Structural Engineering and Mechanics, Vol. 45, No.6 (2013) 803-819
803
Numerical analyses for the structural assessment of steel
buildings under explosions
Pierluigi Olmati , Francesco Petrinia and Franco Bontempib
Department of Structural and Geotechnical Engineering, Sapienza University of Rome, Rome, Italy
(Received September 12, 2012, Revised January 12, 2013, Accepted February 19, 2013)
Abstract. This paper addresses two main issues relevant to the structural assessment of buildings subjected
to explosions. The first issue regards the robustness evaluation of steel frame structures: a procedure is
provided for computing “robustness curves” and it is applied to a 20-storey steel frame building, describing
the residual strength of the (blast) damaged structure under different local damage levels. The second issue
regards the precise evaluation of blast pressures acting on structural elements using Computational Fluid
Dynamic (CFD) techniques. This last aspect is treated with particular reference to gas explosions, focusing
on some critical parameters (room congestion, failure of non-structural walls and ignition point location)
which influence the development of the explosion. From the analyses, it can be deduced that, at least for the
examined cases, the obtained robustness curves provide a suitable tool that can be used for risk management
and assessment purposes. Moreover, the variation of relevant CFD analysis outcomes (e.g., pressure) due to
the variation of the analysis parameters is found to be significant.
Keywords: blast engineering; robustness; progressive collapse; blast action; gas explosions; steel buildings
1. Introduction
An explosion event, having a low probability of occurrence but severe consequences, due to a
possible structural collapse, is a so-called “Low Probability and High Consequences (LP – HC)”
event (Bontempi 2010, Starossek 2009). The high potential losses associated to these events (HSE
2011) make the design of structures for blast loads a key issue. In this respect, three main concepts
are particularly relevant: i) the structural robustness evaluation (Bontempi et al. 2007, Yagob et al.
2009, Ghosn et al. 2010); ii) the quantitative assessment of the blast pressure on the structural
elements (UFC 2008, Dusenberry 2010); iii) the evaluation of the coupling between the dynamic
behavior of the structure and the surrounding air moved by the blast (Fluid-Structure Interaction FSI) (Subramanian et al. 2009, Teich and Gebbeken 2011).
In a damage-based definition (Starossek and Haberland 2011), the structural robustness is the
ability of a structure to withstand local damages without suffering disproportionate consequences
(see e.g., Giuliani 2009, Brando et al. 2012). Strategies and methods for the robustness
Corresponding author, Ph.D. Candidate, E-mail: pierluigi.olmati@uniroma1.it
Associate Researcher, E-mail: francesco.petrini@uniroma1.it
b
Professor, E-mail: franco.bontempi@uniroma1.it
a
804
Pierluigi Olmati, Francesco Petrini and Franco Bontempi
achievement are discussed, within a dependability framework adapted from the electronic
engineering field, in Gentili et al. (2013) and Sgambi et al. (2012). In case of sudden loss of one or
more structural elements (typical failure in case of explosions), robustness is related to the
susceptibility of the system towards progressive or disproportionate collapse (UFC 2009).
Regarding the second topic outlined above, i.e. the assessment of the blast action due to gas
explosions, it is important to highlight the fact that the blast pressure on structural members varies
significantly depending on some particular environmental characteristics, such as room congestion,
failure of non-structural walls and ignition point location. The realistic modeling of the blast load
is therefore fundamental for the reliable evaluation of the structural response, something
particularly difficult in cases of blast scenarios characterized by a complex geometry. In this
respect, a promising tool is provided by Computational Fluid Dynamic (CFD) simulations
(Molkov 1999).
The level of room congestion is an important factor, whose effects can be adequately accounted
for performing CFD analyses (Pritchard et al. 1996). In domestic gas explosions the obstruction
provided by furniture and objects in general causes an increase of the flame turbulence and, as a
consequence, an increase of the flame velocity, something that leads to an increase in the pressure
(Zipf et al. 2007).
Concerning the third topic (the evaluation of the FSI), as reported in Teich and Gebbeken
(2011) it can be stated that while the coupling effects are negligible for stiff or heavy systems (e.g.,
reinforced concrete structures) they significantly influence the structural response of flexible and
light systems, e.g., membrane structures or glazing facades. For flexible systems, the FSI
determines the pressures acting on structural elements and generates an additional (aerodynamic)
structural damping, leading to a different structural response than what obtained by neglecting this
effect. In general, the FSI effects are more relevant in case of blast loads characterized by low
frequencies or low intensity (Subramanian et al. 2009, Teich and Gebbeken 2011).
This study deals with both the evaluation of structural robustness under blast damage scenarios
and the gas explosion simulation using CFD techniques. To this purpose, numerical analyses for
assessing the progressive collapse under blast damage scenarios are shown and detailed
simulations of gas explosion are carried out. The FSI effects are not treated in this paper and are
being be developed in further studies carried out by the authors in the ongoing research project on
analysis of structures subjected to blast loads.
The analyses carried out in this paper are part of a framework for the structural risk assessment
under blast, since they are useful in the evaluation of some particular aspects of risk (e.g.,
progressive collapse vulnerability given a local damage). The structural risk under blast can be
evaluated by the probability of progressive collapse for the structure after an explosion.
Considering a set of blast scenarios, this probability is given by Ellingwood et al. (2007)
P[C] i P[C | LD] P[LD | H i ] P[H i ]
(1)
Where Hi is the hazard related to the blast scenario “i” (where the scenario is defined by the
parameters determining the intensity of the blast action), also known as Intensity Measure (IM) in
other engineering fields (Whittaker et al. 2003, Ciampoli et al. 2011), LD is the structural local
damage, C is the collapse event, P[·|·] indicates a conditional probability, P[·] indicates a
probability, and the summation ∑ is (in theory) extended to all scenarios.
The structural analyses carried out in this paper, can be useful in assessing whether a certain
local damage is able to activate a global collapse (probabilistically considered in Eq. (1) by the
Numerical analyses for the structural assessment of steel buildings under explosions
805
term P[C|LD]), and in assessing the hazard associated with different blast scenarios
(probabilistically considered in Eq. (1) by the term P[H]). For a realistic evaluation of P[LD|H],
FSI models should be implemented, an aspect neglected in this study. This simplification is
considered acceptable due to the considerable stiffness of the structure considered as case study,
but further studies are needed to verify its validity. The probability of progressive collapse P[C] is
not computed in this paper, which focuses on the deterministic numerical analyses that can be
useful for the structural risk assessment under blast. The paper has two aims:
• Provide a tool for the global evaluation of the robustness of steel frame structural systems
subjected to blast-induced damages in terms of “robustness curves”, by extending the
procedure proposed in Giuliani (2009) (not originally related to explosions).
• Quantify the variation of relevant CFD analysis outcomes (e.g., pressure), due to the variation
of the analysis parameters (e.g., room congestion), using sensitivity analysis. This is something
not well investigated in literature, especially for civil structures.
2. Evaluation of the structural robustness under blast damage
A way to characterize the behavior of buildings subjected to explosion is to compute the
dynamic structural response due to a local damage (assumed to be caused by a blast) and
consequently assess the robustness of the structure. The structural robustness can be assessed by
evaluating the residual load bearing capacity of the damaged configurations as illustrated in
Giuliani (2009), where the analysis is based on the assumption of different levels of damage in
various locations. The robustness evaluation procedure presented in the following is based on the
assumption of a certain damage level caused by a generic load, which is able to instantaneously cut
off the contribution of a structural element to the load bearing capacity of the system (Yagob et al.
2009, CPNI 2011). Therefore, the method proposed can be used for the design against actions
generated both by intentional and accidental explosions and by hazards of different type (e.g.,
impact). Focusing on steel frame building systems (such as the one studied in this paper, shown in
Fig. 1), whose key structural elements are the columns at the ground floor (Parisi and Augenti
2012, Almusallam et al. 2010, Valipour and Foster 2010), the local damage level can be identified
by the number of the destroyed key elements. It is assumed that the columns directly acted upon
by the blast wave are instantaneously destroyed, thus the case of partially damaged key elements is
neglected in this study (Crosti et al. 2012). Following these assumptions, the first set of damage
scenarios is defined by the removal of a single key element (column), the second set by the
removal of two key elements, and so on.
Considering the above, two parameters identify the single damage scenario: the location of the
first destroyed key element (L), and the local damage level (N) of the scenario (i.e., the number of
the removed key elements). The specific local damage scenario is then identified as “D-scenario (L
= i; N = j)”, where capital letters indicate parameters and lower case letters indicate the specific
value assumed by the parameters. This means that the generic scenario is obtained by removing a
total number of key elements equal to “j”, and that the first of these elements was the one
positioned in the location number “i”. A set of initial NL damaged key elements defines the Dscenario (L; 1) with (L = 1,…, NL; local damage level N = 1). These scenarios (L; 1) can be
chosen a priori by considering the explosion type (e.g., it is realistic to assume that gaseous
explosions take place in kitchens or boiler rooms, while intentional explosions take place in the
external perimeter of the building). Moreover the generic D-scenario (i; j + 1) corresponding to the
806
Pierluigi Olmati, Francesco Petrini and Franco Bontempi
70 m
local damage level N = j + 1, is heuristically obtained from the previous D-scenario (i; j) by
removing the most stressed key element (critical element for the D-scenario (i; j)) obtained by
caring out a Nonlinear structural Dynamic Analysis (NDA) (Vassilopoulou and Gantes 2011) of
the D-scenario (i; j). The non-linearity is due to both the inelastic behavior of the steel and the
large displacements; the analyses are conducted by considering the effects of live and permanent
loads with the associated masses.
As an outcome of the NDA to the D-scenario (i; j) the damaged structural configuration may
have two kinds of response: a) the critical element for the D-scenario (i; j) does not collapse (i.e., it
remains under a certain conventional response threshold - “arrested damage response”) or, b) the
critical element for the D-scenario (i; j) collapses (i.e., it exceeds the conventional response
threshold - “propagated damage response”). The sequential steps of the procedure are the
following:
• For damaged configurations leading to a “propagated damage response”, the progression of
the collapse is presumed, and the computation proceeds by changing the damage location L = i + 1.
This assumption should need to be verified since, in general, the fact that another element is failing
in consequence of an initial damage, it does not necessary mean that a progressive collapse is
triggered. However the Authors’ opinion is the indirect failure of a key element should be avoided.
• For damaged configurations leading to an “arrested damage response”, two steps are carried
out:
Y
Z
X
Fig. 1 FE model of the building
Numerical analyses for the structural assessment of steel buildings under explosions
807
- The residual strength is computed, this can be estimated in different ways. Here the socalled “pushover analysis” (Pinho 2007, Kalochairetis and Gantes 2011, Lignos 2011) is
used, and the residual strength for the D-scenario (i, j) is identified by the ratio λ%(i, j)
between the ultimate load multiplier of the damaged structure and the one corresponding to
the original undamaged one. The residual strength (pushover) analysis is carried out under
horizontal loads having a triangular distribution along the height of the building. This choice
is made with two motivations in mind: i) horizontal loads can activate both horizontal and
vertical load bearing structural systems of the building and, ii) direct reference is made to
the unlikely eventuality that a seismic aftershock occurs after an explosion. This event is
possible in the case that the explosion occurs after a seismic main shock (e.g., hydrogen
explosions caused by the Japan 2011 earthquake main shock).
- The increase of the local damage level (N = j + 1) as stated before (i.e., by removing the
critical element for the D-scenario (i; j)), and performing a new NDA.
After each “propagated damage response” a robustness curve is obtained, defined by the
variation of the ratio λ%(i, j) with the local damage level (N). Once all the NL locations have been
analyzed a set of curves describing the robustness of the structure under the considered damage
scenarios are obtained (see example of Fig. 2). The whole procedure is summarized in the
flowchart of Fig. 3. The outcome of the analysis gives a representation of the structure robustness
when it is damaged by a blast in the considered locations. These robustness curves under blast
damage scenarios are useful for:
• Risk assessment analysis, if the uncertainties affecting the structural response after a local
damage LD (e.g., due to the uncertain structural characteristics) are considered (e.g., by a
Monte Carlo analysis, see Petrini and Ciampoli (2012)). The dispersion of the robustness
curves for that damage can be useful in evaluating the element P[C|LD] of Eq. (1).
• Risk mitigation analysis, for planning the optimal strategy against the hazard (FEMA 2003),
for example by adopting adequate structural or non-structural measures (UFC 2010) focusing
on the most critical scenario indicated by the robustness curves (the scenario producing the less
robust structural response).
Residual strength λ%(i; j)
100
80
60
40
20
0
0
1
2
3
Local Damage Level
D-scenario (1;N)
D-scenario (3;N)
4
D-scenario (2;N)
D-scenario (4;N)
Fig. 2 Examples of robustness curves under blast damage scenarios
Pierluigi Olmati, Francesco Petrini and Franco Bontempi
808
Select NL
locations
Key elements: columns at
the ground floor.
Damage level (N): number
D-scenario (i; j=1)
N=j+1
Increase damage level
by removing the critical
element for the
D-scenario (i;j)
L=i+1
Arrested
Damage
Response
(ADR)
NO
D-scenario (i;j)
Structural
response
evaluation by
NDA
Does failure
spontaneously
occur to another
key element?
ADR ?
YES
Propagated
damage
response
Progressive collapse is
presumed
(no residual strength)
λ %(i;j) = 0
Residual strength
(pushover) analysis
λ%(i;j) >0
YES
of key elements instantly
removed.
Location (L): position of the
first key element removed (≡
blast location).
NL: number of locations.
D-scenario (i; j): location
(i) and damage level (j).
NDA: non linear dynamic
analysis implementing large
displacements and inelastic
materials.
λ%(i;j) : ratio between the
damaged and undamaged
ultimate load multiplier
(pushover analysis).
ADR: arrested damage
response.
(i,j) Robustness
curve point under
blast damage
NO
NO
i = NL ?
YES
Set of Robustness
curves under
blast damage
Fig. 3 Flowchart of the procedure to evaluate the structural robustness against blast damage
3. Gas explosions: main simulation parameters
Chemical explosions (occurring when there is a very rapid combustion or reaction of chemical
elements) are either due to deflagration or due to detonation (TM 9-1300-214 1990). The “gaseous
explosives” (i.e., cloud of gas – air mixture) usually explode in a deflagration regime. Yet, in some
circumstances, they develop in a detonation regime (Baker et al. 1983), depending on the blast
scenario (gas type; ignition power, location and type; geometry and congestion of the
environment). This study focuses on the deflagration of a premixed gas – air mixture (gas
explosion) occurring in a civil building.
As stated before the CFD simulation is a powerful tool for obtaining an accurate evaluation of
the blast pressure on the structural elements. Several modern CFD codes allow taking into account
Numerical analyses for the structural assessment of steel buildings under explosions
809
accurately the effect of some fundamental phenomena:
• The congestion in the environment. This issue has been extensively studied in industrial
facilities and partially explored in civil structures (domestic congestion). The congestion is
caused by the presence of all the objects inside a room. In the CFD codes the domestic
congestion is implemented in the simulation by modeling solid objects whose effects (e.g.,
turbulence generation) can be considered as an interaction between flow and objects (Dobashi
1997).
• The failure of non-structural walls. When a gas explosion occurs, the failure of non-structural
walls causes the modification of the geometrical scenario and consequently the development of
the entire explosion. The non-structural walls are modeled in the CFD simulation by special
objects having a cut off pressure level.
• The ignition type and position of the gas cloud ignition, which can vary on a case-by-case
basis, and have an important role in the development of the explosion.
The aleatory uncertainty related to the above-mentioned issues is one of the principal reasons
causing the variability of the intensity and direction of the blast action. Of course, a significant
dispersion of results, especially in cases of complex numerical models such as the ones used for
the simulation of gas explosions, is due to the epistemic uncertainty (e.g., model uncertainty). The
issues related to this epistemic uncertainty are not addressed in this paper.
In the case of gas explosions, the “gas region” is defined as the volume containing the cloud of
gas, usually assumed as homogeneous. This gas region can be characterized by the so-called
“Equivalent Ratio” (ER) (GexCon-AS 2009)
Vfuel
VO
2 actual
ER
Vfuel
VO
2 stoichiometric
(2)
Where O2 indicates the Oxygen molecule, Vi (i = “fuel” or “O2”) indicates the volume of the
cloud component “i” at normal atmospheric conditions and the term “fuel” is referred to the
flammable component of the gas cloud (e.g., methane, hydrogen, etc.). The term “actual” refers to
the exploding cloud, while the term “stoichiometric” refers to the quantities of fuel and Oxygen
needed for a balanced chemical reaction. In Eq. (2), the value of the denominator can be derived
from literature, while the value of the numerator in the design phase can be chosen with reference
to experimental data (see for example SFPE 2002), in order to maximize the initial (laminar)
burning velocity, which represents an important aspect for the determination of the severity of the
explosion.
4. Application on a steel building
The procedure introduced above for evaluating structural robustness under blast damage has
been applied to a case study building. On the same building, a number of CFD analyses have been
then performed in order to evaluate the effects of the previously mentioned environmental
parameters (see section 3).
The case study building is an office structure 70 meters high for a total of 20 story, each one
being 3.5 meters high. The layout is rectangular with two protruding edges on the longest side and
Pierluigi Olmati, Francesco Petrini and Franco Bontempi
810
is globally delimited in a 45 × 25 square meters area (see Fig. 1 and Fig. 4). Columns and beams
have European HE cross-sections. The beam-column and beam-beam connections are made by
double angle cleat connections (shear-resisting), while the column-column connections are
moment-resisting welded and bolted connections. In addition to the previous sub-systems,
appropriate braced walls are present in order to support the horizontal loads, these having beamcolumn moment resisting connections, and diagonal tension members that consist in 2L 100x50/8
profiles; the position of the bracing systems is shown in Fig. 5. The floors have a horizontal braced
system that is formed by a set of members having an L 100x50/8 profile. The column cross-section
shapes are shown in Fig. 5 and classified and grouped in Table 1; for each column type (A, B, C,
D) the size of the cross section decreases through the building height. The slab is a steel ribbed
slab, spanning North to South, simply supported by girders and beams (see Fig. 5). The girders
cross-sections are HEA 240, spanning North to South, while the floor beams cross-sections are
HEA 200, spanning West to East. The girders and beams belonging to the braced walls have a
HEB 300 shape. The girders and beams have a span of 5 meters and are placed at 5 meters and 2.5
meters steps respectively. A grade S235 steel is adopted, with a yielding (fyk) and ultimate (fuk)
stress equal to 235 and 360 N/mm2 respectively.
DS(8;1)
5m
DS(3;1)
DS(8;2)
DS(3;2)
1
1
DS(1;1)
y
1
DS(5;1)
15 m
DS(2;1)
DS(2;2)
DS(4;2)
DS(4;1)
1
x
DS(6;1)
15 m
DS(7;1)
15 m
15 m
Braced wall
Key element instantly removed
DS(i;j) Blast Damage Scenario:
(L= i location; N= j local damage level)
DS(i;j)
1
1
Blast Damage Scenario:
(L= i location; N= j local damage level)
DS(L;1)
Fig. 4 Damage scenarios (L; 1), and Damage scenarios (L; 2)
Table 1 Column cross sections
Column type
Quote [m]
0 - 12
12 - 33
33 - 39.5
39.5 - 70
A
HEM 550
HEB 550
HEB 320
HEB 300
B
HEX 700×356
HEX 700×356
HEX 700×356
HEB 550
C
HEB 300
HEB 260
HEB 240
HEB 240
D
HEM 550
HEM 550
HEM 550
HEB 550
Numerical analyses for the structural assessment of steel buildings under explosions
811
N
15 m
W
C
C
B
C
C
B
D
B
A
D
A
A
A
C
B
A
A
A
A
B
A
A
A
B
D
A
A
A
A
A
A
A
A
D
B
B
D
B
A
A
B
D
B
B
C
C
5m
15 m
C
E
C
15 m
15 m
S
Fig. 5 Column types
4.1 Robustness assessment
In what follows, direct reference is made to the flowchart of Fig. 3. Eight locations (L) have
been considered (NL = 8) defining the blast damage scenarios, as indicated in Fig. 4. As previously
stated, the columns at the ground floor have been considered as key elements and the numerical
investigations are carried out removing instantaneously the key element by NDA. In Fig. 1 the
finite element model of the structure developed with Straus7® (G+D Computing HSH 2004) is
shown. Only the frame system is explicitly modeled, both the floors and the live load are taken
into account by considering additional (fictitious) mass density on the beams. The building is
subjected to gravity and the structural properties of the cladding system are not considered. The
structural response to the D-scenario (i; j) is evaluated by carrying out non-linear Lagrangian
(Bontempi and Faravelli 1998) dynamic implicit FE analyses. Explicit FE solver (more capable in
evaluating triggering effects due to local collapses) has been avoided in order to limit the
computational efforts. The use of implicit method is also justified by the fact that, in this specific
structure, the failure (assessed by implicit analyses) of some structural key elements can be
conceptually associated to the propagation of the collapse to other structural parts supported by the
key elements.
An initial damage is considered in the FE model by replacing a column by its reaction force
(computed with the Dead + Permanent + 0.3 Live load combination). In order to minimize inertial
effects caused by this loading phase, a sufficiently slow load ramp is provided. Moreover, a
successive oscillation extinction phase is added (see Fig. 6) where the load factor is maintained
equal to 1. After that the reaction of the key element is suddenly removed to simulate the damage
with a time interval (Δt) smaller than 1/10 of the fundamental time period associated with the
pertinent vertical modal shape of the damaged structure (UFC 2008). The implemented load factor
time history is shown in Fig. 6.
Concerning the material and geometrical nonlinearities, the distributed plasticity model along
the length of the beams and the large displacements assumption are adopted. In Fig. 7 some
moment-curvature diagrams for girders and beams are shown, the softening behavior is not
implemented.
Pierluigi Olmati, Francesco Petrini and Franco Bontempi
812
500
400
Loading phase
Dead + 0.3 Live
Δt
Reaction force of
the key element
10
20
30
time [sec]
40
200
100
0
0.00
0.0
0
HEB 300
HEA 240
HEA 200
300
50
Fig. 6 Load factor time history chart
0.01
22
24
26
28
32
24
34
-12
-16
-20
High
frequency
oscillations
response
extinction
-15
Displacement [m]
-12
-8
Max displacement
-4
25
26
27
0.0
25.5
Residual displacement
Displacement [mm]
25
0.06
Time [sec]
30
0
-9
0.05
Fig. 7 Moment-Curvature diagrams
Time [sec]
20
0.02 0.03 0.04
Curvature [-/m]
-0.6
-1.2
Displacement under collapse
Oscillation
extinction
phase
0.5
Moment [kN m]
Load factor [-]
1.0
-1.8
Fig. 8 Response time history for a node on the top of the removed key element, D-scenario (5;1) (left,
arrested damage response) and D-scenario (6;1) (right, propagated damage response)
The typical vertical displacement time history for a node located on the top of the removed key
element is shown in Fig. 8 for both the “arrested damage response” and “propagated damage
response” with local damage level N = 1. The first one, after the extinction of the initial high
frequency oscillation, shows a decaying response (damped oscillation), while the second one
shows an unbounded response. The computed robustness curves are shown in Fig. 9. It results that
for the selected scenarios, with the local damage level equal to two (D-scenario (L; 2)), the
structure always shows a “propagated damage response” (i.e., a progressive collapse is presumed).
In some cases (D-scenarios (6; 1) and (7; 1)) the collapse progression occurs even at the first level
of local damage. This behavior occurs in all cases where the local damage is located in the external
columns of the building that are not part of braced walls (see Fig. 4). In fact, in all other Dscenarios, for local damage level N = 1 the load originally carried by the removed key element is
re-distributed to a number of adjacent key elements positioned in both floor directions (x and y in
Fig. 4) with respect to the removed one, this allows the development of a double catenary effect (in
x and y directions), something that is not realized in the critical D-scenarios (6; 1) and (7; 1).
As stated before, the results of the robustness analysis under blast damage scenarios can be
useful in planning an optimal risk mitigation strategy. In the present case for example, the
measures of mitigation should primary focus to the external columns.
813
100
Residual strength λ%
(i; j)
Numerical analyses for the structural assessment of steel buildings under explosions
75
50
25
0
0
1
2
Local Damage level
D-scenarios (i;j):
D-scenario (1;N)
D-scenario (2;N)
(1;N)
(3;N)
(4;N)
D-scenario(2;N)
(3;N)
D-scenario
(4;N)
(5;N)
D-scenario(6;N)
(5;N)
(7;N)
(8;N)
D-scenario
(6;N)
Fig. 9 Robustness curves under blast damage
4.2 Blast action evaluation by CFD
With reference to the three fundamental phenomena outlined in section 3 (congestion of the
environment, failure of non-structural walls, ignition type and position), a number of CFD
analyses is carried out in order to evaluate the effects of the scenario parameters on the blast load.
The analyses are carried out using the CFD commercial code Flacs® (GexCon-AS 2009). A set of
gas explosions at the ground floor are modeled where the presence of some commercial activities
and one restaurant are hypothesized, including the kitchen (where the ignition point and the gas
region are located). Methane is assumed to be the fuel and the equivalent ratio (ER), see Eq. (2), is
assumed equal to 1.12, in order to maximize the initial laminar burning velocity. The main features
of the blast scenario are shown in Fig. 10. Different CFD models are considered and they are
resumed in Table 2.
The room congestion is realized by rigid furniture, modeled by still filled blocks in the
uncongested room. Only two room congestion cases have been considered, indicated respectively
as “free room” (where the room is considered without furniture) and as “congested room” (where
furniture is present, see Fig. 11)
When the failure of non-structural walls is considered (“frangible wall” cases), the walls are
modeled by cut-off pressure panels that are able to increase the porosity of the walls from 0
(undamaged wall) to 1 (completely damaged wall) after the crossing of a threshold pressure level
(wall strength). In the “non-frangible walls” cases the walls are undamaged (porosity equal to 0) in
all the simulation. The parameters of the cut-off pressure panels are reported in Table 3 (Lees
1980). Six different ignition locations inside the kitchen have been considered and the ignition
locations are show in Fig. 12.
In order to obtain realistic results in a CFD explosion analysis, the adoption of an appropriate
mesh grid is fundamental. The details of the mesh grid are the following: inside the building
ground floor the edge of the cubical cells is always 0.20 meters, while outside the building the
mesh grid is stretched in order to reduce the total number of cells. The max aspect ratio (the
longest side of the control volume divided by the shortest one) is equal to 5.59, thus lower than 10,
as recommended by GexCon-AS (2009), while the total number of cells is about one million. By
Pierluigi Olmati, Francesco Petrini and Franco Bontempi
814
using a 3.6 GHz CPU computer with 4 Gigabytes of RAM the analysis time of the single scenario
is approximately 12 hours.
Fig. 13 shows the effect of the domestic congestion. Simulations I and II have a different
pressure peak due to the interaction between the flow and the objects inside the building. In the
congested room case (simulation II) the turbulence of the flows increases, consequently both the
burning velocity (see section 2) and the pressure increase as well, inducing more turbulence. By
referring to a certain monitoring point inside the kitchen, the domestic congestion (simulation II)
causes a 43% increase of the pressure peak and a 28% increase of the pressure impulse (area under
the curves reported in Fig. 15) with respect to the uncongested case (simulation I).
In simulation III both failing walls and room congestion are considered. Comparing the results
obtained in simulations II and III the percentage decrements in terms of pressure peak and pressure
impulse (see Fig. 15) are equal to 66% and 77% respectively (Fig. 14). Moreover, the two
explosions are completely different in the spatial development. These results indicate that the
failure of the walls significantly modifies the explosion development.
Closed
windows or doors
gas region
shop
restaurant
elevators
15 m
shop
15 m
kitchen
bar
5m
Boiler
room
5m
Fig. 10 Main features of the blast scenario
Fig. 11 Congested room model
planimetry
quote [m]
6m
a
f
d
c
g
1.5
f
1.3
1.2
a bc
g
0.1
hd e
e
b
5m
furniture
walls
ignition
Fig. 12 Position of the ignition points
Numerical analyses for the structural assessment of steel buildings under explosions
815
Table 2 Performed CFD analysis
Simulation
I
II
III
IV
V
VI
VII
VIII
IX
Type of walls
Non-frangible
Non-frangible
Frangible
Frangible
Frangible
Frangible
Frangible
Frangible
Frangible
0.5 barg
Room congestion
none
yes
yes
yes
yes
yes
yes
yes
yes
0.3 barg
Ignition (Fig. 12)
a
a
a
b
c
d
e
f
g
0.05 barg
Fig. 13 Max pressures. Effect of the domestic congestion; simulation I on the left and simulation II on
the right
In simulation III both failing walls and room congestion are considered. Comparing the results
obtained in simulations II and III the percentage decrements in terms of pressure peak and pressure
impulse (see Fig. 15) are equal to 66% and 77% respectively (Fig. 14). Moreover, the two
explosions are completely different in the spatial development. These results indicate that the
failure of the walls significantly modifies the explosion development.
Fig. 15 shows a comparison between the pressure time histories, in the same monitoring point,
obtained by simulations I, II and III, where the previously mentioned differences can be
appreciated. Moreover, Fig. 15 shows that both the pressure gradient and the time instant
corresponding to the pressure peak are highly influenced by the congestion level. The increase of
the congestion level produces an increase in the pressure gradient, thus anticipating the occurrence
of the pressure peak.
All these results obtained by the CFD computations, clearly shown that the structural design
against such type of explosions cannot be conducted carefully without a specific evaluation of the
action. In terms of design practice, or design standards for civil buildings, these kinds of
simulations can be useful for defining parametric equations with the aim of appropriately defining
the blast load on structural elements, also by taking into account the above described phenomena.
Pierluigi Olmati, Francesco Petrini and Franco Bontempi
816
For risk assessment purposes, due to the high variability of the action with the considered
parameters, specific studies aiming in assessing plausible probability distributions for those
parameters are needed for a correct evaluation of the hazard.
Table 3 Frangible objects characteristics
Mass [kg/m2]
250
100
20
2
Panel
exterior walls
interior walls
windows
doors
0.5 barg
0.3 barg
Pressure of opening [barg]
0.05
0.03
0.015
0.001
0.05 barg
Fig. 14 Max pressures. Effect of the frangible walls: simulation III
0.4
Simulation I
Simulation II
0.15
Simulation III
0.10
Pressure [barg]
Pressure [barg]
0.3
Simulation III Simulation VII Simulation VIII
II
0.2
0.1
VII
0.00
I
0.0
VIII
III
0.05
III
-0.05
-0.1
0.1
0.3
Time [s] 0.5
0.7
Fig. 15 Pressure time history in the kitchen (the
gas region) for the three different
simulations: I, II, and III
0.1
0.3
Time [s]
0.5
0.7
Fig. 16 Pressure time history inside the kitchen
for three analyses with different ignition
locations
Numerical analyses for the structural assessment of steel buildings under explosions
817
5. Conclusions
The robustness curves obtained in this study form a suitable tool that can be helpful for risk
management and assessment. The procedure can be employed to handle different hazards, such as
terrorist attacks or accidental explosions. In particular, the proposed procedure for robustness
assessment is based on the assumption that the structural members directly involved in the blast
fail instantaneously, without any prior evaluation on the blast intensity. Since in the recent years a
number of intentional explosions were caused by truck bombs near the buildings, leading to the
failure of some columns, the previous mentioned assumption seems particularly reliable in case of
intentional explosions. The same approach could be extended for computing the robustness curves
in case of structures subjected to impact of ships and vehicles that engage key structural elements.
The approach based on the removal of key structural elements and on the subsequent
investigation of the dynamic structural nonlinear behavior has been adopted by different authors
(see for example Yagob et al. (2009), Purasinghe et al. (2012), Weerheijm et al. (2009), and
Sasani et al. (2011)), and has been implemented in guidelines (e.g., UFC 2009). To this regard, the
novelty offered by this paper consists in describing the results of this analysis in a synthetic and
fruitful manner, provided by the computation of the robustness curves. Moreover, the proposed
method of evaluation by means of robustness curves, takes into account the dynamic effects of the
structural initial damage by evaluating the structural behavior under impulsive loads.
This can be particularly useful for the structural risk assessment against intentional explosions.
With respect to natural explosions (e.g., gas) instead, a useful tool for the action intensity
evaluation is given by the CFD analyses illustrated in this study.
In the case of gas explosions, the intensity of the blast load depends principally on the activities
inside the building and the explosion occurs mainly in well-identifiable locations, therefore
advanced CFD analyses are particularly suitable to provide realistic assessment of the blast action
which is essential for the assessment of the consequent local damage. From the analyses developed
in this study emerges that, at least for the examined cases, the variation of relevant CFD analysis
outcomes (e.g., pressure) with the parameters mentioned above is indeed significant.
Acknowledgments
The authors gratefully acknowledge Dr. Konstantinos Gkoumas, from Sapienza University of
Rome for his precious comments related to this study. The authors are also grateful to Mr.
Piergiorgio Perin, P.E. and General Manager of HSH srl. The results provided in this paper are the
extended version of those presented at the 2011 World Congress on Advances in Structural
Engineering and Mechanics (ASEM’11plus, Seoul, Korea, 18-23 September 2011).
References
Almusallam, T.H., Elsanadedy, H.M., Abbas, H., Alsayed, S.H. and Al-Salloum, Y.A. (2010), “Progressive
collapse analysis of a RC building subjected to blast loads”, Structural Engineering and Mechanics, 36(3),
301-319.
Baker, W.E., Cox, P.A., Westine, P.S., Kulesz, J.J. and Strehlow, R.A. (1983), Explosion Hazard and
Evaluation, Elsevier, Amsterdam, Netherland.
818
Pierluigi Olmati, Francesco Petrini and Franco Bontempi
Bontempi, F. (2010), “Proc. of Handling Exceptions in Structural Engineering: Structural Systems
Accidental Scenarios Design Complexity”, Rome, Italy.
Bontempi, F., Faravelli, L. (1998), “Lagrangian/Eulerian description of dynamic system”, Journal of
Engineering Mechanics, 124(8), 901-911.
Bontempi, F., Giuliani, L. and Gkoumas, K. (2007), “Handling the exceptions: dependability of systems and
structural robustness”, Proc., 3rd International Conference on Structural Engineering, Mechanics and
Computation (SEMC 2007), Cape Town, South Africa, September.
Brando, F., Cao, L., Olmati, P. and Gkoumas, K. (2012), “Consequence-based robustness assessment of
bridge structures”, Bridge Maintenance, Safety, Management, Resilience and Sustainability - Proceedings
of the 6th International Conference on Bridge Maintenance, Safety and Management, IABMAS 2012, Italy,
Stresa, July.
Ciampoli, M., Petrini, F. and Augusti, G. (2011), “Performance-Based Wind Engineering: Towards a
general procedure”, Structural Safety, 33(6), 367-378.
CPNI (2011), Centre for the Protection of National Infrastructure, Review in international research on
structural robustness and disproportionate collapse, Department of Communities and Local Government,
London, United Kingdom.
Crosti, C., Olmati, P. and Gentili, F. (2012), “Structural response of bridges to fire after explosion”, Bridge
Maintenance, Safety, Management, Resilience and Sustainability - Proceedings of the Sixth International
Conference on Bridge Maintenance, Safety and Management, IABMAS 2012, Italy, Stresa, July.
Dobashi, R. (1997), “Experimental study on gas explosion behavior in enclosure”, J. of Loss Prevention in
the Process Industries, 10(2), 83-89.
Dusenberry, D.O. (2010), Handbook for blast-resistant design of buildings, John Wiley & Sons, Inc.,
Hoboken.
Ellingwood, B.R., Smilowitz, R., Dusenberry, D.O., Duthinh, D. and Carino, N.J. (2007), Best practices for
reducing the potential for progressive collapse in buildings, National Institute of Standards and
Technology, Washington DC, United States.
FEMA (Federal Emergency Management Agency) (2003), Reference manual to mitigate potential terrorist
attacks against building, Risk management series, Washington DC, United States.
G+D Computing, HSH srl (2004), Theoretical manual, theoretical background to the Straus7® finite element
analysis system, Sydney, Australia.
Gentili, F., Giuliani, L. and Bontempi, F. (2013), “Structural response of steel high rise buildings to fire:
system characteristics and failure mechanisms”, Journal of Structural Fire Engineering, 4(1), 9-26.
GexCon-AS (2009), FLACS User's Manual, Bergen, Norway.
Ghosn, M., Moses, F. and Frangopol, D. (2010), “Redundancy and robustness of highway bridge
superstructures and substructures”, Structure and Infrastructure Engineering, 6(1-2), 257-278.
Giuliani, L. (2009), “Structural integrity: robustness assessment and progressive collapse susceptibility”,
Ph.D. Dissertation, Sapienza Università di Roma, Rome, Italy.
HSE - Health and Safety Executive (2001), Reducing risks, protecting people, HSE’s decision-making
process, HSE books.
Kalochairetis, K.E. and Gantes, C.J. (2011), “Numerical and analytical investigation of collapse loads of
laced built-up columns”, Computers and Structures, 89(11-12), 1166-1176.
Lees, F.P. (1980), Loss prevention in the process industries, Butterworths & Co.
Lignos, D.G., Krawinkler, H. and Whittaker A.S. (2011), “Prediction and validation of sidesway collapse of
two scale models of a 4-story steel moment frame”, Earthquake Engineering and Structural Dynamics,
40(7), 807-825.
Molkov, V.V. (1999), “Explosion in building: modeling and interpretation of real accidents”, Fire Safety J.,
33(1), 45-56.
Parisi, F. and Augenti, N. (2012), “Influence of seismic design criteria on blast resistance of RC framed
buildings: A case study”, Engineering Structures, 44, 78-93.
Petrini, F. and Ciampoli, M. (2012), “Performance-based wind design of tall buildings”, Structure and
Infrastructure Engineering, 8(10), 954-966.
Numerical analyses for the structural assessment of steel buildings under explosions
819
Pinho, R. (2007), “Using pushover analysis for assessment of building and bridges”, Advanced earthquake
engineering analysis, International Centre for Mechanical Sciences, 494, 91-120.
Pritchard, D.K., Freeman, D.J. and Guilbert, P.W. (1996), “Prediction of explosion pressures in confined
space”, J. of Loss Prevention in the Process Industries, 9(3), 205-215.
Purasinghe, R., Nguyen, C. and Gebhart, K. (2012), “Progressive collapse analysis of a steel building with
pre-northridge moment connections”, Struct. Design Tall Spec. Build, 21(7), 465-474.
Sasani, M., Kazemi, A., Sagiroglu, S. and Forest, S. (2011), “Progressive Collapse Resistance of an Actual
11-Story Structure Subjected to Severe Initial Damage”, J. Struct. Eng., 137, 893-902.
Sgambi, L., Gkoumas, K. and Bontempi, F. (2012), “Genetic Algorithms for the Dependability Assurance in
the Design of a Long Span Suspension Bridge”, Computer-Aided Civil and Infrastructure Engineering,
27(9), 655-675.
SFPE - Society of Fire Protection Engineers (2002), Handbook of Fire Protection Engineering, Di Nenno,
P.J., Drysdale, D., Beyler, C.L., Walton, D.W., Custer, R.L., Hall, J.R., Watt J. National Fire Protection
Association.
Starossek, U. (2009), Progressive Collapse of Structures, Thomas Telford Publishing, London, United
Kingdom.
Starossek, U. and Haberland, M. (2011), “Approaches to measures of structural robustness”, Structure and
Infrastructure Engineering, 7(7-8), 625-631.
Subramaniam, K.V., Nian, W. and Andreopoulos, Y. (2009), “Blast response simulation of an elastic
structure: Evaluation of the fluid-structure interaction effect”, Int. J. of Impact Engineering, 36(7), 965974.
Teich, M. and Gebbeken, N. (2011), “Structures Subjected to Low-Level Blast Loads: Analysis of
Aerodynamic Damping and Fluid-Structure Interaction”, J. of Structural Engineering, 138(5), 625-635
TM 9-1300-214 (1990), Military explosives, United States Headquarters Department of the Army,
Washington DC, United States.
UFC (Unified Facilities Criteria) (2008), Design of buildings to resist progressive collapse, National
Institute of Building Sciences, Washington DC, United States.
UFC (Unified Facilities Criteria) (2009), Structures to resist the effects of accidental explosions, National
Institute of Building Sciences, Washington DC, United States.
UFC (Unified Facilities Criteria) (2010) Selection and application of vehicle barriers, National Institute of
Building Sciences, Washington DC, United States.
Valipour, H.R. and Foster, S.J. (2010), “Nonlinear analysis of 3D reinforced concrete frames: effect of
section torsion on the global response”, Structural Engineering and Mechanics, 36(4), 421-445.
Vassilopoulou, I. and Gantes, C.J. (2011), “Nonlinear dynamic behavior of saddle-form cable nets under
uniform harmonic load”, Engineering Structures, 33(10), 2762-2771.
Weerheijm, J., Mediavilla, J. and van Doormaal, J.C.A.M. (2009), “Explosive loading of multi storey RC
buildings: Dynamic response and progressive collapse”, Structural Engineering and Mechanics, 32(2),
193-212.
Whittaker, A.S., Hamburger, R.O. and Mahoney, M. (2003), “Performance-based engineering of buildings
and infrastructure for extreme loadings”, Proc., Symposium on Resisting Blast and Progressive Collapse.
New York, United States, December.
Yagob, O., Galal, K. and Naumoski, N. (2009), “Progressive collapse of reinforced concrete structures”,
Structural Engineering and Mechanics, 32(6), 771-786.
Zipf, R.K., Sapko, M.J. and Brune, J.F. (2007), Explosion pressure design criteria for new seals in U.S. coal
mines, Department of Health and Human Services, Pittsburgh, US.