juniorstav 2012 presentation on "the in uence of self-induced and restraint stresses on crack...

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




Introduction

thermal�moisture e�ects

massive structures

block foundations,

gravity dams

medium-thick restrained structures

RC walls of tanks,

nuclear containments,

abutments





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




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





Thermal and moisture analysis

Coupled thermal�moisture equations

T = div(αTT gradT + αTW gradc) +1cbρ

qv

c = div(αWW gradc + αWT gradT )− Kqv





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





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





Implementation

A set of programs:

TEMWIL

thermal�moisture �elds

MAFEM

stress analysis




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





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





Temperature and moisture distribution in section

25

28

31

34

37

40

43

temperature [°C]

with formwork for 28 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



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





Stress maps

Figure 9: Development of temperaturesand resulting stresses

Figure 10: Stress distribution anddeformation of the wall





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


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)





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


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


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)




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.


Juniorstav 2012

Brno, Czech Republic, 26 Jan 2012

juniorstav 2012 presentation on "the in uence of self-induced and restraint stresses on crack...

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