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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

Reinforcement mesh Concrete mesh

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

Air medium

Blast pressure wave front

Column

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)

Advances in Structural Engineering Vol. 18 No. 12 2015 2189

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.

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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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