LCPC developed this model for predicting concrete properties from its composition. Concrete is defined as a granular mixture (from cement to the coarse aggregates) in a water suspension. A concrete with no workability, i.e., no flow, is defined as a concrete where the porosity is filled with water. This statement implies that there is no excess water between the solid components. Therefore, the yield stress can be correlated with the stress needed to initiate flow by overcoming the friction forces between the particles. These forces depend on the number and type of contacts between the particles.
Each component, i, of the mixture is defined by its close packing
density, 
*i
, and the volumetric fraction of solid material (with
respect to a total volume of one),
i. A close packing density, *i , is
defined as the maximum possible value of
i, with all the other j (j
i) being constant. Also, the whole mixture is characterized by
a close packing maximum, *, and the
volumetric fraction of the solid materials,
.
The yield stress, 
0
, can then be defined as:
where f is an increasing function because the yield stress will
increase with increasing value of
i /*i .
To determine the viscosity dependence on the volumetric concentration, we can assume that the speed of each particle under shear is the same and equal to the macroscopic speed. Therefore, it is assumed that the flow of the fluid between the particles is laminar and that the shear resistance will remain proportional to the overall gradient. Thus, if the Bingham equation is assumed to be valid, the plastic viscosity can be deduced to be:
where µ0 is the plastic viscosity of the suspending fluid and g is an increasing function, because the viscosity will increase with increasing concentration of particles.
These equations were tested by comparison with a series of 78 concrete batches in which rheological parameters were measured using the BTRHEOM. The close packing and the volumetric fraction of each component were calculated using the CPM [9]. The plastic viscosity was determined by a best-fit equation, given by the equation below, from the data shown in Figure 4.
Figure 4: Plastic viscosity (µ') of the mortars and concretes as a function of their relative solid concentrations. SP = Superplasticizers or HRWRA; SF = Silica Fume
The yield stress can be calculated by a linear combination of all the components´ volume fraction/close-packing ratios. It appears that different coefficients need to be calculated for concrete with and without High-range Water Reducing Admixtures (HRWRA). The data used were from the same set as used for the viscosity.
For mixtures without HRWRA the yield stress was:
'0
= exp (2.537 + 0.540 K 'g
+0.854 K 's
+1.134 K 'c )
And, for the mixtures with 1% HRWRA (without silica fume), it was:
'0
= exp (2.537 + 0.540 K 'g
+0.854 K 's +
0.224 K 'c )
In these equations, '0
is the yield stress obtained by fitting of the rheometer
results in accordance with the Herschel-Bulkley model. The indices g, s
and c relate to gravel, sand and cement, respectively, and
Kx is equal to (1- x /*x ).
Figure 2: Comparison between experimental values and model values of the yield stress [9]
These results were confirmed with other data sets resulting from variation of the coefficients used in fitting the data [ 36].
This model is part of a larger set of models that can take into account other properties of both fresh and hardened concrete. This model links the composition of the concrete with its performance [36].