Testing of concrete performance starts with measuring concrete rheology, the assessment of how concrete flows into prepared forms before the setting point is reached. The well-known slump test is an empirical measurement of how concrete will flow in a given situation. Work in the last few decades clearly indicates that concrete rheology must be characterized by at least two parameters: yield stress and plastic viscosity. The slump test only measures the yield stress. But plastic viscosity is needed as well to fully understand and predict the rheology of concrete, which in turn determines the workability and flowability of the material.
Because concrete is a mixture of materials crossing many length scales, spanning from micrometer-sized cement grains up to coarse aggregates 20,000 times larger, rheological investigation involves a multi-scale approach. The rheology of the cement paste greatly influences the time-dependent rheology of the concrete, and is itself non-Newtonian and complex in its physical attributes. Concrete's large fraction of aggregates, 60% or more (by volume), also has a very large effect on its rheology. Simultaneous modeling of the hydration process and cement paste rheology is beyond current computational capabilities. Therefore, a combined theoretical-experimental approach has to be taken. As a consequence, cement paste and mortar rheology is measured in a rheometer. The effect of coarse aggregate on concrete rheology is modeled using a dissipative particle dynamics (DPD) approach. This is similar to a molecular dynamics technique for depicting the movement of atoms and molecules, but adapted instead for coarse-aggregate-sized particles. Figure 3 illustrates using the DPD model to show how realistic coarse aggregate particles arrange themselves under mixing forces. The rheological properties of the matrix of the suspension in Fig. 3 are supplied from cement paste and mortar measurements.
Fig. 3: A dissipative particle dynamics (DPD) simulation of coarse aggregate in a mortar matrix flowing under mixing forces.
Experimental measurements of concrete rheology use different concrete rheometers. Several of these different designs are available, and test results are being compared in a current program sponsored partly by ACI. DPD simulations can analyze flow in different rheometer designs and extract fundamental parameters from empirical test forces results. Extracting fundamental rheological parameters like plastic viscosity and yield stress from such experimental measurements will permit their use for analyzing and predicting concrete flow under field conditions. Figure 4 plots the results of experimental and DPD simulations for relative viscosity of a concrete versus the volume fraction of coarse aggregate. Relative viscosity is the plastic viscosity of the concrete divided by the plastic viscosity of its mortar matrix. Figure 4 reveals good agreement between modeling and experimental results, with relative viscosity increasing as more coarse aggregate is added. There has also been work with DPD modeling undertaken for empirical testing of concrete flow in self-compacting concrete (SCC), thus offering the potential for basing these tests on more fundamental materials science.
Fig. 4: Comparison of results using dissipative particle dynamics (DPD) with experimental rheometer data relating the dependence of relative viscosity of fresh concrete on the volume fraction of coarse aggregate. Two different rheometers were used. The solid line has been drawn in only as a guide for the reader's eye
To model the development of cement and concrete properties over time, a proper understanding (and model) of the hydration process is essential. While a complete understanding of cement hydration is still lacking, a significant knowledge base for it has been accumulated over the past 100 years of experimentation. The two most influential parameters for predicting properties of cement and concrete are water-to-cement mass ratio (w/c) and degree of hydration. If degree of hydration (of both cement and pozzolans) can be accurately predicted, many other properties can also be computed. The VCCTL hydration model operates on three-dimensional packings of cement particles having realistic shapes and chemical phase compositions, as was shown in Fig. 1(b). The model dissolves portions of the particles involved, allowing them to react with the surrounding water to produce a hydrated three-dimensional microstructural image of cement paste, where each three-dimensional voxel is occupied by a unique phase of the cement paste.
A hydrated image thus generated can be used to compute various property values, including set point, heat generation and temperature rise, chemical shrinkage and self-desiccation, and ionic diffusivity. In addition, values for mechanical properties can also be calculated. By treating each voxel as a tri-linear finite element, the overall elastic moduli of the cement paste model can be directly computed by using finite element techniques. Recently, investigators undertook careful testing of this combined algorithm. Figure 5 compares model and (experimental) dynamic moduli results for 28- and 56-day-old cement paste samples, graphed as a function of w/c. As can be seen, there is excellent agreement between virtual and experimental results for cement paste. Effective medium theory can then compute the contributions of the aggregates and any accompanying interfacial transition zones to the concrete elastic moduli. The effect of aggregate shape is taken into account quantitatively. This prediction for concrete is being validated at present.
Fig. 5: Comparison of dynamic elastic moduli (Young's modulus E, shear modulus G) virtual testing predictions (dashed lines) to experimentally generated data (solid lines), versus w/c, for 28- and 56-day specimens of cement paste. For each w/c, the upper plot is for 56-day values and the lower is for 28 days. Note: 1 GPa = 145 ksi
Compressive strength is used more in the cement and concrete industries than is elastic moduli. Employing materials science to directly and fundamentally calculate compressive strength based on microstructure is a topic of research at present. The goal is to develop a multi-scale strength of materials technique that can give accurate, microstructure-based predictions of compressive strength. In the meantime, several semi-empirical approaches are possible for the prediction of compressive strength. The first is (based on) Power's gel-space ratio theory. The VCCTL cement hydration model can directly calculate this parameter using the theory, and for any degree of hydration for either portland or blended cements. With at least one experimental measurement of early-age compressive strength to calibrate the parameters of this semi-empirical theory, compressive strength can then be estimated at later ages. Normally, either a 3- or 7-day strength measurement is performed and the resulting strength prefactor is used to predict the 28-day and later strength.
While originally developed for portland cement systems, the theory has recently been applied successfully to blended cement systems. It would be preferable to predict compressive strength development directly without requiring an early-age measurement. Still, the previously mentioned procedure can result in considerable time and cost savings because it reduces the 28-day evaluation window to either 3 or 7 days.
Because elastic moduli development can be accurately predicted with VCCTL software, another semi-empirical approach for predicting compressive strength is to first compute elastic moduli. Compressive strength is then estimated based on a functional relationship between it and elastic moduli. A convenient empirical equation relating Young's modulus and compressive strength, resulting from many experimental results, can be found in ACI 318.An important area for virtual testing is the durability of concrete since conventional test methods tend to be very time consuming. Investigators are considering degradation mechanisms at the microstructural level, and the most recent versions of the VCCTL program permit simulations of sulfate or chloride attack at the level of the cement paste's microstructure. Discussions have also taken place about linking the VCCTL to the SUMMATM durability project, headed by Jacques Marchand of Laval University, to bring durability prediction more closely into the scope of the VCCTL.