numerical simulation of concrete exposed to high temperature damage and explosive · pdf...

1Universität Stuttgart

Institut für Werkstoffe im Bauwesen

NUMERICAL SIMULATION OF CONCRETE EXPOSED TO HIGH TEMPERATURE –DAMAGE

AND EXPLOSIVE SPALLING

Prof. Joško Ožbolt 1

Josipa Bošnjak1, Goran Periškić 1, Akanshu Sharma2

1 Institute of Construction Materials, University of Stuttgart, Germany2 Reactor Safety Division, Bhabha Atomic Research Centre, Mumbai , India

Sponsored by DFG

2

Contents

• Introduction

• Thermo-mechanical (TM) model

• Thermo-hygro-mechanical (THM) model

• Applications of the thermo-mechanical model

– Plain concrete beams in fire

– Reinforced concrete beams in fire

• Applications of the thermo-hygro-mechanical model

– Macro vs. meso scale FE analysis

– Average vs. Local properties (porosity, permeability,..)

– Influence of inhomogeneities on explosive spalling

– Influence of external loading, permeability and rel. humidity on explosive spalling

• Permeability tests at elevated temperatures

• Summary and Conclusions

Universität Stuttgart


3

Introduction

• Concrete does not burn, however, when exposed to fire there are:– Large degradation of mechanical properties

– Large thermal (non-elastic) strains

– Thermal induced damage and explosive spalling

• Limited number of experiments on relatively small structures

• Difficulties in experimental measurements

• Alternative & support – realistic numerical models

• Multi scale modeling (explosive spalling)



4

Explosive spalling of concrete cover



Experimental evidence (high strength concrete):

• Explosive spalling is a local phenomenon: Relatively small volumeof the material on concrete surface fails - potential energy is transformed into kinetic energy + dynamic fracture of concrete

• Main reasons: Pore pressure & thermally induced stresses• Influencing parameters: permeability, humidity, heating rate,

external load, boundary conditions & geometry• Addition of polypropylene prevents explosive spalling;

Reasons: Increase of porosity, permeability, additional microcracking

• Large scatter of measured data

5

• Continuum mechanics– Quasi-static loading conditions– Green-Lagrange strain tensor– Co-rotational stress tensor

• Irreversible thermodynamics• Mechanical model - temperature sensitive microplane model

for concrete• Discretization method - standard finite elements• Smeared crack concept with crack band method as a

localization limiter

Theoretical frameworkmacro & meso FE analysis



6

• Non-mechanical processes:

– Transport of capillary water– Transport of heat– Pore pressure

• Mechanical processes:

– Damage and cracking of concrete

– Dynamic fracture of concrete (explosive spalling)

• Interaction between mechanical and non-mechanical processes

Processes to be modeled



7

Temperature dependent microplane model (mechanical strain)

Finite strains: co-rotational stress & GL strain tensor

Macroscopic temperature dependent concrete properties

Uniaxial tensile strength ft(T,t)

Uniaxial compressive strength fc(T,t)

Tensile fracture energy GF

(T,t)

Compressive fracture energy GC

(T,t) = 100GF

(T,t)

Poisson‘s number = constant

Calculated temperature and time dependentproperties of the microplane model

Kinematic constraint : from ij

V,

D,

Tr

V

0 FV

(V

) D

0 FD

(D,eff

) Tr

0 FTr

(Tr ,eff

,V

)

Weak form of equlibrium:

ij

0 V

0ij

3

2

D

0 (nin

j

ij

3)dS

S

3

2

Tr

0

2(n

i

rj n

j

ri)

S

dS



9

Hygro-thermal part of the model (THM model)(single phase model)



10

Hygro-thermo-mechanical coupling(permeabilty & porosity)



11

Application of the TM model – macro analysis



X

Y

Z

F23F23

F3F3

V1

L1

C1

Plain concrete beams exposed to ISO 834 fire

FE discretization

heating

all in mm

Specimen geometry and loading setup (4 point bending)

12

Plain concrete beam (4-point bending)



0 200 400 600 800Temperature [°C]

0

0.2

0.4

0.6

0.8

1

Rel

ativ

e st

reng

th

C25 (experimental)

C25 (hot strength)

C25 (residual strength)

0 200 400 600 800Temperature [°C]

0

0.2

0.4

0.6

0.8

1

Rel

ativ

e st

reng

th

C45 (experimental)

C45 (hot strength)

C45 (residual strength)

Ultimate load reduction due to fire exposure

(comparision of experimental and numerical results)

13

RC beams exposed to ISO 834 fire

(three-sided exposure)



Specimen geometry and loading setup (4 point bending)

X

Y

Z

FE discretization

X

Y

Z

Reinforcement Measured air temperatures

Concrete

14





Ultimate load reduction due to fire exposure

(comparision of experimental and numerical results)

(a)

0 0.5 1 1.5 2Duration of heating [h]

0

0.2

0.4

0.6

0.8

1

Re

lative

ultim

ate

lo

ad

FE Analysis

Experiment

(b)

0 0.5 1 1.5 2Duration of heating [h]

0

0.2

0.4

0.6

0.8

1

Re

lative

stiff

ne

ss

k1_FE Analysis

k1_Experiment

k2_FE Analysis

k2_Experiment

15





Failure mode and temperature distribution after 60 minutes of fire

Failure mode for the reference beam (without fire exposure)

16

FE mesh

sym.

Investigated parameters:

• permeability

• humidity

• heating rate

• strength of concrete

• the role of geometrical non-linearity

Geometry

Application of the THM model – macro scale

Reasons & mechanism

• temperature induced stresses

• pore pressure

• geometrical instability

• ......



Plane strain

17

Thermal-strain induced stresses (macro analysis)

Str

ess p

ara

llel to

su

rfa

ce

[M

Pa

]

Str

ess n

orm

al to

su

rfa

ce

[M

Pa

]





Explosive spalling – macro scale

Time evolution of relevant quantities at the position of initialization of crack (spalling)

1919

Expected level of local pore pressure (simple engineering model):

n= 0 p= ∞

n= 1 p= 0

n= 0.5 p= ftn= 0.1 p= 9ft

n = porosity

Summary based on numerical studies (macro analysis)

Stresses due to thermal strain alone cause no explosive spalling Pore pressure, mainly controlled by permeability, has dominant influence

on explosive spalling Geometrical instability due to compressive stresses increases the risk of

explosive spalling



20

Explosive spalling – meso scale analysis



Motivation

• Average properties of concrete are not relevant

• Heterogeneity

• Local material properties strongly influence explosive spalling

• Inhomogeneity of heating field influences explosive spalling

• Large scatter of measured data (average pore pressure, average permeability, ..)can be explained by the fact that explosive spalling is localand not global (macroscopic) phenomena

• To realistically study explosive spalling analysis at meso scale is required



• Non-homogeneity of heat flux• Material homogeneity• Permeability of concrete a0 = 6 x 10-14 m/s

homogeneity of temperature field non-homogeneity of temperature field -heat flux over the width varied by 25%

macro scale, homogeneous heat fluxexplosive failure after t= 13,2 min

macro scale, non-homogeneous heat fluxexplosive failure after t= 12,0 min

Influence of inhomogeneity on explosive spalling



• Homogeneity of heat flux• Influence of different distribution of permeability • Random variation of permeability (a0 = 6 x 10-14, a0

1=1 x 10-16)

meso scale, constant permeabilityexplosive failure after t= 15,4 min

meso scale, spatial variation of permeabilityexplosive failure after t= 14,9 min




• Homogeneity of heat flux• Influence of different aggregate configuration (meso scale)• Max. aggregate size d = 8mm (realistic ratio of coarse aggregates in concrete)• Permeability of concrete a0 = 6 x 10-14 m/s

meso scale, spatial distribution of aggregate Aexplosive failure after t= 10,7 min

meso scale, spatial distribution of aggregate Bexplosive failure after t= 9,33 min




• Homogeneity of heat flux• Macro and meso scale model 50 x 50 x 50 mm

macro scale, explosive failure after t= 8,1 min

meso scaleexplosive failure after t= 6,9 min


Section A

Section A

• Influence of external compressive load• Comparison between macro- and meso-scale

Experimental evidence:

External compressive loads enhance explosive spalling !!

Influence of external load on explosive spalling



• Meso scale – Influence of permeability and relative humidity on explosive spalling

Influence of permeability and humidity on explosive spalling



2

4

6

8

10

12

14

16

5.E-16 5.E-15 5.E-14T

ime

to

sp

alli

ng

[m

in]

Permeability [m2]

Time of spalling vs. mortar permeability

VarA_ETK

0

5

10

15

20

25

30

30 40 50 60 70 80 90 100

Tim

e to

sp

alli

ng

[m

in]

Relative humidity [%]

Time of spalling vs. humidity

VarA_ETK

Spalling does not occur at very low humidity level as well as in case of very permeable concrete.



Explosive spalling - meso scale

• Time evolution of pore and volumetric pressure at the position of initialization of crack (spalling)

Permeability at high temperatures - General



dx

dpAkQ

Q [m3] - the volumetric fluxk [m2] - the permeability factor (apparent)A [m2] - the cross-sectional areaη [Pa s] -the dynamic viscosity of the transported fluiddp /dx [Pa/m] - the pressure gradient

p

bkk int 1

Darcy’s law:

Slip flow phenomenon (compressible fluids):

PDE-Pressure decay experiment

pQ)pp(H

)r/rln(k

22

21

12

Apparent permeability:

28

p [Pa] - the pressure (average)kint [m2] - the permeability factor (intrinsic)b [Pa] - the Klinkenberg slip flow coefficient

Permeability at high temperatures - Verification


Institut für Werkstoffe im Bauwesen 29

RILEM Permeability experiment

RILEM Permeability experiment K = 2,6 x 10-17m2

Pressure decay experiment K= 2,0 x 10-17 m2

Permeability test at 20°C:

Permeability at high temperatures - Setup

Concrete specimenUniversität Stuttgart

Institut für Werkstoffe im Bauwesen30

Test setup

Permeability at high temperatures - Setup



Nitrogen outlet

Nitrogen inlet

Experimental results obtained from the literature - Specimens were not dried prior testing (Schneider),residual permeability (Kalifa et al.)

Experiments C50/60 – Specimens kept at 60°C until steady mass state prior to testing

Permeability at high temperatures - Results



• Comparison with experimental data obtained from literature

0.01

0.1

1

10

100

1000

0 100 200 300 400 500

Re

lative

pe

rme

ab

ility

[ki/k(8

0°C

)]

Temperature [°C]

Schneider

Kalifa et al 2001 (Cembureau method)

Kalifa et al 2001 (Hassler method)

Experiment C50/60

Permeability at high temperatures - Results



1E-18

1E-17

1E-16

1E-15

1E-14

0 50 100 150 200 250 300 350

lntr

insi

c p

erm

eabili

ty [m

2]

Temperature [°C]

PP 0%-1

PP 0%-2

PP 0%-3

PP 1%-1

PP 1%-2

PP 1%-3

Experiment - Specimens kept at 60°C until steady mass state prior to testing

• Test results with concrete C80/95 with and without addition of polypropylenefibres

Melting point (160°C)

Loss of thermal stability (120°C)

Microscopic investigation



Virgin concrete

20 min of exposure to 200°C 2 days of exposure to 200°C

PP Fibers

Microscopic investigation



2 days of exposure to 200°C

microcracks

Empty space in polypropylene

36

Summary & conclusions

• Thermo-mechanical phenomena - macro scale

• For explosive spalling thermo-hygro-mechanical model is required

• Explosive spalling is a local phenomenon - local properties are relevant

• Macroscale modelling cannot capture all the aspects of explosive spalling

• Explosive spalling can be properly modeled only at meso scale

• Large scatter of measured data show that the phenomenon is local and notglobal

• Experimental results = PP fibres mitigate explosive spalling

• A new experimental setup for measurement of permeability at hightemperature

• Experiments confirmed that the permeability is the key parameter governingthe explosive spalling. These findings correspond well to the results of thenumerical analysis.

• The designed equipment for measurement of permeability of concrete at hotconditions is simple and reliable.



37

Thank you!



numerical simulation of concrete exposed to high temperature damage and explosive · pdf...

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