To establish a model to link the mixture composition with the rheological properties and to validate such a model, an ambitious experimental plan was developed and conducted. A total of 78 mixtures were made and tested using the slump tests and the rheometer test without vibration. The formulation of the mixtures covers the whole range of mixtures proportions having flow properties measurable by the rheometer. Analysis of the test results led to a modification of the widely-used assumption that concrete behaves as a Bingham fluid. The three-parameter Herschel-Bulkley model was found to be better able to describe the non-linear behavior of fresh concrete than the two-parameter Bingham linear model. The essential argument for using the Herschel-Bulkley model is provided by the self-leveling concretes, for which a calculation of the rheological parameters using the Bingham model often leads to meaningless a negative yield stress. On the contrary, the Herschel-Bulkley model always gives a positive value of yield stress that is reasonably well correlated with the results of the slump test (slump or slump flow depending on the mixture under consideration). Nevertheless, for pratical applications, the Bingham model could still be an effective tool, provided that the method of calculating the yield stress and plastic viscosity parameters is changed. Simple modifications of the Bingham equations have been proposed to give better fits to the data.

A model for predicting the rheological properties of the mortars and concretes (yield stress and plastic viscosity) from the mixture composition, and fundamental characteristics of the components was proposed. To test the general validity of the model, it should be applied to other mixtures with different constituent characteristics.

The plastic viscosity was described as a function of the relative volumetric concentration of solids of the mixture in accordance with a model that, for the mixtures tested, proves to be independent of whether a HRWRA or a mineral admixture (silica fume) is present. As for the yield stress, it is expressed in terms of the sum of the relative solid volumetric concentrations of the particles classes, modified by coefficients that take into account the roughness and size of the particles and their capacity to absorb the HRWRA, if present.

The different forms of the two models for yield stress and plastic viscosity explains the absence of a general correlation between yield stress and plastic viscosity, basis for the development of the fresh concrete rheology [1]. It is possible to explain why high-performance concretes have viscosities that are generally higher that those of ordinary concretes. It was found that HRWRA, acting as a water reducer, lowers the yield stress much more than the plastic viscosity. This also allows one to foresee that the optimal granular proportions of concrete for rheological properties will not be the same for ordinary concrete (without HRWRAs) as for self-levelling concretes (with HRWRAs). Finally, in the presence of HRWRA, the contribution of the cement to the yield stress is much reduced. This explains why, for concretes with a very low yield stress and a normal or high plastic viscosity (the case of self-levelling concretes [44]), the optimal composition is rich in fine materials.

The proposed models need to be validated using a larger pool of constituent materials. If and when validated, they can be easily integrated into a computerized system for mixture proportioning. The plastic viscosity can be estimated from measurements of the size distribution and packing density of the materials. The model for estimating yield stress needs to be further validated to determine whether the values of the parameters apply to a whole family of materials or, must be modified when the components are changed.

Finally, a modification of the standard slump test intended to make it possible to evaluate for fresh concretes the two parameters in the Bingham equation is presented. The procedure has been described in detail and the results of tests on 78 mixtures have been reported. The conclusions are as follows:

• From the final slump and the density of the concrete it is possible to estimate the yield stress in the field for a concrete with slumps greater than 100 mm;
• From the slump times and, yield stress and the density of the concrete an estimate can be made of the plastic viscosity for concretes with slumps between 120 and 260 mm. The range of application is therefore limited to the slump range of most high-performance concretes, currently being used.

The third objective of study, i.e., to provide a field test to estimate rheological parameters, is thus achieved, at least for one category of concretes. Additional areas of research needed to support the development of a standard test method include the following:

• Evaluation of the repeatability and reproducibility of the modified slump test;
• Verification with a wide range of concrete components of the general applicability of the model linking the slump time to the plastic viscosity should be verified with other concretes made of different components;
• Determination of the value of plastic viscosity and yield stress that are required for placement and finishing under different conditions. It must be noted, however, that while the test provides values of the rheological properties that should be useful for quality control purposes, they are unlikely to be sufficiently precise for achieving an optimum mixture composition.
• The rheometer appears to be a valuable tool for monitoring the changes of concrete rheological behavior with time. It can be used for a wider range of concrete flows than does the modified slump test.

8. ACKNOWLEDGEMENTS

The authors wish to specially thank John Winpigler of the National Institutes of Standards and Technology for his participation in the preparation of materials and for the conduct of the rheological tests and Frank Davis, also from NIST, for repair of the concrete mixer. They also have not forgotten the help shown by Pierre Roussel (LCPC) for the tests to identify the binders and by the department of the Physics and Chemistry of Materials of LCPC for the analyses of the components. Finally, they wish to mention the contributions of W.R. Grace Co. which provided the mixer and the HRWRA and the Elkem Company which provided the silica fume. We also would like to thank Drs. James Clifton, Edward Garboczi and Nicholas Carino for the review of this paper.