Ferraris and Martys are developing a new procedure that includes simulation of the concrete flow. The procedure is based on the chart illustrated in Figure 6. The cement paste rheological parameters, yield stress and viscosity, are measured using a laboratory fluid rheometer. The cement paste in this case includes any chemical and mineral admixtures that are selected. Then these values along with the mixture design of the mortar or concrete, i.e., gradation, shape and total content of aggregates, are used as input to a computer simulation. The output is the rheological parameters of concrete. The simulation method is in the process of being developed and is presented below.
Figure 6: Principle of the procedure
To be able to succeed in the procedure illustrated in Figure 6, the rheology of the cement paste needs to be measured in the same conditions experienced in concrete, i.e., at the same shear rate and the same temperature. Barrioulet et al. [37] studied a set of concrete mixtures having cement pastes of various compositions but with the same viscosity, and with various aggregates having the same shape and gradation. They found that the flow of these concretes was not the same. They attributed this difference to the fact that the rheology of the whole is not equal to the rheology of the parts if the interactions between the parts were not considered. It is believed that the error was to measure the viscosity of the cement paste without taking into account the condition of shear experienced by the cement paste in concrete. Therefore, the following three experimental parameters need to be monitored:
In Figure 6, the link between the mixture design/cement paste rheology and the concrete rheology is a simulation model. The simulation of concrete flow is based on a mesoscopic model of complex fluids called "dissipative particle dynamics" (DPD) [43] that blend together cellular automata ideas with molecular dynamics methods. The original DPD algorithm utilized symmetry properties such as conservation of mass, momentum and Galilean invariance to construct a set of equations for updating the position of particles, which can be thought of as representing clusters of molecules or "lumps" of fluid. Later modifications to the DPD algorithm resulted in a more rigorous formulation and improved numerical accuracy. An algorithm for modeling the motion of arbitrary shaped objects subject to hydrodynamic interactions by DPD was suggested by Koelman and Hoogerbrugge (KH) [44 , 45]. The rigid body is approximated by "freezing" a set of randomly placed particles where the solid inclusion is located and updating their position according to the Euler equations.
Martys are currently extending the DPD method to model the flow of concrete as a function of mixture design. The procedure of KH for representing rigid bodies is ideally suited for modeling the flow of concrete because this technique easily allows for the representation of wide distributions of particle size and shape such as are common in concrete. As a test of the DPD method, Martys studied the flow of a suspension of spheres of equal radii under shear as a function of solid fraction and shear rate. Figure 7 shows a configuration of densely packed spheres at a solid fraction (volume of spheres/system volume) of 0.5. A constant rate of strain is applied in opposite directions at the top and bottom of the system.
Figure 8 shows a trace of the sphere positions over several time steps. Near the top and bottom, the spheres flow more smoothly as they respond to the applied strain. In the middle horizontal region the spheres appear to diffuse more as the velocity is zero on average here. Figure 9 shows the effective viscosity as a function of (solid fraction)/(maximum packing fraction of random spheres). Note that at higher solid fractions the suspension exhibits shear thinning.
We have begun to examine the effect of varying the distribution of sizes of the spheres. For instance, at a solid fraction of 0.4, 10 percent of the spheres were replaced with smaller spheres (about 1/6 of the radius) while fixing the total solid fraction. For this simple change in composition the viscosity decreased by about 8 percent. Similar results were found in physical experiments examining the flow of cement paste where some of the cement particles were replaced by fly ash, which are about a factor of 10 smaller in diameter.
Future studies will include evaluation of the effects of particle shape, as ellipsoids with varying aspect ratio replace spheres in the DPD simulations, and we will also investigate the effects of the roughness of walls on the plastic viscosity and yield stress.
To validate the DPD method, rheological properties should be measured using a rheometer that allows the calculation of the rheological parameters in fundamental units. We are in the process of validating the model with data from concrete and cement paste made using the same raw materials.
Figure 7: A configuration of densely packed monosized spheres at a solid fraction (volume of spheres/system volume) of 0.5. The system is composed of 52 spheres.
Figure 8: Traces of the centers of spheres moving under an applied shear strain. Near the top and bottom layer the spheres move along relatively smooth paths. Near the center, the spheres move more slowly as the mean velocity is close to zero in this region.
Figure 9: Viscosity, 
, of
suspension normalized to solvent viscosity,
0 vs. solid fraction,
, normalized to maximum random packing
fraction,
0. The solid (squares and triangles) data
points are computer simulation data, while the X´s and 0´s are derived
from experiments [46] on sheared hard sphere
colloids. The X's correspond to an infinite shear rate limit while the 0's
correspond to the zero shear rate limit. The three simulation data at the
highest solid fraction correspond to different shear rates (approximately a
factor of ten greater with decreasing viscosity on the figure).