Structural Engineering International
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Post-Earthquake Fire Assessment of Reinforced
Concrete Frame Structures
Hugo Vitorino(PhD Student), Paulo Vila Real(Prof.), Carlos Couto(Dr,
Research Assistant) & Hugo Rodrigues(Assoc. Prof.)
To cite this article: Hugo Vitorino(PhD Student), Paulo Vila Real(Prof.), Carlos Couto(Dr,
Research Assistant) & Hugo Rodrigues(Assoc. Prof.) (2023) Post-Earthquake Fire Assessment
of Reinforced Concrete Frame Structures, Structural Engineering International, 33:4, 596-610,
DOI: 10.1080/10168664.2022.2062084
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Published online: 25 May 2022.
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Post-Earthquake Fire Assessment of Reinforced Concrete
Frame Structures
Hugo Vitorino
, PhD Student; Paulo Vila Real
, Prof.; Carlos Couto
, Dr, Research Assistant; Hugo Rodrigues
, Assoc. Prof.,
RISCO, Department of Civil Engineering, University of Aveiro, Portugal. Contact: hugo.vitorino@ua.pt.
DOI: 10.1080/10168664.2022.2062084
Abstract
Earthquakes can cause several catastrophic events and the consequences of
fires in urban areas can be even worse than the consequences of the
earthquake itself. Several numerical models were developed with SAFIR—
software that models the behaviour of structures subject to fire for reinforced
concrete (RC) frames to study their post-earthquake fire behaviour. First, a
calibration was performed to validate the modelling strategy. Subsequently,
two different frame typologies were considered, and a parametric study was
carried out considering as the main variables the location and configuration
of the damage caused by the earthquake and the location of the fire within
the structure. The results show that the damaged RC frames have a lower fire
resistance when compared with the undamaged frames. It was observed that
the difference in time until collapse between an undamaged frame and a
heavily damaged frame can be higher than 2 h. This observation is
particularly relevant since, after a large earthquake, the rescue teams are
generally overloaded, and consequently the response times are higher than
that. This, combined with the reduction of the fire resistance of the reinforced
concrete elements caused by the earthquake, can lead to increased severity
and ultimately to the losses.
Keywords: post-earthquake fire; fire safety; fire resistance; reinforced concrete;
numerical analysis
Introduction
Post-earthquake fires are events with
high consequences for societies
where the damage caused by the fire
can be more severe than the damage
caused by the earthquake itself.
There are examples of major earthquakes that caused several ignitions
leading to fires, namely to conflagrations. The 1906 San Francisco and
the 1923 Kanto earthquakes had
several outbreaks of fire that
evolved into conflagrations. In the
1993 Hokkaido Nansei-oki earthquake, the town of Aonae was
destroyed by conflagration following
the earthquake and a tsunami.1
Damage from post-earthquake fires
may become extensive due to the
limited availability of firefighting
resources in a case where multiple
fires can occur almost simultaneously,
and the arrival of firefighters is hampered by the blockage of streets
from collapsed buildings.1,2
The major causes of post-earthquake
fires are primarily electrical or gas
related, but can also be related to
open flames, hot surfaces, exothermic
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chemical reactions from spilled
chemicals and fires lit intentionally.1–
3
Electrical causes are increasing proportionally in comparison with earlier
earthquakes.2 It is not possible to
eliminate all fire outbreaks after an
earthquake, but it is possible to
reduce the risk of these if some preventive measures are applied.1 For
example, the installation of earthquake shut-off valves in building gas
metres is a solution that decreases
the amount of gas inside a building
after an earthquake.4,5 The structural
and non-structural damage caused by
earthquakes in buildings can lead to
the loss of integrity of passive protection systems. Passive protection
systems can be damaged by cracking,
buckling or breaking, which can lead
to openings that can permit the
increased ventilation of compartment
fires.1 After an earthquake, active fire
protection systems, such as detection,
alarm and suppression systems, may
be malfunctioning, thus becoming
unreliable. This aspect can lead to
undetected ignitions that can cause
large fires which will be more difficult
to extinguish.1,3 The responses to
building fires are a combination of
active and passive fire protection
systems and manual firefighting by a
fire brigade. It is necessary to have
adequate water supplies to be able
to stop the spread of fire, but urban
underground
water
distribution
systems are very vulnerable to earthquake shaking, and failures are
expected after an even moderate
earthquake.1,4 The response of fire
brigades can be impaired owing to
reporting delays caused by failure in
communication systems, impassable
routes or traffic jams.1,3 All these
factors combined, failure of passive
and active fire protection systems,
delays in response of fire brigades
and reduced or exhausted water
supplies will lower the possibilities of
immediate fire extinguishment. Consequently, bigger fires and even conflagrations can occur that can
ultimately lead to the loss of structures and lives.
There are some numerical works that
study post-earthquake fires in structures. Some of these works use a
sequential analysis method for considering the effect of both earthquake and fire on a structure. This
method has three loading stages, the
first one is the application of gravity
loads, which are assumed to be
static and uniform, followed by a
pseudo earthquake load in a pushover style or nonlinear time history
analysis, and in the end, a fire load
is applied to the structure.6–10 The
results of these works for reinforced
concrete (RC) structures show that
structures that have suffered significant damage from earthquakes have
lower fire resistance than undamaged
structures, which indicates the huge
impact of damage to the fire resistance of structures.8 Some studies
have observed that the fire resistance
rating, when whole frames are
exposed to fire, is very similar to the
situation when only the beams are
exposed to fire, suggesting that the
fire resistance of the frames is
mainly dependent on the resistance
of the beams.9,10
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Research on the post-earthquake fire
behaviour of structures is limited,11–
13
especially regarding the experimental investigation of post-earthquake
fire in RC structures. Nevertheless,
there are a few studies on the postearthquake fire behaviour of RC
columns and frames. To study the
fire behaviour of concrete columns
with prior damage, eight RC specimens were subjected to cyclic loadings at room temperature.14 The
damaged specimens and one control
specimen without damage were then
tested considering the ISO 834 fire
curve. The experimental work
showed that, when compared with
the drift ratio, the axial load ratio
had a more significantly adverse
effect on the spalling of the column’s
concrete cover during the cyclic
loading test.14 The severe loss of the
concrete cover in the plastic hinge
region of the columns resulted in
faster heat penetration into the inner
concrete in this region during the subsequent fire test.14 It was found that,
the more severe the damage in the
columns, the less was the maximum
elongation of the column in fire and
the higher the axial load ratio, as
well as the less was the maximum
thermal elongation in the damaged
column. The authors also observed
that the influence of the volumetric
transverse reinforcement ratio on the
axial deformation of damaged
columns was insignificant.14 There
are also studies regarding the performance of RC frames to post-earthquake fire.15–19 The observations of a
single storey RC frame that was subjected to seismic damage and
subsequently to fire showed that the
position of the opening in the compartment and the resulting movement
of the fire plume and hot gases had a
considerable influence on the temperature evolution in the structural sections.15 Consequently, the location of
the fire may or may not overlap with
the locations of the damage resulting
from the seismic action.15 In this
study, it was also reported that the
temperature distribution throughout
the compartment was non-uniform
due to the highly varying surface
fluxes imposed by the fire, which
shows that consideration of a
uniform compartment temperature
in fully developed fires may not be a
very accurate representation.15–17,19
The tests conducted in Ref. [16]
showed the vulnerability of thin
elements (e.g. slabs and shells) of
non–ductile RC frames to spalling in
post-earthquake fire events. The
brick infill walls provided insulation
to the RC structural elements, which
led to a slow transmission of heat to
these elements. This is a beneficial
influence of masonry walls that
should be considered when designing
columns and beams that are integrated in masonry walls.16 In addition,
it was observed that higher levels of
the cyclic loading on the RC frame
induced wider cracks which led to
the development of higher temperatures in the structural elements of
the frame.17,19 The cracks that
appeared in the different elements
during the tests suggest that the
details of the steel reinforcement
may have critical implications for the
global behaviour of the structure
when exposed to fire.17,19 The experimental test demonstrated a better
performance of the RC frames with
ductile detailing because the recommendations that are generally
used for seismic design have a key
role in increasing the fire resistance
of the structure.15,19
The strength and stiffness degradation
that occur at different levels of seismic
demand are important aspects for
understandong the post-earthquake
fire response of structures. Some
studies focused on the nonlinear modelling of the strength and stiffness
degradation to obtain a comprehensive assessment of a structural
system.20 There are also studies that
analysed the common occurrence of
fires in base-isolated structures following a seismic event.21 The increasing
application of base-isolated techniques
to provide seismic protection need to
be complemented with studies regarding the effectiveness of those techniques not only with respect to
seismic behaviour but also with
respect to fire behaviour.21 It is important to have information regarding the
degradation of mechanical properties
during a fire for an understanding of
the seismic performance of an isolated
structure due to the possibility of
aftershocks.21
Post-earthquake fire is a multifaceted
phenomenon, where the behaviour of
structures can depend on many
aspects, some of them perhaps not
immediately identified at first hand. It
is important to have a comprehensive
Structural Engineering International Nr. 4/2023
view when analysing this phenomenon
because there are factors, such as the
ones mentioned previously, that can
significantly affect the safety of the
structures in a post-earthquake fire
scenario.
Simplified Methodology for
Post-Earthquake Fire
Assessment of RC Frames
Numerical Modelling Assumptions
The software SAFIR22,23 was used to
develop the numerical models for
investigating post-earthquake fire on
RC frames. SAFIR can perform the
analysis of structures at elevated temperatures and under ambient temperature, as the thermal and mechanical
analyses are calculated separately and
consecutively. The temperature distribution deeply influences the mechanical response.22,23 The concrete and
steel models defined in SAFIR are
based on the constitutive models
defined in EN 1992-1-2.24 The parameters for the concrete model that
are input are of the aggregate
type (e.g. siliceous or calcareous), the
Poisson ratio and the compressive
and tensile strengths. Transient creep
can be treated implicitly or explicitly
in the model. The implicit formulation
corresponds to the Eurocode model,
while the explicit formulation is a
refinement of the Eurocode model
but is also able to consider the nonreversibility of transient creep strain
when the stress and/or temperature is
decreasing.25,26 The beam finite
element was used in the mechanical
FEM simulations. The beam finite
element is straight in its undeformed
geometry. The position of the beam is
defined by three nodes, two end
nodes and a third node that defines
the position of the local y-axis of the
beam. The geometry of the cross
section is defined by a fibre model.
Each fibre can be of a different
material, which allows the creation of
reinforced concrete sections. Some
assumptions are considered in the
beam element: the cross section
remains
plane
under
bending
moments, yielding is only considered
in the longitudinal direction of the
member, and non-uniform torsion is
considered.23,27 The temperature distribution in the cross section of the
elements is obtained using a 2D analysis. SAFIR uses linear isoparametric
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597
finite elements with classical shape
functions to represent the geometry
and the temperature field in the
element, based on the temperature at
the nodes. Heat transfer by conduction
according to the Fourier law is considered in the material. The temperature field between adjacent elements
does not have a discontinuity. The
temperature changes linearly on all
the borders of the elements and the
temperature at a common border is
the same in both elements.25
The constitutive relationships are
based on the strain decomposition
model of Eq. (1):27
etot = eth + es + etr + ei
(1)
with etot the total strain, obtained from
spatial derivatives of the displacement
field; eth the thermal elongation,
dependent only on the temperature;
es the stress related strain, which contains the elastic and plastic part of
the strain; etr the transient creep, a
term that appears in concrete during
first heating under load; and ei is an
initial strain that can be used either
for initial prestressing or for the
strain that exists in in situ concrete
when it hardens at a moment when
loads already exist in the structure.27
The models considered in the analyses
are SILCON_ETC for the concrete
and STEELEC2EN for the reinforcing
steel. The SILCON_ETC model
represents normal strength concrete,
with siliceous aggregates based on the
laws of part 1–2 of Eurocode 224 and
with explicit transient creep. STEELEC2EN corresponds to reinforcing
carbon steel from EN 1992-1-2.22,24
The numerical modelling strategy consists in the development of several
beam and column cross sections with
different simulated seismic damage
and fire exposure, which are then considered in different frame configurations. The times until collapse of the
frames are compared to ascertain the
most severe fire and damage scenarios.
A scheme of the modelling strategy is
presented in Fig. 1.
Seismic Damage
To consider seismic damage, the first
step is the definition of the cross sections considering both the original
(undamaged) and the seismic damage
situations. To simulate the damage
induced by an earthquake, a reduction
of the cover of the RC elements was
considered. Three damage types were
considered, the damage type D0/D1
corresponds to an intact section (D0)
or a section with minor cracks (D1),
damage D2 corresponds to slight
damage with some concrete spalling,
related to the loss of concrete cover
and simulated by the removal of
exterior fibres (50% of the cover
section) and damage D3 corresponds
the severe damage in the elements,
with large concrete spalling, simulated
Fig. 1: Scheme of the modelling strategy: (a) sections with simulated seismic damage; (b) fire
frontiers in the damaged sections; and (c) different frame configurations
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by the removal of the entire concrete
cover, leaving the longitudinal steel
reinforcement exposed. The same
numerical model was considered for
damage D0 and D1 since, according
to the literature, small cracks do not
significantly influence thermal evolution through concrete.28,29 The
extent of the types of damage considered in this numerical study was
obtained from the definitions of
damage states presented in FEMA
356.30 It was considered that damage
D0/D1, D2 and D3 correspond to
Immediate Occupancy (IO), Life
Safety (LS) and Collapse Prevention
(CP), respectively. At the IO level,
minor damage in the structural
elements is observed; at the LS level,
extensive damage is observed to
beams, spalling of cover and shear
cracking of ductile columns; and at
the CP level, extensive spalling in
columns and beams is observed.9,30,31
At the section level, the damage was
assumed to be different between the
columns and the beams. In the
columns, the damage was considered
to affect all sides of the cross section,
while in the case of beams, damage
was only considered on the bottom
and sides since it was assumed that
the earthquake did not damage the
top side of beams and that there was
no detachment of concrete. Figure 2
represents the sections of the
columns and beams with damage of
types D0/D1, D2 and D3.
The damage that an RC element
(beam or column) suffers after an
earthquake is usually located near the
extremities of the elements. The
observed length of that damage is
usually between 0.5H and 1.5H,
where H is the height of the
section.10 In all the frames that were
Fig. 2: Sections of the columns and beams
with damage D0/D1 (40 mm cover), D2
(20 mm cover) and D3 (no cover)
Structural Engineering International Nr. 4/2023
modelled in this study, the length of
the damage considered was H.
Fire Action
The fire curve considered in the
thermal analyses was the standard
fire curve of ISO 834.32 SAFIR then
calculates the temperature evolution
as a function of time, which is then
used as input data in the subsequent
step to perform the mechanical analysis. In the mechanical analysis, the
structural behaviour is calculated
based on the geometry, support conditions, loads and strength of the
materials. The temperature increase
reduces the strength of the materials
and leads to thermal elongation that
causes an increase in the displacements until the collapse of the structure. In SAFIR, the numerical
analysis will stop at the time specified
by the user (240 min), or if it finds
numerical problems at the material
level, or when it cannot converge to a
state of equilibrium.27,33 The standard
fire curve of ISO 834 is the most
common fire curve considered in the
numerical and experimental work
found in the literature.
Modelling Strategy Validation
Introduction
To evaluate the effectiveness of the
modelling strategy, it was deemed
necessary to develop a numerical
model representative of an experimental work. The experimental work
under consideration is the post-earthquake fire assessment of an RC
column.34,35 The experimental study
consisted in the testing of six columns
under post-earthquake fire conditions.
In the study, ductile and non-ductile
columns were tested at different
levels of earthquake damage and
axial load ratio. The square columns
had a section of 23 cm and a length of
180 cm. The columns had four longitudinal steel bars with a diameter of
12 mm. The columns in the experimental study also had transversal
reinforcement, which was not considered in the numerical simulations,
following the usual strategy found in
the literature for similar studies. The
clear cover of the RC section was
25 mm, the grade of the reinforcement
steel was S500 and the specimens were
cast with an M25 concrete mix.
Additional details can be found in
Refs. [34,35].
Experimental Loading Sequence
The experimental procedure to test the
post-earthquake fire response of the
RC columns consisted of the following
steps:34,35 (i) the column was loaded
statically in pure compression up to
the desired load level and the load
was maintained for at least 45 min
before the application of cyclic
loading; (ii) the axial load was maintained at a constant level, and the
lateral cyclic loading was applied up
to the desired maximum drift level;
(iii) after damaging the column to the
required level of maximum drift, the
lateral and axial loads on the column
were slowly removed. Subsequently,
the column was removed from the
earthquake loading setup and placed
in the compression testing machine
for a load-bearing test under fire conditions; (iv) the damaged portion of
the column was subjected to the fire
curve of ISO 834 for a one-hour duration without loading the column
mechanically; and finally (v) after one
hour of heating, the column was
loaded in axial compression until it
failed. The loading was applied under
displacement controlled at a constant
rate of 2 mm/min. The temperature
change during step (v) was small, and
therefore it could be closely tested
under adiabatic conditions34,35 in the
numerical simulations.
Numerical Analysis Considerations
Three numerical models representative of the experimental tests were
defined in SAFIR. The experimental
details of the specimens considered in
the numerical analysis are presented
in Table 1. The important details considered for the numerical analysis
were the information relating to the
spalled concrete. The time–temperature curve considered in the numerical
analysis is represented in Fig. 3. For
the first hour, the fire curve is the
same as the fire of ISO 834 and after
one hour the temperature remains
constant until the end of the numerical
analysis. The properties of the concrete and reinforcing steel considered
in the numerical analysis are represented in Tables 2 and 3, respectively.
In Fig. 4 are represented three different cross sections that were defined in
SAFIR to simulate the three different
damage situations (spalled concrete)
caused by the cyclic loading. The reinforcing steel is represented in grey.
Figure 4a corresponds to the intact
section (cross-section a), Fig. 4b corresponds to a section with a cover
reduction of 20 mm (cross-section b)
and Fig. 4c corresponds to a section
with a cover reduction of 15 mm
(cross-section c). With these sections
it is then possible to model the
columns that are represented in Fig.
5. Figure 5a corresponds to the specimen ND-E0-A0 where all the
elements of the column have crosssection a. Figure 5b corresponds to
the specimen ND-E6-A350 where
element three has cross-section b and
the remaining elements have crosssection a. Finally, Fig. 5c corresponds
to the specimen D-E6-A350 where
element 3 has cross-section c and the
remaining elements have a crosssection a. The reduction of the cover
considered in the cross sections (Fig.
4) and the length of the elements of
the columns (Fig. 5) are based on
observations regarding the spalled
concrete in the experimental tests.
The information related to the
Spalled concrete
Axial load
capacity after
fire at max.
load (kN)
Ductile
detailing
Earthquake
damage (drift
%)
Axial
load
(kN)
Length
(mm)
Depth
(mm)
ND-E0A0
No
0
0
0
0
1110
ND-E6A350
No
6
350
150
20
709.8
D-E6A350
Yes
6
350
120
15
1108
Specimen
Table 1: Specimen details, concrete spalled during the earthquake and load resistance after
one-hour fire34,35
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599
numerical analysis at 6 mm of deformation is around 1300 kN.
Reinforcing steel properties24,36
Steel model
Fig. 3: Time–temperature curve considered
in the numerical analysis
Modulus of elasticity
210 GPa
Yield strength
550 MPa
Poisson ratio
0.3
Coefficient of
convection
25 W/m2K
Emissivity
Concrete properties
Reinforcing steel
diameter
24
Concrete model
Siliceous
aggregates24
Specific mass of
concrete
2464 kg/m3
Water content
36.96 kg/m3
Coefficient of
convection
25 W/m2K
Emissivity
0.7
Compression
strength
40 MPa
Tensile strength
0
Poisson ratio
0.2
Table 2: Concrete properties used in the
numerical analysis
spalled concrete is presented in Table
1. In the numerical analysis, the fire
curve is applied at the beginning of
the analysis (t = 0) and after one hour
an incremental axial compression
load is applied until the analysis
stops. Only the elements 2, 3 and 4
are subjected to the fire curve, the
temperature
of
the
remaining
elements remains constant at 20°C.
This consideration is based on the
figures presented in the experimental
study.34,35
Hot rolled, class
B24,36
0.7
12 mm
Table 3: Reinforcing steel properties used in
the numerical analysis
Axial Compression Response of the
Columns
The comparison between the experimental and numerical axial compression response of the RC columns
is represented in Figs. 6–8. Although
the peak values of the numerical analysis are different from those observed
experimentally, there is a relatively
good similarity between the experimental and the numerical results
regarding the stiffness of the column.
For the specimen ND-E0-A0 in Fig.
6, the results are similar until a deformation of about 1 mm, after which a
higher stiffness of the experimental
columns is observed when compared
with the numerical columns until a
deformation of about 3.5 mm. The
failure of the experimental RC
column is observed after a deformation of 6 mm while the numerical
analysis stops with a deformation of
almost 7 mm. The peak axial load
capacity after fire, observed in the
experimental results, is 1110 kN and
the axial load observed in the
Fig. 4: Column cross-section discretization: (a) intact section (ND-E0-A0); (b) section with
20 mm depth of spalled concrete (ND-E6-A350); and (c) section with 15 mm depth of
spalled concrete (D-E6-A350)
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In Fig. 7 is represented a comparison
between the experimental and numerical results for the specimen ND-E6A350. The results are very similar
regarding the stiffness of the column.
The numerical results show a slightly
higher axial load capacity of 766 kN
and lower deformation (5.4 mm)
when compared with the experimental
results of 709.8 kN and around 7 mm.
Finally, in Fig. 8 is represented a comparison between the experimental
and numerical results for the specimen
D-E6-A350. The results are very
similar until an axial load capacity
after fire of around 400 kN, after
which the numerical results indicate a
higher stiffness of the columns when
compared with the results of the experimental columns. The peak axial load
capacity after fire of the experimental
columns is 1108 kN while in numerical
columns it is around 900 kN.
In the experimental test, it was
observed that the columns that were
not detailed for ductile behaviour,
with higher confinements, showed a
more significant reduction in axial
load carrying capacity in fire conditions as reported by the authors.35
In the modelling strategy, the confinement reinforcement is not considered.
This aspect could explain the differences observed at the end of the
numerical results, especially on specimens ND-E6-A350 and ND-E0-A0,
which do not include ductile detailing.
Another important issue is that in the
experimental tests the axial load is
applied after one hour of heating;
however, the temperature in the postheating is not reported and was considered constant in the numerical
analysis, which may lead to an overestimation of the results as observed.
The similarity between the experimental and numerical results indicates a
reliable approach to simulating the
damage observed in the RC columns.
Nevertheless, it is necessary to
perform more calibration studies on
other RC elements to ascertain the
reliability of this methodology better.
Certain characteristics of the numerical model, e.g. the fire curve considered in the thermal analysis and
the properties of the materials, need
to be well analysed to guarantee that
the considerations of the numerical
model are according to what was performed in the experimental tests.
Structural Engineering International Nr. 4/2023
Concrete properties24
Siliceous
aggregates24
Concrete model
Fig. 5: Column discretization: (a) specimen ND-E0-A0; (b) specimen ND-E6-A350; and (c)
specimen D-E6-A350
Specific mass of
concrete
2300 kg/m3
Water content
46 kg/m3
Coefficient of
convection
25 W/m2K
Emissivity
0.7
Compression
strength
30 MPa
Tensile strength
0
Poisson ratio
0.2
Table 4: Concrete properties used in the
numerical analysis
Reinforcing steel properties24,36
Steel model
Fig. 6: Comparison between the experimental and numerical results for the specimen ND-E0-A0
Fig. 8: Comparison between the experimental and numerical results for the specimen D-E6-A350
Hot rolled, class
B24,36
Modulus of elasticity
210 GPa
Yield strength
500 MPa
Poisson ratio
0.3
Coefficient of
convection
25 W/m2K
Emissivity
Reinforcing steel
diameter
0.7
25 mm
Table 5: Reinforcing steel properties used in
the numerical analysis
Temperature Evolution at the
Section Level
Fig. 7: Comparison between the experimental and numerical results for the specimen ND-E6-A350
Post-Earthquake Fire
Assessment in RC Frames
In this section, two different frames
are analysed (a one-bay/two-storey
plane frame, and a two-bay/threestorey plane frame). For each frame,
several configurations are considered
regarding the type and location of the
damage and the location of the fire.
The main objective of the analyses is
to compare the times until collapse of
the different frames and identify the
Fig. 9: Section of the columns (8Ø25) and
section of the beams (4Ø25)
scenario that leads to a lower time
until collapse. The comparison of the
times until collapse also allows the
evaluation of the impact of different
types of damage in the post-earthquake fire resistance of the RC frames.
Section Properties and
Characteristics
In Fig. 9 is represented the section of
the columns and the section of the
beams. In Tables 4 and 5 are described
all the properties used in the numerical
analyses of the RC frames.
Structural Engineering International Nr. 4/2023
In this section are presented the temperature profiles of the columns and
beams used later in the analyses of
the RC frames. The size of each fibre
in the sections of the columns and
beams is 1 cm × 1 cm. The temperature
profiles for damage D0/D1, D2 and D3
are presented for the columns and
beams. Each figure has four temperature profiles, corresponding to 1, 2, 3
and 4 h (from left to right). Each reinforcing steel bar is constituted by four
fibres and the contour of the reinforcement is represented with a blue line.
Figures 10–12 represent the temperature profiles of columns with damage
D0/D1, D2 and D3 considering the
curve of ISO 834, and Figs. 13–15 represent the temperature profiles of
beams with damage D0/D1, D2 and
D3 considering the curve of ISO 834
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601
Fig. 10: Temperature profiles of a column with damage D0/D1 at 60, 120, 180 and 240 min
(left to right) considering the curve of ISO 834
it takes around 60 min for the middle
reinforcement to reach the same temperature. The effect of the damage also
has a significant impact on the temperature of the reinforcement; for
instance at 90 min, the temperature
of the corner reinforcement on the
section with damage D3 is about
double the temperature of the corner
reinforcement in the section with
damage D0/D1. This aspect shows the
significant influence that the damage
and the position of the reinforcement
have on the temperature of the
reinforcement.
In the beams, the steel reinforcement
in the bottom has higher temperatures
when compared with the top reinforcement. The explanation of this is the
fact that there is no damage and no
fire frontiers considered on the top
side of the beam.
One-Bay/Two-Storey Plane Frame
Introduction
Fig. 11: Temperature profiles of a column with damage D2 at 60, 120, 180 and 240 min (left
to right) considering the curve of ISO 834
Fig. 12: Temperature profiles of a column with damage D3 at 60, 120, 180 and 240 min (left
to right) considering the curve of ISO 834
To understand the post-earthquake
fire in RC structures better, a numerical model was developed of 15 plane
frames with one bay and two storeys.
A parametric study was defined with
different assumptions regarding the
type of damage, location of the
damage and location of the fire. The
numerical simulations were calculated
using a 2D model. The frame has a permanent load distributed in the beams
(45 kN/m) and point loads in the
columns (370 kN).
The applied vertical loads were
defined to have columns with an axial
load ratio lower than 0.2. Figure 20
represents a scheme of the frame considered in the parametric study. Figure
21 represents the location of the
overall damage that is assumed and
the definition of the compartments,
namely compartment 1 (C1) and compartment 2 (C2).
Frames Characteristics
on three sides. The impact of the cover
reduction on the temperatures of the
steel reinforcement is clear in the
temperature profiles.
reinforcement of the columns, while
Figs. 18 and 19 show the temperature
evolution of the steel reinforcement
of the beams.
With the development of the temperature profiles of the columns and beams
is possible to analyse the temperature
evolution of the steel reinforcement
considering all types of damage.
Figures 16 and 17 show the temperature
evolution
of
the
steel
In the columns, the temperature of the
corner reinforcement is higher when
compared with the temperature of
the middle reinforcement. For
example, considering damage D3,
while it takes 30 min for the corner
reinforcement to reach about 750˚C,
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Scientific Paper
The parametric study comprises six
different configurations that were considered to evaluate the impact of the
damage location and the fire on the
time until collapse of the one-bay/
two-storey frames. In the first configuration (frames 1, 2 and 3), only damage
and fire in compartment 1 were considered. In the second configuration
(frames 4 and 5), damage in both compartments and fire only in compartment 1 were considered. In the third
Structural Engineering International Nr. 4/2023
compared with the frames with
damage D0/D1 (frame without
damage) that were already presented
in the first, third and fifth configurations, respectively. The difference
between the various frames with
damage D0/D1 is then only related to
the location of the fire in the compartments. Thus, there are three frames
with damage D0/D1, frame 1 in the
first and second configuration, frame
6 in the third and fourth configuration,
and finally frame 11 in the fifth and
sixth configuration.
Fig. 13: Temperature profiles of a beam with damage D0/D1 at 60, 120, 180 and 240 min
(left to right) considering the curve of ISO 834 on three sides
Fig. 14: Temperature profiles of a beam with damage D2 at 60, 120, 180 and 240 min (left to
right) considering the curve of ISO 834 on three sides
configuration (frames 6, 7 and 8),
damage in compartment 1 and fire in
both compartments were considered.
In the fourth configuration (frames 9
and 10), damage and fire in both compartments were considered. In the fifth
configuration (frames 11, 12 and 13),
damage in both compartments and
fire in compartment 2 were considered.
Finally, in the sixth configuration
(frames 14 and 15), damage in compartment 1 and fire in compartment 2
were considered. For all the frame configurations, all the levels of damage
were analysed, resulting in a total of
15 different models investigated.
Figure 22 represents the frame configurations considered.
Time Until Collapse
Table 6 and Fig. 23 represent the times
until collapse of one-bay/two-storey
plane frames. For the sake of comparison, it is important to mention that in
Fig. 23, for the second, fourth and
sixth configurations, the frames with
damage D2 and D3 are again
Structural Engineering International Nr. 4/2023
The difference in the time until collapse between frame 1 (damage D0/
D1) and frame 3 (damage D3) is
more than 2 h. This aspect shows the
great influence that the damage has
in the time until the collapse of the
structure. The difference in the time
until collapse between frame 1
(damage D0/D1) and frame 2
(damage D2) is more than 1 h, and
the same is also true between frame 2
(damage D2) and frame 3 (damage
D3). The damage D2 also has a significant impact on the time until collapse
of the structure. The results are quite
similar for the first configuration until
the fifth configuration (frame 1 to
frame 13), which seems to indicate
that, if there is damage and fire in the
same compartment, the fact that
there is damage and/or fire in the
other compartment does not have a
significant impact on the time until
the collapse of the structure. The
exception is in the sixth configuration
(frames 11, 14 and 15), where the
damage and fire are in different compartments. Because of that, it is
observed that the damage in these
frames does not have a significant
impact on the time until collapse of
the structure. As such, it should be
highlighted that the extent of damage
in a compartment that is not exposed
to fire does not significantly contribute
to the overall time until collapse of the
frame.
For the same assumptions regarding
the levels of damage, the different configurations (configuration 1 to configuration 5) have similar times until
collapse. Frame 1 and frame 8 are,
respectively, the ones with maximum
and minimum times until collapse.
The location of the damage and fire
for frame 1 is in compartment 1, but
the damage is assumed to be D0/D1,
which corresponds to the undamaged
case. Frame 8 represents the case that
was considered the most severe
Scientific Paper
603
damage (Damage D3) with both the
fire and location of the damage in the
same compartment (compartment 1).
In this regard, it is however interesting
to note that frame 8 has lower fire
resistance than frame 10, despite the
damage in frame 10 being assumed to
be in both compartments. Although
small, this difference may be related
to the fact that frame 8 has a higher
stiffness than frame 10, which leads
to slightly higher forces that in turn
lead to a faster collapse.
Two-Bay/Three-Storey Plane
Frame
Introduction
Fig. 15: Temperature profiles of a beam with damage D3 at 60, 120, 180 and 240 min (left to
right) considering the curve of ISO 834 on three sides
Following the analysis of the previously presented cases, it was
deemed necessary to study a different
frame typology corresponding to
plane frames with two bays and three
storeys to enlarge the parametric
study on post-earthquake fire in RC
structures. For this typology, 36
frames were defined with different
assumptions regarding the type of
damage, location of the damage and
location of the fire. These numerical
simulations were also developed
using a 2D model and both the geometry of the cross sections and the loads
considered for this new frame typology
were identical to those considered in
the previous case.
Figure 24 represents a scheme of the
frame typology considered in this
case. In Fig. 25 is represented the
location of the damage that is considered and the name of the
compartments.
Fig. 16: Temperature evolution of the column corner reinforcement
Frame Characteristics
Fig. 17: Temperature evolution of the column middle reinforcement
Several configurations were considered to evaluate the impact of the
location of the damage and the fire
on the time until collapse of the twobay/three-storey frames. Six different
configurations
were
considered
regarding the location of the types of
damage and six different configurations regarding the location of the
fire. The configurations regarding the
location of the types of damage
(damage configurations) are represented in Fig. 26. The configurations
regarding the location of the fire (fire
configurations) are represented in
Fig. 27. The numerical models were
defined such that, for each fire configuration, all the damage configurations
were
considered,
thus
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Scientific Paper
Structural Engineering International Nr. 4/2023
Fig. 18: Temperature evolution of the bottom reinforcement of a beam with three fire
frontiers
Figure 28 shows the results of the
frames that are entirely subjected to
damage D0/D1, D2 and D3 and for
each damage configuration all the fire
configurations are considered. Similarly to what was observed for the
one-bay/two-storey frame, for this
new typology, for each fire configuration, a difference is observed in the
time until collapse of about 2 h
between the frames with damage D0/
D1 and the frames with damage D3.
This aspect emphasises the great influence that the damage has on the time
until the collapse of the structure.
The difference in the time until collapse between frames with damage
D0/D1 and frames with damage D2 is
around 1 h, and the same is also
observed between the frames with
damage D2 and the frames with
damage D3. These differences are
similar to those also observed for the
one-bay/two-storey frame.
From the frames considered, the
highest time until collapse is
206.45 min (frame 410) and the
lowest time until collapse is 43.28 min
(frame 403). From the frames considered, frame 410 is the frame with
the lowest amount of damage considered (damage D0/D1 in all compartments) and where the fire
scenario is less severe (fire only in
compartment C11). By contrast,
frame 403 is the frame with the
highest amount of damage considered
(damage D3 in all compartments)
and where the fire scenario is more
severe (fire in all compartments).
Fig. 19: Temperature evolution of the top reinforcement of a beam with three fire frontiers
Fig. 21: Compartments and damage zones
combining all the fire and all the
damage configurations.
Time Until Collapse
Fig. 20: Scheme of the one-bay/two-storey
plane frames considered in the numerical
analyses
Table 7, Fig. 28 and Fig. 29 represent
the times until collapse of the frames
(one-bay/two-storey plane frames).
Structural Engineering International Nr. 4/2023
The results in Fig. 29 show a comparison between three different damage
configurations. The frames with
higher time until collapse, for each
damage configuration, are the frames
where fire is considered in both the
bottom compartments (frames 421,
427 and 433). Although the time until
collapse of these frames is the
highest, it is very similar to the time
until collapse of the frames where the
fire is only considered in compartment
C11 (frames 422, 428 and 434). Even if
the differences are small, it is interesting to notice that the frames with fire
in both bottom compartments have a
better fire resistance when compared
with the frames with fire in only one
of the bottom compartments. A
similar situation was also observed in
the one-bay/two-storey plane frame.
The small difference may be related
to the fact that frames 421, 427 and
433, due to the fire, have lower stiffness
Scientific Paper
605
Fig. 22: Frame configuration (fire and damage distribution)
Damage
Model
Fire
C1
C2
C1
C2
Time until collapse (min)
1
D0/D1
D0/D1
ISO834
–
188.35
2
D2
D0/D1
ISO834
–
117.25
3
D3
D0/D1
ISO834
–
45.61
4
D2
D2
ISO834
–
117.54
5
D3
D3
ISO834
–
45.62
6
D0/D1
D0/D1
ISO834
ISO834
173.3
7
D2
D0/D1
ISO834
ISO834
110.65
8
D3
D0/D1
ISO834
ISO834
40.98
9
D2
D2
ISO834
ISO834
114.39
10
D3
D3
ISO834
ISO834
44.42
11
D0/D1
D0/D1
–
ISO834
176.54
12
D2
D2
–
ISO834
121.93
13
D3
D3
–
ISO834
48.71
14
D2
D0/D1
–
ISO834
176.64
15
D3
D0/D1
–
ISO834
176.5
Table 6: Time until collapse of the frames considered
Fig. 23: Time until collapse of the frames 1 bay and 2 storeys
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Scientific Paper
Fig. 24: Scheme of the two-bay/three-storey
plane frames considered in the numerical
analyses
Fig. 25: Compartments and damage zones
than frames 422, 428 and 434, which
leads to slightly lower forces that consequently leads to a slightly later
collapse.
The lower time until collapse of the
frames that have damage D3 in the
bottom compartments is 43.28 min
(frame 403) and the higher time until
collapse of those frames is 59.92 min
(frame 427), which represents a relative difference of −38%. In this case,
for the two-bay/three-storey plane
frame, the types of damage and
location of the fire considered in the
structure can represent a significant
impact on the time until collapse of
the structure.
Similarly, the lower time until collapse
of the frames that have damage D2 in
the
bottom
compartments
is
103.67 min (frame 417) and the
higher time until collapse of those
frames is 123.67 min (frame 433),
representing a relative difference of
−19%. In this case, observing only
the frames with damage D2 in the
bottom compartment, the types of
damage and location of the fire considered in the structure do not represent such a significant impact on
Structural Engineering International Nr. 4/2023
damage on the fire resistance of RC
structures.
The development of these numerical
investigations allowed the study of
the impact of damage and fire in
reinforced concrete frames (one-bay/
two-storey frames, and two-bay/threestorey frames).
Fig. 26: Location of the types of damage in the configurations considered: damage D0/D1
(green); damage D2 (yellow); damage D3 (red)
Fig. 27: Locations of fire in the configurations considered
the time until collapse of the structure
when compared with the frames that
have damage D3 in the bottom compartments. Nevertheless, a difference
is observed of 20 min in the time until
collapse between these two frames
(frames 417 and 433).
In Fig. 29, when comparing the results
of the two configurations with damage
D3 in the bottom compartments, it is
observed that the times until collapse
are very similar. The difference in
these configurations is in the damage
considered in compartments C21 and
C22 (damage D2 and D0/D1). The
similar times until collapse of these
frames seems to indicate that a slight
variation in the damage considered in
compartments C21 and C22 does not
significantly impact the behaviour of
the frame for more severe damage
(damage D3) in the bottom compartments (compartments C11 and C12).
It is interesting to notice that, in Fig.
29, for each damage configuration,
the frame with lower time until collapse is never the frame with fire in
all compartments. This remark indicates that more compartments on fire
does not necessarily represent a
lower time until collapse of the frame.
Conclusions
The present work starts with the evaluation of the effectiveness of the modelling strategy comparing results from an
experimental test with the proposed
simplified approach. The results
obtained were relatively similar to
those of the experimental study,
showing that the modelling strategy
can be used with a certain reliability
to perform several numerical investigations regarding the impact of
Structural Engineering International Nr. 4/2023
Comparison between the results of the
parametric study of the various models
allowed the observation that the
damaged frames have a lower fire
resistance than the undamaged
frames, especially when the reinforcement is exposed to the fire. It was
observed that the difference in the
time until collapse of an undamaged
frame (damaged D0/D1) and a
heavily damaged frame (damage D3)
can be higher than 2 h.
In the one-bay/two-storey frames, it
was observed that, if there is damage
and fire in the same compartment,
the fact that there is damage and/or
fire in the other compartment does
not significantly change the time
until collapse of the frame. This
aspect is not observed for the twobay/three-storey frames, where the
difference in the time until collapse
of frames with damage D2 and D3 in
the bottom compartments (C11 and
C12) can be significant when considering different fire and damage configurations,
i.e.
different
configurations but with damage D2
and D3 in the bottom compartments,
meaning that the frame geometry
plays an important role in the postearthquake fire resistance.
It was observed that the fire configuration where all the compartments are
exposed to fire does not necessarily
correspond to the worst possible situation regarding the time until collapse,
and certain damage and fire configurations can result in lower times until
collapse.
Finally, it is important to mention that,
as observed in this study, frames with
different characteristics and properties
can lead to different conclusions. In
addition, it is necessary to confirm if
the main findings of this article
remain valid for the 3D behaviour of
complete structures, since the methodology followed herein, in principle,
should be valid for these conditions.
It should be mentioned also that
some studies point to the fact that 3D
modelling to study the post earthquake fire and simulate the load
Scientific Paper
607
Damage
Fire
Model
C11/C12
C21/C22
C31/C32
C11
C12
C21
C22
C31
C32
Time (min)
401
D0/D1
D0/D1
D0/D1
ISO834
ISO834
ISO834
ISO834
ISO834
ISO834
167.42
402
D2
D2
D2
ISO834
ISO834
ISO834
ISO834
ISO834
ISO834
107.63
403
D3
D3
D3
ISO834
ISO834
ISO834
ISO834
ISO834
ISO834
43.28
404
D0/D1
D0/D1
D0/D1
ISO834
ISO834
ISO834
ISO834
–
–
187.04
405
D2
D2
D2
ISO834
ISO834
ISO834
ISO834
–
–
115.42
406
D3
D3
D3
ISO834
ISO834
ISO834
ISO834
–
–
46.42
407
D0/D1
D0/D1
D0/D1
ISO834
ISO834
–
–
–
–
206.33
408
D2
D2
D2
ISO834
ISO834
–
–
–
–
123.08
409
D3
D3
D3
ISO834
ISO834
–
–
–
–
59.42
410
D0/D1
D0/D1
D0/D1
ISO834
–
–
–
–
–
206.45
411
D2
D2
D2
ISO834
–
–
–
–
–
122.58
412
D3
D3
D3
ISO834
–
–
–
–
–
57.83
413
D0/D1
D0/D1
D0/D1
ISO834
–
ISO834
–
–
–
187.5
414
D2
D2
D2
ISO834
–
ISO834
–
–
–
114.19
415
D3
D3
D3
ISO834
–
ISO834
–
–
–
45.92
416
D0/D1
D0/D1
D0/D1
ISO834
–
ISO834
–
ISO834
–
158.25
417
D2
D2
D2
ISO834
–
ISO834
–
ISO834
–
103.67
418
D3
D3
D3
ISO834
–
ISO834
–
ISO834
–
43.83
419
D3
D2
D0/D1
ISO834
ISO834
ISO834
ISO834
ISO834
ISO834
48.65
420
D3
D2
D0/D1
ISO834
ISO834
ISO834
ISO834
–
–
47.50
421
D3
D2
D0/D1
ISO834
ISO834
–
–
–
–
59.83
422
D3
D2
D0/D1
ISO834
–
–
–
–
–
58.67
423
D3
D2
D0/D1
ISO834
–
ISO834
–
–
–
46.67
424
D3
D2
D0/D1
ISO834
–
ISO834
–
ISO834
–
48.17
425
D3
D0/D1
D0/D1
ISO834
ISO834
ISO834
ISO834
ISO834
ISO834
48.51
426
D3
D0/D1
D0/D1
ISO834
ISO834
ISO834
ISO834
–
–
46.08
427
D3
D0/D1
D0/D1
ISO834
ISO834
–
–
–
–
59.92
428
D3
D0/D1
D0/D1
ISO834
–
–
–
–
–
58.75
429
D3
D0/D1
D0/D1
ISO834
–
ISO834
–
–
–
47.17
430
D3
D0/D1
D0/D1
ISO834
–
ISO834
–
ISO834
–
47.08
431
D2
D0/D1
D0/D1
ISO834
ISO834
ISO834
ISO834
ISO834
ISO834
114.50
432
D2
D0/D1
D0/D1
ISO834
ISO834
ISO834
ISO834
–
–
106.58
433
D2
D0/D1
D0/D1
ISO834
ISO834
–
–
–
–
123.67
434
D2
D0/D1
D0/D1
ISO834
–
–
–
–
–
123.01
435
D2
D0/D1
D0/D1
ISO834
–
ISO834
–
–
–
113.67
436
D2
D0/D1
D0/D1
ISO834
–
ISO834
–
ISO834
–
113.58
Table 7: Time until collapse of the frames considered
distribution between columns due to
heating and, most importantly, benefit
from the so-called tensile membrane
608
Scientific Paper
action.37,38 For this reason, the study
carried out in this work will be
further extended to understand better
and increase current knowledge of
the post-earthquake fire phenomenon
in reinforced concrete structures.
Structural Engineering International Nr. 4/2023
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Disclosure Statement
No potential conflict of interest was
reported by the authors.
Funding
This work was supported by Fundação para
a Ciência e a Tecnologia—the Foundation
for Science and Technology (FCT),
Aveiro Research Centre for Risks and Sustainability in Construction (RISCO)
[Grant Number FCT/UIDB/ECI/04450/
2020]; the first named author acknowledges
FCT for providing a PhD grant [Grant
Number SFRH/BD/148582/2019].
ORCID
Hugo Vitorino http://orcid.org/00000002-6213-2119
Paulo Vila Real
http://orcid.org/
0000-0002-7221-410X
http://orcid.org/0000Carlos Couto
0003-0865-2225
http://orcid.org/
Hugo Rodrigues
0000-0003-1373-4540
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Structural Engineering International Nr. 4/2023