Construction and Building Materials 49 (2013) 781–796

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Construction and Building Materials

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Experimental investigation and analytical modeling of the r–echaracteristics in compression of heat-treated ultra-high strengthmortars produced from conventional materials

0950-0618/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.conbuildmat.2013.08.068

⇑ Corresponding author. Tel.: +1 864 633 7114.E-mail addresses: hkizhak@g.clemson.edu (K.V. Harish), jk.dattatreya@gmail.

com (J.K. Dattatreya), mnmegam@gmail.com (M. Neelame.1 Tel.: +91 9964888866.2 Tel.: +91 9444164531.

Kizhakkumodom Venkatanarayanan Harish a,⇑, Jamboor Krishnamurthy Dattatreya b,1,Meyappan Neelamegam c,2

a Glenn Department of Civil Engineering, Clemson University, South Carolina 29634, United Statesb Siddaganga Institute of Technology, Tumkur 572018, Indiac Department of Civil Engineering, Easwari Engineering College (Affiliated to Anna University), Chennai 600089, India

h i g h l i g h t s

� The application of controlled heat to the ultra-high strength mortars (UHSMs) substantially increased their compressive strength.� Steel micro-fibers contributed significantly in improving the r–e and energy absorption characteristics in compression of UHSMs.� UHSMs containing long fibers displayed better r–e characteristics than those containing short fibers.� Analytical modeling of the r–e curve in compression closely represented the experimentally obtained data.

a r t i c l e i n f o

Article history:Received 29 April 2013Received in revised form 21 August 2013Accepted 29 August 2013

Keywords:Ultra-high strength mortarsMicro-fibersAnalytical modelingHeat curingStress–strain characteristicsToughness

a b s t r a c t

In this study, conventional materials were used to prepare ultra-high strength mortars (UHSMs) and theirstress–strain (r–e) characteristics in compression were investigated both experimentally and analyti-cally. The effect of micro-fiber addition on the peak stress, peak strain, modulus of elasticity and energyabsorption were then studied. Test results suggested that heat-treated UHSMs showed significantlyhigher strengths than non-heat-treated UHSMs. The micro-fiber addition significantly improved all thecharacteristics of UHSM. Both linear and non-linear correlations existed between the reinforcement indi-ces of fibers and r–e characteristics of UHSM. The analytical modeling of the r–e curve showed good cor-relation with the experimental data.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

In the early 1990s, the use of conventional materials to obtainhigh target strength cementitious composites has gained signifi-cant attention. Theoretical models were proposed to study thepacking density of mixture using Mooney’s suspension viscositymodel, to identify the important parameters during mix designprocess using maximum paste thickness concept, and to selectingredients and arrive at optimized mixtures based on workability,compressive strength and thermal curing (Solid Suspension Mod-

el). These models were employed to obtain low w/cm mixtureshaving varying porosity [1]. On subjecting such mixtures to watercuring at 20 �C and thermal curing at 90 �C for specific duration,compressive strengths ranging from 177 to 244 MPa and porositiesranging from 0.079 to 0.141 were obtained [1]. A related develop-ment of such mixture led to the invention of a new and special typeof advanced cementitious composite called as ‘‘ultra-high strengthcementitious material (UHSCMs)’’ or ‘‘reactive powder concretes(RPCs).’’ With the incorporation of certain basic principles in theirproduction, the UHSCMs can be well designed to produce desiredlevel of ultra-high strength properties [2].

UHSCMs were initially developed to produce high order com-pressive and flexural strengths ranging from 170 to 230 MPa and40 to 60 MPa, respectively [3]. Other investigations conducted todetermine the energy absorption property of this material indi-cated that the UHSCMs possess very high toughness and fracture

782 K.V. Harish et al. / Construction and Building Materials 49 (2013) 781–796

energies several times higher than conventional concretes [3,4]. Dueto the increased demand for ultra-high performances in bridges, thinsections, precast products and special constructions especially dur-ing the last 5–10 years, UHSCMs are being produced in large quanti-ties. The production of UHSCM involves consideration of differentcriteria for mixture proportioning, particle packing, pore size refine-ment, the selection of heat curing regimes, compaction techniques,etc., and hence, the use of high-quality pre-packed material or pro-prietary products to produce UHSCM has become popular in theindustry [5]. However, the high cost involved in producing UHSCMsaffects the economics. In addition, specific issues related to the pro-curement and use of imported materials from foreign countries, andregulations in using proprietary products within any country mayrestrict state agencies from progressing with some construction pro-jects involving ultra-high performances.

Recent studies have shown that the economics of UHSCMs canbe improved by using local materials and technologies, by includ-ing artificial aggregates and/or small-sized coarse aggregates, andby using higher replacement levels of pozzolans for portland ce-ment based on the application requirements [6–8]. For example,ultra-high strength concretes (UHSCs) containing coarse aggre-gates and ultra-high strength mortars (UHSMs) containing nocoarse aggregates, both belonging to UHSCMs, can be used to ob-tain strength ranges of 80–120 MPa and 120–200 MPa, respec-tively, depending upon the application. These mixtures can beeconomically used in bridges, containment structures, floorings,tanks and foundations.

The ultimate compressive strength and modulus of elasticityare fundamental material parameters used in the design of rein-forced and pre-stressed concrete structures. The stress–strain (r–e) characteristic in compression of UHSCM gains importance espe-cially when using it for special applications as a small change in themixture design used or methodology adopted can significantly al-ter the overall material behavior. The post-peak behavior of non-fi-bered UHSCM has less or no significance due to its brittle natureand the benefits of using steel fibers to improve its post-peakbehavior under compressive, tensile, flexural and impact loadinghas been well investigated [5,9–11]. Unlike the direct or indirecttensile behavior of steel fiber- reinforced UHSCM, its r–e charac-teristics in compression has gained less attention due to two rea-sons. Firstly, non-fibered cement based composites areconsidered to be weak in tension and strong in compression, andthe use of high tensile strength steel fibers have shown to be morebeneficial for tensile loading than for compressive loading, evalu-ated based on the improvements at the peak point of the r–e curve.Secondly, the benefits obtained in the post-peak region of the r–ecurve in compression due to the steel fiber addition are usually less[12,13]. While many research performed in the past with fiberreinforced UHSCM focused on using either conventional steelmacro-fibers or long micro-fibers, only some investigations wereperformed with short steel micro-fiber reinforced UHSCM[2,14,15]. In this study, detailed investigations were performed toexplore the r–e characteristics of steel micro-fiber reinforcedUHSCM under uniaxial compression.

2. Objectives

The principle objectives of the current study are as follow:

Table 1Chemical composition of cement and silica fume.

Powders Oxides composition (% by mass)

SiO2 Al2O3 Fe2O3 CaO MgO

Cement 20.49 5.91 4.07 62.90 1.13Silica fume 94.73 – – – –

(i) To develop non-fibered UHSM mixture based on genericmixture design, available production technique and usingconventional materials.

(ii) To perform experimental investigations and determine theeffect of micro-fiber dosage and its size on the r–e charac-teristics of UHSM subjected to uni-axial compression.

(iii) To predict the r–e characteristics of steel micro-fiber rein-forced UHSM analytically and compare the prediction withthe experimental data.

3. Experimental investigation

The experimental program consists of two parts. The first part involved detailedinvestigations with the production of UHSM from conventionally available materi-als. In this section, 10 UHSM mixtures were selected based on literature review,both with and without silica fume and/or quartz powder. The effect of w/cm onthe compressive strength of UHSM was determined and the mixture that registeredthe maximum strength was modified further based on certain criteria to obtainoptimized mixture proportion. The rate of strength development of the optimizednormal water-cured UHSM was performed to understand the order of compressivestrengths achievable with the used materials. To elevate the target strengths fur-ther, thermal curing was employed and detailed investigations were performedto arrive at an optimized curing regime for UHSM.

The second part dealt with determining experimentally the r–e characteristicsof the optimized UHSM under uniaxial compression. These characteristics includethe stresses and strains at elastic limit [i.e., at 0.40 times the peak stress (0.40rp)], peak point, a post-peak point [i.e., at a micro-strain of 7500 (e7500)] and failurepoint, modulus of elasticity (E), secant modulus (E0) and toughness or energyabsorption capacity. In addition, analytical modeling of the r–e characteristics ofUHSM was performed and compared with the experimental results for determiningthe accuracy of the fit. The effect of micro-fiber addition and its size on the r–echaracteristics of UHSM were studied, and both linear and non-linear model curveswere proposed that related the fiber parameters with the different properties ofUHSM.

3.1. Materials and mixing process

The materials used to produce UHSMs include cement, silica fume, quartz pow-der, silica sand, micro-fibers, water and high-range water reducers. Ordinary port-land cement, confirming to the specifications of IS: 12269 was used. The specificgravity and surface area of the cement was 3.15 and 230 m2/kg (from BET analysis),respectively. The silica fume (SF) was obtained from a conventional source and, itsspecific gravity and surface area (from BET analysis) was 2.20 and 21000 m2/kg,respectively. The chemical composition of cement and silica fume is shown in Ta-ble 1. The particle size distribution of densified silica fume particles is providedin Fig. 1(i) and its average particle size (D50) was �13 lm. Quartz powder (QP)was also obtained from a local source and it contained 99% silicon dioxide. The spe-cific gravity of quartz powder was 2.59 and its particle size distribution is shown inFig. 1(i).

The Indian standard silica sand from Ennore district of India was used as theaggregate. This sand is available in three grades, G1, G2 and G3 as shown inFig. 1(ii), and their D50 value was 400, 600, 1200 lm, respectively. A well gradedsand combination (G1 = 33%; G2 = 25% and G3 = 40%) of the three sand gradeswas used and its D50 was �550 lm. Two sizes of high-carbon steel micro-fibers(6 and 13 mm long), having a diameter and ultimate tensile strength of 0.16 mmand 2000 MPa, respectively, were used. Poly-carboxylate based high-range waterreducer was used as the w/cm in UHSM was low.

The dry mixing of materials was performed in a high-speed shear mixer ma-chine for about ½ a minute to achieve initial homogeneity. The high-range waterreducer was thoroughly mixed with water before adding to the dry mixture. Wetmixing was carried out for 5–15 min until a homogenous and flowable mixturewas obtained. The micro-fibers were then gradually added and the speed of themixer machine was subsequently increased to ensure thorough distribution of mi-cro-fibers. The wet mixture was cast in standard size molds before demolding (after24 h) and subjecting it to appropriate curing regimes.

Na2O K2O TiO2 Mn2O3 SO3 Cl

0.20 0.47 0.20 0.08 1.87 0.0120.51 – – – – –

(i) Particle size distribution of silica fume and quartz powder

(ii) Sieve analysis data of G1, G2, G3 sand and their well graded combination

0

10

20

30

40

50

60

70

80

90

100

Cum

ulat

ive

perc

enta

ge p

assi

ng (%

)

Particle size (microns)

Densified silica fume

Quartz powder 1

19

0

10

20

30

40

50

60

70

80

90

100

000010

0.01 0.1 1 10 100 1000

011

Cum

ulat

ive

perc

enta

ge p

assi

ng (%

)

Sieve size (microns)

G1 sandG2 sandG3 sandWell graded sand

1200

600400

Fig. 1. Particle size distribution of silica fume, quartz powder and sand.

K.V. Harish et al. / Construction and Building Materials 49 (2013) 781–796 783

3.2. Experimental test methods

For all studies in Section 4.1 other than Section 4.1.1, the compression test wasperformed on 70 mm cube specimens after the specified curing period using thestandard IS: 516 test procedure. The compression test on 50 mm cube specimensin Section 4.1.1 was alone performed as per the standard ASTM C 109 test method.

(i) Arrangement of LVDT and strain gauges on the specimen

Fig. 2. Photograph of testing of UHSM cylinde

The r–e characteristic of UHSM under uniaxial compression was obtained byconducting compression test on cylinder specimens of size 100 mm dia. x200 mm height using the MTS Universal Testing Machine (UTM). The photographof the instrumentation on the specimen and the data logger are shown in Fig. 2(iand ii), respectively. Before applying the load, the specimen was first instru-mented with two linear variable differential transformers (LVDTs) for measuringthe axial deformation between the platens as suggested by the RILEM TechnicalCommittee TC 148 (2000) [16]. Then, electrical resistance strain gauges werefixed in the horizontal and vertical direction at the mid-height of the specimento measure its axial and circumferential strains. The specimen was placed andtested under cross head control of the UTM. The loading was applied at a con-stant deformation rate of 0.05 mm per minute from the start of the test untilthe specimen’s peak load was reached. Just after the load started decreasing,the deformation rate was maintained at 0.20 mm per minute to capture thepost-peak behavior of UHSM. The test was continued until the specimen com-pletely failed. The load and deformation readings were recorded automaticallyby a HBM data logger connected to the control system. Since the specimen’scross-sectional area (A) and gauge length (Lg) are known, the r–e curve of thespecimen was plotted from the load-deformation (P–d) data.

The modulus of elasticity (E) of the specimen was obtained using the formulagiven in the ASTM C 469 test procedure, its secant modulus (E0) was computedby calculating the ratio of peak stress (rp) to peak strain ep) and its energy absorp-tion capacity (EA) was calculated by determining the area under the r–e curveusing the trapezoidal rule.

4. Results and discussions

4.1. Production of UHSM from conventional materials

The 10 suitable mixtures selected to produce UHSM from con-ventional materials is shown in Table 2. Silica fume to cement ra-tio, w/cm and quartz powder to cement ratio of the selectedmixtures was in the range of 0.20–0.30, 0.14–0.20 and 0.11–0.40,respectively; these values being typical for producing UHSCM. Ofthe 10 mixtures, the first two (UHSM-1 and UHSM-2) neither con-tained silica fume nor contained quartz powder, and hence, wasconsidered as control mixtures. The next three mixtures (UHSM-3, UHSM-4 and UHSM-5) contained silica fume but not quartzpowder and are described as silica fume mixtures. The last fivemixtures contained both silica fume and quartz powder. Thesemixtures were cast, normal water-cured at 25 �C for a period of28 days and tested for compressive strength as per the ASTM C109 test procedure.

4.1.1. Effect of w/cm on the compressive strength of UHSMThe 28-day compressive strength of UHSM (f 0c;28) for

different w/cm can be represented using the following two stan-dard equations and a very close fit was obtained with reliable R-square values.

(ii) Data logger

r specimens under uniaxial compression.

Table 2Mixture proportions of different UHSMs used in this study.

Ingredients Proportion by weight of different UHSM mixtures

UHSM-1 UHSM-2 UHSM-3 UHSM-4 UHSM-5 UHSM-6 UHSM-7 UHSM-8 UHSM-9 UHSM-10*

Cement 1 1 1 1 1 1 1 1 1 1Silica fume – – 0.20 0.25 0.30 0.27 0.20 0.25 0.23 0.25Quartz powder – – – – – 0.11 0.30 0.31 0.39 0.40Silica sand 1.10 1.10 1.10 1.10 0.77 1.10 1.10 1.67 1.10 1.10Water 0.20 0.17 0.20 0.17 0.23 0.21 0.20 0.25 0.17 0.17w/cm 0.20 0.17 0.17 0.14 0.18 0.17 0.17 0.20 0.14 0.14Superplasticizer RQ RQ RQ RQ RQ RQ RQ RQ RQ RQfc at 28 days (MPa) 67.50 73.89 78.00 87.85 67.74 76.45 72.00 62.79 83.93 85.00

* UHSM-10 is an optimized version of UHSM-9 and more information is provided in Section 4.1.2.

(i) Effect of w/cm on the compressive strength of UHSM

(ii) Rate of compressive strength development of UHSM

50

55

60

65

70

75

80

85

90

95

100

105

28-d

ay c

ompr

essi

ve s

tren

gth

(MP

a)

w/cm

(or)

0

10

20

30

40

50

60

70

80

90

100

0.100 0.125 0.150 0.175 0.200 0.225 0.250

0 5 10 15 20 25 30

Com

pres

sive

str

engt

h, f

' c,t (M

Pa)

Period of curing, t (days)

ATC for

demolding

Initial curing Later curing

Equation (5) with f'c = 85 MPa)

Fig. 3. Effect of w/cm and curing period on the compressive strength of normal-water cured UHSM.

784 K.V. Harish et al. / Construction and Building Materials 49 (2013) 781–796

(i) Abram’s law:

f 0c;28 ¼A

ðBÞ1:5ðw=cmÞ ð1Þ

where A and B are constants equal to 160.4 and 21.05, respectively.The equivalent version of the above formula in the exponential formis provided below:

f 0c;28 ¼ a � e�bðw=cmÞ ð2Þ

where a = A = 160.4; b = 1.5 � ln (B) = 4.57

(ii) Bolomey’s equation:

f 0c;28 ¼ k11

ðw=cmÞ � k2

� �ð3Þ

where k1 and k2 are constants equal to 9.295 and �1.993, respec-tively. The R-square values obtained using Eqs. (1) and (3) were0.9105 and 0.9999, respectively.

Fig. 3(i) shows the effect of w/cm on the 28-day compressivestrength of UHSM. As this figure shows, the strength increases withdecrease in the w/cm used. The strength range obtained with themixtures was �62–88 MPa, with the UHSM-4 producing the max-imum strength. The strength range obtained for the mixtures wassignificantly lower than for the UHSCMs investigated in the past[2,5]. This may be because, the cement and locally available mate-rials used to produce the UHSM are more intended for normal per-formance and not for ultra-high performance.

Of the different mixtures investigated, UHSM-2, UHSM-4 andUHSM-9 registered the highest compressive strength within thecontrol mixtures, silica fume mixtures and those that contained sil-ica fume and quartz powder, respectively. The strength of UHSM-9was �14% higher than UHSM-2 and �4% lower than UHSM-4. De-spite not registering the highest compressive strength within thethree mixtures, UHSM-9 was chosen for further investigation asthe presence of quartz powder in the mixture can significantly in-crease their strength, especially on subjection of the specimens toheat curing.

4.1.2. Adjustments in the selected UHSM mixtures based on optimalfilling ability and pozzolanic reactivity of silica fume and quartzpowder

The role of silica fume in UHSM is to act as an effective binderand micro-filler. Though, silica fume has been found to be effectiveas a binder at dosages between 8% and 15%, its quantity required tocompletely deplete the lime content from the total hydration of ce-ment is �25% [3]. Studies conducted during the past had alsoshown that the optimal filling performance of the binder couldbe achieved by using silica fume at �25% dosage level [1]. Hence,the proportion of silica fume in UHSM-9 was increased from 23%(0.23) to 25% (0.25).

Similar to silica fume, quartz powder has two important roles.As effective filler, it fills the voids between individual cement par-ticles and sand grains. At a later stage during the heat application,its role is to take part in the pozzolanic reaction and undergo trans-formation in its silica structure to form compounds such astobermorite, xonotlite and others [17,18]. The quantity of quartzpowder shall therefore be decided based on a silica to cement ratio

K.V. Harish et al. / Construction and Building Materials 49 (2013) 781–796 785

of 0.62 as suggested by Richard and Cheyrezy using the followingformula in which the silica content is constituted by both quartzpowder and silica fume [3].

Q SF � PSF þ Q Q � PQ

C¼ 0:62 ð4Þ

where QSF is the quantity of silica in silica fume (91–95% or 0.91–0.95); PSF is the proportion of silica fume in the UHSM mixture(25% or 0.25); QQ is the quantity of silica in quartz powder (99%or 0.99); PQ is the quantity of quartz in the UHSM mixture (to bedetermined); C is the proportion of cement in the UHSM mixture(100% or 1).

By using Eq. (4), the quantity of quartz powder was determinedas �0.40. Thus, the proportion of quartz powder (i.e., 0.39) used inUHSM-9 is slightly increased to this value. This revision in theUHSM-9 yielded UHSM-10 and this optimized mixture is usedfor all other investigations.

4.1.3. Rate of strength development of optimized UHSM under NWCThe rate of strength development of UHSM mixture under NWC

was performed (i) to understand the extent to which NWC is help-ful in obtaining the desired target strengths, (ii) to determine ifspecial techniques are needed to further increase the targetstrengths, (iii) to provide as a basis for fixing the period of thermalcuring and (iv) to understand the early and later age strength gains.The compression test was conducted using the IS: 516 test proce-dure on 70 mm cube specimens and the test results between 1 and28 days of curing period is shown in Fig. 3(ii). A regression analysisfor the rate of compressive strength development of UHSM wasperformed using the following Weibull cumulative function asdone by Graybeal [5], with slight changes in the constants used.

f 0c;t ¼ f 0c 1� exp � t � 0:422

� �0:7 !" #

ð5Þ

where f 0c;t = compressive strength of UHSM at time ‘t’ in MPa;f 0c = 28-day compressive strength of UHSM in MPa; t = period of nor-mal water curing in days.

As this figure shows, the UHSM developed a minimum com-pressive strength of �20 MPa (strength level that can be consid-ered sufficient for demolding purposes) after 24 h, a minimumcompressive strength of �50 MPa (strength level equal to that ofhigh strength concrete as per the IS: 456 2000 specification) be-tween 2 and 3 days of initial curing, and a minimum compressivestrength of �80 MPa (strength level equal to that of high strengthor high performance concrete) after 9 days of curing. The 6 days ofinitial curing in normal water just after demolding elevated thestrength from �20 MPa to �76 MPa (�280% increase) and the latercuring in normal water beyond 7 day period elevated the strengthfrom �76 MPa to �85 MPa (�12% increase). The higher percentagestrength increase obtained with mixtures at early curing periodsmay be due to the higher reactivity of the cement compounds atearly ages as can be observed in common portland cement mix-tures [19]. The 28-day compressive strength of UHSM was lowand to elevate its strength further, detailed investigations wereperformed using thermal curing.

4.1.4. Thermal curing for UHSMThe standard NWC used in the previous section or moist air cur-

ing (MAC) at �20–25 �C used in other research can only control therate and extent of moisture loss from the freshly prepared UHSM,and cannot accelerate or promote further curing. To increase thetotal cement hydration, the rate of cement or binder reactivity,and to elevate the target strengths further, heat curing techniqueswere adopted by generalizing the curing regime used in otherresearch.

4.1.4.1. Generalization of curing regime for UHSM from literature. Thecuring regime used by different investigators and the correspond-ing target strengths achieved are provided in Table 3. As the tableshows, the hot water curing (HWC), hot air curing (HAC), steamcuring (SC) and autoclave curing (AC) has been widely employedto elevate strength levels from high to ultra-high levels[3,5,23,26,27]. Both single curing and multiple curing types havebeen used to produce compressive strengths between 115 MPaand 310 MPa. While some investigators used high-quality pre-packed materials to obtain compressive strength over 150 MPausing NWC, others used higher temperatures for shorter durationsor lower temperatures for longer durations to obtain highstrengths. The varying physical and chemical properties of materi-als used by different investigators restrict the direct use of theirinitial heat curing regime in the current study. Hence, the curingregimes provided in this table were considered as a basis to arriveat generalized curing regime for UHSM as shown in Fig. 4(i).

4.1.4.2. Optimization of curing regime for UHSM based on strengthstudies. The optimization of curing regime for UHSM was per-formed by developing a generalized curing regime shown inFig. 4(ii) [obtained from Fig. 4(i)], selecting different curing regimesbased on this generalization, and determining one regime that pro-vide the maximum compressive strength. By fixing the curingduration, curing temperature and curing type for Phase I and III,and varying those for Phase II, 8 different initial curing regimeswere obtained. A curing regime that involved 6 days of NWC justafter 1 day of ATC was considered as the control regime. The effectof these curing regimes on the compressive strength of UHSM isshown in Fig. 5(i) – (a) through (i) – (c) and the salient pointsare discussed in Table 4. The test results obtained in Fig. 5(ii) –(a) can be discussed more effectively by calculating the energyassociated with each curing regime, expressed in terms of ‘matu-rity’ values. The maturity values were determined by multiplyingthe product of the temperature (�C) and period (days) of curingadopted using the following equation:

M ¼Xðd � TÞ ¼ dA � TA þ

XðdT � TTÞ þ dL � TL ð6Þ

where dA and TA are the period and temperature of ATC, respec-tively; dT and TT are the period and temperature of thermal or initialheat curing, respectively; dL and TL are the period and temperatureof later age curing, respectively. The value of dA, and dL is 1 and 21,respectively, and that of TAand TL is equal to 25. Thus for the controlregime (6 day NWC), the maturity (MC) was determined as follows:

MC ¼ 1 day� 25 �Cþ 6 days� 25 �Cþ 21 days � 25 �C

¼ 700 ð�C: daysÞ

Similarly, the maturity values for other curing regimes were calcu-lated using Eq. (6) and the 28-day compressive strengths were plot-ted against these values as shown in Fig. 5(ii) – (b). As this figureshows, an increasing logarithmic trend was found to exist betweenthe maturity values and the 28-day strength of UHSM. In addition, amaturity value of �1200 (�C. days) was found to produce a targetcompressive strength of 127.5 MPa (a 50% increase in compressivestrength beyond the control strength).

A comparison of the test results for CR4 and CR6 indicated thatthe compressive strength of the former was higher despite itsmaturity value being lower, and hence, the former is more benefi-cial than the latter. Similarly, a comparison of the test results forCR5 and CR8 showed that the compressive strength of the formeris slightly higher despite its maturity values being lower. This indi-cates that the hierarchy of heat curing technique and chosen dura-tion can significantly influence the strength properties of UHSM,and a judicious selection of both can result in significant energycost benefits. From the eight curing regimes investigated, both

Table 3Description of various heat curing regimes adopted by some investigators.

Reference Description of the heat curing regime or related techniques used Compressive strength (MPa)

[3] 1 day ATC + 2 day HWC at 90 �C 170–230

[20] 1 day ATC + 3, 7 and 28 day NWC at 20 �C� –1 day ATC + 8, 24 and 48 h HAC at 90 �C1 day ATC + 8 h HAC at 200 �C1 day ATC + 8 h HAC at 250 �C

[21] 1 day ATC + 7 day NWC at 20 �C� 160–2001 day ATC + 4 day HWC at 90 �C1 day ATC + 2 day HAC at 90 �C

[22] 1 day ATC + NWC at 20 �C till test 1701 day ATC + 8 days HAC at 200 �C + 8 days at 250 �C 280–310

[6] 6 h ATC + SC at 90 �C �2001 day ATC + ACC at 160 �C

[23] 50 kN load for 24 h + ACC at 150 �C 243–288

[24] 1 day ATC + NWC till test � 711 day ATC + ACC at 150 �C + pressure of 0.5 MPa for 8 h 91

[25] 1 day ATC + 28 day NWC at 20 �C� 115–1701 day ATC + 6, 12 days SC at 90 �C1 day ATC + ACC at 210 �C + pressure of 2 MPa for 8, 16 and 24 h

[7] 1 day ATC + MC at 20 �C till test 153–2091 day ATC + 2 days SC at 90 �C

Note: ATC – Ambient temperature curing; HWC – hot water curing; NWC – normal water curing; HAC – hot air curing; MC – moist air curing; SC – steam curing;� Indicates that the curing regime contains only NWC after 1 day ATC.

786 K.V. Harish et al. / Construction and Building Materials 49 (2013) 781–796

CR2 and CR4 registered the highest compressive strengths. How-ever, the CR4 was chosen as the optimized curing regime and usedfor all studies conducted then on as its maturity value is lower thanCR2.

4.2. Experimental test results of the stress–strain (r–e) characteristicsof UHSM in compression

The r–e characteristics of UHSM were determined by testing aminimum of three cylinder specimens for each batch using theUTM and by plotting the r–e curve from the experimental data. Ta-ble 5 shows the experimental test results of the r–e characteristicsof UHSM. The co-efficient of variation (Cv) of the obtained resultsvary from �5% to 12% for the stresses, from �8% to 16% for thestrains and �4–11% for the modulus of elasticity. The r–e curvesof three specimens in each batch did not vary significantly untilup to the post-peak micro-strain of 7500–8000. However, somevariations were observed beyond this micro-strain level and failureas also reported in other research [30]. Overall, identical behaviorswere observed with most specimens from the same batch.

4.2.1. Effect of heat treatment on the r–e characteristics of non-fiberedUHSM

The effect of heat treatment on the r–e characteristics of non-fibered UHSM was determined by comparing the r–e curves ofnormal water-cured specimens with that of heat-cured specimensas shown in Fig. 6. As this figure shows, the r–e curves of normalwater- and heat-cured specimens was linearly elastic until up toa significant level before the peak, with the latter having higherslope than the former. Both the specimens failed immediately afterreaching their respective peaks, indicating the brittle nature of thecomposite. The r–e characteristics of the normal water- and heat-cured specimens shown in Table 5 indicate that the heat applica-tion to UHSM increases its strength at elastic limit and peak pointby �33%, its strain at elastic limit and peak point by �12% and�14%, respectively, its E by �5% and its E0 by �16%. The E/E0 valuefor the heat- cured specimens was lower than for the normalwater-cured specimen as obtained by Graybael [5]. The calculatedEA values for the normal water-cured and heat-cured specimens

indicated that the heat application significantly increased thetoughness by 55% at elastic limit and by 37% at peak point, respec-tively. Since the peak and failure points in the r–e curve for thespecimens were very close, the need to improve ductility in thepost-peak region of the stress–strain curve by incorporating fibersinto the composite matrix is now obviously realized.

4.2.2. r–e characteristics of fibered UHSMThe r–e characteristics in compression of UHSM specimens

containing 6 mm and 13 mm long fibers for varying fiber-volumedosages (0–3%) is shown in Fig. 7(i and ii), respectively. The non-fi-bered specimen (UHSM-0%) was considered as the reference orcontrol. As these figures show, a significant improvement in ther–e characteristics of UHSM was observed with the addition of mi-cro-fibers at all dosages, regardless of their size (length). Unlikeconcretes, a linearly elastic behavior was observed until peak forall the mixtures. The fibered UHSM specimens showed slightlyhigher slope in the linearity portion than the non-fibered speci-mens, probably due to the increase in their modulus of elasticitybecause of micro-fiber addition. As far as the post-peak behavioris concerned, the non-fibered specimens failed suddenly afterreaching peak, with almost very low or no post-peak strain capac-ity. However, the fibered specimens endured for a very long timebeyond peak until a significant post-peak strain was reached. Aphotograph of non-fibered and fibered UHSM specimen just aftercompression test is shown in Fig. 7(iii and iv), respectively. Theperformance of the fibered UHSM were evaluated by first deter-mining the stresses and strains at peak and failure points of therespective stress–strain curves, and calculating the strength-over-control (SOC) values, i.e., percentage increase or decrease invalues with respect to that of the control mixture. The Fig. 8(i)through (vi) shows the comparative performance of different mi-cro-fiber sizes on the peak stress (rp), failure stress (rf), peak strain(ep) and failure strain (ef) for varying fiber volume dosages.

4.2.2.1. Stress at peak and failure point on the r–e curve. As theFig. 8(i) shows, the peak stress (rp) of UHSM significantly increaseswith increase in the micro-fiber volume dosage. The maximumSOC value was 51% (at 2% micro-fiber volume dosage) for long fi-

Period of curing (days) Period of curing (days)

Tem

pera

ture

(0 C

)

Tem

pera

ture

(0 C

)

(i) (ii)

Note: • Phase I is described as the setting period from the time the

mixture was cast until it starts gaining sufficient rigidity (~24 hours). A pre-set pressure in the form of a vertical pre-compression load has been applied to the wet mixture (though not in this study) just after casting to decrease its w/cm, reduce its porosity or air voids and increase its density, thereby improving its mechanical properties [28].

• Phase II is described as the initial heat curing period between 1 and 12 days during which heat has been imparted to UHSM for accelerating the reactivity of cement, silica fume and quartz powder. During this phase, the strength of the composite increases significantly with a substantial decrease in its porosity due to the formation of compounds such as tobermorite, truscottite, gyrolite, xonotlite and hillebrandite resulting from hydro-thermal reactions [23, 29]. In this phase, the specimens are subjected to initial heat either by choosing a single curing technique (SC/HWC/OC/ACC) or combination of different techniques using temperatures such as 900 C, 1500 C, 2000 C and 2500 C.

• Phase III is described as later age curing period during which the formed compounds in Phase II are allowed to stabilize.Either an increase or decrease in strength is usually observed due to the application of heat in the previous phase. NWC has been employed until testing to subdue any reactions resulting from thermal curing.

Note: • Curing type and temperature:The curing type employed for

Phase I and III was fixed as ATC (250-300 C) and NWC (250

C), respectively, as used by most investigators. However for Phase II, a combination of NWC (at 250 C), HWC (at 900 C) and HAC (at 2000 C) was employed to serve as normal, moderate and high temperature curing, respectively.

• Curing duration:Phase I period was fixed as 1 day to allow sufficient time for setting, to obtain dimensional stability and to develop sufficient strength (~20 MPa) of the UHSM mixture, before applying initial heat. The application of heat before the setting time of mixture is usually not recommended, as heat can increase the early age strength while causing significant decrease in the later age strengths [29]. Phase II period was fixed as 6 days because the hydration reactions are usually active during the early curing periods until 7 days as can be observed in Figure 3 (ii). Hence, the hydration rates in UHSM can be increased by using appropriate initial heat curing to obtain higher 7-day strength without much compromise in the 28-day strength. Phase III period was fixed as 21 days so that a conventional comparison can be made with the specimens tested after this period and after 7 days, to understand the effect of heat application in Phase II.

(i) From literature (ii) In this study

Fig. 4. Generalized curing regime for UHSM. (See above-mentioned references for further information.)

K.V. Harish et al. / Construction and Building Materials 49 (2013) 781–796 787

bers and 43% (at 3% micro-fiber volume dosage) for short fibers.The significant contribution of micro-fibers may be attributed totheir micro-crack arrest mechanism at the cement matrix [31].Such a behavior is not usually noted with composites containingsteel macro-fibers, as they are capable of arresting only thosecracks that are in close vicinity to each other. The portion of thematrix that is at a relatively longer distance from the fibers isnot significantly stiffened and hence, only less or no improvementshave been reported by other researchers [12,31]. A past researchhad demonstrated the importance of using steel micro-fibers inimproving the peak tensile stress of high-strength cement matri-ces. In that research, the SOC values of fiber reinforced pastesand mortars subjected to uniaxial compression loading were calcu-lated to be in the range of �21–27% and ��10–9%, respectively[14]. The increased SOC values obtained in the current study whencompared with the past study may be due to the use of shorter fi-bers in the latter, the use of heat treatment in the former and thevariation in the material properties and stiffness of the non-fiberedmatrices used in both studies.

At a constant micro-fiber volume dosage of 1% and 2%, the peakstress was 162% and 75% higher for long fibers than for short fibers,respectively, indicating the superior performance of the former. Sucha behavior appears to be contrary to the conventional findings of fiberreinforced concrete that shorter fibers tend to contribute more beforethe peak point than longer fibers. However, it may be noted that therange of fiber length used in the conventional fiber reinforced concreteis between 13 mm and 40 mm, whereas the range of fiber lengths usedin the current study is between 6 and 13 mm. Within such low lengthranges, the longer fibers can perform better than short fibers, providedthe former is well distributed and appropriately spaced within the ma-trix to arrest quick and progressive micro-cracks. The localized spacingof fibers within the matrix due to changes in fiber length appears togovern the peak stress of the composite.

In the case of failure stress as shown in Fig. 8(ii), the non-fiberedUHSM failed immediately after peak and hence, its rf values werehigher than that of fibered UHSM, resulting in a reduction of theSOC values. The initial decrease in the rf values at 1% micro-fibervolume dosage were found to be 35% and 56% for 13 mm and

Note: HAC1 (1 day HAC + 5 day NWC);HAC2 (2 day HAC + 4 day NWC);HAC3 (3 day HAC + 3 day NWC)

Note: HWC1 (1 day HWC + 5 day NWC); HWC2 (2 day HWC + 4 day NWC); HWC3 (3 day HWC + 3 day NWC)

(a) HAC at 200 0 (b) HWC at 90C 0 C

(i) Effect of applying HAC and HWC just after demolding on the compressive strength of UHSM

Note: CR1 (3 day NWC + 3 day HWC); CR2 (3 day NWC + 3 day HAC); CR3 (3 day NWC + 2 day HWC + 1 day HAC); CR4 (2 day NWC + 2 day HWC + 2 day HAC); CR5 (2 day NWC + 3 day HWC + 1 day HAC); CR 6 (2 day NWC + 1 day

HWC + 3 day HAC); CR7 (1 day NWC + 2 day HWC + 3 day HAC) and CR8 (1 day NWC + 3 day HWC + 2 day HAC)

(a) HAC at 200 0 C and HWC at 90 0 C (b) Relationship between 28-day compressive strength and maturity of UHSM

(ii) Effect of applying HAC and HWC after initial NWC on the compressive strength of UHSM

74

8589 9287 89

1818

0

25

50

75

100

125

150

Com

pres

sive

str

engt

h (M

Pa)

Curing period

Control HAC1

HAC2 HAC3

74

8589 9086 8782 83

0

25

50

75

100

125

150

7 days 28 days

7 days 28 days

7 days 28 days

Com

pres

sive

str

engt

h (M

Pa)

Curing period

Control HWC1

HWC2 HWC3

74

85

108114

129 132

115 118125

134

119125128 130

123129

122 124

0

25

50

75

100

125

150

175

200

Com

pres

sive

str

engt

h (M

Pa)

Curing period

Control CR1 CR2CR3 CR4 CR5CR6 CR7 CR8

85

114

132

118

134

125130

129

124

y = 66.14ln(x) - 341.23R² = 0.86

50

60

70

80

90

100

110

120

130

140

150

500 750 1000 1250 1500

28-d

ay c

ompr

essi

ve s

tren

gth

(MP

a)

Maturity (0 C x days)

50% increase beyond control

Fig. 5. Test results with different heat curing regime for UHSM.

788 K.V. Harish et al. / Construction and Building Materials 49 (2013) 781–796

6 mm micro-fibers, respectively. However with micro-fiber addi-tion beyond 1%, a maximum increase in the rf values of 17% wasobserved at 2% fiber-volume dosage for 13 mm micro-fibers anda maximum increase in the rf values of 39% was observed at 3% fi-ber-volume dosage for 6 mm micro-fibers. This increase in the rf

values can significantly increase the energy absorption capacityof the composite, especially when there is a subsequent increasein the failure strain (ef) values. In addition, the SOC values for longfibers were higher than for short fibers, indicating the superior per-formance of the former.

4.2.2.2. Strain at peak and failure point on the r–e curve. As theFig. 8(iii) shows, the SOC values of the peak strain (ep) for the UHSMwas found to significantly increase with micro-fiber addition as ex-pected. At a constant micro-fiber volume dosage of 2%, the SOC val-ues were 31% and 29% for long and short fibers, respectively.

Though the SOC values at 1% dosage was significantly higher forlong fibers than for short fibers, only a slight increase in ep valueswas observed at 2% dosage. Previous studies have shown thateither little or no improvement in the ep values can be observed,with an increase in the micro-fiber volume dosage levels [12,32].In the case of failure strains as shown in Fig. 8(iv), the trend ob-served was similar to that of ep except that the SOC values for fi-bered mixtures were several times higher than for the reference.The maximum SOC values were found to be 3.95 times higher ata 2% micro-fiber volume dosage for long fibers and 4.24 times high-er at a 3% micro-fiber volume dosage for short fibers. At a constantmicro-fiber volume dosage of 2%, the longer fibers performed bet-ter than shorter fibers probably due to the ability of the former towithstand longer strains before failure.

Based on the stress and strain at peak and failure points of ther–e curve, a micro-fiber volume dosage of 2–3% and 2% may be

Table 5r-e parameters of non-fibered and fibered UHSM specimens under uni-axial compression.

Mixture ID Fiber volumedosage

Stress Micro-strain Modulus ofelasticity, E

Secantmodulus, E0

E/E0

At 0.4%rp

At peak,rp

At e7500,r7500

At failure,rf

At 0.4%rp

At rp,ep

e7500 At failure,ef

% MPa MPa MPa MPa GPa GPa

UHSM normal water-cured

0 34 85 – – 899 3008 – 3008 36.86 28.26 1.304

UHSM heat-cured(UHSM-0%)

0 45 113 – – 1020 3437 – 3437 38.51 32.90 1.317

UHSM-1% (lf = 6 mm) 1 49 123 64 50 1297 3820 7500 9000 39.63 32.12 1.234UHSM-2% (lf = 6 mm) 2 58 146 105 67 1400 4442 7500 14000 41.96 32.82 1.278UHSM-3% (lf = 6 mm) 3 65 162 123 75 1250 4851 7500 18000 44.00 33.35 1.319UHSM-1% (lf = 13 mm) 1 55 137 105 74 1369 4252 7500 12000 41.00 32.20 1.273UHSM-2% (lf = 13 mm) 2 69 171 137 80 1615 4501 7500 17000 44.80 38.06 1.177

Table 4Effect of thermal curing on the compressive strength of UHSM.

Figure no. Topic (or) heading Salient points

5(i) – (a) Effect of initial heat application usingHAC at 200 �C (just after demolding) on the 7- and28-day compressive strength of UHSM

� The 7-day strength of UHSM subjected to HAC1, HAC2 and HAC3 was 20%, 17% and 9% higher thanthe control regime, respectively� Among the three initial heat curing regimes adopted, HAC1 registered the highest compressivestrength. In addition, the strength decreases with increase in the heat curing period from 1 day (as forHAC1) to 3 days (as for HAC3), indicating that heat curing applied just after demolding for more than1 day is detrimental to UHSM� The 28-day strengths of these curing regimes were found to mirror their 7-day strengths. Thepercentage increase in strength from 7 days to 28 days was lower (�0%-3%) for heat curing regimesthan for control regime (�14%)

5(i) – (b) Effect of initial heat application usingHWC at 90 �C (just after demolding) on thecompressive strength of UHSM

� The 7-day strength of UHSM subjected to HWC1, HWC2 and HWC3 regimes was higher than thecontrol regime by 20%, 16% and 11%, respectively� The curing of UHSM in hot water at 90 �C for more than 1 day applied just after demolding isdetrimental. The test results (both 7-day and 28-day compressive strengths) and the comparativebehaviors shown in Fig. 5(i) – (b) was found to mirror that of Fig. 5(i) – (a)

5(ii) – (a) Effect of initial heat application usingcombinations of HWC at 90 �C and/or HAC at 200 �C(after allowing sufficientperiod for NWC) on the compressivestrength of UHSM

� The 7- and 28-day strength of heat-treated specimens was 30–55% and 30–50% higher than that ofcontrol specimens, respectively� Of the different initial heat curing regimes adopted, CR2 registered the highest 7-day strength andCR6 registered the highest 28-day strength� By comparing the 7- or 28-day strengths of specimens subjected to different curing regimes, thetemperature, duration and curing technique adopted can be observed to play significant role in thestrength development of UHSM� A comparison of CR1 and CR2 indicates that high temperature curing (200 �C) for a 3 day curingperiod (after 3 days of initial NWC) can offer more strength benefits than low temperature curing(90 �C) for the same curing period� A comparison of strengths of CR1, CR2 and CR3 indicates that a curing combination of low and hightemperature (HWC and HAC) for 3 days (after 3 days of initial NWC) can be used to obtain strengthsbetween CR1 (only HWC) and CR3 (only HAC)

K.V. Harish et al. / Construction and Building Materials 49 (2013) 781–796 789

considered optimum for UHSM while using 6 mm and 13 mm longfibers, respectively.

4.3. Analytical modeling of the r–e curve of UHSM under uniaxialcompression

4.3.1. Proposed analytical modelSeveral efforts have been taken during the past to arrive at ana-

lytical expressions for predicting the r–e behavior of portland ce-ment concrete (PCC) or mortars under uniaxial compression[12,13,33]. These expressions are either directly used or modifiedby applying appropriate boundary conditions or assumptions topredict the behavior of other cement based composites. In thisstudy, the analytical modeling of generalized r–e curve for UHSMunder compression was performed by using the following expres-sion suggested by Fanella and Naaman for fiber reinforced mortars[33].

Y ¼ rrp¼

A � ð eepÞ þ B � e

ep

� �2

1þ C � eep

� �þ D � e

ep

� �2

264

375 ¼ A � X þ B � X2

1þ C � X þ D � X2 ð7Þ

where X is the normalized strain = e/ep; Y is the normalizedstress = r/rp; e – strain at any point on the curve; ep – strain at peakpoint; r – stress at any point on the curve; rp – stress at peak point;A, B, C and D – are constants to be determined from the boundaryconditions of the curve. A schematic diagram of the generalizedr–e curve for UHSM-2% based on the proposed analytical expres-sion is shown in Fig. 9(i). To obtain the experimental data points(dotted lines), the X-axis (i.e., stress at any point) and Y-axis (i.e.,strain at any point) values were divided by the rp and ep of the fi-bered UHSM mixture, respectively. To obtain the constants in theanalytical expression, the co-ordinates of three points on the exper-imental r–e curve for each mixture were chosen. The first point L(Xl, Yl) corresponds to the point at 0.40 rp (end of the linearity re-gion), the second point I (Xi, Yi) corresponds to the inflexion pointin the post-peak region of the curve and the third point F (Xf, Yf) cor-responds to the point at failure. Specifically, the inflexion point foreach mixture was determined from the sudden change in slope at aspecific point on the post-peak portion of the curve. The boundaryconditions for the ascending and descending portion of the curvewere obtained from the past research performed by Fanella andNaaman [33], and the obtained constants for the different UHSM

85.78

113.09

0

25

50

75

100

125

150

175

0 1000 2000 3000 4000 5000 6000 7000 8000

Stre

ss (

MP

a)

Micro-strain (mm/mm)

UHSM - normal water-cured

UHSM - heat-cured

Fig. 6. Comparison of r–e characteristics of non-fibered UHSM specimens sub-jected to NWC and optimized heat curing.

790 K.V. Harish et al. / Construction and Building Materials 49 (2013) 781–796

mixtures are shown in Table 6. By using these constants in Eq. (7),the r–e curves were predicted analytically. Fig. 9(ii) shows the com-parison of normalized r–e curves for different mixtures obtainedusing analytical modeling and experimental investigation, andFig. 10(i) – (a) and (i) – (b) shows the predicted r–e curves for dif-ferent mixtures. As these figures show, the experimental data

(i) Effect of micro-fiber (6 mm long) dosage on σ−ε characteristics

(iii) Photograph of failed UHSM specimen containing no micro-fibers

0

25

50

75

100

125

150

175

200

225

250

Stre

ss (

MP

a)

Microstrain

UHSM-0%UHSM-1% [6 mm]UHSM-2% [6 mm]UHSM-3% [6 mm]

0 4000 8000 12000 16000 20000

Fig. 7. Effect of micro-fiber addition on the r–e cha

points were found to be in very close agreement with the predictedr–e curve for all the mixtures. Hence, the proposed analytical equa-tion and normalized r–e curves can be used as a generalization topredict the r–e curves of micro-fiber reinforced UHSM.

4.3.2. Effect of reinforcement index (RI) of micro-fibers on importantproperties of UHSM

Reinforcement index (RI), defined as the product of Vf used andtheir aspect ratio [i.e., the ratio of the Lf to their Df], has been usedin this study to combine the different fiber parameters (Lf, Df andVf) into one parameter (RI = Vf�Lf/Df), and then to correlate withthe various stress–strain characteristics of UHSM. To understandthe effect of fibers using RI, the weightage factor for Lf, Df and Vf

have been usually assumed by most investigators to be equal[12,33], however, such assumption may not always result in bestcorrelation. Any of the fiber parameters can be more influentialthan others in affecting specific properties of fiber reinforced mix-tures. In order to understand the variable effect of these parame-ters and to accurately use RI as a one-parameter variable fordetermining the effect of steel micro-fibers in UHSM, weightagefactors were assigned for each variable. These factors were raisedto the power of the individual variable in RI to obtain modifiedreinforcement index (RI0) as shown below:

RI0 ¼ ½Vf a:½Lf b

½Df cð8Þ

where a, b and c are the weightage factors for Lf, Df and Vf

respectively.

(ii) Effect of micro-fiber (13 mm long) dosage on σ−ε characteristics

(iv) Photograph of failed UHSM specimen containing 2% micro-fibers

0

25

50

75

100

125

150

175

200

225

250

0 4000 8000 12000 16000 20000

Stre

ss (

MP

a)

Microstrain

UHSM-0%UHSM-1% [13 mm]UHSM-2% [13 mm]

racteristics of UHSM under axial compression.

K.V. Harish et al. / Construction and Building Materials 49 (2013) 781–796 791

The use of RI0 may be helpful when appropriate correlation wasnot achievable with RI as encountered in the past research [12,33].

The effect of reinforcement indices (RI and RI0) on the modulusof elasticity (E), rp and ep is shown in Fig. 10 – (ii) – (a), (ii) – (b) and(ii) – (c), respectively. In all these figures, RI and RI0 were plotted onthe X1 (bottom of the figure) and X2 (top of the figure) axis, respec-tively, and the individual property is plotted on the Y-axis. Thescale for X1 axis (i.e., ranging from 0 to 4) representing RI remainsconstant, as a = b = c = 1 in all the figures. However the scale for X2axis representing RI0 changes based on the weightage factor a, band c that best fitted the individual property. As these figuresshow, the experimental values of the modulus of elasticity, rp

and ep for the UHSM mixtures were then correlated to their corre-sponding RI and RI0 by using the following linear equation.

y ¼ yc þm � RI0 ð9Þ

where y is the property of the micro-fiber reinforced UHSM to bedetermined (unknown); yc is the experimentally determined valuefor the unreinforced UHSM (known); m is the slope of the straightline equation and represents the rate at which the specific propertyincreases with changes in the fiber dosage or geometry.

The weightage factors for RI0, the R-square values and the slopeof Eq. (9) for the above E, rp and ep are shown in Table 7. As thistable shows, not only does the weightage factors for RI0 used to ex-press individual property is different (i.e., a – b – c) but also thoseused to express different properties are different (a for Ef – a forrf – a for ef – a for EAf). For the modulus of elasticity of UHSM,the absolute value of ‘a’ for RI0 (i.e., 1.53) is higher than that of ‘b’or ‘c’ value, and higher than for RI (i.e., a = 1), indicating that the ef-

(i) Effect of micro-fiber dosage on σp

(iii) Effect of micro-fiber dosage on ε

8

29

43

21

51

0

10

20

30

40

50

60

70

80

90

100

SOC

(%

)

Dosage of micro-fibers (%)

6 mm micro-fibers

13 mm micro-fibers

11

29

41

24

31

0

10

20

30

40

50

60

70

80

90

100

SOC

(%)

Dosage of micro-fibers (%)

6 mm micro-fibers

13 mm micro-fibers

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Fig. 8. Effect of micro-fiber dosage and size on rp, rf,

fect of Vf is more dominant than that of Lf or Df. Similar observa-tions can be seen with rp and ep values for UHSM. For rp, ‘c’value for RI’ was negative, indicating that the Df affects directly[like Lf and Vf in Eq. (8)], instead of inversely (i.e., an increase inthe Df results in an increase in the rp of UHSM). However the Vf

and Lf are more dominating factors than Df as the absolute valuesof their weightage factors are higher than that of Df. In addition,the R-square value of the linear equation for E, rp and ep of UHSMusing RI was �0.93, 0.91 and 0.71, respectively. Similarly, the R-square value of the linear equation for E, rp and ep of UHSM usingRI0 was �0.97, 0.98 and 0.92, respectively. With improved R-squarevalues obtained for each property, the RI0 can be found to be morereliable than RI, especially for ep. For E and rp, the R-square valuesfor RI were also reasonably good.

For secant modulus (E0p), i.e., ratio of rp to ep, a direct linearregression model using RI was not found to be accurate as the lin-ear correlation obtained for ep is not reliable. Hence, the followingtwo non-linear regression models are proposed for E0p.

E0f ¼ 1:53 � E0c þ 0:927 � eRI ðR-square value ¼ 0:933Þ ð10Þ

E0f ¼ E0c þ 0:0723 � e2:6712RI ðR-square value ¼ 0:999Þ ð11Þ

However, a direct linear regression model using RI0 was accurate asthe linear correlations obtained for both rp and ep were highly reli-able. The following equations express secant modulus using the lin-ear expressions obtained for rp and ep.

E0f ¼rp

ep¼ 2:4015½RI0r þ rpc

6:5½RI0e þ epc

� �ð12Þ

σf

ε f

-56

-41-34

-35-29

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

SOC

(%

)

Dosage of micro-fibers (%)

6 mm micro-fibers

13 mm micro-fibers

162

307

424

249

395

0

50

100

150

200

250

300

350

400

450

500

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

SOC

(%)

Dosage of micro-fibers (%)

6 mm micro-fibers

13 mm micro-fibers

(ii) Effect of micro-fiber dosage on

(iv) Effect of micro-fiber dosage on

ep and ef of UHSM subjected to axial compression.

Portion of the σσ−ε curve Value of constants

A B C D Ascending portion 1.18 -0.98 -0.82 0.02 Descending portion 0.10 0.39 -1.90 1.39

(i) An example of the proposed analytical model of the σ−ε characteristics for UHSM-2%

Note: *The normalized strain values for the six mixtures on the X-axis of this figure are offset by some constant value

(ii) Comparison of normalized σ−ε curves of different UHSM mixtures in compression obtained from the proposed analytical model and experimental investigation

0.00

0.25

0.50

0.75

1.00

1.25

1.50

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

Nor

mal

ized

str

ess,

Y (

MP

a/M

Pa)

Normalized strain, X (micron/micron)

Proposed analytical model

Experimental data points

(Xl, Yl)

(Xp, Yp)

UHSM-2% - [13 mm micro-fibers]

L

P

F

I (Xi, Yi)

(Xf, Yf)

0.00

0.25

0.50

0.75

1.00

1.25

1.50

0.00 2.50 5.00 7.50 10.00 12.50 15.00 17.50

Nor

mal

ized

str

ess,

Y

Normalized strain, X (micron/micron)

UHSM-0% (Analytical) UHSM-0% (Experimental) UHSM-1% [6 mm] (Analytical)UHSM-1% [6 mm] (Experimental) UHSM-2% [6 mm] (Analytical) UHSM-2% [6 mm] (Experimental)UHSM-3% [6 mm] (Analytical) UHSM-3% [6 mm] (Experimental) UHSM-1% [13 mm] (Analytical)UHSM-1% [13 mm] (Experimental) UHSM-2% [13 mm] (Analytical) UHSM-2% [13 mm] (Experimental)

2

21

AX BXY

CX DX

+=+ +

Fig. 9. Analytical modeling of the stress–strain characteristics of UHSM in compression.

Table 6Constants of the proposed analytical expression for the non-fibered and fibered UHSM.

Mixture Volume of fibers, Vf Reinforcement index, RI* Ascending portion of the curve Descending portion of the curve

% A B C D A B C D

UHSM-0% 0 0.000 1.19 �0.97 �0.81 0.03 – – – –UHSM-1% 1 0.375 1.21 �0.95 �0.79 0.05 �0.14 0.29 �2.14 1.29UHSM-2% 2 0.750 1.28 �0.89 �0.72 0.11 �0.14 0.44 �2.14 1.44UHSM-3% 3 1.125 1.32 �0.84 �0.68 0.16 �0.24 0.49 �2.24 1.49UHSM-1% 1 0.813 1.27 �0.89 �0.73 0.11 �0.50 0.67 �2.50 1.67UHSM-2% 2 1.625 1.18 �0.98 �0.82 0.02 0.10 0.39 �1.90 1.39

* RI – Reinforcement index (Vf�Lf/Df).

792 K.V. Harish et al. / Construction and Building Materials 49 (2013) 781–796

where

RI0r ¼½Vf 1:444:½Lf 0:976

½Df �0:158 ; RI0e ¼½Vf 1:000:½Lf 0:488

½Df 1:816

For other properties of the r–e curve such as stress at failure points(rf), the linear regression models were not found to provide reliable

solutions using both RI and RI0. Hence, the following non-linearmodels were proposed for rf to provide reliable solutions.

rf ¼ 20:58: lnðRIÞ þ 72:79 ðR-square value ¼ 0:9183Þ ð13Þ

4.3.3. Toughness of micro-fiber reinforced UHSMThe effect of micro-fiber dosage on the toughness at the peak

(EAp) and failure (EAf) points is shown in Fig. 11(i) – (a) and (i) –

(a) )b(srebif-orcimmm6 13 mm micro-fibers

(i) Predicted σ−ε curve of UHSM containing different dosages and sizes of micro-fibers

(a) Modulus of Elasticity, E (b) Stress at peak point, σp

0

25

50

75

100

125

150

175

200

225

250

0 5000 10000 15000 20000

Stre

ss (

MP

a)

Microstrain

UHSM - Control

UHSM-1% [6 mm]

UHSM-2% [6 mm]

UHSM-3% [6 mm]

0

25

50

75

100

125

150

175

200

225

250

0 5000 10000 15000 20000

Stre

ss (

MP

a)

Microstrain

UHSM - Control

UHSM-1% [13 mm]

UHSM-2% [13 mm]

y = 0.0277x + 38R² = 0.97

y = 4.48x + 38R² = 0.926

0 50 100 150 200 250 300 350 400

30.0

32.5

35.0

37.5

40.0

42.5

45.0

47.5

50.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

RI'

E (

GP

a)

Reinforcement Index, RI

RIRI'

Influence of micro-fiber dosage and

geometry

~Ec valuey = 2.4015x + 113

R² = 0.984

y = 37.44x + 113R² = 0.913

0 5 10 15 20 25 30 35 40

25

50

75

100

125

150

175

200

225

250

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

RI'

σσ p(M

Pa)

Reinforcement Index, RI

RIRI'

~σc value

Influence ofmicro-fiber dosage

and geometry

2

21

AX BXY

CX DX

+=+ +

2

21

AX BXY

CX DX

+=+ +

(c) Strain at peak point, εp

(ii) Effect of reinforcement indices (RI and RI’) on E, σp and εp properties of UHSM

y = 6.5x + 3437R² = 0.922

y = 9.26x + 3437R² = 0.715

0 50 100 150 200 250 300 350 400

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

RI'

ε p(m

icro

-str

ain)

Reinforcement Index, RI

RIRI'

~εc value

Influence of micro-fiber dosage and

geometry

Fig. 10. Predicted r–e curve and other properties of UHSM from analytical model.

K.V. Harish et al. / Construction and Building Materials 49 (2013) 781–796 793

(b), respectively. As these figures show, the SOC value of the tough-ness for UHSM was found to significantly increase with increase inthe micro-fiber dosage as expected. At a constant micro-fiber vol-ume dosage of 2%, the SOC value for EAp was 74% and 139% forshort and long fibers, respectively, and the percentage increase inthe values due to increase in the fiber length was 87%. Similarlyat the same micro-fiber volume dosage, the SOC value for EAf

was 768% (or 7.68 times) and 506% (or 5.06 times) for short and

long fibers, respectively, and the percentage increase in SOC valuesdue to increase in the fiber length was 51%.

The effect of reinforcement index on the EAp and EAf of the r–ecurve is shown in Fig. 11(ii) – (a) and (ii) – (b), respectively. Asthese figures show, a linear equation similar to Eq. (9) was foundto closely fit all the experimental data points and, both the EAp

and EAf were found to increase with increase in reinforcementindices. For EAp, the weightage factors a, b and c representing RI0

Table 7Weightage factors, R-square value and slope of the linear Eq. (9) for different property.

Property of fibered UHSM*, y Property of non-fibered UHSM**, yc Weightage factor Slope R-square value

a b c

For RI For RI0 For RI For RI0 For RI For RI0 For RI For RI0 For RI For RI0

Ef Ec 1.000 1.530 1.000 1.000 1.000 1.000 4.48 0.0277 0.93 0.97rpf rpc 1.000 1.444 1.000 0.976 1.000 �0.158 37.44 2.4015 0.91 0.98epf epc 1.000 1.000 1.000 0.488 1.000 1.816 9.26 6.3250 0.71 0.92

* Ef, rpf, and epf are the modulus of elasticity, stress at peak point and strain at peak point of the fibered UHSM.** Ec, rpc, and epc are the modulus of elasticity, stress at peak point and strain at peak point of non-fibered UHSM; R-square or R2 is the co-efficient of determination.

(a) On EAp (b) On EAf

(i) Effect of micro-fiber dosage on toughness characteristics of UHSM

(a) On EAp (b) On EAf

(ii) Effect of reinforcement indices on toughness characteristics of UHSM

28

74

119

56

139

0

25

50

75

100

125

150

175

200

SOC

(%

)

Dosage of micro-fibers (%)

6 mm micro-fibers

13 mm micro-fibers

221

506

765

411

768

0

100

200

300

400

500

600

700

800

900

1000

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

SOC

(%

)

Dosage of micro-fibers (%)

6 mm micro-fibers

13 mm micro-fibers

y = 0.1888x + 0.207R² = 0.946

y = 0.4805x + 0.207R² = 0.99

0.0

0.5

1.0

1.5

2.0

2.5

RI'

EA

p(M

Pa)

Reinforcement Index, RI

RIRI"

~EAp value

Influence of micro-fiber dosage

and geometry

y = 0.83x + 0.207R² = 0.93

y = 1.1411x + 0.207R² = 0.906

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

0.0

0.5

1.0

1.5

2.0

2.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

RI'

EA

f(M

Pa)

Reinforcement Index, RI

RIRI"

~EAp value

Influence of micro-fiber dosage

and geometry

(iii) Comparison of toughness values at peak point obtained from experimental investigation and analytical modeling

0.21

0.26

0.36

0.45

0.32

0.50

0.250.28

0.32

0.46

0.32

0.45

0.190.23

0.32

0.39

0.29

0.39

0.00

0.10

0.20

0.30

0.40

0.50

0.60

UHSM (Control) UHSM-1% [6 mm] UHSM-2% [6 mm] UHSM-3% [6 mm] UHSM-1% [13 mm] UHSM-2% [13 mm]

EA

p(M

Pa)

Mixture ID

ExperimentalAnalyticalLinear elastic (assumption)

Fig. 11. Effect of micro-fibers on toughness characteristics of UHSM under uniaxial compression.

794 K.V. Harish et al. / Construction and Building Materials 49 (2013) 781–796

K.V. Harish et al. / Construction and Building Materials 49 (2013) 781–796 795

were found to be 1.322, 0.8572 and �1.984, respectively, and theslope of the linear equation was 0.4805. Similarly for EAf, theweightage factors a, b and c representing RI0 was 1.063, 0.645and �0.958, respectively, and the slope of the linear equationwas 0.83. The negative value for ‘c’ is an indication that Df affectsboth EAp and EAf directly, i.e., an increase in the Df results in theincrease in the EAp and EAf. For EAp, Df appears to be a more dom-inant factor than Lf and Vf, as the absolute values of ‘c’ is higherthan ‘a’ and ‘b’, respectively, whereas for EAf, both Df and Vf aremore dominant than Lf. In addition, higher R-square values wereobtained for RI0 than for RI, indicating that the former is a morereliable indicator of the fiber parameter than the latter.

A comparison of the EAp for the mixtures determined from ana-lytical modeling, experimental investigation and that assuming alinear elastic behavior for UHSM is shown in Fig. 11(iii). As this fig-ure shows, the experimental value for non-fibered UHSM was only11% higher than the value obtained by assuming a linear elasticbehavior. For fibered UHSM, the variations in the experimentallyobtained and assumed values were lower at lower fiber dosage lev-els, indicating that a linear elastic assumption in the UHSM behav-ior is acceptable. However at higher dosages, the experimentalvalues was significantly (15–28%) higher than the values obtainedwith linear elastic behavior. The EAp value for non-fibered UHSMobtained analytically was 19% higher than those obtained experi-mentally. In the case of fibered UHSM, the EAp value obtained ana-lytically was 0–12.5% lower or higher than those obtainedexperimentally, indicating that the analytical equation can be usedas a reliable tool to predict the experimental data.

5. Conclusions

The conclusions that can be drawn from this study are listedbelow:

(1) From the investigations performed to produce non-fiberedUHSM using conventional materials, the following infer-ences are arrived.

– The compressive strength of UHSM under NWC was

inversely proportional to the w/cm used. The range ofstrengths obtained for UHSM was low and hence, theuse of heat curing techniques was essential to elevateits strength levels.

– The use of heat curing with HWC or HAC only for aperiod from 1–3 days just after demolding was noteffective in increasing the compressive strength ofUHSM substantially. However, the use of HWC andHAC after an initial NWC period of 1–3 days and justafter demolding elevated the compressive strength ofUHSM substantially.

– A multiple curing regime involving 1 day ATC at25 �C + 2 day NWC at 25 �C + 2 day HWC at 90 �C + 2 dayHAC at 200 �C + 21 day NWC at 25 �C was found to pro-duce the highest compressive strength and was chosenas the optimized curing regime for UHSM.

(2) From the experimental investigation performed on the r–echaracteristics of UHSM in compression, the following areevident.

– The effect of heat curing was found to improve the r–e

characteristics of non-fibered UHSM substantially, withhigher improvements in its peak strength. The r–e curvefor both non-fibered and fibered UHSM showed a linearlyelastic behavior until peak.

– The fibered UHSM showed better post-peak behaviorthan non-fibered UHSM by withstanding significant loadeven at high strain levels.

– The addition of micro-fibers was found to substantiallyincrease the rp, ep and ef of UHSM, with less improvementin its E and E0 values.

– The longer fibers registered higher rp, ep and ef values forUHSM than shorter fibers.

(3) From the analytical modeling performed on the r–e charac-teristics of UHSM, the following points are evident.

– The proposed analytical model for UHSM was found to

closely fit the experimental data points of the r–e curveand hence, can be used in the prediction of r–e character-istics for concrete structures.

– The reinforcement index of micro-fibers was found to lin-early vary with E, rp and ep of UHSM and non-linearlyvary with its E0, rf and ef.

– By adopting weightage factors for each geometric param-eter (Lf, Vf and Df) of micro-fiber, the modified reinforce-ment index represented a better correlation thanreinforcement index, with more reliable R-square value.The weightage factors for the geometric parameter varieddepending on the r–e characteristics of UHSM.

– The toughness of UHSM was found to increase withincrease in the micro-fiber dosage and length. A linearrelation existed between the toughness of UHSM andreinforcement index of micro-fibers.

Acknowledgements

This entire study was conducted at Structural Engineering Re-search Center (SERC), Council of Scientific and Industrial Research(CSIR), Government of India. The authors convey their acknowl-edgement to the Director, SERC-CSIR for the financial supportand help. We also thank the Chief Scientists of Advanced MaterialsTesting Laboratory, SERC-CSIR for valuable discussions during theentire phase of this study. Special thanks to Dr. James Gibert, Clark-son University for his valuable discussions about analyticalmodeling.

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