An n-layered spherical inclusion model for predicting the elastic moduli of concrete with inhomogeneous ITZ

An n-layered spherical inclusion model is presented in this paper for predicting the elastic moduli of concrete with inhomogeneous interfacial transition zone (ITZ). In this model, concrete is represented as a three-phase composite material, composed of the aggregate, bulk paste, and an inhomogeneous ITZ. An analytical solution for the ITZ volume fraction is derived for the general aggregate gradation. By constituting a semi-empirical initial cement gradient model, the local water/cement ratio, degree of hydration, and porosity at the ITZ are estimated. The inhomogeneous ITZ is then divided into a series of homogenous concentric shell elements of equal thickness. The elastic moduli of concrete are determined by solving the n-layered spherical inclusion problem. Finally, the validity of the model is verified with three independent sets of experimental data and the effects of the maximum aggregate diameter, aggregate gradation, and ITZ thickness on the Young’s modulus of concrete are evaluated in a quantitative manner. The paper concludes that the proposed n-layered spherical inclusion model can be used to predict the elastic moduli of concrete.     

考虑不均匀界面时混凝土弹性模量预测

提出了考虑不均匀界面时混凝土弹性模量预测的解析法。根据界面层上水泥颗粒的分布特性, 给出了界面层上任一点处的局部水灰比和孔隙率。将不均匀界面层划分成一系列同心球壳单元, 通过反演方法确定了每个球壳单元和水泥石基体的弹性模量。将三相混凝土分解成一系列两相复合子结构, 应用两相复合球模型的正确解导出混凝土弹性模量。通过与文献中的两组实验结果比较验证了本文方法的有效性。数值结果表明, 对于给定的骨料体积分数, 混凝土弹性模量随着最大水泥颗粒直径和水灰比的增大而减小, 但随着最大骨料直径的增大而增大, 骨料级配对混凝土弹性模量也有一定的影响。      

混凝土杨氏模量预测的三相复合球模型

提出了混凝土杨氏模量预测的三相复合球模型。在细观水平上将混凝土看成是一种由分散相骨料、中间相界面和连续相水泥浆所组成的三相复合材料。应用混凝土细观结构模拟技术, 获得了任一级配骨料的界面体积分数。模拟结果表明, 李氏近似法高估了界面体积分数, 界面体积分数在很大程度上取决于界面厚度、最大骨料直径和骨料级配。引入三相复合球模型, 给出了混凝土杨氏模量的解析解。将解析解与实验结果进行比较, 证实了本文模型的有效性。数值结果也表明, 对于给定的骨料体积分数, 混凝土杨氏模量随着最大骨料直径和界面杨氏模量的增大而增大, 但随着界面厚度的增大而减小, 骨料级配对混凝土杨氏模量也有较大影响。     

Influence of aggregate content on the migration coefficient of concrete materials using electrochemical method

In order to investigate the effect of coarse aggregate content on the chloride ion migration coefficient of concrete, specimens with different coarse aggregate volume fractions and two water/cement (w/c) ratios of mortar matrix were used. The chloride ion migration coefficient of concrete is obtained using the electrochemical technique to accelerate chloride ion migration in cement-based material and the experimental results were plotted as a function of the fine aggregate volume fraction. The results are analyzed comparing experimental results and theoretical models that represent the concretes as three-phase composite materials. The three phases are the mortar matrix, the coarse aggregate, and the interfacial transition zone between the two. The chloride ion migration coefficient is used to assess the dilution, tortuosity, interfacial transition zone (ITZ) and, percolation effects of coarse aggregate in concrete. It appears that the dilution and tortuosity effects are a dominant factor affecting the chloride ion migration coefficient of concrete in the low volume fraction of coarse aggregate. As the volume fraction of coarse aggregate increases to 40 and 20% in concrete of w/c ratio 0.35 and 0.45, respectively, the ITZ with percolation effects are significantly.     

低应力水平下混凝土中氯离子扩散行为多尺度分析方法

混凝土的扩散渗透性能与其微观结构（包括细观尺度上粗骨料颗粒与砂浆之间的界面过渡区及砂浆本身的微观结构等）密切相关。在微观尺度上,砂浆和界面过渡区均可视为由无孔砂浆基质和孔隙水夹杂相组成的两相复合材料,二者的主要区别表现为孔隙率不同。在外荷载作用下,砂浆和界面过渡区的毛细孔隙率及孔隙连通性会发生改变,从而改变混凝土的扩散渗透性能。基于此,该文建立了低应力水平下混凝土中氯离子扩散行为多尺度理论分析方法,获得了混凝土表观扩散系数与外荷载（以体应变表征）及砂浆和界面过渡区当前孔隙率的定量关系。分析所采用的主要参数为砂浆和界面过渡区的毛细孔隙率、无孔砂浆基质和骨料相的力学参数、骨料相和界面过渡区的体积分数、外荷载等。与已有文献数据对比知,该文分析结果与之吻合良好,表明了理论分析方法的合理性与准确性。此外,基于该方法,探讨分析了混凝土微/细观结构对其宏观扩散性能的影响。     

核电厂预应力混凝土安全壳中氯离子扩散系数的预测方法EI北大核心CSCD

氯离子扩散系数是评价沿海环境中核电厂预应力混凝土安全壳耐久性的重要参数。该文基于两尺度方法,通过分析双轴等压下水泥浆基体、界面和混凝土细观结构,建立了水泥浆基体和界面毛细孔隙率与预应力之间的定量关系。为了量化预应力对微裂纹闭合、产生和扩展的影响,提出了临界毛细孔隙率与预应力之间的经验公式。将混凝土模拟成由骨料、界面和水泥浆基体组成的三相复合材料,获得预应力混凝土氯离子扩散系数比。通过与试验结果比较,校正了经验公式中的两个参数。用三组试验数据初步验证了该预测方法的有效性。     

Modeling the elastic properties of concrete composites: Experiment,differential effective medium theory,and numerical simulation

Concrete is a mixture of cement, water and aggregates. In terms of microstructure, besides the cement paste matrix and aggregate inclusions, there is a third phase, which is called the interfacial transition zone (ITZ), which forms due to the wall effect and can be thought of as a thin shell that randomly forms around each aggregate. Thus, concrete can be viewed as a bulk paste matrix containing composite inclusions. To compute the elastic properties of a concrete composite, a differential effective medium theory (D-EMT) is used in this study by assigning elastic moduli to corresponding bulk paste matrix, ITZ and aggregate. In this special D-EMT, each aggregate particle, surrounded by a shell of ITZ of uniform thickness and properties, is mapped onto an effective particle with uniform elastic moduli. The resulting simpler composite, with a bulk paste matrix, is then treated by the usual D-EMT. This study shows that to assure the accuracy of the D-EMT calculation, it is important to consider the increase in the water:cement mass ratio (w/c) of the ITZ and the corresponding decrease in w/c ratio of the bulk matrix. Because of this difference in w/c ratio, the contrast of elastic moduli between the ITZ and the bulk paste matrix needs to be considered as a function of hydration age. The Virtual Cement and Concrete Testing Laboratory (VCCTL) cement hydration module is used to simulate the microstructure of cement paste both inside and outside the ITZ. The redistribution of calcium hydroxide between ITZ and bulk paste regions can further affect the elastic contrast between ITZ and bulk paste. The elastic properties of these two regions are computed with a finite element technique and used as input into the D-EMT calculation. The D-EMT predictions of the elastic properties of concrete composites are compared with the results measured directly with a resonant frequency method on corresponding composites. This comparison shows that the D-EMT predictions agree well with experimental measurements of the elastic properties of a variety of concrete mixtures.     

荷载作用下饱和水泥浆体中氯离子扩散性能研究

混凝土类水泥浆复合材料中各种尺度的孔隙,如凝胶孔、毛细孔、掺入的气体气泡以及微裂纹等影响着氯离子的扩散性能。孔隙结构参数(如孔隙率)在外荷载作用下会产生变化,进而影响了水泥浆体中氯离子扩散性能。外荷载作用对氯离子扩散行为的影响,可以等效为外荷载所引起的孔隙率的改变对氯离子扩散性能的影响。从微观角度出发,将饱和水泥浆体看作由水泥浆体基质(其孔隙率为零)和孔隙水夹杂相所组成的两相复合材料介质。基于弹性力学理论推导并获得了饱和水泥浆体达到其强度前(即未产生新裂纹前)当前孔隙率与材料初始孔隙率及体应变之间的定量关系,得到了水泥浆体中氯离子扩散系数与这些参数的定量关系。基于Fick第二定律分析了外荷载(体应变)和孔隙率变化对氯离子扩散性能的影响。研究表明:氯离子在饱和砂浆中的扩散系数随孔隙率增大而显著增大;氯离子在砂浆中的扩散系数随压缩体应变的增大而减小,随拉应变增大而增大。     

Influence of internal curing using lightweight aggregates on interfacial transition zone percolation and chloride ingress in mortars

The microstructure of the interfacial transition zone (ITZ) between cement paste and aggregate depends strongly on the nature of the aggregate, specifically its porosity and water absorption. Lightweight aggregates (LWA) with a porous surface layer have been noted to produce a dense ITZ microstructure that is equivalent to that of the bulk cement paste, as opposed to the more porous ITZ regions that typically surround normal weight aggregates. This ITZ microstructure can have a large influence on diffusive transport into a concrete, especially if the individual ITZ regions are percolated (connected) across the three-dimensional microstructure. In this paper, the substitution of LWA sand for a portion of the normal weight sand to provide internal curing (IC) for a mortar is examined with respect to its influence on ITZ percolation and chloride ingress. Experimental measurements of chloride ion penetration depths are combined with computer modeling of the ITZ percolation and random walk diffusion simulations to determine the magnitude of the reduced diffusivity provided in a mortar with IC vs. one with only normal weight sand. In this study, for a mixture of sands that is 31% LWA and 69% normal weight sand by volume, the chloride ion diffusivity is estimated to be reduced by 25% or more, based on the measured penetration depths.     

Influence of aggregate content on the percolated interfacial transition zone of cement‐based materials by using accelerated chloride migration test

Abstract

In this study, the effect of the aggregate content on the chloride migration coefficient at the percolated interfacial transition zone (ITZ) was studied in cement‐based materials. Specimens with three different water‐to‐cement ratios and five different aggregate volume fractions were used. The chloride migration coefficient was measured with the accelerated chloride migration test (ACMT). A three‐phase composite model was used to determine the approximate chloride migration coefficient at the percolated ITZ. The results showed that the approximate chloride migration coefficient at the percolated ITZ increased significantly as more rod‐shaped aggregate was used in the mortar.     

On the relative use of micro-mechanical lattice analysis of 3-phase particle composites

In this paper results obtained from analyses made using a beam lattice model are presented and discussed. The material system studied is a 3-phase particle composite where stiff and strong aggregate particles are embedded in a weaker and softer cement matrix. A third phase exists between these two phases, namely a thin zone enveloping the aggregate particles. This thin zone of extremely weak material is the interfacial transition zone (ITZ). In the composite either the ITZ phase or the matrix phase may percolate. It is shown that the macroscopic behavior of the composite differs significantly when the internal material geometry varies, either by changing the particle density or by varying the ITZ thickness. The results from these analyses could, after an extensive verification/falsification experimental phase, help to construct realistic macroscopic fracture models, [Van Mier JGM. Reality behind fictitious cracks? In: Li VC, Leung CKY, Willam KJ, Billington SL, editors. Proceedings of the 5th international conference on ‘Fracture of concrete and concrete structures’ (FraMCoS-V). Evanston, (IL): IA-FraMCoS; 2004. p.11-30], and might point towards new ways to improve the material.     

Meso-scale numerical investigation on cracking of cover concrete induced by corrosion of reinforcing steel

Concrete cover cracking induced by corrosion of steel reinforcement is a major influencing factor for durability and serviceability of reinforced concrete structures. Here in this study, the influence of concrete meso-structure on the failure pattern of concrete cover is accounted for. The concrete is assumed to be a three-phase composite composed of aggregate, mortar matrix and the interfacial transition zone (ITZ). And a concrete random aggregate structure is established for the study on the mechanical behavior of radial corrosion expansion. In the present simulations, the plasticity damaged model is used to describe the mechanical behavior of the mortar matrix and the ITZ, and it is assumed that the corrosion of steel reinforcement is uniform. The cracking of concrete cover due to steel reinforcement corrosion is numerically simulated. The simulation results have a good agreement with the available test data and they are between the two analytical results. The failure patterns obtained from the macro-scale homogeneous model and the meso-scale heterogeneous model are compared. Furthermore, the influences of ratio of cover thickness and reinforcement diameter (i.e. c/d), the location of the steel reinforcement (i.e., placed at the middle and corner zones) and the concrete tensile strength on the steel corrosion rate when the concrete cover cracks are investigated. Finally, some useful conclusions are drawn.     

The ITZ microstructure,thickness and porosity in blended cementitious composite: Effects of curing age,water to binder ratio and aggregate content

Due to its higher porosity, the interfacial transition zone (ITZ) in cementitious composite is often considered as a weak phase, compared to aggregate and bulk paste. In this paper, we present some results of a study on the ITZ including microstructure, thickness and porosity for the case of a ternary blended cementitious system, i.e., Portland cement, blast furnace slag and limestone filler. In particular, based on the backscattered electron image analysis and the HYMOSTRUC model, the ITZ microstructure, thickness and porosity are investigated in an elaborative way. The effects of casting factors such as curing age, water to binder (w/b) ratio and aggregate content are discussed, and two new formulas are proposed to fit the ITZ thickness and porosity. Results indicate that curing age influences both the ITZ thickness and porosity, while w/b ratio and aggregate content only influence the ITZ porosity.     

Computational homogenization of diffusion in three-phase mesoscale concrete

A three dimensional (3D) mesoscale model of concrete is presented and employed for computational homogenization in the context of mass diffusion. The mesoscale constituents of cement paste, aggregates and interfacial transition zone (ITZ) are contained within a statistical volume element (SVE) on which homogenization is carried out. The model implementation accounts for ITZ anisotropy thereby the diffusivity tensor depends on the normal of the aggregate surface. The homogenized response is compared between 3D and 2D SVEs to study the influence of the third spatial dimension, and for varying mesoscale compositions to study the influence of aggregate content on concrete diffusivity. The computational results show that the effective diffusivity of 3D SVEs is about 40 % greater than 2D SVEs when ITZ is excluded for the SVE, and 17 % when ITZ is included. The results are in agreement with the upper Hashin–Shtrikman bound when ITZ is excluded, and close to the Taylor assumption when ITZ is included.     

A stochastic second‐order and two‐scale thermo‐mechanical model for strength prediction of concrete materials

A stochastic thermo‐mechanical model for strength prediction of concrete is developed, based on the two‐scale asymptotic expressions, which involves both the macroscale and the mesoscale of concrete materials. The mesoscale of concrete is characterized by a periodic layout of unit cells of matrix‐aggregate composite materials, consisting of randomly distributed aggregate grains and cement matrix. The stochastic second‐order and two‐scale computational formulae are proposed in detail, and the maximum normal stress is assumed as the strength criterion for the aggregates, and the cement paste, in view of their brittle characteristics. Numerical results for the strength of concrete obtained from the proposed model are compared with those from known experiments. The comparison shows that the proposed method is validated for strength prediction of concrete. The proposed thermo‐mechanical model is also employed to investigate the influence of different volume fraction of the aggregates on the strength of concrete. Copyright © 2016 John Wiley & Sons, Ltd.     

水泥基复合材料界面过渡区体积分数的定量计算

借助邻近函数公式, 给出了水泥基复合材料集料与浆体间界面过渡区体积分数的定量计算公式, 并采用随机点采样方法验证采用该定量公式计算水泥基复合材料界面过渡区体积分数的可行性。在此基础上, 预测了由符合Fuller 分布的集料制备的混凝土中界面过渡区体积分数随集料体积分数和集料粒径范围的变化曲线。讨论了界面厚度变化、集料体积分数变化以及集料粒径分布变化对界面过渡区体积分数影响的差别, 并给出了衡量界面过渡区重叠程度的定性和定量方法。结果表明: 在常规集料体积分数下, 三者中对界面过渡区体积分数以及界面过渡区重叠程度影响的主次顺序均为: 界面过渡区厚度变化带来的影响> 集料体积分数变化带来的影响> 集料细度变化带来的影响。      

Influence of surface charge on ingress of chloride ion in hardened pastes

The amount of free chloride content in concrete is one of major factors in initiating the corrosion process. The material and environmental factors play a key role in diffusing the chloride ion through the cover concrete to reinforcement. Thus, the electrochemical study is indispensable to understand the mechanism of chloride ingress into concrete. Determination of surface charge and its influence on diffusion of chloride ion into cement matrix of concrete are researched for Ordinary Portland Cement (OPC) paste and cement paste containing Ground Granulated Blastfurnace Slag (GGBS). Different kinds of experiments such as measurement of membrane potential, determination of porosity and pore size distribution, determination of pore solution concentration, and steady state diffusion coefficient of chloride and sodium ions are employed to understand the mechanism of chloride ingress. The obtained results show that the positive surface charge on the pore walls of hardened paste regardless of GGBS’s presents. The surface charge of hardened paste mainly depends on pore solution concentration and cement composition. The physiochemical characteristics of the pores are affecting on transporting ions through it. Hardened paste has greater resistance to diffusing sodium ions than chloride ions. Moreover, there is a strong interaction between transport of chloride ion and surface charge in matured hardened paste.     

Influence of interface properties on fracture behaviour of concrete

Hardened concrete is a three-phase composite consisting of cement paste, aggregate and interface between cement paste and aggregate. The interface in concrete plays a key role on the overall performance of concrete. The interface properties such as deformation, strength, fracture energy, stress intensity and its influence on stiffness and ductility of concrete have been investigated. The effect of composition of cement, surface characteristics of aggregate and type of loading have been studied. The load-deflection response is linear showing that the linear elastic fracture mechanics (LEFM) is applicable to characterize interface. The crack deformation increases with large rough aggregate surfaces. The strength of interface increases with the richness of concrete mix. The interface fracture energy increases as the roughness of the aggregate surface increases. The interface energy under mode II loading increases with the orientation of aggregate surface with the direction of loading. The chemical reaction between smooth aggregate surface and the cement paste seems to improve the interface energy. The ductility of concrete decreases as the surface area of the strong interface increases. The fracture toughness (stress intensity factor) of the interface seems to be very low, compared with hardened cement paste, mortar and concrete.     

干湿循环作用下水泥基复合材料抗氯离子侵蚀性能及其微观结构变化

为了进一步揭示干湿循环条件下氯离子对水泥基复合材料的侵蚀机制,分别研究了两种水灰比水泥混凝土、砂浆及净浆三种层次试件在干湿循环条件下的抗氯离子侵蚀性能。结果发现,干湿循环作用能促进氯离子入侵速度,增加氯离子入侵深度和浓度,并且水胶比越大,干湿循环作用影响效果越明显;掺入矿粉能增加水泥基复合材料抗氯离子入侵性能,并且降低干湿循环作用的影响效果。净浆样品侵蚀前后的微观结构变化表明,干湿循环作用下,经氯盐侵蚀后水泥基复合材料净浆试件表层明显有Friedel盐生成,而矿粉的加入明显增加了样品中Friedel盐的生成量。     

An analytical solution for hydraulic conductivity of concrete considering properties of the Interfacial Transition Zone (ITZ)

As a composite material, hydraulic conductivity of concrete depends on conductivity of its components that are the mortar, aggregates and the Interfacial Transition Zone (ITZ). Since hydraulic conduction is analogous to heat and electrical conduction, analytical models from these analogous areas relating effective conductivity of composite to conductivity of its components can be used to find the effective hydraulic conductivity of concrete as a function of properties of its components, i.e., aggregate, mortar and the ITZ. However, effect of the conduction in the ITZ has not been considered in these models. This paper presents an analytical solution for the hydraulic conductivity of concrete as a three-phase composite material. The solution is an extension to the model originally proposed for conduction of composite media with randomly suspended spheres. Results of the proposed model compare well against the experimental results and those obtained from rigorous numerical analysis using the Finite Element (FE) method. The principal significance of this study lies in the development of a versatile analytical model that can be employed as a quick tool for assessment of hydraulic conductivity of concrete without the need for sophisticated FE models at the meso-scale level. It offers more insight into effect of different components of concrete on its overall conductivity.