MODIFICATION OF THE CONCRETE RHEOMETER TO DETERMINE RHEOLOGICAL PARAMETERS OF SELF- CONSOLIDATING CONCRETE VANE DEVICE

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1 MODIFICATION OF THE CONCETE HEOMETE TO DETEMINE HEOLOGICAL PAAMETES OF SELF- CONSOLIDATING CONCETE VANE DEVICE Ammar Yahia and Kamal H. Khayat Department of Civil Engineering, Université de Sherbrooke, Canada Abstract Workability requirements for successful casting and proper performance of selfconsolidating concrete (SCC) include high deformability and adequate stability. These characteristics depend on the yield stress and plastic viscosity of the concrete. SCC is designed to achieve low yield stress and moderate plastic viscosity in order to improve deformability and segregation resistance. The rheological parameters can be determined using concrete rheometers. Tattersall proposed the two-point workability rheometer and later the MK-III with an H impeller rotating in a planetary motion. Such a rheometer enables to describe the rheology of concrete in terms of flow resistance and torque viscosity. This device does not allow the calculation of the rheological parameters in terms of fundamental values due to the complex shear strain involved during testing. Ideally, rheometer test results should be comparable and independent of the device used, thus facilitating inter-laboratory comparisons and helping improve understanding of SCC s complex behaviour. A study was undertaken to evaluate the possibility of modifying the MK-III rheometer by replacing the H impeller with a four-blade vane device rotating in a co-axial manner. Equations were also derived to convert the torque and rotational velocity values to fundamental parameters of shear stress and shear rate. The use of the modified Tattersall rheometer was validated using various SCC mixtures. In this paper, test results obtained on SCC proportioned with 0.33 and 0.38 w/cm and different nominal size aggregates are reported. Highly viscous SCC mixtures made with relatively low w/cm are shown to fit best the Herschel-Bulkley model. The Herschel-Bulkley model does not lead to the negative yield stress values sometimes encountered when using the linear Bingham model for SCC mixtures that exhibit high thixotropic characteristics. 1. INTODUCTION Self-consolidating concrete (SCC) is designed to achieve high deformability and adequate static and dynamic stability to ensure proper flow into place and self-consolidation, without segregation and blockage during flow. High deformability and proper stability are essential to ensure complete encapsulation of the reinforcement and filling of the formwork. Such concrete is being increasingly used in Canada and elsewhere given its ease of pumping and

2 placement, and hence overall reduction in labor and cost [1]. Successful concrete handling, placement and consolidation depend on the flow behaviour of the mixture. The yield stress and plastic viscosity of the mixture mainly governs such flow. The rheological behaviour of SCC can be determined using a concrete rheometer. Contrarily to cement paste where coaxial cylinder viscometers with small gaps are used, rheological measurements on concrete require the use of relatively wide gap to accommodate the presence of coarse aggregate. The use of a large gap can, however, present difficulties in determining the shear rate across the gap for materials whose viscosity is function of the shear rate, such as concrete. With the growing interest in using and adopting SCC as a standard material for cast in-place and precast concrete operations, and given the complex rheological behaviour of SCC, good understanding of their flow properties is necessary to improve quality control and facilitate mix design procedure. Because of the complexity in assessing fundamental rheology of concrete, various instruments have been proposed. Tattersall was the first to suggest the use of the two-point test where the concrete is mixed in an instrumented mixer []. A number of concrete rheometers were then proposed, such as the modified Tattersall MK-III rheometer with an H impeller rotating in a planetary motion [3]. Such rheometer measures the torque value necessary to maintain a given rotation of the impeller. For example, with the modified Tattersall rheometer, the impeller is rotating at various speeds varying from 0.3 to 0.9 rps and the torque value necessary to maintain a given rotation is monitored. The torque-speed curve can be used to determine the apparent yield stress (g), i.e. flow resistance, and torque plastic viscosity (h) values using a given rheological model, such as the linear Bingham model. Unfortunately, the use of this device does not allow the determination of the fundamental rheological parameters of SCC due to the complex shear strain involved during testing. A comparative study conducted on five different concrete rotational rheometers revealed difference in absolute values produced by the various rheometers [4]. For example, yield stress and plastic viscosity determined on SCC using the BML rheometer ranged from 90 to 140 Pa and from 3 to 45 Pa.s, respectively. In the case of BTHEOM rheometer, these values varied between 500 and 550 and 50 and 78 Pa.s, respectively. heological measurements on concrete using coaxial viscometers can be affected by the wall-slip that may take place at the surface of the rotor, and the discrepancy between values shown by various rheometers is due in part to the slip that can take place during measurements. Furthermore, cement-based materials are time and shear history-dependent materials and their rheological behaviours are affected by various parameters, such as the geometry of the instrument, shear history, test protocol, testing procedure, and mixture parameters, including w/cm, type and dimension of coarse aggregate, as well as the presence of admixture. The objective of the study presented here is to evaluate the possibility of modifying the MK-III rheometer by replacing the H impeller with a four-blade vane device rotating in a coaxial manner. The use of the vane set-up to simulate a coaxial rotation enables the evaluation of rheological parameters in terms of shear stress and shear rate, instead of torque and angular velocity. An attempt is then made to develop equations to convert the torque and rotational velocity values to fundamental shear stress and shear rate parameters.

3 . MODIFICATION OF TATTESALL MK-III HEOMETE - FOU-BLADE VANE The H-shaped impeller rotating in a planetary motion in the IBB rheometer was replaced by a four-blade vane impeller rotating in a coaxial manner. The four-blade vane was used for the first time by Duzy and Boger [5]. The vane consists of four thin blades mounted at equal angles around a smooth cylindrical shaft. In order to eliminate the disturbance that may take place during measurements, especially at high shear rate, each blade has an opening to allow the circulation of concrete (Figure 1). The geometry of the vane as well as opening dimension are optimized to accommodate the presence of coarse aggregate with a maximum size up to 0 mm. With the modified impeller geometry rotating in a co-axial motion, yield stress can occur within the material itself along the localized surface circumscribed by the vane, thus eliminating any wall slip that may take place with coaxial cylinder viscometer. Furthermore, the use of the cross-shaped vane causes less disruption to a sample than introducing the concrete into a conventional geometry, such as coaxial cylinders. The use of the vane set-up rotating in a coaxial manner also enables the determination of the shear rate and shear stress values at the localized surface circumscribed by the vane. Indeed, given the axial rotation and the geometry of the vane, the shear stress and shear rate can be calculated by considering a cylinder of equal dimension as the vane and assuming that the force due to shearing is distributed uniformly over the entire surface of the cylinder. Using the flow curve (shear stress vs. shear rate), rheological parameters can be determined in their fundamental units (Pa and Pa.s instead of N.m and N.m.s). H = 130 r H = 45 h = 100 r = 5 h (Dimensions in mm) Figure 1: Geometry of vane used to determine rheological flow curves

4 3. CALCULATING FUNDAMENTAL SHEA STESS AND SHEA ATE PAAMETES The use of the vane device rotating along a coaxial movement aims to simulate conditions of the coaxial rheometer and produce a well-defined sheared region and a shear field. Indeed, when the vane is rotating, a localized surface circumscribed by the vane is formed, and this cylindrical surface simulates the rotor cylinder in a coaxial viscometer (Figure ). Given the shape of the newly designed vane and its geometry, the torque and rotational speed values can be converted into fundamental units following certain assumptions. Indeed, the torque (T) measured at the central axis of the vane can be converted to shear stress (τ) at the sheared surface circumscribed by the vane, as follows: π H τ dhdθ + π T = τ r drdθ (1) 0 0 where T is the torque measured at the central axis of the vane, H and are the height of the radius of the vane, respectively. The π H term is the lateral area of the sheared surface, and τ is the lateral shear stress. The second term of Eq.1 is due to the shear stress at the top and bottom surface of the sheared cylinder. By assuming the lateral shear stress to be uniformly distributed over the entire surface of the sheared cylinder, the first term in Eq. (1) can be calculated as follows: π 0 0 e T = π Hτ + τ r drdθ () 0 0 e ω τ e τ H r h H = 130 = 45 τ e r = 5 (Dimensions in mm) h = 100 Figure : Shear flow induced during the vane rotation

5 The shear stress may be highest near the outer edges of the vane blades, uniform along the cylindrical wall surface, and a function of radial position r over the circular end surfaces. Indeed, the shear stress (τ e ) acting on both ends of the sheared surface can be calculated using the following equation: τ e r ) = ( m (for r =, τe = τ) (3) τ The parameter m is constant for a given geometry of blade. Assuming m to be independent of the height (H) and to be dependent only on the diameter of the vane, the shear stress due to the end surfaces can be determined using blades of various H and a constant diameter without knowing the value of m. Using the distribution of τ e as given by Eq. (), the development of Eq. (1) can lead to: T τ = (4) 3 4π π H + m + 3 where the value of T is in N.m, that of and H in m, and shear stress is in Pa. For the sake of simplicity, two approaches are considered to estimate the distribution of τ e across the end surfaces: uniform distribution (m = 0) and linear distribution (m = 1). In the case of uniform distribution, the shear stress τ e is equal to the lateral shear stress (τ e = τ), and the shear stress can then be expressed as: T τ = (5) 3 4π π H + 3 Ιn the case of uniform distribution, the shear stress (τ e ) is given by: Therefore, the shear stress can be written as follows: T τ = (6) 3 π H + π r τ e = ( ) In the case of the shear rate, the calculation approach is more complicated, especially in the case of a rheometer with large gap. For small gaps where the ratio between the radius of the vane () and the container (e) is greater than 0.99, the shear rate can be considered as almost constant across the gap. However, in the case of the coaxial viscometer used for concrete, many instruments have of less than 0.99; therefore, the shear rate can change e across the gap. For large gap size used to accommodate the presence of coarse aggregate in concrete, the shear rate (γ) could be estimated as follows: d γ = r ω (7) dr τ

6 then: τ = T π H (8) dω dω dτ dω T dω T r = r = r = (9) 3 dr dτ dr dτ π H r dτ π H r Therefore, the shear rate is given as a function of the shear stress, as follows: dω γ τ dτ = (10) This equation is expanded into a Maclaurin series by Krigger and Elrod [6] to derive an estimated shear rate expression, as follows: where m = 4 ω i ( mln( s)) ( mln( s)) γ ( τ i ) = 1 + mln( s) + (11) Ln( s) 3 45 dln( ω) e, i.e. the slope of the curve Ln(ω) vs. Ln(τ), and s = d ln( τ ) 4. EXPEIMENTAL POGAM 4.1 Materials and Mixture Proportions An experimental program carried out to evaluate the validity of the modified rheometer to determine the rheological parameters of SCC. A number of SCC mixtures proportioned with Type I/II cement, w/cm of 0.33 to 0.38, and crushed aggregate with two different maximum sizes are discussed here to validate ability of the vane geometry to evaluate the rheological parameters of SCC. The cement had a Blaine specific fineness of 390 m /kg. The sand and coarse aggregate had a specific gravity of.65 and.70, and an absorption value of 1.1 and 0.4%, respectively. Two different maximum size of aggregate (MSA) of 19 and 1.5 mm were used. A polycarboxylate-based high-range water reducing agent (HWA) with a solid content of 9% and specific gravity of 1.09 was used. For each SCC, the dosage of HWA was adjusted to achieve a slump flow value of 680 ± 0 mm. SCC mixtures made with 0.33 w/cm can be used in precast applications where early-age strength development is required to achieve the required strength before prestress release. SCC mixtures made with 0.38 w/cm are typical for SCC proportioned with 450 to 475 kg/m 3 binder content. The mixtures investigated in this study are presented in Table TEST POCEDUES All the investigated mixtures were prepared in 80-L batches using a drum mixer. The mixing sequence consisted of wetting the sand and coarse aggregate with one-third part of the mixing water followed by the cement. The remaining water and HWA were introduced over 1 minute, and the concrete was mixed for minutes. The concrete remained at rest in the mixer for minutes to adjust fluidity. The concrete was then remixed for minutes. At the end of mixing, mixtures had a temperature of C.

7 Table 1: Mixture proportioning of SCC used in laboratory validation MSA = 19 mm MSA = 1.5 mm w/cm Type I/II cement, (kg/m 3 ) Water, (kg/m 3 ) w/cm Sand, (kg/m 3 ) Coarse aggregate, (kg/m 3 ) HWA (L/100 kg SCM) Sand/total aggregate, by volume Volume of coarse aggregate, % Volume of mortar, % The temperature and unit weight were first noted, and the slump flow was determined immediately after mixing, corresponding to 10 min after the initial contact of cement and water. The rheological parameters were then evaluated using a modified Tattersall two-point workability rheometer [3] equipped with a four-blade device rotating in a coaxial manner. The test requires the use of a concrete sample of 5 L and involves recording the torque to maintain a given rotational velocity. The rotational velocities were varied between 0.3 and 0.9 rev/s. The testing protocol consisted of gently immersing the vane of the rheometer into the bowl containing the concrete sample. The rheological measurements were obtained by increasing (ascendant) and then decreasing (descendant) the shear rate. The rotational speed is increased gradually from 0.3 rev/s to a maximum speed of 0.9 rev/s for 15 seconds. The highest speed is maintained during 15 seconds to ensure a breakdown of structure before determining the descendant portion of the flow curve. The rotational speed is then reduced in predetermined steps varying from 0.9 to 0.3 rev/s. Each speed is maintained during 15 seconds, and the torque required to shear the material at each rotational speed is then recorded and used to derive the rheological parameters using a given analytical model. The flow curves presented in this paper correspond to the descendant portion. 6. TEST ESULTS AND DISCUSSION The torque-rotation curves of the investigated mixtures are presented in Figure 3. heological parameters (flow resistance and torque viscosity) are then determined from these curves assuming a linear Bingham behavior. The slump flow as well as the flow resistance and torque viscosity values for the investigated SCC mixtures are presented in Table.

8 Torque, T (N.m).0 MSA = 1.5 mm 1.8 w/cm = y = N 1.4 = w/cm = y = N 0.6 = otational speed, N (rev/s) Torque, T (N.m) MSA = 19 mm w/cm = y = N = w/cm = y = N = otational speed, N (rev/s) Figure 3: Torque-rotational speed relationships determined from a Tattersall MK-III rheometer equipped with vane set-up

9 Table : Slump flow values and Bingham rheological parameters MSA = 19 mm MSA = 1.5 mm w/cm Slump flow (mm) Flow resistance (N.m) Torque viscosity (N.m.s) As can be seen in Figure 4, rheological parameters were estimated using the Bingham model. However, due to the non-linear behavior of some of the SCC mixtures, the use of a linear rheological model resulted in negative yield stress estimates. This was especially the case with the more thixotropic mixtures, such as those proportioned with low w/cm of The non-linear Hershel-Bulkley model was used to estimate the rheological parameters to ensure accurate fit of the experimental data. The Hershel-Bulkley model can be expressed as: τ = τ 0 + Κ γ n with τ 0 and Κ parameters corresponding to the yield stress and consistency, respectively. The term n is the power index introduced to take into consideration the shearthinning behavior of the material when n is less than 1 or the shear-thickening behavior when n is greater than 1. The Hershel-Bulkley model leads to the Bingham model when the power index is equal to 1, and K represents the plastic viscosity. The rheological parameters as well as the power index n that were determined by non-linear regression analysis using the Herschel-Bulkley model are presented in Table 3. Table 3: Fundamental rheological parameters of investigated mixtures determined using the Herschel-Bulkley model MSA = 19 mm MSA = 1.5 mm w/cm Slump flow (mm) Yield stress (Pa) Consistency (K) (Pa.s) Power index (n)

10 Shear stress, τ (Pa) MSA = 1.5 mm τ = γ = w/cm = 0.33 w/cm = 0.38 τ = γ = Shear rate, γ (s -1 ) Shear stress, τ (Pa) MSA = 19 mm w/cm = 0.33 τ = γ = w/cm = 0.38 τ = γ = Shear rate, γ (s -1 ) Figure 4: Flow curves determined using the modified Bingham rheological model determined from a Tattersall MK-III rheometer equipped with vane set-up Given the range of slump flow values of the investigated SCC mixtures, relatively low yield stress ranged between 7 and 64 Pa, and moderate consistency values between 170 and 40 Pa.s were obtained. SCC mixtures proportioned with w/cm of 0.33 exhibited higher consistency level than those prepared with w/cm of 0.38, regardless of the MSA. For example, SCC proportioned with w/cm of 0.33 and MSA of 19 mm had a consistency of 413 Pa.s. In the case of SCC with w/cm of 0.38, the consistency was only 11 Pa.s. On the other

11 hand, test results showed that SCC mixtures made with MSA of 19 mm showed higher consistency value than those made with MSA of 1.5 mm, regardless of the w/cm. For a w/cm of 0.33, a consistency value of 413 Pa.s is obtained versus 31 Pa.s in the case of SCC made with MSA of 1.5 mm. In terms of pseudoplastic behaviour, test results showed that for a given w/cm, SCC mixture made with MSA of 1.5 mm exhibited greater shear-thinning characteristics than those made with MSA of 19 mm. SCC proportioned with a w/cm of 0.33 and MSA of 19 mm exhibited a shear thinning behaviour (n = 0.8). Similar SCC with MSA of 1.5 mm exhibited shear thickening behaviour (n = 1.3), which could be attributed to the highly viscous nature of the concrete. 7. CONCLUDING EMAKS Tattersall MK-III rheometer was successfully modified to allow the determination of rheological characteristics of SCC in fundamental values. Flow curve mixtures used to validate the ability of vane geometry to evaluate rheology showed that SCC can present sheartinning or shear thickening characteristics; the latter is obtained for highly thixotropic mixtures. This behaviour depends mainly on MSA and w/cm. Investigated SCC mixtures are shown to fit best the non-linear Herschel-Bulkley model. The use of Herschel-Bulkley model to fit flow curves of SCC enables the determination of non-negative yield stress values; negative yield stress values are sometimes encountered when using the linear Bingham model for SCC mixtures with highly flowable SCC with high thixotropic characteristics. Further testing is being carried out to evaluate the effect of mixture parameters of SCC and rheological test procedure on rheological properties of SCC using the co-axial vane geometry used in the modified Tattersall MK-III rheometer. EFEENCES [1] Khayat, K.H., (1999). Workability, Testing, and Performance of Self-Consolidating Concrete, ACI Materials Journal, 96 (3), pp [] Tattersall, G.H., Banfill, P.F.G., (1983). The heology of Fresh Concrete, Pitman Advanced Publishing Program, New York. [3] Beaupré D., (1994). heology of High-Performance Shotcrete, Ph.D. Thesis, University of British Columbia, Canada. [4] Brower, L.E, Ferraris, C.F., (003). Comparison of Concrete heometers, Concrete International, August, pp [5] Alderman, N.J., Meeten, G.H., Sherwood, J.D., (1991). Vane heometry of Bentonite Gels, Journal of Non-Newtonian Fluid Mechanics, 39, pp [6] Kriger, I. M., Elrod, H., (1953). Direct Determination of the Flow Curve of Non-Newtonian Fluids. II. Shearing ate in the Concentric Cylinder Viscometer, Journal of Applied Physics, 4 (), pp