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

https://doi.org/10.1016/S0008-8846(01)00710-4Get rights and content

Abstract

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.

Introduction

The interfacial transition zone (ITZ) is characterized by gradients in porosity and chemistry which then affect the properties of cementitious composites. The ITZ arises due to a limitation in the packing of cement particles in the vicinity of the surface of aggregates [1] often referred to as the “wall effect.” Scrivener and collaborators have observed an interfacial zone of 30–50 μm thick [2,p.154] in normal concretes by means of image analysis of SEM micrographs. Furthermore, the thickness appears to be independent of the size of the aggregate, however, it does appear to be a function of the size of largest cement particles, and to a lesser degree of the roughness of the aggregates, and the overall water–cement ratio [3].

Nilsen and Monteiro [4] concluded that the ITZ in mortars and concretes must be included in models pertaining to the effective elastic properties of such materials. The basis of their conclusion stemmed from the observation that measured elastic properties for mortars and concretes fall below the lower Hashin-Shtrikman bound computed assuming that concrete is a two-phase (aggregate and homogeneous cement paste) composite. There have been numerous subsequent investigations into the influence of the ITZ on the effective elastic properties of cementitious composites. Yang [5], Ramesh et al. [6] and Li et al. [7], [8] have developed elastic models which approximate the entire ITZ as a single phase with homogeneous properties. As reaffirmed in a recent review [9], the gradients of the elastic properties within the ITZ are important and they have been addressed as a power law variation by Lutz and Zimmerman [10] for the bulk modulus and a piecewise constant variation by Garboczi and Bentz [11]. Both investigations [10], [11] are limited, however, to dilute suspensions of aggregates.

In Section 2, a model is developed for the spatial variation in the water–cement ratio through the ITZ. In addition, a generalized self-consistent model [12], applicable to nondilute concentrations of aggregates, is applied to calculate the effective elastic properties of a mortar. In Section 3, a model for the dependence of the elastic properties of cement paste on water–cement ratio is constructed based on experimental data from the literature. In this paper, it is assumed that the length scale of the cement paste's microstructure is sufficiently small with respect to the size of the aggregate inclusions that it may be accurately modeled as homogeneous. The model is applied in Section 4 to published data on wave speeds in saturated mortars to measure the thickness of the ITZ. Concluding remarks are presented in Section 5.

Section snippets

Model development

In this paper c will be used to denote volume fractions relative to the entire volume of the cementitious composite V while α will be used to denote local volume fractions. Thus, for example (Eq. (1)),ca=1VVαadVwhere the subscript a denotes “aggregate.”

The distribution in the percentage area of anhydrous cement as a function of the distance from the surface of the aggregate x initially after mixing has been computed by Scrivener and Pratt [3, Fig. 1.5] using microstructural gradients measured

Saturated cement paste

Wang et al. [17] measured the variation in the bulk and shear moduli, by way of elastic wave speeds, with respect to various overall water–cement ratios between the range 0.2 and 0.45 for cement pastes made from ASTM Type I/II Portland cement. After demolding the specimens were stored in lime-saturated water until testing thus we will term these pastes to be saturated. These data are presented as diamonds in Fig. 6. Given the limited range of water–cement ratios considered, and the necessity

Application of model

Predictions of the current model are compared with the elastic data [17] for saturated mortar specimens composed of ASTM Type I/II Portland cement and screened 20–30 Ottawa sand with wo=0.3 overall water–cement ratio. Assuming a uniform distribution of aggregate sizes between the 600 and 850 μm sieve openings yields an average radius of ra=363 μm. The moduli of sand are taken as the typical values for a sandstone or quartz-rich rock adopted by Kuster and Toksöz [20]. These elastic properties

Closure

A model has been presented which quantifies the spatial distribution of cement and water–cement ratio gradient through the ITZ of cementitious composites. This model has for the time being assumed that the parameter ac is constant and approximately equal to −0.5. Further investigations are required to ascertain any dependencies that this parameter may have and perhaps if different functional forms of the variation of the cement content through the ITZ are warranted. Specific results were

Acknowledgements

The assistance of Chris Shoemaker is acknowledged as is his support through the Pratt School of Engineering's Engineering Undergraduate Fellows program administered by Martha Absher.

Cited by (0)

View full text