Microstructure-based micromechanical prediction of elastic properties in hydrating cement paste

Elastic properties of hydrating cement paste can be successfully predicted by combination of the hydration model, percolation theory and micromechanical analysis. Reconstruction of hydrating microstructure is based on the 3D digital NIST model of cement hydration, which is enhanced for the prediction of two C-S-H types. Chemical phases in a percolated microstructure served as an input in a two-level analytical or one-level 3D FEM or FFT elastic homogenization. Special mesh generation for the percolated microstructure is discussed as well as its numerical implementation. Good results from FEM and FFT were found for the size of the representative volume element of 50 × 50 × 50 μm, considering water-to-cement ratio in the range from 0.25 to 0.5. While good predictions in well-hydrated cement pastes were obtained for both analytical and numerical approaches, numerical homogenization was found more accurate and versatile for the whole hydration time.     

Influence of inclusion shapes on the effective linear elastic properties of hardened cement pastes

In most micromechanical models applied to cement pastes, particulate phases are modeled as spheres. However, experimental observations clearly show that certain of them are far from being spherical. The present work focuses on the effects of particle phase shapes on the effective isotropic linear elastic moduli of hardened cement pastes (HCP). An attempt to develop a more realistic micromechanical model is proposed by using spheroidal inclusions and including a novel morphological parameter. The latter is identified on the basis of experimental result issue for example from microtomographic images of Portland cement grains. With the help of the proposed model, the validity range of spherical particulate approximations is examined for both sound and leached pastes.     

Modelling elasticity of a hydrating cement paste

Concrete is a complex multi-scale composite involving multi-physics processes. As it is the only evolving component of concrete, the cement paste has a major influence on the mechanical properties of concrete at early age. This paper focuses on the increase of the elastic properties of a cement paste during its hydration. The homogenization theory for disordered media is used in order to estimate the evolution of the effective elastic moduli of the hydrating paste. The morphological model refers to two types of C-S-H (calcium silicate hydrates, main hydration products of Portland cements) distinguished by many authors: inner products or high density C-S-H build up layers surrounding the anhydrous particles, while the outer products or low density C-S-H play the role of a porous matrix.The simulations of the effective Young's modulus at late age during hydration and at the end of hydration prove to be in excellent agreement with the experimental results available in the literature.     

Modeling of hydration reactions using neural networks to predict the average properties of cement paste

This paper presents a hydration model that describes the evolution of cement paste microstructure as a function of the changing composition of the hydration products. The hydration model extends an earlier version by considering the reduction in the hydration rate that occurs due to the reduction of free water and the reduction of the interfacial area of contact between the free water and the hydration products. The BP Neural Network method is used to determine the coefficients of the model. Using the proposed model, this paper predicts the following properties of hardening cement paste: the degree of hydration, the rate of heat evolution, the relative humidity and the total porosity. The agreement between simulation and experimental results proves that the new model is quite effective and potentially useful as a component within larger-scale models designed to predict the performance of concrete structures.     

An inverse method to determine the elastic properties of the interphase between the aggregate and the cement paste

Concrete is a three-phase material consisting of cement paste matrix, discrete inclusions of rock (aggregate), and an interfacial transition zone (ITZ) between the matrix and the inclusions. We model the material as a composite formed by a matrix with embedded spherical particles; each surrounded by a concentric spherical shell. Effective elastic moduli of this composite are evaluated on the basis of the generalized self-consistent scheme (GSCS). This formulation is used to solve the inverse problem of determining the elastic moduli of the ITZ from experimentally known elastic properties of the composite.     

Alkali binding in hydrated Portland cement paste

The alkali-binding capacity of C-S-H in hydrated Portland cement pastes is addressed in this study. The amount of bound alkalis in C-S-H is computed based on the alkali partition theories firstly proposed by Taylor (1987) and later further developed by Brouwers and Van Eijk (2003). Experimental data reported in literatures concerning thirteen different recipes are analyzed and used as references. A three-dimensional computer-based cement hydration model (CEMHYD3D) is used to simulate the hydration of Portland cement pastes. These model predictions are used as inputs for deriving the alkali-binding capacity of the hydration product C-S-H in hydrated Portland cement pastes. It is found that the relation of Na⁺ between the moles bound in C-S-H and its concentration in the pore solution is linear, while the binding of K⁺ in C-S-H complies with the Freundlich isotherm. New models are proposed for determining the alkali-binding capacities of C-S-H in hydrated Portland cement paste. An updated method for predicting the alkali concentrations in the pore solution of hydrated Portland cement pastes is developed. It is also used to investigate the effects of various factors (such as the water to cement ratio, clinker composition and alkali types) on the alkali concentrations.     

Thermodynamic modelling of the hydration of Portland cement

A thermodynamic model is developed and applied to calculate the composition of the pore solution and the hydrate assemblage during the hydration of an OPC. The calculated hydration rates of the individual clinker phases are used as time dependent input. The modelled data compare well with the measured composition of pore solutions gained from OPC as well as with TGA and semi-quantitative XRD data. The thermodynamic calculations indicate that in the presence of small amounts of calcite typically included in OPC cements, C-S-H, portlandite, ettringite and calcium monocarbonates are the main hydration products. The thermodynamic model presented in this paper helps to understand the interactions between the different components and the environment and to predict the influence of changes in cement composition on the hydrate assemblage.     

A multiscale micromechanics-hydration model for the early-age elastic properties of cement-based materials

The E-modulus of early age cement-based materials, and more importantly, its evolution in time, is one of the most critical material-to-structural design parameters affecting the likelihood of early-age concrete cracking. This paper addresses the problem by means of a multistep micromechanics approach that starts at the nanolevel of the C-S-H matrix, where two types of C-S-H develop in the course of hydration. For the purpose of homogenization, the volume fractions of the different phases are required, which are determined by means of an advanced kinetics model of the four main hydration reactions of ordinary portland cement (OPC). The proposed model predicts with high accuracy the aging elasticity of cement-based materials, with a minimum intrinsic material properties (same for all cement-based materials), and 11 mix-design specific model parameters that can be easily obtained from the cement and concrete suppliers. By way of application, it is shown that the model provides a quantitative means to determine (1) the solid percolation threshold from micromechanics theory, (2) the effect of inclusions on the elastic stiffening curve, and (3) the development of the Poisson's ratio at early ages. The model also suggests the existence of a critical water-to-cement ratio below which the solid phase percolates at the onset of hydration. The development of Poisson's ratio at early ages is found to be characterized by a water-dominated material response as long as the water phase is continuous, and then by a solid-dominated material response beyond the solid percolation threshold. These model-based results are consistent with experimental values for cement paste, mortar, and concrete found in the open literature.     

Numerical and analytical effective elastic properties of degraded cement pastes

Cement pastes are heterogeneous materials composed of hydrates, anhydrous products and pores of various shapes. They are generally characterized by a high particle concentration and phase contrasts, in particular in the case of degraded materials which exhibit important porosity. This paper compares the performance of several classical effective medium approximation schemes (Mori–Tanaka, Zheng-Du, self-consistent) through their ability to estimate the mechanical parameters of cement paste samples obtained numerically. For this purpose, finite element simulations are performed on 3D structures to compute for each sample accurate values of these mechanical properties. For these simulations, the cement paste is considered as a matrix of C–S–H in which are embedded inclusions of anhydrous, hydration products, and pores. In order to evaluate the importance of the particle shape, two types of samples are generated, one with only spherical inclusions and the other containing both spherical and prismatic particles. Simulations with three perpendicular loading directions and both uniform and mixed boundary conditions are performed in order to verify that the dispersion in the computed elastic moduli is low, or equivalently that the generated structures are close to representative volume elements (RVEs). It is shown that the considered effective medium approximation schemes, except the self-consistent one, provide relatively good estimations of the overall mechanical parameters when compared to simulation results, including when both particle volume fraction and phase contrast are high. The analytical methods taking into account the particle shapes also give estimates close to the corresponding numerical simulations, the latter confirming the influence of the particle form.     

A model investigation of the influence of particle shape on portland cement hydration

The NIST Virtual Cement and Concrete Testing Laboratory (VCCTL) is used to simulate the influence of particle shape on the hydration kinetics and setting of portland cement. Building on previous work in reconstructing particle shapes from real cements, real-shape particles are used to produce three-dimensional digitized cement paste microstructures, and the hydration of these microstructures is tracked using VCCTL. The degree of hydration and percolation of solids is monitored and compared to experimental data at several water-cement ratios. The simulations predict that shapes of particles influence cement hydration in two ways: the additional surface / volume ratio relative to spherical particles results in greater rates of hydration, and the anisometry in shape influences the degree of hydration at which the particles and hydration products percolate to form a stiff three-dimensional network.     

Water-cement ratio gradients in mortars and corresponding effective elastic properties

Water-cement ratio gradients are modeled through the interfacial transition zone (ITZ) of a mortar with spherical inclusions. The model is a function of the over-all water-cement ratio, volume fraction and radius of sand, specific gravity of cement and thickness of ITZ. Based on experimental data from the literature, the dependence of saturated, homogeneous cement paste is modeled as a function of water-cement ratio. Subsequently, the effective bulk and shear moduli for mortars are determined using a generalized self-consistent method. Finally, application of the model to data in the literature pertaining to elastic wave speeds in saturated mortars composed of 20-30 screened sand with an overall water-cement ratio of 0.3 yielded a mean ITZ thickness of 48.3 μm.     

Influence of citric acid on the hydration of Portland cement

Citric acid can be used to retard the hydration of cement. Experiments were carried out to investigate the influence of citric acid on the composition of solid and liquid phases during cement hydration. Analyses of the solid phases showed that dissolution of alite and aluminate slowed down while analyses of the pore solution showed that citric acid was removed almost completely from the pore solution within the first hours of hydration. The complexation of the ions by citrate was weak, which could also be confirmed by thermodynamic calculations. Only 2% of the dissolved Ca and 0.001% of the dissolved K formed complexes with citrate during the first hours. Thus, citric acid retards cement hydration not by complex formation, but by slowing down the dissolution of the clinker grains. Thermodynamic calculations did not indicate precipitation of a crystalline citrate species. Thus, it is suggested that citrate sorbed onto the clinker surface and formed a protective layer around the clinker grains retarding their dissolution.     

Young's modulus of cement paste at elevated temperatures

Calcium silicate hydrate is a porous hydrate that is sensitive to temperature and readily loses strength at elevated temperatures. Mechanical and chemical changes in the microstructure, due to escaping water, can significantly affect the mechanical properties, but these changes occur over different temperature ranges. By measuring Young's modulus as a function of temperature using the dynamic mechanical analyzer, the temperature range in which the greatest change in stiffness occurs can be identified. Additional mineralogy, pore size distribution, and composition analysis from high temperature X-ray diffraction, nitrogen sorption, and thermogravimetric analysis will demonstrate the changes in the microstructure. The results demonstrate that over 90% of the loss in stiffness occurs below 120 °C. Therefore, the damage is due to microcracking caused by pore water expansion and evaporation and not the change in mineralogy or composition. More damage, as indicated by greater loss in stiffness, occurs in stiffer and less permeable samples where higher stresses can develop.     

A multi-technique investigation of the nanoporosity of cement paste

The nanometer-scale structure of cement paste, which is dominated by the colloidal-scale porosity within the C-S-H gel phase, has a controlling effect on concrete properties but is difficult to study due to its delicate structure and lack of long-range order. Here we present results from three experimental techniques that are particularly suited to analyzing disordered nanoporous materials: small-angle neutron scattering (SANS), weight and length changes during equilibrium drying, and nanoindentation. Particular attention is paid to differences between pastes of different ages and cured at different temperatures. The SANS and equilibrium drying results indicate that hydration of cement paste at 20 °C forms a low-density (LD) C-S-H gel structure with a range of gel pore sizes and a relatively low packing fraction of solid particles. This fine structure may persist indefinitely under saturated conditions. However, if the paste is dried or is cured at elevated temperatures (60 °C or greater) the structure collapses toward a denser (less porous) and more stable configuration with fewer large gel pores, resulting in a greater amount of capillary porosity. Nanoindentation measurements of pastes cured at different temperatures demonstrate in all cases the existence of two C-S-H structures with different characteristic values of the indentation modulus. The average value of the modulus of the LD C-S-H is the same for all pastes tested to date, and a micromechanical analysis indicates that this value corresponds to the denser and more stable configuration of LD C-S-H. The experimental results presented here are interpreted in terms of a previously proposed quantitative “colloid” model of C-S-H gel, resulting in an improved understanding of the microstructural changes associated with drying and heat curing.     

Influence of hydration on the fluidity of normal Portland cement pastes

The rheological properties of cement paste strongly influence the workability of concrete. It is known that early hydration processes alter phase composition and microstructure of cement pastes. These processes affect fluidity and setting behaviour of cement paste. While many studies tried to measure and model rheological properties of cement pastes, only a few studies assessed the influence of the hydrate morphology on the fluidity of cement pastes.Results of the present study compare the influence of long prismatic hydrates (i.e. syngenite, secondary gypsum) on the fluidity of cement pastes with the effect of other hydrates (AFm).To induce the formation of certain hydration products the cement composition was modified by addition of set regulators and alkali sulphates. Furthermore a combination of various analytical methods such as fluidity (viscometric) testing and microstructural analysis (phase quantification by XRD-Rietveld analysis, investigation by Environmental SEM, BET analysis etc.) was performed. Results are implemented into a fundamental discussion on the influence of various hydration products on the fluidity of the paste.     

Modeling and simulation of cement hydration kinetics and microstructure development

Efforts to model and simulate the highly complex cement hydration process over the past 40 years are reviewed, covering different modeling approaches such as single particle models, mathematical nucleation and growth models, and vector and lattice-based approaches to simulating microstructure development. Particular attention is given to promising developments that have taken place in the past few years. Recent applications of molecular-scale simulation methods to understanding the structure and formation of calcium–silicate–hydrate phases, and to understanding the process of dissolution of cement minerals in water are also discussed, as these topics are highly relevant to the future development of more complete and fundamental hydration models.     

Hydration kinetics modeling of Portland cement considering the effects of curing temperature and applied pressure

A hydration kinetics model for Portland cement is formulated based on thermodynamics of multiphase porous media. The mechanism of cement hydration is discussed based on literature review. The model is then developed considering the effects of chemical composition and fineness of cement, water-cement ratio, curing temperature and applied pressure. The ultimate degree of hydration of Portland cement is also analyzed and a corresponding formula is established. The model is calibrated against the experimental data for eight different Portland cements. Simple relations between the model parameters and cement composition are obtained and used to predict hydration kinetics. The model is used to reproduce experimental results on hydration kinetics, adiabatic temperature rise, and chemical shrinkage of different cement pastes. The comparisons between the model reproductions and the different experimental results demonstrate the applicability of the proposed model, especially for cement hydration at elevated temperature and high pressure.     

Thermodynamic modelling of the effect of temperature on the hydration and porosity of Portland cement

The composition of the phase assemblage and the pore solution of Portland cements hydrated between 0 and 60 °C were modelled as a function of time and temperature. The results of thermodynamic modelling showed a good agreement with the experimental data gained at 5, 20, and 50 °C. At 5 and at 20 °C, a similar phase assemblage was calculated to be present, while at approximately 50 °C, thermodynamic calculations predicted the conversion of ettringite and monocarbonate to monosulphate.Modelling showed that in Portland cements which have an Al₂O₃/SO₃ ratio of > 1.3 (bulk weight), above 50 °C monosulphate and monocarbonate are present. In Portland cements which contain less Al (Al₂O₃/SO₃ < 1.3), above 50 °C monosulphate and small amounts of ettringite are expected to persist. A good correlation between calculated porosity and measured compressive strength was observed.     

A colloidal interpretation of chemical aging of the C-S-H gel and its effects on the properties of cement paste

The properties, structure, and behavior of cement paste, including surface area, drying shrinkage, creep, and permeability are discussed with the assumption that the C-S-H gel is an aggregation of precipitated, colloidal-sized particles that undergoes chemical aging. A basic thesis of this paper is that C-S-H particles bond together over time, increasing the average degree of polymerization of the silicate chains and causing the C-S-H to become stiffer, stronger, and denser. This process occurs slowly at ambient temperatures, but can be greatly accelerated by elevated temperature curing and is also encouraged by drying, which introduces large local strains that may provide a microstructural basis for creep sites. This chemical aging process of C-S-H can thus affect many of the physical properties of cement paste, and there is particular relevance for the complex shrinkage and creep behavior of this material. The effects of a short heat treatment, which causes rapid aging, depend strongly on the moisture of the paste when it is heated. Many of the observations and insights presented here are not new. The primary objective of this paper is to demonstrate, by reporting a variety of published findings in one place, the significant amount of evidence that has been generated over the past 50 years favoring this interpretation. Another objective is to show that the properties and behavior of the C-S-H gel, and of cement paste, do not require a layered microstructure. Separating chemical aging effects from other changes, such as continued hydration, may well lead to a better understanding of the microstructural causes of creep and shrinkage.     

Porosity study on free mineral addition cement paste

A study of the hydration process and the porosity evolution in a cement paste is presented. The analysis of porosity was made in samples with water to cement ratios (w/c) of 0.24, 0.40 and 0.60 at age of 3, 7, 28 and 365 days, respectively. Information on the evolution of total porosity and on the strength of the paste were obtained using positron annihilation lifetime spectroscopy (PALS), scanning electron microscopy (SEM), X-ray diffraction (XRD), mechanical tests (compression and flexion) and water absorption techniques. Specifically, positron lifetime technique allowed us to analyze the evolution of gel and capillary porosity during the hydration process. Using a simple function proposed, reasonable fits to the experimental data of the porosity evolution as a function of the compression strength were obtained.