juniorstav 2012 presentation on "the in uence of self-induced and restraint stresses on crack...
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Full text available: https://www.researchgate.net/publication/236171627_The_influence_of_self-induced_and_restraint_stresses_on_crack_development_in_reinforced_concrete_wall_subjected_to_early-age_thermalshrinkage_effects?ev=prf_pubTRANSCRIPT
The in�uence of self-induced and restraint stresses
on crack development in a reinforced concrete wall
subjected to early-age thermal�shrinkage e�ects
MSc. Eng. Agnieszka KNOPPIK-WRÓBEL
Silesian University of TechnologyFaculty of Civil Engineering
Brno, Czech Republic, 26 Jan 2012
IntroductionNumerical model
Analysis of RC wallConclusions
Thermal�moisture e�ectsThermal�shrinkage 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
IntroductionNumerical model
Analysis of RC wallConclusions
Thermal�moisture e�ectsThermal�shrinkage cracking
Introduction
thermal�moisture e�ects
massive structures
block foundations,
gravity dams
medium-thick restrained structures
RC walls of tanks,
nuclear containments,
abutments
Agnieszka Knoppik-Wróbel Self-induced vs. restraint stresses in early-age RC wall
IntroductionNumerical model
Analysis of RC wallConclusions
Thermal�moisture e�ectsThermal�shrinkage cracking
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
Agnieszka Knoppik-Wróbel Self-induced vs. restraint stresses in early-age RC wall
IntroductionNumerical model
Analysis of RC wallConclusions
Thermal and moisture analysisThermal�shrinkage strainsStress analysisImplementation
General assumptions
1 phenomenological modeldecoupling of thermal�moisture and mechanical �elds
full coupling of thermal�moisture �elds
2 stress state determined under the assumption thatthermal�moisture strains have distort character
3 viscoelasto�viscoplastic material model of concrete
Agnieszka Knoppik-Wróbel Self-induced vs. restraint stresses in early-age RC wall
IntroductionNumerical model
Analysis of RC wallConclusions
Thermal and moisture analysisThermal�shrinkage strainsStress analysisImplementation
Thermal and moisture analysis
Coupled thermal�moisture equations
T = div(αTT gradT + αTW gradc) +1cbρ
qv
c = div(αWW gradc + αWT gradT )− Kqv
Agnieszka Knoppik-Wróbel Self-induced vs. restraint stresses in early-age RC wall
IntroductionNumerical model
Analysis of RC wallConclusions
Thermal and moisture analysisThermal�shrinkage strainsStress analysisImplementation
Thermal�shrinkage strains
Imposed thermal�shrinkage strains εn:
volumetric strains
dεn =[dεnx dεny dεnz 0 0 0
]calculated based on predetermined temperature and humidity
dεnx = dεny = dεnz = αT dT + αW dW
Agnieszka Knoppik-Wróbel Self-induced vs. restraint stresses in early-age RC wall
IntroductionNumerical model
Analysis of RC wallConclusions
Thermal and moisture analysisThermal�shrinkage strainsStress analysisImplementation
Stress analysis
viscoelastic area
σ = Dve(ε− εn − εc)
viscoelasto�viscoplastic area
σ = Dve (ε− εn − εc − εvp)
Figure 2: Failure surface
possibility of crack occurrence
sl =τoct
τ foct
Figure 3: Damage intensity factor
Agnieszka Knoppik-Wróbel Self-induced vs. restraint stresses in early-age RC wall
IntroductionNumerical model
Analysis of RC wallConclusions
Thermal and moisture analysisThermal�shrinkage strainsStress analysisImplementation
Implementation
A set of programs:
TEMWIL
thermal�moisture �elds
MAFEM
stress analysis
Agnieszka Knoppik-Wróbel Self-induced vs. restraint stresses in early-age RC wall
IntroductionNumerical model
Analysis of RC wallConclusions
Input dataThermal�moisture analysisStress 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 m0.7
m
4.0
m
4.0 m
0.7 m
ZY
X
0.4 m
Figure 4: Geometry and �nite element mesh of analysed walls
Agnieszka Knoppik-Wróbel Self-induced vs. restraint stresses in early-age RC wall
IntroductionNumerical model
Analysis of RC wallConclusions
Input dataThermal�moisture analysisStress analysis
Thermal�moisture �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
Agnieszka Knoppik-Wróbel Self-induced vs. restraint stresses in early-age RC wall
IntroductionNumerical model
Analysis of RC wallConclusions
Input dataThermal�moisture analysisStress 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 dayswith 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), m
3/m
3
with formwork for 28 days
with formwork for 3 days
70 cm
12.0
12.5
13.0
13.5
14.0
14.5
15.0
moisture content
(x100), m
3/m
3
with formwork for 28 dayswith formwork for 3 days
40 cm
Figure 8: Moisture content distribution at the thickness the wall [◦C] after 3.5 days
Agnieszka Knoppik-Wróbel Self-induced vs. restraint stresses in early-age RC wall
IntroductionNumerical model
Analysis of RC wallConclusions
Input dataThermal�moisture analysisStress analysis
Stress maps
Figure 9: Development of temperaturesand resulting stresses
Figure 10: Stress distribution anddeformation of the wall
Agnieszka Knoppik-Wróbel Self-induced vs. restraint stresses in early-age RC wall
IntroductionNumerical model
Analysis of RC wallConclusions
Input dataThermal�moisture analysisStress 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, M
Pa
Time, daysinteriorsurface
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, M
P
Time, daysinteriorsurface
Figure 11: Total stress development in time
Heatingphase
interiorsurface
70‐cm thick wall
Coolingphase
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
Heatingphase
interiorsurface
40‐cm thick wall
Coolingphase
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)
Agnieszka Knoppik-Wróbel Self-induced vs. restraint stresses in early-age RC wall
IntroductionNumerical model
Analysis of RC wallConclusions
Input dataThermal�moisture analysisStress 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, M
P
Time, daysinteriorsurface
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, M
P
Time, daysinteriorsurface
Figure 13: Self-induced stress development in time (EF ' 0)
70‐cm thick wall
Heatingphase
interiorsurface
Coolingphase
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
Heatingphase
interiorsurface
Coolingphase
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)
Agnieszka Knoppik-Wróbel Self-induced vs. restraint stresses in early-age RC wall
IntroductionNumerical model
Analysis of RC wallConclusions
Conclusions
1 Thermal�shrinkage cracking of massive cocnrete structures is awell-known problem.
2 Thermal�shrinkage cracking a�ects medium-thick elements ifexternally-restrained.
3 Restraint stresses play the main role.4 Self-induced stresses share depends directly on the thickness of
the element.
Agnieszka Knoppik-Wróbel Self-induced vs. restraint stresses in early-age RC wall
Juniorstav 2012
Brno, Czech Republic, 26 Jan 2012