Transcript Document 7454950

Lecture #13
Properties of Hardening
Concrete
Curing
Cracking Factors
Temperature and Evaporation
Thermal Stress
  ET T
Temperature change
Coefficient of thermal
expansion
Concrete stiffness
Cracking stress
Concrete Thermal Contraction
 th
 CTE
ΔT
T
T set
= ΔTα CTE
= Coefficient of thermal expansion ~ 5*10-6 /oF
= Difference in concrete temperature (T) and the
concrete setting temperature (T set)
= T set - 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).
= 0.95(T conc + TH)
Concrete Thermal Contraction (con’t)
T conc = Concrete placement temperature at construction (oF).
Assume this value (approx. 80 oF)
ΔTH = Change in concrete temperature due to heat of hydration
= H u Cα d  c p ρ 
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
 d = 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
E  33
3
2
E  0.043
'
c
f ( psi)
3
2
'
c
f (GPa)
Strength(ft) vs. Time
Tensile Strength (psi)
250
200
150
ft = a log (t) + b
100
50
0
0
50
100
Tim e (hours)
150
200
40
30
20
10
0
-10
-20
0
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
M  T  To t
t
o
To = Datum Temperature
T = Average Concrete Temperature
over Time “t”
M = Maturity
ARRHENIUS EQUATIONS
t
te   e
E 1
1
 

R  273T 273Tr



0
E = Activation Energy
R = Gas Constant
te = Equivalent Age or Time
t
LABORATORY TESTING
FIELD MEASUREMENT
Procedures for using maturity method involve laboratory
testing and field measurements.
Elastic Modulus
C on cre te E-Modu l u s
vs. Hydrati on
40
E-Modulus
(GPa)
35
30
25
20
15
10
5
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Degree of hydratiom
1
D\4 Sawn Joint
Sawcut Timing
and Depth
Curing
Strength
Factors
3
  1001  Pcap 3
 0.68 
 MPa
 100
w  0.32 
 c

Relative Humidity at ¾ inch
RH of Concrete (%)
100
90
80
70
60
50
0
5
10
15
Time (hours)
20
25
Effective Curing
Thickness
Effective
Curing
Thickness
Relative Humidity
0.98
0.96
0.94
0.92
0.9
0
0.5
1
0 hour
12 hours
24 hours
48 hours
72 hours
1.5
2
2.5
3
3.5
Depth from Surface
1
1.00
0.80
150
0.60
100
0.40
50
Wind
0
0
1
2
3
0.20
Evaporation Rate
(kg/m2/hr)
Accumulative
Evaporation (grams)
200
0.00
4
5
6
Effective Curing Thickness
(inches)
Curing Quality
2.0
1.0
Wind
0.0
Age of Concrete (hours)
120
0.25
100
0.20
80
0.15
60
0.10
No Wind
0.05
0
0.00
0
2
4
6
8
10
Age of Concrete (hours)
Accumulative Evaporation
Evaporation Rate
12
Effective Curing Thickness
(inches)
0.30
20
2
3
4
5
6
10
12
Age of Concrete (hours)
140
40
1
Evaporation Rate
Evaporation Rate
(kg/m2/hr)
Accumulative
Evaporation (grams)
Accumulative Evaporation
0
6.0
5.0
4.0
3.0
No Wind
2.0
1.0
0.0
0
2
4
6
8
Age of Concrete (hours)
Model of CSH
Structure of CSH
Nature of Concrete Creep and Shrinkage
a
Elastic
recovery
Creep
strain
Elastic
strain
Creep
recovery
Irreversible
creep
Concrete
unloaded
Time after loading
Typical creep curve for cement paste.
Burger Model
Constant Stress
(Creep)
Strain
time
b
Free shrinkage (no load)
sh
Microstrain
Basic creep (no drying)
bc
Loading and drying
dc
cr
bc tot
sh
Time
Creep of cement under simultaneous loading & drying.
62 =free shrinkage;  =basic creep (specimen loaded but
sh
bc
not drying); dc=drying creep; cr=total creep strain;
tot=total strain (simultaneous loading & drying)
UPPER JACK PLATE
LOAD BARS
LOWER JACK PLATE
UPPER LOAD PLATE
6 X 3 IN. PLUG (CONCRETE)
C
C
C = 6 X 12 IN. TEST CYLINDERS
C
C
C
6 X 3 IN. PLUG (CONCRETE)
LOWER LOAD PLATE
UPPER BASE PLATE
SPRINGS
LOWER BASE PLATE
Spring-Loaded Creep Frame
Horizontal Mold for Creep Specimens
Cracking Frame
The Cracking Frame Test
specimen
T =
1210-6K-1
strain gauge
T = 1.010-6K-1
Crack in Specimen
Preparation of Fracture Specimens
Determination of Creep
 Fs 
 crp   v   e  

 Ec Ac 
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 Creep Strain
Accumulative vs. Time
2.5E-04
Time of Cracking
2.0E-04
1.5E-04
1.0E-04
5.0E-05
0.0E+00
0
20
40
60
Age of Concrete (hours)
Equation 1
Net Difference
80
Burger Model
Constant Stress
(Creep)
Strain
time
 con   p 1  Va 
n
Aggregate Effects
Effects of Paste Properties
Effect of age of loading
on the creep strain.
Effect of w/c ratio on the
shrinkage strain.
Mechanisms of Creep and Shrinkage
•Creep
It 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. As
the space between particles becomes less and less the degree
of creep becomes less and less.
•Drying Shrinkage
Moisture 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.
ACI Committee 209 Method
This method is based upon a method proposed by Branson
and Christiason (2.3) and was developed by ACI Committee 209
(2.4) In 1982, ACI Special Publication 76 (2.5) gives an updated
but not significantly changed version of this method.
This method uses the
creep strain
t
elastic strain at the time of loading
as the creep coefficient.
Shrinkage – ACI
The shrinkage strain sh t at t days after the end of initial
curing is
a
sh t 
where
t
f t
a
sh u
sh t
t
= ultimate shrinkage strain

sh u
sh t 
= 415 to 1070 micro-strain
35  t
 = 0.9 to 1.10
and f = 20 to 130 days
In the absence of specific data for local aggregate and conditions Committee 209
suggests that  sh   780 sh (micro-strains)
u
With
 sh
= product of applicable correction factors
  t a    h s    c 
The equations for the correction factors are given in Table A
Creep – ACI 209
The creep coefficient
t 
where
u

d
 t at t days after loading is given by
t
d t

u
= ultimate creep coefficient
= 1.30 to 4.15
= 0.40 to 0.80
= 6 to 30 days
t 
t 0.60
10  t
0.60
u
In the absence of specific data for local aggregates and conditions
Committee 209 suggests that
where
 u  2.35 C
C
= product of applicable correction factors
  t a    h s    c 
The equations for the correction factors are given in Table A
Strength and Modulus of Elasticity

The concrete strength at t days is given by
 f 'c t

t
a
t
 f 'c 28
with suggested values of
a = 4.0 days
= 0.85
for most cured ordinary Portland cement concrete. The modulus
of elasticity Ec at t days is given by
Ect  0.043 w3 ( f 'c )t
which is often taken as
when E and f’c are in MPa
Ect  4730 ( f 'c ) t
Notes
Correction Factors
Shrinkage
Creep
Loading Age
t a  loading age
in days
1.25  t a 
0.118
Relative
Humidity
  % relative
1.27  0.0067
humidity
for   40%
Average
Thickness
h=average
thickness in mm
150 < h < 300
Concrete
Composition
s= slump in mm
1.14 - 0.00092 h
for 1st yr. of
loading
1.10 - 0.00067 h
ultimate value
0.82 + 0.00264s
  % fine aggregate 0.88  0.0024
c= cement content
kg/m3
1.40  0.010 for 40%< <80%
3.00-0.030 for 80%   <100%
1.23 - 0.0015 h during 1st year
1.17 - 0.0014 h ultimate value
0.89 + .00161s
0.30  0.014 for  <50%
0.90+0.002 for  >50%
-
  % air content 0.46  0.09  1
0.75 + .00061c
0.95  0.008
Table A ACI Creep and Shrinkage Correction Factors