A hydrophobic-carbonization coupled chloride diffusion binding prediction method and system

Abstract

The application discloses a hydrophobic-carbonization coupled chloride ion diffusion and binding prediction method and system, and belongs to the field of inorganic cementing material durability numerical analysis and multi-field coupled modeling. The method comprises the following steps: dividing the internal chloride ion of the material into free and bound chloride ions, and establishing a total chloride ion concentration expression relationship; under the condition of two-dimensional transmission, a chloride ion diffusion-binding coupled control equation is established based on the mass conservation and Fick diffusion law, and a hydrophobic correction factor and a carbonization influence factor are introduced; the Langmuir isothermal adsorption model and the first-order kinetic equation are used to describe the chloride ion binding behavior; the non-steady-state migration and binding process of the chloride ion in the cementing material is numerically solved, and the space-time distribution of the chloride ion concentration under different conditions is obtained. The application can quantitatively describe the coupled influence of hydrophobic modification and carbonization on the diffusion and binding behavior of the chloride ion, has high prediction precision, and is suitable for durability analysis and engineering life evaluation of alkali-activated materials and geopolymer.

Description

Technical Field

[0001] This invention belongs to the field of numerical analysis of the durability of inorganic cementitious materials and multi-field coupling modeling. Specifically, it relates to a diffusion-binding coupling model and its establishment method for predicting the diffusion and binding behavior of chloride ions in alkali-activated materials or geopolymers under the conditions of hydrophobic modification and carbonization coupling. Background Technology

[0002] Alkali-activated materials and geopolymers have broad application prospects in marine engineering, coastal infrastructure, and structures in salt-corrosion environments due to their low carbon emissions and good mechanical properties. However, during service, these materials are inevitably exposed to both chloride corrosion and carbon dioxide carbonization environments. The continuous intrusion of chloride ions is one of the key factors inducing steel corrosion and durability deterioration. Existing research shows that the transport behavior of chloride ions in alkali-activated materials is not only controlled by pore structure and diffusion channels but also closely related to the gel's ability to bind chloride ions. Simultaneously, the carbonization process causes gel decalcification, pore structure reconstruction, and changes in the chemical environment of the pore solution, significantly weakening the material's ability to bind chloride ions and altering its diffusion characteristics. To suppress chloride ion intrusion, a technical route of hydrophobic modification of alkali-activated materials by introducing organosilicon hydrophobic agents has been proposed in recent years. Hydrophobic modification can change the wettability of pore walls and reduce the continuity of the pore liquid phase, thereby inhibiting chloride ion migration to some extent. However, in actual service environments, hydrophobic modification usually coexists with the carbonization process, and the two have a coupled influence mechanism on chloride ion transport and binding behavior. Most existing chloride ion transport models are based on traditional cement systems, typically considering only the diffusion process or introducing simple empirical binding terms into the diffusion model, making it difficult to reflect changes in gel binding characteristics in alkali-activated materials. Furthermore, existing models generally fail to integrate changes in pore wall wettability caused by hydrophobic modification with microstructure evolution due to carbonization into the same prediction framework, resulting in insufficient accuracy in chloride ion transport prediction under hydrophobic-carbonization coupling conditions.

[0003] Therefore, there is an urgent need to establish a physically interpretable predictive model that can simultaneously describe the diffusion and binding behavior of chloride ions under the coupling effect of hydrophobic modification and carbonization, so as to meet the engineering requirements of durability design and service life assessment of alkali-activated materials. Summary of the Invention

[0004] The purpose of this invention is to overcome the deficiencies in the prior art and to address the problem that it is difficult to accurately predict the chloride ion diffusion and binding behavior under the coupling effect of hydrophobic modification and carbonization. This invention provides a method and system for predicting chloride ion diffusion and binding under hydrophobic-carbonization coupling, which can quantitatively describe chloride ion diffusion, gel binding and their coupling effects with the evolution of hydrophobic modification and carbonization within a unified framework.

[0005] The specific technical solution adopted in this invention is as follows:

[0006] In a first aspect, the present invention provides a method for predicting chloride ion diffusion binding via hydrophobic-carbonation coupling, as detailed below:

[0007] S1: The total chloride ions inside the cementitious material are divided into free chloride ions in the pore solution and bound chloride ions in the solid phase or gel structure according to their existence state, and the expression relationship between the total chloride ion concentration and the free chloride ion concentration and the bound chloride ion concentration is established.

[0008] S2: Based on the expression relationship described in S1, a two-dimensional diffusion control equation is constructed under two-dimensional spatial transport conditions according to the total chloride ion mass conservation equation, and the free chloride ion diffusion flux is defined at the same time.

[0009] S3: Based on the two-dimensional diffusion control equation described in S2, a diffusion equation for free chloride ions is established based on Fick's diffusion law, and the diffusion process is coupled with the binding process to form a diffusion-binding coupling control equation for total chloride ions; subsequently, a hydrophobic correction factor and a carbonization influence factor are introduced to modify the diffusion-binding coupling control equation to obtain the first formula.

[0010] S4: The Langmuir isothermal adsorption model is used to describe the equilibrium relationship between free chloride ions and bound chloride ions, and a first-order kinetic equation is introduced to describe the process of the bound chloride ion concentration evolving towards equilibrium over time, thus obtaining the second formula;

[0011] S5: Based on the first formula and the second formula, the unsteady migration and binding behavior of total chloride ions in cementitious materials is numerically solved to obtain the spatial distribution and temporal evolution of free chloride ions and bound chloride ions inside the cementitious materials.

[0012] Preferably, the cementing material is an alkali-activated material or a geopolymer material.

[0013] Preferably, in S2, the two-dimensional space is a two-dimensional geometric calculation domain consisting of the normal direction of the exposed surface of the cementitious material and the direction parallel to it.

[0014] Preferably, in S2, the two-dimensional diffusion control equation is:

[0015] ;

[0016] in, Total chloride ion concentration, kg / m³ 3 ; For time, d; This represents the diffusion flux of free chloride ions; It is a two-dimensional gradient operator.

[0017] Preferably, in S3, the diffusion-binding coupling control equation is:

[0018] ;

[0019] in, The free chlorine concentration in the pore solution is expressed in kg / m³. 3 ; The effective diffusion coefficient; For bound chloride ions in solid or gel structures, kg / m 3 .

[0020] Furthermore, in S3, a hydrophobicity correction factor is introduced. For the effective diffusion coefficient Corrections were made to characterize the effect of changes in pore wall wettability caused by hydrophobic modification on chloride ion migration ability, i.e.

[0021] ;

[0022] in, The baseline diffusion coefficient for the unhydrophobic modified material;

[0023] The hydrophobicity correction factor is characterized by the contact angle of the cementitious material pore wall, and the relationship between the hydrophobicity correction factor and the contact angle is established using an exponential function, i.e.

[0024] ;

[0025] in, The current contact angle, The initial contact angle of the unmodified material. These are the fitting parameters.

[0026] Furthermore, in S3, a carbonization influencing factor is introduced. The degree of carbonization was correlated with changes in chloride ion diffusion capacity and with hydrophobic correction factors. Coupling was used to establish the effective diffusion coefficient under the coupling effect of hydrophobic modification and carbonization. The expression:

[0027] ;

[0028] in, Normalized carbonization degree; The degree of carbonization, ranging from 0 to 100%; carbonization influencing factor. ; This is a carbonization-sensitive parameter.

[0029] Preferably, in S4, the second formula is:

[0030] ;

[0031] in, To combine the reaction rate constant, s -1 ; To balance the concentration of bound chloride ions, kg / m 3 ; and These are the parameters of the Langmuir isotherm, representing binding capacity and binding affinity, respectively.

[0032] Preferably, in step S5, the numerical solution is performed using the finite element method; the numerical calculation software includes, but is not limited to, finite element analysis software such as COMSOL Multiphysics, ABAQUS, or ANSYS.

[0033] Secondly, the present invention provides a hydrophobic-carbonization coupled chloride ion diffusion binding prediction system, comprising:

[0034] The concentration expression relationship construction module is used to divide the total chloride ions inside the cementitious material into free chloride ions in the pore solution and bound chloride ions in the solid phase or gel structure according to their existence state, and to establish the expression relationship between the total chloride ion concentration and the concentrations of free chloride ions and bound chloride ions.

[0035] A two-dimensional diffusion control equation construction module is used to construct a two-dimensional diffusion control equation based on the expression relationship obtained by the concentration expression relationship construction module, under two-dimensional spatial transport conditions according to the total chloride ion mass conservation equation, and simultaneously define the free chloride ion diffusion flux.

[0036] The diffusion-binding coupling control equation construction and correction module is used to establish a diffusion equation for free chloride ions based on the two-dimensional diffusion control equation obtained by the two-dimensional diffusion control equation construction module and Fick's diffusion law, and to couple the diffusion process with the binding process to form a diffusion-binding coupling control equation for total chloride ions; subsequently, a hydrophobic correction factor and a carbonization influence factor are introduced to correct the diffusion-binding coupling control equation to obtain the first formula.

[0037] The auxiliary equation construction module is used to describe the equilibrium relationship between free chloride ions and bound chloride ions using the Langmuir isothermal adsorption model, and introduces a first-order kinetic equation to describe the evolution of the bound chloride ion concentration towards equilibrium over time, thus obtaining the second equation.

[0038] The numerical solution module is used to numerically solve the unsteady migration and binding behavior of total chloride ions in cementitious materials based on the first formula obtained by the diffusion-binding coupling control equation construction and correction module and the second formula obtained by the auxiliary equation construction module, so as to obtain the spatial distribution and temporal evolution of free chloride ions and bound chloride ions inside the cementitious materials.

[0039] Compared with the prior art, the present invention has the following advantages:

[0040] (1) A unified physical model of chloride ion diffusion-binding behavior under the coupling effect of hydrophobic modification and carbonization was established.

[0041] This invention introduces both hydrophobic modification factors and carbonization influence factors within the same theoretical framework, coupling the chloride ion diffusion process with the gel binding kinetics process. This enables a quantitative description of the synergistic effect of hydrophobic modification and carbonization on chloride ion migration and binding behavior, overcoming the problem of existing models treating the two separately and failing to reflect the coupling effect in actual service environments.

[0042] (2) The physical meaning of the model parameters is clear, and the prediction results have good interpretability and reliability.

[0043] The hydrophobic correction factor introduced in this invention is characterized based on the change in pore wall wettability. The carbonization influence factor is directly related to the degree of carbonization of the material. The binding behavior is described by Langmuir isotherm adsorption and kinetic equations. All parameters can be calibrated by experimental means, avoiding the stacking of empirical parameters and improving the physical rationality and engineering credibility of chloride ion diffusion and binding prediction results.

[0044] (3) It is applicable to the durability analysis of alkali-activated materials and geopolymers and has high engineering application value.

[0045] The method of this invention can be implemented within the framework of finite element numerical calculation, and can predict the chloride ion intrusion behavior of alkali-activated materials or geopolymers under the conditions of hydrophobic modification and carbonization coupling, providing effective technical support for the durability design and service life assessment of related materials in marine engineering and coastal infrastructure. Attached Figure Description

[0046] Figure 1 The triangular mesh model established in the embodiment;

[0047] Figure 2 The fitted curve of the Langmuir isotherm adsorption model obtained in the examples;

[0048] Figure 3 The fitted curve of free chloride ions obtained in the examples;

[0049] Figure 4The theoretical curve of bound chloride ions calculated in the examples;

[0050] Figure 5 The theoretical curve of free chloride ions calculated in the examples;

[0051] Figure 6 The above is a spatiotemporal distribution cloud map of free chloride ions calculated in the examples; where (a) initial state (0 d); (b) exposure for 5 d; (c) exposure for 15 d; (d) exposure for 25 d; (e) exposure for 35 d. Detailed Implementation

[0052] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below. Technical features in various embodiments of the present invention can be combined accordingly without mutual conflict.

[0053] This invention provides a hydrophobic-carbonization coupled method for predicting chloride ion diffusion and binding. This method can simultaneously obtain the concentration distribution of free chloride ions, the concentration distribution of bound chloride ions, and the temporal evolution characteristics of the chloride ion diffusion-binding process. The method includes: 1) dividing chloride ions inside the material into free chloride ions and bound chloride ions, and establishing an expression relationship for the total chloride ion concentration; 2) establishing a chloride ion diffusion-binding coupling control equation based on mass conservation and Fick's diffusion law under two-dimensional transport conditions; 3) describing the chloride ion binding behavior using the Langmuir isothermal adsorption model and first-order kinetic equations; 4) introducing a hydrophobic correction factor to correct the effective diffusion coefficient through pore wall wettability; 5) introducing a carbonization influence factor to correlate the degree of carbonization with the change in diffusion capacity, and coupling it with the hydrophobic correction factor to establish an expression for the effective diffusion coefficient under the combined action of hydrophobicity and carbonization; 6) numerically solving the unsteady migration and binding process of chloride ions in cementitious materials based on the model to obtain the spatiotemporal distribution of chloride ion concentration under different conditions.

[0054] The method of the present invention specifically includes the following steps:

[0055] S1, Chloride ion state classification and total amount expression:

[0056] The total chloride ions inside the cementitious material are divided into free chloride ions in the pore solution and bound chloride ions in the solid phase or gel structure according to their existence state, and the expression relationship between the total chloride ion concentration and the concentrations of free chloride ions and bound chloride ions is established.

[0057] In a preferred embodiment of the present invention, the cementing material may be an alkali-activated material or a geopolymer material.

[0058] In a preferred embodiment of the present invention, the total chloride ion concentration is expressed as the sum of the free chloride ion concentration and the bound chloride ion concentration, as shown in the following formula:

[0059] ;

[0060] in The position vector (m) in two-dimensional space; For time (d); Total chloride ion concentration (kg / m³) 3 ), The concentration of free chlorine in the pore solution (kg / m 3 ), The concentration of bound chlorine in the solid phase or gel (kg / m³) 3 ).

[0061] S2, Two-dimensional mass conservation and definition of diffusion flux:

[0062] Based on the expression relationship obtained from S1, in the two-dimensional space transmission condition (i.e., along) - A two-dimensional diffusion control equation is constructed based on the total chloride ion mass conservation equation for in-plane migration, and the free chloride ion diffusion flux is defined.

[0063] In a preferred embodiment of the present invention, the two-dimensional space is a two-dimensional geometric calculation domain consisting of the normal direction of the exposed surface of the cementitious material and the direction parallel to it.

[0064] As a preferred embodiment of the present invention, the two-dimensional diffusion control equation is:

[0065] ;

[0066] in, Total chloride ion concentration, kg / m³ 3 ; For time, d; This represents the diffusion flux of free chloride ions; The two-dimensional gradient operator is defined as follows:

[0067] .

[0068] S3, Fick's diffusion law and diffusion-binding coupling control equations:

[0069] Based on the two-dimensional diffusion control equation obtained in S2, a diffusion equation for free chloride ions is established based on Fick's diffusion law. The diffusion process is then coupled with the binding process to form a diffusion-binding coupled control equation for total chloride ions. Subsequently, a hydrophobic correction factor and a carbonization influence factor are introduced to modify the obtained diffusion-binding coupled control equation, resulting in the first formula.

[0070] In a preferred embodiment of the present invention, in the porous solution, the migration of free chloride ions is mainly driven by the concentration gradient, and is described using Fick's first law:

[0071] ;

[0072] in, The effective diffusion coefficient is used to characterize the combined effects of pore structure characteristics, interfacial wettability, and microstructure evolution on chloride ion migration. The diffusion-binding coupling governing equation is then obtained as follows:

[0073] ;

[0074] in, The free chlorine concentration in the pore solution is expressed in kg / m³. 3 ; The effective diffusion coefficient; For bound chloride ions in solid or gel structures, kg / m 3 Specifically, the left side of the equation represents the change in the concentration of free chloride ions in the porous solution over time; the first term on the right side is the diffusion term of free chloride ions in two-dimensional space, and the second term represents the consumption effect of the binding process on the concentration of free chloride ions.

[0075] S31, Hydrophobic modification improves diffusion (wettability factor):

[0076] Hydrophobic modification inhibits the effective diffusion of chloride ions by altering the wettability of the pore walls and reducing the continuity of the pore liquid phase. To quantitatively describe the effect of hydrophobic treatment, a hydrophobic correction factor is introduced. For the effective diffusion coefficient Corrections were made to characterize the effect of changes in pore wall wettability caused by hydrophobic modification on chloride ion migration. The effective diffusion coefficient is expressed as...

[0077] ;

[0078] in, The baseline diffusion coefficient for the unmodified hydrophobic material. Hydrophobicity correction factor. Closely related to the wettability of the material surface, this embodiment characterizes it through the contact angle of the pore wall of the cementitious material, and establishes the relationship between the two in an exponential form:

[0079] ;

[0080] in, The current contact angle, The initial contact angle of the unmodified material. These are the fitting parameters.

[0081] S32, Carbonization's modification of diffusion and hydrophobic-carbonization coupling:

[0082] Carbonization causes gel decalcification, pore structure reconstruction, and changes in transport channels, thereby further affecting chloride ion diffusion behavior. To quantify the impact of carbonization on diffusion capacity, a carbonization influencing factor is introduced. The degree of carbonization was correlated with changes in chloride ion diffusion capacity and with hydrophobic correction factors. Coupling was used to establish the effective diffusion coefficient under the coupling effect of hydrophobic modification and carbonization. The expression:

[0083] ;

[0084] in, Characterize the changes in diffusion capacity caused by carbonization; To normalize the degree of carbonization, it is defined as

[0085]

[0086] in, The degree of carbonization ranges from 0% to 100%.

[0087] Carbonization Influence Factors Described in exponential form as:

[0088] ;

[0089] in, A carbonization-sensitive parameter used to characterize Changes with the degree of carbonization.

[0090] Therefore, the first formula obtained after corrections through processes S31 and S32 is:

[0091] .

[0092] S4, combining isotherms and kinetic equations:

[0093] The Langmuir isothermal adsorption model is used to describe the equilibrium relationship between free chloride ions and bound chloride ions, and a first-order kinetic equation is introduced to describe the evolution of the bound chloride ion concentration toward equilibrium over time, resulting in the second formula.

[0094] In a preferred embodiment of the present invention, in the Langmuir isotherm adsorption model, adsorption parameters are used to characterize the binding capacity and affinity of the gelling material for chloride ions. The reaction rate constant of the first-order kinetic equation is used to characterize the binding rate of chloride ions in the gel structure.

[0095] In a preferred embodiment of the present invention, the local equilibrium relationship between bound chloride ions and free chloride ions is described using the Langmuir isotherm adsorption model, and the equilibrium bound chloride ion concentration can be expressed as:

[0096] ;

[0097] in, To balance the concentration of bound chloride ions (kg / m³) 3 ); and All parameters are Langmuir isotherm parameters, representing binding capacity and binding affinity, respectively.

[0098] Considering that the chloride ion binding process does not reach equilibrium instantaneously, but evolves gradually over time, a first-order kinetic equation is introduced to describe the evolution of the bound chloride ion concentration towards equilibrium, i.e., the second equation is:

[0099] ;

[0100] in, To combine the reaction rate constant (s -1 ), used to characterize the binding rate of chloride ions in gel structures.

[0101] S5: By combining the first and second formulas above, the unsteady migration and binding behavior of total chloride ions in cementitious materials is numerically solved to obtain the spatial distribution and temporal evolution of free chloride ions and bound chloride ions inside the cementitious materials.

[0102] In a preferred embodiment of the present invention, the numerical solution can be performed using the finite element method. The computational software used in the finite element method is COMSOL Multiphysics, ABAQUS, or ANSYS.

[0103] The methods and effects of the present invention will be specifically illustrated below through examples.

[0104] Example

[0105] This embodiment provides a method for predicting chloride ion diffusion and binding via hydrophobic-carbonization coupling, using a pure slag-based alkali-activated cementitious material system as the research object. By constructing a diffusion-binding coupled partial differential equation and determining the model parameters through numerical inversion, the migration behavior and chemical fixation process of chloride ions within the material are quantitatively predicted. The specific implementation method is as follows:

[0106] 1. Determination of Research Object and Computational System

[0107] In this embodiment, the cementing material is a pure slag-based alkali-activated cementing material, free of fly ash, metakaolin, or other admixtures, to avoid interference from the coexistence of multiple gel phases on the identification of model parameters. Under alkali activation conditions, the material system mainly forms a cementing structure dominated by C-(A)-SH gel, and its pore structure and chemical bonding characteristics are highly representative.

[0108] The model calculations are described using a two-dimensional geometric domain. The two-dimensional plane is composed of the normal direction (intrusion depth direction) of the exposed material surface and a parallel direction, used to simulate the unsteady intrusion process of chloride ions from the surface into the interior of the material under unilateral exposure conditions. The two-dimensional model significantly reduces the computational degrees of freedom while ensuring accurate characterization of diffusion gradients and binding behavior, making it suitable for parameter inversion and simulation of long-term service processes.

[0109] In this embodiment, the thickness length of the computational domain is set to 0.05 m to cover the maximum possible penetration depth of chloride ions within the experimental timescale. The computational domain is divided into free triangular meshes, and the mesh size is verified through independence analysis to ensure that the calculation error of free chloride ion concentration at key locations is less than a preset threshold. The two-dimensional mesh model is as follows: Figure 1 As shown.

[0110] 2. Numerical Implementation Method of Diffusion-Coupling Control Equations

[0111] Chloride ions within the cementitious material are classified according to their state of existence into free chloride ions in the pore solution and bound chloride ions in the gel or solid structure. The total chloride ion concentration is represented by the superposition of the free chloride ion concentration and the bound chloride ion concentration. Under two-dimensional transport conditions, a chloride ion migration control equation is established based on the principle of mass conservation, and chloride ion diffusion flux and a two-dimensional gradient operator are defined.

[0112] The migration of free chloride ions in porous solutions is described by Fick's diffusion law, and the effects of pore structure, interfacial wettability, and microstructure evolution on diffusion behavior are comprehensively characterized by the effective diffusion coefficient, thus constructing a diffusion-binding partial differential equation. A binding term is introduced into the diffusion governing equation, coupling the diffusion process and the chloride ion binding process within the same governing equation, thereby describing the co-evolutionary behavior of free and bound chloride ion concentrations.

[0113] The diffusion-binding coupling control equations are solved numerically using the finite element method, specifically the PDE Module in COMSOL Multiphysics software in this embodiment. The physics interface used is "Coefficient FormPDE," which allows direct input of the diffusion-reaction coupling control equations. The free chloride ion concentration is the primary unknown variable, and it is solved in conjunction with the chloride ion concentration using a first-order kinetic equation, thus achieving the coupling of the diffusion process and chemical binding within a unified computational framework.

[0114] The model employs a non-steady-state time-dependent solution method. Time discretization can be achieved using an implicit multi-step integration scheme, and adaptive time step control is enabled to maintain numerical stability and computational accuracy in both the early gradient steep stage of diffusion and the later diffusion-combination cooperative stage.

[0115] 3. Computational Domain, Mesh Generation, and Boundary Condition Settings

[0116] The computational domain is set as a finite-depth region along the material thickness direction to cover the maximum possible penetration depth of chloride ions within the target timescale. The exposed surface of the material is set to a constant free chloride ion concentration boundary condition (in this embodiment, the boundary concentration is taken from the experimentally measured free chloride ion concentration value on the specimen surface after 35 days of exposure), while the remaining boundaries are set to no-flux boundary conditions to simulate the chloride ion migration behavior of the specimen under lateral and back-side closed or symmetrical conditions. The initial conditions are set to zero for both the free chloride ion concentration and the bound chloride ion concentration inside the material, corresponding to the initial state before chloride salt corrosion.

[0117] The mesh generation adopts a free triangular mesh form, and the calculation results at key depth locations are not sensitive to changes in mesh scale through mesh independence analysis, thereby reasonably controlling the calculation scale while ensuring calculation accuracy.

[0118] 4. Determination of parameters for the chloride ion binding model

[0119] The equilibrium relationship between chloride ions and free chloride ions is described using an isothermal adsorption model. In this embodiment, the Langmuir isothermal adsorption model is used to reflect the chloride ion fixation characteristics under conditions of limited binding sites. Specifically, in this embodiment, the Langmuir isotherm parameters are obtained by fitting experimental binding data of pure slag-based alkali-activated materials in uncarbonized and carbonized states. The binding capacity parameter α of the uncarbonized sample is 1.0705 kg / m³. 3 The affinity parameter β is 0.0936 m. 3 / kg, goodness of fit R 2 The value was 0.9426; the corresponding α for the carbonized sample was 0.3297 kg / m³. 3β is 0.0209 m 3 / kg, goodness of fit R 2 The value is 0.9526. The Langmuir isotherm adsorption fitting results are as follows: Figure 2 As shown in the figure. The results indicate that the concentrations of bound chloride ions and free chloride ions in the material under different conditions conform to the Langmuir-type adsorption relationship, demonstrating that the model can effectively describe the binding behavior of chloride ions in the system. Compared with the uncarbonized state, the isothermal adsorption curves under carbonization conditions shift downwards overall, indicating that the equilibrium bound chloride ion concentration of the material decreases under the same free chloride ion concentration, reflecting that carbonization weakens the material's adsorption and solidification capacity for chloride ions. This change is closely related to the evolution of gel composition and structure, the reduction in the number of effective binding sites, and the alteration of the interfacial chemical environment caused by carbonization, providing a basis for selecting the binding term parameters in the diffusion-binding coupling model.

[0120] To account for the non-transient nature of the chloride ion binding process, a first-order kinetic equation is introduced to describe the gradual evolution of the bound chloride ion concentration towards equilibrium, enabling the model to reflect the time effect of chloride ion binding. Specifically, in this embodiment, considering that the chloride ion binding process gradually approaches equilibrium over time, a first-order kinetic model is introduced to describe the evolution of the bound chloride ion concentration. That is, it is assumed that the bound chloride ion concentration reaches 99.99% of its equilibrium value at 35 days, and the binding reaction rate constant is determined through numerical inversion. In this embodiment, the reaction rate constant is considered. The fitting curve of free chloride ions calculated based on this parameter is as follows: Figure 3 As shown, the results calculated based on the chloride ion theory are as follows: Figure 4 As shown, its evolution over time and tendency to stabilize are consistent with experimental observations. These results indicate that the established diffusion-binding coupling model can simultaneously reflect the kinetic processes of free chloride ion migration and bound chloride ion generation, providing a reliable basis for numerical prediction of chloride ion transport behavior.

[0121] 5. Numerical characterization of parameters related to hydrophobic modification and carbonization

[0122] Hydrophobic modification inhibits chloride ion migration by altering the wettability of the material's pore walls and reducing the continuity of the pore liquid phase. A hydrophobic correction factor is introduced into the model to correct the effective diffusion coefficient. This correction factor is related to the material's pore wall wettability parameter, which can be characterized by the contact angle. An exponential function is used to establish the relationship between the two. In this embodiment, the hydrophobic modification sensitivity parameter is obtained by inverting the diffusion behavior of different hydrophobically modified samples. for .

[0123] Carbonization affects chloride ion diffusion capacity by inducing gel decalcification, pore structure reconstruction, and changes in transport channels. A carbonization influence factor is introduced into the model to parameterize the degree of carbonization and correlate it with the effective diffusion coefficient. In this embodiment, the carbonization-sensitive parameter is obtained by comparing and inverting the diffusion coefficients of carbonized and uncarbonized samples. The value of 0.1367 indicates that the carbonization process as a whole improves the effective diffusion capacity of chloride ions.

[0124] Furthermore, the hydrophobic modification factor and the carbonization influence factor are incorporated into the effective diffusion coefficient expression to establish a diffusion-binding prediction model under the coupling effect of hydrophobic modification and carbonization.

[0125] 6. Numerical Solution Process and Result Output

[0126] By numerically solving the diffusion-binding coupling control equation, two-dimensional spatial distribution cloud maps of free and bound chloride ion concentrations inside the material under different exposure times, as well as concentration evolution curves along the invasion depth, can be obtained. This quantitatively reveals the spatiotemporal evolution characteristics of the transition from a diffusion-dominated stage to a diffusion-binding coupling controlled stage during chloride ion invasion. In this embodiment, the time-dependent solver in COMSOL Multiphysics is used to numerically calculate the diffusion-binding coupling control equation, with a calculation time range of 0-35 days. Adaptive time step and error control mechanisms are enabled during the solution process to ensure numerical stability and convergence.

[0127] Based on the above numerical calculation method, the two-dimensional spatial distribution of free chloride ion concentration inside the material under different exposure times was obtained, such as... Figure 5 As shown, in the initial stage of exposure, chloride ions mainly exhibit an unsteady intrusion process from the surface of the specimen into the interior. As the exposure time increases, the distribution pattern of chloride ions inside the material gradually changes, indicating that the diffusion process and the chemical bonding process have different controlling effects on chloride ion migration behavior at different stages.

[0128] by Figure 6Taking the two-dimensional spatiotemporal distribution cloud map of free chloride ions as an example, the stage characteristics of chloride ion migration can be analyzed more intuitively. In the initial stage of exposure (0-5 days), free chloride ions are mainly concentrated near the exposed surface of the specimen, forming a large concentration gradient along the penetration depth. The high concentration area rapidly advances into the material over time, indicating that chloride ion migration in this stage is dominated by diffusion. As the exposure time extends to 15 days, the penetration front of free chloride ions further advances, but its advancement rate is significantly slower than in the initial stage. The concentration gradient in the two-dimensional distribution cloud map gradually slows down, indicating that the diffusion driving force begins to weaken. In the middle and late stages (25-35 days), the distribution of free chloride ions inside the material gradually becomes flat, and the expansion of the high concentration area is limited, indicating that the chloride ion migration process has gradually changed from being controlled by simple diffusion to being controlled by a synergistic effect of diffusion and chemical binding.

[0129] As can be seen from the above embodiments, the chloride ion diffusion and binding prediction method proposed in this invention, based on hydrophobic-carbonization coupling, can quantitatively describe chloride ion diffusion, binding, and their coupling effects with hydrophobic modification and carbonization evolution within a unified physical framework. It has good fitting accuracy to the experimental results, verifying the effectiveness and engineering applicability of this invention.

[0130] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the invention. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, all technical solutions obtained through equivalent substitution or transformation fall within the protection scope of the present invention.

Claims

1. A method for predicting chloride ion diffusion binding via hydrophobic-carbonation coupling, characterized in that, Specifically as follows: S1: The total chloride ions inside the cementitious material are divided into free chloride ions in the pore solution and bound chloride ions in the solid phase or gel structure according to their existence state, and the expression relationship between the total chloride ion concentration and the free chloride ion concentration and the bound chloride ion concentration is established. S2: Based on the expression relationship described in S1, a two-dimensional diffusion control equation is constructed under two-dimensional spatial transport conditions according to the total chloride ion mass conservation equation, and the free chloride ion diffusion flux is defined at the same time. S3: Based on the two-dimensional diffusion control equation described in S2, establish the diffusion equation for free chloride ions based on Fick's diffusion law, and couple the diffusion process with the binding process to form the diffusion-binding coupling control equation for total chloride ions; Subsequently, a hydrophobicity correction factor and a carbonization influence factor are introduced to modify the diffusion-binding coupling control equation, resulting in the first formula. S4: The Langmuir isothermal adsorption model is used to describe the equilibrium relationship between free chloride ions and bound chloride ions, and a first-order kinetic equation is introduced to describe the process of the bound chloride ion concentration evolving towards equilibrium over time, thus obtaining the second formula; S5: Based on the first formula and the second formula, the unsteady migration and binding behavior of total chloride ions in cementitious materials is numerically solved to obtain the spatial distribution and temporal evolution of free chloride ions and bound chloride ions inside the cementitious materials. In S3, the diffusion-binding coupling control equation is: ； in, The free chlorine concentration in the pore solution is expressed in kg / m³. 3 ; The effective diffusion coefficient; For bound chloride ions in solid or gel structures, kg / m 3 ; In S3, a hydrophobic correction factor is introduced. For the effective diffusion coefficient Corrections were made to characterize the effect of changes in pore wall wettability caused by hydrophobic modification on chloride ion migration ability, i.e. ； in, The baseline diffusion coefficient for the unhydrophobic modified material; The hydrophobicity correction factor is characterized by the contact angle of the cementitious material pore wall, and the relationship between the hydrophobicity correction factor and the contact angle is established using an exponential function, i.e. ； in, The current contact angle, The initial contact angle of the unmodified material. These are the fitting parameters; In S3, a carbonization influencing factor is introduced. The degree of carbonization was correlated with changes in chloride ion diffusion capacity and with hydrophobic correction factors. Coupling was used to establish the effective diffusion coefficient under the coupling effect of hydrophobic modification and carbonization. The expression: ； in, Normalized carbonization degree; The degree of carbonization, ranging from 0 to 100%; carbonization influencing factor. ; It is a carbonization-sensitive parameter; In S4, the second formula is: ； in, To combine the reaction rate constant, s -1 ; To balance the concentration of bound chloride ions, kg / m 3 ; and These are the parameters of the Langmuir isotherm, representing binding capacity and binding affinity, respectively.

2. The method for predicting chloride ion diffusion binding via hydrophobic-carbonization coupling according to claim 1, characterized in that, The cementing material is an alkali-activated material or a geopolymer material.

3. The method for predicting chloride ion diffusion binding via hydrophobic-carbonization coupling according to claim 1, characterized in that, In S2, the two-dimensional space is a two-dimensional geometric calculation domain consisting of the normal direction of the exposed surface of the cementitious material and the direction parallel to it.

4. The method for predicting chloride ion diffusion and binding via hydrophobic-carbonization coupling according to claim 1, characterized in that, In S2, the two-dimensional diffusion control equation is: ； in, Total chloride ion concentration, kg / m³ 3 ; For time, d; This represents the diffusion flux of free chloride ions; It is a two-dimensional gradient operator.

5. The method for predicting chloride ion diffusion binding via hydrophobic-carbonation coupling according to claim 1, characterized in that, In S5, the numerical solution is performed using the finite element method, and numerical solutions are achieved using finite element analysis software including COMSOL Multiphysics, ABAQUS, and ANSYS.

6. A hydrophobic-carbonation coupled chloride ion diffusion binding prediction system, characterized in that, include: The concentration expression relationship construction module is used to divide the total chloride ions inside the cementitious material into free chloride ions in the pore solution and bound chloride ions in the solid phase or gel structure according to their existence state, and to establish the expression relationship between the total chloride ion concentration and the concentrations of free chloride ions and bound chloride ions. A two-dimensional diffusion control equation construction module is used to construct a two-dimensional diffusion control equation based on the expression relationship obtained by the concentration expression relationship construction module, under two-dimensional spatial transport conditions according to the total chloride ion mass conservation equation, and simultaneously define the free chloride ion diffusion flux. The diffusion-binding coupling control equation construction and correction module is used to establish the diffusion equation of free chloride ions based on the two-dimensional diffusion control equation obtained by the two-dimensional diffusion control equation construction module, and to couple the diffusion process with the binding process to form the diffusion-binding coupling control equation of total chloride ions. Subsequently, a hydrophobicity correction factor and a carbonization influence factor are introduced to modify the diffusion-binding coupling control equation, resulting in the first formula. The auxiliary equation construction module is used to describe the equilibrium relationship between free chloride ions and bound chloride ions using the Langmuir isothermal adsorption model, and introduces a first-order kinetic equation to describe the evolution of the bound chloride ion concentration towards equilibrium over time, thus obtaining the second equation. The numerical solution module is used to numerically solve the unsteady migration and binding behavior of total chloride ions in cementitious materials based on the first formula obtained by the diffusion-binding coupling control equation construction and correction module and the second formula obtained by the auxiliary equation construction module, so as to obtain the spatial distribution and temporal evolution law of free chloride ions and bound chloride ions in the cementitious materials. The diffusion-binding coupling control equation is: ； in, The free chlorine concentration in the pore solution is expressed in kg / m³. 3 ; The effective diffusion coefficient; For bound chloride ions in solid or gel structures, kg / m 3 ; By introducing a hydrophobic correction factor For the effective diffusion coefficient Corrections were made to characterize the effect of changes in pore wall wettability caused by hydrophobic modification on chloride ion migration ability, i.e. ； in, The baseline diffusion coefficient for the unhydrophobic modified material; The hydrophobicity correction factor is characterized by the contact angle of the cementitious material pore wall, and the relationship between the hydrophobicity correction factor and the contact angle is established using an exponential function, i.e. ； in, The current contact angle, The initial contact angle of the unmodified material. These are the fitting parameters; By introducing carbonization influencing factors The degree of carbonization was correlated with changes in chloride ion diffusion capacity and with hydrophobic correction factors. Coupling was used to establish the effective diffusion coefficient under the coupling effect of hydrophobic modification and carbonization. The expression: ； in, Normalized carbonization degree; The degree of carbonization, ranging from 0 to 100%; carbonization influencing factor. ; It is a carbonization-sensitive parameter; The second formula is ； in, To combine the reaction rate constant, s -1 ; To balance the concentration of bound chloride ions, kg / m 3 ; and These are the parameters of the Langmuir isotherm, representing binding capacity and binding affinity, respectively.

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