overview - university of...
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Overview
• Introduction to concrete at high temperature
• Introduction to spalling
• Coupled hygro-thermal-mechanical model
• Benchmark examples and results
• Conclusions
• Future developments
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• 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
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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.
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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
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• Difficult to define
• Simply:
• A loss of material from the cross-section of a concrete member (sometimes explosively)
Spalling
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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
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Spalling
Controversy over causes of spalling
Build up of
pore pressures
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Spalling
Controversy over causes of spalling
Thermally induced stresses
Combination of both
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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)
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( ) ( )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∂
− + =∂
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• 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
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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}
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Isolate contributions of
• thermally induced stresses
• pore pressure
Numerical Investigations
( ) 0Pore
Pα′∇ ⋅ − + =σ I b 0∇⋅ + =σ b
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Concrete Wall
With Pore Pressure term Without Pore Pressure term
Permeability =1××××10-17m2; Relative Humidity = 1%
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Concrete Wall
With Pore Pressure term Without Pore Pressure term
Permeability =5××××10-21m2; Relative Humidity = 90%
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Concrete WallPermeability =5××××10-21m2; Relative Humidity = 90%
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Concrete Column
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Concrete ColumnPermeability =1××××10-19m2; Relative Humidity = 65%
Mech
Damage
Stress
Pore
Pressure
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Concrete ColumnPermeability =1××××10-19m2; Relative Humidity = 65%
With Pore
Pressure term
Without
Pore
Pressure term
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Concrete ColumnPermeability =1××××10-21m2; Relative Humidity = 80%
Mech
Damage
Pore
Pressure
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Concrete Column
Open boundary – free heat and mass transfer
Closed boundary – no heat and mass transfer
0.43m
0.13m
0.04m
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Concrete I-beam
Mech
Damage
Stress
Pore
Pressure
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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
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Further Work
• Consider additional geometries• I-beam• Round column• Tunnel linings• Etc.
• Investigation of damage model effects
• Consider multi-scale approach
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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
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