Rheology, defined as “the study of deformation and flow”, provides a measure between shear stress and rate of deformation. The corresponding constitutive equation can be employed to describe mathematically the flow of fresh concrete. Concrete composed of cement particles, aggregates, water and air, can be characterized as suspended solid particles (aggregate) in viscous media (cement paste) [1], [2], [3], [4], [5]. Numerous constitutive equations have been proposed to characterize the rheology of fresh concrete as suspensions, but only Bingham model and Herschel and Bulkley (HB) model have received wide acceptance. For normal concrete, experimental data have confirmed that the flow of fresh concrete follows Bingham’s material model, i.e.:

$$\tau ={\tau}_{0}+n\dot{\gamma}$$(1)

In which *τ* is the shear stress (Pa), *τ*_{0} the yield stress (Pa), *n* the plastic viscosity (Pa s), and $\dot{\gamma}$ the shear strain rate (1/s). *τ*_{0} and $\dot{\gamma}$ are referred to as Bingham material properties with the first property providing a measure of the shear stress required to initiate flow and the second one a measure of the material resistance to flow after the material begins to flow. These two rheological properties are therefore needed to quantitatively characterize the flow of fresh concrete. Murata and Kikukawa [6] implemented Roscoe’s [7] equation to quantify the plastic viscosity of concrete, and proposed the following methodology: Calculate the plastic viscosity of cement paste by postulating that cement particles are suspended in water, i.e. there are no physical or chemical interactions between the cement particles and water. Then by recognizing that Roscoe’s equation was developed with the premise that the particles are solid, spherical, and identical in shape and size, they proposed an extension to account for the irregularly shaped and non-uniform size of the particles. They proposed the following relation

$${}^{i}{n}_{r}=\frac{{}^{i}n}{{}^{i}{n}_{0}}={\mathrm{(}1\text{-}\frac{{}^{i}\phi}{{}^{i}C}\mathrm{)}}^{{\text{-}}^{i}k}$$(2)

where ^{i}*k*=^{i}*k*_{1} *φ*+ ^{i}*k*_{2}, superscript “*i*” is set equal to 1 for cement paste, 1gr becomes the relative plastic viscosity of cement paste, 1g the plastic viscosity of cement paste, 1g0 the plastic viscosity of water, 1u the volumetric concentration of cement, 1C the percentage of absolute volume of cement, and 1k the coefficient of agglomerated cement particles and coefficients ^{i}*k*_{1}, ^{i}*k*_{2} are constant and are found through regression.

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