2.3.1 Using the Mixing Truck as a Rheometer

To transform a truck mixer into a rheometer requires that at least two entities be measured: the rotational speed of the drum and the power consumption or torque used by the mixer motor during rotation. To obtain both the yield stress and the viscosity it is necessary to obtain data at several speeds. The methodology proposed here requires the measurement of the power during mixing, the load volume, the mass of concrete, and the shear rate in the concrete, which is deduced from the drum rotational speed and geometrical characteristics. The values of these two variables (power and shear rate) at different speeds may be plotted against each other. The slope of this resulting curve according to the Bingham model will give the plastic viscosity and the intercept at zero shear rate will give the yield stress. The concrete truck mixer used (Fig. 1) was fitted with a device capable of measuring the oil pressure to turn the drum (also called slump meter). The drum speed using a stopwatch. The Bingham test involves sweeping shear rates from high to low and measuring the stress at various shear rates. Therefore, the drum was turned at the highest possible speed, 1.74 rad/s (16.66 rpm), and then gradually decreased in discrete steps to zero while the oil pressure was measured. The calculation method to determine the shear rate in the drum from the speed and the truck geometrical characteristics was developed in Ref. [12]. The truck used had a capacity of about 7.5 m³, with a drum radius, R, of 1.20 m. The maximum drum speed, n, was 1.74 rad/s (16.66 rpm or 0.278 rps). These data were provided without uncertainty information by the manufacturer of the truck. The tangential velocity of concrete in the drum during mixing (Fig. 2b) can be calculated using Eq. (1):

with n in rad/s and R in m.

Fig. 1. View of the used truck, the slump indicator (bottom left) and the interior of the drum (top right).

The truck drum used is inclined at a small angle ², 12.5º, to allow the concrete to slide to the front of the drum during mixing. The front of the drum is located behind the driver's seat (Fig. 1). Along the length of the drum, a blade is attached perpendicular to the side of the drum, making a relative angle, θ, with the axis of the drum. This angle determines the pitch of the spiral made by the blades and it ranges from 55º to 70º. The average value of the cotangent of the angle can be calculated as follows:

(2)

This value is used to calculate the velocity of the concrete, V_c−m, inside the drum as it moves forward due to combined effect of the blades and the drum rotation, as shown in Eq. (3).

(3)

An approximate value of the shear rate in the concrete, , can be calculated using Eq. (4):

(4)

where :

δ: side length of the element of concrete considered (Fig. 2a)
y: the displacement during the time interval t
t: time required for the displacement of the element of concrete considered
For example, if δ is 0.06 m, with a V_c−m of 1.11 m/s, then the interval t is equal to 0.06/1.11 or 0.054 s and the shear rate:

(5)

There are other regions of higher shear rates between the nearly static material along the blade at the shell and these flowing elements. However, as Ref. [12] explains, it can be estimated that the maximum shear rate applied to concrete in the drum does not exceed 30 s⁻¹.

Fig. 2. Geometrical characteristics of the drum of the used mixing truck. (a) Flow of plastic concrete relative to blades during mixing. The concrete flow was modelled as continuous discrete finite elements. The square elements have δ = 0.06 m sides. The higher shear rate is certainly localized at the angled end of the blade. (b) details of flow of concrete around one of the blades.