Chloride Diffusion In Concrete Research Articles

Time-dependent concrete chloride diffusion coupled with nonlinear chloride binding: An analytical study

Both the temporal dependence of chloride diffusion coefficient and the effect of nonlinear chloride binding substantially affect the behavior of concrete chloride diffusion. This study develops an exact chloride diffusion solution that accommodates the above two factors by introducing a simplified but reasonably realistic nonlinear chloride binding isotherm. The introduction of this isotherm makes it possible to achieve an analytical solution to a highly nonlinear chloride diffusion equation that involves a free chloride concentration dependent dimensionless factor which reflects the effect of chloride binding. First, a time-dependent chloride diffusion model incorporating the introduced isotherm is established with the corresponding exact solution derived. The proposed solution is successfully validated against two existing analytical solutions and a numerical solution. Parametric study is conducted using the proposed solution to investigate how the parameters regarding chloride ingress influence the corrosion initiation time, and results show that the increase of the initial effective chloride diffusivity or the before-ingress age decreases the corrosion initiation time bringing an acceleration of a different level to chloride diffusion while the increase of the age factor prolongs the corrosion initiation time decelerating chloride diffusion to some extent, and as each of the three nonlinear chloride binding associated parameters (i.e., the deflection-point concentration, the former slope and the latter slope) increases, the corrosion initiation time rises and the retardation effect on chloride diffusion is enhanced to a various extent. Lastly, to demonstrate the practical validity of the proposed solution, the solution is applied to reproducing a reported chloride diffusion test, and it turns out that our solution reproduces the diffusion test reasonably well, justifying its practical validity.

Reliability-based conformity control method for chloride diffusivity of coastal reinforced concrete buildings

Chloride diffusivity significantly affects the durability of coastal reinforced concrete (RC) buildings, and is one of the major concerns in practice. However, its design and conformity control are commonly based on “deem-to-satisfy” methodology, and consequently it's difficult to evaluate the building's durability performance. In this paper, a reliability-based conformity control method for diffusivity is proposed to eliminate the gap. First, the existing empirical method and semi-empirical method are reviewed, and their drawbacks are addressed according to the reliability assessment. Then, based on the statistical acceptance sampling theory and the engineering practice of Hong Kong-Zhuhai-Macau sea-link project, the reliability-based method for diffusivity is proposed, which can be applied in the construction of coastal RC buildings. In this method, effects of local environmental conditions (e.g., temperature and humidity) on chloride diffusivity are considered, and the relation between diffusion coefficient for design (Da0) and for conformity control (Dnssm) is suggested accordingly. Finally, the conformity control for the concrete's chloride diffusivity of an accessory RC building in the Shantou Harbor is taken as the example, and the schemes by empirical method, semi-empirical method and reliability-based method respectively are established. Their acceptable quality level (AQL) and limiting quality level (LQL), probabilities of acceptance and outcomes in terms of durability reliability are evaluated and compared. It is found that the reliability-based method can offer the schemes that is consistent with the design target, and reject most of the nonconforming lots without harming the producers' benefits.

Fractal derivative model with time dependent diffusion coefficient for chloride diffusion in concrete

More research and experiments have indicated that, under different water cement ratios, the binding effect of concrete on chloride ions and the blocking effect of hydration on chloride ions are clearly dominant. During this time period, the diffusion rate of chloride ions will increase or decrease with time, resulting in the classical Fickian diffusion law no longer being applicable. This study establishes an improved fractal model with a time-dependent diffusion coefficient for chloride diffusion in concrete. An explicit solution is derived in terms of the complementary error function. The proposed model is verified by fitting the chloride ion concentration data from different concrete immersion tests. The results show that the fractal model can fit the data in different spatial scales, and the corresponding prediction accuracy is rather high when compared to the three integer order models with constant, variable diffusion coefficient, and curing age. Therefore, the fractal derivative model is feasible in describing the anomalous diffusion of chloride ions in concrete.

Clarifying the effects of volume proportion and surface area of aggregate on chloride diffusivity of concrete through microstructural design

Increasing the aggregate proportion usually reduce the chloride diffusivity of concrete, but may also increase the chloride diffusivity as more interfacial transition zone (ITZ) is introduced with increased surface area of aggregate. Since both packing density and surface area of aggregate varied simultaneously with its particle size distribution (PSD), effects of volume proportion and surface area of aggregate on the chloride diffusivity of concrete has not been clarified separately yet. In the present study, we established a database containing over 500,000 aggregate PSDs and their corresponding packing density and specific surface area using the Compressible Packing Model (CPM) and photogrammetric 3D reconstruction. By individually controlling target volume proportion or surface area of aggregate, effects of aggregate volume proportion and surface area on the mechanical properties and chloride diffusivity of concrete were evaluated. Then an empirical equation, in consideration of aggregate size-dependent ITZ thickness the tortuosity, was proposed to describe the relationship between chloride diffusion coefficient and aggregate proportion and surface area, and a strategy for aggregate PSD optimization was provided to meet chloride diffusivity requirement, which offer an approach for enhancing the chloride resistance of concrete.

Physics-informed deep neural network for modeling the chloride diffusion in concrete

Chloride diffusion in concrete is a complex chemo-physical process and it is of pivotal importance to forecast the initiation time of corrosion. But limited equations are accessible to simulate the chloride diffusion considering the nonlinear chloride binding capacity of concrete. This study proposes a physics-informed deep neural network to simulate the chloride diffusion mechanism and forecast the distribution of chloride concentrations in concrete. Physical laws are formulated as a loss term to guide the training process and to mitigate the data required for model training. The physical constraint loss (based on the governing equation and boundary conditions) and the training loss (based on the neural network) are then fused to produce the loss function. Different experimental cases are first employed to validate the proposed model and then the model is compared to numerical applications and purely data-driven approaches. Results revealed that the proposed model could effectively simulate the chloride transport behavior and forecast the diffusion coefficient of concrete with high precision over other states of art methods. The application of this method to the temporal and spatial domains of the chloride concentration within the concrete samples showed its potential as a powerful tool for investigating concrete properties.

Time-dependent similarity and micro-mechanism of chloride diffusivity of fly ash concrete in different environments

Based on the exposure test of fly ash (FA) concrete in different environments, chloride diffusion coefficients and main microstructural parameters measured by mercury intrusion porosimetry and their time-dependent properties were analysed. Then, the effect of FA content on time-dependent chloride diffusivity and microstructural parameters was investigated. Finally, according to similarity theory and Jaccard coefficient, the similarities of instantaneous chloride diffusion coefficient and main microstructural parameters between two environments were discussed. Results show the proportion of pores with size ≥100 nm has the best correlation with chloride diffusivity of concrete. Besides, chloride diffusion coefficients and main microstructural parameters decrease with exposure time. The decreasing rate increases with the increase of FA content. Moreover, in the laboratory environment with high temperature and high salinity, an acceleration effect on chloride diffusion can be observed. Results of similarity analysis indicate that chloride diffusivity and the main microstructural parameters at an exposure time of 320 days in the laboratory environment are the most similar to those on site at an exposure time of 840 days. For concrete with FA content not more than 40%, the Jaccard coefficients of similar criterion parameters related to chloride diffusivity and microstructural parameters are all greater than 0.87.

Exploring Exact Effects of Various Factors on Chloride Diffusion in Cracked Concrete: ABAQUS-Based Mesoscale Simulations

Chloride ion attack is a major cause of concrete durability problems, and existing studies have rarely addressed the effects of damage zones. In this paper, an improved mesoscale model including five phases was constructed using the finite element software ABAQUS to study the diffusivity of chloride ions in cracked concrete. It was found that the damage zone is negligible when the crack width is less than 50 μm, while the width and depth of the damage zone are about 15 times the crack width and 15% of the crack depth when the crack is greater than 50 μm. The results show that the diffusion of chloride is greatly influenced by the crack width, while it is little-influenced by the crack shape. Low water-cement ratio and adequate hydration of the concrete are also key factors affecting chloride diffusion. In contrast, regular rounded aggregates have a positive effect on reducing chloride diffusion compared to irregularly shaped aggregates, and this effect becomes weaker with increasing service time. In addition, the protective layer can effectively prevent the diffusion of chloride in concrete. Therefore, when designing marine concrete, efforts should be made to ensure that the concrete has a low water-cement ratio, adequate hydration, less cracking and a protective layer.

Application of 3D cellular automata-based analysis to chloride diffusion process in concrete bridges

Chloride-induced corrosion is one of the main reasons for degrading the serviceability and reliability of concrete bridge structures in severe environments. Consequently, a more accurate simulation of the chloride diffusion process is essential for a durable design. This paper performs a three-dimensional (3D) cellular automata (CA) model that accurately simulates chloride diffusion in concrete. The model's accuracy was investigated by comparing the results with Fick's second law (FSL), 2D-CA model, and experimental data. The 3D-CA model is improved and applied to simulate the chloride diffusion in a concrete bridge, considering the effect of multiple factors such as relative environmental humidity, variations in temperature, stresses, water-cement ratio (w/c), concrete degradation, corrosion propagation, cracking, and time. The 3D-CA model algorithms were developed using Python to accomplish this goal. The life span of the concrete bridge was assessed based on critical regions of the corrosion beginning and concrete cracking time. The 3D-CA model provides a more suitable approach to simulating chloride diffusion and predicting the initial corrosion time of reinforcement bars. It can also provide a basis for establishing a maintenance strategy with low-cost solutions for evaluating risk areas and constructing durable projects.

A Mesoscopic Model for Predicting the Chloride Diffusivity’ Representative Volume Element in Concrete as a Random Composite

Chloride diffusivity is the most crucial factor for evaluating durability and predicting service life of concrete structures exposed to chloride environment. In the present paper, concrete is considered as a random heterogeneous composite of three phases: the aggregates, the matrix, and the interfacial transition zones (ITZ) between them. A mesoscopic model has been established based on the random aggregate model and a numerical model for calculating the chloride diffusivity has been proposed. The influences of aggregate size and the properties of the interfacial transition zones on chloride diffusivity of concrete are also discussed. The chloride diffusivity is size dependent because aggregates are randomly distributed in concrete. The chloride diffusivity under different sizes is analyzed by numerous numerical simulations, and the representative volume element (RVE) of chloride penetration into concrete is researched by the statistical method.

Analytical solution for chloride diffusion in concrete with the consideration of nonlinear chloride binding

An analytical study is presented on the diffusion of chloride in concrete coupled with the effect of nonlinear chloride binding. A double-segment piecewise linear chloride binding isotherm (the DS-PWL isotherm) is proposed that can fit well quite a number of experimentally measured chloride binding isotherms which were reported by many published works. The proposal of the DS-PWL isotherm makes feasible the development of analytical solutions for chloride diffusion in concrete that accommodate nonlinear chloride binding, which is not feasible at present. Based on the proposed isotherm, an analytical solution is obtained for one-dimensional diffusion of chloride in a semi-infinite concrete medium in the context of nonlinear chloride binding. The obtained solution is successfully validated against numerical solution for mathematical correctness while the proposed analytical model is shown to be in tolerably good agreements with a reported chloride diffusion experiment. Moreover, the proposed model is also shown to be in good agreements with the Freundlich-based model, exhibiting a desirable applicability. Parametric study is conducted using the proposed solution to examine the influence of each of the three DS-PWL characterizing parameters on chloride diffusion. Finally, the proposed solution is applied to investigating the influence of nanomaterial addition (the dosage of addition and the type of the nanomaterial added) on the service life of an RC structure member subjected to chloride ingress.

Simulation Approach for Random Diffusion of Chloride in Concrete under Sustained Load with Cellular Automata

Steel bar corrosion caused by chloride is the major reason for concrete structure durability failures in a corrosive environment. An accurate simulation of chloride ion diffusion in concrete is hence critical to durability design, maintenance, and reinforcement of concretes in erosive environments. To accurately simulate actual chloride ion diffusion in concretes, an improved three-dimensional neighborhood type is proposed according to the mechanism of chloride ion diffusion in concrete, and a three-dimensional cellular automaton model (3D CA model) for describing the diffusion process of chloride in concrete is established based on this neighborhood type. The accuracy and correctness of simulation results obtained from the 3D CA model were verified by comparison with Fick’s second law analytical solutions. Based on the 3D CA model, an improved modified 3D CA model is developed (3D RTCA model) which takes into account random chloride ion distribution in concrete, the time dependence of the coefficient of chloride ion diffusion, and the structure stress level effect on chloride ion diffusion. Numerical simulation results reveal that the 3D RTCA model has higher calculation accuracy in predicting long-term concentration of chloride in concretes, and the simulation results are closer to experimental findings than analytical results obtained based on Fick’s second law. Compared with Fick’s second law analytical solutions, the 3D RTCA model can reflect more truly the cross-sectional stress level effect on chloride ion diffusion through simple local evolution rules. Besides, the 3D RTCA model can genuinely describe the randomness and uncertainty of the chloride diffusion process. The 3D RTCA model developed in the current study provides a novel perspective and method to investigate chloride ion diffusion in concrete from structural level.

Effect of Interface Transition Zone and Coarse Aggregate on Microscopic Diffusion Behavior of Chloride Ion.

Concrete is a multiphase composite material composed of coarse aggregate, cement mortar, and interface transition zone (ITZ). It is of great significance to study the effect of ITZ and coarse aggregate on chloride microscopic diffusion behavior for predicting the service life of reinforced concrete (RC) structures. By introducing the random distribution function, a random coarse aggregate model considering the randomness of the thickness of the ITZ was established. Furthermore, a two-dimensional (2D) chloride ion diffusion mesoscopic model was developed by specifying different diffusion properties for different phase materials of concrete. Moreover, the effects of coarse aggregate rate, ITZ thickness, and ITZ diffusion property on chloride ion diffusion behavior were investigated in this paper. The research showed that the aggregate has hindrance and agglomeration action on chloride ion diffusion. Although the volume content of the ITZ was very small, less than 0.2% of the total volume of concrete, the effect of the ITZ on the chloride diffusion in concrete cannot be ignored. More importantly, the mechanism of promoting chloride diffusion in the ITZ was revealed through the chloride diffusion trajectory. The research revealed the transmission mechanism of chloride ions in the meso-structure of concrete and provides theoretical support for the design of RC structures in coastal areas.

Modelling of convection, diffusion and binding of chlorides in concrete during wetting-drying cycles

Moisture convection in concrete is an important factor affecting the chloride diffusion in concrete. This paper presents a comprehensive study on the transport of moisture, carbon dioxide and chloride ions in concrete when subjected to wetting and drying cycles. A numerical model considering not only the transport of individual components but also the interaction between them is developed. The latter includes the concrete carbonation, chloride binding, the effect of concrete carbonation on chloride binding capacity, and the time-varying boundary conditions of carbon dioxide and chloride caused due to wetting and/or drying. The results obtained from the study demonstrate that when moisture convection and concrete carbonation in the convection zone near the exposed surface are involved the chloride indeed exhibits an increase in a thin layer next to exposed surface before it decreases with the distance as observed in many experiments.

Machine learning approach for investigating chloride diffusion coefficient of concrete containing supplementary cementitious materials

Chloride diffusion coefficient is an important durability indicator in durability design of concrete structure according to performance-based approach. However, this indicator is difficult to anticipate and design due to a variety of factors such as mix design of concrete, the replacement of supplemental cementitious materials (SCMs), and binder selection. This study proposes an extensive number of machine learning algorithms to predict the chloride diffusion coefficient of concrete containing Supplementary Cementitious Materials (SCMs) such as silica fume, ground granulated blast furnace slag, and fly ash. A database containing nine input variables is created, eight machine learning models consisting of Support Vector Machine (SVM), Extreme Learning Machine (ELM), K-Nearest Neighbors (KNN), Light Gradient Boosting (LGB), Extreme Gradient Boosting (XGB), Random Forest (RF), Gradient Boosting (GB), AdaBoost (AdB) are evaluated via performance criteria such as Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE), coefficient of correlation ® and Root Mean Square Error (RMSE). Gradient Boosting model has highest performance in prediction of chloride diffusion coefficient. SHapley Additive exPlanations (SHAP), Individual Conditional Expectation ICE and Partial Dependence Plot PDP 2D allow the most influential inputs to be identified, quantify the influence of input variables on chloride diffusion of concrete. Selection of the best ML algorithm Gradient Boosting is useful to develop a dependable soft computing tool in durability design of concrete structure including the mix design optimization and binder selection.

Formation Factor Concept for Non-Destructive Evaluation of Concrete's chloride diffusion coefficients

Estimation of chloride diffusion coefficient (Drcm) is an integral part of service life assessment of vulnerable concrete structures due to chloride induced corrosion. This study focuses on the suitability of an alternate non-destructive, low-cost approach of estimating diffusion coefficients through electrical resistivity and formation factor as a replacement of conventional destructive migration tests. The variation in formation factor for 60 concrete mixes with different Supplementary Cementitious Materials (SCM) types (fly-ash, slag) and proportions (0–40%) along with multiple mix parameters (w/cm ratio and target slump) were studied after 365 days of curing. Drcm values predicted from formation factor approach were found to be in close proximity to the coefficients obtained from migration test but however, required certain modifications to ensure conservative estimations. Tentative modification factors were developed for each binder separately as well as for all blended mixes. Based on the obtained factored Drcm values using the modification factor, it was demonstrated that it is possible to ensure reliable and conservative estimation of corrosion initiation time of any mixes without the requirement of destructive testing.

Effect of aggregate morphology on physical tortuosity of chloride diffusive path at meso-scale of concrete

The effect of the aggregate morphology on the chloride diffusivity of concrete was evaluated from the perspective of the physical tortuosity of the diffusive path at meso-scale. Three morphological indices, i.e., convexity, aspect ratio and circularity, were defined. A novel method by using the Fourier transform was proposed to simulate the meso-scale model of concrete. The physical tortuosity was defined based on the chloride diffusive streamline at meso-scale. The effects of aggregate morphological indices on the physical tortuosity were analysed by the multiple linear regression. The results show that: (1) the physical tortuosity increases when: (1) the area fraction of the aggregate increases; (2) the circularity decreases while the convexity and aspect ratio of aggregates increase; 3) the ITZ diffusivity decreases. (2) the area fraction and circularity of the aggregate have the first and second dominant effects on the physical tortuosity, while the effects of the convexity and aspect ratio are ignorable. (3) The chloride diffusivity of the interfacial transition zone between the cement paste and aggregate has a noticeable effect on the physical tortuosity. Based on the results, analytical models were proposed to fast evaluate the physical tortuosity.

Time dependent correlation of permeability of fly ash concrete under natural tidal environment

Based on the long-term exposure test of fly ash concrete under natural tidal environment, the gas permeability coefficient, water permeability coefficient, chloride concentration and microstructure parameters of fly ash concrete were tracked and tested. Relationships between permeability and exposure time as well as fly ash content were analysed. Time dependent models for permeability of concrete were established, and time dependent relationships among water/gas permeability, and chloride diffusivity were discussed. Based on the results of mercury intrusion porosimetry (MIP), the influence of fly ash content on time dependent porosity and pore size distribution (PSD) of concrete were analysed. Results show that fly ash can significantly reduce the porosity, instantaneous chloride diffusion coefficients, water and intrinsic gas permeability coefficients after the same exposure time. A time dependent chloride diffusivity model is established based on the time dependent intrinsic gas permeability coefficients. With the increasing exposure time and fly ash content, the proportions and contributive porosity (100 nm < d < 1000 nm) decrease gradually. Water and intrinsic gas permeability as well as chloride diffusivity of concrete are more closely related to the contributive porosity of large capillary pores (100-1000 nm).

Effects of additives on water permeability and chloride diffusivity of concrete under marine tidal environment

The influences of fly ash (FA), slag (SG), silica fume (SF) and basalt fiber (BF) on time dependent water permeability, chloride diffusivity and microstructure of concrete were studied. Time dependent models for water permeability coefficient (Kw) and instantaneous chloride diffusion coefficient (Dins) were established. Time dependent porosity, pore size distribution (PSD) and contributive porosity (ρc) were determined by MIP. Results show that SF and FA have the best effects on reducing Kw before 240 d. The effects of SF and SG on reducing Dins are relatively poor, due to their small dosage. Kw and Dins are increased by adding BF at early exposure period, but decreased after 240 d. Time dependent Dins and Kw is basically consistent with time dependent porosity. The stable reduced proportion of pores with size greater than 100 nm and corresponding ρc are the leading factors to the decreasing porosity. The correlation between ρc with pore size of 100 nm-1000 nm has a higher correlation with Kw than Dins.

Electrochemical and microscopic analysis on corrosion behavior of steel bars in slag/fly ash-cement paste subjected to seawater attack

A series of corrosion experiments of cement paste-steel bar specimens with different contents of slag and fly ash were performed to investigate the influence of slag/fly ash on the corrosion behavior of steel bars in concrete under seawater. In this investigation, the corrosion behavior of specimen was electrochemically monitored by open-circuit potential (OCP), Tafel polarization (TP) and electro chemical impedance spectra (EIS). Meanwhile, SEM/EDS and XRD were applied to microscopically analyze the microstructure deterioration of materials. Results showed that, replacing cement with slag/fly ash caused a decrease in Ca(OH)2 as well as an increase in C-S-H gel and Friedel's salt in concrete, which can improve the chloride-solidification ability and slow down the chloride diffusion in concrete by both physical adsorption and chemical binding, and thereafter promoting the corrosion resistance of steel bars in concrete in marine environment. Compared to slag, the equal replacing content of fly ash can contribute to a better improving effect on the corrosion resistance of reinforced concrete in marine environment. In this study, a replacement of cement by 20% slag+20% fly ash led to an optimum improving effect on its corrosion resistance. In addition, the results also indicate that the corrosion of reinforced concrete caused by seawater attack does not occur at a uniform rate, but it can firstly maintain a long-term uncorroded state, and then develops rapidly after pitting corrosion occurs.

Exposure duration and sub-zero temperature effects on concrete chloride diffusion decay index and binding

Accurate prediction of corrosion initiation period and service life of reinforced concrete structures requires accurate determination of their chloride diffusion coefficient and binding capacity. Temperature and exposure duration affect these properties, but there is paucity of knowledge regarding the effects of long-term exposure to sub-zero temperatures. Hence, the effects of sub-zero temperature, T, and exposure duration, t, on the chloride diffusion decay index, m, and binding in ordinary Portland cement concrete are investigated. Non-steady natural diffusion tests are conducted at + 5, 0, −5 and −15 °C for 3, 6, 12 and 18 months, and at the end of each period, the total and free chloride concentration profiles are determined. The index m is found to vary over a wide range, it being directly proportional to T and inversely to t. It drastically deviates from the commonly assumed value of 0.2 in the literature. Chloride binding is found to obey the Freundlich isotherm. The coefficient α of the isotherm equals 1.0 ± 0.16 and is only slightly dependent on T or t while its exponent β varies from 0.178 to 0.502, without exhibiting a systematic relationship with either parameter. Binding is noticed to increase with drop in temperature for the first three months of exposure, but over longer exposure durations, no systematic relationship is observed.