The rheological behavior of a fluid such as cement paste, mortar or concrete is most often characterized by at least two parameters, τ0 and µ , as defined by the Bingham equation [7]:
|
τ = τ0 + µ
|
(1) |
where τ is the shear stress applied to the material
(in Pa), τ0 is the yield
stress (in Pa), µ
is the plastic viscosity in (Pa·s), and
is the shear strain
rate (also called the strain gradient) (in s−1). The yield
stress and the plastic viscosity are the Bingham parameters that
characterize the flow properties of the material. For special concretes,
such as self-leveling concretes, a third parameter might be necessary to
correctly represent the shear rate-shear stress relationship. Other
equations have been used for describing the concrete flow, because in
certain circumstances concrete flow does not obey the Bingham equation
[5, 6]. The
cement paste on the other hand is either described as a Newtonian fluid
(τ0 = 0,
µ
0) or a Bingham fluid (τ0
0, µ
0).
Figure 1 explains why if only one of the two
parameters is determined, prediction of a material field performance might
not be correct. To determine the yield stress and the viscosity of cement
paste, mortar or concrete, the instrument must be able to measure stresses
generated at a minimum of two different shear rates
[7]. Nevertheless, most of the instruments or methods in use for
concrete are either not able to shear the concrete at various shear rates,
or the shear rates are not measured or controlled [8]. Therefore only one of the two Bingham parameters can be estimated.
Tattersall [7] was the pioneer in developing a
concrete rheometer with controlled shear rates capable of measuring the
stresses in concrete. Presently, three commercially available rheometers
exist capable of varying: IBB
[9], BML viscometer [7
, 10] and the BTRHEOM [11,
12]. The results of research presented in
[5], were obtained using the BTRHEOM because it
gives the rheological parameters in fundamental units, i.e., Pa and
Pa·
s for yield stress and viscosity respectively. The instruments mentioned
above can be used for mortar, although some tests specifically designed for
mortar do exist, i.e., the flow table [13].
The situation for cement paste is different, because the largest particle size is still small enough to allow the use of a fluid rheometer designed for other materials.
Figure 1: Definition of the Bingham parameters for concrete flow
Most researchers use a concentric cylinder geometry [4, 14], because it is the most common geometry available, but great precautions need to be taken to avoid sedimentation and slippage. Also, the gap or distance between the two cylinders is fixed. Therefore, the values obtained are those of bulk cement paste, not of the cement paste confined between two aggregates, preventing a possible correlation with concrete. The only geometry that allows a variable gap is the parallel plate (see Figure 2). Few researchers [3 15, 16] use this geometry for cement paste. Unfortunately, the only part that the three researchers from [15, 16, 3] have in common is the geometry of the instrument. The data and the scope of their research are all different. It is beyond the scope of this paper to discuss their different approaches.
The shear history of a cement paste affects its flow parameters, therefore it is important to handle the cement paste with the same shear rate as it will experience in concrete. The shear rate of cement paste in concrete during mixing and placement was established by Helmuth at 70 s-1 [4]. Also the shear rate applied to the cement paste in concrete during a rheological test is from 3 to 24 s-1, as determined when the calculation are based on the shear rate applied to concrete in a BTRHEOM rheometer [5].
The mixing method affects the rheological response of the cement paste [15], therefore a controlled speed mixer is the best method to insure that the cement paste is always mixed in the same way. The method was designed by PCA [4]. It will be shown how this new method improves the reproducibility of the results.
Figure 2: Parallel plate geometry
Depending on the cement paste content of a given concrete, the gap between the aggregates can vary significantly. To estimate the average gap between aggregates we used a mathematical method developed by Garboczi and Bentz [17] based on equations developed by Lu and Torquato [18]. The aggregates are treated as spheres suspended in a cement paste matrix. The volume of paste contained in a shell of thickness r around each aggregate is accurately given by the equations, even allowing for overlaps between shells. The value of r is computer where 99 % of the paste is contained in the shells, and the gap is taken to be twice this value. The mathematical calculation has been shown to be very accurate for a wide range of concretes using numerical analysis [19]. As examples of concretes to calculate the gap, concretes described in ref. [5] were used. The gaps were computed to be between 0.16 mm and 0.22 mm. These gaps are much smaller than gaps used by most researchers in concentric cylinders geometries, which are in the range of 0.7 mm to 1 mm. The gaps calculated to be in concrete are of the order of 2-3 times the maximum particle size of the cement, while the gap used by most researchers is 20-25 times the particle size. These large gaps lead to measurements of the bulk values of the cement paste rheological parameters and not the " correct" value to be used to correlate cement paste rheology with concrete rheology.
In summary, a test for cement paste that is designed to be used to predict concrete rheology should have a mixing pattern that reproduces the shear history of concrete, a gap between the plates of the rheometer that is related to the cement paste content of the concrete, and a shear rate sweep range that corresponds to the shear rate range of the concrete tested.