Prediction method for long-term waterproof performance and leakage rate of shield tunnel joint

Abstract

The invention relates to the research field of shield tunnel joint waterproof performance under the effect of a sealing gasket, and provides a shield tunnel joint long-term waterproof performance and leakage rate prediction method, which comprises the following steps: carrying out an assembly force test on the sealing gasket to obtain a non-linear relationship between the compression strain and the equivalent compression modulus of the sealing gasket; performing morphology scanning on the contact surface of the sealing gasket through an AFM test to obtain surface morphology parameters of the rubber surface of the sealing gasket; obtaining percolation pressure considering the long-term aging behavior by using a multi-scale contact theory and a percolation theory; by combining the self-sealing effect of the sealing gasket, the critical leakage water pressure of the joint can be obtained; the critical hydraulic opening degree under contact of the sealing gasket is obtained on the basis of a Persson model, and the leakage rate of the sealing gasket at each stage under the influence of different seam opening and dislocation forms and long-term aging of rubber is predicted on the basis of the cubic law. According to the method, an existing shield tunnel joint waterproof design method can be improved, and guidance is provided 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 common in shield tunnels during long-term operation, of which leakage at joints accounts for the vast majority. Local water leakage will also induce other defects such as large deformation of the lining structure and cracking of the lining. The joint leakage behavior is mainly dominated by the sealing gasket embedded in the groove at the joint, which is affected by the opening and misalignment of the joint, as well as the performance of the sealing gasket itself. Therefore, understanding and predicting the waterproof mechanism of the sealing gasket is crucial to the long-term safety of tunnel operation.

[0003] Theoretically, leakage in rubber waterproofing contacts such as gaskets is a typical percolation behavior, and the leakage is gradual. At the same time, the contact surface still retains a certain contact pressure at the critical leakage. However, the existing gasket waterproofing theory generally simplifies the above complex contact relationship, assuming that the critical leakage water pressure is equivalent to the gasket contact pressure under the critical leakage state, and also ignores the long-term aging factor of the gasket. In addition, there are few prediction methods for calculating the leakage of gaskets, and most of the existing calculation theories rely on the fitting of experimental data, lacking theoretical and universal applicability.

[0004] In order to avoid water leakage and other structural damage caused by insufficient consideration of the hydraulic degradation behavior of joints during tunnel operation, it is necessary to accurately evaluate and predict the leakage behavior of joints during the design stage, and provide a more universal prediction method for joint waterproofing performance that takes into account the long-term aging behavior of gaskets. By embedding aging-related parameters into the calculation model, the research can deeply analyze the influence of various parameters on joint waterproofing and seepage rate, thereby improving the design method of joint waterproofing system. 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 solution of the present invention is as follows:

[0007] A method for predicting the long-term waterproof performance and leakage rate of a shield tunnel joint 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 contact surface of the sealing gasket at different aging degrees through AFM test to obtain the surface morphology parameters of the sealing gasket rubber; perform equivalent transformation on the problem of the contact between the two sealing gaskets to obtain the equivalent contact surface elastic modulus and the roughness power spectrum of the rigid matrix;

[0010] Step 3: Calculate the percolation pressure of the gasket contact surface considering the 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 correct 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, and 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 the calculation of gasket percolation pressure.

[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 curve diagram 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 curve diagram showing the leakage rate of the sealing gasket before and after aging as a function of external water pressure in the embodiment. DETAILED DESCRIPTION

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

[0022] The present invention 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, guidance is provided 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 non-linear relationship.

[0024] Specifically include:

[0025] Step 1.1: a sealing gasket groove similar to the joint structure is set in the loading mold, and the sealing gasket is vertically loaded by a testing machine to obtain a series of vertical external loads and corresponding compression displacements of the sealing gasket, forming multiple groups 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 compressive strain ε are 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] In the formula, 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 (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. 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 degrees through AFM test to obtain the surface morphology parameters of the gasket rubber, including surface roughness power spectrum, roughness coefficient, and rms (root-mean-square) roughness peak height and slope. In addition, perform equivalent transformation on the problem of two gaskets contacting each other to obtain the equivalent contact surface elastic modulus and the roughness power spectrum of the rigid matrix.

[0033] The specific steps include:

[0034] Step 2.1 Scan the surface morphology of the sealing 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 problem of two gaskets contacting each other is equivalent to the problem of a rigid rough substrate contacting an elastic body, such as 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 modulus 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, the relative contact area A(ζ) / A0 between the gaskets is used to determine whether the leakage condition is met. The relationship between the relative contact area A(ζ) / A0 and the nominal contact pressure p can be given by formula (7):

[0048]

[0049] In the formula, A and A0 are the real contact area and the 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 of the sealing gasket and the nonlinear compression mechanical properties 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 makes corrections on this basis 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 Relationship Figure 4 As shown. In the critical leakage state (when leakage just begins), 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 and calculate the slope k0 of the self-sealing effect by 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 changes 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 joint 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 misalignment of the sealing gasket, and w g is the top width of the gasket.

[0067] Step 4.3 Calculate the critical seepage water pressure P corrected by the 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”, the influence of the contact surface percolation pressure was considered:

[0069]

[0070] Step 5: Based on the Persson model, the critical hydraulic opening of the gasket contact surface is obtained, and 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 by the 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 equation (16):

[0078]

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

[0080]

[0081] In the formula, is u c 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 The external water pressure when it is 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 equation (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] Width of contact surface of seepage channel L y Take 1 to calculate the seepage 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, take 1.84MPa.

[0099] Based on the above parameters, the final predicted seepage volume 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 amount of staggered seams 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 6 mm, 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 obtained by this method before and after aging are as follows: Figure 6 As shown, the opening value is 6mm. The results show that rubber aging also promotes the seepage rate. In addition, with the increase of external water pressure, the seepage rate increases significantly in the last stage of the seepage stage, indicating that the seal contact enters 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 is not intended to 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 contents shall be deemed as equivalent effective embodiments and shall 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: Includes 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 contact surface of the sealing gasket at different aging degrees through AFM test to obtain the surface morphology parameters of the sealing gasket rubber; perform equivalent transformation on the problem of the contact between the two sealing gaskets to obtain the equivalent contact surface elastic modulus and the roughness power spectrum of the rigid matrix; Step 3: Calculate the percolation pressure of the gasket contact surface considering the long-term aging behavior using multi-scale contact theory and percolation theory; Step 4: Combine the self-sealing effect of the sealing gasket and correct 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, and 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. A method for predicting the long-term waterproof performance and leakage rate of a shield tunnel joint as claimed in claim 1, characterized in that: The step 1 comprises: Step 1.1: a sealing gasket groove similar to the joint structure is set in the loading mold, and the sealing gasket is vertically loaded by a testing machine, so as to obtain a series of vertical external loads and corresponding compression displacements of the sealing gasket, and form multiple groups 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 compressive strain ε are converted into the equivalent compression modulus E of the sealing gasket g , thereby obtaining a data set of sealing gasket compression strain-equivalent compression modulus; In the formula, 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 result is 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. A method for predicting the long-term waterproof performance and leakage rate of a shield tunnel joint as claimed in 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. A method for predicting the long-term waterproof performance and leakage rate of a shield tunnel joint as claimed in claim 1, characterized in that: The step 2 comprises: Step 2.1 Scan the surface morphology of the sealing 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 topographic 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): In the formula, 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 modulus 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. A method for predicting the long-term waterproof performance and leakage rate of a shield tunnel joint as claimed in 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 as claimed in claim 5, characterized in that: It is defined 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. A method for predicting the long-term waterproof performance and leakage rate of a shield tunnel joint as claimed in claim 1, characterized in that: Step 4: Under 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 equal; 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 and calculate the slope k0 of the self-sealing effect by 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 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 : k0=aε 2 (11) In the formula, a is the correction coefficient of the empirical formula; According to the sealing mechanism of the gasket, when the joint is in a fully closed state, k0 is close to 1; Step 4.2: Calculate the sealing coefficient κ considering the staggered seam by formula (12); Where, β is the correction coefficient of the sealing coefficient, s is the amount of misalignment of the sealing gasket, and w g is the width of the top surface of the sealing gasket; Step 4.3 Calculate the critical seepage water pressure P corrected by the percolation pressure using formula (13): wc ; 8. A method for predicting the long-term waterproof performance and leakage rate of a shield tunnel joint as claimed in 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 current leakage stage is determined by the relationship between P and , 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: In the formula, γ is a constant, and the function P(q,p,ζ) is obtained by formula (15): P(q,p,ζ)=erf(w(q,ζ)pE * ) (15) The function w(q,ζ) is obtained from equation (16): Then, the critical hydraulic opening u is obtained by formula (17): c (ζ): In the formula, is u c 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 The external water pressure when it is 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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