Applicability of rheological models to high-performance grouts containing supplementary cementitious materials and viscosity enhancing admixture

Transcription

1 Materials and Structures / Matériaux et Constructions, Vol. 36, July 3, pp Applicability of rheological models to high-performance grouts containing supplementary cementitious materials and viscosity enhancing admixture A. Yahia 1 and K. H. Khayat 2 (1) Taiheiyo Cement Corporation, Osaku, Sakura-City, Japan (2) Department of Civil Engineering, Université de Sherbrooke, Sherbrooke, J1K 2R1, Québec, Canada ABSTRACT The knowledge of yield stress and plastic viscosity of cement-based materials is of special interest in various applications, including consolidation grouting, post-tensioning systems, and for numerical simulations. These rheological parameters are generally estimated from the shear stress-shear rate data using an empirical model. Highly pseudoplastic systems may not be adequately modeled using flow models typically used for conventional grouts. This paper summarizes the results of a study undertaken to evaluate the applicability of a number of analytical models to fit experimental data obtained on cement grout. In total, 44 grouts containing silica fume replacements of 1.5%, 3%, and 5%, by mass of cementitious materials, blast furnace slag substitutions of % and %, and various combinations of high-range water-reducer and viscosity-enhancing admixture were evaluated. All mixtures were prepared with. water-cementitious material ratio. Test results highlight the difficulties encountered when using conventional models to fit flow data of highly pseudoplastic mixtures of low yield stress. This is true for mixtures incorporating a viscosity-enhancing admixture, especially when combined with low dosage of high-range water-reducer. In general, the Herschel- Bulkley, Robertson, De Kee, and Casson models were found to be adequate for use with highly pseudoplastic grouts. A new model is proposed to provide better fitting of rheological profiles of highly flowable, yet stable, pseudoplastic mixtures that exhibit particularly low yield stress values. RÉSUMÉ Les paramètres rhéologiques, soit le seuil de rigidité et la viscosité plastique, des suspensions de ciment sont des paramètres importants pour le contrôle de la qualité de ces matériaux. Ces paramètres sont généralement estimés à partir de la courbe d écoulement en utilisant un modèle empirique. Les mélanges contenant un agent de viscosité montrent cependant un comportement pseudo-plastique largement plus important que les mélanges sans agent de viscosité. Les modèles empiriques utilisés pour simuler le comportement rhéologique des coulis ordinaires ne sont alors pas adéquats pour reproduire les courbes d écoulement des coulis pseudo-plastiques. Dans cet article, on se propose d évaluer la validité de différents modèles empiriques pour décrire le comportement rhéologique des coulis pseudo-plastiques. Quarante-quatre coulis contenant 1,5%, 3% et 5%, de la masse de liant, de la fumée de silice, du laitier de haut fourneau à des dosages entre et % et différentes combinaisons de superplastifiant et d agent de viscosité ont été évalués. Les résultats de cette étude ont montré qu il est difficile de décrire le comportement rhéologique des coulis pseudo-plastiques en utilisant des modèles empiriques linéaires. En général, les modèles de Herschel-Bulkley, Robertson, De Kee et Casson sont adéquats pour décrire le comportement rhéologique des coulis pseudo-plastiques. En outre, un nouveau modèle non linéaire est proposé pour mieux décrire les rhéogrammes des coulis pseudoplastiques ayant un faible seuil de rigidité. 1. INTRODUCTION The knowledge of rheological parameters of the paste is of prime importance to predict the ease of placement. For example, the maximum distance of penetration (L) of a laminar grout injected in a capillary-type crack can be expressed as L Pe d, where Pe is the injection pressure, d is the opening width of the crack, and is the yield stress of the grout [1]. Yield stress is estimated from the shear stress versus shear rate data (flow curve) using an empirical model to fit the experimental data /3 RILEM 2

2 Materials and Structures / Matériaux et Constructions, Vol. 36, July 3 Cement grouts are dense suspensions of solid particles of complex rheological behavior that is affected by several physical and chemical factors. This includes the water-tocementitious materials ratio (W/CM), particle-size distribution and composition of the binder, experimental procedures, and viscometer geometry. Such behavior is further complicated by the use of chemical admixtures, such as high-range water-reducer (HRWR) and viscosityenhancing admixture (VEA), as well as supplementary cementitious materials (SCM) employed to enhance fresh and hardened properties. The incorporation of VEA can accentuate the shear-thinning behavior of the grout. This can be due to an increase in the degree of association between adjacent VEA polymer chains at low shear rates, which increases the resistance to deformation [2-5]. The rheological behavior of cement grout incorporating VEA is therefore affected by the test procedure, including the maximum shear rate and duration of shear application. Various investigations have been carried out on cement paste to investigate flow behavior [6-9]. Such studies indicate that cement grout exhibits flow characteristics markedly different from those of a simple Newtonian fluids [6, 1]. Unlike a Newtonian fluid, a cement grout behaves as a pseudoplastic material with yield stress. This is reflected by a structural breakdown or structural build-up depending on the concentration of the suspension, duration of shearing cycle, and rate of hydration [6, 8, 9]. The estimation of rheological parameters from flow curve is usually based on empirical models that take into account the test procedure, the shear history, and the time dependency behavior. The Bingham model is the mostly used to fit flow curve, generated from viscometric data, of conventional cement grout. New generation grout mixtures made with specialty chemical admixtures and SCM can exhibit higher degree of pseudoplasticity than conventional grouts [5]. This is characterized by a decrease in apparent viscosity with the increase in shear rate. Such grouts can also undergo considerable structural breakdown with time following the application of a constant shear rate. Therefore, the rheological behavior of high-performance grout can exhibit a non-linear shear stress-shear rate relationship, which is time dependent. Furthermore, the rheological behavior is pseudoplastic, hence limiting the applicability of linear flow models [11, 12]. The objective of this study is to review some of the flow models that can be used to describe rheological behavior of cement-based grouts and evaluate their suitability for highperformance grout systems. 2. RESEARCH SIGNIFICANCE Due to the complexity of the rheological behavior of cement paste, most attempts to describe rheological behavior of grout have been empirical in nature. The Bingham model is commonly used for conventional grout. However, chemical admixtures and supplementary cementitious materials are increasingly used in grout mixtures with improved mechanical properties and durability. The resulting high-performance grouts that can be highly pseudoplastic may therefore be better described using flow models other than the Bingham model. 3. REVIEW OF SOME EMPIRICAL MODELS Widely used empirical models employed to describe rheological behavior of neat cement grout, or other similar suspensions, are reviewed here. 3.1 Bingham model The Bingham model is given by: = + p. (1) where is the shear stress (Pa), is the yield stress (Pa),. p is the plastic viscosity (Pa.s), and is the shear rate (s -1 ). The yield stress corresponds to the minimum shear stress required to initiate flow, below which the mixture does not undergo permanent deformation and behaves as an elastic material. The constant of proportionality between shear stress and shear rate is referred to as the apparent viscosity. The Bingham model has been widely used to describe rheological behavior of cement-based materials [6]. It is relatively easy to incorporate into analytical solutions and can fit a wide range of data over a limited range of shear rates. 3.2 Herschel-Bulkley model The Herschel-Bulkley model is similar to the Bingham model, except for the addition of a power index for the shear rate. The model can be presented as a combination of the Bingham and Power models: = + K. n where K is the consistency and n is the power index that represents the deviation from a Bingham behavior. This equation describes a fluid with a yield stress and a nonlinear relationship between shear stress and shear rate. When the power index (n) is less than or greater than 1, the fluid exhibits shear-thinning or shear-thickening behavior, respectively. The Herschel-Bulkley model leads to the Bingham model when n is equal to 1 where the consistency can represent plastic viscosity. This model was reported to be adequate in describing the rheological behavior of neat cement grout with W/C of.3 to. [1]. Atzeni et al. (1985) used this model successfully to correlate data obtained by measurements conducted with cone and plate viscometer to describe the rheological behavior of cement grout with W/C ranging between.3 and.45 [13]. 3.3 Casson model The Casson model has two adjustable parameters and is given by the following equation: (2) = ( ). (3) where is the apparent viscosity at very high shear rate. 3

3 Yahia, Khayat This model was found to be unsatisfactory to describe rheological behavior of neat cement grout with W/C ranging between. and. [13]. It was also found unsatisfactorily when applied to a conventional cement grout with.5 W/C [14]. This is attributed to the solid phase concentration in the investigated grouts that is considerably higher than that contemplated by the theoretical development of the model [13]. 3.4 Eyring model This model has two adjustable parameters and is expressed as follows: = a sinh -1 (b. ) (4) Atezeni et al. (1985) carried out rheological studies on grouts made with portland cement and blended cements containing pouzzolana, blast furnace slag, and fly ash with W/CM ranging between.3 and.45. The authors compared the degree of prediction of flow properties of grouts using the Herschel-Bulckley, Casson, Eyring, and vom Berg models. The authors found that the best fits were obtained with the Eyring s and the Herschel-Bulkley models, whereas the vom Berg model was adequate only at low-shear rates [13]. Papo (1998) reported that the Eyring model yields inadequate fitting of experimental data compared to the Bingham, Shangraw, Casson, and Herschel-Bulkley models for neat cement paste with.34 to.42 W/C [14]. 3.5 Robertson-Stiff model The Robertson-Stiff model has three adjustable parameters and is given by the following expression: = A (. + B) n (5) This model leads to the Bingham model when n is equal to 1, is equal to AB, and the plastic viscosity is equal to A. The model becomes equivalent to the Newton model when B is equal to and n is equal to 1. The Robertson-Stiff model was found to enable accurate description of shear rate-shear stress data of various viscous drilling fluids and cement slurries with W/C ranging between.3 and.5 [11]. 3.6 De Kee model This model has three parameters, as follows: = + p. ē. (6) where is a time-dependent parameter. This model was not employed to describe the rheological behavior of cement grout, but rather the rheological behavior for hydrolyzed polyacrylamide solutions containing g/l of NaCl [15]. The hydrolyzed polyacrylamide solution was reported to exhibit shearthinning behavior at low shear rates and shear-thickening at high shear rates. The critical shear rate where the solution changes from shear-thinning to shear-thickening was found to be equal to 27.4 s -1. Predicted and experimental data for viscosity and the primary normal stress coefficient of mixtures made with such solutions were found to be in good agreement. 3.7 Vom Berg model This model has three adjustable parameters that include a yield stress and two other constants. The model is given by the following equation: = + b sinh -1 ċ (7) This relationship was originally developed to evaluate the effect of solid concentration and cement particle-size distribution on rheological properties of cement paste [1]. The range of solid concentrations covered in the study was.44 to.29, corresponding to W/C of. to.. This model was further used to study the rheological behavior of neat cement paste with W/C ranging between.3 and.45 [13]. The model was found to be suitable to fit experimental shear stress data at low shear rates only [13]. This is may be due to the type of viscometer in use, the range of applied shear rates, as well as the low W/C. 4. EXPERIMENTAL PROGRAM The experimental program presented in this paper consisted of three parts (Table 1). 4.1 Materials and mixture proportions A Type 1 CSA cement complying with ASTM C15 was used. Welan gum was used for the VEA. Welan gum is a highly effective polyscharide that can increase viscosity, even at low addition rates [3-5]. The gum was prehydrated in water at 1% concentration using a highshear blender rotating at approximately rpm. A naphthalene-based HRWR with a solid content of 42% and a specific gravity of 1.21 was used. Water in the HRWR was accounted for to maintain constant W/CM. All grouts had a fixed W/CM of., typical of high-performance structural grouts. Table 1 - Summary of investigated mixtures VEA dosage: HRWR dosage:.75%.4% 2.5% Phase 1 VEA mixtures Phase 2 Grout with silica fume Phase 3 Grout with blast furnace slag Silica fume content: 1.5% 3% 5% Blast furnace Slag content: % 3% % HRWR-VEA combination:.8%.5% 1.% -.4%.8% -.3% 1.5% -.4% HRWR-VEA combination:.8%.5% 1.% -.4%.8% -.3% 1.5% -.4% 4

4 Materials and Structures / Matériaux et Constructions, Vol. 36, July 3 Table 2 summarizes the mixture proportioning and experimental results obtained on grouts containing various HRWR-VEA combinations (Phase 1). The mixtures investigated in Phases 2 and 3 are presented in Tables 3 and 4, respectively. Table 2 - Experimental test results obtained for grout mixtures investigated in Phase 1 VEA HRWR Mini slump at various shear rates (s -1 ) (% SCM) (% SCM) (mm) All grouts were prepared in batches of 4 L and mixed in a Helice-type mixer with a blade rotating at 25 rpm. This is necessary to ensure complete dispersion and homogeneous suspension of the binder. At the end of mixing, grouts had a temperature of 23 3 C. The mixing procedure consisted of adding the water and HRWR to the mixer along with the prehydrated VEA. The cementitious materials were introduced gradually over s. The grout was further mixed for s, allowed to rest for 3 s, then mixed again for s. 4.2 Test procedures The temperature and unit weight were first noted, and the mini-slump spread was determined 5 min after the initial contact of water with cement. The dimension of the mini-slump cone are proportional to those of the slump cone used for concrete (ASTM C-143) with a diameter of 38 mm at the bottom and 19 mm at the top and a high of 57 mm [16, 17]. Two coaxial cylinder viscometers (FANN 35 and CHAN 35) were employed to evaluate rheological properties. In both cases, a gap-size of 1.17 mm and a stationary inner-cylinder with 38 mm height were used. A 35-mL sample of grout was used for such measurements. The shear stress was determined at 5 rotation speeds for the FANN 35 viscometer and 11 speeds for the CHAN 35 viscometers. The rotational velocities were varied between 1 and 3 rpm, corresponding to shear rates of 1.7 to 51 s - 1, respectively. The flow curve was noted for both the ascending and descending legs of the shear stress-shear rate curve. Each shear value was maintained for a duration of s to achieve near equilibrium state. At the highest shear rate level, the grout was sheared for s before starting the descendant curve. A typical rheological profile obtained from tests conducted using a rotating viscometer to study the rheological behavior of a mixture made with 1% HRWR and various VEA dosages is plotted in Fig. 1. The up-curve corresponds to the undisturbed state of the grout where shear stress measurements were obtained by increasing the shear rate (ascending curve). The descending shear stress-shear rate curve was obtained in a similar manner reflecting the rheological behavior of the grout following a given shear history. The experimental shear stresses considered in this investigation were taken from the ascending curve. 5. DATA ANALYSIS For each of the 44 grout mixtures evaluated in this study, the shear stress data corresponding to different shear rates were fitted using the empirical models reviewed earlier. This was carried out to determine the various constants necessary for the expression of each model (such as, p, K, A, B, and In order to evaluate the accuracy of each model in fitting the experimental shear stress-shear. rate ( - ) data, the standard error (S) between predicted and measured shear stresses was calculated for each grout and model combination. The estimated standard error considered is the sample variance of residual values, namely S², can be expressed as follows: S 2 = N ( exp cal i i ) 2 i 1 N P The term (N-P) refers to the degree of freedom calculated as the number of experimental shear measurements (N) minus the number of unknown constants exp required for each model (P). The i value is the experimental shear stress measured at a shear rate of i s -1. cal The i value is the calculated (estimated) shear stress obtained at a shear rate corresponding to i s -1. The ( exp i - cal i ) 2 term is the sum of square difference between the experimentally measured and calculated shear stresses at a given shear rate of i s -1. The standard error (S) between the measured shear stress values and those estimated using empirical models was used to compare the suitability of the models to fit the flow curve for the tested mixtures. Low S values indicate that the model enables adequate fitting of the rheological behavior of the grout [18, 19]. (8) 5

5 Yahia, Khayat Table 3 - Experimental test results obtained for grout mixtures containing silica fume (Phase 2) Silica fume HRWR-VEA Mini slump Experimental shear stress (Pa) at various shear rate (s -1 ) (% SCM) (% SCM) (mm) Table 4 - Experimental test results for grout mixtures containing blast furnace slag (Phase 3) Blast furnace slag HRWR-VEA Mini slump Experimental shear stress (Pa) at various shear rate (s-1 ) (% SCM) (% SCM) (mm) RESULTS AND DISCUSSION The mini slump spread of 23 mixtures evaluated in Phase 1 are listed in Table 2. These values ranged between and 1 mm. They varied between and 135 mm for the 12 mixtures tested in Phase 2 (Table 3), and between and 165 mm for the nine grouts investigated in Phase 3 (Table 4). Test results derived from the viscometric data indicate the existence of hysteresis loop given the structural breakdown of the grout, as indicated in Fig. 1. It is important to note that whenever the dial indicator for the shear stress was not stable (oscillating around the actual dial indicator) after the s test period for a given shear rate, the value corresponding to shear stress was not considered in deriving the regression, which explains some missing values in Tables 3 and 4. As shown in Fig. 1, the structural breakdown degree is more important for grouts containing higher dosages of VEA, reflecting the effect of the VEA on enhancing the shear- thinning behavior through physical action [2-5]. The shear stress-shear rate values presented in Tables 2, 3 and 4 show that all of investigated grouts exhibited a pseudoplastic behavior. Tables 5, 6, and 7 summarize the S values obtained for mixtures investigated in Phases 1, 2, and 3, respectively. It HRWR = 1% up down 3 5 Shear rate (s-1).75%.5%.3% VEA = % Fig. 1 - Typical flow behavior obtained from test on rotating viscometer. is important to note that it was not possible to fit the Eyring s and vom Berg s models to the grouts tested in this paper, even those with a limited shear-thinning response. Therefore, the comparison between measured and estimated values is further evaluated for the five remaining models. 6.1 Grouts with HRWR and VEA and no supplementary cementitious materials As indicated in Table 5 and Fig. 2, for % cement mixtures with no VEA, the worst fitting of the experimental shear stress values (highest S) was obtained with the more 6

6 Materials and Structures / Matériaux et Constructions, Vol. 36, July 3 Table 5 - Standard error (S) of shear stresses obtained for grouts investigated in Phase 1 VEA HRWR Bingham Casson Herschel Robertson De Kee Equation (9) (% SCM) (% SCM) (S) (S) (S) (S) (S) (S) Mean value Table 6 - Standard error (S) of shear stresses obtained for grouts investigated in Phase 2 VEA HRWR-VEA Bingham Casson Herschel Robertson De Kee Equation (9) (% SCM) (% SCM) (S) (S) (S) (S) (S) (S) Mean value viscous grouts, regardless of the model in use. The Bingham model resulted in the least favorable fitting, especially for mixtures with low HRWR content. An S value of 8.1 was obtained with Bingham model compared to 4.3, 3.,.9, and.9 when the Casson, De Kee, Robertson, and Herschel models were employed, respectively. Lower S values were, however, obtained with the increase in HRWR content, regardless of the model in use. For example, with the Bingham model the grouts with no VEA and.4% HRWR (mini slump of 9 mm) had an S value of 8.1. The S value decreased to.4 when the dosage of HRWR increased to 1% (mini slump of 1 mm). Similarly, the S value decreased from 4.3 to.2 when the HRWR content increased from.4% to 1% with the use of the Casson model to fit the experimental shear stress data. In general, the Herschel-Bulkley, Robertson, and De Kee models allowed better fitting of the experimental shear stress data (lower S values). However, a high S value of 3. was obtained with the De Kee model, compared to.9 with the Herschel-Bulkley and Robertson models, when dealing with the more viscous grouts that exhibited higher shear-thinning response (mini slump of 9 mm). For mixtures incorporating relatively low VEA content of.2% to.3%, poor fitting of shear stress data was obtained for the more viscous mixtures proportioned with low HRWR contents, regardless of the model in use. In general, the worst prediction was obtained with the Bingham model, especially for the more viscous grout containing.6% HRWR (mini slump ranging between and 115 mm). For example, for grout made with.2% VEA and.6% HRWR, an S value of 8.3 was obtained when applying the Bingham model. This value was 5.6, 3.8, 3.5, and 2.5 when the Casson, Herschel- Bulkley, De Kee, and Robertson were used, respectively. Increasing the VEA dosage to.3% yielded higher S values for all models compared to mixtures incorporating lower VEA contents (.2%). For mixtures with.3% VEA, the Bingham model resulted, in general, in the worst fitting. For example, the S values for grouts incorporating.3% VEA and HRWR ranging between.6% and 1.5% varied from 16 to.6 for the Bingham model. These values were 5.4 to.4 and 6.4 to.2 for the De Kee and Robertson models, respectively. The performance of the regression was enhanced for all models in the case of highly flowable grouts incorporating relatively high HRWR content. For example, when fitting the flow curve of grout made with.3% VEA, the S value decreased from 19.4 to.2 and 12.1 to.1 with the increase of HRWR from.6% to 1.5% using the Herschel-Bulkley and Casson models, respectively. Such enhancement in the regression analysis (lower S) associated with the grout of greater fluidity was observed for the grouts made with all three VEA dosages of.2%,.25% and.3%, regardless of the model in use. 7

7 Yahia, Khayat Table 7 - Standard error (S) of shear stresses obtained for grouts investigated in Phase 3 Slag HRWR-VEA Bingham Casson Herschel Robertson De Kee Equation (9) (% SCM) (% SCM) (S) (S) (S) (S) (S) (S) Mean value and.75% VEA and HRWR contents of.8% to 2.5%, the S values ranged between 6.7 and 1.6, when the Bingham model was employed to fit the flow curve. When the De Kee, Herschel-Bulkley, and Casson models were used for mixtures with.5% VEA, the resulting S values ranged between 1.8 and.2, 1.9 and.4, and 3.4 and.5, respectively. In general, the increase in HRWR content led to lower S values that reflected better fitting of the experimental shear stress data, regardless of the model in use. This is may be due to the low shearthinning behavior resulted from the 1 1 Experimental Bingham Casson 1 De Kee Casson-De Kee 1.3%.2% VEA = % HRWR =.6% 3 5 Shear rate (s -1 ) HRWR =.8% 3 5 Shear rate (s -1 ).4%.3%.2% VEA = % Experimental Bingham Casson De Kee Casson-De Kee HRWR = 1%.3% 3 5 Shear rate (s -1 ).4% VEA = %.75% HRWR = 1.5% VEA =.3% 3 5 Shear rate (s -1 ) Fig. 2 - Flow curves for mixtures prepared with % cement and various VEA-HRWR combinations (Phase 1). 1.5%.75%.4% When dealing with higher VEA dosages, in general the Bingham model led to the worst fitting for mixtures evaluated in Phase 1. For example, for grouts with.5% increase HRWR dosage. By comparing predicted and measured shear stress values at various shear rates, it is clear that the limitation of the 8

8 Materials and Structures / Matériaux et Constructions, Vol. 36, July 3 Experimental Bingham Casson De Kee Casson-De Kee.5% -.8% SF = 1.5% 3 5 Shear Rate (s -1 ).4% - 1%.4% - 1.5% VEA-HRWR.3% -.8% SF = 3% 3 5 Shear Rate (s -1 ).4% - 1%.5% -.8%.4% - 1.5% VEA - HRWR.3% -.8% Fig. 3 - Flow curves for mixtures prepared with 1.5% and 3% silica fume (Phase 2) Experimental Bingham Casson Slag = % De Kee Casson-De Kee.3% -.8%.5% - 1.5% VEA - HRWR % -.6% Slag = %.4% -.8%.5% - 1.5% VEA - HRWR % -.6% 3 5 Shear Rate (s -1 ) 3 5 Shear Rate (s -1 ) Fig. 4 - Flow curves for mixtures prepared with % and % blast furnace slag (Phase 3). Bingham model is due to the poor fitting of the shear stress data at low shear rates. The linear shape of the Bingham model does not allow accurate fitting of the region corresponding to the low shear rates, i.e. the shear-thinning region. However, at high-shear rates, the Bingham model resulted in good prediction of the shear stress values. Therefore, the model can be considered to be mostly suitable to predict flow profiles at high shear rates where the shape is mostly linear. The mean standard errors (S) obtained with the Herschel-Bulkley, Robertson, and De Kee models when fitting shear stress data for the 23 investigated mixtures in Phase 1 (% cement) are 2.3, 2., and 1.8. Such values were 2.6 and 4. when using the Casson and Bingham models, respectively. The De Kee, Robertson, and Herschel-Bulkley models then appear to be more accurate in fitting the measured shear stress-shear rate data for mixtures made with % cement containing different combinations of HRWR and VEA (mean S values ranging between 1.8 and 2.3). When dealing with grouts that exhibit limited degree of shear-thinning (mixtures with mini slump spread superior to 115 mm), the Herschel-Bulkley, Robertson, Casson and De Kee models are shown to yield better fitting of shear stress-shear rate data (maximum mean S values of 1.3 compared to 1.9 obtained with Bingham and 9

9 Yahia, Khayat Robertson models). The conventional Bingham model resulted in higher S values of Grouts made with silica fume replacements In general, the degree of fitting of experimental data given the various rheological models was less accurate (higher S values) for mixtures made with silica fume than those without any silica fume. On the other hand, the fitting was more accurate (lower S values) for the more fluid grouts containing low silica fume substitutions than those containing high silica fume replacement. Indeed, all five models allowed acceptable prediction of rheological behavior for grouts with 1.5% and 3% silica fume. In general, the Robertson and De Kee models resulted in better fitting of experimental data for grouts containing 1.5% and 3% silica fume replacement than the Bingham, Casson, and Herschel-Bulkley models (Table 6 and Fig. 3). The incorporation of silica fume in mixtures containing low VEA dosage of.3% resulted in higher consistency. For a given combination of HRWR-VEA, a high S value was obtained when the silica fume content increased to 5%, regardless of the model in use. For example, an S value of 1.9 was obtained when using the Robertson model for grout with 1% HRWR,.4% VEA, and 1.5% silica fume. This value was 6.8 and 19.5 when the silica fume increased to 3% and 5%, respectively. However, for the same VEA content of.4%, increasing the HRWR dosage from 1 to 1.5% resulted in a decrease in the S value to 1.1, 1.9, and 11.9 for mixtures with 1.5%, 3%, and 5% silica fume, respectively. All of the investigated models resulted in poor fitting of the measured shear stress-shear rate data in grouts with 5% silica fume. The Bingham and Herschel-Bulkley models did not provide accurate fitting of the shear stress-shear rate data of silica fume mixtures with S values as high as 34. This was true regardless of the fluidity and silica fume content. Indeed, the highest average S values of.5 and 1.5 were obtained with the Herschel-Bulkley and Bingham models, respectively. On the other hand, S values of 7.8, 6.2, and 6.1 were obtained with the Casson, De Kee, and Robertson, respectively. Regardless of the silica fume content, the Herschel-Bulkley model did not provide a good degree of fitting of the measured shear stress-shear rate data, except for a power index (n) of Grouts with blast furnace slag replacements Mixtures with blast furnace slag showed higher fluidity and lower pseudo-plastic response than those made with % cement of Phase 1. Except for the more viscous mixture made with % slag,.8% HRWR, and.3% VEA, all of the investigated rheological models yielded accurate fitting of the experimental data in the case of mixtures made without any VEA, and regardless of the blast furnace slag content (Table 7 and Fig. 4). For mixtures with % blast furnace slag, the Robertson model resulted in the best fit, regardless of the HRWR-VEA combination, while the Herschel-Bulkley, Casson, Bingham, and De Kee models resulted in the highest S values. This was especially true for the more viscous mixtures, such as those incorporating.3% VEA and.8% HRWR. Better fitting of measured shear stress-shear rate data was obtained when increasing the blast furnace slag content resulting in greater fluidity, regardless of the model in use. For example, when using the Herschel-Bulkley, Casson, Bingham, and De Kee models for the mixture with.8%-.3% HRWR-VEA containing % of slag, the corresponding S values were 9.9, 9., 4., and 4., respectively. These values decreased to.5,.9,.5, and.5, respectively, when the slag content increased to %. The mean S values of mixtures with blast furnace slag were lower than 2.1 for all models. The lowest value of 1.1 was obtained with the Robertson model. The mean S value for the Bingham and Casson models was 2.1, and 1.8 for the De Kee and Herschel-Bulkley models. All five models provided acceptable fitting of the measured rheological data for grouts containing blast furnace slag. The accuracy of fitting rheological profiles using the various classical models for the slag mixtures can be due to their lower viscosity and absence of the nonlinearity portion of the shear stress-shear rate curves. Indeed, the shear-thinning behavior observed with such grouts was lower than that encountered with % cement mixtures or those containing silica fume. 6.4 Discussion Based on the above results, the Eyring s and Von Berg s models should not be used to describe the rheological behavior of specialty grouts similar to those investigated in this paper, even when the mixtures is highly fluid. None of the evaluated rheological models was found to enable accurate fitting of shear stress-shear rate data of all investigated mixtures. Difficulties were encountered mostly when modeling the non-linear portion of the flow curve observed at low shear rate, i.e. the shear-thinning region. The conventional Bingham model did provide better fitting of shear stress-shear rate data, especially in the case of grout with relatively low consistency. The limitation of this model lies mainly in fitting the shear stress data at low shear rate. For grouts incorporating VEA and made with % cement, the De Kee, Robertson, Herschel-Bulkley, and Casson models were found to be more accurate in reproducing the measured shear stresses than the Bingham model. The investigated models provide adequate fitting of the experimental data in case of mixtures with 1.5% and 3% silica fume replacements. Higher standard error values were obtained, however, for mixtures with 5% silica fume replacement. In general, the Robertson and De Kee models allowed better fitting of shear stresses. The five selected rheological models provide suitable fitting of the data of grouts with blast furnace slag, which exhibited greater fluidity and lower degree of shearthinning than the other mixtures. The Robertson model resulted in the best degree of fitting of the experimental shear stresses with S values ranging between.3 and 2.9. Considering all 44 high-performance grout mixtures that were investigated in this paper, the Robertson and De Kee models provide the best fitting of shear stress-shear rate data. Mean S values of 2.9 and 3. were obtained with these models when applied to all 44 tested mixtures. Higher mean values of 3.9, 5.4, and 7.2 resulted when using the Casson, Bingham, and Herschel-Bulkley models, respectively. Favorable degree of fitting of the rheological data was observed when dealing with highly fluid mixtures, regardless 41

10 Materials and Structures / Matériaux et Constructions, Vol. 36, July 3 of the model in use. The accuracy of fitting rheological data of such grouts can be due to the lower shear-thinning response as the mixture start to behave more like a Newtonian fluid. When dealing with a more shear-thinning grout of greater yield value, such as in the case of mixtures incorporating VEA and low HRWR content, lower degree of fitting was obtained (highest S values). Such limitation in fitting the shear stress-shear rate data can be due to the nonlinear portion of the flow curve observed at low shear rates, especially in the case of highly pseudoplastic grout. With the increase in HRWR dosage, the pseudoplastic effect decreases, and the experimental data take a more linear shape, thus becoming easier to fit using the reviewed models. 7. NEW PROPOSED MODEL Given the pseudoplastic behavior of the tested grouts, an attempt is made to develop a new model to provide better prediction of rheological response. Any material exhibiting a pseudoplastic, or shear-thinning behavior with a yield stress can reach an equilibrium structure within a given period under shearing. This is confirmed by the viscosity predicted at the highest shear rate using the Casson model. Generally, the shear stress values obtained in such a case (at the highest shear rate) were similar for all investigated grouts. However, the plastic viscosity predicted by the De Kee model seems to have a physical sense since it provides adequate correlation with the mini slump spread, which can be closely correlated to yield stress [2, 13]. By examining the estimated vs. experimental shear stress data, it can be observed that the Casson model generally predicts higher shear stresses at low shear rates and lower shear stresses at high shear rates. Furthermore, the De Kee model results in shear stresses that are lower than those estimated using the Casson model, which are slightly higher than the experimental data. Contrary to the Casson model, better fitting of shear stress-shear rate data at high shear rates was obtained when using the De Kee model. Therefore, it seems to be possible to more accurately estimate the shear stress-shear rate data using a new model consisting of a combined Casson and De Kee models, as follow: = ( ). e -. where is the shear stress, is the yield stress, p is the plastic viscosity, and is a time-dependent parameter. A grout can exhibit shear-thinning and shear-thickening characteristics whenever the value of is positive or negative, respectively. By examining the results presented in Tables 5, 6 and 7 for grouts investigated in Phases 1, 2, and 3, respectively, it can be observed that the De Kee-Casson model (Equation (9)) can result in better prediction of shear stresses than those of the Casson and De Kee models taken individually. This is the case even for grouts with silica fume and blast furnace slag. For mixtures with no VEA, the standard error (S) varied from 4.3 to.2 when using the Casson model and from 3. to.4 with the De Kee model. However, the spread of S values ranged from 1.2 to.2 when using the proposed model. (9) For highly viscous mixtures with mini slump spread of 9 mm, a mean S value of 1.2 was obtained when using the proposed model compared to 4.3 and 3. associated with the Casson and De Kee models, respectively. In the case of grouts containing VEA, low S values were generally obtained when using the proposed model. For example, the grout with.75% VEA, the resulting S values ranged between 2.3 and.7 when using the Casson model and between 1.5 and.8 when using the De Kee model; these values ranged however from.7 to.3 when applying the proposed model. This indicates greater accuracy of the model to fit the experimental shear stress data. An overall mean S value of 1.7 was obtained when using the proposed model for all mixtures made with % cement. The proposed model resulted in more accurate fitting of flow curves for mixtures incorporating 1.5% and 3% silica fume than the De Kee and Robertson models, except for the mixtures containing 5% silica fume. The new proposed model provided similar fitting of the flow curves as that obtained with the Robertson model. The fitting was better than that obtained when using the De Kee model for grouts made with blast furnace slag. In general, the proposed model yields more accurate fitting of shear stress-shear rate data of the 44 investigated mixtures with low mean S value of 1.8. This value is lower than the 2.9 and 3. results obtained with the Robertson and De Kee models, respectively. 8. CONCLUSIONS Given the materials, geometry of viscometer, and measurement procedure used in this investigation and the above results, the following conclusions can be made: 1. The Eyring s and Von Berg s models are not valid to describe rheological behavior of specialty cement grouts. 2. Better fitting of rheological shear stress-shear rate data can be obtained for fluid grout with low pseudoplastic response that behaves closer to a Newtonian fluid. The worst fitting can be obtained for VEA mixtures containing low dosage of HRWR that are highly pseudoplastic with a well-pronounced non-linear flow region at low shear rates. 3. The five remaining models can fit accurately the rheological flow data of grouts made with blast furnace slag that exhibits limited pseudoplastic behavior. The Robertson model resulted in the best prediction, especially when dealing with blast furnace slag content of %. 4. The De Kee, Robertson, Herschel-Bulkley, and Casson models enable better fitting of the rheological profiles of grouts made without any supplementary cementitious materials of medium to high VEA content; the Bingham model leads to the worst fit of these mixtures. 5. The Robertson and De Kee models can be more accurate to fit flow curves of mixtures with silica fume, with the latter showing better results for grouts containing 5% silica fume. 6. The proposed combined De Kee-Casson model leads to better prediction of rheological profiles of highperformance grout, especially when dealing with mixtures that contain supplementary cementitious 411

11 Yahia, Khayat materials and VEA with relatively high degree of pseudoplasticity. CONVERSION FACTORS 1 cm =.3937 in. 1 L = 61 in. 3 t C = (t F - 32)/1.8 1 kg/m 3 = lb/yd 3 Pa.s = cp = 1 P REFERENCES [1] Lombardi, G., The role of cohesion in cement grouting of rock, 15 th Congress on Large Dams, International Commission on Large Dams, Q.58, R.13, Lausanne, 3 (1985) [2] Ghio, V.A., Monteiro, P.J.M. and Gjørv, O.E., Effects of polysaccharide gums on fresh concrete properties, ACI Materials Journal 91 (6) (1994) 2-6. [3] Ghio, V.A., Monteiro, P.J.M. and Demsetz, L.A., The rheology of fresh cement paste containing polysaccharide gums, Cement and Concrete Research 24 (2) (1994) [4] Khayat, H.K., Effects of antiwashout admixtures on fresh concrete properties, ACI Material Journal 92 (2) (1995) [5] Khayat, H.K. and Yahia, A., Effect of welan gum-highrange water-reducer combinations on rheology of cement grout, ACI Material Journal, 94 (5) (1997) [6] Tattershall, G.H. and Banfill, P.F.G., The Rheology of Fresh concrete, in Pitman Advanced Publishing Program, New York (1983). [7] Lapasin, R, Papo, A. and Rajgelj, S., Flow behavior of fresh cement pastes, a comparison of different rheological instruments and techniques, Cement and Concrete Research 13 (1983) [8] Banfill, P.F.G. and Saunders, D.C., On the viscometric examination of cement pastes, Cement and Concrete Research 11 (3) (1981) [9] Shaughnessy, R. and Clark, P.E., The rheological behavior of fresh cement paste, Cement and Concrete Research 18 (3) (1988) [1] Vom Berg, W., Influence of specific surface and concentration of solids upon the flow behavior of cement pastes, Magazine of Concrete Research 31 (19) (1979) [11] Jones, T.E.R. and Taylor S., A mathematical model relating the flow curve of a cement paste to its Water/Cement ratio, Magazine of Concrete Research 29 (11) (1977) [12] Darby, R., Viscoelsatic fluids: an introduction to their properties and behavior, Chemical Processing and Engineering 9, New York: Dekker, C., 1976, 637 p. [13] Atzeni, C., Massida, C. and Sanna, U., Comparison between rheological models for Portland cement pastes, Cement and Concrete Research 15 (1985) [14] Papo, A., Rheological models for cement pastes, Mater. Struct. 21 (1988) [15] De Kee, D. and Chan Man Fong, C.F., Rhelogical properties of structured fluids, Polym. and Engineering Science 34 (1994) 438 p. [16] Kantro, D.L., Influence of water reducing admixtures on properties of cement paste - A miniature slump test, Cement, Concrete, and Aggregate, CCAGDP 2 (2) (19) [17] Khayat, H.K. and Yahia, A., Simple field tests to characterize fluidity and washout resistance of structural cement grout, Cement, Concrete and Aggregate (1) (1998) [18] Box, E.P., Hunter, W.G. and Hunter, J.S., Statistics for experimenter: an introduction to design, data analysis, and model building, Wiley Series in Probability and Mathematical Statistics, (1978) 653 p. [19] Baillargeon, G., Probability, Statistics and Regression Techniques, SMG Editions, (1989) 631 p (in French). Paper received: April 9, 1; Paper accepted: July 25, 2 412