Utility of statistical models in proportioning selfconsolidating

Transcription

1 Materials and Structures/Matériaux et Constructions, Vol. 33, June 2000, pp TECHNICAL REPORTS Utility of statistical models in proportioning selfconsolidating concrete K. H. Khayat, A. Ghezal and M. S. Hadriche Université de Sherbrooke, Sherbrooke, QC, Canada Paper received: July 1st, 1999; Paper accepted: September 20, 1999 A B S T R A C T In addition to sound material selection, the mix design of self-consolidating concrete requires careful tailoring of mixture constituents to secure a proper balance between contradictory properties necessary for the successful production of such a complex material. Mixture optimization of self-consolidating concrete often requires several trial batches to secure the required characteristics. This paper reviews statistical models developed using a factorial design approach to understand the effect of mixture parameters on key responses, including slump flow, rheological parameters, filling capacity, V-funnel flow time, surface settlement, and compressive strength. The models are valid for mixtures with 0.37 to 0.50 W/CM, 360 to 600 kg/m 3 of binder, 240 to 400 l/m 3 of coarse aggregate, 0.05 to 0.20% of viscosity-enhancing agent, by mass of water, and 0.3 to 1.1% of high-range water reducer, by mass of binder. Although the predicted response changes with the deviation from material characteristics used in establishing the models, the models remain quite useful in determing the significance of mixture parameters and their interactions on self-consolidating concrete properties. This paper demonstrates the usefulness of the models in establishing trade-offs among mixture parameters necessary for mixture optimization and compares the effect of changes in such parameters on key self consolidating concrete responses. The utility of the models to establish correlation between different workability characteristics useful for quality control is also highlighted. R É S U M É La formulation des bétons autoplaçants nécessite une attention particulière dans la sélection des constituants afin d assurer un équilibre entre les propriétés contradictoires et nécessaires à l obtention de ce matériau. L optimisation des mélanges des bétons autoplaçants exige plusieurs gâchées d essais pour garantir toutes les propriétés requises. Ce travail passe en revue les modèles statistiques développés par l approche des plans factoriels pour comprendre l effet des facteurs sur les réponses recherchées, à savoir : l étalement, les paramètres rhéologiques, la capacité de remplissage, l entonnoir, le tassement et la résistance à la compression. Les modèles proposés sont valables pour un rapport E/L compris entre 0,37 et 0,50, une teneur en liant de 360 à 600 kg/m 3, un volume en granulats variant entre 240 et 400 l/m 3, un dosage en agent d amélioration de la viscosité compris entre 0,05 et 0,20% de la masse totale en eau et un dosage en superplastifiant variant entre 0,3 et 1,1% de la masse totale du liant. Néanmoins, les réponses prédites changent en s éloignant des caractéristiques des matériaux employés pour l élaboration des modèles, l intérêt des modèles est prouvé en démontrant l effet des paramètres de mélanges et leurs interactions sur les propriétés des bétons autoplaçants. Ce travail tente de démontrer l utilité des modèles pour l établissement d un consensus entre les différents paramètres et une optimisation des mélanges ainsi que de comparer l effet du changement des paramètres de mélanges sur les réponses. Le présent article discute également l intérêt des modèles en vue de trouver des corrélations entre les caractéristiques de maniabilité en matière de contrôle de qualité. 1. WORKABILITY OF SCC Self-compacting concrete (SCC) is a special type of concrete that should flow into place and around obstructions under its own weight without segregation and flow blockage and with no significant separation of material constituents thereafter until the setting. The successful casting of SCC necessitates that the concrete exhibits a certain balance between deformability and stability. A SCC is typically characterized by a low yield value to ensure high deformability and a moderate viscosity to secure sufficient stability and filling of the formwork. The mixture proportioning of SCC is complex and involves the tailoring of several variables to strike a balance between the workability requirements affecting the sucessful casting of SCC. Flowability through restricted Editorial Note Prof. Dr. Kamal Khayat is a RILEM Staff Member. He participes in RILEM TCs 145-WSM (Workability of Special concrete Mixes) and 174-SCC (Self-Compacting Concrete) /00 RILEM 338

2 Khayat, Ghezal, Hadriche spacing is affected by inter-particle friction among solid particles that increases in the vicinity of obstacles due to greater collision of solid particles near such obstructions that leads to greater viscosity. Concrete with low cohesion can exhibit segregation near obstructions that can result in eventual blockage [1-2]. The rheological parameters of the concrete should therefore be optimized to maintain uniform suspension of the aggregate through restricted spacing. In addition to mixture composition, the aggregate properties (nominal size, particle shape) and section characteristics (clear spacing among obstacles) affect the restricted deformability of SCC among closely spaced obstacles. Once into place, the SCC must exhibit adequate stability to limit bleeding, segregation, and surface settlement that can weaken the characteristics of the hardened concrete, including strength, bond to reinforcing steel, and impermeability. With the growing interest in using SCC and the complexity of mixture proportioning, it is essential to better understand the effect of mixture parameters governing material performance. Limited guidelines exist for proportioning SCC. The optimization of such concrete necessitates carrying out several trial batches to achieve adequate balance between deformability, stability, and mechanical properties. Typically, mixture optimization involves a regression approach where one parameter is changed at a time to assess its influence on properties of interest. This however does not permit the understanding of the relative influence of mixture parameters and their interactions on concrete characteristics. This paper reviews statistical models established by the authors [3] to model the response of key SCC properties. The main objective of this paper is to demonstrate the utility of the models in facilitating the test protocol to optimize SCC and achieve balance among the various properties required for the successful flow and stability as well as compressive strength. 2. DEVELOPMENT OF STATISTICAL MODELS A 2 (5-1) statistical experimental design was used to establish models to describe key concrete properties [3]. The five parameters used in the modelling were the cementitious material content (CM), W/CM, concentrations of high-range water reducer (HRWR) and viscosity-enhancing agent (VEA), as well as the volume of coarse aggregate (Vca). The modelled experimental region consisted of mixtures ranging between coded variables of - 2 to + 2 (Table 1). The derived statistical Table 1 Values of coded variables Parameter Central point 1 2 W/CM CM (kg/m 3 ) VEA (% water) HRWR (% CM) Vca (l/m 3 ) models are valid for mixtures made with ranges of W/CM of 0.37 to 0.50, CM of 360 to 600 kg/m 3, Vca of 240 to 400 l/m 3, concentrations of VEA of 0.05 to 0.20%, by mass of water, and HRWR of 0.3 to 1.1%, by mass of binder. Since the error in predicting the responses increases with the distance from the center of modelled region, it is advisable to limit the use of the models to an area bound by coded values corresponding to to limits [3]. The relationship enabling the transfer of absolute values to coded variables is: X = (A - A 0 )/ X, with X being the coded variable measured with the step like units, A is the absolute value in normal units, A 0 is the value (measured in normal units) applicable to absolute variable at the center of the modelled region, and X is the step [3]. For the 32 mixtures used in the statistical study, well graded, crushed limestone aggregate with a nominal size of 20 mm and a natural siliceous sand (2.36 FM) were used. A naphthalene-based HRWR was used along with a set retarder to enhance fluidity retention. A ternary blend of 3% silica fume and 20% Class F fly ash (Blaine of 410 kg/m 2 ) and 77% Type 10 Canadian cement (Blaine of 345 kg/m 2 ) was used. Kelco-Crete (welan gum) premixed with part of the HRWR was employed for the VEA. For each concrete, the slump flow, relative flow resistance (g) and relative torque viscosity (h) were determined. The IBB rheometer [4] was used to obtain g and h derived by linear regression of the torque-angular velocity data to fit the Bingham flow model. The facility of concrete to spread through restricted spacing was evaluated using the filling capacity and V-funnel flow tests described in Fig. 1 [3, 5, 6]. For the V-funnel, the flow time was noted as the time between the removal of the outlet and flow seizure. The maximum settlement was evaluated by monitoring the surface settlement of a column of concrete measuring 700-mm in height and 200 mm in diameter cast into a PVC tube [7]. A simple segregation test was employed and involved gently pouring concrete from a 2-L container over a 5-mm mesh opening screen. Mortar passing through the mesh after 5 min. is determined to derive a segregation index [8]. Finally compressive strength was determined on watercured, mm cylinders. The derived models are summarized below with the mixture variables expressed in coded values. The models reflect the relative significance of each parameter on key responses. For example, the slump flow is shown to increase mostly with the increase in CM followed by an increase in W/CM, decrease in VEA, increase in Vca and then various coupled effects. The majority of the models had high correlation coefficients (R 2 ). The segregation model is not reported because of its low R 2 and repeatability. Based on the six central points, the errors in estimating slump flow, filling capacity, flow time, g and h parameters can be ± 20 mm, 6%, 0.5 s, 0.24 Nm, and 1.1 Nm.s, respectively. These values were 339

3 Materials and Structures/Matériaux et Constructions, Vol. 33, June 2000 Fig. 1 Schematic of the V-funnel and filling capacity apparatuses. ± 0.024%, 1 MPa, and 1.6 MPa for the settlement, and the 7- and 28-day strengths, respectively [3]. On average, for 15 tested mixtures (six central points and nine mixtures used in simulation), the mean predicted-tomeasured ratios of slump flow, filling capacity, flow time, g, h, settlement, and 7- and 28-day compressive strengths were found to be 0.99, 0.99, 1.04, 1.42, 1.20, 1.40, 0.98, 1.01, respectively [3]. Slump flow (mm) = CM + 74 W/CM HRWR - 35 VEA Vca CM.CM HRWR.HRWR VEA.W/CM HRWR.W/CM CM.W/CM W/CM.W/CM R 2 = 0.95 g (Nm) = ( CM W/CM Vca CM.CM CM.W/CM Vca.CM) 2 R 2 = 0.83 h (Nm.s) = CM W/CM Vca VEA CM.W/CM CM.CM VEA.W/CM Vca.HRWR W/CM.W/CM Vca.CM HRWR.CM R 2 = 0.98 Filling capacity (%) = CM W/CM HRWR VEA CM.CM 7.0 CM.W/CM VEA.W/CM HRWR.VEA R 2 = 0.90 V-funnel flow time (s) = EXP ( CM W/CM Vca CM.CM CM.W/CM VEA.CM Vca.Vca HRWR.CM Vca.CM HRWR.HRWR) R 2 = 0.90 Settlement (%) = CM Vca VEA HRWR.CM Vca.W/CM Vca.CM HRWR.VEA HRWR.W/CM Vca.VEA Vca.HRWR VEA.VEA R 2 = day compressive strength (MPa) = W/CM CM HRWR Vca Vca.Vca VEA.VEA CM.CM Vca.HRWR VEA.W/CM Vca.VEA W/CM.W/CM R 2 = day compressive strength (MPa) = W/CM CM Vca.CM VEA.VEA CM.CM R 2 = EXPLOITATION OF STATISTICAL MODELS The statistical models can be used to evaluate the effects of a group of variables on key responses of SCC and trade-offs among various parameters required to secure similar responses. The models are also useful to establish relationships between various responses that can be determined with different constraints on material performance. 3.1 Trade-off between mixture parameters The impact of reducing the W/CM on the increase in HRWR demand to maintain constant slump flow and filling capacity are illustrated in Figs. 2 and 3, respectively. This is done for mixtures with relatively low and high CM contents and fixed Vca and VEA values set at the center of the modelled region (coded values of 0). For any W/CM and HRWR content, that are taken in 340

4 Khayat, Ghezal, Hadriche Fig. 2 W/CM-HRWR contour diagrams of slump flow (mm). Fig. 3 W/CM-HRWR contour diagrams of filling capacity (%). Fig. 4 W/CM/HRWR-CR contour diagrams of slump flow (mm). the recommended region of to + 1.5, the concrete made with 540 kg/m 3 of CM had greater deformability and filling capacity than that containing 420 kg/m 3 of CM. The trade-off illustrates that the decrease in W/CM necessitates an increase in HRWR to maintain a fixed slump flow, especially in the case of concrete with the lower CM content. Slump flow contour diagrams are also presented in Fig. 4 to show trade-offs between W/CM and HRWR in mixtures made with low and medium dosages of VEA corresponding to approximate coded values of - 1 and + 1. For the range of slump flow values of interest to SCC, it can be seen that at 0.08% VEA, the increase in W/CM from 0.38 to 0.43, with the HRWR fixed at 0.55% increases the slump flow from approximately 550 to 780 mm. Such increase in W/CM leads however to a limited change in slump flow in concrete with 0.18% VEA (from 630 to 690 mm). The higher VEA SCC can be considered less sensitive to changes in water content, which is important to secure a robust mixture. Unlike changes in W/CM, both VEA mixtures seem to have similar slump flow response with increase in HRWR. For example, at 0.41 W/CM, changes in HRWR dosage from 0.40 to 0.55% can increase slump flow from approximately 550 to 680 mm for both mixtures made with 0.08 and 0.18% VEA. With a higher W/CM of 0.43, such increase in HRWR can result in a slump flow change of 670 to 780 mm in the 0.08% VEA concrete and 590 to 690 mm in the other SCC, both of which showing similar increases in the nonrestricted deformability. The contour diagrams of slump flow and filling capacity in Figs. 5 and 6 illustrate the trade-offs between HRWR and CM for mixtures with 0.39 and 0.48 W/CM. The Vca and VEA values are set to the central points for both mixtures. The increase in CM reduces the HRWR demand required to increase slump flow and filling capacity. This is especially the case for the lower W/CM SCC necessitating greater HRWR dosage. As indicated in Fig. 5a, the increase in CM from 475 to 510 kg/m 3 enables the reduction of HRWR from 0.85 to 0.65% while maintaining a constant slump flow of 650 mm. The increase in W/CM also enables the reduction in CM. For example, for a SCC made with 0.7% HRWR, the increase in W/CM from 0.39 to 0.48 enables the decrease of CM content from 490 to 420 kg/m 3 while maintaining a constant slump flow of 650 mm. Such simulation enables testing the impact of trade-offs between CM content and W/CM and their impact on cost, strength, and other properties of interest to the SCC. Fig. 5 HRWR-CM contour diagrams of slump flow (mm). Fig. 6 HRWR-CM contour diagrams of filling capacity (%). 341

5 Materials and Structures/Matériaux et Constructions, Vol. 33, June 2000 Fig. 7 Multiple regression of slump flow, flow time, and filling capacity [3]. Fig. 8 Filling capacity workability boxes of mixtures with 600 to 700 mm slump flow. 3.2 Relationship between workability responses. The derived statistical models can facilitate the establishment of relationships between responses of various tests of interest to the successful casting of SCC. Fig. 7 plots contour diagrams of filling capacity values that vary with slump flow and V-funnel flow time. This relationship was derived from 275 virtual mixtures using a special computer program to optimize mixture proportioning (Autoban [9]). The multiple regression equation below is valid for mixtures with slump flow values between 550 and 780 mm, minimum filling capacity of 40%, maximum flow time of 20, maximum 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) with R 2 of 0.80 and 6% standard deviation. The six values noted in Fig. 7 correspond to mixtures in reference 3 for which the values of filling capacity were predicted given measured slump flow and flow values. These values are in close agreement with the measured values reported in parenthesis. For the plotted region corresponding to flowable, yet stable, mixtures, it is shown that the V-funnel flow test is not sufficient to describe the facility of the SCC to flow through restricted areas. 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 agrees with the findings of Ozawa et al. [6] that recommend combining the V-funnel flow test with slump flow to assess restricted deformability of SCC. The statistical models were used to establish a workability region for the filling capacity response. As shown in Fig. 8, the criteria is based on the g and h parameters. All SCC mixtures used to identify the workability regions have slump flow values of 600 to 700 mm and a maximum segregation index of 40%. For the majority of cases, mixtures with approximate g values between 0.25 and 0.75 Nm and h values of 2 to 11 Nm.s can achieve high filling capacity of 80 to 95%. Another rheological region can be identified where the majority of points correspond to filling capacity values of 70 to 80%. The SCC designated as 1 has a low h value but a moderate g value and an estimated slump flow of 620 mm. Its filling capacity is limited to 70%, mainly due to its lack of stability (settlement of 0.74%). This was also the case for mixture 2 that has a slump flow of 610 mm, a filling capacity of 73% and a high settlement of 0.82%. The SCC designated as 3 has a very low g value and an estimated slump flow of 725 mm, a low settlement of 0.30% yet a limited filling capacity of 70%. This is mainly because of the high Vca value of 400 l/m 3. Mixture 4 has a slump flow of 700 mm, a low settlement of 0.26%, but again a filling capacity of 70% due to the high Vca value (360 l/m 3 ). 3.3 Testing effect of mixture parameters on various responses The statistical models can be used to evaluate the impact of mixture composition on SCC properties. Although the models were derived for a specific set of materials, variations in material characteristics will change the estimate of the response. However, the general tendencies regarding the relative impacts of mixture parameters on given responses should remain relevant and hence useful to select directions in the mixture proportioning of SCC. The effects of increasing HRWR on changes in slump flow, V-funnel flow time, and filling capacity are illustrated in Fig. 9 for two mixtures with 500 kg/m 3 of CM and Vca of 330 l/m 3. For the concrete with 0.40 W/CM and 0.05% VEA (0.02% by mass of CM), the increase in HRWR lowers the internal resistance to flow and increases slump flow. Both the flow time and filling capacity increase with slump flow reaching peak values at around 700 mm. A further increase in deformability does not secure reduction in flow time and increase in filling capacity due to a lack of cohesion. Such cohesion is necessary to ensure uniform deformation through the 342

6 Khayat, Ghezal, Hadriche Fig. 9 Relationship between slump flow, flow time, and filling capacity of mixture made with different W/CM and VEA values. Fig. 10 Effect of Vca on slump flow and flow time of SCC of different composition. tapered outlet of the funnel and the close spaces of the filling capacity apparatus. Local collision of solids and coagulation of coarse aggregate can interfere with the deformability. In the case of the other SCC made with 0.45 W/CM and 0.18% VEA (0.08% by mass of CM), the restricted deformability increases linearly with HRWR dosage and slump flow consistency. This concrete has a lower sandto-paste volume (S/pt) of 0.65 compared to 0.92 for the other mixture. Despite the increase in water content, the incorporation of proper dosage of VEA can maintain good suspension of coarse aggregate and reduce interparticle collision of aggregate particles in the vicinity of various obstructions. As given in the slump flow model, the increase in Vca enhances free deformability; however, the influence on restrained deformability remains complex. The three SCC mixtures in Fig. 10 are selected with sufficient VEA and HRWR concentrations to secure low g and moderate h values. The comparison of their performance levels is carried out to test the effect of CM and W/CM on flow time and its variation with slump flow. Initially, the addition of coarse aggregate is shown to increase slump flow and reduce the V-funnel flow time. However, with further increase in Vca, the slump flow continues to increase but so does the flow time. The latter is due to the increase of inter-particle friction of solids at the tapered outlet of the V funnel that increases with coarse aggregate and sand contents. A reduction in cohesion resulting from an increase in slump flow leads to some local separation of material constituents and collision of solids. This can slow down the efflux of concrete through the restricted outlet. The increase in W/CM from 0.41 to 0.45 for mixtures made with 480 kg/m 3 of CM reduces the sand content and results in faster efflux time, even at higher slump flow values. This tendency is also improved with the increase of CM from 480 to 570 kg/m 3 that further reduces the sand content. The influence of Vca, W/CM, and HRWR on filling capacity is illustrated in Fig. 11 for SCC mixtures with relatively high contents of CM (520 and 570 k/m 3 ) and low VEA concentrations. In Fig. 11a, the increase in Fig. 11 Effect of Vca and W/CM parameters on slump flow and filling capacity. W/CM from 0.38 to approximately 0.40 is shown to increase the filling capacity. However, a further increase in W/CM to 0.44, with a corresponding reduction of HRWR to maintain a slump flow of 630 mm, results in a reduction in filling capacity, regardless of the Vca value. Higher values of filling capacity are secured when the Vca is limited to 280 l/m 3. The peak W/CM corresponds here to the optimum value necessary to enhance deformability without mitigating stability. Any additional increase in W/CM increases inter-particle friction and collision near restricted areas, limiting the filling capacity. The decrease in Vca reduces the volume of solids and reduces the risk of any interference of the flow. The graphs shown in Fig. 11b reproduce the relationship between the W/CM and filling capacity for mixtures with high CM content of 570 kg/m 3 and medium Vca of 320 l/m 3. The concentration of HRWR is adjusted to secure various slump flow values. Peak filling capacity of 100% is obtained for SCC with 750 mm slump flow and W/CM of 0.40 to The stability of such concrete is mainly assured by the high concentration of fines that increases cohesiveness. The increase in W/CM for a given CM factor, or vice versa, increases the water content and paste volume. Therefore, for the Vca value in Fig. 12 corresponding to the central point of the modelled region, and a fixed VEA dosage, the increase in water content is shown to impact h (relative torque viscosity). The points in Fig. 343

7 Materials and Structures/Matériaux et Constructions, Vol. 33, June 2000 Fig. 12 Influence of W/CM and total water content on h. 12a are derived for mixtures with different W/CM and CM contents. A clear relationship can be identified between the water content and h for each slump flow level, 630 and 700 mm, secured by adjusting the HRWR dosage. At lower water contents of 180 l/m 3, a significant difference is obtained between h values of the two slump flow consistency levels. This spread diminishes with the increase in water content. Similar behaviour is obtained with SCC mixtures with 630-mm slump flow containing different W/CM and CM values (Fig. 12b). At relatively low W/CM of 0.38, the reduction in CM can greatly increase the h response, and reduce the filling capacity (Fig. 8). With the increase in W/CM to , the spread in h resulting from an increase in CM content is shown to considerably decrease. The surface settlement response suggests that the settlement can be controlled by increasing the VEA concentration and reducing the paste volume, corresponding to an increase in aggregate content. Such effects are presented in Fig. 13 where the influence of VEA dosage, CM content, and W/CM of settlement of SCC is examined. The concrete mixtures have a fixed Vca of 320 l/m 3 and slump flow of 650 mm. The increase in VEA from 0.08 to and 0.18% is shown to reduce the maximum settlement from 0.85 to 0.6 and 0.4%, respectively, in concrete with 0.43 W/CM and 570 kg/m 3 of CM. The lowering of W/CM from 0.43 to 0.39 for concrete containing 570 kg/m 3 of CM leads to a decrease in settlement when low and medium VEA concentrations are incorporated. Finally, reducing the CM from 570 to 480 kg/m 3 in mixtures with 0.43 W/CM also decreases settlement. 4. CONCLUSION The proposed statistical models can simplify the test protocol required to optimize a given mixture by reducing the number of trial batches needed to achieve a balance among mixture variables. This is due to the use of the models in conducting simulations of various variables to secure adequate deformability, stability, and strength. 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 Fig. 13 Effect of VEA and CM contents and W/CM on maximum surface settlement. influence of key variables on SCC properties. The derived models are shown to be useful to understand interactions between mixture parameters affecting key SCC characteristics and to derive relationships between the various responses of interest for mixture optimization and quality control. 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. and Okamura, H., Development of high performance concrete, Journal of the Faculty of Engineering, the University of Tokyo (B) XLI (3) (1992) [3] Khayat, K. H., Ghezal, A. and Hadriche, M. S., Factorial design models for proportioning self-consolidating concrete, Mater. Struct. 32 (223) (1999) [4] Beaupré, D., Rheology of high performance concrete, Ph.D. Thesis, University of British Columbia, Canada (1994). [5] Yurugi, M., Sakata, N., Iwai, M. and Sakai, G. Mix proportion for highly workable concrete, Proceedings, Concrete 2000, Dundee (1993) [6] 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) [7] Manai, K., Evaluation of the effect of chemical and mineral admixtures on the workability, stability, and performance of selfcompacting concrete, (available in French) Masters Thesis, Université de Sherbrooke, Canada (1995) 182 p. [8] Fujiwara, H., Nagataki, S. and Otsuki, N., Study on reducing unit powder content of high fluidity concrete by controlling powder particle size distribution, Proceedings of Japan Society of Civil Engineerings N-532, vol. 30, pp (December 1996). [9] Hadriche, M. S., Modelisation of fresh and hardened performance of SCC: optimisation and mixture composition, (available in French) Masters Thesis, Université de Sherbrooke, Canada (1998), 244 p. 344