Juniorstav 2012 Presentation on "The in uence of self-induced and restraint stresses on crack development in a reinforced concrete wall subjected to early-age thermal-shrinkage effects"

The inuence of self-induced and restraint stresses
on crack development in a reinforced concrete wall
subjected to early-age thermalshrinkage eects
MSc. Eng. Agnieszka KNOPPIK-WRÓBEL
Silesian University of Technology
Faculty of Civil Engineering
Brno, Czech Republic, 26 Jan 2012

Introduction
Numerical model
Analysis of RC wall
Conclusions
Thermalmoisture eects
Thermalshrinkage cracking
Introduction
concrete curing
cement hydration process
dissipation of heat and migration of moisture
temperature and moisture gradients
stresses
self-induced restraint stresses in structure
Agnieszka Knoppik-Wróbel Self-induced vs. restraint stresses in early-age RC wall

Introduction
Numerical model
Analysis of RC wall
Conclusions
Introduction
thermalmoisture eects
massive structures
block foundations,
gravity dams
medium-thick restrained structures
RC walls of tanks,
nuclear containments,
abutments

Introduction
Numerical model
Analysis of RC wall
Conclusions
Crack development in RC walls
Cracks in RC walls
high L/H - external restraint
mainly restraint stresses
Figure 1: Real cracks observed in RC wall

Introduction
Numerical model
Analysis of RC wall
Conclusions
Thermal and moisture analysis
Thermalshrinkage strains
Stress analysis
Implementation
General assumptions
1 phenomenological model
decoupling of thermalmoisture and mechanical elds
full coupling of thermalmoisture elds
2 stress state determined under the assumption that
thermalmoisture strains have distort character
3 viscoelastoviscoplastic material model of concrete

Introduction
Numerical model
Analysis of RC wall
Conclusions
Stress analysis
Implementation
Coupled thermalmoisture equations
˙T = div(αTT gradT + αTW gradc) +
1
cbρ
qv
˙c = div(αWW gradc + αWT gradT) − Kqv

Introduction
Numerical model
Analysis of RC wall
Conclusions
Stress analysis
Implementation
Imposed thermalshrinkage strains εn:
volumetric strains
dεn = dεn
x dεn
y dεn
z 0 0 0
calculated based on predetermined temperature and humidity
dεn
x = dεn
y = dεn
z = αT dT + αW dW

Introduction
Numerical model
Analysis of RC wall
Conclusions
Stress analysis
Implementation
Stress analysis
viscoelastic area
˙σ = Dve( ˙ε − ˙εn − ˙εc)
viscoelastoviscoplastic area
˙σ = Dve ( ˙ε − ˙εn − ˙εc − ˙εvp)
Figure 2: Failure surface
possibility of crack occurrence
sl =
τoct
τf
oct
Figure 3: Damage intensity factor

Introduction
Numerical model
Analysis of RC wall
Conclusions
Stress analysis
Implementation
Implementation
A set of programs:
TEMWIL
thermalmoisture elds
MAFEM
stress analysis

Introduction
Numerical model
Analysis of RC wall
Conclusions
Input data
Thermalmoisture analysis
Stress analysis
Material, technological and geometrical data
concrete fcm = 35 MPa, fctm = 3 MPa and Ecm = 32 GPa;
steel class RB400;
cement type CEM I 42.5R, 375 kg/m3;
temp.: ambient Tz = 25◦C, initial of concrete Tp = 25◦C;
wooden formwork of 1.8 cm plywood - removed after 28 days,
no insulation, protection of top surface with foil.
20.0 m
0.7m
4.0m
4.0 m
0.7 m
Z
Y
X
0.4 m
Figure 4: Geometry and nite element mesh of analysed walls

Introduction
Numerical model
Analysis of RC wall
Conclusions
Input data
Stress analysis
Thermalmoisture elds
Figure 5: Temperature distribution in the wall [◦C] after 1.2 days
Figure 6: Moisture distribution in the wall (x100) after 1.2 days

Introduction
Numerical model
Analysis of RC wall
Conclusions
Input data
Stress analysis
Temperature and moisture distribution in section
25
28
31
34
37
40
43
temperature [°C] with formwork for 28 days
with formwork for 3 days
70 cm
15
18
21
24
27
30
33
temperature [°C]
with formwork
for 28 days
with formwork
for 3 days
40 cm
Figure 7: Temperature distribution at the thickness the wall [◦C] after 3.5 days
12.0
12.5
13.0
13.5
14.0
14.5
15.0
moisture content
(x100), m3/m3
70 cm
12.0
12.5
13.0
13.5
14.0
14.5
15.0
moisture content
(x100), m3/m3
with formwork
for 28 days
with formwork
for 3 days
40 cm
Figure 8: Moisture content distribution at the thickness the wall [◦C] after 3.5 days

Introduction
Numerical model
Analysis of RC wall
Conclusions
Input data
Stress analysis
Stress maps
Figure 9: Development of temperatures
and resulting stresses
Figure 10: Stress distribution and
deformation of the wall

Introduction
Numerical model
Analysis of RC wall
Conclusions
Input data
Stress analysis
Total stresses
1.0
1.5
2.0
a
70‐cm thick wall
‐2.0
‐1.5
‐1.0
‐0.5
0.0
0.5
0 2 4 6 8 10 12 14 16 18 20
Stress, MPa
Time, days
interior
surface
1.0
1.5
2.0
a
40‐cm thick wall
‐2.0
‐1.5
‐1.0
‐0.5
0.0
0.5
0 2 4 6 8 10 12 14 16 18 20
Stress, MP
Time, days
interior
surface
Figure 11: Total stress development in time
Heating
phase
interior
surface
70‐cm
thick wall
Cooling
phase
4.0 m
‐2.0 ‐1.0 0.0 1.0 2.0
Stress, MPa
phase
‐2.0 ‐1.0 0.0 1.0 2.0
Stress, MPa
phase
0.7 m
Heating
phase
interior
surface
40‐cm
thick wall
Cooling
phase
4.0 m
‐2.0 ‐1.0 0.0 1.0 2.0
Stress, MPa
phase
‐2.0 ‐1.0 0.0 1.0 2.0
Stress, MPa
phase
0.7 m
Figure 12: Total stress distribution at the height of the wall (XY = 0)

Introduction
Numerical model
Analysis of RC wall
Conclusions
Input data
Stress analysis
Self-induced stresses
1.0
1.5
2.0
a
70‐cm thick wall
‐2.0
‐1.5
‐1.0
‐0.5
0.0
0.5
0 2 4 6 8 10 12 14 16 18 20
Stress, MP
Time, days
interior
surface
1.0
1.5
2.0
a
40‐cm thick wall
‐2.0
‐1.5
‐1.0
‐0.5
0.0
0.5
0 2 4 6 8 10 12 14 16 18 20
Stress, MP
Time, days
interior
surface
Figure 13: Self-induced stress development in time (EF 0)
70‐cm
thick wall
Heating
phase
interior
surface
Cooling
phase
4.0 m
‐2.0 ‐1.0 0.0 1.0 2.0
Stress, MPa
phase
‐2.0 ‐1.0 0.0 1.0 2.0
Stress, MPa
phase
0.7 m
40‐cm
thick wall
Heating
phase
interior
surface
Cooling
phase
4.0 m
‐2.0 ‐1.0 0.0 1.0 2.0
Stress, MPa
phase
‐2.0 ‐1.0 0.0 1.0 2.0
Stress, MPa
phase
0.7 m
Figure 14: Self-induced stress distribution at the height of the wall (XY = 0)

Introduction
Numerical model
Analysis of RC wall
Conclusions
Conclusions
1 Thermalshrinkage cracking of massive cocnrete structures is a
well-known problem.
2 Thermalshrinkage cracking aects medium-thick elements if
externally-restrained.
3 Restraint stresses play the main role.
4 Self-induced stresses share depends directly on the thickness of
the element.

Juniorstav 2012
Brno, Czech Republic, 26 Jan 2012

Juniorstav 2012 Presentation on "The in uence of self-induced and restraint stresses on crack development in a reinforced concrete wall subjected to early-age thermal-shrinkage effects"

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