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Lecture #13

Properties of Hardening Concrete

Curing

Cracking Factors

Temperature and Evaporation

Thermal Stress

TE T Temperature change

Coefficient of thermal expansion

Concrete stiffness

Cracking stress

Concrete Thermal Contraction

= = Coefficient of thermal expansion ~ 5*10-6 /oF

= Difference in concrete temperature (T) and the concrete setting temperature (T set)

= T set - T

T = Variation of the average concrete temperature after placement. Assume this variation tracks closely to the 24-hour ambient air temperature cycle (after a 72 hour period).

T set = 0.95(T conc + TH)

th CTEΔTα

CTEΔT

Concrete Thermal Contraction (con’t)

T conc = Concrete placement temperature at construction (oF).

Assume this value (approx. 80 oF) = Change in concrete temperature due to heat of hydration = Hu = Total heat of hydration per gram (kJ/g)

= 0.007 (Tconc) – 3x10-5 (Tconc)2 –0.0787

C = amount of cement (grams) per m3

= Degree of hydration (estimate to be approximately 0.15-0.2) cp = Specific heat of cement = 1.044 kJ/g

= Density of concrete ~ 2400 kg/m3

HΔT ρcCαH pdu

d

Strength(ft) vs. Time

0

50

100

150

200

250

0 50 100 150 200

Time (hours)

Ten

sile

Str

eng

th (

psi

)

ft = a log (t) + b

TE

MP

ER

AT

UR

E (

C)

40

30

20

10

0

-10

-200 12 24 36 48 60 72 84 96

TIME (hours)

FIGURE 1. The Nurse-Saul Maturity Function

S

M, te

Maturity

Maturity Concepts

Nurse - Saul Equation (units: Temp – Time)

Maturity: Product of time & temperature

To = Datum TemperatureT = Average Concrete Temperature over Time “t”M = Maturity

tTTM o

t

o

ARRHENIUS EQUATIONS

tet rTTR

Et

e

273

1

273

1

0

E = Activation Energy

R = Gas Constant

te = Equivalent Age or Time

LABORATORY TESTING FIELD MEASUREMENT

Procedures for using maturity method involve laboratorytesting and field measurements.

Elastic Modulus

Concrete E-Modulus vs. Hydration

0

5

10

15

20

25

30

35

40

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Degree of hydratiom

E-M

odulu

s

(G

Pa)

D\4 Sawn JointD\4 Sawn Joint

Sawcut Timing and Depth

Curing

StrengthFactors

MPa

cw

Pcap

3

3

32.0

68.01001100

Relative Humidity at ¾ inch

50

60

70

80

90

100

0 5 10 15 20 25

Time (hours)

RH

of C

oncr

ete

(%)

EffectiveCuringThickness

Effective Curing Thickness

Curing Quality

0

50

100

150

200

0 1 2 3 4 5 6

Age of Concrete (hours)

Acc

umul

ativ

e E

vapo

ratio

n (g

ram

s)

0.00

0.20

0.40

0.60

0.80

1.00

Eva

pora

tion

Rat

e (k

g/m

2/hr

)

Accumulative Evaporation Evaporation Rate

0.0

1.0

2.0

0 1 2 3 4 5 6


Effe

ctiv

e C

urin

g Th

ickn

ess

(inch

es)

0

20

40

60

80

100

120

140

0 2 4 6 8 10 12


Acc

umul

ativ

e E

vapo

ratio

n (g

ram

s)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Eva

pora

tion

Rat

e (k

g/m

2/hr

)

Accumulative Evaporation Evaporation Rate

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 2 4 6 8 10 12


Effe

ctiv

e Cu

ring

Thic

knes

s (in

ches

)

WindWind

No WindNo Wind

Model of CSHStructure of CSH

Nature of Concrete Creep and Shrinkage

Typical creep curve for cement paste.

aM

icro

stra

in

Time after loading

Creepstrain

Elasticrecovery

Creeprecovery

Irreversible creep

Concreteunloaded

Elastic strain

Burger Model

Constant Stress(Creep)

time

Strain

Creep of cement under simultaneous loading & drying.62sh=free shrinkage; bc=basic creep (specimen loaded but not drying); dc=drying creep; cr=total creep strain;tot=total strain (simultaneous loading & drying)

b Free shrinkage (no load)

Basic creep (no drying)

Loading and drying

Mic

rost

rain

Time

sh

sh

bc

bc

dccr

tot

Spring-Loaded Creep Frame

C

C

C

C

C

6 X 3 IN. PLUG (CONCRETE)

C = 6 X 12 IN. TEST CYLINDERS

6 X 3 IN. PLUG (CONCRETE)

UPPER JACK PLATE

LOAD BARSLOWER JACK PLATE

UPPER LOAD PLATE

LOWER LOAD PLATEUPPER BASE PLATE

SPRINGSLOWER BASE PLATE

Horizontal Mold for Creep Specimens

Cracking Frame

The Cracking Frame Test

specimen strain gauge

T = 1.010-6K-1

T = 1210-6K-1

Crack in Specimen

Preparation of Fracture Specimens

Determination of Creep

vs

crp ec c

F

E A

where crp = Creep strain

v = Shrinkage strain (ASTM C 157)

e = Frame strain

Fs = Force in concrete (F)

Ec = Modulus of elasticity of concrete (F/L-2)

Ac = Specimen cross sectional area (L2)

Accumulative vs. Time

0.0E+00

5.0E-05

1.0E-04

1.5E-04

2.0E-04

2.5E-04

0 20 40 60 80


Acc

umul

ativ

e C

reep

Str

ain

Equation 1 Net Difference

Time of Cracking

Burger Model

Constant Stress(Creep)

time

Strain

Aggregate Effects

napcon V 1

Effects of Paste Properties

Effect of age of loadingon the creep strain.

Effect of w/c ratio on the shrinkage strain.

Mechanisms of Creep and Shrinkage

•CreepIt is a complex process involving slipping of surfaces

past one another within the structure of C-S-H. It is a function of pore structure and ease of slippage of C-S-H particles. Asthe space between particles becomes less and less the degree of creep becomes less and less.

•Drying ShrinkageMoisture loss is driven by the ambient relative humidity.

As moisture escapes from the capillaries, menisci are created and capillary stresses are developed. As more moisture is evaporated, smaller and smaller menisci are created. This action creates stress

and causes slippage between C-S-H particles.

This method is based upon a method proposed by Bransonand Christiason (2.3) and was developed by ACI Committee 209(2.4) In 1982, ACI Special Publication 76 (2.5) gives an updatedbut not significantly changed version of this method.

This method uses the

as the creep coefficient.

ACI Committee 209 Method

creep strain

elastic strain at the time of loading t

Shrinkage – ACI

The shrinkage strain at t days after the end of initial curing is

where

= ultimate shrinkage strain= 415 to 1070 micro-strain

= 0.9 to 1.10and f = 20 to 130 days

In the absence of specific data for local aggregate and conditions Committee 209 suggests thatWith

= product of applicable correction factors

The equations for the correction factors are given in Table A

ushtsh t

t

35

sh t

sh t

780 (micro-strains)sh shu

sh

usha

a

tshtf

t

at h s c

The creep coefficient at t days after loading is given by

where= ultimate creep coefficient

= 1.30 to 4.15 = 0.40 to 0.80 d = 6 to 30 days

In the absence of specific data for local aggregates and conditionsCommittee 209 suggests thatwhere

= product of applicable correction factors

The equations for the correction factors are given in Table A

uttd

t

utt

t 60.0

60.0

10

t

u

2.35u C C

Creep – ACI 209

at h s c

The concrete strength at t days is given by

with suggested values of a = 4.0 days = 0.85

for most cured ordinary Portland cement concrete. The modulusof elasticity Ec at t days is given by

which is often taken as

when E and f’c are in MPa

28'' cttc fa

tf

30.043 ( ' )ct c tE w f

tcct fE )'(4730

Strength and Modulus of Elasticity

Notes Correction FactorsCreep Shrinkage

Loading Age

0.1181.25 at

Relative Humidity

Average h=average 1.14 - 0.00092 h 1.23 - 0.0015 h during 1st year Thickness thickness in mm for 1st yr. of

150 < h < 300 loading 1.10 - 0.00067 h 1.17 - 0.0014 h ultimate value ultimate value

Concrete s= slump in mm 0.82 + 0.00264s 0.89 + .00161s Composition

c= cement content - kg/m3 0.75 + .00061c

Table A ACI Creep and Shrinkage Correction Factors

loading age

in days

at

% relative

humidity

1.27 0.0067

40%for

1.40 0.010 for 40%< <80%

3.00-0.030 for 80% <100%

% fine aggregate 0.88 0.00240.30 0.014 for <50%

0.90+0.002 for >50%

0.95 0.0080.46 0.09 1 % air content