 5.1 According to the external water pressure P w and critical leakage water pressure P wc and breakdown water pressure P wb The relationship between the current leakage stage is determined. The leakage stage is divided into three stages: percolation stage (P w ≤P wc ), leakage stage (P wc <P w ≤P wb ) and breakdown phase (P wb <P w ).

[0073] Step 5.2 Based on equations (14) to (17), the average hydraulic opening of the sealing gasket contact surface under the effective stress of the contact surface is calculated.

[0074]

[0075] Where, constant γ = 0.4, and function P(q, p, ζ) is obtained from equation (15):

[0076] P(q,p,ζ)=erf(w(q,ζ)pE * ) (15)

[0077] The function w(q,ζ) is obtained from formula (16):

[0078]

[0079] Then, the critical hydraulic opening u is obtained by formula (17): c (ζ):

[0080]

[0081] Where, is u c (ζ), A′(ζ) is the first-order derivative of A(ζ).

[0082] Step 5.3 Based on the critical hydraulic opening u c The sealing gasket permeability Q at different seepage stages is calculated by formula (18):

[0083]

[0084] Where, P wb is the effective contact pressure P cont External water pressure when reduced to 0, L x and L y are the contact surface widths in the seepage direction and perpendicular to the seepage direction, respectively; μ is the viscosity of water, which is 0.001 Pa·s.

[0085] Application Examples

[0086] Taking a shield tunnel joint sealing gasket as an example, the theoretical application of the method of the present invention is carried out, and the influence of rubber aging factors is evaluated. g 37mm, height h g 22mm, h rms is 0.118 μm, q0 and q1 are 1×10 5 m -1 and 1×10 10 m -1 The roughness coefficient H of the sealing gasket rubber before and after aging is 0.85 and 0.75 respectively.

[0087] The equivalent compression modulus E of the sealing gasket obtained by fitting the assembly force test results g for:

[0088] E g =3+1.429×10 -6 exp(36.81ε) (19)

[0089] According to the test results, the slope k0 of the self-sealing effect is:

[0090] k0=4.66ε 2 (20)

[0091] Since the self-sealing effect slope k0 is determined by an empirical formula, the equivalent Poisson's ratio v can be obtained based on formula (10): eff :

[0092]

[0093] The rms slope ξ obtained by formula (4) when the roughness coefficient H is 0.85 and 0.75 is 0.22 and 0.513 respectively. E is determined by empirical formula (19) g And v determined by formula (21) eff The equivalent contact surface elastic modulus E can be obtained by formula (5): * Subsequently, based on E * And the known rms slope ξ can be used to calculate the percolation pressure P through formula (9) perc .

[0094] In this example, the effect of staggered seams is not considered (s = 0 mm), so the sealing coefficient κ = 1, and the critical leakage water pressure formula is simplified to:

[0095]

[0096] Seepage channel contact surface width L y Take 1 to calculate the seepage rate per meter. Since the staggered joints are not considered, the contact surface width L x Take the top width of the gasket, that is:

[0097] L x =w g =22mm (23)

[0098] P wb According to the definition, it is taken as 1.84MPa.

[0099] Based on the above parameters, the final predicted seepage rate Q can be calculated by formula (18).

[0100] Figure 5 The critical leakage water pressure of the gasket before and after aging is given as a function of the seam opening. The results show that the increase in the seam opening will cause a decrease in water resistance. In addition, the aging of the gasket will significantly cause a decrease in waterproof performance. It can be seen that when the opening is 6mm, the critical leakage water pressure P wc It dropped from 1.66MPa to 1.41MPa, which is still higher than the design value of 1.3MPa. Therefore, the sealing gasket can still meet the design requirements under long-term aging conditions.

[0101] The curves of the sealing gasket seepage rate and external water pressure before and after aging obtained by this method are as follows: Figure 6 As shown, the opening is taken as the design value of 6mm. The results show that rubber aging also promotes seepage. Furthermore, with increasing external water pressure, the seepage rate increases significantly in the final stage of the seepage phase, indicating that the seal contact has entered the breakdown stage under the action of external water pressure.

[0102] The above description is only a description of the preferred embodiments of the present application and does not limit the scope of the present application. Any changes or modifications made by any person skilled in the art based on the above disclosed technical content should be regarded as equivalent valid embodiments and fall within the scope of protection of the technical solution of the present application.

Claims

1. A method for predicting the long-term waterproof performance and leakage rate of shield tunnel joints, characterized in that: Including steps: Step 1: Through the gasket assembly force loading test, the nonlinear relationship between the compressive strain and the equivalent compression modulus of the gasket in the groove is obtained; Step 2: Scan the surface morphology of the gasket contact surface at different aging levels through AFM testing to obtain the surface morphology parameters of the gasket rubber surface. Perform an equivalent transformation on the contact between the two gaskets to obtain the equivalent contact surface elastic modulus and the roughness power spectrum of the rigid substrate. Step 3: Calculate the percolation pressure of the gasket contact surface considering long-term aging behavior using multi-scale contact theory and percolation theory; Step 4: Combine the self-sealing effect of the sealing gasket and modify the contact pressure relationship under the critical leakage state based on the percolation pressure to obtain the critical leakage water pressure of the joint; Step 5: Based on the Persson model, the hydraulic opening of the gasket contact surface is obtained. Based on the cubic law, the leakage rate of the gasket at each stage under different joint opening and misalignment forms and the influence of long-term rubber aging is calculated.

2. The method for predicting the long-term waterproof performance and leakage rate of a shield tunnel joint according to claim 1, characterized in that: The step 1 comprises: Step 1.1: A sealing gasket groove having a structure similar to that of a joint is provided in a loading mold, and the sealing gasket is vertically loaded using a testing machine, thereby obtaining a series of vertical external loads and corresponding compression displacements of the sealing gasket, thereby forming multiple sets of vertical external load-compression displacement data sets; Step 1.2 Convert the data in the vertical external load-compression displacement data set: convert the compression displacement into the sealing gasket compression strain ε, and convert the obtained vertical external load F N And the compression strain ε is converted into the equivalent compression modulus E of the sealing gasket g , thereby obtaining the sealing gasket compressive strain-equivalent compression modulus data set; Where, F N is the vertical external load per linear meter, w g is the width of the top surface of the sealing gasket; Step 1.3, the converted test results are the gasket compression strain ε-gasket equivalent compression modulus E g The data set is fitted to obtain the empirical formula of the equivalent compression modulus of the sealing gasket.

3. The method for predicting the long-term waterproof performance and leakage rate of a shield tunnel joint according to claim 2, characterized in that: The step 1.3 is fitted using the empirical formula shown in formula (2): Yes g =E0+b exp(cε) (2) Where E0, b and c are fitting constants.

4. The method for predicting the long-term waterproof performance and leakage rate of a shield tunnel joint according to claim 1, characterized in that: The step 2 includes: Step 2.1 Scan the surface morphology of the gasket at different aging degrees through AFM test, and obtain the surface roughness power spectrum C through formula (3) g (q): Where q is the topography wave number at the current observation scale, H is the roughness coefficient, <h 2 > is the square value of the surface profile height, <h 2 > Take h rms is the rms roughness peak height, q0 is the minimum morphological wave number; The rms slope ξ is obtained by equation (4): Where q1 is the maximum morphological wave number; Step 2.2: The contact problem between the two gaskets is equivalent to the contact problem between a rigid rough substrate and an elastic body. The elastic modulus E* of the equivalent contact surface is calculated by formula (5): Where E1 and E2 are the Young's moduli of the solids on both sides of the contact surface; v1 and v2 are their respective Poisson's ratios; v eff is the equivalent Poisson's ratio of the gasket; The roughness power spectrum C(q) of the equivalent rigid matrix is ​​calculated by formula (6): C(q)=C1(q)+C2(q)=2C g (q) (6) Where C1(q) and C2(q) are the roughness power spectra of the solids on both sides of the contact surface, C g (q) is the power spectrum of the surface roughness of the sealing gasket.

5. The method for predicting the long-term waterproof performance and leakage rate of a shield tunnel joint according to claim 1, characterized in that: Step 3: Based on the percolation theory in a two-dimensional framework, the relative contact area A(ζ) / A0 between the gaskets is used to determine whether the leakage condition is met. Define the percolation pressure P perc is the average contact pressure of the sealing gasket when the relative contact area A(ζ) / A0 reaches the leakage condition, and the percolation pressure P perc Calculated by formula (9): Where erfinv is the inverse error function.

6. A method for predicting the long-term waterproof performance and leakage rate of a shield tunnel joint according to claim 5, characterized in that: When the relative contact area A(ζ) / A0 reaches 0.4, the contact surface begins to leak, and the percolation pressure P perc Calculated by formula (9′):

7. The method for predicting the long-term waterproof performance and leakage rate of a shield tunnel joint according to claim 1, characterized in that: Step 4: In the critical leakage state, the critical leakage water pressure P wc and percolation pressure P perc The sum of the total contact stress P c When the staggered effect is considered, the sealing coefficient κ is used to correct the critical leakage water pressure; The step 4 specifically includes: Step 4.1 Determine the slope k0 of the self-sealing effect using the equivalent Poisson's ratio or empirical formula; By the equivalent Poisson's ratio v eff The formula for calculating k0 is shown in formula (10); When considering the nonlinear self-sealing effect that varies with compressive strain, k0 is obtained by the empirical formula with ε as the variable, as shown in Equation (11), and the corresponding equivalent Poisson's ratio v is obtained at the same time eff : k0=aε 2 (11) Where a is the correction coefficient of the empirical formula; According to the sealing mechanism of the gasket, when the joint is in a completely closed state, k0 is close to 1; Step 4.2: Calculate the sealing coefficient κ considering the staggered seam using formula (12); Where, β is the correction coefficient of the sealing coefficient, s is the amount of gasket stagger, w g is the width of the top surface of the sealing gasket; Step 4.3 Calculate the critical leakage water pressure P corrected by percolation pressure using formula (13) wc ; 8. The method for predicting the long-term waterproof performance and leakage rate of a shield tunnel joint according to claim 1, characterized in that: The step 5 specifically includes: Step 5.1 According to the external water pressure P w and critical leakage water pressure P wc and breakdown water pressure P wb The relationship between P and , determines the current leakage stage, which is divided into three stages: percolation stage, leakage stage and breakdown stage; specifically, when P w ≤P wc When P wc <P w ≤P wb When P wb <P w When , it is the breakdown stage; Step 5.2 Based on equations (14) to (17), the average hydraulic opening of the sealing gasket contact surface under the effective stress of the contact surface is calculated. Where γ is a constant and the function P(q,p,ζ) is obtained from equation (15): P(q,p,ζ)=erf(w(q,ζ)pE * ) (15) The function w(q,ζ) is obtained from formula (16): Then, the critical hydraulic opening u is obtained by formula (17): c (ζ): Where, is u c (ζ), A′(ζ) is the first derivative of A(ζ); Step 5.3 Based on the critical hydraulic opening u c The sealing gasket permeability Q at different seepage stages is calculated by formula (18): Where, P wb is the effective contact pressure P cont External water pressure when reduced to 0, L x and L y are the contact surface widths in the seepage direction and perpendicular to the seepage direction, respectively, and μ is the viscosity of water.

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