疲劳荷载与氯盐耦合作用下混凝土中氯离子扩散行为的试验研究

混凝土桥梁在服役过程中经常同时承受疲劳荷载和氯离子侵蚀,但现有研究多未考虑疲劳和氯离子侵蚀的耦合作用。本文研究了疲劳荷载与氯盐侵蚀耦合作用下混凝土中氯离子的扩散行为,并运用超声检测表征混凝土的疲劳损伤,以建立疲劳损伤与氯离子扩散性能之间的关系。研究结果表明:随着疲劳压应力水平提高,超声参数表征的混凝土损伤值也逐渐增大;应力水平低于0.4时,不同疲劳应力水平对混凝土中氯离子浓度分布没有明显影响,氯离子扩散系数甚至略有减小,这应是应力水平较低时混凝土中微孔隙和裂缝被压缩而降低了氯离子的扩散能力;应力水平为0.5及0.6时,混凝土中氯离子浓度显著提高,扩散系数明显增大,并且与应力水平呈正相关;超声参数表征的混凝土损伤与氯离子渗透性的发展趋势不一致,表明由于混凝土内部缺陷分布的不均匀性使得超声技术难以定量表征荷载引起的混凝土损伤。     

Chloride diffusion in porous concrete under conditions of variable temperature

A diffusion model is presented in this study for describing diffusion of chloride ion in porous concrete under nonisothermal conditions. The process is to simulate chloride diffusion in concrete exposed to daily cyclic temperature change. The effects of cyclic and constant temperatures on the chloride diffusion behavior in concretes are investigated. The time for chloride concentration to reach the corrosion threshold of the reinforcing steel is determined for a given water-to-cement ratio and thickness of concrete layer. Results indicate that the temperature and water-to-cement ratio play a vital role in governing the chloride diffusion process.

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Chlorid-Diffusion in porösem Beton unter dem Einfluß von Temperaturänderungen

Zusammenfassung Es wird ein Diffusionsmodell vorgestellt, das die Diffusion von Chloridionen in porösem Beton unter nichtisothermen Bedingungen beschreiben soll, wobei sowohl die täglichen zyklischen, wie auch sprunghaften Temperaturänderungen zugrunde gelegt werden. Berechnet wird die Zeitspanne bis zum Erreichen der Korrosionsschwelle an der Stahlarmierung, und zwar als Funktion des Wasser-Zement-Verhältnisses und der Schichtdicke des Betons. Die Ergebnisse zeigen, daß der Chlorid-Diffusionsprozeß hauptsächlich vom Temperatur- und Wasser-Zement-Verhältnis regiert wird.

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Nomenclature b amplitude parameter in the cyclic temperature function - C chloride concentration - Cp specific heat capacity - D effective chloride diffusion coefficient - D _o preexponential factor - E activation energy - k thermal conductivity of concrete - L thickness of concrete slab - R gas constant - t time - T temperature - T _o initial temperature - w water-to-cement ratio - x spatial coordinate - thermal diffusivity,k/( Cp) - density of concrete     

A new procedure to measure effective molecular diffusion coefficients of salts solutions in building materials

The aim of this work is to present a mathematical and experimental formulation of a new simple procedure for the measurement of effective molecular diffusion coefficients of a salt solution in a water-saturated building material. This innovate experimental procedure and mathematical formulation is presented in detail and experimental values of “effective” molecular diffusion coefficient of sodium chloride in a concrete sample (w/c = 0.45), at five different temperatures (between 10 and 30 °C) and four different initial NaCl concentrations (between 0.1 and 0.5 M), are reported. The experimental results obtained are in good agreement with the theoretical and experimental values of molecular diffusion coefficient presented in literature. An empirical correlation is presented for the prediction of “effective” molecular diffusion coefficient over the entire range of temperatures and initial salt concentrations studied.     

Modeling the Chlorides Transport in Cementitious Materials By Periodic Homogenization

In this work, we develop a macroscopic model for diffusion–migration of ionic species in saturated porous media, based on periodic homogenization. The prior application is chloride transport in cementitious materials. The dimensional analysis of Nernst–Planck equation lets appear dimensionless numbers characterizing the ionic transfer in porous media. Using experimental data, these dimensionless numbers are linked to the perturbation parameter ${\varepsilon}$ . For a weak-imposed electrical field, or in natural diffusion, the asymptotic expansion of Nernst–Planck equation leads to a macroscopic model coupling diffusion and migration at the same order. The expression of the homogenized diffusion coefficient only involves the geometrical properties of the material microstructure. Then, parametric simulations are performed to compute the chloride diffusion coefficient through different complexity of the elementary cell to go on as close as possible to experimental diffusion coefficient of the two cement pastes tested.     

Experimental determination of the diffusion coefficients of wood in isothermal conditions

The diffusion coefficients of frake (Terminalia superba) were determined in the radial, tangential, and longitudinal directions at tree different temperatures: 30°C, 35°C an 40°C. The longitudinal diffusion coefficient is larger than the transverse diffusion coefficient. In addition the radial coefficient is larger than the tangential coefficient.     

Articular cartilage with intra- and extrafibrillar waters – mass transfer and generalized diffusion

The present analysis complements the chemo-mechanical model of articular cartilage developed in Loret and Simões [Loret, B., Simões, F.M.F., 2004. Articular cartilage with intra- and extrafibrillar waters. A chemo-mechanical model. Mech. Mater. 36 (5–6), 511–541; Loret, B., Simões, F.M.F., 2005a. Mechanical effects of ionic replacements in articular cartilage. Part I – The constitutive model. Biomech. Model. Mechanobiol. 4 (2–3), 63–80. Part II – Simulations of successive substitutions of NaCl and CaCl₂, 81–99], where only equilibria were considered, and therefore time was absent. The focus here is, first, to present how transport phenomena are aggregated to the porous media framework, and, second, to detail the constitutive equations of these transports. Indeed, these equations are developed in the context of a three-phase multi-species electro-chemo-mechanical model that accounts for the effects of two water compartments, namely intrafibrillar water stored between collagen fibrils and extrafibrillar water covering the negatively charged proteoglycans. The electrolyte circulating the two fluid phases contains ions sodium Na⁺, calcium Ca²⁺ and chloride Cl⁻.Species diffuse within their phase. They transfer from one fluid phase to the other. The various sources of dissipation are built in a thermodynamic framework, segregated and decoupled via the Clausius–Duhem inequality.Linear and non-linear equations of mass transfer are proposed along an onsagerist approach.The generalized diffusion in the extrafibrillar compartment accounts for Darcy's law of seepage through the porous solid skeleton, Fick's law of ionic diffusion, and Ohm's law of electric flow. An original derivation of the constitutive equations of generalized diffusion is proposed. Indeed, the dissipation inequality is written in two forms, which are required to be equivalent. This approach has the advantage of delivering the general structure of the diffusion matrix. It also displays in explicit form the degrees of freedom for possible refinements. Simple assumptions, phrased in terms of entities that are standard in transport of porous media, allow to recover arrowhead diffusion matrices. Comparison with an earlier proposal is detailed.An osmotic coefficient is found to be hidden in the equations, and anomalous negative osmosis is observed to take place for both sodium chloride and calcium chloride electrolytes.Finally, an experimental setup to measure transport properties is analyzed. The model describes correctly the increase and leveling of the experimental diffusion coefficient, and no additional ad hoc constitutive assumptions are needed in contrast to some suggestions in the literature.The results are presented for sodium chloride NaCl and calcium chloride CaCl₂.     

Quantification of Density-Driven Natural Convection for Dissolution Mechanism in CO<Subscript>2</Subscript> Sequestration

Dissolution of CO₂ into brine causes the density of the mixture to increase. The density gradient induces natural convection in the liquid phase, which is a favorable process of practical interest for CO₂ storage. Correct estimation of the dissolution rate is important because the time scale for dissolution corresponds to the time scale over which free phase CO₂ has a chance to leak out. However, for this estimation, the challenging simulation on the basis of convection–diffusion equation must be done. In this study, pseudo-diffusion coefficient is introduced which accounts for the rate of mass transferring by both convection and diffusion mechanisms. Experimental tests in fluid continuum and porous media were performed to measure the real rate of dissolution of CO₂ into water during the time. The pseudo diffusion coefficient of CO₂ into water was evaluated by the theory of pressure decay and this coefficient is used as a key parameter to quantify the natural convection and its effect on mass transfer of CO₂. For each experiment, fraction of ultimate dissolution is calculated from measured pressure data and the results are compared with predicted values from analytical solution. Measured CO₂ mass transfer rate from experiments are in reasonable agreement with values calculated from diffusion equation performed on the basis of pseudo-diffusion coefficient. It is suggested that solving diffusion equation with pseudo diffusion coefficient herein could be used as a simple and rapid tool to calculate the rate of mass transfer of CO₂ in CCS projects.     

The maximal Lyapunov exponent of a co-dimension two-bifurcation system excited by a bounded noise

In the present paper,the maximal Lyapunov exponent is investigated for a co-dimension two bifurcation system that is on a three-dimensional central manifold and subjected to parametric excitation by a bounded noise.By using a perturbation method,the expressions of the invariant measure of a one-dimensional phase diffusion process are obtained for three cases,in which different forms of the matrix B,that is included in the noise excitation term,are assumed and then,as a result,all the three kinds of singular boundaries for one-dimensional phase diffusion process are analyzed.Via Monte-Carlo simulation,we find that the analytical expressions of the invariant measures meet well the numerical ones.And furthermore,the P-bifurcation behaviors are investigated for the one-dimensional phase diffusion process.Finally,for the three cases of singular boundaries for one-dimensional phase diffusion process,analytical expressions of the maximal Lyapunov exponent are presented for the stochastic bifurcation system.     

Coupled Water and Salt Transport in Porous Materials: Rapid Determination of a Varying Diffusion Coefficient from Experimental Data

A direct method for an accurate and rapid evaluation of a varying salt diffusion coefficient, \(D\) , from experimental data is proposed for a coupled water and salt transport in porous materials. The evaluation uses data on the moisture and salt concentration profiles and is based on a formula obtained from the Boltzmann-Matano method. The coupled transport is described by the diffusion-advection model of Bear and Bachmat. A simple expression for \(D\) in the center of the concentration interval is deduced from the formula to provide a rapid estimate on \(D\) . Possible extensions of this analytical approach are pointed out, suggesting that it can serve as a convenient general tool in engineering calculations. The theoretical results are applied to a laboratory experiment in which a coupled moisture and chloride transport had been investigated in a lime plaster, and the chloride diffusion coefficient had been obtained numerically in dependence on the chloride concentration. The agreement with the numerical results is shown to be rather good, except at low concentrations where our analytical results should be more reliable. It is also shown that the unusually high value of the calculated chloride diffusion coefficient—about three orders of magnitude higher than for free chloride ions in water—cannot be explained by possible inaccuracies in the measurements and/or numerical calculations. The reason is that changes in the measured profiles’ data could cause a change in \(D\) of just the same order of magnitude. This shows that, besides diffusion and advection, additional mechanisms take part in the considered chloride transport.     

Effects of the method of identification of the diffusion coefficient on accuracy of modeling bound water transfer in wood

An alternative approach to determining the bound water diffusion coefficient is proposed. It comprises a method for solving the inverse diffusion problem, an improved algorithm for the bound-constrained optimization as well as an alternative submodel for the diffusion coefficient’s dependency on the bound water content. Identification of the diffusion coefficient for Scots pine wood (Pinus sylvestris L.) using the proposed inverse approach is presented. The accuracy of predicting the diffusion process with the use of the coefficient values determined by traditional sorption methods as well as by the inverse modeling approach is quantified. The similarity approach is used and the local and global relative errors are calculated. The results show that the inverse method provides valuable data on the bound water diffusion coefficient as well as on the boundary condition. The results of the identification can significantly improve the accuracy of mass transfer modeling as studied for drying processes in wood.