Factorial design models for proportioning selfconsolidating

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1 Materials and Structures/Matériaux et Constructions, Vol. 32, November 1999, pp Factorial design models for proportioning selfconsolidating concrete K. H. Khayat, A. Ghezal and M. S. Hadriche Université de Sherbrooke, Sherbrooke, QC, Canada J1K 2R1 TECHNICAL REPORTS Paper received: September 29, 1998; Paper accepted: April 19, 1999 A B S T R A C T A factorial design was carried out to model the influence of key mixture parameters on properties affecting the performance of self-consolidating concrete (SCC). Such responses included slump flow and rheological parameters, filling capacity and V-funnel flow to assess restrained deformability, surface settlement to evaluate stability after casting, and compressive strength. Thirty two mixtures were prepared to derive the statistical models and nine others to evaluate their accuracy. The models are valid for a wide range of mixture proportioning. The paper presents the derived models that unable the identification of underlying primary factors and their interactions that influence the modelled responses of interest for self-consolidating concrete. Such parameters can be useful to reduce the test protocol needed for the proportioning of self-consolidating concrete. The usefulness of the models to better understand trade-offs between mixture parameters and compare the responses obtained from various test methods are highlighted. R É S U M É Pour la formulation du béton autoplaçant (BAP) plusieurs gâchées s imposent, étant donné qu il faut maîtriser tous les facteurs affectant les propriétés à l état frais et durci du béton. Des modèles statistiques ont été générés à partir de la réalisation d un plan d expérience. Ces modèles identifient les paramètres importants de la formulation sur la performance du béton autoplaçant : la déformabilité caractérisée par l essai de l étalement, les paramètres rhéologiques, la capacité de remplissage, et l entonnoir; la stabilité traduite par le test du tassement et la résistance à la compression. La modélisation a nécessité un total de 32 gâchées de béton. Neuf autres mélanges ont été ajoutés afin de vérifier la validation des modèles établis. Ce papier présente les modèles générés qui traduisent l effet des paramètres principaux ainsi que leur intéractions sur les réponses mesurées. L utilité des modèles à établir une meilleure compréhension entre les paramètres des mélanges et de trouver des corrélations entre les différents tests réalisés est discutée. 1. INTRODUCTION Self-consolidating concrete (SCC) is a highly flowable concrete that can spread easily through restricted sections under its own weight without segregation and blockage. Such concrete is used to ensure the filling of congested sections and areas with restricted access to vibration. It is also employed to improve the productivity of concrete placement and site working conditions resulting from noise reduction due to the elimination of vibration consolidation. The proportioning of SCC is complicated because of the various contradictory requirements needed to ensure excellent flow characteristics and proper mechanical properties. For example, a highly flowable SCC should have a relatively low yield value to ensure good deformability but an adequate resistance to segregation and bleeding until the onset of hardening. An increase in water-to-cementitious materials ratio (w/cm) can secure high deformability, however, it can reduce the cohesiveness and cause segregation of aggregate that can lead to blockage of the flow. Inter-particle friction between coarse aggregate, sand, and fines increases the internal resistance to flow, hence limiting the deformability and speed of flow of the fresh concrete. Such friction is especially high when the concrete flows through a restricted spacing because of the greater collision between the various solids that increase viscosity. A local increase in aggregate density in a poorly viscous system can lead to coagulation and arching of the aggregate and Editorial Note Prof. Dr. K. H. Khayat works at the University of Sherbrooke, a RILEM Titular member. He participates to the work of RILEM TC 145-WSM (Workability of special concrete mixes) and of RILEM TC 174-SCC (Self-Compacting Concrete) /99 RILEM 679

2 Materials and Structures/Matériaux et Constructions, Vol. 32, November 1999 an interference with the deformability of the concrete in a restricted area [1-4]. Inter-particle friction between cement grains can be reduced by using a high-range water reducer (HRWR) to disperse the cement grains. A high dosage of HRWR can however lead to segregation and blockage of the flow. The combined use of HRWR and viscosity-enhancing agent (VEA) or a HRWR and a low w/cm can reduce the free water content necessary to ensure adequate viscosity and maintain good suspension of coarse aggregate and reduce inter-particle collision and coagulation of solid particles during the flow. In addition to providing adequate stability during placement, the concrete should have a proper stability in the formwork until hardening to minimize bleeding and segregation. This is important to secure homogeneous properties of the hardened concrete. Ensuring adequate stability is critical in deep sections where highly flowable concrete can exhibit segregation and bleeding and a non uniform distribution of mechanical properties, bond to reinforcing steel, and microstructure [5-7]. The contradicting workability requirements needed for successful placement of SCC necessitate tailoring a concrete mixture to ensure good balance between deformability and stability to prevent blockage during the flow and ensure a homogeneous suspension of the concrete constituents. Such homogeneous distribution is necessary to ensure adequate structural performance and durability. Engineers are faced with the complex task of manipulating several variables to enhance concrete performance and reduce cost. Some guidelines exist for mixture proportioning of SCC to reduce the extent of trial mixtures required to strike a balance between the various contradicting mixture requirements. The recommendations are mainly based on increasing the paste volume, reducing the coarse aggregate volume and sand to powder ratio, optimizing the granular squelette of all solids, etc. For the most part they treat a specific class of concrete and may require special test equipment or software [8-11]. The majority of mix design guidelines do not consider the specific effect of mixture parameters and their interactions on concrete performance. The objective of this paper is to illustrate the feasibility of using a statistical experimental design approach to identify the relative significance of primary mixture parameters and their coupled effects on relevant properties of SCC. The models can be used to evaluate the potential influence of adjusting mixture variables on concrete properties required to ensure successful development of SCC. Such simulation can help identify potential mixtures with a given set of performance criteria that can be tried in the laboratory, hence simplifying the test protocol needed to optimize SCC. 2. FACTORIAL DESIGN APPROACH Five key mixture parameters that can have significant influence on mixture characteristics of SCC were selected to derive mathematical models for evaluating relevant properties of SCC. The five variables included the concentrations of VEA and HRWR, the w/cm, the content of cementitious materials (CM), and the volume of coarse aggregate (Vca). The concrete responses that were modelled were the slump flow, and rheological parameters to evaluate the deformability of concrete in a non-restrained area, as well as the filling capacity and V- funnel flow time to evaluate the deformability in a restrained area that reflect its deformability and resistance to blocking. The other modelled responses included the surface settlement, segregation resistance, and compressive strength (fc) after 7 and 28 days. The underlying factors that influence fresh concrete properties and strength development are too complicated to permit the development of an exact mathematical model. Therefore, an empirical statistical model was derived over a wide working range of mixture proportioning. A statistical experimental design was used to evaluate the influence of two different levels for each of the five mixture variables on the relevant concrete properties. Such a two-level factorial design requires a minimum number of tests for each variable. The initial levels of the five selected mixture variables were carefully chosen after reviewing the demand constraints imposed by the targeted concrete properties. Given the fact that the expected responses do not vary in a linear manner with the selected variables and to enable the quantification of the prediction of the responses, a central composite plan was selected where the response can be modelled in a quadratic manner. Such a plan enables the evaluation of the five selected mixture parameters with each studied in five distinguished levels: codified values of -α, -1, 0, 1, and α. The α value is chosen so that the variance of the response predicted by the model would depend only on the distance from the center of the modelled region. The value α is equal to N F 1/4 where N F is the number of fractional factorial points = 16 (α = 16 1/4 = 2). The 32 mixture combinations used in the factorial design consisted first of 16 mixtures for the fractional factorial plan where the mixtures were set at coded values of -1 and +1. The fractional factorial design was expanded to include 10 additional mixtures where each variable was adjusted separately at the extreme α value of -2 and +2 with the other variables maintained at the 0 central points. This was done to consider extreme values of the five principal variables on the measured responses. Six replicate central points were prepared to estimate the degree of experimental error for the modelled responses. The coded variables are calculated as follows: coded w/cm = (absolute w/cm ) / coded CM = (absolute CM - 480) / 60 coded VEA = (absolute VEA ) / coded HRWR = (absolute HRWR - 0.7) / 0.2 coded Vca = (absolute Vca - 320) / 40 The experimental region modelled in this study is illustrated in Table 1. Although the models are valid for mixtures between the -2 and +2 regions, it is recommended to limit their use to the area bound by coded values corresponding to -1.5 to This can eliminate the outer regions approaching the edges of the modeled 680

3 Khayat, Ghezal, Hadriche Table 1 Grain-size distribution of sand and coarse aggregate Factors Central point w/cm CM (kg/m 3 ) VEA (% water) HRWR (% CM) Vca (l/m 3 ) region since the prediction error increases with the distance from the center. 3. MATERIAL PROPERTIES A proven ternary binder was used in this study to enhance rheological properties and strength. The binder contains 3% silica fume and 20% Class F fly ash. The chemical analysis of the Type 10 cement, silica fume, and fly ash are given in Table 2. A continuously graded, crushed limestone coarse aggregate made of two sizes of 14-5 and 20-5 mm to enhance particle packing was used. The bulk specific gravity and absorption of the combined aggregate are 2.74 and 0.39%, respectively. A well-graded natural siliceous sand with a fineness modulus, bulk specific gravity, and absorption of 2.36, 2.69, and 0.63%, respectively, was used. The grain-size distributions of the two coarse aggregate types and the sand are given in Table 3. A naphthalene-based HRWR conforming to the Canadian Standard CSA3-A266.6-M85. A hydroxyl carboxylic acid-based set retarder conforming to Canadian Standard CSA3-A266.2.M78 was used at a set dosage of 100 ml/100 kg of binder to enhance fluidity retention. Kelco-Crete welan gum was selected for the VEA to enhance stability of the fresh concrete. The Kelco-Crete was premixed with part of the HRWR to facilitate dispersion. 4. EXPERIMENTAL PROCEDURES 681 Table 2 Chemical and physical properties of cementitious materials Silica Fly ash Cement fume SiO Al 2 O C 3 S = 59.6 Fe 2 O C 2 S = 14.5 CaO C 3 A = 6.4 MgO C 4 AF = 7.9 Na 2 O eq C 1.9 fc (MPa) LOI days = 20 7 days = 27 Specific gravity Bulk unit weight (kg/m 3 ) 280 Blaine (m 2 /kg) Surface area B.E.T. (m 2 /kg) % passing 45 µ m Table 3 Grain-size distribution of sand and coarse aggregate Sieve size (mm) mm mm Sand All mixtures were prepared in 60-L batches with a rotating drum mixer. The batching sequence consisted of homogenizing the sand and aggregate for 30 s, then adding 75% of the mixing water and all of the HRWR that is not present in the VEA-HRWR dispersion. Following 30 s of mixing, the CM was added, and the mixing was resumed for one minute. The remaining water was then added and followed by the VEA-HRWR dispersion and set retarder. The concrete was mixed for three minutes, and after two minutes of rest, the mixing was resumed for two additional minutes. For each mixture, the slump flow was measured, and the relative flow resistance (g in Nm) and torque viscosity (h in Nm.s) were determined using the IBB rheometer [12]. The test involves recording the torque required to maintain a four-finger impeller rotating in a planetary motion at an angular speed of 0 to 1.2 revolutions per second. The descending flow curve was used for linear regression analysis to determine g and h according to the Bingham flow model. The facility of aggregate particles and mortar to change their flow paths and spread through a restricted area without blockage was evaluated using the V-funnel test shown in Fig. 1 similar to that suggested by Ozawa et al., 1994 [13]. The flow of the concrete is noted as the time between the removal of the outlet and the seizure of flow. The filling capacity test shown in Fig. 2 was used to determine the facility of the concrete to deform readily among closely spaced obstacles [14]. The test involves the casting of concrete in the non-reinforced Fig. 1 - Schematic of the V-funnel apparatus.

4 Materials and Structures/Matériaux et Constructions, Vol. 32, November 1999 Fig. 2 - Schematic of the filling capacity apparatus. section at a constant rate up to a height of 220 mm and observing the facility of the concrete to flow in the restricted region. The maximum theoretical filling capacity is 100%. A simple test that can be used to evaluate the stability of concrete following casting and until hardening was used [15-16]. An 800-mm high PVC column measuring 200 mm in diameter is filled with approximately 700 mm of concrete to monitor surface settlement. An LVDT fixed on top of a thin Acrylic plate anchored to the top surface of the concrete column was used to monitor surface settlement. For the segregation test, a fresh concrete sample was gently poured from a 2-L container over a 5-mm mesh to observe the quantity of mortar passing through the screen after 5 minutes [17]. The mass of the mortar passing through the screen was compared to the theoretical volume of mortar in the 2-L sample to determine the segregation index. A stable concrete should exhibit an index lower than 5% [17]. Six mm cylinders were cast and moist-cured to determine fc after 7 and 28 days. 5. DERIVED STATISTICAL MODELS The derived models along with correlation coefficients and Prob. > t values are given in Table 4. The estimates for each parameter refer to the coefficients of the model found by a least square approach. The Prob. > t term is the probability of getting an even greater t statistic, in absolute value, that tests whether the true parameter is zero. Probabilities less than 0.05 are often considered as significant evidence that the parameter is not zero, i.e. that the contribution of the proposed parameter has a highly significant influence on the measured response. The correlation coefficient (R 2 ) values of the proposed models for slump flow, filling capacity, flow time, h, g, settlement, and 7- and 28-day fc are 0.95, 0.90, 0.90, 0.98, 0.83, 0.76, 0.91, and 0.83, respectively. For the majority of the models, the high R 2 values demonstrate excellent correlation considering that at least 90% of measured values can be accounted for with the proposed models. The presentation in Table 4 enables the comparison of various parameters and the interactions of modelled responses. For the majority of the parameters the probabilities, it can be noted that there is less than 5% chance, or 95% confidence limit, that the contribution of a given parameter to the tested response exceeds the value of the specified coefficient. A negative estimate signifies that an increase of the given parameter results in a reduction of the measured response. For example, an increase in w/cm increases the slump flow and reduces the V- funnel flow time. For any given response, the presence of parameters with coupled terms, such as w/cm.w/cm, indicates that the influence of this term on the modelled response is quadratic. The models in Table 4 give an indication of the relative significance of various mixture parameters on each response. For example, the 28-day fc value is found to be affected mainly by the changes in w/cm followed by a reduction of the coupled effect of Vca.CM, and in a third level by the reduction in CM, VEA.VEA, and CM.CM. The segregation model is not given as it had relatively low R 2 and repeatability. Nine mixtures were selected to verify the ability of the proposed models to predict the measured responses. The duplicate mixtures were selected to cover a wide range of proportioning. Table 5 shows the mean measured responses of the six replicate mixtures, coefficients of variation (C.O.V.), as well as the standard errors with 95% confidence limit for each of the measured properties. The relative experimental errors for the slump flow, filling capacity, surface settlement, and 7- and 28- day f c are shown to be limited to 3 to 7%. On the other hand, the relative error for the V-funnel flow time and the h rheological parameter was approximately 13%, while that of the g parameter was 34%. The latter value is expected to decrease with the increase in relative yield value, since the mean g value of the highly flowable SCC corresponding to the central points was a very low value of 0.7 Nm. The six central point mixtures used to establish the repeatability of the results (Table 5) were used along Table 5 Repeatability of test results Slump flow Filling Flow h (Nm.s) (mm) capacity (%) time (s) Mean (N = 6) Standard deviation Relative error 95% confidence limit (%) g (Nm) Settlement 7-day fc 28-day fc (%) (MPa) (MPa) Mean (N = 6) Standard deviation Relative error 95% confidence limit (%) 682

5 Khayat, Ghezal, Hadriche Table 4 Parameter estimates of all derived models Slump Flow Filling capacity Ln (Flow time) h R 2 = 0.95 R 2 = 0.90 R 2 = 0.90 R 2 = 0.98 Parameter Estimate prob Estimate Prob Estimate Prob Estimate Prob > t > t > t > t Intercept w/cm CM VEA NS NS HRWR NS NS NS NS Vca NS NS w/cm.w/cm NS NS NS NS CM.CM HRWR.HRWR NS NS CM.w/cm VEA.w/cm NS NS HRWR.w/cm NS NS NS NS NS NS HRWR.VEA NS NS NS NS NS NS HRWR.CM NS NS NS NS Vca.CM NS NS NS NS Vca.HRWR NS NS NS NS NS NS VEA.CM NS NS NS NS NS NS Vca.Vca NS NS NS NS NS NS SQ-RT gsettlement 7-day fc 28-day fc R 2 = 0.83 R 2 = 0.76 R 2 = 0.91 R 2 = 0.83 Parameter Estimate prob Estimate Prob Estimate Prob Estimate Prob > t > t > t > t Intercept w/cm NS CM VEA NS NS NS NS NS NS HRWR NS NS NS NS NS NS Vca NS NS w/cm.w/cm NS NS NS NS NS NS CM.CM NS NS VEA.VEA NS NS CM.w/cm NS NS NS NS NS NS VEA.w/cm NS NS NS NS NS NS HRWR.w/cm NS NS NS NS NS NS HRWR.VEA NS NS NS NS NS NS HRWR.CM NS NS NS NS NS NS Vca.CM NS NS Vca.w/cm NS NS NS NS NS NS Vca.VEA NS NS NS NS Vca.Vca NS NS NS NS NS NS Vca.HRWR NS NS NS NS with the duplicate nine mixtures to compare the measured-to-predicted values of the eight reported responses. As shown in Fig. 3, for the measured-to-predicted value comparison, the estimated errors corresponding to 95% confidence limits are indicated. These values were determined for the highly flowable mixtures corresponding to the central point that exhibited a mean slump flow of 735 mm. The estimated errors for the 683 slump flow, filling capacity, flow time, and g and h parameters were ± 20 mm, ± 6%, 0.5 s, 0.24 Nm, and 1.1 Nm.s, respectively. These values were 0.024%, 1 MPa, and 1.6 MPa for the surface settlement, 7 and 28-day fc values, respectively. Except for the surface settlement model, the comparison of the measured responses of the 15 mixtures to predicted values is good, as the measured values lie close to the predicted ones. On the average, for the 15 duplicative mixtures (6 central points + 9 simulation), the mean ratio of predicted-to-measured slump flow, filling capacity, flow time, g, h, surface settlement, 7 and 28-day fc were 0.99, 0.99, 1.04, 1.42, 1.20, 1.40, 0.98, 1.01, respectively. 6. LIMITATIONS AND EXTENSION OF EXISTING MODELS Although the statistical models were developed to cover a wide range of mixture proportioning, the precision in prediction of the responses will change with the deviation from the set of materials used in deriving these models, however, the models can still be used for mixture optimization and simulation when presented with a different set of materials providing that such materials have limited effect on the prediction accuracy of the modelled responses. For example, a future mixture proportioning could involve different combinations and types of CM but the same aggregate, VEA, and HRWR types used in the original factorial experimental design. Such new binder is likely to influence the prediction models in Table 4, but to what degree remains to be seen. A logical design approach would be to use the existing model to predict the optimal design, then carry out selected tests to quantify the influence of the new binder on the model. A minimal estimate is obtained by repeating selected tests at levels within the desired range for the new job specifications, for example, a specified slump flow of 600 to 675 mm, a filling capacity greater than 70%, and minimum 28-day fc of 35 MPa. These mixtures are selected because the predicted properties from the existing model lie within the specified range of fluidity, filling capacity, and strength. The data obtained from the duplicated mixtures are then compared with the predicted values from the existing models. This approach was carried out using seven SCC

6 Materials and Structures/Matériaux et Constructions, Vol. 32, November EXPLOITATION OF THE DERIVED MODELS Fig. 3 - Examples of measured properties vs. values predicted from statistical models. The derived models are useful to understand interactions between mixture parameters affecting important characteristics of SCC. This understanding can simplify the test protocol because the models identify the relative significance of each variable, thus providing key information required to optimize the design. It is important to note that the statistical approach used here can be applied easily to mixtures made using other materials to modify the existing models. The utility of such models to assist in the selection of trial mixtures is illustrated through a few examples. The proposed models can also be used to test the effects of a group of variables on properties affecting the quality of SCC. For example, the effect of increasing the w/cm vs. the dosage of HRWR on slump flow and filling capacity is shown in Figs. 5 and 6, respectively, for mixtures with relatively low and high CM contents and fixed contents of coarse aggregate and VEA. For any w/cm value and HRWR content, the concrete made with the higher CM content of 540 kg/m 3 had clearly greater deformability and filling capacity than that containing 420 kg/m 3 CM content. The decrease in w/cm necessitates an increase in the dosage of HRWR to maintain a fixed slump flow, especially in the case of concrete with a mixtures prepared with the same sand, coarse aggregate, HRWR, and VEA used in the development of the models, except for the CM combinations that was different than the 3% SF + 20% FA original binder. An eighth mixture was also used and incorporated a binder with the same CM but a different cement. All eight mixtures had w/cm of 0.41, 185 l/m 3 of CM, and 300 l/m 3 of coarse aggregate. Although the CM content has the highest influence on the slump flow and filling responses, the change in CM type that can alter several properties, such as the grain-size distribution, granular porosity, water and admixture demand, and kinetics of hydration, did not exhibit significant effect on the degree of prediction. As can be seen in Fig. 4, the majority of the predicted slump flow and filling capacity values were within 20 mm and 6%, respectively, from the measured values that constitute the experimental errors for the repetition of the slump flow and filling capacity tests. The above approach can be used to verify the reliability of other models of interest to proportioning SCC. The variation between the new tests and predicted values is expected to increase with the deviation from the materials used in the original study. Depending on the level of deviation, a limited number of mixtures can be prepared to adjust the existing models to reflect the influence of the new materials on relevant concrete properties. Fig. 4 - Measured slump flow and filling capacity vs. predicted values of mixtures made with various binders (all mixtures had same aggregate, HRWR, and VEA). 684

7 Khayat, Ghezal, Hadriche Fig. 5 - Variations of slump flow with w/cm and HRWR. Fig. 6 - Variations of filling capacity with w/cm and HRWR Table 6 Comparison of deformability, filling capacity, and cost of stable SCC mixtures Mixture w/cm CM (kg/m 3 ) VEA (% water) HRWR (%CM) Vca (l/m 3 ) Slump flow (mm) Filling capacity (%) Material cost (CAN $/m 3 ) lower content of CM. At high contents of HRWR, a curvature in the responses is observed that can be either due to a direct consequence of the mixture or an artificial consequence of the quadratic model. In Fig. 5 and 6, the central regions highlighted in white correspond to the area where prediction error is the lowest, as the error of prediction increase with the distance from the central point of the modelled region. The curvature of the filling capacity response in the high precision central region is an actual characteristic of the material. An increase in HRWR in a mixture with a fixed w/cm can lower viscosity and increase filling capacity. However, with the increase in HRWR content, the filling capacity begins to drop as a result of partial blockage of the aggregate as the viscosity decreases with the increase in HRWR. The models can be used to select optimized economical mixtures. This can reduce the effort often required in carrying out trial batches for mixture optimization. For example, Table 6 compares the deformability, filling capacity and material cost of seven SCC mixtures that exhibit good resistance to segregation (maximum segregation index of 10%). The unit cost of the concrete was calculated to reflect only material cost. For the seven mixtures made with a moderate CM of 440 to 460 kg/m 3 and 0.41 to 0.46 w/cm, the HRWR dosages were adjusted to yield mixtures with slump flow of 650 to 700 mm and minimum filling capacity of 60%. In general, it Fig. 7 - Relationship between filling capacity, slump flow, and flow time. can be seen that for the highly flowable concrete, the increase in filling capacity necessitates an increase in concrete cost. For example, mixtures 4 and 7 have the same CM, VEA, and Vca values and resulted in similar slump flow but different filling capacity results. The predicted filling capacity of mixture 4 is 78% compared to 87% for the other SCC that is expected to cost 7 CAN $/m 3 more than mixture 4. One of the most useful applications of the existing models is the establishment of relationships between the responses of various test methods, which fairly independent on the materials in use. For example, a relationship between the filling capacity, slump flow, and flow time values can be derived for a given set of highly stable SCC (Fig. 7). Such a relationship derived from 275 virtual SCC mixtures selected to ensure a minimum filling capacity and slump flow of 40% and 550 mm, respectively, a maximum flow time of 20 sec and segregation index of 60%, and 28-day compressive strength greater than 28 MPa. The multiple regression equation is expressed as follows: Filling capacity (%) = slump flow (mm) flow time (s) 685

8 Materials and Structures/Matériaux et Constructions, Vol. 32, November 1999 with R 2 of 0.80 and a standard deviation of 6%. The contour diagrams of filling capacity shown in Fig. 7 illustrate that for a given slump flow value the decrease in filling capacity is accompanied by a drop in the V-funnel flow time. The six values noted on Fig. 7 correspond to actual results of mixtures prepared to derive the original statistical models for which the values of filling capacity were predicted given measured slump flow and flow values. These results are in close agreement with the measured values reported in parenthesis. While the derived relationship is not exclusive for all materials, it shows that for the plotted region corresponding to stable SCC, the V-funnel flow test does not provide good indication of deformability through restricted spacing. Concrete with a flow time of 5 s can have a slump flow of 580 mm and 65% filling capacity but also a slump flow of 700 mm and 77% filling capacity. This trend confirms the findings in reference 13 that recommend combining the V-funnel flow time with slump flow to reflect the filling capacity level of the concrete. 8. CONCLUSION The models established using a factorial design approach are valid for a wide range of mixture proportioning and provide an efficient means to determine the influence of key variables on SCC properties. Such understanding can facilitate the test protocol required to optimize SCC, hence reducing the effort necessary to optimize specified concrete to secure balance between various variables affecting flowability, deformability, stability, and strength. Although the models are based on a given set of materials, they can be easily used as a building block to augment future studies involving other materials. The existing models enable the comparison of the possible responses of the different test methods to identify trends useful for quality control (for example, relationships between yield value and settlement for different mixtures). REFERENCES [1] Nanayakkara, A., Ozawa, K. and Maekawa, K., Flow and segregation of fresh concrete in tapered pipes, Proceedings, 3rd International Symposium on Liquid-Solid Flows, ASME, FED- 75 (1988) [2] Ozawa, K., Maekawa, K., Kunishima, M. and Okamura, H., High-performance concrete based on the durability of concrete structures, Proceedings, 2nd East Asia Pacific Conference on Structural Engineering and Construction, Chiang-Mai (1989). [3] Ozawa, K., Maekawa, K. and Okamura, H., Development of high performance concrete, Journal of the Faculty of Engineering, the University of Tokyo (B) XLI (3) (1992) [4] Nagataki, S. and Fujiwara, H., Self-compacting property of highly flowable concrete, ACI SP 154 (1995) [5] Khayat, K. H., Manai, K. and Trudel, A., In-situ mechanical properties of wall elements cast using self-consolidating concrete, ACI Materials Journal 94 (6) (1997) [6] Khayat, K. H., Use of viscosity-modifying admixture to reduce top-bar effect of anchored bars in fluid concrete, Ibid. 95 (2) (1998) [7] Petrov, N., On the bond and corrosion resistance of steel reinforcement embedded in self-consolidating concrete, (only available in French) Masters Thesis, Université de Sherbrooke, Canada (1995). [8] Okamura, H. and Ozawa, K., Mix design for self-compacting concrete, Concrete Library of the Japan Society of Civil Engineering, (25) (1995). [9] Sedran, T., de Larrard, F., Hourst, F. and Contamines, C., Mix design of self-compacting concrete (SCC), Proceedings, RILEM International Conference on Production Methods and Workability of Concrete, Ed. Bartos, P. J. M., Marrs, D. L. and Cleland, D. J., E&FN Spon, London (1996) [10] Sedran, T. and de Larrard, F., Rene-LCPC: software to optimize the mix design of high performance concrete, Proceedings, BHP 96, 4th International Symposium on Utilization of High Strength/High Performance Concrete, Ed. de Larrard, F., Lacroix, R., Paris (1996) [11] Petersson, O., Billberg, P. and Van, B. K., A model for self compacting concrete, Proceedings, RILEM International Conference on Production Methods and Workability of Concrete, Ed. Bartos, P. J. M., Marrs, D. L., and Cleland, D. J., E&FN Spon, London, (1996) [12] Beaupré, D., Rheology of high performance concrete, Ph.D. Thesis, University of British Columbia, Canada (1994). [13] Ozawa, K., Sakata, N. and Okamura, H., Evaluation of selfcompactability of fresh concrete using the funnel test, Proceedings, Japan Society of Civil Engineering (25) (June 1995) [14] Yurugi, M., Sakata, N., Iwai, M. and Sakai, G. Mix proportion for highly workable concrete, Proceedings, Concrete 2000, Dundee (1993). [15] Manai, K., Evaluation of the effect of chemical and mineral admixtures on the workability, stability, and performance of selfcompacting concrete, (only available in French) Masters Thesis, Université de Sherbrooke, Canada (1995). [16] Trudel, A., Workability, uniformity, and structural behavior of high-performance self-compacting concrete, (only available in French) Masters Thesis, Université de Sherbrooke, Canada (1996). [17] Study on reducing unit powder content of high fluidity concrete by controlling powder particle size distribution, Concrete Library of JSCE N-28 (December 1996). 686