The Herschel-Bulkley model appears to offer some benefit in describing the flow behavior of concretes. However, its ability needs further confirmation. Nevertheless, after a systematic fitting of 62 tests dealing with HPCs made in the past at the Laboratoire Central des Ponts et Chaussées (LCPC), the b parameter was only rarely equal to 1. Further, a link seems to exist between a and b (Figure 3 ). However, this link could depend on some mixture-design parameters, e.g., the presence of HRWRA.
Figure 3. - Relationship between a and b parameters, in a set of High-Performance Concretes tested at LCPC.
From a practical viewpoint, a 3-parameter model may be difficult to handle (especially if the aim is to specifiy the rheological characteristics, and to control them by optimizing the mixture-design). If a systematic link exists between a and b in equation (3), then the model only contains two independent parameters. If the relationship between a and b is not general, another solution would be to keep the Bingham model, with parameters deduced from the HB model. Then the yield stress would be 0 , and the equivalent plastic viscosity µ' would be calculated enabling the Bingham straight line to give the best possible approximation of the HB curve, in a certain strain gradient range [ 0, max ] (Fig. 4.). By using the least square method, it is found that:
In this case, µ' would become a good parameter for characterizing the secondary aspects of concrete workability. For the mixtures tested, max = 6 s-1 (see Table 2).
Figure 4. - Approximation of the HB rheogram by a modified Bingham straight line.
The authors would like to thank John Winpigler and Frank Davis for their valuable help in performing the tests and setting up the needed instruments. Also their appreciation goes to W.R. Grace Co. for providing the concrete mixer and the HRWRA used in this study.