Blast load and its analysis

Blast Load and
Its Analysis
Design of Blast Resistant Structures

Khobar Towers bombing in Saudi Arabia
25/06/1996

Need
:
Increase in number of terrorist attacks.
To minimize damage to the assets
To minimize the loss of life.
To protect historical monuments and important buildings
To subside social panic

Moving
vehicle
attack
Stationary
vehicle
bomb
Exterior
attack
Arsons
Others
Ballistic
attacks

What is blast ?
The detonation of a condensed high explosive generates
hot gases under pressure upto 300 kilobar and a
temperature about 3000-4000°C. The resulted compressed
air expands outward from the centre of the blast and
causes formation of wave in a wind medium having a
velocity greater than sound. So this blast wave causes air
pressure to rise and which is known as side on
overpressure. As the blast wave or shock wave traverses
path the overpressure gradually decreases. Now a vaccum
pressure zone gets generated behind the shock wave.

An explosion is a rapid release of potential energy characterized by eruption
enormous energy to the atmosphere.
A part of energy is converted to thermal energy radiation (flash) and a part
is coupled as air blast and shock waves which expand radially

Response of blast at various distances from the
source of explosion

Figure: Blast wave pressure – Time history
Pso = Peak side on overpressure
Pso - = Negative max overpressure
td + is always less than td – and Pso + is always greater than Pso -

Design Consideration
As the impulse of the negative zone is less than the impulse of the positive
zone, the negative face is usually not taken into account for the design
purpose.
1.Explosive charge weight
2.Stand off distance

This is the distance from the source of explosion at which the blast effect
caused by standard charge weight is just equivalent to as caused by W
charge at distance R .
Scaled distance Z =
𝑅
𝑊
(
1
3)

Empirical relationships :
1.Brode (1955) :
2. Newmark and Hansen (1961) :
3. Mills (1987) :

Dynamic pressure:
The air behind the front of the blast wave
moves along the same direction as wind
but with smaller velocity. These winds
result in loading of duration more than
positive phase. So the pressure caused
by these winds is called dynamic
pressure.
q(t) =qo * f(t)
The maximum value of dynamic pressure
=
Fig: Positive phase duration of over pressure
(parentheses) and dynamic pressure for 1 KN burst
The positive phase duration for overpressure and
dynamic pressure can be selected from fig

When wave front is obstructed by a structure a reflected blast wave gets generated
having higher pressure than the incident pressure. This pressure is called reflected
pressure. The reflection factor depends upon the orientation of the structure.
The maximum reflected overpressure =
Where,
Po = atmospheric or ambient pressure
As Pr > Pso , Pr is taken as design parameter.

IS Code provision:
As per IS 4991 – 1968 , the value of
the Pso, qs , Pr computed from
Table 1 for 1 tonne detonation
amount.
The pressure time relationship in
the positive phase are idealised by
using a straight line starting with
the maximum pressure value but
terminating at a time td or tq .

Fig : Assumed Plot
Fig : Actual Plot

Closed Rectangular Structure
Open or Drag type structures
There are two types of structures :

 Front face—The net pressure acting on the front face at any time t is
reflected overpressure Pr or (Ps + Cd * q) whichever is greater.

Cd = drag coefficient given in Table – 2 of IS 4991 - 1968
Pr = reflected overpressure which drops from the peak value Pro to overpressure
(Ps + Cd * q) in clearance time tc
tc =
3𝑆
𝑈
Where
S = H or B/2 whichever is less
U = Shock front velocity = M.a
Where
a= velocity of sound in air which may be taken as 344m/s at mean sea level at 20° C
and
M = Mach no. of the incident pulse given by 1 + 6𝑃so/7𝑃a
The value of the M for various conditions are also tabulated in
Table -1 of IS 4991 - 1968

The maximum reflected overpressure,
The net average loading on the front face (B X H) as function of time is shown in fig
depending on whether tc is smaller than or equal to td. The pressure Pro, Pso and qo
and time td are for actual explosion determined according to the Scaling laws.

The average loading on the rear face
(B X H) is taken as shown in Fig.-7
where the time has been reckoned
from the instant the shock first strikes
the front face. The time interval are
the following:
𝐿
𝑈
= The travel time of shock from
front to rear face
4𝑆
𝑈
= Pressure rise time on back face
Rear face:

Roof and side walls :
When tr > td ,the load on
roof and side walls may
be considered as moving
triangular pulse having
the peak value of
overpressure Pro or (Ps0 +
Cd * q0) and time td as
shown in fig 7b.
When td > Transit time (tr) =
𝐿
𝑈
,the pressure diagram is given in fig.

The net translation pressure on the obstructing areas of element may be taken
as shown in fig.
Where Cd= drag coefficient
depending upon shape of the
structure
tq = ½ to

Problem : Calculate the impulse of a blast load on a building
for positive phase using the given parameters.
Given Parameters
Detonation Amount 0.1tonne
Distance from ground Zero 30m
Height of Building 3m
Width of Building 10m
Length of Building 8m
Pa (ambient pressure) 1kg/cm2

a) Characteristics of the blast
Scaled Distance 64.63304m
From table -1 Assume Pa=1 kg/cm2
Pso 0.35367kg/cm2
Pro 0.806452kg/cm2
Qo 0.04219kg/cm2
to 37.70826mil sec
td 28.32257mil sec
Actual to 17.50262mil sec
Actual td 13.14617mil sec
M (Mach No.) 1.141554
Velocity of sound 344m/s
Shock front velocity (U) 392.6946m/s 0.392695m/mil sec
b)Pressures on the building
S (H or B/2 whichever is less) 3 m
Clearance time(t𝑐) 22.91858mil sec
> tdTransit time (t𝑡) 20.37207mil sec
Pressure rise time on back face (t𝑟) 30.5581mil sec

0.81
00
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 2 4 6 8 10 12 14
Peakreflectedoverpressure(Kg/cm2)
Time (mili sec)
Average front face loading

Solution:
From the graph-
Total impulse of force = 0
𝑡
𝑃(𝑡)𝑑𝑡
=
1
2
(0.81+0) * 13.15 * 102 *(Area)
=
1
2
(0.81+0) * 13.15 * 102 *10*3 N-Sec
= 15977 N-sec

Problem: A 25m high full water tank is subjected to a force as
shown in the previous graph. Natural time period Tn = 1.12 sec.
The force is caused by above ground explosion. Neglecting effect of
damping, calculate base shear & moment at the base of tower
supporting the tank. The mass of the water tank = 10000 kg.

Lateral deflection at any time, u =
1
𝑚𝑤 0
Ƭ
𝑃 Ƭ 𝑆𝑖𝑛 𝑤 𝑡 − Ƭ 𝑑Ƭ =
umax =
1
𝑚𝑤 0
Ƭ
𝑃 Ƭ 𝑑Ƭ
=
159277
10000∗(2 /1.12)
= 0.285 m
Base Shear = K*umax = mw2 *umax
= 10000 * (2∏/1.12)2 * 0.285
= 89604 N = 89.6 KN
Maximum Bending Moment = Base Shear * Height
= 89.6 * 25
= 2240 KN-m

Charge
Weight
(tonne)
Pro
(kg/cm2)
td
(mil sec)
t 𝐜
(mil sec)
0.2 1.266034 13.91818 21.72694
0.3 1.679215 14.40166 20.87335
0.4 2.102653 14.5682 20.13651
0.5 2.468371 14.83824 19.58105
1 4.2 15.39 17.63895
Stand off Distance = 30m

0
1.266034
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 2 4 6 8 10 12 14 16
Reflectedoverpressure(kg/cm2)
Equivalent Pulse time (mili sec)
Reflected overpressure Vs td
For Charge weight = 0.2 tonne

0
1.679215
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 2 4 6 8 10 12 14 16

2.102653
0
0
0.5
1
1.5
2
2.5
0 2 4 6 8 10 12 14 16

2.468371
0
0
0.5
1
1.5
2
2.5
3
0 2 4 6 8 10 12 14 16

0
15.39
0
2
4
6
8
10
12
14
16
18
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
For Charge weight = 1 tonne

Tonne Pro
0.1 0.806452
0.2 1.266034
0.3 1.679215
0.4 2.102653
0.5 2.468371
1 4.2
y = 0.649x3 - 1.8276x2 + 5.0602x + 0.3183
R² = 1
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 0.2 0.4 0.6 0.8 1 1.2
PEAKREFLECEDPRESSURE(KG/CM2)
DETONATION WT (TONNE)
Detonation Wt. vs Peak Reflected
Pressure

Stand off
Distance
(m)
Pro
(kg/cm2)
td
(mil sec)
t 𝐜
(mil sec)
10 12.13074 4.48978 13.6224
15 3.62087 7.473143 18.19483
20 1.857502 9.611829 20.55338
25 1.146493 11.4432 22.0064
30 0.806452 13.14617 22.91858
Detonation amount = 0.1 tonne

For stand off Distance = 10 m
12.13074
0
0
2
4
6
8
10
12
14
0 1 2 3 4 5

0
7.473143
0
1
2
3
4
5
6
7
8
0 0.5 1 1.5 2 2.5 3 3.5 4

0
9.611829
0
2
4
6
8
10
12
0 0.5 1 1.5 2

0
11.4432
0
2
4
6
8
10
12
14
0 0.2 0.4 0.6 0.8 1 1.2 1.4

0
13.14617
0
2
4
6
8
10
12
14
0 0.2 0.4 0.6 0.8 1

Distanc
e from
ground
Zero (m)
Pro
(kg/cm2)
10 12.13074
11 8.927811
12 6.830638
13 5.269227
14 4.159479
15 3.62087
16 3.106777
17 2.652022
20 1.857502
30 0.806452
y = 3013.5x-2.458
R² = 0.9874
0
2
4
6
8
10
12
14
0 5 10 15 20 25 30 35
Peakreflectedpressure(kg/cm2)
Distance from ground zero (m)
Distance from ground zero vs Peak reflected overpressure plot (for
0.1tonne detonation amount)

Scope of the Work :
• The main objective of the present study is to design a G+6
storey RCC building considering blast load, earth quake
load, wind load.
• It is required to compare the design of the same building
without blast load and including the blast load.
• Ductile detailing of the structural members need to be
done.

References:
• Ngo, T., Mendis, P., Gupta, A. & Ramsay, J.
“Blast Loading and Blast Effects on Structures – An Overview”
The University of Melbourne, Australia (2007)
• Activity A5 - Blast Simulation Technology Development
“Calculation of Blast Loads for Application to Structural Components”
Administrative Arrangement No JRC 32253-2011 with DG-HOME (2013)
• IS 4991 ‘‘CRITERIA FOR BLAST RESISTANT DESIGN OF
STRUCTURES FOR EXPLOSIONS ABOVE GROUND” (1968)
• Remennikov, A
“A Review of Methods for Predicting Bomb Blast Effects on Buildings”
University of Wollongong (2003), alexrem@uow.edu.au

• Draganić, H., Sigmund V.
“BLAST LOADING ON STRUCTURES” (2003)
• NBM Media article on “Blast Loading and Its Effects on Structures”

Blast load and its analysis

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