1 Introduction
Concrete pumping involves the flow of a complex fluid under high pressure in a pipe, and thus predicting flow behaviors of concrete pumping is challenging research area. For the characterization and prediction of the flow of concrete pumping, the fundamental understanding of various factors is needed, which include rheological properties, dynamic segregation, stability of constituent materials, geometry of a pumping circuit, slip layer formed between bulk concrete and a pipe wall, and relationship between the pressure and flow rate. The flow of concrete in a pipe differs from the one of typical viscous fluids like water or oil. The primary difference is that concrete is a yield stress fluid. Therefore, there is at the center of the pipe (i.e. around the symmetry axis where the shear stress is equal to zero) a zone where the concrete is not sheared (Jacobsen et al.
2009). Most researches on concrete pumping in the literature account for the yield stress and the existence of the unsheared zone (Vassiliev
1953; Kaplan et al.
2005; Feys and Schutter
2005) by assuming that concrete behaves as either the Bingham fluid or the Herschel Buckley fluid. The second reason for the difference is that under the action of shear, the redistribution of particles occurs within a pipe, which is a common feature of particle suspensions. Initially well mixed particles in a concentrated suspension flows undergo migration from high shear rate regions to low shear rate regions (Phillips et al.
1992; Ingber et al.
2009; Lu et al.
2008). During concrete pumping, shear concentrates in the fluid layer of material depleted of the coarsest particles of concrete. Therefore, the pumping of concrete can be generally considered to be the shearing of an annular layer of unknown thickness and made of a material with certain rheological properties.
While particle collisions in highly sheared and/or highly concentrated zones enforce particles to migrate from these zones, it is counterbalanced by the local increase in concrete viscosity resulting from this migration (i.e. in the bulk). The shear induced particle migration (Choi et al.
2013a) is due to the competition between gradients in particle collision frequency and gradients in the viscosity of concrete within a pipe. When cement particles migrate, they encounter a high viscosity of bulk concrete, in which sand and gravel particles have already migrated and should be prevented from migrating inside the bulk. Therefore, the migration of small particles like cement particles can be neglected, compared to the migration of large particles, such as sand and gravel particles. Because of such migration characteristics, the slip layer is generated along the high shear and/or concentrated zone, which can be considered, as an approximation, as being similar to the constitutive cement paste in concrete pumping. This layer is often called the lubrication layer or the slippage layer.
The existence of the lubrication layer was first suggested by Aleekseev (
1952) and Weber (
1968). Morinaga (
1973) noted that based on theoretical flow behaviors of concrete, the pumping of concrete would not be possible without the formation of the lubrication layer. Sakuta et al. (
1979) reported that the flow properties of the bulk material were irrelevant; the only property that matters is the ability of the material to form this layer. Jacobsen et al. (
2009) conducted experimental research with colored fresh concrete after flowing ordinary concrete to observe the flow conditions in various pipes. Rossig and Frischbeton (
1974) pumped colored concretes in a pipe for the direct observation of the flow profiles. Their results revealed the existence of a high velocity and paste rich zone at the vicinity of the pipe wall. The thickness of the lubrication layer was estimated in the range of 1 mm and 5 mm (Choi et al.
2013a,
b; Browne and Bamforth
1977). Feys and Schutter (
2005) reported that the thickness and rheological properties of the layer appear to depend on the mix proportions of the pumped concrete. The macroscopic consequences of this layer on the pumping pressure were considered by introducing interface properties measured macroscopically using a tribometer to the pumping process prediction (Kaplan et al.
2005). In summary, the formation and characteristics of the lubrication layer are essential on concrete pumping and thus a detailed analysis of the layer is necessary to understand flow behaviors.
Several studies have examined the rheology of cement slurries which is the constituent material of the lubrication layer for other applications, which include the descriptions of the thixotropic behavior (Papo
1988), and the hysteresis effects in the shear rate/shear stress relationship (Xuequan and Roy
1984; Atzeni et al.
1985; Grzeszczyk and Kucharska
1988). Modified consistometers have been applied to provide gel build up information, as used by Keating and Hannant (
1990). Banfill and Kitching (
1990) used controlled stress rheometers to examine the yield stresses of cement slurry.
As one of the important information of the rheology, the viscoelastic properties are associated with the slurry microstructure. Several researchers have investigated viscoelastic properties of cement slurry mixtures. Tattersall and Banfill (
1983) demonstrated that the paste undergoes the breakdown of structure while the amplitude of shear increases. Cooke et al. (
1988) examined viscoelastic parameters for both flowing and curing cement slurries. Chow et al. (
1988) discussed the use of the viscoelastic parameters as an alternative to consistometer studies. Saaka et al. (
2001) measured viscoelastic properties of cement paste, and illustrated the effect of wall slip on the shear yield stress. Figura and Prud’homme (
2010) considered the viscoelastic response of cements with curing-rate control additives. However, little attention has been paid to the viscoelastic properties of flowing materials for examining the flow behaviors, particularly in the pumping industry.
Therefore, the present study examined the viscoelastic properties using dynamic oscillatory measurements to quantify the flow behavior of concrete pumping. Dynamic modulus measurements on the cement paste, which could be considered a constituent material of the lubrication layer, were taken. Steady shear measurements were simply conducted to examine the basic rheological properties like the yield stress and the plastic viscosity while the dynamic oscillatory tests were performed to evaluate the dynamic modulus. The relationship between the measured yield stresses and the dynamic modulus was derived and the implications of the correlation are discussed.
2 Theoretical Background for Viscoelastic Measurements
A dynamic oscillatory shear test is a rheological technique that provides information on viscoelastic materials. This is a dynamic method, in which strain or stress oscillates according to a sinusoidal function. The measured output is the level of stress or strain and the extent to which the stress and strain is in phase with the applied strain or stress. By limiting the strain to small amplitude, the particles remain in close contact with one another and the microstructure is not disturbed.
When a material of a yield stress fluid is sheared under an applied sinusoidal oscillation with a sufficiently small amplitude, the measured dynamic behavior may be linear and can be analyzed in terms of the theory of linear viscoelasticity. Details of the theory and the methods for measuring the viscoelastic properties are well documented in the literature (Ferry
1970; Marin
1988; Nguyen and Boger
1992; Schultz and Struble
1993).
In general, the oscillatory strain at time
t is defined as
$$ \gamma = \gamma_{0} \sin (\omega t) $$
(1)
where
\( \gamma \) is the strain at time
\( t \),
\( \gamma_{0} \) is the strain amplitude, and
\( \omega \) is the frequency. The resulting shear stress is sinusoidal and proportional to the shear strain in the out-of-phase mode
$$ \tau = \tau_{0} \sin \,(\omega t + \delta ) $$
(2)
where
\( \tau_{0} \) is the maximum shear stress and
\( \delta \) is the phase angle between the applied strain wave and the stress response. The shear stress (Eq. (
2)) can be expressed using two viscoelastic terms, in-phase term and out-of-phase term, as expressed below;
$$ \tau = \tau ' + \tau '' = \gamma_{0} (G'\sin (\omega t) + G^{\prime \prime }\cos (\omega t)) $$
(3)
where
\( G^{\prime } \) is the storage modulus and
\( G^{''} \) is the loss modulus. The storage modulus
\( G^{'} \), representing the in-phase component of stress, is a measure of the elastic energy stored per deformation cycle. The loss modulus,
\( G^{\prime \prime } \), representing the out-of-phase component, is associated with the dissipated viscous energy per cycle. The ratio of
\( G^{\prime \prime } \) to
\( G^{\prime } \) provides the tangent of the phase angle. A perfectly elastic fluid leads to
\( G^{''} \) = 0 and
\( \delta \) = 0, whereas an inelastic viscous fluid results in
\( G^{'} \) = 0 and
\( \delta \) = 90°. In viscoelastic liquids, both moduli are nonzero and the phase angle, which lies between 0° and 90°, depends on the relative contribution between the elastic effect and the viscous effect. Through the dynamic oscillatory measurements, the oscillatory parameters,
\( G^{'} \) and
\( G^{''} \), can be analyzed to determine viscoelastic properties.