Mechanics and Physics of Creep, Shrinkage, and Durability of Concrete: A Tribute to Zdeněk P. Bažant

This keynote lecture presents a broad, yet concise, overview of the advances at Northwestern University since ConCreep-8, triggered by the success in 2008 in enforcing the release of the (legally sealed) data on the tragic 1996 collapse and the preceding, grossly excessive, deflections of the record-span segmental box-girder bridge in Palau. Subsequent analysis put the main blame for the excessive deflections on wrong design codes or recommendations. This revelation stimulated an extensive effort, generously funded by DoT and NSF, to advance the knowledge of concrete creep. First, several advances, presented in detail in other papers at ConCreep-9, are briefly reviewed; they include: 1) assembly of a greatly enlarged database of laboratory creep and shrinkage data for various concretes, with and without admixtures; 2) collection of a database on deflections of 69 segmental bridges, mostly excessive; 3) development of an improved creep and shrinkage prediction model (labeled "B4") and its joint statistical calibration by both databases; 4) improved rate-type algorithm for creep analysis in which the inverse Laplace transform is used in each time step to obtain the current retardation spectrum; 5) a realistic viscoplastic constitutive law for prestressing steel, applicable to time-varying strain and temperature; and 6) an improved algebraic formula for converting the aging compliance function to the relaxation function. Development of new formula for cyclic creep is described next, in detail. The formula is derived from Paris' law for the growth of micrometer size cracks. Its consequences for segmental bridges of various spans are discussed. The final discussion outlines new theoretical results showing that one mechanism causing the hysteresis of nanopore water sorption-desorption isotherms consists of snap-through instabilities of water content, and of molecular coalescence. The nanopore water content matters for the disjoining pressure and the corresponding microprestress which destabilizes the bonds whose ruptures and restorations cause creep.

Small-angle X-ray scattering (SAXS) and small-angle neutron scattering (SANS) are widespread experimental tools for the investigation of the microstructure of random heterogeneous materials such as granular porous media. Such experiments allow operating on macroscopic samples and provide quantitative 3D information at length-scales between 1 and 500 nm while keeping sample preparation to a minimum. SANS or SAXS can also be considered as fingerprints of the morphology, allowing to test and to discard some microstructure hypotheses. In this presentation, an analysis of various reconstructed, polydisperse, granular, porous media is proposed. The evolution of the computed small angle scattering with the level and the nature of the polydispersity (ranging from monodisperse to very large polydispersity) are presented. Finally, our results are critically analyzed and reviewed in the perspective of hardened cement pastes.

Mechanical and viscoelastic behavior of cement crucially depends on the Calcium-Silicate-Hydrate (C-S-H) gels, the "glue" of cement, and on the slow evolution (aging) of its local composition and morphology. Hence, design of high performance and more environmentally friendly cement demands a deeper understanding of physical processes underlying the precipitation process, when the C-S-H gel develops, and cement sets. C-S-H gel forms and become denser by precipitation of colloidal particles of few nanometers within a couple of hours. To access the relevant length and time scale for the development of the microstructure and of the mechanical strength of C-S-H gel, we developed a coarse-grained colloidal model for precipitation of C-S-H nano-particles using a combination of Monte Carlo and Molecular Dynamics numerical simulations. The microstructure of C-S-H gel is determined by the chemical conditions and the continuous particle precipitation that drives the system out of equilibrium. In our simulations, we control the chemical conditions by the effective interaction of the C-S-H particles and the particle precipitation rate. Here, we compare results on the evolution of C-S-H microstructure for two different effective interactions that comply with experimental and theoretical finding on C-S-H, and different precipitation rates. In particular, we can monitor the development and the evolution of the microstructure and mechanical properties of C-S-H during the precipitation. Combining this information, we aim at rationalizing how the precipitation process can be tuned to control the microstructure formation and, hence, the mechanical performance of C-S-H.

Strength of cement pastes increases overlinearly with decreasing capillary porosity, such as suggested by the gel-space ratio model of Freyssinet (1933). This model, however, cannot explain that strength of mature sub-stoichiometric cement pastes increases with decreasing w/c-ratio, such as observed by Fagerlund (1972). The latter observation might well stem from a strengthening effect of unhydrated clinker grains, but until very recently an etiological model for quantification of this effect was out of reach. This provides the motivation for the present study, where we envision that the strength of microscopic cement hydrates is the limiting factor for the load carrying capacity of macroscopic cement paste samples. In more detail, we envision a stress-based strength criterion for microscopic hydrate needles, whereby the involved hydrate strength constant is determined from the results of nanoindentation experiments on low-density C-S-H, performed by Constantinides and Ulm (2006). Strength upscaling is performed within the framework of continuum micromechanics (Pichler et al., 2008-2013). Model-predicted macrostrength values of cement pastes (exhibiting different compositions and different maturities) agree very well with strength values measured at three different laboratories. The validated model confirms that strength of cement pastes is strongly influenced by capillary porosity, and that unhydrated clinker grains act as significantly strengthening reinforcements for mature substoichiometric pastes (Pichler et al. 2013).

Concrete creeps, and this creep must be well characterized and modeled to properly design civil engineering infrastructures. Here, we present some results on the creep properties of cementitious materials obtained by using the indentation technique. Firstly, we show that minutes-long microindentations on cement paste yield a quantitative measurement of their long-term logarithmic creep kinetics, which can be used to predict the rate of long-term creep of concrete. Then, by performing microindentations, we study the effect of relative humidity on the long-term creep properties of hydrated C₃S samples, compacted samples made of pure C-S-H, and compacted samples made of pure CH. The last part is dedicated to a study by nanoindentation of the creep properties of C-S-H phases directly within a hydrated cement paste. We identify scaling relations independent of mix proportion and heat treatment, which we can explain by drawing a thorough analogy between the mechanical behavior of C-S-H and that of clays.

A mesoscopic model is introduced for shear plasticity of disordered materials. Plastic deformation is assumed to result from series of local reorganizations. The structural disorder is modeled by spatial fluctuations of plastic thresholds on a discretized lattice. The elastic interaction induced by local rearrangements are described by the far-field stress induced by an Eshelby inclusion. A complex phenomenology emerges from the interplay between disorder and elastic interactions. The macroscopic yield stress can be analyzed as the critical threshold of a depinning transition. This analogy with a dynamic phase transition naturally enables to predict finite size scaling. In the same way, creep behavior of disordered solids can be analyzed as the thermal rounding of the critical transition. A logarithmic creep behavior is recovered.

Calcium Silicate Hydrate gel (C-S-H) is the main product of the cement hydration process responsible for strength and durability of concrete. While C-S-H can be obtained from Portland cement hydration, the process of hydrating cement produces other by-products such that make it difficult to characterize C-S-H solely. C-S-H is synthesized here by mixing calcium oxide (CaO) with fumed silica (SiO₂) and a large amount of deionized water (H₂O), making C-S-H slurry. Two Cao/SiO₂ mixture ratios of 1.5 and 0.7 were examined. The slurry was filtered to remove excess water for 24 hours and then dried at 11% relative humidity (RH) using Lithium Chloride for 5 weeks. The produced C-S-H powder was compacted under 400 MPa to produce C-S-H. Nano-creep of the composite C-S-H with the two calcium silica (C/S) mixture ratios was determined using nanoindentation. The experiments showed that C-S-H with 0.7 C/S has higher elastic modulus and lower creep compliance compared with C-S-H with 1.5 C/S. Microstructural investigations using ²⁹Si nuclear magnetic resonance (NMR), Transmission Electron Microscopes (TEM), Thermal Gravimetric Analysis (TGA) and X-ray diffraction (XRD) analysis were performed to explain the observations. Microstructural investigations showed a significant increase in silicate polymerization at 0.7 C/S ratio compared with 1.5 C/S. The high level of polymerization might be able to explain the reduced creep of C-S-H at low C/S ratios.

To explain the similarities between a glass and amorphous C-S-H, a C-S-H molecular structure with stoichiometry of (CaO)_1.7(SiO₂)₁(H₂O)_1.9 is produced using a mixed reactive-nonreactive force field modeling. As the consequence of reactive modeling using REAXFF potential, part of water molecules in the interlayer spacing dissociate into hydroxyl groups and proton, which produces Ca-OH bonds. In addition, it is shown that monomers condensate to produce dimmers. This reduces the monomer content and increases the mean silicate chain length. Comprehensive topological analysis is performed to identify the local environment of each atom, which is indicative of short range order in C-S-H. Specially, the topological analysis is shown to be essential to distinguish between oxygen atoms in water, hydroxyl groups, silica chain and calcium oxide sheets. The medium range order in C-S-H is shown to exist using first sharp diffraction pattern derived from structure factor calculations.

The C-S-H gel is the main constituent of cement, up to 70% of the final material. It is the phase that gives cohesion to the material and is mainly responsible for cement's properties, including creep. Understanding the intrinsic mechanical properties of the C-S-H gel and how it responds to applied load is, therefore, of vital importance for the design of the new generation of Portland Cement. However, the heterogeneous nature and characteristic length scale of the C-S-H gel makes an experimental determination of its properties very challenging. Therefore, atomic scale simulations are a valuable alternative to investigate the atomic scale forces and processes that govern creep and shrinkage. In this work, we study the mechanical processes that take place when the solid C-S-H is subject to a shear strain, using reactive force field molecular simulations. We have chosen two systems to model the C-S-H gel: the perfect mineral tobermorite and the glass-like C-S-H model developed by Pellenq, et. al. (Pellenq, et. al., 2009). First, we have computed the elastic properties of both models. Second, we investigate the global and local stresses generated in the systems under large deformations, with the aim to understand the atomic forces that govern the mechanical response of the structures. The obtained results help to understand the changes that happen in the C-S-H gel under load.

Metal-organic frameworks are a new class of microporous materials that garner a lot of attention for their potential applications in the fields of separation, strategic gas capture and storage, and catalysis. However, there is still little microscopic information available on their hydrothermal and mechanical stability, even though these properties are crucial for practical applications. In this paper, we detail our recent efforts to address these issues using a large gamut of molecular simulation methods: quantum chemistry calculations, first principles molecular dynamics and force field-based molecular dynamics.

We show how nuclear magnetic spin-lattice relaxation dispersion of proton-water (NMRD) can be used to elucidate the effect of cellulose ethers on water retention and hydration delay of freshly-mixed white cement pastes. NMRD is useful to determine the surface diffusion coefficient of water, the specific surface area and the hydration kinetics of the cement-based material. In spite of modifications of the solution's viscosity, we show that the cellulosic derivatives do not modify the surface diffusion coefficient of water. Thus, the mobility of water present inside the medium is not affected by the presence of polymer. However, these admixtures significantly modify the surface fraction of mobile water molecules transiently present at solid surfaces. This quantity measured, for the first time, for all admixed cement pastes is thus relevant to explain the water retention mechanism.

An important feature of the water sorption in cement has been the pronounced hysteresis. The hysteresis in capillary pores has been explained by so-called "ink-bottles" theory and/or the meniscus theory. In contrast, the hysteresis in gel pores (nanopores) received little attention. This paper investigated the sorption hysteresis in cement slits via atomistic simulations. Tobermorite 11 was adopted to represent the cement atomistic structures. In order to create the surface for adsorption, the Wollastonite chains in Tobermorite 11 were removed and the dangling bonds were saturated with hydrogen atoms. Charges were balanced to be neutral for the whole simulation cell. The sorption isotherms were calculated using the Sorption module in Material Studio (a commercial software for MD simulations), which calculates adsorption isotherms for water in the pores from a series of fixed pressure simulations. Three Tobermorite11 slits of widths H = 10 Å, 20 Å and 30 Å were studied. The temperature was kept at 298 K. The results for all three slits showed significant and slit-size-dependent hysteresis sorption-desorption loops. The hysteresis shrinks when the width of the slits decreases. The role of Coulomb interaction in the hysteresis, as well as the water molecular density within the slits, were discussed. The results on sorption hysteresis in nano slits can be used to revise/refine the existing water hysteresis models for cement and concrete. This paper provides the pathway towards a better understanding of creep and drying shrinkage of ordinary Portland cement on the nanoscale.

Sorption isotherms are frequently used to characterize the structure of porous materials such as cement. Their interpretation has been somewhat hindered by the large hysteresis observed between the adsorption and desorption processes. Here, we model the hysteresis due to pore blocking, whereby water condensed in small pores prevents propagation of a vapour interface into the pore structure, trapping water condensed in larger pores in a metastable state. The model identifies the adsorption isotherm as more useful in determining the pore size distribution. Additionally, and of particular interest, it provides a way of calculating an additional structural parameter, quantifying the exposure of mesopores (gel pores) to the surrounding atmosphere. This exposure is higher for samples with higher water-to-cement ratio, suggesting that it is mediated by capillary pores. The model also allows calculation of the connectivity of the pore structure, although the intertwined influences of exposure and connectivity make the latter difficult to interpret.

We show how the pore size and relative humidity are two competitive confinement factors that control the multi-scale water transport in disordered materials. These factors are characterized by proton NMR spectroscopy, relaxometry and diffusometry as well as conductivity and X-ray micro-tomography. We first use MCM41, calibrated, micro-porous silicates to focus on the drastic impact of the pores sizes on the moisture transport at micro-scales. Then, we use synthetized control pore glass (CPG) with controlled meso- and macro-pore networks for illustrating the impact of the relative humidity on the moisture transport. These two limiting factors allow understanding of the two power-law behaviors found in NMR relaxation distributions used as a robust tool for studying the aging process of cement-based materials. We believe that this approach can be extended to a large class of multi-scale porous materials.

Cement paste has a complex mesoscale structure, and small changes in its pore network potentially cause large variation in measurements such as the water isotherm (also nitrogen). We deconvolute the water isotherm with the help of advanced computational techniques, hypotheses, and a re-examination of published data. The pore system is divided into four different categories, each containing water with its own physical properties. By viewing the highly interdependent roles of water in each of the pore categories as a system, new insights are gained regarding possible mechanisms that control drying, shrinkage, and creep, and experimental strategies for verification.

The experiments were comprised of diffusion cell tests and mortar bar tests with sodium silicate (Na₂SiO₃) and lithium silicate (Li₂SiO₃) solutions, followed by a range of post-analyses such as DSC, XRD and EPMA. The diffusion coefficients of Na⁺ ions were 10 times more than Li⁺ ions. This result shows that lithium ions are better adsorbed into cement hydration products. The results of mortar bar tests backed up this finding. It was observed that, regardless of Li₂SiO₃ concentration, the specimens did not expand, which suggests no ASR occurrence. However, in the case of Na₂SiO₃ solution, a very interesting phenomenon occurred. Specimens immersed in 0.5 mol/L solution revealed a large expansion. In contrast, an early low expansion in the case of 2.5 mol/L Na₂SiO₃ solution was observed up to 7 days, but subsequently vanished. One explanation is that ASR occurs before CSH gel production halts the reaction process as confirmed by EPMA results.

Small angle X-ray scattering analyses of the nanostructure of hardened cement paste proved to be a highly suitable method to study structural changes due to creep of the material during loading. The short-term loading and creep experiments described in this paper were carried out on small, hardened, cement paste samples (10 x 10 x 0.4 mm³). The specimens were subjected to a compressive load in the plane of the platelets while being penetrated by an X-ray beam perpendicular to the platelet, leading to a scattering of the X-ray beam. By using the Bragg's law for X-ray diffraction in combination with Porod's theorem for X-ray scattering, these experiments allow for a direct insight into micro-structural processes on the 10^-9 to 10^-7 m scale occurring during shrinkage, creep, and creep recovery of hardened cement paste specimen stimulated by in-situ drying, loading and unloading of the sample. Whereas previous experiments of the authors were limited to investigation in vacuum, similar experiments can now be performed in any climatic condition. The gained results indicate that creep of hardened cement paste under load leads to an increase of the inner specific surface of the material, probably related to inter-crystalline processes.

The non-uniformity of the moisture distribution in drying concrete specimens results in differential shrinkage. If the specimen thickness tends to zero, theoretically, the so-called infinitesimal shrinkage would occur. Since the latter may not be determined directly by experimental means, a method for the inverse analysis of shrinkage tests has been developed. Laboratory-sized concrete specimens are subjected to drying, whereby the mass loss and the deformation are measured. Then, the material-specific relationship between the unhindered infinitesimal shrinkage strain and the relative humidity is retrieved from the experimental results by inverse analysis of the respective test. Drying is simulated by using the non-linear diffusion theory. In the mechanical model, elastic and viscoelastic strain - as well as cracking and strain softening - are taken into account in addition to the unhindered local shrinkage. Sensitivity analyses have shown that the measurement of the mass loss and the determination of the desorption isotherm should be conducted with high accuracy in order to obtain reliable inverse analysis results.

Many amorphous materials display a logarithmic creep behavior, driven by the rare occurrence of complex, hardly detectable, microscopic, structural rearrangements. Following recent developments in experimental techniques and modeling, we develop here a new approach based on transition state theory and on activation energies computed from molecular simulations of shear tests. Our results predict the logarithmic creep of an amorphous, model structure of cement at the molecular and meso- scales. We investigate the interplay of cooperative processes at the different length-scales and establish connections with creep phenomena in other materials.

The mesomechanical model for concrete, previously developed for purely mechanical actions, is used as the basis for coupled durability mechanics calculations. Until now, the phenomena studied include drying shrinkage, external sulfate attack and mechanical effects of high temperatures. On-going work is focusing on alkali-silica reaction (ASR). From the chemical viewpoint, ASR is represented with a three-field, diffusion-reaction, chemical model which is shown to qualitatively and quantitatively reproduce some experimental measurements of sandwich-type specimens subject to standardized accelerated ASR tests. The model developed includes the recently identified role of calcium in this type of expansive reactions.

This work aims to characterize the creep behavior of the major microstructure constituents of cement paste by means of a novel approach which combines Nanoindentation Technique (NT) and Scanning Electron Microscopy with X-ray microanalysis (SEM-EDS). We first performed a large grid of nano-indentation tests on different cement paste samples. The tests were carried out in displacement-control by imposing a maximum penetration depth of 150 nm for 600 seconds. The surface was finely polished according to an optimized protocol to reach very low roughness, verified by Atomic Force Microscopy (AFM) techniques. Then, we performed the chemical analysis of all the indented points by SEM-EDS. The chemical analysis allowed selecting the indentation tests which likelycorrespond to pure phase. One of the advantages of such a coupling technique is that there is no need of statistically deconvoluting the distributions of the measured properties to estimate the property of the phases. For instance, the relaxation curves' load-time for the C-S-H phase was selected with and without carbonation. Finally, we perform a finite element analysis of the relaxation behavior of the selected points by means of a viscous model for concrete which splits the deviatoric long term creep and the volumetric short term creep. Eventually, this simplified model-based approach provided the creep coefficient of the so-identified Calcium-Silicate-Hydrates (C-S-H), Calcium-Hydroxide (CH) and belite (C2S), monosulfoaluminate (AFm) phases. The conclusions of this work provided new insights on the identification of the creep properties of the sub-micrometer phase composing the cement phase.

This work is focused on the chemo-mechanical characterization of cement-based materials. A novel approach is presented which combines the classical grid indentation technique with x-ray energy dispersive microanalysis method. Two oil-well cement systems with different combination of silicious filler are examined, both, from mechanistic and chemical points of view. The characteristic x-rays of major elements, silicon, calcium and aluminum are measured over the indentation region and mapped back on the indentation points. Measured intensities together with indentation hardness and modulus are considered as the set of observables used in the deconvolution analysis. Inference of the number of phases, their average properties and clustering of experimental observations are executed in the framework of Finite Mixture Models with Gaussian component density function. The calcium-silica-hydrate gel is successfully isolated at the indentation scale from other phases of cement hydration and its mechanical response linked to the calcium-to-silicon ratio quantified with x-ray wavelength dispersive spectroscopy.

The correspondence principle is widely used to estimate the effective behaviour of non-ageing linear viscoelastic composites, as it allows taking advantage of homogenization approaches originally developed in the elastic framework. However, this principle is no longer valid when the phases exhibit ageing. A recently proposedapproach overcomes this limitation: homogenization of random media can be used on composites made up of isotropic, ageing, linear, viscoelastic phases. In this paper, the latter is applied to estimate the effective viscoelastic behaviour of solidifying composite materials, that is porous materials subjected to gradual precipitation of solids into pore space. This theory developed by Bažant shows that even if the behaviour of the precipitated material is non-ageing, the effective behaviour exhibits ageing due to the microstructure evolution with time. Modelling the solidifying material as a set of fictitious ageing linear viscoelastic phases, homogenization can be taken advantage of to estimate the effective behaviour. This allows investigation of precipitation mechanisms other than the parallel arrangement initially considered by the solidification theory, such as a rough, simplified, model of cement paste. The effective ageing creep is found to be highly dependent on both the precipitation mechanism and kinetics.

Concrete is a heterogeneous material that develops delayed strains under a constant load. These deformations are related to micromechanisms which occur in its microstructure. To model this behaviour, a new numerical multi-scales method is suggested. Based on a method for the calculation of the effective response for a non-aging material, an extension to aging materials has been developed. This method operates directly in space-time and avoids the difficulties of Laplace Carson transform inversion. The delayed strains are calculated in a representative elementary volume thanks to classical finite elements method which allows determining the components of the creep compliance tensor. First of all, calculations have been performed for a uni-axial loading to model the creep strain at different scales in order to give the visco-elastic property of calcium silicate hydrates. Then, the evolution of the microstructure with age has been considered to model the creep at early ages of concrete.

In this study, we present a coupled creep and damage model for describing the behavior of cementitious materials. The creep model is based on a multiscale approach where the material is represented as a composite made of a linear viscoelastic matrix with distributed spherical elastic inclusions and pores. The Mori-Tanaka scheme is then applied in the Laplace-Carson space to this composite material. Exact analytical expressions of the moduli in the time space are derived in simpler cases when a limited number of Maxwell elements are involved to describe the matrix behavior. The model is compared to finite element simulations results carried out on 3D mesostructures. Several configurations of mesostructures with different volume fractions of spherical inclusions ranging from 25 to 40% and boundary conditions are analyzed. The creep model is further coupled to the isotropic damage model due to (Mazars 1986) at the macroscale, based on the concept of pseudo-strains which allows reformulating the initial viscoelastic problem as an equivalent elastic one. The evolutions of the damage variable are governed by an equivalent pseudo-strain calculated from the pseudo-strains tensor. The model is then applied to the simulation of concrete basic creep tests at different temperatures.

This paper presents a three-dimensional micromechanical model for concrete creep at early age. In this mode, concrete is treated as a two-phase composite material with an aging matrix (cement paste) and inclusions (aggregates). The uniaxial creep behavior of the aging matrix is described by Bazant's solidification theory, which models aging by volume growth of non-aging viscoelastic products of cement hydration. However, the bulk modulus of the matrix is assumed to be time-independent and the inclusion behavior is assumed to be elastic. The Mori-Tanaka scheme is adapted for determining the effective shear and bulk creep operators of the composite material. To enable numerical determination of concrete creep compliance and relaxation functions, continuous integral operators are approximated by matrix operators acting in finite-dimensional spaces. Effective creep operators (which represent overall properties of the composite) are evaluated as rational functions with matrix arguments.

Since drying is a very slow process, a strong gradient of drying shrinkage occurs in concrete members leading, at the macroscopic level, to the rise of tensile stresses at the surface and compressive stresses at the core. Therefore, it may lead to superficial cracking. In addition, crossing cracks and/or debonding (at the interface with a substrate) may also occur in thin members if drying shrinkage is restrained. In order to study these phenomena, a new device based on digital image correlation (DIC) was set up. A post-processing tool is then proposed to capture the mapping of shrinkage strains and to determine the evolution of the cracking patterns. It was used successfully to observe, quantify and analyze cracking of a coating mortar due to the restraint of drying shrinkage by a rigid substrate (concrete block).

Drying shrinkage is a very slow process, leading to self-equilibrated stresses and eventually to cracking, which can be observed at two scales. On the one hand, at the macroscopic scale, the concrete skin shrinkage is restrained by the concrete core. On the other hand, at the mesoscopic scale, the cement matrix shrinkage is restrained by the aggregates. To simultaneously study the influence of the two aforementioned phenomena (self-restraint at the macroscopic and mesoscopic scale), numerical simulations have been performed on a mesostructure (explicitly including the aggregates and mortar). On an ordinary concrete, results show that when creep is not taken into account, drying shrinkage leads to misleading results — an important damage field arises rapidly. Whereas, taking creep into account changes and delays the cracking pattern. The consequences are a reduction of the apparent Young modulus and tensile strength which are slightly more important when skin effect is taken into account.

The behaviour of cementitious materials under drying depends on the behaviour of each phase of this material (cement paste and aggregates mainly), which are very different. Indeed, cement paste shrinkage is restrained by the aggregates under drying. The stresses induced by these strain incompatibilities between these two components at meso scale are added to the ones due to macroscopic drying shrinkage gradients. These stresses lead to debonding at the cement paste/aggregate interfaces (circumferential cracks) and to the growth of intergranular cracks (radial cracks). Influence of size and volume fraction of granular inclusions on cracking induced has already been experimentally studied, showing cracking patterns function of volume fraction and size of inclusions. The aim of this paper is to numerically simulate this hydro-mechanical behaviour at meso scale by taking into account the heterogeneity at this scale. A simplified representation of the mesostructure is adopted, using a spherical inclusion scheme of various sizes and volume fractions. A weakly hydro-mechanical coupling is used. Drying and basic creep are also taken into account. A discrete representation of cracking is adopted permitting to represent the failure due to the hydric loading appearing at the interface between aggregate and cement paste and inside the cement paste.

The study presented in this paper deals with the influence of the water saturation of natural aggregates on shrinkage and cracking sensitivity of concrete at early age. Limestone crushed gravels were specially chosen for this study due to their high porosity. The degree of water saturation of gravels varied, from a given concrete mixture, keeping the total water content constant. Significant variations of the plastic shrinkage and early age autogenous deformations were observed. Due to the kinetics of absorption of gravels, the water content remaining in cement paste was different from the effective water content. This was confirmed by the values of mechanical properties and porosimetry. The evolutions of elastic modulus and tensile strength were experimentally assessed and used to compare the cracking sensitivity of the three studied concretes by evaluating the self generated stresses.

Freezing and thawing cycles in northern regions lead to serious deterioration in bridges and dictate the need for early repair or replacement. The use of polyvinyl alcohol (PVA) fibers in cementitious composites improves durability because of their ability to withstand large deformations due to its strain-hardening and multi-cracking ability. However, the addition of fibers alone to a cementitious matrix may not be adequate in providing resistance to freezing and thawing beyond the standard 300 cycles. The addition of superhydrophobic admixtures to fiber-reinforced composites results in an air void system with small, well-dispersed air voids allowing for better resistance to freezing and thawing. Moreover, the superhydrophobicity of the air void surface provides a water-repellent effect, ensuring that water does not attach to the surface of the air voids. This research demonstrates that the addition of superhydrophobic admixtures to fiber-reinforced composites provides improved freeze-thaw resistance by demonstrating a durability factor of 100 through as many as 700 accelerated (-50°C to 20°C) freeze-thaw cycles in fresh water and 5% NaCl solution. Additionally, the accelerated freeze-thaw testing provides a more efficient method for testing freezing and thawing in cementitious materials.

In this study, two types of accelerated tests were conducted to determine the corrosion rate of a reinforcing bar in concrete. Tensile test specimens were used for these accelerated tests. In one test, the chloride content of the concrete in the specimens was varied at three levels. The corrosion rate of the reinforcing bar increased with the chloride content. The increasing ratio of the corrosion rate with increase in the chloride content became large when the specimens were subjected to repeated loadings before the start of testing. The corrosion rate was promoted by the generation of internal cracking. In the other accelerated test, two types of aggregates were used for the concrete of the tensile test specimens to change the shrinkage characteristics. Repeated loading was also employed. The test results show that corrosion was initiated in a shorter time period when the width of internal cracking was large.

The porosity of hardened cement paste changes when it is exposed to the actual environments, and it may be expected that the chemical structure of the C-S-H undergoes changes. The C-S-H is the main component, comprising 60% or more by volume of hardened cement paste, and this study focuses on changes in the chemical structure of C-S-H. Deterioration induced by ammonium nitrate solution was accompanied by changes in the pore structure as well as structural changes in the C-S-H in the hardened cement paste. It was ascertained that when evaluating the decreases in the elastic modulus of the hardened cement paste, both the pore structure and the structure of the C-S-H must be considered.

Nanotechnology is providing challenging research avenues in the field of construction materials as the developed materials exhibit novel physical and chemical properties. In the present studies, sol-gel process has been employed to prepare amorphous, dispersed, spherical silica nanoparticles. Further, these silica nanoparticles were supplemented to cementitious system for comparative mineralogical and morphological attributes of calcium-silicate-hydrate (C-S-H) gel. The results of these studies showed that the addition of silica nanoparticles up to 3.0% significantly improved the compressive strength of cement mortar. Addition of silica nanoparticles into cement paste improves the micro-structure of the cement system and calcium leaching is significantly reduced as silica nanoparticles react with calcium hydroxide (CH) and thereby forming a denser C-S-H gel. It was found that CH content in silica nanoparticles incorporated cement paste reduced 90% at 1 day and up to 59% at 28 days. Further, to investigate the durability aspects, chloride permeability of cement mortar was assessed using accelerated electro migration experiment with a glass cell apparatus. To find the chloride ion concentration at different intervals of time, a UV-Visible spectrophotometer was used. It was observed that incorporation of nanosilica in cement mortar significantly improved resistance to chloride ion diffusion as compared to silica fume samples. Silica nanoparticles with 3% addition improved the chloride ion resistance up to ~43%, whereas silica fume improved only 15%. Therefore, it can be concluded that the microstructure of the cement can be tuned with the help of nanoparticles, thus producing more durable and sustainable cementitious materials. SEM and TGA techniques have been employed for the comparative morphological and mineralogical aspects of cementitious system.

Superabsorbent polymers (SAP) are a new type of admixture. They can store many times more water than their own weight. They can be used for internal curing of concrete and for mitigation of shrinkage. By adding 0.7 % SAP by mass of cement, autogenous shrinkage of low water-cement ratio concrete can be suppressed completely. By adding only 0.35 %, autogenous shrinkage can be reduced by 80 % compared to concrete without SAP. Total shrinkage of drying concrete (the sum of autogenous and drying shrinkage) is also reduced considerably. The paper reports about experimental investigations on cement paste and concrete which show the favorable effect of SAP on shrinkage. Results will be shown and discussed in the light of the mechanism of autogenous shrinkage and the effect of SAP on the water balance in concrete.

Recent incentives to reduce the carbon footprint of Portland cement (PC) concrete have sparked the research and development of eco-friendly products such as alkali-activated slag (AAS) concrete. AAS is a promising product, capable of developing compressive strengths comparable to PC concrete. However, its large drying and autogenous shrinkage (the latter being the focus of this paper) have impeded its marketability and use in the construction industry. The mechanisms and parameters that control the self-desiccation of AAS are relatively unknown. Chemical shrinkage, the driving force of autogenous shrinkage, has never been measured for AAS systems; however, it has been theoretically estimated to be much higher than that of PC. The first step in determining why the autogenous shrinkage of AAS is so large is to investigate its chemical shrinkage. This research focuses on proper measurement of the chemical shrinkage of AAS and the parameters that affect the results.

An apparatus has been designed to study the volumetric changes under controlled curing conditions. The apparatus is capable of measuring the chemical shrinkage as well as the macroscopic volumetric changes of sealed and saturated specimens under controlled pressure and temperature. Specifically, when measuring separately the macroscopic deformation (bulk shrinkage) and the water absorption of a saturated specimen, we find that the sum of the bulk deformations and water absorption adds up to the chemical shrinkage. Furthermore, while we observe pore pressure drops in the hydrating cement paste, even in the presence of an infinite supply of pressurized water (i.e. chemical shrinkage test conditions), bulk shrinkage occurs even in the absence of negative liquid pressure and at (almost) zero effective stress. That is, at (very) early ages, driving forces other than capillary forces are at work to cause bulk shrinkage.

Synthetic superabsorbent polymers (SAP) were studied here as chemical admixtures in mitigating autogenous shrinkage of high-strength concrete or mortar. The sorptivity of the SAPs was quantified in saline solutions which mimicked the ionic composition of cement pore solution and in the cement pore solution itself. Ca²+ ions essentially modified this sorptivity. SAPs of maximum anionicity released the stored ionic solution swiftly to a large extent, whereas SAPs containing acrylamide as a comonomer retained the liquid over a longer term. These kinetics could be directly linked to the efficiency of the SAPs in mitigating autogenous shrinkage of high-strength mortar. The SAPs which released liquid freely reduced autogenous shrinkage significantly less than the more retentive SAPs. Finally, the compressive strength of the mortars under investigation was determined. It became obvious that only a well-balanced selection of SAP type and dosage in conjunction with the most appropriate amount of extra water for internal curing has no negative effect, but can even lead to an increase in compressive strength.

Structures managers need a better prediction of the delayed failure of concrete structures, especially for very important structures like nuclear power plant encasement. Sustained loadings at high level (above 75% of loading capacity of the structure) can lead to structure failure after some time. In this study, a series of 4-point bending tests was performed in order to characterize the creep behaviour of pre-cracked beams under high load level. The specimens were made of normal strength concrete. A power law relationship is observed between the secondary deflection creep rate and the failure time. It is also shown that when crack propagation occurs during the creep loading, the creep deflection rate increases with the creep loading level and with the crack propagation rate.

This paper mainly studies uniaxial tensile creep behavior of pre-cracked steel fiber-reinforced concrete (SFRC). A series of uniaxial tensile creep tests were carried out on SFRC cylinder specimens which were pre-cracked at 0.2 mm. The pre-cracked specimens were loaded at the load level of 30% of maximum pre-cracking load for three months under constant temperature of 20 degrees and relative humidity of 60%. Time-dependent crack opening displacements (COD) were continuously measured by LVDTs. For the specimens with pre-cracking COD of 0.2 mm, the maximum creep deformation is almost the same as the initial elastic deformation. Among the various rheology models, Burgers' model was employed to describe the creep behavior. A damage factor was introduced in order to consider the gradual debonding behavior at the fiber/matrix interface.

Concrete structures with a long-term serviceability may be impacted by the time-dependent strains. In this study, creep strains modeling is performed by a rheological model. The long-term viscoelasticity and the influence of the loading on the specific creep are taken into account. The impact of the dissymmetry between tensile and compressive creep is studied with the numerical simulation of a four-point bending creep test. According to the results, a reliable, long-term, structural analysis has to consider this possible dissymmetry of basic creep.

In this study, microcracks in slag concretes with water-to-binder ratio (w/b) of 0.5 and 0.3 were subjected to temperature regime-simulated steam curing in early ages and were characterized by the combination of acoustic emission (AE) technique and mechanical tests. By using a new-shaped wave-guide, which reduced the distance from cracking points to wave-guide, effect of attenuation in detecting AE signals was significantly mitigated. Due to analysis of AE parameters, crack mode in slag concretes was clarified. The result showed that they were very different in each stage of temperature history and in each type of concrete. This research also revealed the capacity of high alite cement (HAC) in improving resistance against microcracking of slag concrete. However, cracking resistance of HAC slag concrete in case of w/b of 0.3 was higher than that in case of w/b of 0.5.

The micro-scratch test and its analysis continue to grow in the fields of material science and engineering, particularly as it relates to materials at smaller scales being used for fracture resistance. In this study, white cement paste specimens were cast, extracted and their hydration was stopped at desired curing ages. A Rockwell probe was used to scratch the surface of the specimens to determine the fracture toughness at that age. Classical Brazilian split-cylinder tests were also performed to compliment the scratch tests. The excellent convergence of the raw data allows the increase of fracture toughness and splitting strength over time to be determined. Finally, Irwin's characteristic length, which is proportional to the fracture process zone size, is determined and shown to asymptotically reach a constant size.

Emergent interest in geological carbon dioxide (CO2) sequestration has brought a need for understanding the mechanism of potential degradation of oil well cement (OWC) in carbonated brine. In this paper, Type G OWC paste specimens - produced with water-to-binder (w/b) ratio of 0.45 and incorporating 0, 1 and 3% nanosilica by weight of cement - are hydrated for 28 days under two conditions, room condition (20 °C with 0.1 MPa pressure) and a simulated oil well condition (80 °C with 10 MPa pressure). Conditions of geosequestration in a sandstone formation at a depth of 1 km, were simulated by bubbling CO2 into a heated vessel containing 0.5 M NaCl (brine). Fresh cured OWC cylindrical specimens were exposed to this environment. Slices of the cement specimens were taken periodically, during and after exposure, to quantify degradation progression. The modulus of elasticity of the specimens was examined prior to and after exposure, and a damage metric was computed. The results show that the addition of 1% nanosilica can significantly limit OWC degradation in carbonated brine environments. Furthermore, microstructural characterization using BET-N2, X-ray diffraction (XRDA) and ²⁹Si nuclear magnetic resonance (NMR) was performed to explain the macroscale observations.

We have measured - by digital holographic interferometry - the dissolution rate constant of gypsum in water containing various phosphonates, small molecules or polymers, known to adsorb at the gypsum crystal surface. According to the assumption of reaction-driven pressure solution creep, dissolution inhibitors of gypsum should also inhibit humid creep of gypsum plaster. This was checked by measuring (by rheometry) the shear creep rate of gypsum plaster containing these phosphonates in a saturated humid environment. Validating the assumption, all of these phosphonates appear to be efficient anti-creep admixtures of humid set plaster. The polymeric ones have the complementary advantage to be easier to use, with a less delicate dosage.

The effects of coarse recycled concrete aggregates on long-term behavior of concrete (shrinkage and creep) are investigated. Most important, corresponding prediction models have been compared with experimental findings, obtaining a systematic underestimation of results. The adhered mortar of the recycled concrete aggregates is determined and its influence on the final concrete properties is investigated as its content and porosity can influence the final properties of the new concrete.

Among all of the advantages of concrete elements, improving ductility and energy absorbency has always been a great challenge. This paper reports on an experimental study of the effects of polyvinyl alcohol fibers on fracture energy of concrete and its comparison with steel fiber-reinforced concretes. Energy absorbency of the concrete was measured according to the ACI544 impact test code. Compressive- and impact-resistance of polyvinyl fiber-reinforced concretes were also measured. Stress-strain curve in compressive tests are reported.

When subjected to natural drying, concrete structures are submitted to desiccation shrinkage. This shrinkage has to be taken into account when designing the reinforcement, especially in the case of large structures such as the containment vessels of nuclear power plants. In this paper, we discuss the assessment of desiccation shrinkage, focusing on a possible size effect on the final value of the shrinkage. Experimental results are used to investigate the effect of structure size on drying shrinkage. When these tests are analysed with respect to the square root of time to the notional size ratio, in order to get rid of the kinetic of drying which is a diffusive process, indeed a size effect is obtained. Nevertheless, it is not possible to explain this size effect using a coupled model (except, of course, the size effect due to drying, i.e. the kinetics effect). The physical meaning of this size effect seems to be due to a collateral effect of the different sizes of the samples. For larger samples, the temperature during hydration is higher and there are consequences on the microstructure and then on the delayed behaviour.

The paper reports some highlights of the theoretical development included in JCI computer code for hygro-thermal drying, chemo-mechanical volume change, and damage in cementitious material. Only a few are reported in this paper due to the limited space. The first highlight is the theoretical development of drying shrinkage in the period from fresh concrete to hardened concrete. The second is the method to estimate crack widths and its discrete interval lengths from the smeared crack model. Validity of this theoretical model is shown in comparison with the real size experiment performed at the Metropolitan Highway Corporation.

Stress analysis, considering spatial distribution of shrinkage and time-dependent deformation characteristic, should be carried out in order to predict accurately tensile stress and associated crack in concrete member under restraint drying shrinkage. In particular, a constitutive model for concrete that can adequately express tensile creep under drying is of importance. A new apparatus for sustaining tensile test of concrete was developed in this study to obtain reliable data of tensile creep of concrete, which can be a basis to develop an accurate computational model. The testing system, using cylindrical specimen, ensures comparison between experimental and analytical results under ideal conditions. Tensile stress and strain of the specimen can be precisely and stably controlled by inducing tensile load into the specimen as a reaction of compressive load in steel rod connected by screw. Consequently, time-dependent tensile behavior (i.e., stress, strain and cracking) of concrete can be tested under various loading and drying path programs. Test results obtained the proposed apparatus are demonstrated. Numerical simulation of tensile behavior of concrete is also conducted in this study. It was verified that reduction of tensile stiffness and cracking stress of concrete under drying can be simulated by strain softening near the surface due to restrained shrinkage.

Presented is a new model, labeled B4, which can overcome some of the shortcomings of the CEB-fib, ACI, JSCE and GL prediction models for concrete creep and shrinkage. The B4 model represents an extension and systematic recalibration of the theoretically founded model B3, a 1995 RILEM recommendation. In addition to introducing the so far missing separation of autogenous and drying shrinkage, model B4 takes into account the cement type and admixture parameters, as well as the effects of various types of aggregate. The new predictors for the creep compliance function more accurately, capture the composition information, and are recalibrated to match the multi-decade behavior. This behavior has recently been documented by observed deflection records of many bridges, which is evidence that has so far been systematically underestimated. The improved model was calibrated through a joint optimization of a new, significantly enlarged database of laboratory creep and shrinkage tests and a new database of bridge deflection records.

The age-adjusted effective modulus method (AAEM) is a standard ACI and CEB-fib for simplified estimates of the creep response of concrete structures. The AAEM requires the user to supply the relaxation function, R(t, t'), of the concrete to be used. This function may be obtained through numerical methods, but more easily from a simple closed-form formula. Such a formula was first presented by Bažant and Kim in 1979, but was improved in 2012 by Bažant, Hubler, and Jirásek. This paper summarizes and discusses this recent improvement to the closed-form approximation of R(t, t'), which gives a more accurate representation of the multi-decade creep.

The aim of the research described in this paper is to assess the deformation of cracked reinforced concrete beams under both short- and long-term service loading. Beams are subjected to short-time bending tests, including loading cycles with different peak values leading to concrete cracking (pre-cracking tests) and long-term tests under sustained loading. Long-term deflection appears to be much more important than the deflection due to short-term loading and leads to important permanent deformation after unloading. After 6 months under sustained loading, the overall instantaneous stiffness of all beams was substantially reduced.

An effective flexural stiffness equation for long-term deflection of prestressed concrete with and without cracks is proposed. The equation is derived by assuming a linear strain distribution through the section, as well as considering creep, axial shrinkage and shrinkage gradient of concrete. The effect of creep is considered by applying the effective Young's modulus method, which means that the histories of stress and shrinkage are not considered. The effects of prestressing steel and reinforcement restraining deformation due to creep and shrinkage are also incorporated into the equation. The tension stiffness of concrete with cracks is considered based on Branson's equation. An existing one span-prestressed concrete cantilever girder bridge with a box type-section is adopted for verifying the validity of the proposed equation by comparing the measured excessive deflection with the calculated values. The verification results showed that the calculated deflection agreed roughly well with the observed values.

The stress relaxation of prestressing steel tendons is normally measured at constant strain and constant temperature. The measurement results, embodied in empirical formulas, are then directly used to predict the prestress losses. This classical approach is contingent upon assuming the strain changes during structural lifetime to be negligible compared to the initial strain in steel, and the temperature changes to be unimportant. Recently, however, it transpired that, in creep-sensitive structures (such as large-span, segmentally erected, box girders) dominated by their self-weight, the strain changes in concrete are not negligible and the temperature rise in concrete slabs exposed to sun may be important. To take this into account, the existing empirical formulas used in the European (CEB-fib) Model Code and the American practice, which are valid only for constant strain and constant temperature, are now generalized to arbitrary time-variable strain and variable temperature, heeding obvious asymptotic restrictions and the fact that steel is a viscoplastic material whose constitutive principles are well known. The resulting formula is a memory-less, nonlinear equation for the viscoplastic strain rate of steel as a function of the current stress, strain and temperature. Close fits of all the main test data from the literature, including the available data on the effect of strain changes and temperature changes, are achieved. The effect of temperature is found to be important and is formulated on the basis of the activation energy of viscoplastic flow of metals.

Within the following contribution, a material law is presented which allows for the prediction of the basic creep and relaxation behavior of young, normal, and high-strength concretes. It distinguishes between reversible delayed elastic strains and irreversible flow strains and considers the complex nonlinear creep behavior under constant and variable stresses. The stress-strain behavior corresponds to that of a series connection of different, thermodynamically sound, rheological elements with aging mechanical parameters. The model was based on a comprehensive experimental program on the creep and relaxation behavior of young concretes.

At early ages, thermal stresses that develop as a consequence of cement hydration can cause the evolving concrete tensile strength to be reached and cracks to appear. A technique to recover the internal heat source and the thermophysical properties (specific heat and thermal conductivity) during hydration process of both normal strength concrete and high-performance concrete is presented in order to solve the direct heat transfer problem of concrete structures. Composite and pozzolanic binder were used. From experimental data, an inverse algorithm was implemented to obtain these parameters, the evolution of Young's modulus was obtained through a maturity model, and both were combined with the finite element method. The goal is to provide a numerical tool consisting of the use of the inverse method to estimate the thermophysical properties of the material during early stages of hydration. The result provides a good approximation to the experimental data. It is concluded that the proposed method is accurate, stable, and efficient for the analysis of early-ages concrete behavior.

Engineered cementitious composites (ECC) are cementitious materials with high deformability and mixed organic fibers in order to ensure the high toughness. A study with the aim of high strengthening of the boundary beam is carried out. However, in high strengthening, it is reported that temperature in the member exceeds 100°C caused by heat of cement hydration. When temperature in the member exceeds 100°C, it is worried that heat of cement hydration affects the performance of organic fibers in the member. Then, in order to control the temperature rise by heat of cement hydration, the analytical study was carried out on effects of control in the countermeasure using pipe cooling system. In this report, the experiments for verifying the effect of pipe cooling in this study will be carried out and the results will be also reported.

In this study, a new numerical method of pipe-cooling thermal analysis is presented in order to achieve arbitrary layout of the cooling pipe independent of FEM mesh arrangement. Then, some thermal analyses for concrete structural model with pipe cooling system are executed and validity of the proposed numerical method is discussed. As a result, it is confirmed that the proposed analytical procedure can simulate quite rational temperature histories despite the cooling pipe layout independent of FEM mesh arrangement.