A method and system for marine pile chloride diffusion analysis

Abstract

The application discloses a marine pipe pile chloride ion diffusion analysis method and system, wherein the method steps comprise the following steps: acquiring marine pipe pile parameters of a marine pipe pile to be detected; obtaining a chloride ion diffusion analysis equation considering time-varying surface chloride ion concentration based on the marine pipe pile parameters; and completing chloride ion diffusion analysis in the interior of the marine pipe pile to be detected based on the chloride ion diffusion analysis equation. The surface chloride ion concentration of the analysis method is related to time, and the chloride ion transmission condition of the marine pipe pile under different surface chloride ion concentration conditions can be simulated.

Description

Technical Field

[0001] This application relates to the field of marine engineering, specifically to a method and system for chloride ion diffusion analysis of marine pipe piles. Background Technology

[0002] Marine pipe piles are widely used in major coastal industrial and civil construction projects, including cross-sea bridge projects, coastal highway projects, port projects, and offshore platform structures. With the continuous development of coastal areas worldwide, the demand for marine pipe piles is expected to increase. However, constructing marine pipe piles in the marine environment leads to corrosion, particularly due to the presence of chlorides. This corrosion can cause concrete cracking, steel rusting, and other problems, which can seriously affect the normal operation of the marine pipe piles. Therefore, it is necessary to predict the durability performance of pipe piles in the marine environment to ensure their safety during use.

[0003] Chloride ions in the marine environment are a major cause of durability failure in marine pipe piles. Therefore, scientists and engineers often use the diffusion process of chloride ions in pipe piles to predict their durability life in the marine environment and assess their durability performance. Currently, research on chloride ion diffusion in marine pipe piles is still very limited. Surveys indicate that existing methods for analyzing chloride ion diffusion in marine pipe piles often assume a constant chloride ion concentration on the pile surface. However, field measurements and experimental data show that the chloride ion concentration on the pile surface changes continuously over time. Furthermore, some scholars have pointed out that ignoring the time-varying changes in surface chloride ion concentration may lead to significant errors in the estimated durability life of marine pipe piles obtained using chloride ion diffusion analysis methods. Therefore, proposing a chloride ion diffusion analysis method for marine pipe piles that considers the time-varying surface chloride ion concentration has significant practical implications. Summary of the Invention

[0004] To address the technical problems mentioned above, this application provides a method for predicting and evaluating the durability performance of marine pipe piles by analyzing the main causes of durability failure, thereby ensuring the safety of marine pipe piles during use.

[0005] To achieve the above objectives, this application provides a method for chloride ion diffusion analysis of marine pipe piles, comprising the following steps:

[0006] Obtain the parameters of the marine pipe pile to be tested;

[0007] Based on the parameters of the marine pipe pile, a chloride ion diffusion analysis equation considering the time-varying surface chloride ion concentration is obtained;

[0008] Based on the chloride ion diffusion analysis equation, the chloride ion diffusion analysis inside the marine pipe pile to be tested was completed.

[0009] Preferably, the parameters of the marine pipe pile include: ion concentration on the pipe pile surface, pipe pile size, and diffusion coefficient.

[0010] Preferably, the method for obtaining the chloride ion diffusion analysis equation includes:

[0011] The transport process of chloride ions from the marine environment into the interior of the marine pipe pile from its outer boundary includes:

[0012]

[0013] In the formula, c(t, r) represents the chloride ion concentration at a distance r of the marine pipe pile at time t; D represents the chloride ion diffusion coefficient of the marine pipe pile; r represents the radial distance of the concrete; and t represents time.

[0014] Before being deployed in the marine environment, the internal structure of a marine pipe pile includes:

[0015] c(0,r)=0 (2)

[0016] After being deployed in the marine environment, the changes in chloride ion concentration on the outer surface of marine pipe piles include:

[0017] c(t,r e ) = c s f(t) (3)

[0018] In the formula, c(t, r) e ) indicates the chloride ion concentration on the outer surface of the marine pipe pile; c s The concentration of chloride ions in seawater is represented by f(t); the time-dependent influencing factor is represented by r. e Indicates the outer radius of the marine pipe pile;

[0019] After being deployed in a marine environment, the changes in chloride ion concentration on the inner surface of marine pipe piles include:

[0020] c(t,r0)=0 (4)

[0021] In the formula, c(t, r0) represents that the chloride ion concentration on the inner surface of the marine pipe pile is 0;

[0022] Combining equations (1) to (4), the chloride ion diffusion analysis equation is obtained.

[0023] Preferably, the methods combining formulas (1) to (4) include:

[0024] Define a new function c * (t,r):

[0025] c * (t,r)=c(t,r)-b(t)(r-r0) (5)

[0026] In the formula, r0 and r e These represent the inner and outer radii of the marine pipe pile, respectively.

[0027] Substituting equation (5) into equations (1) to (3), we obtain

[0028]

[0029] c * (0,r)=-b(0)(r-r0) (7)

[0030] c * (t,r0)=0 (8)

[0031] c * (t,r e )=0 (9)

[0032] The finite Weber transformation is applied to equations (6) to (9); the processed governing equations and boundary conditions are combined to obtain:

[0033]

[0034] The initial conditions are obtained after processing using the finite Weber transformation:

[0035]

[0036] In the formula,

[0037]

[0038]

[0039]

[0040] R0(β m ,r)=Y0(β m r e )J0(β m r)-J0(β m r e )Y0(β m r);

[0041] β m via J0(β) m r0)Y0(β m r e )=J0(β m r e )Y0(β m r0) is obtained;

[0042] J0 and Y0 represent the first and second type 0 Bessel functions, respectively; m represents the sequence number of the eigenvalue β.

[0043] The solution to equation (10) is:

[0044]

[0045] Where C m This indicates the parameter to be determined, which is determined by the initial conditions:

[0046]

[0047] Perform a finite Weber inverse transform on equation (12):

[0048]

[0049] in,

[0050] Finally, substituting equation (14) back into equation (5), we get:

[0051]

[0052] This application also provides a chloride ion diffusion analysis system for marine pipe piles, including: a detection module, a construction module, and an analysis module;

[0053] The detection module is used to acquire the marine pipe pile parameters of the marine pipe pile to be detected;

[0054] The construction module is used to obtain a chloride ion diffusion analysis equation that takes into account the time-varying surface chloride ion concentration based on the parameters of the marine pipe pile;

[0055] The analysis module is used to perform chloride ion diffusion analysis inside the marine pipe pile under test based on the chloride ion diffusion analysis equation.

[0056] Preferably, the parameters of the marine pipe pile include: ion concentration on the pipe pile surface, pipe pile size, and diffusion coefficient.

[0057] Preferably, the workflow of the building module includes:

[0058] The transport process of chloride ions from the marine environment into the interior of the marine pipe pile from its outer boundary includes:

[0059]

[0060] In the formula, c(t, r) represents the chloride ion concentration at a distance r of the marine pipe pile at time t; D represents the chloride ion diffusion coefficient of the marine pipe pile; r represents the radial distance of the concrete; and t represents time.

[0061] Before being deployed in the marine environment, the internal structure of a marine pipe pile includes:

[0062] c(0,r)=0 (17)

[0063] After being deployed in the marine environment, the changes in chloride ion concentration on the outer surface of marine pipe piles include:

[0064] c(t,r e ) = c s f(t) (18)

[0065] In the formula, c(t, r) e ) indicates the chloride ion concentration on the outer surface of the marine pipe pile; c s The concentration of chloride ions in seawater is represented by f(t); the time-dependent influencing factor is represented by r. e Indicates the outer radius of the marine pipe pile;

[0066] After being deployed in a marine environment, the changes in chloride ion concentration on the inner surface of marine pipe piles include:

[0067] c(t,r0)=0 (19)

[0068] In the formula, c(t, r0) represents that the chloride ion concentration on the inner surface of the marine pipe pile is 0;

[0069] Combining equations (16) to (19), the chloride ion diffusion analysis equation is obtained.

[0070] Preferably, the method combining formulas (16) to (19) includes:

[0071] Define a new function c * (t,r):

[0072] c * (t,r)=c(t,r)-b(t)(r-r0) (20)

[0073] In the formula, r0 and r e These represent the inner and outer radii of the marine pipe pile, respectively.

[0074] Substituting equation (20) into equations (16) to (18), we obtain

[0075]

[0076] c * (0,r)=-b(0)(r-r0) (22)

[0077] c * (t,r0)=0 (23)

[0078] c *(t,r e )=0 (24)

[0079] The finite Weber transformation is applied to equations (21) to (24); the processed governing equations and boundary conditions are combined to obtain:

[0080]

[0081] The initial conditions are obtained after processing using the finite Weber transformation:

[0082]

[0083] In the formula,

[0084]

[0085]

[0086]

[0087] R0(β m ,r)=Y0(β m r e )J0(β m r)-J0(β m r e )Y0(β m r);

[0088] β m via J0(β) m r0)Y0(β m r e )=J0(β m r e )Y0(β m r0) is obtained;

[0089] J0 and Y0 represent the first and second type 0 Bessel functions, respectively; m represents the sequence number of the eigenvalue β.

[0090] The solution to equation (25) is:

[0091]

[0092] Where C m This indicates the parameter to be determined, which is determined by the initial conditions:

[0093]

[0094] Perform a finite Weber inverse transform on equation (27):

[0095]

[0096] in,

[0097] Finally, substituting equation (29) back into equation (20), we get:

[0098]

[0099] Compared with the prior art, the beneficial effects of this application are as follows:

[0100] The analytical method proposed in this application has a time-dependent surface chloride ion concentration, which can simulate the chloride ion transport of marine pipe piles under different surface chloride ion concentration conditions. Attached Figure Description

[0101] To more clearly illustrate the technical solutions of this application, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0102] Figure 1 This is a schematic diagram of the method flow of an embodiment of this application;

[0103] Figure 2 This is a schematic cross-sectional view of a cylindrical marine pipe pile according to an embodiment of this application;

[0104] Figure 3 This is a schematic diagram illustrating the verification results of an embodiment of this application;

[0105] Figure 4 This is a schematic diagram of the system structure according to an embodiment of this application. Detailed Implementation

[0106] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0107] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0108] Example 1

[0109] like Figure 1 The diagram shown is a schematic representation of a method flow according to an embodiment of this application. The steps include:

[0110] S1. Obtain the parameters of the marine pipe pile to be tested.

[0111] The parameters of marine pipe piles include: ion concentration on the pipe pile surface, pipe pile size, and diffusion coefficient.

[0112] S2. Based on the parameters of the marine pipe piles, a chloride ion diffusion analysis equation considering the time-varying surface chloride ion concentration is obtained. The steps include:

[0113] In this embodiment, the analysis method is applicable to marine pipe piles with cylindrical cross-sections, such as... Figure 2 As shown. The inner and outer radii of the cylindrical cross-section marine pipe pile are r0 and r1, respectively. e r0, r e In ensuring r e It can be any positive number greater than r0. The marine pipe pile is surrounded by the marine environment, with its outer boundary in direct contact with the marine environment and its inner boundary not in contact with the marine environment.

[0114] Chloride ions in the marine environment are continuously transported from the outer boundary of the marine pipe pile into the interior of the marine pipe pile through diffusion. The above transport process is described by the following formula (1).

[0115]

[0116] In the formula, c(t, r) represents the chloride ion concentration at a distance r of the marine pipe pile at time t; D represents the chloride ion diffusion coefficient of the marine pipe pile; r represents the radial distance of the concrete; and t represents time.

[0117] Considering that the marine pipe pile does not contain chloride ions before being put into the marine environment, it is represented by equation (2):

[0118] c(0,r)=0 (2)

[0119] Equation (2) indicates that at time t=0, there are no chloride ions at any position inside the marine pipe pile.

[0120] Since the marine environment is in contact with the outer boundary of the marine pipe pile, chloride ions from the marine environment can adhere to the outer surface of the marine pipe pile. Considering the time-varying nature of the surface chloride ion concentration, it is expressed by the following equation (3):

[0121] c(t,r e ) = c s f(t) (3)

[0122] In the formula, c(t, r) e ) indicates the chloride ion concentration on the outer surface of the marine pipe pile; c s The concentration of chloride ions in seawater is represented by f(t); the time-dependent influencing factor is represented by r. eThis indicates the outer radius of the marine pipe pile.

[0123] Since the marine environment does not come into contact with the inner boundary of the marine pipe pile, there is no surface chloride ion concentration on the inner surface of the marine pipe pile, which is expressed by the following formula (4):

[0124] c(t,r0)=0 (4)

[0125] In the formula, c(t, r0) indicates that the chloride ion concentration on the inner surface of the marine pipe pile is 0.

[0126] Equations (1) to (4) constitute a mathematical model for a method of chloride ion diffusion analysis of marine pipe piles that considers time-varying surface chloride ion concentration. By solving equations (1) to (4), a method for chloride ion diffusion analysis of marine pipe piles that considers time-varying surface chloride ion concentration is obtained.

[0127] Solution process:

[0128] Define a new function c * (t,r) is as follows:

[0129] c * (t,r)=c(t,r)-b(t)(r-r0) (5)

[0130] in

[0131] Substituting equation (5) into equations (1) to (3), we get:

[0132]

[0133] c * (0,r)=-b(0)(r-r0) (7)

[0134] c * (t,r0)=0 (8)

[0135] c * (t,r e )=0 (9)

[0136] Equations (6) to (9) are processed using the finite Weber transformation. Then, the processed governing equations and boundary conditions are combined to obtain:

[0137]

[0138] The initial conditions, after being processed by the finite Weber transformation, are as follows:

[0139]

[0140] In the formula,

[0141]

[0142]

[0143]

[0144] R0(β m ,r)=Y0(β m r e )J0(β m r)-J0(β m r e )Y0(β m r);

[0145] β m via J0(β) m r0)Y0(β m r e )=J0(β m r e )Y0(β m r0) is obtained;

[0146] J0 and Y0 represent the first and second type 0 Bessel functions, respectively; m represents the sequence number of the eigenvalue β.

[0147] Equation (10) is a first-order differential equation, and its solution is:

[0148]

[0149] Among them, C m This represents a parameter to be determined, which can be determined through initial conditions, as shown below:

[0150]

[0151] Then, by performing a finite Weber inverse transform on equation (12), we can obtain...

[0152]

[0153] In the formula,

[0154] Finally, substituting equation (14) back into equation (5) yields the solution for the chloride ion transport analysis method for marine pipe piles, as follows:

[0155]

[0156] S3. Based on the chloride ion diffusion analysis equation, complete the chloride ion diffusion analysis inside the marine pipe pile to be tested.

[0157] Based on the mathematical model obtained above, the chloride ion diffusion analysis of marine pipe piles with time-varying surface chloride ion concentration was completed.

[0158] Example 2

[0159] To verify the accuracy of the method in this application, this embodiment provides a specific operating procedure, including the following steps:

[0160] Parameters obtained: Based on the survey, the chloride ion concentration on the surface of the pipe pile, the pipe pile size, and the diffusion coefficient were obtained. Figure 3 (a) presents the measured chloride ion concentration data on the surface of the pipe pile specimens, through analysis of... Figure 3 (a) data can be fitted nonlinearly to obtain the time-varying model c of chloride ion concentration on the pipe pile surface. s f(t)(where c) s =2.4%, f(t) = (1-e -0.0037t (t is the number of days). Afterwards, the inner and outer radii of the pipe pile specimen were measured to be r0 = 0 cm and r... e =5cm, diffusion coefficient is D=3.9×10 -12 m 2 / s.

[0161] Output data: Time-varying model of chloride ion concentration on the surface of the pipe pile (c) s f(t), inner and outer radii r0 and r of the pipe pile e Substituting the diffusion coefficient D into the analytical solution (Equation (15)) yields the result as shown below. Figure 3 The solid line in (b) represents the chloride ion concentration on the surface of the pipe pile. If the time-varying nature of the chloride ion concentration on the pipe pile surface is not considered, i.e., the effect of f(t) is ignored, the chloride ion concentration on the surface of the pipe pile is only c. s c s r0, r e Substituting D into the analytical solution, we can obtain... Figure 3 (b) is the dashed line.

[0162] Application data: Figure 3 The point data in (b) are experimental data, obtained by... Figure 3 Comparing the solid and dashed lines in (b) with the experimental data, it can be seen that the solid lines match the experimental data much better than the dashed lines, demonstrating the superiority of the chloride ion diffusion analysis method for marine pipe piles that considers the time-varying nature of surface chloride ion concentration.

[0163] Example 3

[0164] like Figure 4The diagram shown is a schematic representation of the system structure according to an embodiment of this application, including: a detection module, a construction module, and an analysis module. The detection module is used to acquire the marine pipe pile parameters to be tested; the construction module is used to obtain a chloride ion diffusion analysis equation considering time-varying surface chloride ion concentration based on the marine pipe pile parameters; and the analysis module is used to complete the chloride ion diffusion analysis inside the marine pipe pile to be tested based on the chloride ion diffusion analysis equation.

[0165] The following will, in conjunction with this embodiment, explain in detail how this application solves technical problems in real life.

[0166] First, the detection module is used to obtain the parameters of the marine pipe pile to be tested; the parameters of the marine pipe pile include: ion concentration on the surface of the pipe pile, pipe pile size and diffusion coefficient.

[0167] Subsequently, based on the parameters of the marine pipe piles, the construction module derives a chloride ion diffusion analysis equation that considers the time-varying surface chloride ion concentration. The process includes:

[0168] The transport process of chloride ions from the marine environment into the interior of the marine pipe pile from its outer boundary includes:

[0169]

[0170] In the formula, c(t, r) represents the chloride ion concentration at a distance r of the marine pipe pile at time t; D represents the chloride ion diffusion coefficient of the marine pipe pile; r represents the radial distance of the concrete; and t represents time.

[0171] Before being deployed in the marine environment, the internal structure of a marine pipe pile includes:

[0172] c(0,r)=0 (17)

[0173] After being deployed in the marine environment, the changes in chloride ion concentration on the outer surface of marine pipe piles include:

[0174] c(t,r e ) = c s f(t) (18)

[0175] In the formula, c(t, re) represents the chloride ion concentration on the outer surface of the marine pipe pile; s denoted by ; f(t) represents the chloride ion concentration in seawater; ; re represents the time-dependent influencing factor; and re represents the outer radius of the marine pipe pile.

[0176] After being deployed in a marine environment, the changes in chloride ion concentration on the inner surface of marine pipe piles include:

[0177] c(t,r0)=0 (19)

[0178] In the formula, c(t, r0) indicates that the chloride ion concentration on the inner surface of the marine pipe pile is 0.

[0179] By solving equations (16) to (19), a method for analyzing the diffusion of chloride ions in marine pipe piles that takes into account the time-varying surface chloride ion concentration can be obtained.

[0180] Solution process:

[0181] Define a new function c * (t,r):

[0182] c * (t,r)=c(t,r)-b(t)(r-r0) (20)

[0183] In the formula, r0 and r e These represent the inner and outer radii of the marine pipe pile, respectively.

[0184] Substituting equation (20) into equations (16) to (18), we get:

[0185]

[0186] c * (0,r)=-b(0)(r-r0) (22)

[0187] c * (t,r0)=0 (23)

[0188] c * (t,r e )=0 (24)

[0189] The finite Weber transformation is applied to equations (21) to (24); the processed governing equations and boundary conditions are combined to obtain:

[0190]

[0191] The initial conditions are obtained after processing using the finite Weber transformation:

[0192]

[0193] In the formula,

[0194]

[0195]

[0196]

[0197] R0(β m ,r)=Y0(β m r e )J0(βm r)-J0(β m r e )Y0(β m r);

[0198] β m via J0(β) m r0)Y0(β m r e )=J0(β m r e )Y0(β m r0) is obtained;

[0199] J0 and Y0 represent the first and second type 0 Bessel functions, respectively; m represents the sequence number of the eigenvalue β.

[0200] The solution to equation (25) is:

[0201]

[0202] Where C m This represents a parameter to be determined, which is determined by initial conditions:

[0203]

[0204] Perform a finite Weber inverse transform on equation (27):

[0205]

[0206] in,

[0207] Finally, substituting equation (29) back into equation (20), we get:

[0208]

[0209] Finally, the analysis module, based on the chloride ion diffusion analysis equation, completed the chloride ion diffusion analysis inside the marine pipe pile to be tested.

[0210] The embodiments described above are merely preferred embodiments of this application and are not intended to limit the scope of this application. Any modifications and improvements made to the technical solutions of this application by those skilled in the art without departing from the spirit of this application shall fall within the protection scope defined by the claims of this application.

Claims

1. A method for chloride ion diffusion analysis of marine pipe piles, characterized in that the steps include... include: Obtain the parameters of the marine pipe pile to be tested; Based on the parameters of the marine pipe pile, a chloride ion diffusion analysis equation considering the time-varying surface chloride ion concentration is obtained; The methods include: The transport process of chloride ions from the marine environment into the interior of the marine pipe pile from its outer boundary includes: (1) In the formula, c(t, r) represents the chloride ion concentration at a distance r of the marine pipe pile at time t; D represents the chloride ion diffusion coefficient of the marine pipe pile; r represents the radial distance of the concrete; and t represents time. Before being deployed in the marine environment, the internal structure of a marine pipe pile includes: (2) After being deployed in a marine environment, the changes in chloride ion concentration on the outer surface of marine pipe piles include: (3) In the formula, c(t, r) e ) indicates the chloride ion concentration on the outer surface of the marine pipe pile; c s The concentration of chloride ions in seawater is represented by f(t); the time-dependent influencing factor is represented by r. e Indicates the outer radius of the marine pipe pile; After being deployed in a marine environment, the changes in chloride ion concentration on the inner surface of marine pipe piles include: (4) In the formula, c(t, r0) represents that the chloride ion concentration on the inner surface of the marine pipe pile is 0; Combining equations (1) to (4), the chloride ion diffusion analysis equation is obtained; The methods combining formulas (1) to (4) include: Define a new function : (5) In the formula, ;r0 and r e These represent the inner and outer radii of the marine pipe pile, respectively. Substituting equation (5) into equations (1) ~ (3), we get... (6) (7) (8) (9) The finite Weber transformation is applied to equations (6) to (9); the processed governing equations and boundary conditions are combined to obtain: (10) The initial conditions are obtained after processing using the finite Weber transformation: (11) In the formula, ； ； ； ； pass get; , Let m represent the first and second type of 0th-order Bessel functions, respectively; m represents the eigenvalues. β Serial number; The solution to equation (10) is: (12) in This indicates the parameter to be determined, which is determined by the initial conditions: (13) Perform a finite Weber inverse transform on equation (12): (14) in, ; Finally, substituting equation (14) back into equation (5), we get: (15)； Based on the chloride ion diffusion analysis equation, the chloride ion diffusion analysis inside the marine pipe pile to be tested was completed.

2. The method for chloride ion diffusion analysis of marine pipe piles according to claim 1, characterized in that, The parameters of the marine pipe pile include: ion concentration on the pipe pile surface, pipe pile size, and diffusion coefficient.

3. A chloride ion diffusion analysis system for marine pipe piles, said system being used to implement the method described in any one of claims 1-2, characterized in that, include: Detection module, construction module, analysis module; The detection module is used to acquire the marine pipe pile parameters of the marine pipe pile to be detected; The construction module is used to obtain a chloride ion diffusion analysis equation that takes into account the time-varying surface chloride ion concentration based on the parameters of the marine pipe pile; The analysis module is used to perform chloride ion diffusion analysis inside the marine pipe pile under test based on the chloride ion diffusion analysis equation.

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