Prediction of the chloride diffusion coefficient of concrete

It has been experimentally verified that the structure of the interfacial transition zone (ITZ) in concrete differs from that of bulk cement paste. As such, concrete should be modeled as a three-phase material at a mesoscopic level. This paper presents a three-phase composite model for predicting the chloride diffusion coefficient of concrete. Taking the inclusion as aggregate and the matrix as cement paste, the composite circle model is established by adding an ITZ layer in between the inclusion and the matrix. Solving the asymmetrical problem analytically, a closed-form solution for the chloride diffusion coefficient of concrete is derived. After verifying this model with experimental results, the effects of the aggregate area fraction, the chloride diffusion coefficient of ITZ, the ITZ thickness, the maximum aggregate diameter and the aggregate gradation on the chloride diffusion coefficient of concrete are evaluated in a quantitative manner. It is found that the chloride diffusion coefficient of concrete decreases with the increase of the aggregate area fraction and the maximum aggregate diameter, but increases with the increase of the chloride diffusion coefficient and thickness of ITZ. It is also found that the aggregate gradation has a significant influence on the chloride diffusion coefficient of concrete.     

The theory of non-steady state fracture kinetics analysis—2: Non-steady state crack propagation in stress corrosion cracking

The extension of the kinetics theory of thermally activated crack propagation to the analysis of non-steady state conditions leads to a series of n homogeneous linear first order differential equations. The theory is applied to Regions I and II of stress corrosion cracking, controlled by the cyclically repeating two-step consecutive energy barrier system of corrosion reaction and bond breaking. For the model the system of n differential equations representing the crack tip concentration distribution is reduced to three expressions. The analysis provides a means by which the existence and the duration of the transition state can be determined, a necessary information for both steady state and for high frequency stress corrosion fatigue tests.     

Lattice modeling of chloride diffusion in sound and cracked concrete

Reinforced concrete structures are frequently exposed to aggressive environmental conditions. Most notably, chloride ions from sea water or de-icing salts are potentially harmful since they promote corrosion of steel reinforcement. Concrete cover of sufficient quality and depth can ensure protection of the steel reinforcement. However, it is necessary to study the effects of material heterogeneity and cracking on chloride ingress in concrete. This is done herein by proposing a three-dimensional lattice model capable of simulating chloride transport in saturated sound and cracked concrete. Means of computationally determining transport properties of individual phases in heterogeneous concrete (aggregate, mortar, and interface), knowing the concrete composition and its averaged transport properties, are presented and discussed. Based on numerical experimentation and available literature, a relation between the effective diffusion coefficient of cracked lattice elements and the crack width was adopted. The proposed model is coupled with a lattice fracture model to enable simulation of chloride ingress in cracked concrete. The model was validated on data from the literature, showing good agreement with experimental results.     

Long-term chloride diffusion in silica fume concrete in harsh marine climates

Supplementary cementitious materials such as silica fume are typically necessary for producing high performance concrete for marine environments in hot regions, such as the Persian Gulf. Silica fume use generally improves the strength and/or durability properties of the concrete. This paper investigates the effects of silica fume on various properties of concrete specimens that were exposed to Persian Gulf conditions. Samples were taken at the ages of 3, 9 and 36 months and analyzed to determine the chloride diffusion coefficient. The results show that partial cement replacement with up to 7.5% silica fume reduces the diffusion coefficient, whereas for higher replacement rates the diffusion coefficient does not decrease significantly. Also time-dependent chloride diffusion and compressive strength of concrete containing silica fume are investigated.     

Coupling between the crack propagation velocity and the vapour diffusion in concrete

In this study, it is shown that the toughness of concrete calculated using the classical compliance method is not an intrinsic property of the material, since it depends on the loading rate even in the quasi-static condition. It would seem that this toughness is a decreasing linear function of the crack propagation velocity, at least in the range of crack propagation velocities obtained in the test presented. It is proposed that the propagation of a crack in concrete may be investigated from the standpoint of the propagation of a crack under conditions of confined viscoelasticity; a possible physical explanation of this confined viscoelasticity (this is an hypothesis) is coupling between the microcracking at the end of the propagating macrocrack and water vapour diffusion.     

Prediction of long-term chloride diffusion in silica fume concrete in a marine environment

Chloride-induced corrosion is the main factor in determining the durability and service life of the reinforced concrete structures exposed to marine environments. Recognition of chloride diffusion phenomenon in concrete and developing a prediction model that can estimate the service life of the concrete structures subject to long-term exposure is vital for aggressive marine environments. The present study focuses on developing such a prediction model of chloride diffusion coefficient for silica fume concrete under long-term exposure to a durability site located in the southern region of Iran. All investigations are based on 16 concrete mix designs containing silica fume with variable water-to-binder ratios exposed to sea water for maximum period of 60 months. This empirical model is developed by applying regression analysis based on Fick’s second law on the experimental results and is compared with previous studies in this area. This comparison indicates that the predicted chloride diffusion coefficient level is within a ±25% error margin in the specimens. The results indicate that reducing the water-to-binder ratio and adding the silica fume to a dosage of 10% reduces the chloride diffusion coefficient in concrete. This study also confirms that the chloride diffusion coefficient increases with temperature and decreases over time.     

氯盐环境下港珠澳工程混凝土耐久性质量控制

针对传统模型采用一致协调浓度矩阵和Taylor级数展开难以兼顾计算精度、效率和数值稳定性的缺陷,研究提出了一种基于集中浓度矩阵和精细积分法的氯离子时变扩散模型：通过引入等效扩散时间,将氯离子的时变扩散控制方程变换为等效常扩散控制方程;基于伽辽金加权余量法,建立了基于集中浓度矩阵的氯离子时变扩散有限元模型;结合Padé级数展开技术,提出了基于集中浓度矩阵和精细积分法的氯离子时变扩散模型;通过与传统有限元模型、解析模型和自然暴露试验数据的对比分析,验证了该模型的有效性。分析表明：与传统的一致协调浓度矩阵相比,采用集中浓度矩阵具有更高的计算精度,而且可以避免振荡和负值等数值不稳定性问题;与传统的Taylor级数展开相比,采用Padé级数展开只需较小的尺度因子就可以保证计算精度,计算效率大幅提高;该模型不仅可以同时兼顾计算精度、效率和数值稳定性,而且对空间离散网格和时间步长的依赖性相对较小。     

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.     

Transient meshless boundary element method for prediction of chloride diffusion in concrete with time dependent nonlinear coefficients

Chloride-induced corrosion of steel reinforcements has been identified as one of the main causes of deterioration of concrete structures. A feasible numerical method is required to predict chloride penetration in concrete structures. A transient meshless boundary element method is proposed to predict chloride diffusion in concrete with time dependent nonlinear coefficient. Taking Green's function as the weighted function, the weighted residue method is adopted to transform the diffusion equation into equivalent integral equations. By the coupling of radial integral method and radial basis function approximation, the domain integrals in equivalent control equations are transformed into boundary integrals. Following the general procedure of boundary element meshing and traditional finite difference method, a set of nonlinear algebraic equations are constructed and are eventually solved with the modified Newtonian iterative method. Several numerical examples are provided to demonstrate the effectiveness and efficiency of the developed model. A comparison of the simulated chloride concentration with the corresponding reported experimental data in a real marine structure indicates the high accuracy and advantage of the time dependent coefficient and nonlinear model over the conventional constant coefficient model.     

Kirchhoff transformation analysis for determining time/depth dependent chloride diffusion coefficient in concrete

This article uses the Kirchhoff transformation method to solve a non-steady one-dimensional diffusion equation when the apparent diffusion coefficient is expressed as a function of time, depth, and concentration of chloride for concrete exposed to chloride environment. The analytical results obtained by the proposed method, which are coincided with those calculated from the Boltzmann–Matano methodology under specific condition, can be used to conveniently predict the chloride diffusion process physically and chemically so that the traditional natural diffusion test to obtain time/depth dependent apparent diffusion coefficient may be greatly simplified. Two new simplified methods to effectively process the experimental results from the natural diffusion test are proposed: one is called the long-specimen-at-one-specific-time method using fewer specimens at one time and the other the short-specimen-at-long-elapsed-time method using more specimens at various service times. Two numerical examples are provided to illustrate the application of these two proposed methods.     

An experimental study on the effect of chloride penetration on moisture diffusion in concrete

Chloride penetration and moisture diffusion are two important transport processes for studying the long-term durability of concrete. The chloride penetration and moisture transfer in concrete are considered as two coupled transport processes. An experimental study was conducted for determining the related material parameters in the coupled transport processes. For the coupled moisture diffusion, we consider that the total moisture fluxJ _H ^t is resulted from two driving forces: the gradient of moistureH, and the gradient of free chlorideC _f , that is,J _H ^t =?D _H-H grad(H)?D _H-Cl grad(C _f′ ). In this formulation, two transport parameters are involved: the moisture diffusion coefficientD _H-H and the coupled moisture diffusion coefficient due to chloride diffusionD _H-Cl . A seepage test was designed specifically for determining the two transport parameters. The test data showed that the chloride penetration accelerates the moisture diffusion significantly. The two transport parameters were determined using the present test data. The result showed thatD _H-Cl is not a constant, but depends linearly on the free chloride concentration.     

Determination of diffusion coefficient of chloride in concrete: an electrochemical impedance spectroscopic approach

For predicting the service life of concrete structures in marine environment, diffusion of chloride (D) is an important parameter. Electro-migration tests and ponding tests are two techniques conventionally adopted, however they are destructive in nature. EIS (Electrochemical impedance spectroscopy) being non-destructive appears a promising technique to arrive at ‘D_R’ (D from EIS) in situ in structures. The D_R of ordinary Portland cement concrete (OPC) was compared with that of Portland pozzolana cement concrete (PPC). The effect of curing on D_R was analyzed. The splash zone condition was created by subjecting the specimens to alternate wetting and drying cycles. At the end of 28 days of curing, the D_R of PPC concrete is only 66.7% of that obtained in OPC concrete. A linear correlation was established between D_R and the porosity of the concrete_. Due to pozzolanic reaction, the rate of pore refinement is faster in PPC concrete compared to OPC concrete. In M25-PPC concrete at the end of 28 days of curing, the pore size is decreased to 14.6% of that obtained at the end of 3 days of curing. The reduction of pore size by densification of pore structure due to pozzolanic reaction reduces the D_R value in PPC concrete. In 30 MPa concrete the D_R under wet cycle is 3 times higher than in dry cycle, which implied that corrosion is initiated 3 times faster in concrete exposed to the splash zone condition.     

Concrete durability presented by acceptable chloride level and chloride diffusion coefficient in concrete: 10-year results in marine site

Generally, concrete with high resistance to the marine environment should have high compressive strength, a low chloride diffusion coefficient (D _C), and a high acceptable chloride level (Ac). Considering all parameters simultaneously, this study evaluated the degree of fly ash concrete durability based on 10-year results in a marine site. Based on the concrete durability (Ac/D _C, as compared to cement concrete with a W/B ratio of 0.45) and compressive strength, the degree of concrete durability proposed in this study indicates that fly ash concretes with a W/B ratio of 0.45 and 15–35 wt % fly ash replacement exhibit high-quality performance in a marine site.     

Pseudo-coating model for predicting chloride diffusion into surface-coated concrete in tidal zone: Time-dependent approach

There are three fundamental physical types for repairs by surface treatment on concrete, i.e., coating, penetrant, and sealer. Due to the inconsistency in using the penetrant-based model in a previous study, three limitations occur. To avoid the limitations, this paper proposes a simple pseudo-coating model embedded in a Fick-based time-dependent approach for modeling the performance of surface-coated concrete in the tidal zone subjected to chloride attack. In addition, the time-dependent regression equation is also developed and combined in computation. To validate the approach, the chloride diffusion predicted by the developed approach is compared to that measured in the previous study. From the study, it is found that the nonlinear and linear surface chloride functions are suitable for uncoated and coated concrete, respectively. The sensitivity analysis shows that the chloride content in concrete is most sensitive to the time-dependent parameter in the surface chloride functions. The surface coating can either decrease or increase initial surface chloride, and the deterioration rate of the surface coating depends on coating materials. By considering the change of the surface chloride after surface treatment, two criteria are proposed to assess the lifetime of coating materials, i.e., equivalent amount of surface chloride, and equivalent instantaneous slope of surface chloride. And, the lifetime is calculated and compared to other literatures. The service life extension of concrete structures with different surface coatings is also compared. The benefit of combining the repair by surface coating with the durability design by increasing concrete cover is also shown.     

Why are crack paths in concrete and mortar different from those in PMMA?

Experiments by Bazant and Pfeiffer on concrete and mortar seem to indicate that crack growth does not necessarily take place under Mode I conditions. In order to investigate the influence of the material, experiments were carried out in PMMA with similar geometry to that used by Bazant and Pfeiffer and a numerical simulation was made assuming Mode I crack growth. The experimental results for PMMA differ significantly from those in concrete and mortar, but agree closely with the result from the numerical simulations. The difference is believed to be explained by the fact that small-scale yielding conditions are not realized well enough in concrete and mortar. A fairly large region of small cracks probably influences the crack growth direction.     

Physicomechanical state of the plate in diffusion saturation with nonlinear diffusion

Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 25, No. 2, pp. 42–45, March–April, 1989.     

Effect of silica fume addition and repeated loading on chloride diffusion coefficient of concrete

In this paper, the effect of silica fume (SF) on the chloride diffusion coefficient of concrete subjected to repeated loading was examined. Portland cement was replaced by 5 and 10 % SF. Five cycles repeated loadings were applied to concrete specimens, the maximum loadings were 40 and 80 % of the axial cylinder compressive strength ( $ f_{\text{c}}^{\prime } $ ), respectively. The diffusion coefficients were calculated from the steady state in the chloride migration test using the Nernst-Planck equation. The service life of concrete in chloride environment was predicted by Life-365 model. The results indicate that the diffusion coefficients of concrete containing 5 and 10 % SF replacements are lower than that of the control concrete at the age of 28 days. This trend increases with the increase of SF replacement. Five cycles repeated loading at 40 % $ f_{\text{c}}^{\prime } $ or 80 % $ f_{\text{c}}^{\prime } $ increase the diffusion coefficients (D ₂₈) for all mixes investigated in this study. However, the effect of 80 % $ f_{\text{c}}^{\prime } $ on D ₂₈ of concrete with 10 % SF is significantly lower than that of the control concrete without SF. Compared with the control concrete without SF, 10 % SF replacements increase the service life of concrete by more than 10 times.     

Slipforming with fibre-reinforced concrete for efficient crack control

The paper presents the results of slipforming field trials carried out to investigate the potential of polypropylene fibre reinforced concrete in reducing the need for anti-cracking conventional reinforcement in slipform construction. Three trials are reported in which polypropylene fibre reinforced concrete of different strengths ranging between 43 and 54 N mm^?2 was used to replace conventional reinforcement in normal concretes. In addition steel fibre (melt-extract) reinforced concrete of strength 60 N mm^?2 was also used in one of the trials. In order to achieve optimum mix design, use was made of pulverized fuel ash, silica fume and admixtures such as superplasticizer, retarder and air entrainer as required. The results of the field trials confirm the promising potential of fibre-reinforced concrete in eliminating the need for conventional anti-cracking reinforcement in slipform construction.