Overview

• Introduction to concrete at high temperature

• Introduction to spalling

• Coupled hygro-thermal-mechanical model

• Benchmark examples and results

• Conclusions

• Future developments

• liquid water - capillary menisci

Pores fully or partially filled with:

• water vapour

• adsorbed water

• dry air

Cement paste:• highly porous, hygroscopic material

• 28% gel pores (≤ 2.6nm in diameter)

• up to 40% capillary pores (1µm-1mm)

Concrete at High Temperature

• Complex behaviour dependent on:

• composite structure

• physics & chemistry of cement paste

{Wate r

On exposure to high temperature:

• heat is conducted and convected• changes in fluid content:

e.g. evaporation; migration

• changes in chemical composition

• → changes in physical structure

• e.g. dehydration, chemical damage

Concrete at High Temperature

Overall, results in changes to:• physical properties:

• thermal conductivity,permeability, porosity, etc.

• mechanical properties:• strength, stiffness, fracture energy, etc.

Mechanical behaviour:• free thermal expansion• transient thermal creep - LITS• mechanical & thermal damage

• Elasto-plasticity• Basic creep• Drying creep• Shrinkage

Ideal model, considers:• all these (largely non-linear)

processes• all their coupled interactions

Such a model is very complex

Concrete at High Temperature

• Difficult to define

• Simply:

• A loss of material from the cross-section of a concrete member (sometimes explosively)

Spalling

Spalling

1st Channel Tunnel Fire: • 10-hour fire• 700°C

• Severe structural damage:• complete spalling of liner

• Cost $1.5m/day for 6 month closure

Spalling

Controversy over causes of spalling

Build up of

pore pressures

Spalling

Controversy over causes of spalling

Thermally induced stresses

Combination of both

Hygro-Thermal-Mechanical Model

• Considers concrete as a deformable, multi-phase material

• S - solid skeleton

• L - liquid water/free (evaporable) water,

• G - Gas (dry air + water vapour)

• Elastic-damage (thermal and mechanical damage)

( ) ( )t

Et

LDLL

LL

∂

∂+−⋅−∇=

∂

∂ ρερε&J

( )LV

VG Et

&+⋅−∇=∂

∂J

ρε ~

( )A

AG

tJ⋅−∇=

∂

∂ ρε ~

( ) ( ) ( ) ( )t

ETCTkt

TC LD

DLE∂

∂−−∇⋅−∇−⋅−∇=

∂

∂ ρελλρρ &v

Hygro-Thermal-Mechanical Model

• Momentum balance

• Free (Evaporable) Water mass conservation

• Water Vapour mass conservation

• Dry Air mass conservation

5 conservation equations

Energy conservation

( )' 0ij ij pore i

j

P bx

σ αδ∂

− + =∂

• Discretised in space - finite element formulation• Discretised in time - generalised mid-point, finite difference

scheme

• Where,

( ) 0=∇⋅∇− uKuC &

Hygro-Thermal-Mechanical Model

;

0

0

0

=

MVMPMT

AVAPAT

TVTPTT

uVuPuTuu

KKK

KKK

KKK

KKKK

K

=

V

GP

T

u

ρ~

u;

0

0

0

0000

=

MVMPMT

AVAPAT

TVTPTT

CCC

CCC

CCCC

0

100

200

300

400

500

600

700

800

900

1000

0 10 20 30 40 50 60

Tem

pe

ratu

re (

°C)

Time (min)

Concrete elements• wall• column• I-beam

Different levels of pore pressures• Moisture contents• Permeabilities

Numerical Investigations

ISO834 FireCurve}

Isolate contributions of

• thermally induced stresses

• pore pressure

Numerical Investigations

( ) 0Pore

Pα′∇ ⋅ − + =σ I b 0∇⋅ + =σ b

Concrete Wall

With Pore Pressure term Without Pore Pressure term

Permeability =1××××10-17m2; Relative Humidity = 1%

Concrete Wall

With Pore Pressure term Without Pore Pressure term

Permeability =5××××10-21m2; Relative Humidity = 90%

Concrete WallPermeability =5××××10-21m2; Relative Humidity = 90%

Concrete Column

Concrete ColumnPermeability =1××××10-19m2; Relative Humidity = 65%

Mech

Damage

Stress

Pore

Pressure

Concrete ColumnPermeability =1××××10-19m2; Relative Humidity = 65%

With Pore

Pressure term

Without

Pore

Pressure term

Concrete ColumnPermeability =1××××10-21m2; Relative Humidity = 80%

Mech

Damage

Pore

Pressure

Concrete Column

Open boundary – free heat and mass transfer

Closed boundary – no heat and mass transfer

0.43m

0.13m

0.04m

Concrete I-beam

Mech

Damage

Stress

Pore

Pressure

Conclusions

• Damage/fracture patterns qualitatively agree with the experimental observations of spalling

• Thermally induced stresses seem to be the primary cause of damage and (by inference) spalling

• Pore pressures seem to have a negligible (or at most secondary) effect

Further Work

• Consider additional geometries• I-beam• Round column• Tunnel linings• Etc.

• Investigation of damage model effects

• Consider multi-scale approach

Further Work

• Multi-scale approach

Experimentation& Characterisation

MacroscaleSimulations

MicroscaleSimulations

Experim

ental validation

of simulations

Sim

ulations inform design

& fo

cus of expe

riments D

evel

op v

irtua

l lab

orat

ory

Multiscale framew ork:

Computational homogenization

for scale transition

(Edinburgh)

(Newcastle) (Glasgow)

Exp

erim

enta

l val

idat

ion

of s

imul

atio

ns

TripartiteResearchStrategy