# Investigations of Mixing Technique on the Rheological Properties of Self-Compacting Concrete
## 1 Introduction  
Production of a concrete that reaches compaction under its own weight is one of the significant advances in modern concrete technology. Self-compacting concrete (SCC) was first developed in Japan owing to the needs of procedures capable of promoting production [1]. The main advantages of SCC can be ascribed to its autogenous levelling and reaching a proper compaction, even when passing through the steel bars. Production of SCC mitigates the conventional means of compaction by vibration, hence leading to less noise and energy, as well as a reduction in labor cost and execution time [2]. The successful use of SCC is based on its high filling ability, high passing ability, and good stability [3, 4]. The first concerns the ability of concrete to change its shape and flow around barriers. The second corresponds to the capability of passing narrow spaces. The third points to a high resistance against static segregation (separation of coarse aggregate and paste) and dynamic segregation (which takes place during transport and casting). SCC is characterized by a low yield value (to readily spread the concrete away from the discharge site) and a relatively high viscosity (to maintain a homogeneous dispersion). It normally contains a higher amount of fine powders than conventional concrete in order to achieve self-compaction. Utilizations of a viscosity modifying admixture (VMA), along withadequate superplasticizer, enable an excellent workability and an adequate segregation resistance while the concrete is pumped or cast into place until the onset of hardening [5]. The rheological properties of fresh SCC significantly influence the mechanical performances and durability properties of the concrete structures [6]. Rheology is the study of the flow of matter, primarily in a liquid state. In this respect, materials with complex microstructure are typically of high interest [7]. The formulation mostly applied for characterizing the steady-state rheological properties, with thixotropy [8] and workability loss not considered, is the well-known Bingham model [9]. This model provides a linear relationship between the shear rate \(\dot{\gamma}\) [1/s] and the shear stress \(\tau\) [Pa] by introducing two variables, yield stress \(\tau_{0}\) [Pa] and plastic viscosity \(\mu\) [Pa-s], as shown in Equation (1). \[\tau=\tau_{0}+\dot{\mu\dot{\gamma}}, \tag{1}\]  
It has been reported, however, that the rheological behavior of fresh SCC is non-linear. The apparent viscosity increases with an increase of the shear rate, i.e., shear thickening [4], and vice versa for the shear thinning [10; 11]. The shear thickening behavior is particularly important at high shear rates when mixing and pumping. Significant shear thickening and shear thinning are undesirable to the engineering application of SCC [12]. In cases of a higher viscosity, a larger amount of energy is required to maintain adequate flow. In some cases [10], the yield stress extrapolated from the Bingham model is negative, which is in reality not possible. Since the non-linear behavior is often observed for SCC, the H-B (Herschel-Bulkley) model as shown in Equation (2) has been proposed. It is considered that the shear thickening appears when \(n>1\) while the shear thinning appears when \(n<1\), where the \(n\) value indicates the degree of shear thickening response [13; 14]. In addition, the modified Bingham model as shown in Equation (3) has also been put forward to describe the rheological properties of fresh SCC, with the shear thickening occurring if \(c/\mu>0\) and the shear thinning occurring if \(c/\mu<0\)[15]. \[\tau=\tau_{0}+K\dot{\gamma}^{n}\;(\tau\geq\tau_{0}), \tag{2}\]  
\[\tau=\tau_{0}+\mu\dot{\gamma}+c\dot{\gamma}^{2}, \tag{3}\]  
where \(\tau\) is the shear stress in Pa; \(\tau_{0}\) is the yield stress in Pa; \(\mu\) is the plastic viscosity in Pa-s; \(\dot{\gamma}\) is the shear rate in 1/s; \(n\) is the flow index; \(K\) is the consistency factor in Pa-s; and c is the second order parameter in Pa-s\({}^{2}\).