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This paper seeks to explore the vulnerability of a typical reinforced concrete (RC) building against progressive collapse as a consequence of internal blast. The emphasis has been on the local model analysis for which two approaches – one involving the use of CONWEP and another using fluid-structure interaction through Alternate Lagrangian Eulerian (ALE) element formulation - have been employed. The finite element model of the structure was created using LS-DYNA, which uses explicit time integration algorithms for solution. The results of the study are proposed to be used to control or prevent progressive collapse of the building. In order to validate the employed numerical models, blast test results of a RC column available in literature were validated using LS-DYNA modeling of the RC column. The deformation response of the column was compared which showed acceptable prediction.
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1. INTRODUCTION
Historic records show that some of the major events
such as the partial collapse of the Ronan Point
apartment building in 1968 due to a gas explosion, the
attack on the Murrah Federal building in 1995, and
the terrorists attacks on the World Trade Center and the
Pentagon in 2001, have heightened interest in
the structural engineering community for better
understanding the phenomena of progressive collapse
resistance and failure of structures through
experimental and analytical research. This has resulted
in the development of general procedures and
guidelines for the design and analysis of structures for
progressive collapse prevention, and their
implementation on design codes and standards. In
parallel, US government agencies such as the General
Service Administration (GSA 2003) and the
Department of Defense (DoD 2005), have developed
guidelines for assessing the potential for progressive
Advances in Structural Engineering Vol. 18 No. 12 2015 2181
Progressive Collapse Analysis of RC Buildings Against
Internal Blast
Y.A. Al-Salloum
1
, T.H. Almusallam
1
, M.Y. Khawaji
1
, T. Ngo
2
, H.M. Elsanadedy
1
and
H. Abbas
1,*
1
Department of Civil Engineering, King Saud University, Riyadh 11421, Saudi Arabia
2
Department of Infrastructure Engineering, University of Melbourne, VIC 3010, Australia
(Received: 20 October 2014; Received revised form: 11 June 2015; Accepted: 26 June 2015)
Abstract: This paper seeks to explore the vulnerability of a typical reinforced concrete
(RC) building against progressive collapse as a consequence of internal blast. The
emphasis has been on the local model analysis for which two approaches – one
involving the use of CONWEP and another using fluid-structure interaction through
Alternate Lagrangian Eulerian (ALE) element formulation - have been employed. The
finite element model of the structure was created using LS-DYNA, which uses explicit
time integration algorithms for solution. The results of the study are proposed to be
used to control or prevent progressive collapse of the building. In order to validate the
employed numerical models, blast test results of a RC column available in literature
were validated using LS-DYNA modeling of the RC column. The deformation
response of the column was compared which showed acceptable prediction.
Key words: progressive collapse, blast pressure, finite element analysis, RC building.
collapse of buildings. The approaches adopted by
different codes and design strategies have been
reviewed and discussed by many investigators
(Almusallam et al. 2010a; Dusenberry 2002;
Ellingwood 2006; Kaewkulchai and Williamson 2004;
Mohamed 2006; Nair 2006; Starossek 2006; Starossek
and Wolff 2005). Important issues examined by
investigators include abnormal events leading to
progressive collapse, assessment of loads, analysis
methods, and design philosophy. In recent years, the
development of analysis methods for evaluating the
progressive collapse potential of an existing or new
building has been an imperative subject. Advantages
and disadvantages of different approaches for
progressive collapse analysis have been discussed by
Marjanishvili and Agnew (2006) and Marjanishvili
(2004).
The dynamic analysis procedures proposed by
Kaewkuchai and Williamson (2004) seem to work well
*
Corresponding author. E-mail: abbas_husain@hotmail.com; Fax: +966-114673600; Tel: +966-114670638.
consequence of internal blast. The emphasis has been on
the local model analysis for which two approaches – one
involving the use of ConWep (1990) and another using
fluid-structure interaction by employing Alternate
Lagrangian Eulerian (ALE) element formulation - have
been employed. The finite element model of the
structure was created using LS-DYNA software (2007),
which uses explicit time integration algorithms for
solution. The results of the study are proposed to be
used to control or prevent progressive collapse of the
building. The numerical modeling procedure has been
validated using same finite element (FE) simulation
adopted for RC column blast experiments available in
literature (Wood 2008).
2. GENERAL DESCRIPTION OF BUILDING
A typical RC framed building taken for progressive
collapse analysis is shown in Figure 1. The outer
perimeter of 42 × 42 m in plan is four storey high
including two basement floors, whereas rest of the six
storeys are 30 × 30 m in plan, as shown in Figure 1 with
inner perimeter line. Thus the layout of the building
results in a low height bay surrounding the main core of
the building which may act as a sacrificial corridor for
outside blast. The structural system consists of 25 cm
thick flat plate slabs supported on octagonal columns
with 25 cm side as shown in the Figure 1. The type of
façade provided for the building is glass façade for the
ground and the first floor and masonry and glass for all
the other floors.
Based on the threat identification criteria, two
potential internal blast scenarios L1 and L2 (Figure 1)
were assumed. The possible threat scenario of internal
blast was investigated as it is more critical than external
blasts. The provision of car parking in the basement of
the building with uncontrolled access was one of the
major factors for this consideration. The charge location
in the first blast scenario was considered to be close to
the RC core, as it is the most critical element in the
building. The location of the blast charge in the second
scenario was chosen to be close to a corner column,
which was found to be the next most critical vertical
supporting member. The corner farthest from the RC
core was selected because the RC core has the least
influence on the corner column. A charge of 1000 kg as
TNT equivalent was placed at L1 and L2 at 1 m height
above the lower basement floor level, assuming that it is
carried in a vehicle.
2.1. Finite Element Model
The FE modeling was carried out in two stages – the
local model stage to assess the individual columns
performance against blast pressures and the global
2182 Advances in Structural Engineering Vol. 18 No. 12 2015
Progressive Collapse Analysis of RC Buildings Against Internal Blast
for a two-bay structure. The application of the
procedures for structures that have more than two bays
will generate inaccurate structural responses. Instead of
applying dynamic loads to the entire building they used
a dynamic analysis procedure, based on the column
removal scenario, to represent the dynamic responses of
structures associated with progressive collapse.
Furthermore, the analysis procedures proposed by
Buscemi and Marjanishvili (2005) are originally for
single-degree-of-freedom (SDOF) systems, whereas the
energy-based methods proposed by Dusenberry and
Hamberger (2006) are only useful for a simple structure.
The application of the approaches requires further
development. It is obvious that a dynamic analysis
procedure is required to capture the actual response of a
structure. In addition, the alternate load path approach
for progressive collapse analysis is based on the
dynamic response of the structure due to the instant and
clear removal of load bearing elements, such as a
column. This approach is easily applied because of its
simplicity and directness (Nair 2006) and its
independence from specific causes (Ellingwood and
Leyendecker 1978). However, it is still necessary to
understand the characteristic of the structure’s response
due to particular causes. More accurate analysis
methods are required in order to predict the extent of
damage to the structures (Almusallam et al. 2010a,
2010b).
Luccioni et al. (2004) carried out an analysis for the
structural collapse of a reinforced concrete (RC)
building caused by a blast load using 3D solid elements
for RC columns, beams and masonry walls. The
comparison of numerical results with photographs of
the collapsed structure by blast load showed that the
numerical analysis reproduced the collapse of
the building under the blast load. This demonstrates that
the simplifying assumptions made for the structure and
materials are allowable for this type of analysis. In a
study carried out by Krauthammer et al. (2002), a
procedure was developed for studying progressive
collapse and established a reliable structural damage
assessment procedure to predict a possible future phase
of progressive collapse. Marjanishvili (2004)
summarized the progressive collapse procedures
defined in GSA (2003) and DoD (2005) guidelines and
discussed their advantages and disadvantages. The mesh
size dependency, a key issue in blast analysis of
structures, has been recently investigated by Nam et al.
(2008). The authors concluded that the reasonable mesh
size which ensures the objectivity of analysis results
controls the hourglass effect.
This paper seeks to explore the vulnerability of a
typical RC building against progressive collapse as a
modeling stage to assess the overall response of the
structure due to the failure of the critical columns. The
analyses were performed using LS-DYNA FE code –
version 971.
2.1.1. Local model
Two different modeling approaches viz. Lagrange and
ALE have been employed for the local damage
assessment of columns in the vicinity of the location of
blast. In the Lagrange model, air was not modeled
whereas in the ALE model, air was modeled.
(a) Lagrange model
The critical structural components being the perimeter
columns in the vicinity of the VBIED, a typical column
model was built in order to establish its vulnerability.
The concrete volume in the columns was modeled using
8-node reduced integration solid hexahedron elements.
These elements have three degrees of freedom at each
node. Single point volume integration is carried out by
Gaussian quadrature. Hourglass control is provided in
order to avoid the zero energy modes. The one point
integration solid element was employed for maintaining
the numerical stability of the model during the analysis.
The transverse and longitudinal reinforcements of the
columns were modeled as a discrete component using
two-node beam elements with Hughes-Liu cross-section
integration element formulation. The octagonal column
was replaced by circular column of equivalent area for
the purpose of local modeling. The column
reinforcement consists of 10 bars of 20 mm diameter as
longitudinal reinforcement and 12 mm diameter hoop
ligatures at 300 mm spacing. Figure 2 shows the model
details.
Concrete is a complex heterogeneous material that
exhibits nonlinear inelastic behavior under multi-axial
stress states. To accurately predict the concrete
response and failure modes under various loading
conditions, the key material characteristics, which
include the influence of confinement on strength and
energy absorption capacity, compressive hardening and
softening behaviors, volumetric expansion upon
cracking, tensile fracture and softening, biaxial
response and strain rate effects under dynamic load
(Crawford et al. 2012) must be captured in the
constitutive model. In the current study, the Karagozian
& Case concrete model (MAT_72R3) in LS-DYNA,
which was developed by Malvar et al. (1997, 2000) and
Magallanes et al. (2010) was adopted to model the
concrete material. The deviatoric strength of
MAT_72R3 is defined by three independent failure
surfaces, including the initial yield surface, maximum
failure surface and residual surface, which are written
as follows (Magallanes et al. 2010):
(1)
σ
=+
+
pa
p
aap
()
ii
ii
0
12
Advances in Structural Engineering Vol. 18 No. 12 2015 2183
Y.A. Al-Salloum, T.H. Almusallam, M.Y. Khawaji, T. Ngo, H.M. Elsanadedy and H. Abbas
X
Y
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
4.95
0.25
0.25
Main street
(30 m wide)
1. All dimensions are in m.
2. No. of storeys = 2 (Basement) + 8 = 10
3. Storey height = 4 m
4. Glass facade on ground and I storey and masonry wall
with glass windows on the rest
5. Flat slab: 250 mm thick
6. Thickness of concrete core = 250 mm
7. Blast scenario for location L1 shown hatched
Column
Notes:
Section
6.00 6.00 6.00 6.00 6.00 6.00 4.95
Blast
Locations:
L1 (41.08, 0.92, 1 m)
L2 (24.00, 23.00, 1 m)
1.3
0.25
0.25
3.50
L2
RC CORE
L1
Side street
(15 m wide)
Figure 1. Building plan at ground floor level Reinforcement mesh
where p is the hydrostatic pressure and a
0i
, a
1i
and a
2i
are parameters that define the three surfaces. The values
of parameters a
0i
, a
1i
and a
2i
for the three surfaces viz.
yield, maximum and residual surfaces were taken as
(10.13 MPa, 0.625, 0.00567 /MPa), (13.41 MPa,
0.4463, 0.00178 /MPa) and (0, 0.447, 0.00261 /MPa)
respectively.
For hardening, the current failure surface is linearly
interpolated between the yield and maximum surfaces
based on the value of the damage parameter
η
as
shown in Eqn 2. A similar interpolation is performed
between the maximum and residual surfaces for
softening in Eqn 3.
(2)
(3)
In the above equations, Δσ
y
, Δσ
m
and Δσ
r
are the
yield, maximum and residual surfaces, and
η
varies
between 0 and 1 depending on the accumulated effective
plastic strain parameter λ, which is defined as:
(4)
(5)
where r
f
is the strain rate enhancement factor; b
1
and
b
2
are the damage scaling exponents and
λ
ε
ε
=
+
<
d
r
p
rf
p
p
f
ft
b
p
1
0
2
0
for
λ
ε
ε
=
+
d
r
p
rf
p
p
f
ft
b
p
1
0
1
0
for
ΔΔΔΔ
σησ σ σ
= +()
mr r
ΔΔΔΔ
σησ σ σ
= +()
my y
is the effective plastic strain
increment. The damage scaling exponents b
1
and b
2
govern the softening of the unconfined uniaxial stress-
strain curve in compression and tension, respectively
(Malvar et al. 2000). To ensure constant fracture energy
dissipation, b
2
is determined iteratively until the area
under the stress–strain curve for a uniaxial unconfined
tensile test coincides with G
f
/ h, where G
f
and h are the
fracture energy and element size, respectively.
Similarly, b
1
is found using a uniaxial unconfined
compressive test. The strain rate effect was captured in
MAT_72R3 by modifying the failure surface and
damage function λ through the modified damage
function in Eqns 4 and 5. A radial rate enhancement on
the concrete failure surface was implemented and the
enhanced strength Δσ
e
corresponding to pressure p is
determined as follows (Malvar et al. 2000):
(6)
where γ
f
is the strain rate enhancement factor or
Dynamic Increase Factor (DIF).
(b) ALE model
Each element in the ALE element formulation is
allowed to contain a mixture of different materials,
while at the same time is allowed to deform. The ALE
mesh adapts to the position and shape of the material
during the simulated event and the material deforms.
The ALE formulation may be thought of as an algorithm
that performs the material remapping automatically. An
ALE formulation consists of a Lagrangian time step
followed by a remap time step which determines the
incremental remap of the material.
The LS-DYNA ALE multi-material solver is capable
of detecting fluid (ALE formulation) – structure
(Lagrangian formulation) interaction. The activation of
fluid structure coupling option searches for intersection
between the Lagrange part and the ALE part. The
independent movements of the Lagrangian-Eulerian
common coupling points are tracked if an intersection is
detected inside an Eulerian element. Penetrations are
detected based on these independent material
movements. The coupling forces computed from these
penetrations will then be re-distributed back onto both
meshes. Hence, the Lagrangian mesh and Eulerian mesh
must overlap with each other so that their intersections
may be detected. The fluid-structure interaction can
only occur due to these intersections.
Traditionally, blast analysis using ALE approach
requires the blast charge and air component to be
ΔΔ
σγσ
γ
ef
f
p
=
εεε
=
d
2
3
p
ij
p
ij
p
2184 Advances in Structural Engineering Vol. 18 No. 12 2015
Progressive Collapse Analysis of RC Buildings Against Internal Blast
Figure 2. Mesh discretization of column for local modeling
modelled as ALE multi-material elements, whereas the
structure needs to be modelled as Lagrange elements
constrained in the ALE multi-material elements. This
modelling approach often requires a large number of air
elements to be included in the model, which is not
efficient in terms of computational cost. Instead of the
full scale ALE blast modelling, the blast load
application in this study is achieved by applying the
CONWEP blast function (ConWep 1990) onto a layer of
air elements which will act as the blast wave front. The
model shown in Figure 3 employs Lagrange formulation
for RC component and ALE formulation for air
component. The air component covers the area of 1 m
by 1 m with 5 m height. In this model, flow out
boundary conditions were defined at the end of the air
volume such that the pressure waves were allowed to
exit the air domain with no reflection (Sherkar 2010).
This allowed for the use of a smaller sized air
component, which reduced computational costs.
2.1.2. Global model
For the overall response of the structure, the global
model of the building was developed using beam and
shell elements. The beam elements were employed to
represent the beams and columns, while the shell
elements were used to represent the core wall, floor
slabs, retaining walls and facade. The completed global
model is shown in Figure 4. RC columns were modeled
as two-node Hughes-Lui beam elements with tension,
compression, torsion, and bending capabilities. The
element has six degrees of freedom at each node – three
translations and three rotations. This element allows a
different unsymmetrical geometry at each end and
permits the end nodes to be offset from the centroidal
axis of the beam. A plane through three nodes defines
the orientation of the principal plane of the beam. Four-
node Belytschko-Tsay shell element with bending and
membrane capabilities was used, which being valid for
Advances in Structural Engineering Vol. 18 No. 12 2015 2185
Y.A. Al-Salloum, T.H. Almusallam, M.Y. Khawaji, T. Ngo, H.M. Elsanadedy and H. Abbas
Figure 3. ALE model details
Masonry facade
Glass facade
RC retaining walls
RC slabs
RC columns
Figure 4. Finite element model of the building
2186 Advances in Structural Engineering Vol. 18 No. 12 2015
Progressive Collapse Analysis of RC Buildings Against Internal Blast
Blast load
Load
Gravity load
T Time (s)
Figure 5. Loading stages (T = 0.1 for local model and blast
experiment simulation; T = 2.5 for global models)
Table 1. Constitutive parameters
Local model
Compressive Youngís Yield
Material Constitutive Density strength modulus stress Failure
model (kg/m
3
) (MPa) (GPa) (MPa) strain
Concrete Concrete
component Damage Rel3 2320 40 N/A N/A N/A
Plastic
Reinforcement Kinematic 7850 N/A 203.5 500 0.4
Global model – Concrete and reinforcement
Steel reinforcement
Material / Compressive Tensile
Structural Constitutive Density strength strength Young’s Yield
element model (kg/m
3
) (MPa) (MPa) modulus Stress
(GPa) (MPa)
RC columns /
Slab / Retaining
wall Concrete EC2 2500 40 2.53 200 500
Global model – Façade
Material Constitutive Density Young’s Yield
model (kg/m
3
) modulus Poisson’s stress Failure
(GPa) ratio (MPa) strain
Plastic
Glass façade Kinematic 2400 50 0.2 5 0.006
Plastic
Masonry façade Kinematic 1800 18 0.2 15 0.003
flat plate, warpage is not included. The element has six
degrees of freedom at each node – three translations and
three rotations. Stress stiffening and large deflection
capabilities are included.
The constitutive model adopted for RC was the
“Concrete Eurocode (EC2)” model, which is suitable for
beam and shell elements. The Concrete EC2 material
model is capable of representing plain concrete, discrete
reinforcement bars, and concrete with smeared
reinforcement, which is predominantly used in the
global model. The model is capable of representing
tensile cracking, compressive crushing, reinforcement
yielding, hardening and failure.
The failure of the façade system in the model is
governed by the failure strain threshold. This modeling
approach is adequate as a visual aid to establish the
damage on the façade system in a blast event since façade
system performance would have a very small contribution
towards the overall structural system performance against
blast pressures. A plastic failure strain of 0.6% is adopted
for glass façade to cater for the limited ductility due to the
contribution of the laminates. Whereas, a plastic failure
strain of 0.3% is adopted for masonry façade to cater for
the corrective motion of wall due to lateral loading. The
constitutive parameters for the different elements in the
structure are summarized in Table 1.
2.2. Blast Load Application
In the Lagrange analysis for local model of the column,
the gravity load (estimated as a pressure of 6.0 MPa) was
applied as a ramp function and the explosion of 1000 kg
equivalent weight of TNT was set to trigger at 0.10 s as
shown in Figure 5. The charge weight was combined
with different stand-off distances. This feature of
applying blast loading is available in LS-DYNA through
the LOAD_BLAST card where the location and the
charge weight of the blast may be specified. The package
calculates the blast pressure distribution on the contact
segments using ConWep (1990).
In the analysis, the loads on the critical element have
to be applied in two stages to account for both gravity
and blast loads. The gravity load was applied as a ramp
loading function, and maintained constant once it had
reached the peak gravity load level at 2.5 s. The blast
pressure was applied to the façade component of the
structure using the in-built CONWEP function in LS-
DYNA (2007). Figure 5 illustrates the load stages in the
model.
In the ALE model, the linear polynomial equation of
state was used to establish the blast pressure
propagation in air with the following properties (Chung
et al. 2010; Vulitsky and Karni 2002):
Density = 1.293 kg/m
3
; Initial pressure = 101 kPa
Adiabatic constant (γ ) = 1.4 thus C4 = C5 = γ−1 = 0.4
Initial energy = 250 kJ/m
3
2.2.1. Internal explosion amplification factor
When an explosion occurs within a structure, the
structure will be subjected to the extremely high initial
shock front (free-air pressures), and the effects of the
high temperatures and accumulation of gaseous
products produced by the explosion (gas pressure).
Provisions for venting of the gas pressures will reduce
the gas pressure duration. The gas pressure in an internal
blast load is dependent on several factors such as the
internal volume, target dimensions and vent area of the
threat scenario. A perfect confinement would result in a
quasi-static loading condition, whereby the confined gas
pressure would be retained within the structure for an
extended period of time. However, a perfect
confinement is rarely achievable without specifically
designed structure since energy would be dissipated and
pressure wave would escape into other area of the
building through breached components.
In addition to the free-air pressure, CONWEP
(ConWep 1990) can be used to estimate the gas pressure
within the structure. The volume of the structure is the
volume of the level in which the threat event occurs,
which is 7056 m
3
(42 × 42 × 4 m – referring to Figure
1). Figure 6 shows a pressure time history comparison
between gas pressure of perfectly confined 1000 kg
TNT equivalent explosion and free-air pressure of 1000
kg TNT equivalent explosion. The figure highlights the
quasi-static nature of the gas pressure as compared to
the impulsive free air pressure. In the analysis of a
confined explosion event, the structure would have to
withstand both free air pressure and quasi-static gas
pressure, which would yield an overly conservative
result. Hence, a realistic vent area would need to be
assumed or established in the analysis.
The CONWEP loading subroutine of LS-DYNA
cannot take into account the gas pressure in confined
explosion. Hence, in order to account for this effect, an
amplification factor has been applied to the CONWEP
blast pressures. The amplification factor has been
established as the factor required for obtaining an
equivalent gas pressure impulse. Table 2 shows that the
variation of amplification factor with the vent area. The
amplification factor could range between 1.5 and 2.7
depending on the vent area assumption. In this case
study the opening area is assumed to be the one span
floor slab area, directly above the charge, between
columns (i.e. 6 × 6 m). Hence an amplification factor of
1.7 is used in the analysis.
3. NUMERICAL MODEL VERIFICATION
In order to validate the employed numerical models, a
RC three-column specimen tested under blast load by
Wood (2008) was modeled by LS-DYNA and a
comparison was made between the experimental and
numerical results. The specimen has three circular
columns, as shown in Figure 7, connected to 150 mm
thick RC slabs at columns’ base as well as at their top
Advances in Structural Engineering Vol. 18 No. 12 2015 2187
Y.A. Al-Salloum, T.H. Almusallam, M.Y. Khawaji, T. Ngo, H.M. Elsanadedy and H. Abbas
180
150
120
90
60
30
0
0 0.5 1 1.5 2
msec
2.5 3 3.5 4
MPa
Airblast pressure
Gas pressure
1.2
1
0.8
0.6
0.4
0.2
0
0 100 200 300 400
msec
500 600 700 800
MPa
Airblast pressure
Gas pressure
(a) X-axis magnified (b) Y-axis magnified
Figure 6. Comparison between blast pressure and gas pressure
2188 Advances in Structural Engineering Vol. 18 No. 12 2015
Progressive Collapse Analysis of RC Buildings Against Internal Blast
end. The columns were 2.44 m long and 254 mm in
diameter. Each column was reinforced with 6 φ10 mm
deformed bars and φ10 mm hoops at a spacing of 152
mm c/c. All reinforcement was of Grade 60, and the
reinforcement and detailing was designed based on the
provisions of ACI 318-11 (ACI 2011). Two of the three
columns (Columns 2 and 3) were strengthened and one
of them (Column 1) was not strengthened. Column 1
(unstrengthened) was taken for the purpose of FE
Table 2. Internal blast amplification factor (Unconfined reference pressure = 186 MPa; Unconfined impulse,
I
uc
= 105 MPa-ms)
Gas pressure*
Opening PI
c
Factor
(m
2
) (MPa) (MPa-ms) (I
c
/I
uc
)
20 0.6401 286 2.72
25 0.6401 241 2.29
30 0.6401 209 1.99
35 0.6401 186 1.77
40† 0.6401 1.45 0.0137
75† 0.6401 1.12 0.0106
100† 0.6401 1.12 0.0106
* P = pressure; I
c
= Confined impulse
† The low factor indicate that internal blast with an opening of greater than 40 m
2
yields very low gas pressure. The blast may thus be treated as unconfined.
The vented reference pressures taken is 1000 kg TNT at 2 m stand-off distance
Hole for suspending
the charge
Column 3
Column 2
Column 1
Crack sensor
connectors
1
Figure 7. Three-column specimen tested by Wood (2008)
validation. The compressive strength of concrete was
45.6 MPa, whereas the yield strength and modulus of
elasticity of steel were 560 MPa and 200 GPa,
respectively. The blast charges used were 1.81, 4.54 and
13.6 kg as TNT equivalent and all the charges were
suspended in the centroid of the three-column specimen
and located at the mid height of the column. The
explosion of the three charges was done one after the
other in sequence by keeping some idle time in between
two consecutive events. The blast load application in the
numerical simulation was also done in the same manner.
Column 1 was modeled using the same elements and
material models discussed previously in Section 2.1.1
for local model. The FE mesh of the column in shown in
Figure 8. Fixed boundary conditions were assigned for
(a) Full model (b) Rebars only
Figure 8. FE mesh of Column 1 tested by Wood (2008)
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Y.A. Al-Salloum, T.H. Almusallam, M.Y. Khawaji, T. Ngo, H.M. Elsanadedy and H. Abbas
0.15
0.1
0.05
0
0 0.05
A
A
A
A
A
X-displacemet
0.1 0.15
Time (sec)
0.2 0.25 0.3
Figure 9. FE deflection at mid-height of Column 1
the top and bottom nodes of the column. The gravity
load was applied as a ramp function over a period of 0.1
s as shown in Figure 5. The blast loads impinging on the
contact segments of the column were calculated by LS-
DYNA software using ConWep (1990). The contact
segments of the blast were the solid elements of the
front face of the column which were taken to be in
contact with the blast (Elsanadedy et al. 2011, 2014).
First blast load was set to trigger at 0.1 s as shown in
Figure 5. The subsequent blasts, not shown in the
figure, were triggered by keeping idle time between two
consecutive blasts.
The variation of the deflection of the mid height of
column with time is shown in Figure 9. It is seen from
Figure 9 that the displacement for the first two blast
events was very small. The third blast event was
considered at 0.1 s after which there is a sudden
increase in permanent deformation. The final deflected
shape of the column as predicted from the FE model is
shown in Figure 10(a). The final deformed shape of the
column as observed during the test is shown in Figure
155 mm
(a) FE analysis
(b) Experimental
127 mm
(5")
(c) Predicted by wood (2008)
14121086
Charge weight (kg)
Permanent mid-height deflection (mm)
42
0
0
20
40
60
80
100
120
140
160
180
13.6 kg
(30 Ibs)
1.81 kg
(4 Ibs)
4.54 kg
(10 Ibs)
Column 1
Column 2
Column 3
Figure 10. Deformed shape for Column 1
10(b), which is quite comparable with the shape
obtained from the FE analysis. A comparison with the
experimental value shows that the predicted value of
mid-height lateral displacement is only 20% higher than
the experimental value but the prediction is better than
that reported in by Wood (2008) wherein the predicted
value is reported as 160 mm as illustrated in Figure
10(c). This shows acceptable prediction by the
numerical model used in this study.
4. RESULTS AND DISCUSSION
4.1. Local Model Analysis
After the numerical validation was completed using
blast experimental results taken from the literature (see
Section 3), the numerical modeling was extended to the
local analysis of a column modeled in Section 2.1.1.
Moreover, the CONWEP analysis approach is the same
as that adopted by the authors in earlier studies
(Elsanadedy et al. 2011). In the local analysis the failure
criteria of the typical column is defined as the loss of
gravitational load. The typical column model was
subjected to varying charge weight/stand-off
combination. The columns in the building are located at
regular grid at an interval of 6 m as shown in Figure 1.
In threat scenarios 1 and 2, the analysis indicates that
a charge weight of 1000 kg TNT equivalent (large van)
is adequate to induce the failure criteria of the typical
column at a distance of 13 m. This indicates that
columns within two spans of the structure would fail
when subjected to the blast threat. Figure 11 shows the
typical column damage observed in the analysis. An
amplification factor of 1.7 is assumed as established
above.
2190 Advances in Structural Engineering Vol. 18 No. 12 2015
Progressive Collapse Analysis of RC Buildings Against Internal Blast
T = 0 ms T = 15 ms T = 30 ms T = 70 ms
Damage levels
2.000e + 00
1.800e + 00
1.600e + 00
1.400e + 00
1.200e + 00
1.000e + 00
8.000e 01
6.000e 01
4.000e 01
2.000e 01
0.000e 00
Figure 11. Typical damaged column
˚
T = 0 ms T = 10 ms T = 12.5 ms T = 17.5 ms
Volume traction
1.000e + 00
9.000e 01
6.000e 01
5.000e 01
4.000e 01
3.000e 01
2.000e 01
1.000e 01
0.000e + 00
8.000e 01
7.000e 01
Figure 12. Column – blast wave interaction
Damage levels
2.000e + 00
1.800e + 00
1.600e + 00
1.400e + 00
1.200e + 00
1.000e + 00
8.000e 01
6.000e 01
4.000e 01
2.000e 01
0.000e + 00
CONWEP function
(at 70 msec after
blast pressure arrival)
(at 95 msec after
blast pressure arrival)
ALE model
Figure 13. Column damage comparison
The contours shown in Figure 11 and latter in Figure
13 show the damage level on the concrete elements,
whereby the damage in the elements is rated between 0
to 2 depending on its severity (0 – no damage, 2 – loss
of strength).
4.1.1. Comparison of ALE and Lagrange model
Figure 12 shows the blast wave propagation in ALE model
as the blast pressure engulfs the column. The failure modes
of both models are in general agreement as shown in
Figure 13. A closer in section on the vertical displacement
time history of the column (Figure 14) indicates that the
CONWEP model seemed to have failed earlier than the
ALE model. This is caused by the discrepancies of load
transfer between the two models. However, since the
difference is almost negligible, the CONWEP approach
was adopted for the rest of the analysis in order to maintain
computational cost efficiency.
Advances in Structural Engineering Vol. 18 No. 12 2015 2191
Y.A. Al-Salloum, T.H. Almusallam, M.Y. Khawaji, T. Ngo, H.M. Elsanadedy and H. Abbas
Time (sec)
Displacement (mm)
0 0.04 0.08 0.12 0.16 0.2 0.24
10
9
8
7
6
5
4
3
2
1
0
Blast pressure
arrival
Column failure
(CONWEP)
Column failure
(ALE model)
ALE model
CONWEP function
Figure 14. Vertical displacement comparison
Figure 15. Partial collapse of the building
5. CONCLUSIONS
A practical approach for the progressive collapse
analysis of buildings for internal blasts is presented. The
method employs the use of amplification factor for
considering the effect of confinement on blast pressure.
The local model analysis for damage of column due to
blast loading compares two different approaches for the
application of blast pressure – one involving the use of
CONWEP and another using fluid-structure interaction
by employing Alternate Lagrangian Eulerian (ALE)
element formulation. The comparison indicates almost
negligible difference in the damages observed in the two
approaches, thus in order to maintain computational cost
efficiency the CONWEP approach may be enough for
local damage assessment. The results of the study are
proposed to be used to control or prevent progressive
collapse of the building. The blast test results of RC
columns available in literature were used for the
validation of employed numerical models. The
deformation response of columns was compared which
showed acceptable prediction.
ACKNOWLEDGEMENT
The authors express their appreciation to the
International Twinning Program under Vice-Rectorate
for Graduate Studies and Research of King Saud
University, Riyadh, for the financial grant for this
project. Thanks are also extended to the MMB Chair for
Research and Studies in Strengthening and
Rehabilitation of Structures, at the Department of Civil
Engineering, King Saud University for providing
technical support.
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2192 Advances in Structural Engineering Vol. 18 No. 12 2015
Progressive Collapse Analysis of RC Buildings Against Internal Blast
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A progressive collapse is a chain reaction type of failure which follows damage to a relatively small portion of a structure. Progressive collapse constitutes an unacceptable hazard in many buildings, and thus procedures for its control should be incorporated in building standards. Design strategies for reducing the risk of initial failure and for controlling the amount of damage that occurs are presented and their relative advantages are covered. Design criteria are given for the reduced loads to be carried by a damaged structure.
Conference Paper
A concise methodology for evaluating the predisposition of a structure to progressive collapse is presented in this paper. A graphical modeling aid may be developed and used to investigate the potential for progressive collapse by evaluating the maximum ductility and corresponding rotations of critical structural load-bearing elements. Thus, a conventional dynamic computation with initial conditions can give an indication of the potential for progressive collapse of a structure.
Article
Recent improvements are made to Release III of the Karagozian & Case (K&C) concrete model. This three-invariant plasticity and damage-based constitutive model is widely used to model a number of materials, including normal and lightweight concrete, concrete masonry, and brick masonry, to compute the effects of quasi-static, blast, and impact loads on structures. This most recent version of the model, made available starting with LS-DYNA ® v971 as *MAT_CONCRETE_DAMAGE_REL3, incorporates a number of improvements to the original model that are described in this paper. The model now exhibits: (a) an automatic input capability for generating the data for generic concrete materials and (b) methods to reduce mesh-dependencies due to strain-softening. A simple method is implemented to regularize the fracture energy by internally scaling the damage function for the generic concrete model parameters. For user-defined material parameters, a method is developed that can preserve fracture energy using the results of either single-element or multi-element simulations. Finally, concrete loading rate effects are discussed and guidance is provided on properly modeling such effects with the model.
Article
The paper seeks to explore some aspects of the current state of knowledge on progressive collapse in the technical literature covering blast loads and structural analysis procedure applicable to reinforced concrete (RC) buildings. The paper describes the progressive collapse analysis of a commercial RC building located in the city of Riyadh and subjected to different blast scenarios. A 3-D finite element model of the structure was created using LS-DYNA, which uses explicit time integration algorithms for solution. Blast loads were treated as dynamic pressure-time history curves applied to the exterior elements. The inherent shortcomings of notional member removal have been taken care of in the present paper by simulating the damage of structural elements through the use of solid elements with the provision of element erosion. Effects of erosion and cratering are studied for different scenarios of the blast.
Article
"Disproportionate collapse" is structural collapse disproportionate to the cause; it is often, though not always, progressive, where "progressive collapse" is the collapse of all or a large part of a structure precipitated by damage or failure of a relatively small part of it. There have been many attempts to develop design guidelines and criteria that would reduce or eliminate the susceptibility of buildings to this form of failure. In recent years, the particular focus has been on the prevention of progressive collapse due to deliberate attack. The present study suggests, however, that these guidelines and criteria may be of limited value. Arguably the most important deficiency in the state of the art of design to prevent disproportionate or progressive collapse is uncertainty about the design event: We have the technology now to design for almost anything, but most recent building failures due to explosions and terrorist attacks have involved insults to the building not anticipated in design guidelines and criteria.