A Chloride Ion Diffusion-Phase Field Coupling Analysis Method for Corrosion Damage in Reinforced Concrete

Abstract

This invention relates to a chloride ion diffusion-phase field coupling analysis method for corrosion damage in reinforced concrete. The method includes determining the chloride ion diffusion-phase field coupling analysis method and establishing multi-field coupling of chloride ion diffusion and phase field. It achieves full-process analysis of chloride-induced corrosion damage in reinforced concrete and predicts concrete durability. The method also involves macroscopic simulation of the corrosion process of reinforced concrete by chloride ion diffusion, comparing and verifying the correctness of the chloride ion diffusion-phase field coupling analysis method. Furthermore, it conducts parametric analysis to explore the influence of single or multiple reinforcements, protective layer thickness, or reinforcement position on cracking and durability degradation of reinforced concrete. Based on unified phase field theory, gradient damage theory, damage mechanics theory, and finite element simulation technology, this invention improves the accuracy of concrete durability prediction by performing full-process analysis of chloride-induced corrosion damage in reinforced concrete through multi-field coupling.

Description

Technical Field

[0001] This invention relates to a chloride ion diffusion-phase field coupling analysis method for corrosion damage of reinforced concrete, which is used to assess and predict the damage and failure process of reinforced concrete structures in marine or high-chloride environments, and belongs to the field of reinforced concrete durability assessment. Background Technology

[0002] Concrete is the most widely used man-made material in the world. When exposed to harsh environments, numerous factors can lead to the degradation of its durability. Among these, chloride ion corrosion causing steel reinforcement corrosion and damage is one of the most significant factors for reinforced concrete structures in marine or high-chloride environments. Chloride ions corrode concrete primarily through diffusion, infiltration, migration, and convection. In saturated concrete, diffusion is the dominant transport mechanism. Chloride ion corrosion causes the passivation film to rupture, allowing oxides to reach the steel reinforcement surface and cause corrosion. Simultaneously, the formation of cracks in the concrete exacerbates chloride ion corrosion, and the altered transport mode significantly accelerates the rate at which chloride ions reach the steel reinforcement surface. Steel reinforcement corrosion reduces the net cross-sectional area of ​​the steel reinforcement, thereby decreasing its strength and load-bearing capacity, and affecting the structural safety. Furthermore, since the chloride ion diffusion governing equation is a partial differential equation, obtaining an analytical solution is extremely difficult when the boundary conditions are complex.

[0003] Therefore, there is an urgent need to provide a more universal solution that can better capture complex behaviors such as crack deflection and aggregate bridging in concrete, better reveal the rust expansion and cracking process of reinforced concrete under chloride salt environment, and thus make accurate predictions of concrete durability. Summary of the Invention

[0004] This invention provides a chloride ion diffusion-phase field coupling analysis method for corrosion damage in reinforced concrete. Based on the unified phase field theory, gradient damage theory, damage mechanics theory, and finite element simulation technology, it analyzes the entire process of chloride salt corrosion-induced damage and failure in reinforced concrete through multi-field coupling, thereby improving the accuracy of concrete durability prediction.

[0005] The technical solution adopted by this invention to solve its technical problem is:

[0006] A chloride ion diffusion-phase field coupling analysis method for corrosion damage in reinforced concrete includes the following steps:

[0007] Step S1: Determine the chloride ion diffusion-phase field coupling analysis method and establish multi-field coupling of chloride ion diffusion-phase field;

[0008] Step S2: Based on the multi-field coupling of chloride ion diffusion-phase field established in Step S1, conduct a full-process analysis of chloride salt corrosion-induced damage and failure of reinforced concrete, and predict the durability of reinforced concrete.

[0009] Step S3: Perform a macroscopic simulation of the damage process of chloride salt erosion on reinforced concrete, and verify the correctness of the chloride ion diffusion-phase field coupling analysis method.

[0010] Step S4: Based on the validated chloride ion diffusion-phase field coupling analysis method, conduct parametric analysis to explore the effects of single or multiple reinforcements, protective layer thickness, or reinforcement position on cracking and durability degradation of reinforced concrete.

[0011] As a further preferred embodiment of the present invention, the specific steps for determining the chloride ion diffusion-phase field coupling analysis method in step S1 are as follows:

[0012] Step S11: Establish a chloride ion diffusion coefficient model, determine the chloride ion diffusion coefficient D, and correct the chloride ion diffusion coefficient model using influence factors and correction coefficients;

[0013] Step S12: Based on the chloride ion diffusion coefficient D determined in Step S11, establish constitutive relations for the multiphysics coupling of chloride ion diffusion and phase field, as well as the functional relationship between the phase field variables characterizing damage and cracking and the chloride ion diffusion coefficient in the unified phase field damage theory. The stress-strain constitutive relation expression is as follows:

[0014]

[0015] The constitutive relation of the phase field is expressed as follows:

[0016]

[0017] The chemical potential-concentration constitutive relation is expressed as follows:

[0018]

[0019] The functional relationship between the phase field variable characterizing damage and cracking and the chloride ion diffusion coefficient in the unified phase field damage theory is as follows:

[0020]

[0021] In formulas (1), (2), (3), and (4), ε is the effective stress tensor, σ is the stress, ψ is the total free energy of the system, Λ is the chemical modulus (Λ > 0), μ is the concentration, Q is the driving force for crack damage evolution, D0 is the initial chloride ion diffusion coefficient in the concrete, α is the ratio of the chloride ion diffusion coefficient at the damage crack to D0, and c, d0, and n are model parameters. Among them, g(d) must satisfy: g(0)=1, g(1)=0, g'(d)<0, g'(1)=0;

[0022] As a further preferred embodiment of the present invention, the chloride ion diffusion-phase field coupling analysis method determined in step S1 also includes a steel rust expansion model established by finite element analysis of the process of steel rust expansion leading to cracking of the reinforced concrete interface and peeling of the protective layer, which transforms the expansion effect of steel on the concrete interface into mechanical behavior.

[0023] As a further preferred embodiment of the present invention, the method for determining the chloride ion diffusion-phase field coupling analysis in step S1 further includes obtaining a linear finite element equation set by integrating the discretized equations of the displacement field and the phase field sub-problem. In the process of unstable crack propagation, an operator segmentation algorithm that updates the phase field and the displacement field sequentially is used to decouple the displacement sub-problem and the phase field sub-problem.

[0024] The linear finite element equations are as follows:

[0025]

[0026] As a further preferred embodiment of the present invention, the specific steps for analyzing the entire process of chloride salt corrosion-induced damage to reinforced concrete and predicting the durability of reinforced concrete in step S2 are as follows:

[0027] Step S21: Select Abaqus as the platform for realizing the chloride ion diffusion-phase field coupling analysis method;

[0028] Step S22: Define the element tangential stiffness matrix and nodal force vector in the model using the Abaqus UEL subroutine. Each node of each element in the mesh has four degrees of freedom: x-direction displacement degree of freedom, y-direction displacement degree of freedom, phase field variable degree of freedom, and chloride ion concentration degree of freedom. The x-direction displacement degree of freedom and y-direction displacement degree of freedom simulate the rust expansion process of the steel reinforcement, and the phase field variable degree of freedom characterizes the damage and cracking condition of the concrete.

[0029] Step S23: Implement data interaction and visualization of calculation results during the solution process through the Abaqus UMAT subroutine;

[0030] As a further preferred embodiment of the present invention, in step S3, the destruction process of chloride salt erosion of reinforced concrete is macroscopically simulated, and the phase field and concentration field are coupled during the macroscopic simulation.

[0031] As a further preferred embodiment of the present invention, the specific steps for performing parametric analysis in step S4 are as follows:

[0032] Step S41: Keeping the diameter of the reinforcing bars unchanged, investigate the effect of the concrete cover thickness on the cracking and spalling modes of reinforced concrete under chloride salt environment.

[0033] Step S42: Keeping the diameter of the reinforcing bar unchanged, simulate the damage and failure of concrete caused by the rust expansion of the corner reinforcing bar for different reinforcing bar positions, and explore the influence of different reinforcing bar positions on the spalling mode and durability degradation of the concrete cover.

[0034] Step S43: Based on the validated chloride ion diffusion-phase field coupling analysis method, establish a numerical model of rust expansion cracking of reinforced concrete under chemical-mechanical coupling environment, and analyze the entire process of durability degradation of reinforced concrete components under chloride salt environment.

[0035] By employing the above technical solutions, the present invention has the following beneficial effects compared to the prior art:

[0036] The chloride ion diffusion-phase field coupling analysis method for corrosion damage of reinforced concrete provided by this invention utilizes the unified phase field theory to establish a coupled model that simultaneously considers chloride ion diffusion, steel corrosion, and concrete damage and cracking. During the simulation, the coupled phase field and concentration field reveal the corrosion expansion and cracking process of reinforced concrete under chloride salt environment. It better captures complex behaviors such as crack deflection and aggregate bridging in concrete, providing a more accurate prediction of concrete durability. Attached Figure Description

[0037] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0038] Figure 1 This is a schematic diagram of steel bar corrosion provided by the present invention;

[0039] Figure 2 This is a flowchart of the method for analyzing the entire process of damage and failure caused by chloride salt corrosion in reinforced concrete and predicting the durability of concrete provided by the present invention.

[0040] Figure 3a In the diagram, 3a1 is a plan view of reinforced concrete, and 3a2 is a diagram of grid division.

[0041] Figure 3b Figures 3b1-3b4 are example diagrams of concrete failure modes when De = 20 mm, considering coupling.

[0042] Figure 3c Figures 3c1-3c4 are example diagrams of concrete failure modes when De = 20mm without considering coupling.

[0043] Figure 3d This is a comparison chart of chloride ion concentration on the surface of steel bars after 19 months of concrete exposure, provided in the embodiments of the present invention.

[0044] Figure 4a 4a1-4a3 are schematic diagrams considering the influence of protective layer thickness on concrete failure modes under coupled conditions;

[0045] Figure 4b This considers the edge σ of the protective layer under coupling conditions. x Stress distribution diagram;

[0046] Figure 5a Figures 5a1-5a4 are example diagrams of the failure mode of concrete in the corner region with De = 20mm under the condition of coupling.

[0047] Figure 5b Figures 5b1-5b4 are example diagrams of the failure mode of concrete in the corner region with De = 30mm under the condition of coupling.

[0048] Figure 6 This considers the coupling condition where De = 20mm on the outer surface of the concrete protective layer. x Stress distribution diagram;

[0049] Figure 7a This is a schematic diagram of the geometric model and boundary conditions of reinforced concrete;

[0050] Figure 7b Figures 7b1-7b4 are example diagrams of the failure mode of reinforced concrete when S=32mm under the condition of coupling.

[0051] Figure 8a Figures 8a1-8a4 are example diagrams of the failure mode of reinforced concrete when S=80mm under the condition of coupling.

[0052] Figure 8b Figures 8b1-8b4 are example diagrams of the failure mode of reinforced concrete when S=80mm is considered under coupling conditions;

[0053] Figure 8c Figures 8c1-8c4 are example diagrams of the failure modes of reinforced concrete when S=96mm under coupled conditions. Detailed Implementation

[0054] The invention will now be described in further detail with reference to the accompanying drawings.

[0055] As described in the background section, the current control equation for chloride ion diffusion is a partial differential equation. When the boundary conditions are complex, it becomes particularly difficult to analyze the process of steel corrosion. Therefore, this application proposes a chloride ion diffusion-phase field coupling analysis method for corrosion damage of reinforced concrete. This analysis method is based on the unified phase field theory, gradient damage theory, damage mechanics theory and finite element simulation technology, and analyzes the entire process of chloride salt corrosion damage to reinforced concrete through multi-field coupling.

[0056] Specifically, the following steps are included:

[0057] Step S1: Determine the chloride ion diffusion-phase field coupling analysis method and establish multi-field coupling of chloride ion diffusion-phase field;

[0058] Step S2: Based on the multi-field coupling of chloride ion diffusion-phase field established in Step S1, conduct a full-process analysis of chloride salt corrosion-induced damage and failure of reinforced concrete, and predict the durability of reinforced concrete.

[0059] Step S3: Perform a macroscopic simulation of the damage process of chloride salt erosion on reinforced concrete, and verify the correctness of the chloride ion diffusion-phase field coupling analysis method.

[0060] Step S4: Based on the validated chloride ion diffusion-phase field coupling analysis method, conduct parametric analysis to explore the effects of single or multiple reinforcements, protective layer thickness, or reinforcement position on cracking and durability degradation of reinforced concrete.

[0061] Regarding the analytical method for establishing the multi-field coupling of chloride ion diffusion and phase field in step S1, this application provides two preferred embodiments, both of which can effectively capture complex behaviors such as crack deflection and aggregate bridging in concrete. The specific steps of the first analytical method are as follows:

[0062] Step S11: Establish a chloride ion diffusion coefficient model, determine the chloride ion diffusion coefficient D, and correct the chloride ion diffusion coefficient model using influence factors and correction coefficients;

[0063] In this step, the chloride ion diffusion coefficient model can be categorized as follows: (1) Constant diffusion coefficient model: For homogeneous concrete models, to simplify calculations, the chloride ion diffusion coefficient is assumed to be constant, i.e., D = D0. (2) Time-varying diffusion coefficient model: The constant diffusion coefficient model is very convenient for calculation. However, considering the actual situation, the longer the time, the denser the internal structure of the concrete becomes due to hydration, enhancing the concrete's resistance to chloride ion erosion. Considering the influence of the concrete hydration process, the chloride ion diffusion coefficient in the concrete decreases with increasing exposure time, proving that the diffusion coefficient is time-varying. Therefore, the improved relationship between the chloride ion diffusion coefficient and time is: Where D0 is the chloride ion diffusion coefficient at time t0. In actual analysis, t0 is often taken as the 28th day of the concrete curing period, and m is a model constant. ⑶ Complex diffusion coefficient model: As a heterogeneous material, concrete has a relatively complex internal structure. Factors such as water-cement ratio, aggregate content, microcracks, and natural defects all affect the ability of chloride ions to erode concrete. In addition, during use, the temperature and humidity of the concrete exposure environment, as well as the damage and cracking of the concrete, all affect the ability of chloride ions to erode concrete. Therefore, the chloride ion diffusion coefficient model can be further modified by using influencing factors and correction coefficients.

[0064] Step S12: Based on the chloride ion diffusion coefficient D determined in Step S11, establish constitutive relations for the multiphysics coupling of chloride ion diffusion and phase field, as well as the functional relationship between the phase field variables characterizing damage and cracking and the chloride ion diffusion coefficient in the unified phase field damage theory. The stress-strain constitutive relation expression is as follows:

[0065]

[0066] The constitutive relation of the phase field is expressed as follows:

[0067]

[0068] The chemical potential-concentration constitutive relation is expressed as follows:

[0069]

[0070] The functional relationship between the phase field variable characterizing damage and cracking and the chloride ion diffusion coefficient in the unified phase field damage theory is as follows:

[0071]

[0072] In formulas (1), (2), (3), and (4), ε is the effective stress tensor, σ is the stress, ψ is the total free energy of the system, Λ is the chemical modulus (Λ > 0), μ is the concentration, Q is the driving force for crack damage evolution, D0 is the initial chloride ion diffusion coefficient in the concrete, α is the ratio of the chloride ion diffusion coefficient at the damage crack to D0, and c, d0, and n are model parameters. Among them, g(d) must satisfy: g(0)=1, g(1)=0, g'(d)<0, g'(1)=0.

[0073] The first analytical method also includes a steel reinforcement corrosion expansion model established by finite element analysis of the process of steel reinforcement corrosion expansion leading to cracking of the reinforced concrete interface and spalling of the protective layer. This model transforms the expansion effect of the steel reinforcement on the concrete interface into a mechanical behavior. The reason for this transformation is that when the chloride ion concentration around the steel reinforcement reaches the critical value for steel reinforcement corrosion expansion, the steel reinforcement begins to corrode and expand, leading to cracking of the reinforced concrete interface and spalling of the protective layer. In order to conduct finite element analysis on this process, it is first necessary to transform the expansion effect of the steel reinforcement on the concrete interface into a mechanical behavior.

[0074] The second analytical method is presented next, which mainly integrates the discretized equations of the displacement field and phase field sub-problems, resulting in the following linear finite element equations:

[0075]

[0076] The second analysis method for obtaining the linear finite element equations involves dividing the multiphysics coupled solid domain Ω into a finite element mesh M. h Where h is the mesh size, the displacement, phase field, and chloride ion concentration at the element nodes are interpolated using the Voigt notation as follows:

[0077]

[0078] Where m is the number of nodes, and i represents node i. It is based on the node shape function N i The interpolation diagonal matrix for the components, and That is, the node shape function N i C indicates the chloride ion concentration (unit: %).

[0079] The gradients of strain, phase field variables, and chloride ion concentration can be expressed as:

[0080]

[0081] In the formula The displacement-strain matrix, and Let be the spatial derivative matrix of the shape functions, expressed as follows:

[0082]

[0083] Using the law of conservation of mass and the law of divergence, we obtain the weak form of the chloride ion diffusion governing equation:

[0084]

[0085] Where Ω is the solution domain for solid diffusion, μ is the chemical potential driving chloride ion diffusion, and J is the concentration flux of chloride ion concentration.

[0086] Applying the divergence theorem to the equation, we can obtain:

[0087]

[0088] In the formula, Let n be the boundary of the solid diffusion field, and n represent the outward normal on the boundary.

[0089] Combining these equations, we obtain the constitutive equation for chloride ion diffusion in solids:

[0090]

[0091] q = J·n

[0092] The variational form of the chloride ion diffusion equation can be written as:

[0093]

[0094] Based on the variational form of the chloride ion diffusion equation, assuming δC represents an arbitrary imaginary change in chloride ion concentration, we can obtain a residual vector expression for chloride ion concentration.

[0095]

[0096] The expression for the diffusion stiffness matrix is ​​defined as follows:

[0097]

[0098] The concentration-capacity matrix is ​​defined as follows:

[0099]

[0100] Diffusion flux vector expression:

[0101]

[0102] Combining the above equations, we obtain the discretized chloride ion transport equation:

[0103]

[0104] Finally, considering the displacement field and phase field, it can be expressed as follows:

[0105]

[0106] It is important to explain here that the decoupling displacement subproblem and phase field subproblem are solved using an interleaved approach. This is because, during the unstable crack propagation process, using the global Newton-Raphson iteration algorithm (i.e., direct solution) often encounters convergence problems. As the crack begins to propagate, the stiffness matrix undergoes degradation, and the stress field changes accordingly, making it impossible to obtain a stable solution implicitly. Although the total energy of the system is a non-convex function of the global unknown (u,d), it is individually an externally convex function of the displacement field and phase field. Based on this characteristic, an operator partitioning algorithm that updates the phase field and displacement field sequentially can be used, i.e., an interleaved solution.

[0107] After establishing the multi-field coupling of chloride ion diffusion and phase field, it is necessary to conduct a full-process analysis of chloride salt corrosion leading to damage and failure of reinforced concrete and to predict the durability of reinforced concrete, i.e., step S2. The specific implementation steps provided in this application are as follows:

[0108] Step S21: Select Abaqus as the platform for realizing the chloride ion diffusion-phase field coupling analysis method;

[0109] Step S22: Taking the isoparametric two-dimensional quadrilateral four-node element as an example, the element tangential stiffness matrix and nodal force vector in the model are defined through the Abaqus UEL subroutine. Considering that each node of each element in the mesh has four degrees of freedom, namely the conventional displacement degrees of freedom (i.e., x-direction displacement degrees of freedom and y-direction displacement degrees of freedom), phase field variable degrees of freedom, and chloride ion concentration degrees of freedom, the x-direction displacement degrees of freedom and y-direction displacement degrees of freedom simulate the rust expansion process of steel bars, and the phase field variable degrees of freedom characterize the damage and cracking state of concrete.

[0110] Step S23: Implement data interaction during the solution process and visualize the calculation results through the Abaqus UMAT subroutine.

[0111] In the above simulation of the entire process of chloride salt corrosion causing damage to reinforced concrete, the corrosion expansion process of steel bars is simulated by displacement loading, and the damage and cracking status of concrete is characterized by phase field variables, thereby realizing the whole process analysis of chloride salt corrosion causing damage to reinforced concrete and the prediction of concrete durability.

[0112] In step S3, a macroscopic simulation of the damage process of chloride salt erosion of reinforced concrete is performed. Macroscopic simulation is a common method, but a prominent feature of this application is that the phase field and concentration field are coupled during the macroscopic simulation. That is, the simulation is based on the chloride ion diffusion-phase field coupling analysis method provided in steps S1 and S2 of this application, so as to improve the accuracy of the analysis method.

[0113] The specific steps for performing parametric analysis in step S4 are as follows:

[0114] Step S41: Keeping the diameter of the reinforcing bars unchanged, investigate the effect of the concrete cover thickness on the cracking and spalling modes of reinforced concrete under chloride salt environment.

[0115] Step S42: Keeping the diameter of the reinforcing bar unchanged, simulate the damage and failure of concrete caused by the rust expansion of the corner reinforcing bar for different reinforcing bar positions, and explore the influence of different reinforcing bar positions on the spalling mode and durability degradation of the concrete cover.

[0116] Step S43: Based on the validated chloride ion diffusion-phase field coupling analysis method, establish a numerical model of rust expansion cracking of reinforced concrete under chemical-mechanical coupling environment, and analyze the entire process of durability degradation of reinforced concrete components under chloride salt environment.

[0117] Example:

[0118] To verify the accuracy of the chloride ion diffusion-phase-field coupling analysis method for reinforced concrete corrosion damage provided in this application, this application provides embodiments. Table 1 shows the influence of the reinforcement location on concrete surface cracking under chloride erosion conditions.

[0119] Table 1. Influence of Reinforcement Location on Concrete Surface Cracking

[0120]

[0121] As shown in Table 1, the concrete near the corner reinforcement is more prone to damage and cracking than the concrete around the central reinforcement. Therefore, in practical engineering, greater attention needs to be paid to the service life of the concrete in the corner area. Furthermore, it was found that appropriately increasing the clear spacing between the reinforcement bars can help prevent concrete delamination.

[0122] In the first analytical method provided for determining the chloride ion diffusion-phase-field coupling analysis, the expansion effect of the steel reinforcement on the concrete interface is transformed into mechanical behavior. Currently, three commonly used mechanical equivalent methods are equivalent force loading, equivalent displacement loading, and equivalent temperature loading. Since the simulation method of equivalent displacement loading is relatively clear, the approach is more explicit, and the modeling and related calculation processes are very simple, the preferred embodiment uses the equivalent displacement loading simulation method. The preferred embodiment is shown below. Figure 1 The equivalent displacement loading model shown assumes that the expansion of the steel reinforcement due to corrosion acts on the node at the reinforced concrete interface, and takes half the area on both sides of the node for the following analysis:

[0123] Assume there is a volume ΔV of steel reinforcement corrosion expansion. r The calculation expression is:

[0124] ΔV r =αΔV steel

[0125] In the above formula, ΔV steel The volume of the original steel reinforcement is lost, and α is the ratio of the volume of steel reinforcement corrosion products to the volume of the original steel reinforcement consumed. Studies have shown that α can be taken as 2-6 depending on the composition of the steel reinforcement corrosion products.

[0126] ΔV can be obtained from geometric relationships. r With ΔV steel The calculation expression:

[0127]

[0128]

[0129] In the above formula, R b Let be the initial radius of the reinforcing bar. The equivalent expansion displacement of the reinforcing bar corrosion on the reinforced concrete boundary can be obtained as follows:

[0130]

[0131] The next step is to conduct a full-process analysis of chloride erosion-induced damage to reinforced concrete and predict the concrete's durability. Specific steps are as follows: Figure 2 As shown, ① a reinforced concrete model is established, with an initial time T = 0, and the iteration time increment step Δt is determined; ② the initial chloride ion boundary conditions and displacement boundary conditions are obtained, and the phase field damage evolution and chloride ion diffusion under the current time increment step are solved; ③ the chloride ion concentration at the reinforced concrete interface nodes is stored in the Fortran language's common module; ④ it is determined whether the chloride ion concentration value at the reinforced concrete interface nodes reaches the critical value of the steel corrosion concentration; ⑤ if the critical value of the steel corrosion concentration is reached, the time when the steel begins to rust is recorded, and the amount of steel corrosion δ at the corresponding node is calculated based on the chloride ion concentration value at the interface node. corr And based on the amount of steel corrosion δ corr Calculate the equivalent radial displacement δ. Before reaching the critical value of steel corrosion concentration, the equivalent radial displacement at the interface node is 0. ⑥ In the current time step, apply the equivalent radial displacement at each node to the interface node through the Abaqus Disp subroutine to update the model displacement boundary conditions. Calculate the phase field damage evolution and chloride ion diffusion through the UEL and UMAT subroutines to obtain the damage distribution and chloride ion diffusion of the reinforced concrete model, and output the chloride ion concentration at the reinforced concrete interface node, updating the concentration value originally stored in the common module. ⑦ Repeat steps ①-⑥ in this manner, relying on the UEL, UMAT subroutines and Fortran language to establish data transfer and processing within the time increment step, to realize the whole process analysis of chloride salt corrosion damage to reinforced concrete.

[0132] Step S3 employs a coupled analysis method to simulate corrosion damage in reinforced concrete under chloride salt environments. Table 2 lists the results. Figure 3a The geometric model and boundary conditions of the homogeneous concrete are shown.

[0133] Table 2 Numerical simulation parameters of concrete in the border zone

[0134]

[0135] Boundary condition C of chloride ion concentration on the surface of concrete slab s =3%, the other three boundaries are closed boundaries with a flux of 0. Critical rust expansion concentration C of reinforcing steel. r =0.1%. Considering the influence of concrete damage cracks on the chloride ion diffusion coefficient, the following functional relationship between the phase field variable and the chloride ion diffusion coefficient is established:

[0136]

[0137] After establishing the above functional relationship, based on the macroscopic simulation process of concrete cracking due to rust expansion and peeling of the protective layer, considering both coupling and non-coupling cases, Figure 3b To consider the simulation process of concrete being exposed to the environment for a long time under coupled conditions, Figure 3c This is a simulation of the long-term exposure of concrete to the environment without considering coupling. Figure 3a and Figure 3b As can be seen, when the steel reinforcement first begins to rust and expand, the damage mainly occurs on the surface of the concrete cover above the reinforcement and on both sides of the steel reinforcement-concrete interface. With increasing exposure time and deepening corrosion, cracks on both sides of the steel reinforcement-concrete interface begin to extend towards the concrete cover. After establishing the coupling relationship between the phase field variables and the chloride ion diffusion coefficient, the damage cracks caused by rust expansion inside the concrete accelerate the diffusion rate of chloride ions within the concrete, leading to intensified steel reinforcement corrosion and premature cracking of the concrete surface. The chloride ion concentration at any point on the steel reinforcement surface considering the coupling is higher than that without considering the coupling, indicating a more severe degree of corrosion. Figure 3d A comparison of chloride ion concentrations on the surface of reinforcing steel bars after 19 months of concrete exposure is presented. These comparisons clearly illustrate the importance of establishing the coupling relationship between the chloride ion diffusion coefficient and phase field variables in predicting concrete cracking and durability degradation under chloride salt environments.

[0138] Step S4 involves investigating the effects of single-reinforced, multi-reinforced, cover thickness, and rebar position on concrete cracking and durability degradation to conduct parametric analysis. First, the influence of cover thickness on damage to single-reinforced concrete caused by corrosion expansion of central rebar is investigated. Specifically, while keeping the rebar diameter constant, the influence of concrete cover thickness on the cracking and cover spalling modes of reinforced concrete under chloride conditions is explored. Numerical simulation parameters are shown in Table 3.

[0139] Table 3 Numerical Simulation Parameters

[0140]

[0141] Considering both coupled and uncoupled cases, the concrete cover thickness is taken as 10mm, 20mm, and 30mm, respectively. The boundary condition for chloride ion concentration on the upper surface of the concrete slab is C. s =3%, the remaining surface flux is 0, the critical rust expansion concentration of the reinforcing steel is C r =0.1%.

[0142] Figure 4aThe crack propagation and failure modes of reinforced concrete with different cover thicknesses are presented under the condition of coupling. Comparison of the results in the figures shows that the fracture phase-field model can automatically evolve cracks without pre-setting the crack propagation direction, and can better handle complex phenomena such as crack tortuosity. Furthermore, it can be concluded that the time for concrete surface cracking and cover detachment is delayed with increasing cover thickness. Figure 4b The stress distribution in the x-direction at the edge section of the outer surface of reinforced concrete members with different cover thicknesses, considering coupling effects, is presented. It can be seen that the stress distribution in the x-direction on the outer surface of the cover is symmetrical. The maximum value of the tensile normal stress is located directly above the reinforcing bar, gradually decreasing along both sides to zero before transforming into compressive stress, and finally approaching zero. (Comparison) Figure 4b The curve shows that as the thickness of the concrete cover changes, the tensile stress zone remains basically stable, while the compressive stress zone decreases with the increase of the cover thickness.

[0143] Next, a simulation of concrete damage caused by the rust expansion of corner reinforcement was conducted. To investigate the influence of different reinforcement locations on the spalling mode and durability degradation of the concrete cover, the numerical simulation parameters, except for the reinforcement location, were consistent with those used in the numerical simulation investigating the influence of cover thickness on the damage of monoreinforced concrete caused by the rust expansion of central reinforcement.

[0144] Figure 5a as well as Figure 5b All data consider the coupling effect when examining the cracking and failure processes of corner reinforced concrete members with different cover thicknesses. In a corner reinforced concrete member with a cover thickness of 20mm, cracks initiated at the reinforcement-concrete interface after 7.23 months of concrete exposure, propagating towards the upper and right surfaces of the concrete. Simultaneously, cracks appeared on the upper surface, with the cracks extending inwards. With a cover thickness of 30mm, surface cracking of the concrete cover occurred after 17.50 months of exposure. The most damaging cracks initiated on the right surface of the cover and propagated inwards, leading to the detachment of the cover in the corner area. Comparing the cracking time of concrete with different cover thicknesses, the surface cracking time of the concrete cover was delayed with increasing cover thickness.

[0145] Figure 6 The figure compares the chloride ion concentration on the steel reinforcement surface and the outer contour boundary of the steel reinforcement after corrosion, considering the coupling and non-coupling conditions after the concrete surface cracks with a protective layer thickness of 20mm. It can be seen from the figure that when coupling is considered, the chloride ion concentration on the steel reinforcement surface, the degree of steel reinforcement corrosion and the amount of expansion are all higher than the results without considering coupling. This shows the necessity and effectiveness of coupling the chloride ion diffusion coefficient with the phase field variables that characterize damage cracks.

[0146] Finally, using the chloride ion diffusion-phase-field coupling analysis method, a numerical model of rust expansion cracking in reinforced concrete under a chemical-mechanical coupling environment was established to analyze the entire process of durability degradation of reinforced concrete components under chloride salt conditions. The geometric model and boundary conditions for multiple parallel reinforced concrete sections are as follows: Figure 7a As shown in Table 4, the numerical simulation parameters are referenced.

[0147] Table 4 Numerical Simulation Parameters for Reinforced Concrete

[0148]

[0149] Figure 7b The process of concrete cracking caused by the corrosion expansion of multiple reinforcing bars under coupling effects is presented. In the initial stage, horizontal band-like damage appears between the reinforcing bars. With the erosion of chloride ions and the deepening of corrosion, the band-like damage between the reinforcing bars gradually evolves into horizontal cracks, connecting the three reinforcing bars in pairs within the concrete. Damage on both sides of the left and right reinforcing bars gradually evolves into cracks, extending towards the concrete cover surface near the chloride ion concentration boundary. After nearly 9.9 months of concrete exposure, the cover peels off in a "layered" manner. Furthermore, compared to the initial result without chloride ion concentration (i.e., C0 = 0%), the initial result with chloride ion concentration (i.e., C0 > C0) shows significant improvement. r The concrete with the protective layer cracked and detached nearly 16.4 months earlier, greatly shortening the service life of the concrete structure.

[0150] Figures 8a-8c The influence of the clear spacing between reinforcing bars on concrete damage is presented. As the clear spacing between reinforcing bars increases, cracks between them are no longer horizontal. The corrosive expansion of the left and right reinforcing bars gradually weakens the compressive effect on the concrete surrounding the central reinforcing bar, leading to damage to the concrete cover above the central reinforcing bar and the appearance of through cracks. These phenomena demonstrate that corrosion of multiple reinforcing bars leads to different crack initiation and failure modes. The multiple reinforcing bars influence each other, and this influence weakens as the clear spacing between them increases. However, excessive spacing between reinforcing bars leads to a decline in the performance of the concrete structure. This analysis provides some assistance in designing the spacing of reinforcing bars within reinforced concrete, aiming to avoid horizontal cracks between reinforcing bars before structural failure while ensuring the good performance of the reinforced concrete structure.

[0151] In summary, the chloride ion diffusion-phase field coupling analysis method for reinforced concrete corrosion damage provided in this application is established based on unified phase field theory, gradient damage theory, damage mechanics theory, and finite element simulation technology. It analyzes the entire process of chloride salt corrosion-induced damage and failure in reinforced concrete through multi-field coupling. Compared with traditional damage mechanics-based calculation methods, this application can better capture complex behaviors such as crack deflection and aggregate bridging in concrete, and better reveal the rust expansion and cracking process of reinforced concrete under chloride salt environment, thereby enabling accurate prediction of concrete durability.

[0152] Those skilled in the art will understand that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the meaning consistent with their meaning in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as herein.

[0153] The meaning of "and / or" as used in this application includes situations where each exists alone or both exist simultaneously.

[0154] The term "connection" as used in this application can mean a direct connection between components or an indirect connection between components through other components.

[0155] Based on the above-described preferred embodiments of the present invention, and through the foregoing description, those skilled in the art can make various changes and modifications without departing from the inventive concept. The technical scope of this invention is not limited to the contents of the specification, but must be determined according to the scope of the claims.

Claims

1. A chloride ion diffusion-phase field coupling analysis method for corrosion damage in reinforced concrete, characterized in that: Includes the following steps: Step S1: Determine the chloride ion diffusion-phase field coupling analysis method and establish multi-field coupling of chloride ion diffusion-phase field; Step S2: Based on the multi-field coupling of chloride ion diffusion-phase field established in Step S1, conduct a full-process analysis of chloride salt corrosion-induced damage and failure of reinforced concrete, and predict the durability of reinforced concrete. Step S3: Perform a macroscopic simulation of the damage process of chloride salt erosion on reinforced concrete, and verify the correctness of the chloride ion diffusion-phase field coupling analysis method. Step S4: Based on the validated chloride ion diffusion-phase field coupling analysis method, conduct parametric analysis to explore the effects of single or multiple reinforcements, protective layer thickness, or reinforcement position on cracking and durability degradation of reinforced concrete. In step S1, the specific steps for determining the chloride ion diffusion-phase-field coupling analysis method are as follows: Step S11: Establish a chloride ion diffusion coefficient model, determine the chloride ion diffusion coefficient D, and correct the chloride ion diffusion coefficient model using influence factors and correction coefficients; Step S12: Based on the chloride ion diffusion coefficient D determined in Step S11, establish constitutive relations for the multiphysics coupling of chloride ion diffusion and phase field, as well as the functional relationship between the phase field variables characterizing damage and cracking and the chloride ion diffusion coefficient in the unified phase field damage theory. The stress-strain constitutive relation expression is as follows: （1） The constitutive relation of the phase field is expressed as follows: （2） The chemical potential-concentration constitutive relation is expressed as follows: （3） The functional relationship between the phase field variable characterizing damage and cracking and the chloride ion diffusion coefficient in the unified phase field damage theory is as follows: （4） In the formula, , These represent the damage degree and energy degradation function, respectively. For the effective stress tensor, For stress, The total free energy of the system, It is the chemical modulus, and , For concentration, As the driving force for crack damage evolution, denoted as the initial diffusion coefficient of chloride ions in concrete. The chloride ion diffusion coefficient at the damaged crack and The ratio, , n are model parameters. , ,in, Must meet: .

2. The chloride ion diffusion-phase field coupling analysis method for corrosion damage in reinforced concrete according to claim 1, characterized in that: The chloride ion diffusion-phase field coupling analysis method determined in step S1 also includes a steel rust expansion model established by finite element analysis of the process of steel rust expansion leading to cracking of the reinforced concrete interface and peeling of the protective layer, which transforms the expansion effect of steel on the concrete interface into mechanical behavior.

3. The chloride ion diffusion-phase field coupling analysis method for corrosion damage in reinforced concrete according to claim 1, characterized in that: The method for determining chloride ion diffusion-phase field coupling analysis in step S1 also includes obtaining a linear finite element equation set by integrating the discretized equations of the displacement field and phase field sub-problems. During the unstable crack propagation process, an operator segmentation algorithm that updates the phase field and displacement field sequentially is used to decouple the displacement sub-problem and the phase field sub-problem. The linear finite element equations are as follows: ， in, , , , , , , These are, respectively, the displacement stiffness matrix, the damage stiffness matrix, the diffusion stiffness matrix, the displacement column matrix, the damage column matrix, the concentration column matrix, and the concentration capacity matrix. , , These are the time derivatives of the displacement matrix, damage matrix, and concentration matrix, respectively. , , These are the nodal load array, the damage residual array, and the concentration residual array, respectively.

4. The chloride ion diffusion-phase field coupling analysis method for corrosion damage in reinforced concrete according to claim 1, characterized in that: The specific steps for analyzing the entire process of chloride salt corrosion leading to damage and failure in reinforced concrete and predicting the durability of reinforced concrete in step S2 are as follows: Step S21: Select Abaqus as the platform for realizing the chloride ion diffusion-phase field coupling analysis method; Step S22: Define the element tangential stiffness matrix and nodal force vector in the model using the Abaqus UEL subroutine. Each node of each element in the mesh has four degrees of freedom: x-direction displacement degree of freedom, y-direction displacement degree of freedom, phase field variable degree of freedom, and chloride ion concentration degree of freedom. The x-direction displacement degree of freedom and y-direction displacement degree of freedom simulate the rust expansion process of the steel reinforcement, and the phase field variable degree of freedom characterizes the damage and cracking condition of the concrete. Step S23: Implement data interaction during the solution process and visualize the calculation results through the Abaqus UMAT subroutine.

5. The chloride ion diffusion-phase field coupling analysis method for corrosion damage in reinforced concrete according to claim 4, characterized in that: In step S3, a macroscopic simulation of the damage process of chloride salt erosion on reinforced concrete is performed, in which the phase field and concentration field are coupled.

6. The chloride ion diffusion-phase field coupling analysis method for corrosion damage in reinforced concrete according to claim 5, characterized in that: The specific steps for performing parametric analysis in step S4 are as follows: Step S41: Keeping the diameter of the reinforcing bars unchanged, investigate the effect of the concrete cover thickness on the cracking and spalling modes of reinforced concrete under chloride salt environment. Step S42: Keeping the diameter of the reinforcing bar unchanged, simulate the damage and failure of concrete caused by the rust expansion of the corner reinforcing bar for different reinforcing bar positions, and explore the influence of different reinforcing bar positions on the spalling mode and durability degradation of the concrete cover. Step S43: Based on the validated chloride ion diffusion-phase field coupling analysis method, establish a numerical model of rust expansion cracking of reinforced concrete under chemical-mechanical coupling environment, and analyze the entire process of durability degradation of reinforced concrete components under chloride salt environment.

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