Cement & Concrete Composites 59 (2015) 38–48

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Cement & Concrete Composites

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The rheology of cementitious suspensions: A closer look at experimentalparameters and property determination using common rheologicalmodels

http://dx.doi.org/10.1016/j.cemconcomp.2015.03.0010958-9465/� 2015 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +1 480 965 6023; fax: +1 480 965 0557.E-mail addresses: kevance@asu.edu (K. Vance), gsant@ucla.edu (G. Sant),

Narayanan.Neithalath@asu.edu (N. Neithalath).

1 It should be noted that a ‘‘zero’’ strain rate does not practically exist. Astrain rate (even if infinitesimally small) needs to be applied in order toresistance to flow (shear stress). The apparent ‘‘zero’’ strain rate ismathematical simplification through which a value for the yield stress is ob

Kirk Vance a, Gaurav Sant b, Narayanan Neithalath a,⇑a School of Sustainable Engineering and the Built Environment, Arizona State University, Tempe, AZ 85287, United Statesb Laboratory for the Chemistry of Construction Materials, Department of Civil and Environmental Engineering, University of California, Los Angeles, CA 90095, United States

a r t i c l e i n f o

Article history:Received 3 December 2014Received in revised form 16 February 2015Accepted 3 March 2015Available online 10 March 2015

Keywords:Cementitious pastesRheologyYield stressGapShear rateRheological models

a b s t r a c t

This paper investigates the influence of gap between parallel plates, surface texture of the bottom plate,and mixing intensity on the yield stress and plastic viscosity of cementitious suspensions extracted usingthe Bingham model. Special emphasis is paid toward understanding the effects of shear rate range anddifferent rheological models on the flow parameters. It is shown that the use of a wider shear rate range(0.1–100/s), can be beneficial in obtaining a reasonable portion of the stress plateau in the shearstress–shear rate relationship, which facilitates a model-less, yet accurate extraction of yield stress.The Bingham model that considers only the linear region (i.e. �5–100/s) overestimates the yield stressas indicated by the stress asymptote while the Herschel–Bulkley (H–B) equation applied in the0.1–100/s shear rate range underestimates the yield stress. Further lowering the evaluated shear raterange (i.e. 0.005–100/s) does substantially improve the H–B prediction of yield stress.

� 2015 Elsevier Ltd. All rights reserved.

1. Introduction and background

Rheological studies of concentrated suspensions of solid parti-cles in a continuous liquid medium are commonly used to assessthe characteristics of materials in industries ranging from food topharmaceuticals to construction materials. The flow behavior ofthese concentrated suspensions is influenced by surface contactsbetween solid particles and interparticle forces such as van DerWaals and steric forces [1]. Rheological studies of cementitioussuspensions provide an understanding of how these materialsbehave in the fresh state and serve to monitor structure develop-ment that dictates the development of the mechanical properties[2]. However, in order to apply rheological experiments to cemen-titious suspensions, it is important to clearly understand the influ-ences of experimental parameters and the selected rheologicalmodel on the measured and predicted characteristics of flow toestablish their relevance and applicability.

Rheological experiments are typically carried out using a rota-tional rheometer, which monitors the change in torque requiredto change the shear rate (constant strain) or the change in strainrequired to change the torque (constant stress). There exist several

experimental parameters of significance, including but not limitedto: testing geometry (parallel plate, coaxial cylinder, cup, vane,etc.), the gap between shearing surfaces, roughness of the shearingsurfaces, testing temperature, and the state of dispersion deter-mined by the particle characteristics and the mixing method.Bingham, Herschel–Bulkley, and/or Casson models [3–6] are com-monly applied to the shear stress–shear rate response to extractthe rheological parameters (mainly yield stress and plastic viscos-ity) that describe flow.

Previous studies [3,7,8] have reported the influence of the experi-mental setup on the yield stress and plastic viscosity of cementitioussuspensions extracted using a Bingham model. The plastic viscosityis a measure of the rate of increase in shear stress with increasingstrain, and is thus a measure of the flowability of a fluid. The plasticviscosity of fluid suspensions is thought to be primarily influencedby interparticle friction and surface contacts [9], wherein decreasingthe interparticle (friction) forces by increasing particle spacing (orby decreasing surface contacts) results in a decrease in plastic vis-cosity. The yield stress is a more complex parameter, defined asthe non-zero (finite) stress at a ‘‘zero’’ strain rate.1 Several methods

non-zeroobtain a

thus atained.

Fig. 1. The particle size distributions of OPC, 3 lm limestone, and fly ash, asmeasured using a light scattering analyzer.

K. Vance et al. / Cement & Concrete Composites 59 (2015) 38–48 39

have been proposed to determine the yield stress, including: anextended duration constant stress experiment [10], stress growthand strain reduction experiments [11], and oscillatory experiments[12]. Yield stress is typically determined in cementitious suspensionsusing strain reduction experiments with reverse extrapolation to azero strain rate using a rheological model fit to the measured shearstrain rate–shear stress dataset [9].

Yield stress has been attributed to the effects of both the surfacecontacts between particles which prevent flow (jamming) below acertain applied stress, as well as interparticle attractive forces[1,13,14]. Yield stress is commonly reported as the stress requiredto initiate flow of a fluid [9]; however some authors distinguishbetween a dynamic yield stress and static yield stress [15]. Thedynamic yield stress is the stress required to maintain flow onceit has commenced, while the static yield stress is the stressrequired to initiate flow from rest. This indicates that the dynamicyield stress is a model-dependent parameter, i.e. the choice ofmodel can have a significant influence on the calculated yieldstress, as can be seen from the data presented in [3]. This distinc-tion is significant when comparative rheological studies of cemen-titious suspensions are to be performed, as selection of differentshear rate ranges or models will result in substantial variationsin the calculated yield stress, indicating that the dynamic yieldstress is not a material parameter in the truest sense. This paperexplores this idea in some detail in the context of cementitioussuspensions. Furthermore, an understanding of the influence ofthe shear history of the suspension, as represented using differentmixing procedures is developed in addition to new evaluations ofthe influences of experimental parameters including: the gapbetween shearing surfaces and the surface roughness of the bot-tom plate on the measured rheological response.

2. Experimental program

2.1. Materials

The materials used in this study are a commercially availableType I/II ordinary portland cement (OPC) conforming to ASTM C150 [16], Class F fly ash conforming to ASTM C 618 [17], and lime-stone powder of 3 lm median particle size, conforming to ASTM C568 [18]. The particle size distributions of these materials are pre-sented in Fig. 1 and their compositions in Table 1.

For all the cementitious suspensions considered, cement wasreplaced by either limestone or fly ash on a volumetric basis toensure that the comparisons are consistent. The suspensions wereprepared at a constant volumetric water-to-solid ratios, (w/s)v, of1.42, equivalent to mass-based water-to-solid ratio, (w/s)m, ofapproximately 0.45. No chemical admixtures were used.

2.2. Experimental parameters and suspensions

The rheological response of the suspensions is considered in thecontext of four distinct parameters: (i) gap between the top andbottom plates in a parallel plate configuration (top plate diameterof 50 mm, serrated to a depth of 1.0 mm), (ii) roughness and sur-face treatment of the bottom plate2 (serrated to a depth of0.15 mm, or resin-coated sandpaper3 of mean surface roughness,MSR = 0.12 mm or 0.017 mm), (iii) type and speed of mixing of thesuspension, and (iv) range of shear rates considered. Further detailsregarding the parameters are provided in Table 2. The suspensions

2 The influence of the surface condition of the Peltier plate on rheologicameasurements including the effects of slippage and plug flow have been reportedelsewhere [3,19].

3 Care should be taken to ensure that the sandpaper is non-absorbent as otherwiseit will result in changes in water availability and thus the rheological parameters.

l

consisted of: (i) OPC + water (referred to as OPC) and (ii)OPC + limestone + water (referred to as LS) where the fine limestone(d50 � 3 lm) replaced 10% of OPC by volume, and (iii) OPC + flyash + water (referred to as FA) where fly ash replaced 10% OPC byvolume. A gap of 2.0 mm, a bottom plate with 0.15 mm deep serra-tions, a shear rate of 5-to-100/s, and high-shear mixing correspond-ing to ASTM C 1738 [20] were used as the general ‘‘default’’evaluation parameters. Three replicate samples were produced andtested for each mixture and experimental condition.

2.3. Mixing and testing procedure

All powders were dry blended prior to the addition of water. Toinvestigate the effects of mixing on the rheological response, fourdifferent mixing procedures were used – three involving a highshear mixer and the fourth using a hand-held kitchen mixer. Allthe mixing procedures consisted of an initial powder additionphase, followed by initial mixing, a covered rest period, and finalmixing. Table 3 illustrates the four different mixing proceduresalong with the mixing speeds, time, and rest durations. For allthe three high shear mixing procedures, the powder blendingspeeds and the rest durations are the same. The differences lie inthe initial mixing speed after adding water, and in the final mixingspeed and its duration. The mixing condition of the highest inten-sity, both with respect to speed and duration is the one similar toASTM C1738 (but differing in the initial speed and rest period), andis described as 12-30-12-90. The first and third numbers representthe initial mixing speed after powder blending and the final mixingspeed after the rest period, in 1000� rpm (i.e. the number 12 infirst and third positions in the above sequence indicates12,000 rpm), and the second and fourth numbers represent theduration (in seconds) of initial and final mixing steps respectively.

In addition to the effects of mixing procedure, gap, and surfacecondition, the influence of the selected shear rate range on therheological properties was also investigated. These experimentswere of three different types: (i) a ‘‘normal’’ shear rate rangebetween 5 and 100/s, typical of the range used in typical rheologi-cal studies of cement pastes [3,7], (ii) a ‘‘low’’ shear rate range,between 0.1 and 10/s, and (iii) a ‘‘wide’’ shear rate range, from0.1 to 100/s, which encompasses both prior ranges. All rheologicalsequences consisted of a ramp-up pre-shear phase lasting approxi-mately 80 s to homogenize the paste, an instantaneous ramp-down

Table 1Oxide compositions and specific surface areas of the raw materials used in this study.

Material SiO2 (%) Al2O3 (%) Fe2O3 (%) CaO (%) MgO (%) SO3 (%) Na2O (%) K2O (%) LOI (%) SSA (m2/kg)

OPC 21.0 3.86 3.55 63.8 1.83 2.93 0.12 0.48 1.99 470Fly ash 58.4 23.8 4.19 7.32 1.11 0.44 1.43 1.02 0.5 218

Limestone powder contains 95–97% CaCO3 as per the manufacturer with a Blaine’s specific surface area of 2396 m2/kg.

Table 2Details regarding experimental variables, their range, and the suspensioncharacteristics.

Variable Levels of the variables (w/s)v Cementreplacement level(vol.%)

Limestone Flyash

Gap 1.0, 1.5, 2.0 mm 1.42 0, 10 0, 10Surface

condition ofthe bottomplate

Serrated bottom plate(0.15 mm deep serrations),adhesive backed sand paper– 40, 150 grit (mean surfaceroughness = 0.12 mm and0.017 mm)

1.42 0, 10 0, 10

Shear rate 5–100/s, 0.1–10/s, 0.1–100/s; see Fig. 2

1.42 0, 10 0, 10

Mixing 4 different types, see Table 3 1.42 0, 10 0, 10

40 K. Vance et al. / Cement & Concrete Composites 59 (2015) 38–48

which is followed by a ramp-up, and then immediately followed bya ramp-down. The pre-shear, up-ramp, and down-ramp sequencesfor the three different shear rate ranges are shown in Fig. 2(a)–(c).

For all the experiments, the time elapsed from the addition ofwater to the powder, to the beginning of rheological measure-ments, including the time to set the gap, was about 5 min.Rheological measurements were carried out on samples of freshcementitious suspensions using a rotational rheometer in a parallelplate configuration, provided with Peltier elements located in the

Table 3Mixing procedures and corresponding details relevant to suspension preparation.

Procedure type Description Powder blendinspeed, rpm

12-30-12-90 High shear 400012-30-12-30 Shorter duration during final mixing 40004-30-4-30 Lower speeds and shorter durations

during both initial and final mixing4000

Hand-held mixer Lowest speeds and shorter durationsduring both initial and final mixing

–

Fig. 2. The rheological procedures applied over: (a) ‘‘normal’’ she

bottom plate which were conditioned to 25 ± 0.1 �C. Except duringthe pre-shear phase, data is collected every second at each step,until steady state has been achieved, as defined by three consecu-tive torque measurements within 5% of each other, at which timethe experiment advances to the next shear rate. The time expendedat each shear step in which data is collected is typically 5 s, with amaximum step duration of 15 s. Shear stress and shear rate datawere extracted using TA Instruments’ TRIOS software package.

The rheological model parameters for the ‘‘normal’’ shear raterange (5–100/s) were calculated using a least squares fitting tothe Bingham model of the down-ramp data as shown in Eq. (1)[21]. The use of the Bingham model in this shear rate range is jus-tified by the generally linear nature of the shear stress–shear rateresponse. The rheological parameters for the ‘‘wide’’ shear raterange (0.1–100/s) were calculated using a least squares fitting ofthe down-ramp data to two different models, sometimes referredto as generalized Bingham models: i.e. the Herschel–Bulkley modelshown in Eq. (2) [22], and the Casson model shown in Eq. (3) [23].

Bingham : s ¼ sy þ gp_c ð1Þ

Herschel—Bulkley : s ¼ sy þ K _cn ð2Þ

Casson :ffiffiffisp¼

ffiffiffiffiffisy

pþ

ffiffiffiffiffiffiffig1

p ffiffiffi_c

qð3Þ

The latter models were used because of their ability to bettercapture non-linearities in the data that manifests at lower shearrates. In these equations, s is the shear stress (in Pa), sy is the yieldstress (in Pa), gp is the plastic viscosity (in Pa s), _c is the shear rate

g Initial speed after mixingwater, rpm (duration)

Rest period Final mixing speed,rpm (duration)

12,000 (30 s) 120 s 12,000 (90 s)12,000 (30 s) 120 s 12,000 (30 s)4000 (30 s) 120 s 4000 (30 s)

– (30 s) 120 s – (30 s)

ar range, (b) ‘‘low’’ shear range, and (c) ‘‘wide’’ shear range.

K. Vance et al. / Cement & Concrete Composites 59 (2015) 38–48 41

(in s�1), K is the consistency index which is a measure of the aver-age viscosity of the fluid, and n is the flow behavior index [3,22],which ranges between 0-and-1 for shear thinning suspensions[9], and g1 (in Pa s) is the viscosity at an infinite shear rate [24].

3. Results and discussions

3.1. Influence of gap between parallel plates on the measuredrheological properties

This section discusses the influence of the gap between theupper and lower parallel plates on the yield stress and plastic vis-cosity as determined using a Bingham model for a shear rate of 5-to-100/s. All the other experimental variables were maintained at‘‘default’’ levels as described in Section 2.2. The upper plate inthe parallel plate configuration is set to three different gaps:1.0 mm, 1.5 mm, and 2.0 mm. In order to obtain consistent results,it has been reported that the gap should be at least an order ofmagnitude larger than the size of the largest characteristic inclu-sion phase in the suspension [25,26]. The particle size distributionsshown in Fig. 1 confirm that this criterion is satisfied here.Moreover, the ideal gap also depends on the depth of the serrationsin the upper and lower plates, and the plate diameter [3,27]. Giventhe depth of plate serrations and the different combinations ofcement replacement materials used in this work, a minimum gapsize of at least 1.0 mm was selected [28]. The required gap alsodepends on the shear rate – larger shear rates are needed to ensureuniform flow across a larger gap, whereas larger shear rates in asmaller gap can cause flow instabilities due to the increased likeli-hood of turbulent flow, and an increased likelihood of particle con-tact with the shearing surfaces [29].

Fig. 3 presents the results for three different gaps for a plain OPCsuspension and a suspension with 10% OPC (by volume) replacedby 3 lm limestone, at a (w/s)v of 1.42. The general trend indicatesthat increasing the gap results in increasing yield stress bybetween approximately 10% and 40% as the gap is increased from1 to 2 mm. This response is consistent with the data presented in[4], but opposite of that reported in [3]. Additionally, increasingthe gap results in a decrease in or relatively unchanged value ofthe plastic viscosity, in line with [3]. As shown in Fig. 3, the effectof the gap on plastic viscosity is minimal for the plain OPC suspen-sion and more pronounced in the case of the suspension containinglimestone. It is also observed that as the gap is decreased, the qual-ity of fit becomes slightly poorer as indicated by lower coefficientsof determination (R2) (from 0.93 to 0.95 at 2 mm and 0.84 to 0.91at 1 mm). Cementitious suspensions that do not contain rheology

Fig. 3. The influence of gap on the rheological properties, estimated using theBingham model.

modifying chemical admixtures behave as shear thinning suspen-sions [9], where flow is enabled by the formation of shear bandswithin the suspension. The apparent viscosity thus decreases withincreasing shear rates as these bands form [1]. This behavior mayexplain the apparently counterintuitive observation of increasingyield stress with increasing gap, as narrower gaps produce a largernumber of turbid shear bands, while wider gaps produce fewer, butmore intense shear bands [30]. Furthermore, normal forces actingon the suspension that result from higher evaluation volumes withincreasing gap, which increases the sample weight, may result inincreased interparticle forces that inhibit the ability of the pasteto (initiate) flow, which also contributes to a higher observed yieldstress.

The general decrease in plastic viscosity with increasing gap canbe explained as follows: in particulate suspensions, increasing thegap results in decreased effects of confinement. This effect isenhanced in the presence of limestone, as the inclusion of lime-stone increases the spacing between cement particles by interrupt-ing interparticle forces between the cement particles. More studiesare needed to explain the combined influences of confinement,shear banding, and interparticle forces on plastic viscosity of suchsuspensions.

3.2. Influence of the surface condition of the bottom plate

Measurement of rheological properties can be considerablyinfluenced by the friction between the sample and the shearingsurface. Several studies have shown that the use of a smooth shear-ing surface increases the likelihood of slippage and plug flowwhich can result in incorrect estimations of the rheological proper-ties [9,31–33]. This section adds to this premise by studying theeffects of surface roughness, as described by the mean surfaceroughness (MSR), which is the arithmetical mean height of theirregularities measured from the datum surface, on the rheologicalparameters as determined using the Bingham model (Eq. (1)). Thebottom plate with 0.15 mm deep serrations has a MSR = 0.15 mm,and the MSR values of the other surfaces (sandpaper) used areshown in Table 2.

Fig. 4 presents the influences of surface roughness on the rheo-logical properties. Three surface conditions were used, rangingfrom a serrated bottom plate (MSR = 0.15 mm) to 150 grit sandpa-per (MSR = 0.017 mm), at a constant gap value of 2.0 mm. In gen-eral, the yield stress remains relatively constant and the plasticviscosity increase with increasing MSR, as can be observed fromFig. 4. Since slip is caused due to a localized decrease in the solidconcentration near the shearing surface [32], the use of textured

Fig. 4. The influence of the surface condition of the bottom plate one therheological properties as estimated using the Bingham model.

Fig. 5. The influence of mixing procedure on the rheological properties as estimatedusing the Bingham model.

42 K. Vance et al. / Cement & Concrete Composites 59 (2015) 38–48

surfaces acts to maintain the solid fraction near-constant in thevicinity of these surfaces. Hence, as the roughness increases, theplastic viscosity increases [32,33].

3.3. Influence of mixing procedure on rheological properties asestimated using the Bingham model

The shear history of fresh cementitious suspensions, which isattributed mainly to the mixing process, influences their rheologi-cal properties [9]. Different mixing methodologies influence sus-pension rheology due to their ability to induce varying levels ofparticulate dispersion, i.e. in controlling agglomeration and floc-culation [34,35]. To better understand these effects, this sectionevaluates the influences of mixing procedure on the rheologicalparameters (yield stress and plastic viscosity) as determined usingthe Bingham model.

The influence of mixing methodologies on measured rheologicalproperties of OPC and 10% 3 lm limestone containing suspensionsis presented in Fig. 5. It is evident that maintaining a consistentmixing procedure is critical when comparing rheological experi-ments. Both the yield stress and plastic viscosity are noticeablyhigher when a hand-held mixer is used, as compared to mediumand high shear rate mixing using an industrial blender. This drasticincrease in the yield stress occurs due to the fact that the hand-held mixer does not impose high enough shear rates to ensureproper dispersion of the particles and break up agglomerates.The inadequate dispersion, i.e. enhanced agglomeration, aids inthe retention of free water within the flocs [35,36], and inter-particle bond formation, all of which act to restrict the flow ofthe suspension. In the case of mixing procedures that employ highshear rates, there is a consistent trend of decreasing plastic viscos-ity with increasing mixing intensity (both in terms of speed andduration). As the shear rate (i.e. the mixing speed) is increased,the mixing shifts from primarily extensive to intensive [37]4, andthus particle dispersion increases and agglomerations are reducedor destroyed [34,35,38]. This results in a decrease in interparticlesurface contacts and friction forces, thereby increasing the fluidityof the suspension. It is also notable that the influence of limestoneaddition varies across different mixing regimes. The plastic viscosityreduces on limestone incorporation across all mixing cases. On theother hand, the dependence of yield stress on limestone incorpora-tion is inconsistent; both the lowest (hand-held) and highest (highshear) intensity mixing result in decreased yield stress of 6% and15% respectively while the intermediate levels show an increase inyield stress of between 10% and 20% as compared to the OPC suspen-sion. This indicates that modifications to mixing procedures mayproduce different results as well as different interpretations whencomparing suspensions containing multiple solids with varying par-ticle characteristics. While this could be attributed to competingeffects of dispersion/agglomeration and bond destruction/formation,it is another example of yield stress being highly dependent onexperimental parameters as will be discussed in the followingsection.

3.4. Influence of shear rate and model selection on rheological propertyinterpretations

3.4.1. Shear rate range effectsA discussion of the influence of shear rates on the yield stress

and plastic viscosity as determined using the three shear rate

4 It should be noted that extensive or distributive mixing causes a rearrangement ofthe components of the mixture and is responsible for the spatial (re)distribution ofthe particles within the fluid matrix while intensive or dispersive mixing normallyinvolves a rupture of agglomerates through shear stresses at the particle/host fluidinterface.

ranges reported in Section 2.2: (a) 5–100/s, (b) 0.1–10/s, and (c)0.1–100/s is presented here. While several different cementitioussuspensions of (w/s)v = 1.42 (including ternary blends of limestoneof different particle sizes and fly ash) were evaluated, the results ofthree representative suspensions: (i) OPC, (ii) 10% OPC replaced by3 lm limestone, and (iii) 10% OPC replaced by fly ash, are pre-sented in Figs. 6–8. The datasets are plotted in both linear and loga-rithmic scales so as to appropriately elucidate the differences atlower shear rates. Note the appearance of a shear stress plateauat lower shear rates when the shear rate axis is plotted in the loga-rithmic scale, which is similar in trend to that reported in [39]. Thefit lines shown on these plots are applicable for the Bingham modelfor the ‘‘normal’’ range which is generally linear (5–100/s) and theHerschel–Bulkley and Casson models on the ‘‘wide’’ shear range(0.1–100/s) as presented in Eqs. (1)–(3). The Herschel–Bulkley(H–B)H–B model was not fit on datasets for the ‘‘normal’’ range,where the shear rate-shear stress response was quite linearbecause fitting the three-parameter H–B model (Eq. (2)) to a lineardataset does not provide unique fits, i.e. there exist multiplecombinations of the parameters (i.e. even within the constraintssuch as 0 6 n 6 1.0) with negligible least squares error and veryhigh coefficients of determination5. The non-linearity of the datain the ‘‘wide’’ shear rate range experiments makes the use of H–Band Casson models applicable in such cases. Furthermore, the H–Bmodel also does not provide a direct indication of the plastic viscos-ity of the suspension. Coefficients of determination (R2) for these fitswere always greater than 0.90, with the H–B model showing thehighest R2 values in many instances. While this aspect often favorsthe use of the H–B model for particulate suspension rheology [39–41], key evidence provided later in the paper highlights inadequaciesof this and other commonly used models in the context of rheologi-cal parameter (yield stress in particular) estimation.

In Fig. 6 which shows shear rate-shear stress relationships forOPC–water suspensions, there is a consistent shear stress offsetof about 15 Pa between the ‘‘normal’’ and ‘‘wide’’ shear rate rangedata, which was observed in several repeat measurements. Thesuspensions containing 10% of limestone or fly ash (by volume)as cement replacement do not demonstrate this offset to such adegree, although an offset is present between the ‘‘low’’ and ‘‘wide’’

5 Many commercial equation-fitting programs pick one among the many possiblembinations, based on the initial assumed values of the fitting parameters. While the

se of H–B model has been suggested by some researchers over the Bingham modelven in the event of a linear shear stress–shear rate relationship to avoid obtainingegative s0 values, this approach is not ideal. This section of the paper provides

couen

suggestions to overcome these artifacts of such ‘‘spurious curve fitting’’.

Fig. 6. The influence of shear rate range and the selected model on rheological properties for the plain OPC suspension on: (a) linear scale, and (b) logarithmic scale.

Fig. 7. The influence of shear rate range and the selected model on the rheological properties for 10% 3 lm limestone containing suspension on: (a) linear scale, and (b)logarithmic scale.

Fig. 8. The influence of shear rate range and the selected model on the rheological properties for 10% fly ash containing suspension: (a) linear scale, and (b) logarithmic scale.

K. Vance et al. / Cement & Concrete Composites 59 (2015) 38–48 43

shear rate range data. To investigate the origin of the stress offsetbetween the ‘‘wide’’ and ‘‘normal’’ shear range data in Fig. 6, anadditional experiment was performed using another OPC suspen-sion to determine if this effect may be specific to the cement used.The ‘‘normal’’ and ‘‘wide’’ experiments were then carried out asbefore, and an offset of about 7 Pa was noted. A ‘‘modified-wide’’

(wide-mod) experiment was added with the aim of maintainingan identical shear history between the ‘‘normal’’ and ‘‘wide-mod’’data up to the peak stress value of the up-ramp. Thus, the pre-shear and up-ramp strain rates from Fig. 2(a) (‘‘normal’’) and thedown ramp strain rates from Fig. 2(c) (‘‘wide’’) were used togetherto form the ‘‘modified-wide’’ experiment.

44 K. Vance et al. / Cement & Concrete Composites 59 (2015) 38–48

The shear rate-shear stress response of the suspension sub-jected to this regime, along with its response when subjected tothe ‘‘normal’’ and ‘‘wide’’ shear rate ranges are presented inFig. 9. It is noted from this figure that the ‘‘wide-mod’’ range resultsin an almost identical peak shear stress as that in the ‘‘normal’’shear rate range experiment, which is expected given the identicalshear histories of the paste up to that point. After the point ofmaximum stress, in the down-ramp, the flow curves of the suspen-sions subjected to the ‘‘normal’’ and ‘‘wide-mod’’ regimes diverge,with the suspension subjected to the ‘‘wide-mod’’ regimeexperiencing less total strain (because of the reduced time – seeFig. 2c) while showing a higher level of shear stress. This supportsthe idea that this stress offset is likely related to the differences inshear history of the suspension, wherein a reduction in the totalstrain experienced by the OPC suspension results in varying levelsof structure build-up and breakdown as discussed in [42]. The off-set is expected to be less significant in Figs. 7 and 8, i.e. in the pres-ence of limestone and fly ash as the relatively inert nature of theseparticles and their influences in aiding suspension fluidity limitsthe role of structural build-up over the course of the experiment[2]. Further studies to accurately ascribe the origins of this behav-ior are needed.

The Bingham model has been shown to be applicable only overa limited range of shear rates [21,43], below which the shear

Fig. 9. Investigations of shear stress offset using a ‘‘modified-wide’’ experiment on OPC suis constructed by combining the ‘‘normal’’ and ‘‘wide’’ shear evaluation regimes.

Fig. 10. (a) The predicted shear rate vs. shear stress response extrapolated from data ivalues. Results of the Bingham model are fit over the shear rate range of 5–100/s, and theand (b) shear stress–shear rate response for a number of particulate suspensions composa stress plateau at low shear rates for various suspensions.

rate-shear stress response becomes non-linear, as indicated by adownward curvature of the dataset, when the model breaks down.As such, its applicability to cementitious suspensions (Figs. 6–8and [5,23]) is clearly unreliable. The linear portion of the relation-ship between shear stress and shear rate, where the Binghammodel is applicable, has been proposed to be similar to Region IIIin a typical creep curve [43], as shown in Fig. 10(a). When lowshear rates, typically below 1/s are used, as is the case in the‘‘wide’’ and ‘‘low’’ ranges in Figs. 6–8, a zone corresponding to aportion of Region II (i.e. constant shear stress with increasing shearrate – secondary creep) also emerges. Theoretically, if local particledensities were maintained in such a way that the shear bandsremained intact at yet lower shear rates – on the order to 10�3-to-10�4 (below the torque limit of the rheometer), these rheologi-cal curves would take a form similar to that presented in [43] forCheng’s yield stress material [11] where Regions I–III are evident– i.e. the material changes from a Newtonian behavior through apower-law type region to another Newtonian-like behavior [43]with increase (or decrease) in shear rate.

In Fig. 10(a), a portion of Region II is constructed using datafrom the wide shear rate measurements (solid circles) for 10%3 lm limestone modified suspensions, while the remaining data(open circles) is estimated as described in [43]. Thus, if a portionof Region II is captured in addition to Region III by measuring the

spension: (a) linear scale, and (b) logarithmic scale. The ‘‘modified-wide’’ evaluation

n Fig. 7 (LS-Wide). Closed circles are measured data, open circles are extrapolatedHerschel–Bulkley and Casson models are fit over the shear rate range from 0.1–100/sed in water (three types of cement, fly ash, and slag) to demonstrate the existence of

K. Vance et al. / Cement & Concrete Composites 59 (2015) 38–48 45

response at low enough shear rates (i.e. over a shear rate range of0.1-to-100/s instead of 5-to-100/s [11]), then the asymptotic value(i.e. 46 Pa in Fig. 10a) can be considered to be representative of thedynamic or ‘‘apparent’’ yield stress of the material. The ‘‘wide’’shear rate range considered in this study satisfies this criterionas it includes enough of Region II that the asymptotic yield stressvalue can be determined. Clearly, the yield stress is overestimatedby the Bingham model (61 Pa) due to the rheological response notbeing determined at low enough shear rates. The effects of H–B andCasson models will be discussed later in the paper.

To explore if the plateau region in the rheological response isparticle-independent, ‘‘wide’’ shear rate range (0.005-to-100/s)rheological experiments were conducted using suspensions ofthe following materials in water: Type II/V cement, intergroundlimestone cement, fly ash, and a ground granulated blast furnaceslag. The (w/s)v ratios were varied so as to obtain a suspension thatwas stable, and not prone to overflowing or segregation underapplied shear. The shear stress–shear rate response for all thesesuspensions are shown in Fig. 10(b). It is seen that, regardless ofthe particle type, the shear stress plateau (Region II) which isindicative of the apparent yield stress is visible. In fly ash–waterand slag–water suspensions, the plateau is present, but at verylow shear rates, the shear stress tends to further increase, indicat-ing a flow instability identified by the formation of shear bands[44,45]. As presented, this curve is applicable for the ramp downof shear rates, and hence it is proposed that this behavior is indica-tive of the destruction of the shear bands that were formed athigher shear rates. This supports the idea that in suspensions withthis behavior, the interparticle forces are not enough to preventparticles from settling into the region of shear band formation,increasing local particle density and thereby increasing the mea-sured shear stress. However, the presence of a shear stress plateauin each of these suspensions provides: (1) a direct method for theaccurate estimation of apparent yield stress and (2) indicates thatthis shear stress plateau response, is a generalized phenomenon.

Figs. 6–8 illustrate the experimental independence of plasticviscosity irrespective of the shear rate range of the experiment.For example, the slopes of the shear stress–shear strain relationsin Region III, irrespective of the shear history, are around0.20 Pa s, thus indicating that the plastic viscosity remainsindependent of the experimental methodology selected. As thethree shear rate ranges (i.e. ‘‘normal’’, ‘‘low’’, and ‘‘wide’’) impartdifferent shear histories to the suspension, this shows that beyond

0 10 20 30 40 50 60 70 80 90 100Shear Stress (Pa)

0

50

100

150

200

250

300

350

400

450

500

Visc

osity

( Pa-

s)

OPCLSFA

FA App. Y.S.

Fig. 11. Viscosity–shear stress relationships for the suspensions evaluated, toillustrate the apparent yield stress. The apparent yield stress, which is denoted by aconstant rising portion in the shear stress–viscosity plot is also marked in figure.

a point, the rate of increase in stress with increase in strain (plasticviscosity) is reasonably independent of shear history.

The apparent yield stress can be better identified using anapparent viscosity (ratio of shear stress to shear rate)-shear stressplot (see Fig. 11), wherein the apparent yield stress is the point atwhich the viscosity drastically increases without any concomitantincrease in stress, i.e. a value which is equal to that noted at theleftmost end of the stress plateau shown in Figs. 6–8. It shouldbe noted that complications in precise identification of this pointwhich indicates the yield stress, and the lack of models to fit a wideenough range of the shear response, have led to deliberations onthe applicability of yield stress to particulate suspensions[11,43,46–49].

3.4.2. Rheological model effectsTo allow for a concise discussion of the influences of rheological

models, the results of the ‘‘wide’’ shear rate range (0.1–100/s)experiments are re-plotted in Fig. 12(a)–(c) for: (i) the OPC suspen-sion, and the suspensions containing (ii) 10% of 3 lm limestoneand (iii) 10% of fly ash. Once again, the Bingham model is fit tothe linear portion of the ‘‘wide’’ shear rate dataset (from 10-to-100/s), whereas the H–B and Casson models are fit to the entireshear rate range, i.e. from 0.1-to-100/s. The fit parameters andthe apparent yield stress corresponding to the stress plateau arealso denoted in figures for all suspensions. Table 4 depicts theapparent yield stress values to facilitate comparison of the differ-ent commonly used models and the proposed stress-plateauapproach.

It is noted that the Bingham model significantly overestimatesthe apparent yield stress as compared to the apparent yield stressdetermined from the stress plateau. Note that the linear nature ofthe Bingham equation makes it illogical to force-fit it to the non-linear region observed at low shear rates (Figs. 6–8). The extentof overestimation is suspension-specific, ranging from 35% forthe limestone system to 50% for the fly ash and OPC systems. Ingeneral, the Casson model estimates the apparent yield stress rea-sonably well, though the quality of the fit as indicated by the R2

value is poorer than the other models considered. This is an out-come of the half-power relationship that is incapable of adequatelyrepresenting the relatively linear range at higher shear rates.Further, the second parameter in the Casson model, i.e. g1, is notexpected to be useful for cementitious suspensions given the lowerbounds of shear rates experienced in practical applications [27].The Herschel–Bulkley model underestimates the yield stress forall suspensions to varying degrees: by approximately 40%, 20%and 50% for OPC, limestone, and fly ash systems respectively.Also, while the Herschel–Bulkley model provides a good fit to thedata over the selected shear rate range with the highest R2 valuesof all models considered, concerns do exist. For example: a visualobservation of the fits in Fig. 12 shows an adequate match of theH–B model with the data including the Y-intercept (yield stress),however, when the model parameters are considered, the under-estimation of yield stress is significant and on the order notedabove. In general, it can be concluded that the true asymptote thatis representative of the apparent yield stress lies between the s0

values predicted by the Bingham and H–B models.To determine if the predictive capability of the H–B model could

be improved, a series of experiments were conducted over a yetwider shear range rate (0.005-to-100/s) to better capture the stressplateau (Region II). Expectedly, the apparent yield stress predictedby the H–B model was shown to be refined by the addition of moredata in the lower shear rate range. For example, the H–B yieldstress was within 5% of the true asymptotic value for the case ofOPC suspension. Moreover, increasing the number of data pointsobtained in the stress plateau (i.e. when much lower shear rateranges are used), results in better the estimation of yield stress

Fig. 12. The influence of selected rheological model using ‘‘wide’’ shear rate range data on the estimated yield stress for: (a) OPC–water suspension, (b) 10% 3 lm limestonecontaining suspension, and (c) 10% fly ash containing suspension.

Table 4Tabulated determined yield stress values (Pa) using different models and the model-less stress plateau approach.

Bingham H–B Casson Stress plateau

OPC 63.35 24.32 45.45 42LS 63.55 37.07 49.09 47FA 48.61 16.27 34.57 32

46 K. Vance et al. / Cement & Concrete Composites 59 (2015) 38–48

according to the H–B model. This shows that the use of H–B modelto estimate yield stresses is unreliable when insufficient data in thelower shear rate range (significantly beyond the linear shear rate-stress response) is available, and the improved accuracy of thismodel in predicting the apparent yield stress is attributed primar-ily to the statistical weighting resulting from including additionaldata at low shear rates. This is a significant aspect to consider ifthe H–B model is to be applied to estimate the rheological proper-ties, in a comparative or absolute sense of cementing systems.

It is furthermore noted from Fig. 12 that the influence of lime-stone incorporation on yield stress is different when different mod-els (Eqs. (1)–(3)) are used. The incorporation of 3 lm limestone isshown to have a negligible effect on yield stress as compared to theOPC suspension when the Bingham model is used. However theapparent yield stress determined from the stress asymptote andthe yield stresses estimated from the Casson and Herschel–Bulkley models are higher for the limestone modified suspension

when compared to that of the OPC suspension. The dominant effectof increased amount of smaller particles (d50 of 3 lm for limestoneas opposed to 8.8 lm for OPC) in increasing the water demand isresponsible for this observation. In the case of fly ash modified sus-pension, all the models as well as the experimental asymptotic val-ues show a decrease in yield stress when compared to the OPCpaste, which is the trend expected due to the spherical nature offly ash particles that enhance the fluidity of the suspension.

The foregoing discussions illustrate the influence of rheologicalmodels on the extracted flow characteristics of cementitious sus-pensions and emphasize the effects of model selection and experi-mental parameters on the applicability and reliability of a givenmodel. This is significant, as erroneous selections can result in con-siderable imprecisions in yield stress determinations, though to alesser extent in the case of plastic viscosity. Further, it illustratesthat the yield stress determined from the Bingham model is likelynot a true flow parameter, rather it is an artifact of model-basedand experimental limitations. As such, its application may lead toincorrect conclusions when used in comparative studies of cemen-titious suspensions.

4. Summary and conclusions

This paper has presented a detailed study on the influence ofexperimental parameters and models on the rheological responseof cement suspensions. The major findings of this study are:

K. Vance et al. / Cement & Concrete Composites 59 (2015) 38–48 47

� An increase in the Bingham yield stress and decrease in plasticviscosity was observed with increasing gap, attributable tochanges in the local particle density and influence of increasedparticle contacts with the shearing surface. Increasing surfaceroughness (i.e. for the range studied), resulted in little changein the Bingham yield stress and increasing plastic viscosity.� The shear history imparted to the paste through mixing was

found to significantly influence the yield stress and plastic vis-cosity. With increasing mixing intensity, the plastic viscositywas noted to decrease due to the effectiveness of the mixingprocedure in reducing the tendency of agglomeration in thepaste.� Lowering the shear rate range in the rheological experiments

(to 0.1/s) revealed the existence of a well-defined shear stressplateau. This corresponds to a drastic increase in apparent vis-cosity with minimal increase in stress, and this value of theshear stress is recommended to be used as the apparent yieldstress of the suspension. Significantly, such evaluations facili-tate the model-less extraction of yield stress. However, plasticviscosities estimated as the slope of the line fit to the linearregion of the shear stress–shear rate stress response were notedto be less influenced by shear rate effects.� The influences and artifacts of the rheological model used in

extraction of the apparent yield stress are highlighted. Whencompared to the value at the stress plateau, the Bingham andH–B models, overestimate and underestimate respectively, theapparent yield stress of a given cementitious suspension. Theprediction of the Casson model was noted to be more accurate,but at the cost of a poorer mathematical fit to the rheologicaldataset. The yield stress estimated by H–B model was foundto be comparable to the (true) apparent yield stress noted fromthe shear stress asymptote when rheological evaluations wereextended to much lower shear rates. This improvement is afunction of the statistical weighting in the least squares fit,rather than an indicator of the efficiency of the H–B model tocomprehensively estimate the flow response.

Acknowledgements

The authors gratefully acknowledge the National ScienceFoundation for the financial support for this research (CMMI1068985). The materials were provided by U.S. Concrete, OMYAA.G, and Headwaters Resources, and are acknowledged. The firstauthor acknowledges the Dean’s Fellowship from the Ira A.Fulton Schools of Engineering at Arizona State University (ASU).This research was conducted in the Laboratory for the Science ofSustainable Infrastructural Materials (LS-SIM) at Arizona StateUniversity (ASU). The contents of this paper reflect the views ofthe authors who are responsible for the facts and accuracy of thedata presented herein, and do not necessarily reflect the viewsand policies of the funding agency, nor do the contents constitutea standard, specification, or a regulation.

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