Two-dimensional Chloride Research Articles

Mixed Bayesian Network for reliability assessment of RC structures subjected to environmental actions

Under environmental action, reinforced concrete (RC) structures might suffer from reinforcement corrosion caused by the surrounding environment, dramatically reducing structural reliability and threatening social development. However, most of the existing reliability assessment methods for RC structures only focused on the structural performance at the design stage given the original unchanged environment, ignoring the effects of realistic exposure conditions and inspection results on reliability evaluation. Thus, this paper develops a general reliability assessment framework based on a Mixed Bayesian network (MBN), incorporating three modules, i.e., durability assessment, load-bearing capacity analysis, and time-dependent reliability analysis. In MBN, separate sub-BNs are built based on different modules and connected by pinch point variables where probabilistic information is transmitted via soft evidence. Besides, this framework considers time-dependent environmental parameters and two-dimensional chloride transport and their effects on reliability. Meanwhile, adjustment coefficients are applied to improve the results of the analytical mechanical model with respect to different limit states through the finite element model (FEM). The proposed MBN framework is illustrated for a corroded RC beam under a marine atmospheric environment to investigate the effects of environmental modeling, chloride transport patterns, and concrete crack inspection on reliability assessment. The results indicate that under the assumed conditions in the case study, early inspection of large cracks may significantly overestimate the failure probability by about 500%. Besides, failure probability might be underestimated by about 95%, ignoring the time-variant environment and two-dimensional chloride transport.

Maintenance modeling and cost assessment for repaired reinforced concrete structures exposed to chloride attack in coastal areas in Vietnam

One of the primary causes that can reduce the lifespan of concrete structures is chloride-induced corrosion of reinforcing steel. Recent research has shown that material properties, exposure conditions and climatic conditions have a significant influence on the structural deterioration of reinforced concrete (RC) structures, especially in marine environments. The objective of this paper is to predict the durability of RC structures damaged by chloride-induced corrosion in near-shore environments in Vietnam, considering regular repair activities. A two-dimensional model of chloride penetration in square cross-section RC columns repaired by cover replacement techniques is studied. Two repair methods with different shapes (orthogonal and circular) are considered. The effects of the different repair methods on the life span of structures are investigated in case studies in Vietnam that consider the variations of annual temperature and humidity in three coastal areas such as Danang, Haiphong, and Ho Chi Minh City. Finally, maintenance and repair costs during the lifetime of structures are calculated for each case. The study suggests that for RC structures exposed to two-dimensional chloride ingress, the most critical areas for assessing chloride concentration, predicting corrosion initiation, and planning repair schedules are the corners of the columns. In addition, the chloride-induced corrosion process is strongly influenced by the local weather conditions, especially in areas with high humidity. The repair method with circular concrete replacement seems to be more efficient in terms of maintenance schedule and cost than the repair method with orthogonal concrete replacement.

Time-dependent reliability analysis of reinforced concrete beams considering marine environmental actions

Under marine atmospheric environments, reinforced concrete (RC) structures may suffer from structural deterioration induced by environmental actions, affecting structural performance and safety. Thus, it is essential to evaluate and predict the deterioration process of an RC structure subject to environmental actions. This paper proposes a novel and generic computational framework to assess the time-dependent reliability of an RC beam under environmental actions. This framework includes a comprehensive life-cycle performance assessment model that considers climate change, two-dimensional chloride transport, the coupling effects and corrosion non-uniformity of reinforcement, and the nonlinear behavior of RC beams, which is validated by experimental studies. Additionally, performance functions for an RC beam are established for different failure modes, and their time-dependent probabilistic information and reliability index are captured using the probability density function-informed method (PDFM). To demonstrate the computational processes of the developed framework under practical marine atmospheric conditions, illustrative cases are presented. The accuracy and efficiency of the proposed method are validated by traditional Monte Carlo Simulation (MCS). Results indicate that the proposed method is feasible and efficient, aiding the life-cycle design and maintenance of RC structures.

Modelling two-dimensional chloride diffusion in repaired RC structures for sustainable maintenance management

Both public and private infrastructure management agencies are responsible for chloride-related corrosion damage to coastal reinforced concrete (RC) structures, which often requires extensive repairs. These repairs are intended to provide serviceability and safety while reducing costs and environmental impact. While there are many repair methods, techniques, and materials available, little is known about their long-term performance and durability. This study examines two-dimensional chloride ingress into square cross section RC columns and their durability using cover replacement techniques with several shapes, thicknesses, locations, and repair times. First, a two-dimensional repair model is developed to simulate these repair strategies and predict their serviceability performance. Two orthogonal concrete replacement strategies (OCR1 and OCR2) and one circular concrete replacement strategy (CCR3) are studied. Next, a method to evaluate and compare maintenance strategies in terms of durability, cost, and environmental impact is also considered. The results of this study reveal that the corners of a column are the most critical areas to evaluate chloride concentration when predicting the time of corrosion initiation and estimating repair time. For long-term maintenance management, the circular concrete replacement strategy is recommended over orthogonal concrete replacement for repair of RC columns exposed to chloride-induced corrosion. The CCR3 strategy requires fewer repairs and achieves higher cost-effectiveness and sustainability compared to the other strategies.

Durability degradation simulation of RC structure based on gamma process considering two-dimensional chloride diffusion and life probabilistic prediction

In this paper, based on the gamma process, a new method for predicting the life of reinforced concrete (RC) structures eroded by chloride is presented considering two-dimensional (2D) chloride diffusion. First, according to the chloride diffusion theory, an analytical model and a finite difference numerical model considering 2D chloride diffusion under the action of multiple factors were established. Based on this, the Monte Carlo method and method proposed in this study were employed to predict the initial rust time of RC structures eroded by chloride. Histograms of the initial rust time and probability density function obtained using the two methods mentioned above were compared and analyzed to verify the validity of the proposed method. Finally, the life prediction model of the RC structure considering the initial rust time T1, rust expansion cracking time T2, and time when the concrete surface crack width reaches the limit crack width T3 was established, and its applicability was verified through an analysis of an engineering example. The research indicates that the gamma process-based probability models can approximately predict the time required for rebar corrosion of an RC structure eroded by chloride considering 2D diffusion.

Dynamic Bayesian network for durability of reinforced concrete structures in long-term environmental exposures

Reinforced concrete (RC) structures under the marine environment may be subjected to chloride-induced corrosion of reinforcement, which significantly impacts the structural serviceability and reliability and further affects the sustainability and development of society. However, most of the existing durability assessment methods for RC structures only address their static and deterministic durability prediction and assessment at the design stage given the constant environment, ignoring the influences of stochastic environmental effects, uncertainties in structural properties, and inspection results. To this end, this paper proposes a dynamic Bayesian network (DBN) based durability assessment framework combined with a deterioration model that considers random changes in environmental parameters, convective chloride ion transport, and corrosion-induced cracking of concrete. In this framework, two-dimensional chloride transport and its influences on the durability deterioration assessment are concerned and achieved using the finite difference method. Besides, to reduce the deviations in probabilistic evaluation, the good-lattice-point-set-partially stratified-sampling (GLP-PSS) method is employed to establish a DBN framework. The proposed DBN framework is used for sensitivity analysis through a real-world example to examine the effects of the environmental model, chloride transport mode, and inspection results of concrete crack on durability assessment.

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.

Durability Degradation Simulation of Rc Structure Based on Gamma Process Considering Two-Dimensional Chloride Diffusion and Life Probabilistic Prediction

Durability Degradation Simulation of Rc Structure Based on Gamma Process Considering Two-Dimensional Chloride Diffusion and Life Probabilistic Prediction

Evaluation of Biaxial Strength Deterioration for Coastal Bridge Piers under Non-uniform Corrosion

Coastal bridge piers in the corrosive marine environment inevitably deteriorate over time, leading to a reduction in their strength. In the present study, a biaxial strength prediction method for non-uniform corroded bridge piers under axial force and biaxial bending moments is proposed by extending the applicable range of the load contour method. First, a method to establish the three-dimensional interaction surface is developed on the basis of the fiber-section model, which considers the two-dimensional chloride diffusion, the degradation of reinforcement and concrete. The proposed methodology is verified by a biaxial quasi-static test of the locally corroded bridge column specimens. Then, through further case study, the time-dependent characteristics of the interaction surface for bridge piers in the splash and tidal region and the atmospheric region are investigated. Finally, the expression of surface exponent is obtained from the interaction surface, which can be used in Bresler's load contour method to evaluate the deterioration in the biaxial strength of coastal bridge piers. The analytical results conclude that the expression of surface exponent can be divided into three stages including the constant stage, decrease stage and increase stage during the pier's service life. Axial compression ratio and corrosion degree are two important factors which influence the biaxial strength deterioration for different corrosion regions of the coastal bridge pier.

Two-dimensional monolayer salt nanostructures can spontaneously aggregate rather than dissolve in dilute aqueous solutions

It is well known that NaCl salt crystals can easily dissolve in dilute aqueous solutions at room temperature. Herein, we reported the first computational evidence of a novel salt nucleation behavior at room temperature, i.e., the spontaneous formation of two-dimensional (2D) alkali chloride crystalline/non-crystalline nanostructures in dilute aqueous solution under nanoscale confinement. Microsecond-scale classical molecular dynamics (MD) simulations showed that NaCl or LiCl, initially fully dissolved in confined water, can spontaneously nucleate into 2D monolayer nanostructures with either ordered or disordered morphologies. Notably, the NaCl nanostructures exhibited a 2D crystalline square-unit pattern, whereas the LiCl nanostructures adopted non-crystalline 2D hexagonal ring and/or zigzag chain patterns. These structural patterns appeared to be quite generic, regardless of the water and ion models used in the MD simulations. The generic patterns formed by 2D monolayer NaCl and LiCl nanostructures were also confirmed by ab initio MD simulations. The formation of 2D salt structures in dilute aqueous solution at room temperature is counterintuitive. Free energy calculations indicated that the unexpected spontaneous salt nucleation behavior can be attributed to the nanoscale confinement and strongly compressed hydration shells of ions.

Numerical modelling and experimental validation of two-dimensional chloride concentration distribution within concrete

An efficient finite element model for two-dimensional (2D) time-dependent chloride diffusion (2D-TCD) was proposed to describe the chloride concentration distribution within the corner and edge areas of concrete members. Governing equation as well as boundary and initial conditions for 2D-TCD were established first. Then the lumped concentration matrix (LCM) for 2D-TCD was derived based on the Galerkin's weighted residual method and the trapezoidal formula. Moreover, an efficient finite element model for 2D-TCD was proposed based on the precise time-integration method and the Padé series expansion technology. Finally, the accuracy and efficiency of the proposed model were validated by comparing with the analytical model, traditional finite element model and experimental data. Analysis shows that the proposed model overcomes the numerical stability problems (such as oscillations and negative values) of traditional models by adopting the LCM to establish finite element equation of 2D chloride diffusion. Meanwhile, the computational accuracy and efficiency of the proposed model are higher than those of the traditional models, since it adopts the Padé series expansion instead of the Taylor series expansion to derive the general solution of 2D chloride diffusion. Moreover, the proposed model can not only balance the computational accuracy, efficiency and numerical stability, but also be insensitive to the meshed sizes of spatial grids and time steps.

Multi-Scale Simulation of Two-Dimensional Chloride Transport Under the Effect of Bending Load in Concrete

Chloride transport in marine concrete under loading is the main cause of its structural deterioration. The traditional numerical simulation assumes that the coefficient of chloride transport is constant, resulting in a large deviation in the prediction results. Based on the porous medium theory, micromechanics theory, and the idea of equivalent homogenization, a multi-scale model of the effective diffusion variable coefficient of chloride transport under bending load was established, which was calculated and programmed by the numerical analysis. The results show that the prediction values of the two-dimensional variable coefficient model are basically consistent with those in the literature, and the prediction accuracy is significantly improved. In addition, the theoretical simulation proves that the bending load affects the porosity of the cement matrix, and then the diffusion coefficient of chloride is changed in concrete. The compression zone can slow down the chloride transport process, while tension zone will accelerate it. The chloride concentration under tension zone is 42.1% higher than that under compression zone when the diffusion time is 200 days and the concrete depth is 15 mm.

Modelling of two-dimensional chloride diffusion concentrations considering the heterogeneity of concrete materials

Chloride ingression into reinforced concrete (RC) is currently considered an important reason behind the deterioration of RC structures exposed to aggressive environments. Previous studies have been mostly devoted to investigations on the one-dimensional transport characteristics of chloride in concrete; however, for the RC structures exposed to marine environment, the corners and edges of various components are often subjected to two-dimensional chloride penetration. Moreover, concrete is generally considered a typical heterogeneous material because of its coarse aggregate being randomly distributed in a cement paste. Both the two-dimensional chloride diffusion behaviour and the heterogeneity of concrete materials have large influences on the chloride concentration distribution in concrete. For the investigations in this paper, using the coarse aggregate volume fraction (CAVF) to quantify the heterogeneity of concrete materials, an indoor experiment for exploring the two-dimensional chloride diffusion behavior of concrete under real-time tidal cycles in a marine environment was carried out. The two-dimensional chloride diffusion concentrations within concrete specimens cast using different CAVFs of Vca = 0, 0.2, 0.3, 0.4, and 0.5 were tested at various exposure periods of t = 30, 70, 100, 140, and 180 days. The decreased percentages for the tested two-dimensional chloride diffusion concentrations increased with increasing CAVF, and the percentage values decreased from −4.95%, −5.22%, −6.29%, and −7.46% to −65.52%, −73.68%, −91.56%, and −97.22% for Vca = 0.2, 0.3, 0.4, and 0.5 in relation to Vca = 0 in the diagonal sample holes of the concrete specimens, respectively. The quantitative influence of Vca = 0.5 on the two-dimensional chloride diffusivity showed an average reduction of approximately 50.79% for each exposure period in relation to the specimen values for Vca = 0. On the basis of the two impact factors related to the exposure period (If (t)) and the CAVF (If (Vca)), a time-dependent model for predicting the two-dimensional chloride diffusion concentration in concrete by accounting for the heterogeneity of concrete materials was developed and compared with those determined by the meso-scopic numerical simulation method and physical experiment. The comparisons exhibited that the two-dimensional chloride concentrations assessed by the model and numerical simulation were almost within a ±20% error margin, validating the accuracy, correctness and reasonability of the prediction model developed in this paper.

Durability assessment of reinforced concrete structures considering global warming: A performance-based engineering and experimental approach

Reinforced concrete (RC) structures under marine atmospheric environment usually suffer from chloride ingress, which could impair structural serviceability and performance within the service life. Performance-based engineering, as an approach to design structures with predictable and defined performance, has attracted increased attention. In this paper, the developed probabilistic performance-based durability engineering (PBDE) approach is used as a novel attempt to integrate different computational modules (i.e., exposure analysis, deterioration, repair analysis, and impact/consequence analysis) within the durability assessment and management process of RC structures incorporating the experimental results. To begin with, a probabilistic environmental model is developed using the measured data to account for global warming, the seasonal and daily variation of temperature, etc. Additionally, deterioration analysis is conducted considering two-dimensional chloride transport and non-uniformity of corrosion. The experimental studies are conducted to verify the relevant numerical results. Subsequently, consequence analysis is performed to aid the maintenance process of RC structures. Uncertainties associated with material properties, model, and environmental scenarios, as well as the effect and cost of maintenance actions, are incorporated within the developed framework, which is illustrated using a real-world example. Compared to the traditional durability assessment approach, non-uniformity of corrosion, 2D convection-dominated chloride transport model, and climate change effects are assessed in a probabilistic manner.

Rebar corrosion in coral aggregate concrete: Determination of chloride threshold by LPR

Chloride threshold is a significant index to judge the initial corrosion of rebar in concrete structures, and a key parameter for durability analysis and service life design of reinforced concrete structures. In the present wok, the corrosion rate of rebar embedded in coral aggregate concrete and the chloride ion diffusion law of coral aggregate concrete was studied by the linear polarization resistance method and two-dimensional chloride diffusion model, respectively. Depending on the relationship between the surface free chloride content of rebar and its corrosion rate, the chloride threshold values of different rebar in coral aggregate concrete were finally determined. The results indicate that the corrosion rate of rebar in coral aggregate concrete gradually decreases with the increase of concrete strength grade and cover thickness, and the order of anti-corrosion performance of reinforcements from high to low is: epoxy resin coated steel, 2205 duplex stainless steel, 316 L stainless steel, organic coated steel and ordinary steel. The chloride threshold values (% by weight of concrete) of these reinforcements in coral aggregate concrete were determined and ranked from small to large as follows: ordinary steel (＜0.15%), organic coated steel (＜ 0.21%), 316 L stainless steel (0.33% ∼0.41%), 2205 duplex stainless steel (＞0.46%) and epoxy resin coated steel (＞0.49%). Additionally, there is a remarkable regression relation of corrosion rate between surface free chloride contents and cover thickness of reinforcement, which has a great significance of the research of steel corrosion in coral aggregate concrete.

Experimental and cellular-automata-based analysis of chloride ion diffusion in reactive powder concrete subjected to freeze–thaw cycling

Natural soaking and accelerated freeze–thaw cycling experiments were conducted using NaCl solution to study chloride ion diffusion in reactive powder concrete. The chloride ion diffusion coefficient for specimens subjected to natural soaking was calculated using Fick’s second law. That for specimens subjected to freeze–thaw cycling was calculated using a newly proposed method that considers the damage resulting from freeze–thaw cycling. The coefficient first decreased and then increased as the number of cycles increased. A cellular-automata-based two-dimensional chloride ion diffusion model that considers the time dependence and impact of freeze–thaw cycling damage was established. The chloride ion diffusion and distribution in reactive powder concrete subjected to natural soaking and freeze–thaw cycling in NaCl solution were simulated using Matlab program that was based on the proposed model. The boundary condition for the cellular-automata model should be the surface chloride ion concentration instead of the chloride ion concentration of the solution. The acceleration of chloride ion diffusion due to freeze–thaw cycling damage can be well-simulated by introducing the freeze–thaw damage factor. A comparison of simulation and experimental results showed that this model can simulate and predict chloride ion diffusion in reactive powder concrete effectively.

Investigation on the cracking behavior of concrete cover induced by corner located rebar corrosion

Non-uniform corrosion of reinforcement causes concrete cracking in chloride contaminated RC structures. Due to the special boundary conditions, the concrete cover with corner located rebar is often subjected to the attack of chloride ions in a marine environment from two directions, and thus the corresponding non-uniform corrosion distribution should be different from the one for side-located rebar. The aim of the work is to explore the effect of corner located rebar corrosion on the cracking of cover concrete. For corner located rebar, an improved non-uniform corrosion distribution model was established based on the analysis results of two-dimensional chloride diffusion in concrete. Considering the heterogeneities of concrete, a meso-scale mechanical model and method for the study on the failure behavior of concrete cover was built. In the analysis model and method, the non-uniform radial displacement distribution was adopted to simulate the corrosion expansion behavior of the rebar. The cracking of concrete cover with corner located rebar was simulated and studied. The present approach was verified by the available experimental observations. The influences of concrete heterogeneity, corrosion distribution types, rebar diameter and concrete cover thickness on the failure patterns of concrete cover and the expansive pressure were investigated. The simulation results indicate that the developed approach can well describe the cracking behavior of cover concrete and the corrosion-expansion behavior of steel rebar.

Numerical Analysis of the 2-Dimensional Diffusion Models of Choride Ions Based on the FDM with Alternating Direction Implicit Schemes

Chloride ion etching is a significant reason for the damage of the reinforced concrete structures. Diffusion effect is considered to be the main form of which the chloride ion invades into the reinforced concrete structures. Assuming infinite diffusion medium, based on the Chlorine ion diffusion equation, and accounting for the effects of temperature and moisture, models of chloride diffusion in two-dimensional infinite body with consistent coefficient of diffusion and different coefficient of diffusion in both directions are formulated .Two-dimensional chloride ion diffusion behavior was simulated, which proved the diffusion coefficient has a larger effect on the diffusion behavior of the chloride ion. Through these comparisons, we can analysis that model with different coefficient of diffusion in both directions is more suitable for the actual conditions.

Compensation length of two-dimensional chloride diffusion in concrete using a boundary element model

The boundary element method (BEM) has been widely employed in engineering practice. However, the BEM is not commonly used in numerical analysis of chloride diffusion in concrete and might yield unsatisfactory results if the time duration is significantly long for concrete exposed to chloride environment. In this work, we propose the compensation length of chloride diffusion in concrete, as well as the compensation coefficient based on the error function. The fundamental solution relevant to the governing partial differential equation is presented for chloride diffusion in concrete, enabling the development of the boundary element scheme. In particular, the two-dimensional diffusion analysis is investigated in detail by using the BEM model, featuring the proposed compensation length to achieve superior numerical results. Specifically, the time interval is sparsely discretized into several sub-domains in the BEM model, while the spatial domain is discretized along the boundary of the computational diffusion field, resulting in considerably fewer unknowns in chloride diffusion analysis. Several numerical examples are presented to demonstrate the effectiveness and accuracy of the BEM with compensation length and to illustrate excellent results using the 2-D BEM formulation for chloride diffusion near the intersection of exposed surfaces of concrete specimens.

A comprehensive probabilistic model of chloride ingress in unsaturated concrete

Corrosion induced by chloride ions has become a critical issue for many reinforced concrete structures. The chloride ingress into concrete has been usually simplified as a diffusion problem where the chloride concentration throughout concrete is estimated analytically. However, this simplified approach has several limitations. For instance, it does not consider chloride ingress by convection which is essential to model chloride penetration in unsaturated conditions as spray and tidal areas. This paper presents a comprehensive model of chloride penetration where the governing equations are solved by coupling finite element and finite difference methods. The uncertainties related to the problem are also considered by using random variables to represent the model’s parameters and the materials’ properties, and stochastic processes to model environmental actions. Furthermore, this approach accounts for: (1) chloride binding capacity; (2) time-variant nature of temperature, humidity and surface chloride concentration; (3) concrete aging; and (4) chloride flow in unsaturated conditions. The proposed approach is illustrated by a numerical example where the factors controlling chloride ingress and the effect of weather conditions were studied. The results stress the importance of including the influence of the random nature of environmental actions, chloride binding, convection and two-dimensional chloride ingress for a comprehensive lifetime assessment.