Research Article Stress-Strain Relationship of Ca OH -Activated...

Research ArticleStress-Strain Relationship of Ca(OH)2-Activated HwangtohConcrete

Keun-Hyeok Yang1 Ju-Hyun Mun2 and Hey-Zoo Hwang3

1 Department of Plant Architectural Engineering Kyonggi University Suwon Kyonggi-do 443-760 Republic of Korea2Department of Architectural Engineering Graduate School Kyonggi University Suwon Kyonggi-do 443-760 Republic of Korea3 Department of Architecture Mokpo National University Jeonnam 534-729 Republic of Korea

Correspondence should be addressed to Keun-Hyeok Yang yangkhkyonggiackr

Received 2 January 2014 Accepted 29 January 2014 Published 4 March 2014

Academic Editors I B Topcu and J Zheng

Copyright copy 2014 Keun-Hyeok Yang et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

This study examined the stress-strain behavior of 10 calcium hydroxide (Ca(OH)2)-activated Hwangtoh concrete mixes The

volumetric ratio of the coarse aggregate (119881agg) and the water-to-binder (WB) ratio were selected as the main test variables TwoWB ratios (25 and 40) were used and the value of 119881agg varied between 0 and 400 and 0 and 465 for WB ratiosof 25 and 40 respectively The test results demonstrated that the slope of the ascending branch of the stress-strain curve ofCa(OH)

2-activated Hwangtoh concrete was smaller and it displayed a steeper drop in stress in the descending branch compared

with those of ordinary Portland cement (OPC) concrete with the same compressive strength This trend was more pronouncedwith the increase in theWB ratio and decrease in119881agg Based on the experimental observations a simple and rational stress-strainmodel was established mathematically Furthermore the modulus of elasticity and strain at peak stress of the Ca(OH)

2-activated

Hwangtoh concrete were formulated as a function of its compressive strength and119881aggThe proposed stress-strain model predictedthe actual behavior accurately whereas the previous models formulated using OPC concrete data were limited in their applicabilityto Ca(OH)

2-activated Hwangtoh concrete

1 Introduction

With the increasing importance of leadership in energy andenvironmental design (LEED) certifications for buildings andreducing greenhouse gas (GHG) emissions many concreteindustry players are strongly focusing on minimizing theuse of ordinary Portland cement (OPC) Although OPChas played a prominent role in building and infrastructuredevelopment as the basic component of concrete and mortarthe production of a ton of OPC is commonly associated withthe following environmental issues [1ndash4] (1) CO

2emissions

of 08ndash09 ton which is approximately 7 of the total GHGemissions into the earthrsquos atmosphere (2) very high energyconsumption including 90ndash100 kWh of electric power and 3-4GJ of thermal energy owing to the plasticity temperatureexceeding 1300∘C (3) natural resource depletion including180ndash190 kg of bituminous coal and 20ndash30 kg of crude oilFor these reasons the development of concrete with nil or

minimal cement has attracted significant attention since thelate 1980s

Hwangtoh has gained more interest recently as a sourcematerial for low-cement concrete especially in Korea andChina because it is known to be eco-friendly with highabsorption capacity and self-purifying characteristics aswell as offering health benefits by virtue of emitting farinfrared radiation [5ndash7] Hwangtoh is primarily clay formedby the weathering of rocks and composed of more than70 inorganic substances some organic material waterand air Yang et al [6 7] established that the workabilityand compressive strength development in calcium hydroxie(Ca(OH)

2)-activated Hwangtoh mortars are comparable to

those of OPC mortars with the same mixing proportionsHowever more extensive use of Hwangtoh concrete instructural engineering applications warrants precise evalu-ations of its inherent characteristics including mechanicalproperties inelastic deformation behavior and durability In

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 846805 9 pageshttpdxdoiorg1011552014846805

2 The Scientific World Journal

Table 1 Chemical composition of Hwangtoh ( by mass)

SiO2 Al2O3 Fe2O3 CaO MgO K2O Na2O TiO2 MnO LOIlowast

5250 3290 431 040 437 150 200 069 024 109lowastLoss on ignition

Table 2 Details of Ca(OH)2-activated Hwangtoh concrete mix proportions and summary of test results

Group Specimenlowast 119882119861 () 119878119886 () 119881agg () Unit weight (kgm3)119908119888(kgm3) 1198911015840

119888(MPa) 119864

119888(MPa) 120576

012057605

119882 119861 119878 119866 119878119901

I

25ndash100

25

100 00

180 720

1469 0

108

2419 308 17468 00033 0003825ndash75 75 143 1102 372 2424 331 18563 00031 0004225ndash60 60 229 882 595 2426 350 19873 00032 0004825ndash45 45 314 661 818 2429 350 22040 00028 0005425ndash30 30 400 441 1041 2431 369 23607 00028 00062

II

40ndash100

40

100 00

180 450

1709 0

54


119882119861 water-to-binder ratio by weight 119878119886 fine aggregate-to-total aggregate ratio by volume 119881agg volumetric ratio of coarse aggregate119882 water 119861 binder119878 fine aggregate 119866 coarse aggregate 119878119901 polycarboxylate-based high-range water-reducing admixture 119908119888 dry density of concrete 119891

1015840

119888 compressive strength

119864119888 modulus of elasticity 1205760 strain at peak stress and 12057605 strain corresponding to 051198911015840119888after the peak stress

lowastIn specimen names the first and second parts refer to the119882119861 ratio and 119878119886 ratio respectively for example 25ndash75 refers to Ca(OH)2-activated Hwangtohconcrete mix with119882119861 and 119878119886 ratios of 25 and 75 respectively

particular the compressive stress-strain relations of concreteincorporating a new binder should definitely be evaluatedfor use in the rational analysis and design of structuralelements because the cohesion between pastes and aggregateparticles significantly influences the extent of increase instrain due to the applied load [8] The stress-strain rela-tions are typically understood through various experimentsand formulated using simple equations However no suchexperimental observations on the stress-strain relations ofCa(OH)

2-activated Hwangtoh concrete are available in exist-

ing literatureThe objective of the present study is to propose a simple

and rational model for obtaining the nonlinear stress-straincurves for Ca(OH)

2-activated Hwangtoh concrete under

compression To formulate the key factor determining theslopes of the ascending and descending branches of thecurves 10 concrete mixes were prepared with a range ofwater-to-binder (119882119861) ratios by weight and fine aggregate-to-total aggregate ratios (119878119886) by volume The developedmodel was then compared with existing models [9ndash11] thatwere empirically derived from the test data on OPC concreteFurthermore the modulus of elasticity and strain at peakstress of Ca(OH)

2-activated Hwangtoh concrete were com-

pared with those of OPC concrete collected from a variety ofspecimens [12] with compressive strength in similar ranges

2 Experimental Program

21Materials Hwangtoh acquired high pozzolanic reactivityas a result of its calcination at a temperature of 850∘Cusing theHoffmanmethodThe calcinated Hwangtoh which was used

as a source material was activated by 75 Ca(OH)2 This

Hwangtoh contained less calcium oxide (CaO) but was richin both silicon oxide (SiO

2) and aluminium oxide (Al

2O3)

as inferred from Table 1 This indicates that the chemicalcomposition of Hwangtoh is very similar to that of fly ashandor metakaolin [13] All dry powdered alkali activatorswere preblended with the source materials in dry form

The measurement of the physical properties of materialsrevealed the specific gravity and specific surface area ofHwangtoh to be 28 and 3200 cm2g respectivelyThe specificgravity fineness modulus and water absorption of the sand(used as the fine aggregate) were 242 251 and 17respectively and those of the crushed granite (used as thecoarse aggregate with a maximum size of 19mm) were26 675 and 11 respectively The specific gravity andmaximum particle sizes of Ca(OH)

2were 224 and 212 120583m

respectively

22 Specimen Mix Characteristics In general with increasein the compressive strength of concrete the initial slope of itsstress-strain curve increases whereas the descending branchof the curves after peak stress has a more rapidly decreasingslope [14] Moreover concrete displays higher modulus ofelasticity (119864

119888) and smaller strain (120576

0) values at peak stress

than do mortars and pastes indicating that the volumetricratio of the coarse aggregates (119881agg) directly affects the stress-strain curve of concrete[15 16] Considering these criticalfactors the 10 cementless concrete mixes using Ca(OH)

2-

activated Hwangtoh binder were prepared with a range of119882119861 and 119878119886 ratios as listed in Table 2 The selected 119882119861ratios were 25 and 40 and within each of these ratios the

The Scientific World Journal 3

P (Load)

Concrete specimen(Φ100 times 200mm)

Electrical resistancestrain gauge

Compressometer

Steel plates

LVDT(for longitudinaldisplacement)

100

200

100

UTM bed

Spherical hinge

(for transverseLVDT

displacement)

Figure 1 Test setup and instrumentation for test region (all dimensions are in mm)

119878119886 ratio of the mixes for each119882119861 ratio varied from 30 to100 in intervals of 15 The concrete specimen with an 119878119886ratio of 100 indicates a mortar without coarse aggregatesAs a result 119881agg ranged between 0 and 400 and 0and 465 for119882119861 ratios of 25 and 40 respectively Theunit water content was fixed at 180 kgm3 for all concretemixes To achieve workability of the mixes for casting apolycarboxylate-based high-range water-reducing agent wasadded with binder ratio by weight of 15 and 12 forconcretemixes with119882119861 ratios of 25 and 40 respectively

23 Testing All concrete specimens were mixed using a panmixer of 035m3 capacity and equipped with rubber wiperblades The initial slump of fresh concrete was measured inaccordance with the ASTMC143 provision [17] Immediatelyafter casting all specimens used for plotting the stress-straincurve were cured at a constant temperature and relativehumidity of 23 plusmn 2∘C and 70 plusmn 5 respectively until testingat an age of 28 days All steel moulds were removed after1 day The stress-strain curve was recorded using 100 times200mm cylindrical concrete specimens equipped with acompressor meter comprising linear variable differentialtransducers (LVDTs) of 50mm capacity on both sides asshown in Figure 1 The compressometer was combined witha convenient unbounded device for measuring transversestrain Electrical resistance strain gages with gage length of75mm were also attached to the specimens Prior to testingboth ends of each cylinder were leveled using a grindingmachine Concentric load was applied using a universaltesting machine of 500 kN capacity equipped with a closed-loop servocontrol system Each specimen was preloaded to20 of its compressive strength after which its position wasadjusted based on strain gage and LVDT readings to achievea concentric axial load A spherical hinge was also positionedbetween the testing machine head and the specimens to

minimize eccentricity in case of a large deformation Toobtain a complete stress-strain curve a low strain rate of20times10

minus4 permin was employed Testing was continued untilthe final crushing of the concrete All test data were capturedby a data logger and stored automatically Using themeasuredstress-strain curve the 119864

119888was calculated at 40 peak stress

in accordance with the ASTM C469 provision [17]

3 Test Results and Discussion

31 General Behavior and Crack Propagation Longitudinalcracking started at 50ndash60 of the peak stress within themid-height section of the specimen The stress at whichcracks developed was independent of 119881agg As the appliedload increased the initial crack propagated toward the topand bottom surfaces of the specimens As a result the failureof specimens after peak stress was governed by the timewhen the longitudinal crack joined the top and bottomsurfaces of the specimenThewidth of the longitudinal cracksincreased sharply at 80ndash85 of the peak stress whichwas accompanied by a rapid increase in the longitudinaland transverse strains as shown in Figure 2 The rates ofincrease in those strains increased as 119881agg decreased Withrapid increase in transverse strain the volumetric change ofthe specimens started to shift from compression to tensionThis threshold point was found to occur at approximately80 and 95 of the peak stress for concrete mixes with119881agg of 0 and 40 respectively This implies that therate of increase in transverse strain due to the opening oflongitudinal cracks decreases as119881agg increases After the peakstress failure tended to occur along the longitudinal crackswhich commonly formed in the pastes between the aggregateparticles The drop in stress subsequent to peak stress wasmore rapid in concrete mixes with 119881agg = 0 than those


0

02

04

06

08

1

12

minus0002 0002 0004 0006 0008

Strain

Longitudinal strainLateral strainVolumetric change

0

Nor

mal

ized

stre

ss (fcfc

)998400

Tension Compression

(a) Specimen of 25ndash100 (119881agg = 0)

minus0002 0002 0004 0006 00080

Strain

0

02

04

06

08

1

12


Nor

mal

ized

stre

ss (fcfc

)998400

Tension Compression

(b) Specimen of 25ndash30 (119881agg = 400)

Figure 2 Typical strain behavior of Ca(OH)2-activated Hwangtoh

concrete under axial compressive load

with119881agg = 40 Figure 2 also shows that aggregate interlockaction is expected along the longitudinal cracks

32 Compressive Strength Table 2 summarizes the test resultsincluding the compressive strength (1198911015840

119888)119864119888 and strains of the

Ca(OH)2-activatedHwangtoh concrete specimensThe value

of1198911015840119888increased by 189ndash252 times as the119882119861 ratio decreased

from 40 to 25 The rate of this increase also increasedgradually as 119881agg decreased At both 119882119861 ratios the con-crete specimens developed lower 1198911015840

119888than did OPC concrete

with no supplementary cementitious materials as shown inFigure 3 However the overall pattern of the decrease in 1198911015840

119888

corresponding to an increase in the 119882119861 ratio was similarin both concrete types The best-fit curve for 1198911015840

119888confirmed

that a119882119861 ratio not exceeding approximately 30 is requiredfor structural applications of Ca(OH)

2-activated Hwangtoh

concrete The 1198911015840119888of the test concrete also decreased as 119881agg

decreased (Table 2) at rates of 17 and 38 for119882119861 ratios

0

20

40

60

80

100

20 30 40 50 60 70 80

WB ratio ()

fc

(MPa

) Best fit curve forOPC concrete

Best fit line forCa(OH)2-activated Hwangtoh concrete

Ca(OH)2-activated Hwangtoh concrete

998400

OPC concrete (Yang et al 2010)

Figure 3 Effect of the water-to-binder ratio (119882119861) on compressivestrength (1198911015840

119888)

of 25 and 40 respectively as the 119878119886 ratio increased from30 to 100 The effect of 119881agg on 119891

1015840

119888was more prominent

for a higher 119882119861 ratio Higher coarse aggregate contentleads to lower shrinkage and lower bleeding resulting inless damage to the bond between the aggregate particles andpastes [8] Hence the coarse aggregate content is regarded asthe secondary factor influencing the strength development inconcrete especially for one with a higher119882119861 ratio

33 Stress-Strain Behavior The stress-strain curves obtainedfor the concrete mixes are plotted in Figure 4 The shape ofall curves was a second-degree parabola with its vertex at thepeak stress point However the slopes of the ascending anddescending branches of the curves heavily depended on the1198911015840

119888and 119881agg values Similar to observations on OPC concrete

[9ndash11] the curves were almost linear up to approximatelyone-half of the peak stress point showing that their initialslope increased as 1198911015840

119888andor 119881agg increased Normal-weight

aggregates possess elastic modulus values that are 15ndash50times higher than those of pastes [14] causing the initial slopeof the curves to rise with increase in 119881agg Additionally theslope of the descending branch was steeper and less steepwith increasing 1198911015840

119888and 119881agg respectively though a slightly

higher value of 1198911015840119888was obtained for the concrete mix with

a higher 119881agg value but the same 119882119861 ratio Overall thedescending branch of the curve for concrete mixes with119881agg = 0 (ie specimens 25ndash100 and 40ndash100) was veryshort compared to those for mixes with coarse aggregatesThese trends were more pronounced for a119882119861 ratio of 25than for 40 leading to the inference that the mechanicalinterlocking of the coarse aggregate along the cracks relivesthe brittle fracture (as indicated by the descending branch)and improves the compressive strength of the concrete

34 Modulus of Elasticity (119864119888) The relationship of 1198911015840

119888and

119864119888of the Ca(OH)

2-activated Hwangtoh concrete is shown

in Figure 5 The figure also shows the test data for normal-weight OPC concrete with 1198911015840

119888not exceeding 50MPa as well

as predictions made by Carreira and Chursquos model [9] In


0

5

10

15

20

25

30

35

40

0 0002 0004 0006 0008

Strain

Stre

ss (M

Pa)

25ndash10025ndash7525ndash60

25ndash4525ndash30

(a) 119882119861 = 25

0

5

10

15

20

25

30

35

40

0 0002 0004 0006 0008

Strain

Stre

ss (M

Pa)


40ndash4540ndash30

(b) 119882119861 = 40

Figure 4 Stress-strain curves measured for Ca(OH)2-activated

Hwangtoh concrete

0

10000

20000

30000

40000

50000

60000

0 10 20 30 40 50

f 998400c (MPa)

Ec

(MPa

)

OPC concrete

Predictions by Carreira and Chursquos model

Best fit curve forOPC concrete

Best fit curve forCa(OH)2-activated Hwangtoh concrete


Figure 5 Modulus of elasticity (119864119888) as a function of compressive

strength (1198911015840119888)

y = 3010x

R2 = 097

y = 3610x

R2 = 052

0

10000

20000

30000

40000

50000

3 4 5 6 7 8 9 10

(f998400c )05 times (1 + Vagg 100)

075 (MPa)


Ec

(MPa

)

OPC concrete (f 998400c = 15 50MPa)ndash

Figure 6 Regression analysis for modulus of elasticity (119864119888)

their model the unit weight (119908119888) of normal-weight concrete

was assumed to be 2300 kgm3 The 119864119888of the concrete was

commonly lower than the best-fit curves determined forOPCconcrete and predictions of Carreira andChursquosmodel [9]Thedevelopment of bond microcracks at the interfaces betweenpastes and aggregate particles accelerates the nonlinearity ofthe stress-strain curves [14] possibly causing the cohesionbetween them to be lower in Ca(OH)


binder than OPCIn general the 119864

119888of concrete can be expressed as a func-

tion of 1198911015840119888and 119908

119888[14] However it was difficult to determine

the effect of 119908119888on the 119864

119888of the tested Ca(OH)

2-activated

Hwangtoh concrete because the variation in the119908119888values (in

the test) was very minimal at the same119882119861 ratios rangingbetween 2419 and 2431 kgm3 2321 and 2335 kgm3 for119882119861ratios of 25 and 40 respectivelyMoreover119864

119888was affected

by 119881agg (showing a slightly lower value in specimens with an119878119886 ratio of 60 than those with an 119878119886 ratio of 45 at similar1198911015840

119888) owing to the considerably higher modulus of elasticity in

aggregates than in pastes when individually subjected to loadIn addition an increase in the continuous cracks joining thebondmicrocracks that developed at the interface between thepastes and aggregate particles leads to a faster rate of increasein strain [8] To formulate a simple equation for119864

119888 influential

parameters such as1198911015840119888and119881agg were repeatedly combined and

adjusted through a trial-and-error approach until a relativelyhigh correlation coefficient (1198772) was obtained Based on aregression analysis of the test results the 119864

119888of Ca(OH)

2-

activated Hwangtoh concrete with 1198911015840119888lt 40MPa can be

empirically expressed as follows (see Figure 6)

119864119888= 3010(119891

1015840

119888)05

(1 +

119881agg

100)

075

(MPa) (1)

35 Strain at Peak Stress (1205760) MacGregor and Wight [14]

established that 1205760of concrete increases with increase in 1198911015840

119888

This trend was also verified for the test case from the datalisted in Table 2 As a result the existent equations for 120576

0

have mostly been empirically developed only as a function of


Ca(OH)2-activated Hwangtoh concreteOPC concrete (f998400c = 15 50MPa)

y = 00344x + 00011

R2 = 0511

y = 008x

R2 = 093

0

00005

0001

00015

0002

00025

0003

00035

0004

00045

002 0025 003 0035 004 0045 005

(f998400cEc)05(1 + Vagg 100)

minus05

120576 0

ndash

Figure 7 Regression analysis for strain (1205760) at peak stress

1198911015840

119888 However Ca(OH)

2-activatedHwangtoh concrete demon-

strated higher values of 1205760than did OPC concrete with the

same 1198911015840119888 as shown in Figure 7 These 120576

0values also increased

slightly as119881agg decreased because the increase in paste volumereduced the 119864

119888and accelerated the nonlinearity of the stress-

strain curves especially after the development of longitudinalcracks However none of the predicted equations [9ndash11]consider the effect of 119881agg on the strain although the formeris evidently the secondary factor causing the increasing strainrate Based on a regression analysis of the test results the 120576

0

of Ca(OH)2-activated Hwangtoh concrete can be written as

follows (see Figure 7)

1205760= 008(

1198911015840

119888

119864119888

)

05

(1 +

119881agg

100)

minus05

(2)

4 Mathematical Equations for Stress-StrainRelations

Figure 4 confirms that the compressive stress-strain curveof Ca(OH)

2-activated Hwangtoh concrete is parabolic and

hump-shaped with its vertex at the peak stress point Thisphysically means that the tangential modulus of elasticityhas the maximum value at the origin gradually decreases tozero at the peak stress point and becomes negative throughthe descending branch of the curve In this study the sameassumption and the following nonlinear equation [9 11 12]were applied for generating a complete curve

119884 =(1205731+ 1)119883

1198831205731+1 + 1205731

(3)

where 119884(= 1198911198881198911015840

119888) is the normalized stress 119883(= 120576

1198881205760) is the

normalized strain and119891119888is the concrete stress corresponding

to strain 120576119888 Equation (3) gives the following physical mean-

ings (1) 119884 = 0 when 119883 = 0 representing the origin point(2) 119884 = 1 when 119883 = 1 representing the peak stress point

y = minus017x + 0166

R2 = 086

00000

00010

00020

00030

00040

00050

00060

00070

092 0925 093 0935 094

(f998400cEc)001(1 + Vagg 100)

minus003

120576 05

Figure 8 Regression analysis for 12057605

of Ca(OH)2-activated Hwang-

toh concrete

(3) 119889119891119888119889120576119888= 0 when119883 = 1 or at the peak stress point

Hence the factor 1205731in (3) is a key parameter for determining

the slopes of the ascending and descending branches of thecurve with its values commonly differing in each branchTo determine the slope of the ascending branch 119864

119888was

selected as the reference parameter Because 119864119888is defined as

a secant modulus joining the origin and 40 of the peakstress substituting it in (3) results in the following equationfor determining 120573

1for the ascending branch

04(119883119886)1205731+1

+ (04 minus 119883119886) 1205731minus 119883119886= 0 for 120576

119888le 1205760 (4)

where119883119886= 04119891

1015840

1198881198641198881205760

In contrast some reviews [12 18] concluded that thesecant modulus joining the origin and 50 of the peakstress can be regarded as an adequate reference point toderive the slope of the descending branch Hence the presentstudy formulated an equation for determining 120573

1for the

descending branch using the secant modulus at 051198911015840119888as the

reference point as follows

(119883119889)1205731+1

+ (1 minus 2119883119889) 1205731minus 2119883119889= 0 for 120576

119888gt 1205760 (5)

where 119883119889= 120576051205760and 12057605

is the strain corresponding to051198911015840119888after peak stress The values of 120573

1in the nonlinear

equations (4) and (5) can be calculated through numericalanalysis for the given material properties of 119864

119888 1205760 and 120576

05

41 Strain at 50 of Peak Stress in Descending Branch (12057605)

The slope of the descending branch of the curve depends on1198911015840

119888and 119881agg as inferred from Table 1 A regression analysis

was conducted using these parameters (as shown in Figure 8)similar to the procedure employed for 120576

0to propose a simple

equation for 12057605 yielding the following equation

12057605= minus017 [(

1198911015840

119888

119864119888

)

001

(1 +

119881agg

100)

minus003

] + 0166 (6)

42 Key Parameter (1205731) An analytical parametric study was

conducted to formulate 1205731 which determines the slopes


Table 3 Statistical values of NRMSEs calculated by comparing stress-strain curves of various models to experimental data

Error coefficientslowast Prediction modelsCarreira and Chu [9] Wee et al [11] Lu and Zhao [10] This study

120574119890119898

0238 0254 0259 0091120574119890119904

0075 0072 0050 0039lowast120574119890119898 and 120574119890119904 refer to the mean and standard deviation respectively of the NRMSE calculated for each specimen using the following equation

NRMSE = (1(119891119888)119898)sum [((119891119888)Exp minus (119891119888)Pre)2119899]12

where (119891119888)119898 is themean of themeasured stress (119891119888)Exp and (119891119888)Pre are experimental and predicted stressesrespectively and 119899 is the number of measured points

of the ascending and descending branches For given 1198911015840119888

and 119881agg the material properties of 119864119888 1205760 and 120576

05were

calculated using (1) (2) and (6) respectively Subsequentlythe two non-linear equations ((4) and (5)) were solvedusing the Newton-Raphson method Considering the prac-tical strength development in Ca(OH)


concrete the variables1198911015840119888and119881agg in the analytical parametric

study were selected to range between 10 and 50MPa and0 and 60 respectively Finally the analytically obtainedresults were statistically optimized to drive the following 120573

1

equations for the ascending branch (Figure 9(a)) and thedescending branch (Figure 9(b))

1205731= 033 explfloor065(

1198911015840

119888

1198910

)

05

(1 +

119881agg

100)

02

rfloor for 120576119888le 1205760

(7)

1205731= 043 explfloor21(

1198911015840

119888

1198910

)

05

(1 +

119881agg

100)

minus25

rfloor for 120576119888gt 1205760

(8)

where1198910(= 10MPa) is the reference value for the compressive

strength of concrete A higher value of 1205731in (3) produces

larger slopes of the ascending and descending branchesHence an increase in the value of 119881agg in (7) and (8) resultsin a higher value of 119864

119888and less steep slope of the descending

branch as observed in Figure 4In summary the compressive stress-strain relations for

unconfined Ca(OH)2-activated Hwangtoh concrete can be

generalized as follows

119891119888= [(1205731+ 1) (120576

1198881205760)

(1205761198881205760)1205731+1

+ 1205731

]1198911015840

119888 (9)

where 1205760and 120573

1are obtained using (2) and (7) or (8)

respectively The stress-strain relations proposed for theconcrete need to be reexamined for strengths of more than40MPa because these equations have been derived using thelimited test data pertaining to the present study

5 Comparisons of Model and Test Results

Figure 10 shows the typical comparisons of the predictedand measured curves for different 119882119861 ratios and 119881aggvalues The figure also displays the curves pertaining toprevious models [9ndash11] that were empirically formulatedusingOPC test data Table 3 lists themean (120574

119890119898) and standard

0 05 1 15 2 25 3 35 40

05

1

15

2

25

3

35

4

Best fit curvey = 033exp(065x)

R2 = 099

f998400c = 10 50MPaVagg = 0 60

1205731

(f998400cf0)05(1 + Vagg 100)

02

ndashndash

(a) For ascending branch

0

1

2

3

4

5

6

7

8

9

10

0 02 04 06 08 1 12

1205731

(f998400cf0)05(1 + Vagg 100)

25minus


R2 = 098

f998400c = 10 50MPaVagg = 0 60

ndashndash

(b) For descending branch

Figure 9 Formulation of 1205731through numerical analysis

deviation (120574119890119904) of the normalized root-mean-square errors

(NRMSE) calculated for each stress-strain curve In generalthe previous models commonly overestimate the slope ofthe ascending branch and underestimate the value of 120576

0

This trend is more pronounced with the increase in 1198911015840119888and

decrease in119881agg Furthermore the equations proposed by [9]and Wee et al [11] overestimate the stress in the descendingbranch particularly for concrete with low119881agg Consequentlythe previous models yield high values for 120574

119890119898(gt0238) and

120574119890119904(gt0050) and are limited in their applicability toCa(OH)

2-

activated Hwangtoh concrete and the error associated withthem gradually increases as 119881agg decreases

In contrast to the previous models for OPC concrete thepredictions obtained from the proposedmodel for Ca(OH)

2-

activated Hwangtoh concrete are in better agreement with


0

5

10

15

20

25

30

35

0 0001 0002 0003

Strain

Stre

ss (M

Pa)

(a) Specimen 25ndash100 (119882119861 = 25 119881agg = 0)

Strain

Stre

ss (M

Pa)

0

5

10

15

20

25

30

35

40

0 0002 0004 0006 0008

(b) Specimen 25ndash30 (119882119861 = 25 119881agg = 40)

Strain

Stre

ss (M

Pa)

ExpCarreira and ChuWee et al

Lu and ZhaoThis study

0

2

4

6

8

10

12

14

0 0002 0004

(c) Specimen 40ndash100 (119882119861 = 40 119881agg = 0)

Strain

Stre

ss (M

Pa)



0

5

10

15

20

25

0 0002 0004 0006

(d) Specimen 40ndash30 (119882119861 = 40 119881agg = 465)

Figure 10 Typical comparisons of predicted and measured stress-strain curves for various119882119861 ratio and 119881agg values

test results showing relatively higher accuracy for bothascending and descending branches judging from the con-siderably lower NRMSE values (0091 and 0039 for 120574

119890119898

and 120574119890119904 resp) These results are consistent with the actual

responses in particular they accurately reflect the effect of119881agg on 120576

0and the slopes of the ascending and descending

branches Hence the proposed model is useful for accuratelyevaluating the compressive stress-strain behavior of low- andmedium-strength Ca(OH)


6 Conclusions

The present study examined the stress-strain behavior ofCa(OH)

2-activated Hwangtoh concrete with different 119882119861

and 119881agg values The 119864119888and 1205760values of the specimens were

compared to those of OPC concrete compiled by Yang et alBased on the experimental data a simple equation wasestablished to reasonably predict the stress-strain relations ofCa(OH)

2-activated Hwangtoh concrete under compression


though further verification is required for strengths of morethan 40MPa because of the limited data used for empiricalfitting From the experimental and comparative observationsthe following conclusions may be drawn

(1) For the same 119882119861 the 1198911015840119888of Ca(OH)

2-activated

Hwangtoh concrete was commonly lower than thatof OPC concrete however the test concrete gainedstrength development comparable to that of struc-tural concrete at a119882119861 less than 30

(2) With decrease in 119881agg the slope of the ascendingbranch of the stress-strain curve and 1198911015840

119888decreased

whereas 1205760and the declining slope of the descending

branch of the curve increased This observation wasmore pronounced as the119882119861 ratio increased

(3) Compared to OPC concrete with the same 1198911015840119888

Ca(OH)2-activated Hwangtoh concrete had lower 119864

119888

and larger 1205760 showing greater discrepancy as 119881agg

decreased Hence the119864119888and 1205760of Ca(OH)

2-activated

Hwangtoh concrete could be formulated as a functionof 1198911015840119888and 119881agg

(4) Previousmodels formulated usingOPC concrete datarevealed limitations in their applicability to Ca(OH)

2-

activated Hwangtoh concrete whereas the proposedstress-strain model predicted the actual behaviorquite accurately as evidenced by the much lowerNRMSE values

Conflict of Interests

The authors declare that they have no conflict of interestsregarding the publication of this paper

Acknowledgment

This research was supported by the Public Welfare and SafetyResearch Program through the National Research Founda-tion of Korea (NRF) funded by the Ministry of Science ICTand Future Planning (No 2013067519)

References

[1] B L Damineli F M Kemeid P S Aguiar and V M JohnldquoMeasuring the eco-efficiency of cement userdquo Cement andConcrete Composites vol 32 no 8 pp 555ndash562 2010

[2] E Gartner ldquoIndustrially interesting approaches to ldquolow-CO2rdquo

cementsrdquo Cement and Concrete Research vol 34 no 9 pp1489ndash1498 2004

[3] S O Ogbeide ldquoDeveloping an optimization model for CO2

reduction in cement production processrdquo Journal of EngineeringScience and Technology Review vol 3 no 1 pp 85ndash88 2010

[4] K H Yang J K Song and K I Song ldquoAssessment ofCO2reduction of alkali-activated concreterdquo Journal of Cleaner

Production vol 39 no 1 pp 265ndash272 2013[5] H Z Hwang A study on the method activating kaolin and

mortar amp concrete mixed with active kaolin [PhD thesis] SeoulNational University Seoul Republic of Korea 1997

[6] K-H Yang H-Z Hwang and S Lee ldquoEffects of water-binderratio and fine aggregate-total aggregate ratio on the propertiesof hwangtoh-based alkali-activated concreterdquo Journal of Mate-rials in Civil Engineering vol 22 no 9 pp 887ndash896 2010

[7] K-H Yang H-Z Hwang S-Y Kim and J-K Song ldquoDevelop-ment of a cementless mortar using hwangtoh binderrdquo Buildingand Environment vol 42 no 10 pp 3717ndash3725 2007

[8] AMNevilleProperties of Concrete AddisonWesley LongmanNew York NY USA 1995

[9] D J Carreira and K-H Chu ldquoStress-strain relationship forplain concrete in compressionrdquo Journal of the American Con-crete Institute vol 82 no 6 pp 797ndash804 1985

[10] Z-H Lu and Y-G Zhao ldquoEmpirical stress-strain model forunconfined high-strength concrete under uniaxial compres-sionrdquo Journal of Materials in Civil Engineering vol 22 no 11pp 1181ndash1186 2010

[11] T H Wee M S Chin and M A Mansur ldquoStress-strainrelationship of high-strength concrete in compressionrdquo Journalof Materials in Civil Engineering vol 8 no 2 pp 70ndash76 1996

[12] KH Yang and J I Sim ldquoModeling of themechanical propertiesof structural lightweight concrete based on size effectsrdquo TechRep Department of Plant Architectural Engineering KyonggiUniversity 2011

[13] P Dinakar P K Sahoo and G Sriram ldquoEffect of metakaolincontent on the properties of high strength concreterdquo Interna-tional Journal of Concrete Structures and Materials vol 7 no 3pp 215ndash223 2013

[14] J GMacGregor and J KWightReinforcedConcreteMechanicsand Design Prentice-Hall New York NY USA 2006

[15] T T Ghebrab and P Soroushian ldquoMechanical properties ofcement mortar development of structure-property relation-shipsrdquo International Journal of Concrete Structures and Materi-als vol 5 no 1 pp 3ndash10 2011

[16] K H Yang J H Mun and J K Song ldquoTests on cementlessalkali-activated slag concrete using lightweight aggregatesrdquoInternational Journal of Concrete Structures and Materials vol5 no 2 pp 125ndash131 2011

[17] ASTM C 143 C 469 Annual Book of ASTM Standards V 402ASTM International West Conshohocken Pa USA 2012

[18] A vanGysel and L Taerwe ldquoAnalytical formulation of the com-plete stress-strain curve for high strength concreterdquo Materialsand Structures vol 29 no 193 pp 529ndash533 1996

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Table 1 Chemical composition of Hwangtoh ( by mass)

SiO2 Al2O3 Fe2O3 CaO MgO K2O Na2O TiO2 MnO LOIlowast

5250 3290 431 040 437 150 200 069 024 109lowastLoss on ignition

Table 2 Details of Ca(OH)2-activated Hwangtoh concrete mix proportions and summary of test results

Group Specimenlowast 119882119861 () 119878119886 () 119881agg () Unit weight (kgm3)119908119888(kgm3) 1198911015840

119888(MPa) 119864

119888(MPa) 120576

012057605

119882 119861 119878 119866 119878119901

I

25ndash100

25

100 00

180 720

1469 0

108


II

40ndash100

40

100 00

180 450

1709 0

54


119882119861 water-to-binder ratio by weight 119878119886 fine aggregate-to-total aggregate ratio by volume 119881agg volumetric ratio of coarse aggregate119882 water 119861 binder119878 fine aggregate 119866 coarse aggregate 119878119901 polycarboxylate-based high-range water-reducing admixture 119908119888 dry density of concrete 119891

1015840

119888 compressive strength

119864119888 modulus of elasticity 1205760 strain at peak stress and 12057605 strain corresponding to 051198911015840119888after the peak stress

lowastIn specimen names the first and second parts refer to the119882119861 ratio and 119878119886 ratio respectively for example 25ndash75 refers to Ca(OH)2-activated Hwangtohconcrete mix with119882119861 and 119878119886 ratios of 25 and 75 respectively

particular the compressive stress-strain relations of concreteincorporating a new binder should definitely be evaluatedfor use in the rational analysis and design of structuralelements because the cohesion between pastes and aggregateparticles significantly influences the extent of increase instrain due to the applied load [8] The stress-strain rela-tions are typically understood through various experimentsand formulated using simple equations However no suchexperimental observations on the stress-strain relations ofCa(OH)

2-activated Hwangtoh concrete are available in exist-

ing literatureThe objective of the present study is to propose a simple

and rational model for obtaining the nonlinear stress-straincurves for Ca(OH)

2-activated Hwangtoh concrete under

compression To formulate the key factor determining theslopes of the ascending and descending branches of thecurves 10 concrete mixes were prepared with a range ofwater-to-binder (119882119861) ratios by weight and fine aggregate-to-total aggregate ratios (119878119886) by volume The developedmodel was then compared with existing models [9ndash11] thatwere empirically derived from the test data on OPC concreteFurthermore the modulus of elasticity and strain at peakstress of Ca(OH)

2-activated Hwangtoh concrete were com-

pared with those of OPC concrete collected from a variety ofspecimens [12] with compressive strength in similar ranges

2 Experimental Program

21Materials Hwangtoh acquired high pozzolanic reactivityas a result of its calcination at a temperature of 850∘Cusing theHoffmanmethodThe calcinated Hwangtoh which was used

as a source material was activated by 75 Ca(OH)2 This

Hwangtoh contained less calcium oxide (CaO) but was richin both silicon oxide (SiO

2) and aluminium oxide (Al

2O3)

as inferred from Table 1 This indicates that the chemicalcomposition of Hwangtoh is very similar to that of fly ashandor metakaolin [13] All dry powdered alkali activatorswere preblended with the source materials in dry form

The measurement of the physical properties of materialsrevealed the specific gravity and specific surface area ofHwangtoh to be 28 and 3200 cm2g respectivelyThe specificgravity fineness modulus and water absorption of the sand(used as the fine aggregate) were 242 251 and 17respectively and those of the crushed granite (used as thecoarse aggregate with a maximum size of 19mm) were26 675 and 11 respectively The specific gravity andmaximum particle sizes of Ca(OH)

2were 224 and 212 120583m

respectively

22 Specimen Mix Characteristics In general with increasein the compressive strength of concrete the initial slope of itsstress-strain curve increases whereas the descending branchof the curves after peak stress has a more rapidly decreasingslope [14] Moreover concrete displays higher modulus ofelasticity (119864

119888) and smaller strain (120576

0) values at peak stress

than do mortars and pastes indicating that the volumetricratio of the coarse aggregates (119881agg) directly affects the stress-strain curve of concrete[15 16] Considering these criticalfactors the 10 cementless concrete mixes using Ca(OH)

2-

activated Hwangtoh binder were prepared with a range of119882119861 and 119878119886 ratios as listed in Table 2 The selected 119882119861ratios were 25 and 40 and within each of these ratios the


P (Load)



Compressometer

Steel plates


100

200

100

UTM bed

Spherical hinge

(for transverseLVDT

displacement)











0

02

04

06

08

1

12

minus0002 0002 0004 0006 0008

Strain


0

Nor

mal

ized

stre

ss (fcfc

)998400

Tension Compression


minus0002 0002 0004 0006 00080

Strain

0

02

04

06

08

1

12


Nor

mal

ized

stre

ss (fcfc

)998400

Tension Compression












119888


119888confirmed





0

20

40

60

80

100

20 30 40 50 60 70 80

WB ratio ()

fc

(MPa




998400



119888)


1015840












119888and

119864119888of the Ca(OH)






0

5

10

15

20

25

30

35

40

0 0002 0004 0006 0008

Strain

Stre

ss (M

Pa)


25ndash4525ndash30

(a) 119882119861 = 25

0

5

10

15

20

25

30

35

40

0 0002 0004 0006 0008

Strain

Stre

ss (M

Pa)


40ndash4540ndash30

(b) 119882119861 = 40


Hwangtoh concrete

0

10000

20000

30000

40000

50000

60000

0 10 20 30 40 50

f 998400c (MPa)

Ec

(MPa

)

OPC concrete






strength (1198911015840119888)

y = 3010x

R2 = 097

y = 3610x

R2 = 052

0

10000

20000

30000

40000

50000

3 4 5 6 7 8 9 10

(f998400c )05 times (1 + Vagg 100)

075 (MPa)


Ec

(MPa

)









tion of 1198911015840119888and 119908




2-activated



119888was affected




119888 influential



119888of Ca(OH)

2-



119864119888= 3010(119891

1015840

119888)05

(1 +

119881agg

100)

075

(MPa) (1)



119888


0




y = 00344x + 00011

R2 = 0511

y = 008x

R2 = 093

0

00005

0001

00015

0002

00025

0003

00035

0004

00045

002 0025 003 0035 004 0045 005

(f998400cEc)05(1 + Vagg 100)

minus05

120576 0

ndash


1198911015840









0



1205760= 008(

1198911015840

119888

119864119888

)

05

(1 +

119881agg

100)

minus05

(2)





119884 =(1205731+ 1)119883

1198831205731+1 + 1205731

(3)

where 119884(= 1198911198881198911015840


1198881205760) is the




y = minus017x + 0166

R2 = 086

00000

00010

00020

00030

00040

00050

00060

00070

092 0925 093 0935 094

(f998400cEc)001(1 + Vagg 100)

minus003

120576 05



toh concrete




119888was




04(119883119886)1205731+1

+ (04 minus 119883119886) 1205731minus 119883119886= 0 for 120576

119888le 1205760 (4)

where119883119886= 04119891

1015840

1198881198641198881205760


1for the



(119883119889)1205731+1

+ (1 minus 2119883119889) 1205731minus 2119883119889= 0 for 120576

119888gt 1205760 (5)

where 119883119889= 120576051205760and 12057605


1in the nonlinear


119888 1205760 and 120576

05







12057605= minus017 [(

1198911015840

119888

119864119888

)

001

(1 +

119881agg

100)

minus003

] + 0166 (6)






120574119890119898

0238 0254 0259 0091120574119890119904






05were





1


1205731= 033 explfloor065(

1198911015840

119888

1198910

)

05

(1 +

119881agg

100)

02

rfloor for 120576119888le 1205760

(7)

1205731= 043 explfloor21(

1198911015840

119888

1198910

)

05

(1 +

119881agg

100)

minus25

rfloor for 120576119888gt 1205760

(8)








119891119888= [(1205731+ 1) (120576

1198881205760)

(1205761198881205760)1205731+1

+ 1205731

]1198911015840

119888 (9)

where 1205760and 120573






0 05 1 15 2 25 3 35 40

05

1

15

2

25

3

35

4


R2 = 099

f998400c = 10 50MPaVagg = 0 60

1205731

(f998400cf0)05(1 + Vagg 100)

02

ndashndash


0

1

2

3

4

5

6

7

8

9

10

0 02 04 06 08 1 12

1205731

(f998400cf0)05(1 + Vagg 100)

25minus


R2 = 098

f998400c = 10 50MPaVagg = 0 60

ndashndash





0



119890119898(gt0238) and


2-



2-



0

5

10

15

20

25

30

35

0 0001 0002 0003

Strain

Stre

ss (M

Pa)


Strain

Stre

ss (M

Pa)

0

5

10

15

20

25

30

35

40

0 0002 0004 0006 0008


Strain

Stre

ss (M

Pa)



0

2

4

6

8

10

12

14

0 0002 0004


Strain

Stre

ss (M

Pa)



0

5

10

15

20

25

0 0002 0004 0006




119890119898






6 Conclusions









2-activated



119888decreased





119888



2-activated



2-




Acknowledgment


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










P (Load)



Compressometer

Steel plates


100

200

100

UTM bed

Spherical hinge

(for transverseLVDT

displacement)











0

02

04

06

08

1

12

minus0002 0002 0004 0006 0008

Strain


0

Nor

mal

ized

stre

ss (fcfc

)998400

Tension Compression


minus0002 0002 0004 0006 00080

Strain

0

02

04

06

08

1

12


Nor

mal

ized

stre

ss (fcfc

)998400

Tension Compression












119888


119888confirmed





0

20

40

60

80

100

20 30 40 50 60 70 80

WB ratio ()

fc

(MPa




998400



119888)


1015840












119888and

119864119888of the Ca(OH)






0

5

10

15

20

25

30

35

40

0 0002 0004 0006 0008

Strain

Stre

ss (M

Pa)


25ndash4525ndash30

(a) 119882119861 = 25

0

5

10

15

20

25

30

35

40

0 0002 0004 0006 0008

Strain

Stre

ss (M

Pa)


40ndash4540ndash30

(b) 119882119861 = 40


Hwangtoh concrete

0

10000

20000

30000

40000

50000

60000

0 10 20 30 40 50

f 998400c (MPa)

Ec

(MPa

)

OPC concrete






strength (1198911015840119888)

y = 3010x

R2 = 097

y = 3610x

R2 = 052

0

10000

20000

30000

40000

50000

3 4 5 6 7 8 9 10

(f998400c )05 times (1 + Vagg 100)

075 (MPa)


Ec

(MPa

)









tion of 1198911015840119888and 119908




2-activated



119888was affected




119888 influential



119888of Ca(OH)

2-



119864119888= 3010(119891

1015840

119888)05

(1 +

119881agg

100)

075

(MPa) (1)



119888


0




y = 00344x + 00011

R2 = 0511

y = 008x

R2 = 093

0

00005

0001

00015

0002

00025

0003

00035

0004

00045

002 0025 003 0035 004 0045 005

(f998400cEc)05(1 + Vagg 100)

minus05

120576 0

ndash


1198911015840









0



1205760= 008(

1198911015840

119888

119864119888

)

05

(1 +

119881agg

100)

minus05

(2)





119884 =(1205731+ 1)119883

1198831205731+1 + 1205731

(3)

where 119884(= 1198911198881198911015840


1198881205760) is the




y = minus017x + 0166

R2 = 086

00000

00010

00020

00030

00040

00050

00060

00070

092 0925 093 0935 094

(f998400cEc)001(1 + Vagg 100)

minus003

120576 05



toh concrete




119888was




04(119883119886)1205731+1

+ (04 minus 119883119886) 1205731minus 119883119886= 0 for 120576

119888le 1205760 (4)

where119883119886= 04119891

1015840

1198881198641198881205760


1for the



(119883119889)1205731+1

+ (1 minus 2119883119889) 1205731minus 2119883119889= 0 for 120576

119888gt 1205760 (5)

where 119883119889= 120576051205760and 12057605


1in the nonlinear


119888 1205760 and 120576

05







12057605= minus017 [(

1198911015840

119888

119864119888

)

001

(1 +

119881agg

100)

minus003

] + 0166 (6)






120574119890119898

0238 0254 0259 0091120574119890119904






05were





1


1205731= 033 explfloor065(

1198911015840

119888

1198910

)

05

(1 +

119881agg

100)

02

rfloor for 120576119888le 1205760

(7)

1205731= 043 explfloor21(

1198911015840

119888

1198910

)

05

(1 +

119881agg

100)

minus25

rfloor for 120576119888gt 1205760

(8)








119891119888= [(1205731+ 1) (120576

1198881205760)

(1205761198881205760)1205731+1

+ 1205731

]1198911015840

119888 (9)

where 1205760and 120573






0 05 1 15 2 25 3 35 40

05

1

15

2

25

3

35

4


R2 = 099

f998400c = 10 50MPaVagg = 0 60

1205731

(f998400cf0)05(1 + Vagg 100)

02

ndashndash


0

1

2

3

4

5

6

7

8

9

10

0 02 04 06 08 1 12

1205731

(f998400cf0)05(1 + Vagg 100)

25minus


R2 = 098

f998400c = 10 50MPaVagg = 0 60

ndashndash





0



119890119898(gt0238) and


2-



2-



0

5

10

15

20

25

30

35

0 0001 0002 0003

Strain

Stre

ss (M

Pa)


Strain

Stre

ss (M

Pa)

0

5

10

15

20

25

30

35

40

0 0002 0004 0006 0008


Strain

Stre

ss (M

Pa)



0

2

4

6

8

10

12

14

0 0002 0004


Strain

Stre

ss (M

Pa)



0

5

10

15

20

25

0 0002 0004 0006




119890119898






6 Conclusions









2-activated



119888decreased





119888



2-activated



2-




Acknowledgment


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

02

04

06

08

1

12

minus0002 0002 0004 0006 0008

Strain


0

Nor

mal

ized

stre

ss (fcfc

)998400

Tension Compression


minus0002 0002 0004 0006 00080

Strain

0

02

04

06

08

1

12


Nor

mal

ized

stre

ss (fcfc

)998400

Tension Compression












119888


119888confirmed





0

20

40

60

80

100

20 30 40 50 60 70 80

WB ratio ()

fc

(MPa




998400



119888)


1015840












119888and

119864119888of the Ca(OH)






0

5

10

15

20

25

30

35

40

0 0002 0004 0006 0008

Strain

Stre

ss (M

Pa)


25ndash4525ndash30

(a) 119882119861 = 25

0

5

10

15

20

25

30

35

40

0 0002 0004 0006 0008

Strain

Stre

ss (M

Pa)


40ndash4540ndash30

(b) 119882119861 = 40


Hwangtoh concrete

0

10000

20000

30000

40000

50000

60000

0 10 20 30 40 50

f 998400c (MPa)

Ec

(MPa

)

OPC concrete






strength (1198911015840119888)

y = 3010x

R2 = 097

y = 3610x

R2 = 052

0

10000

20000

30000

40000

50000

3 4 5 6 7 8 9 10

(f998400c )05 times (1 + Vagg 100)

075 (MPa)


Ec

(MPa

)









tion of 1198911015840119888and 119908




2-activated



119888was affected




119888 influential



119888of Ca(OH)

2-



119864119888= 3010(119891

1015840

119888)05

(1 +

119881agg

100)

075

(MPa) (1)



119888


0




y = 00344x + 00011

R2 = 0511

y = 008x

R2 = 093

0

00005

0001

00015

0002

00025

0003

00035

0004

00045

002 0025 003 0035 004 0045 005

(f998400cEc)05(1 + Vagg 100)

minus05

120576 0

ndash


1198911015840









0



1205760= 008(

1198911015840

119888

119864119888

)

05

(1 +

119881agg

100)

minus05

(2)





119884 =(1205731+ 1)119883

1198831205731+1 + 1205731

(3)

where 119884(= 1198911198881198911015840


1198881205760) is the




y = minus017x + 0166

R2 = 086

00000

00010

00020

00030

00040

00050

00060

00070

092 0925 093 0935 094

(f998400cEc)001(1 + Vagg 100)

minus003

120576 05



toh concrete




119888was




04(119883119886)1205731+1

+ (04 minus 119883119886) 1205731minus 119883119886= 0 for 120576

119888le 1205760 (4)

where119883119886= 04119891

1015840

1198881198641198881205760


1for the



(119883119889)1205731+1

+ (1 minus 2119883119889) 1205731minus 2119883119889= 0 for 120576

119888gt 1205760 (5)

where 119883119889= 120576051205760and 12057605


1in the nonlinear


119888 1205760 and 120576

05







12057605= minus017 [(

1198911015840

119888

119864119888

)

001

(1 +

119881agg

100)

minus003

] + 0166 (6)






120574119890119898

0238 0254 0259 0091120574119890119904






05were





1


1205731= 033 explfloor065(

1198911015840

119888

1198910

)

05

(1 +

119881agg

100)

02

rfloor for 120576119888le 1205760

(7)

1205731= 043 explfloor21(

1198911015840

119888

1198910

)

05

(1 +

119881agg

100)

minus25

rfloor for 120576119888gt 1205760

(8)








119891119888= [(1205731+ 1) (120576

1198881205760)

(1205761198881205760)1205731+1

+ 1205731

]1198911015840

119888 (9)

where 1205760and 120573






0 05 1 15 2 25 3 35 40

05

1

15

2

25

3

35

4


R2 = 099

f998400c = 10 50MPaVagg = 0 60

1205731

(f998400cf0)05(1 + Vagg 100)

02

ndashndash


0

1

2

3

4

5

6

7

8

9

10

0 02 04 06 08 1 12

1205731

(f998400cf0)05(1 + Vagg 100)

25minus


R2 = 098

f998400c = 10 50MPaVagg = 0 60

ndashndash





0



119890119898(gt0238) and


2-



2-



0

5

10

15

20

25

30

35

0 0001 0002 0003

Strain

Stre

ss (M

Pa)


Strain

Stre

ss (M

Pa)

0

5

10

15

20

25

30

35

40

0 0002 0004 0006 0008


Strain

Stre

ss (M

Pa)



0

2

4

6

8

10

12

14

0 0002 0004


Strain

Stre

ss (M

Pa)



0

5

10

15

20

25

0 0002 0004 0006




119890119898






6 Conclusions









2-activated



119888decreased





119888



2-activated



2-




Acknowledgment


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

5

10

15

20

25

30

35

40

0 0002 0004 0006 0008

Strain

Stre

ss (M

Pa)


25ndash4525ndash30

(a) 119882119861 = 25

0

5

10

15

20

25

30

35

40

0 0002 0004 0006 0008

Strain

Stre

ss (M

Pa)


40ndash4540ndash30

(b) 119882119861 = 40


Hwangtoh concrete

0

10000

20000

30000

40000

50000

60000

0 10 20 30 40 50

f 998400c (MPa)

Ec

(MPa

)

OPC concrete






strength (1198911015840119888)

y = 3010x

R2 = 097

y = 3610x

R2 = 052

0

10000

20000

30000

40000

50000

3 4 5 6 7 8 9 10

(f998400c )05 times (1 + Vagg 100)

075 (MPa)


Ec

(MPa

)









tion of 1198911015840119888and 119908




2-activated



119888was affected




119888 influential



119888of Ca(OH)

2-



119864119888= 3010(119891

1015840

119888)05

(1 +

119881agg

100)

075

(MPa) (1)



119888


0




y = 00344x + 00011

R2 = 0511

y = 008x

R2 = 093

0

00005

0001

00015

0002

00025

0003

00035

0004

00045

002 0025 003 0035 004 0045 005

(f998400cEc)05(1 + Vagg 100)

minus05

120576 0

ndash


1198911015840









0



1205760= 008(

1198911015840

119888

119864119888

)

05

(1 +

119881agg

100)

minus05

(2)





119884 =(1205731+ 1)119883

1198831205731+1 + 1205731

(3)

where 119884(= 1198911198881198911015840


1198881205760) is the




y = minus017x + 0166

R2 = 086

00000

00010

00020

00030

00040

00050

00060

00070

092 0925 093 0935 094

(f998400cEc)001(1 + Vagg 100)

minus003

120576 05



toh concrete




119888was




04(119883119886)1205731+1

+ (04 minus 119883119886) 1205731minus 119883119886= 0 for 120576

119888le 1205760 (4)

where119883119886= 04119891

1015840

1198881198641198881205760


1for the



(119883119889)1205731+1

+ (1 minus 2119883119889) 1205731minus 2119883119889= 0 for 120576

119888gt 1205760 (5)

where 119883119889= 120576051205760and 12057605


1in the nonlinear


119888 1205760 and 120576

05







12057605= minus017 [(

1198911015840

119888

119864119888

)

001

(1 +

119881agg

100)

minus003

] + 0166 (6)






120574119890119898

0238 0254 0259 0091120574119890119904






05were





1


1205731= 033 explfloor065(

1198911015840

119888

1198910

)

05

(1 +

119881agg

100)

02

rfloor for 120576119888le 1205760

(7)

1205731= 043 explfloor21(

1198911015840

119888

1198910

)

05

(1 +

119881agg

100)

minus25

rfloor for 120576119888gt 1205760

(8)








119891119888= [(1205731+ 1) (120576

1198881205760)

(1205761198881205760)1205731+1

+ 1205731

]1198911015840

119888 (9)

where 1205760and 120573






0 05 1 15 2 25 3 35 40

05

1

15

2

25

3

35

4


R2 = 099

f998400c = 10 50MPaVagg = 0 60

1205731

(f998400cf0)05(1 + Vagg 100)

02

ndashndash


0

1

2

3

4

5

6

7

8

9

10

0 02 04 06 08 1 12

1205731

(f998400cf0)05(1 + Vagg 100)

25minus


R2 = 098

f998400c = 10 50MPaVagg = 0 60

ndashndash





0



119890119898(gt0238) and


2-



2-



0

5

10

15

20

25

30

35

0 0001 0002 0003

Strain

Stre

ss (M

Pa)


Strain

Stre

ss (M

Pa)

0

5

10

15

20

25

30

35

40

0 0002 0004 0006 0008


Strain

Stre

ss (M

Pa)



0

2

4

6

8

10

12

14

0 0002 0004


Strain

Stre

ss (M

Pa)



0

5

10

15

20

25

0 0002 0004 0006




119890119898






6 Conclusions









2-activated



119888decreased





119888



2-activated



2-




Acknowledgment


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











y = 00344x + 00011

R2 = 0511

y = 008x

R2 = 093

0

00005

0001

00015

0002

00025

0003

00035

0004

00045

002 0025 003 0035 004 0045 005

(f998400cEc)05(1 + Vagg 100)

minus05

120576 0

ndash


1198911015840









0



1205760= 008(

1198911015840

119888

119864119888

)

05

(1 +

119881agg

100)

minus05

(2)





119884 =(1205731+ 1)119883

1198831205731+1 + 1205731

(3)

where 119884(= 1198911198881198911015840


1198881205760) is the




y = minus017x + 0166

R2 = 086

00000

00010

00020

00030

00040

00050

00060

00070

092 0925 093 0935 094

(f998400cEc)001(1 + Vagg 100)

minus003

120576 05



toh concrete




119888was




04(119883119886)1205731+1

+ (04 minus 119883119886) 1205731minus 119883119886= 0 for 120576

119888le 1205760 (4)

where119883119886= 04119891

1015840

1198881198641198881205760


1for the



(119883119889)1205731+1

+ (1 minus 2119883119889) 1205731minus 2119883119889= 0 for 120576

119888gt 1205760 (5)

where 119883119889= 120576051205760and 12057605


1in the nonlinear


119888 1205760 and 120576

05







12057605= minus017 [(

1198911015840

119888

119864119888

)

001

(1 +

119881agg

100)

minus003

] + 0166 (6)






120574119890119898

0238 0254 0259 0091120574119890119904






05were





1


1205731= 033 explfloor065(

1198911015840

119888

1198910

)

05

(1 +

119881agg

100)

02

rfloor for 120576119888le 1205760

(7)

1205731= 043 explfloor21(

1198911015840

119888

1198910

)

05

(1 +

119881agg

100)

minus25

rfloor for 120576119888gt 1205760

(8)








119891119888= [(1205731+ 1) (120576

1198881205760)

(1205761198881205760)1205731+1

+ 1205731

]1198911015840

119888 (9)

where 1205760and 120573






0 05 1 15 2 25 3 35 40

05

1

15

2

25

3

35

4


R2 = 099

f998400c = 10 50MPaVagg = 0 60

1205731

(f998400cf0)05(1 + Vagg 100)

02

ndashndash


0

1

2

3

4

5

6

7

8

9

10

0 02 04 06 08 1 12

1205731

(f998400cf0)05(1 + Vagg 100)

25minus


R2 = 098

f998400c = 10 50MPaVagg = 0 60

ndashndash





0



119890119898(gt0238) and


2-



2-



0

5

10

15

20

25

30

35

0 0001 0002 0003

Strain

Stre

ss (M

Pa)


Strain

Stre

ss (M

Pa)

0

5

10

15

20

25

30

35

40

0 0002 0004 0006 0008


Strain

Stre

ss (M

Pa)



0

2

4

6

8

10

12

14

0 0002 0004


Strain

Stre

ss (M

Pa)



0

5

10

15

20

25

0 0002 0004 0006




119890119898






6 Conclusions









2-activated



119888decreased





119888



2-activated



2-




Acknowledgment


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












120574119890119898

0238 0254 0259 0091120574119890119904






05were





1


1205731= 033 explfloor065(

1198911015840

119888

1198910

)

05

(1 +

119881agg

100)

02

rfloor for 120576119888le 1205760

(7)

1205731= 043 explfloor21(

1198911015840

119888

1198910

)

05

(1 +

119881agg

100)

minus25

rfloor for 120576119888gt 1205760

(8)








119891119888= [(1205731+ 1) (120576

1198881205760)

(1205761198881205760)1205731+1

+ 1205731

]1198911015840

119888 (9)

where 1205760and 120573






0 05 1 15 2 25 3 35 40

05

1

15

2

25

3

35

4


R2 = 099

f998400c = 10 50MPaVagg = 0 60

1205731

(f998400cf0)05(1 + Vagg 100)

02

ndashndash


0

1

2

3

4

5

6

7

8

9

10

0 02 04 06 08 1 12

1205731

(f998400cf0)05(1 + Vagg 100)

25minus


R2 = 098

f998400c = 10 50MPaVagg = 0 60

ndashndash





0



119890119898(gt0238) and


2-



2-



0

5

10

15

20

25

30

35

0 0001 0002 0003

Strain

Stre

ss (M

Pa)


Strain

Stre

ss (M

Pa)

0

5

10

15

20

25

30

35

40

0 0002 0004 0006 0008


Strain

Stre

ss (M

Pa)



0

2

4

6

8

10

12

14

0 0002 0004


Strain

Stre

ss (M

Pa)



0

5

10

15

20

25

0 0002 0004 0006




119890119898






6 Conclusions









2-activated



119888decreased





119888



2-activated



2-




Acknowledgment


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

5

10

15

20

25

30

35

0 0001 0002 0003

Strain

Stre

ss (M

Pa)


Strain

Stre

ss (M

Pa)

0

5

10

15

20

25

30

35

40

0 0002 0004 0006 0008


Strain

Stre

ss (M

Pa)



0

2

4

6

8

10

12

14

0 0002 0004


Strain

Stre

ss (M

Pa)



0

5

10

15

20

25

0 0002 0004 0006




119890119898






6 Conclusions









2-activated



119888decreased





119888



2-activated



2-




Acknowledgment


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












2-activated



119888decreased





119888



2-activated



2-




Acknowledgment


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Research Article Stress-Strain Relationship of Ca OH -Activated...

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Transcript of Research Article Stress-Strain Relationship of Ca OH -Activated...