Chapter 3. Development and characterisation of shock and impact loading
3.2 Fundamentals of blast loading
3.2.4 Blast parameters
The scaled distance is defined based on the standoff distance and equivalent amount of TNT (trinitrotoluene) used in the detonation. The application of TNT (trinitrotoluene) is commonly considered as a reference. When a high explosive other than TNT was used, then the equivalent energy is acquired by using the charge factor (CF). The charge factor is the ratio of the actual mass of the charge to the mass of the TNT equivalent. The various charge factors for different explosives based on the specific energy ratio is presented in Table 3.2.
Therefore, the scaled distance, ‘Z’ is defined as
3
Z R
W (3.2)
where, ‘R’ is the standoff distance from the detonation source to the target point in metre, and ‘W’ is the weight of the TNT equivalent charge of explosive in kilogram.
All the blast parameters are fundamentally dependent on the amount of energy released by an explosion which generates the blast wave and the distance from the blast. The effect of the distance on various blast parameters is thus described using scaled distance. According to Hopkinson-Cranz law, during the explosion of two charges with the similar geometry but have different charge weight are situated at the same scaled distance from the target produces similar blast waves as long as they are under the same atmospheric conditions.
ii) Peak overpressure (Pso)
During a blast scenario, the shock wavefront reaches a point, and the pressure rises instantaneously to a maximum magnitude above the ambient pressure. This peak pressure is also referred to be side-on peak overpressure
Pso . The magnitude of the peak overpressure and the velocity of propagated shock wave decreases with the increase in the distance from the detonation point. After reaching a peak magnitude, the pressure decreases exponentially until it reaches the ambient pressure. This entire duration is referred as positive phase duration. Further, the pressure decays and becomes smaller than the ambient value called as negative pressure, which is longer than the positive phase, and the minimum pressure value is denoted as Pso. During this negative phase, the structures will be experienced to the suction forces. This suction pressure can leads to the development of glass fragments and removal of building cladding and facades. The positive phase induces much more damage to any structure when compared to the negative phase of the explosion due to its higher magnitude. Therefore, the negative phase is often not considered during the design process as they don't create much impact on the structural integrity of buildings under blast loads. The positive phase duration is indicated by td and the negative phaseduration by td. Researchers have proposed various equations to estimate the peak incident pressure for the different blast situations like spherical or air and hemispherical or surface blasts (Brode 1955). The peak overpressure due to the spherical blast is given as below.
3
2 3
6.7 1 for 10 bar 0.975 1.455 5.85
+ 0.019 for 0.1< 10 bar
so so
so so
P P
Z
P P
Z Z Z
(3.3)
Table 3.2 Explosives and charge factors (CF) (Bangash 2006; Hetherington and Smith 2014)
Explosives Mass specific energy
(kJ/kg) Qe
TNT Equivalent (CF)
Q Qe TNT
TNT 4520 1.00
GDN (glycol dinitrate) 7232 7232/4250 = 1.6
Pyroxilene 4746 1.05
Pentrinite 6689.6 1.48
Dynamite 5876 1.30
Schneiderite 3164 0.70
Dinitrotoluene (DNT) 3164 0.70
Compound B
[0.6RDX + 0.4TNT] 5190 1.148
RDX (Cyclonite) 5360 1.185
HMX 5680 1.256
Nitroglycerin (liquid) 6700 1.481
Blasting gelatin 4520 1.000
60% Nitroglycerin dynamite 2710 0.600
ANFO 3930 0.870
Semtex 5660 1.250
Newmark and Hansen (1961) introduced a relationship to estimate the maximum blast overpressure
Pso , for a high explosive charge detonates at the ground surfaces as,3 3
6784 93
so
W W
P R R (3.4)
where,
‘W’ is the charge weight in metric tons of TNT,
‘R’ is the distance of the surface from the center of the spherical explosion in m,
Kinney and Graham (2013) proposed the following formula for the incident overpressure
Pso in kPa, and the positive phase duration in ms,2
2 2 2
808(1 ( / 4.5)
1 ( / 0.048) 1 ( / 0.32) 1 ( / 1.35)
so atm
P Z
P Z Z Z
(3.5)
and
10
1/3 3 6 2
980 1 ( / 0.54)
1 ( / 0.02) 1 ( / 0.74) 1 ( / 6.9)
d Z
t
W Z Z Z
(3.6)
where, Patm= 103.25 kPa is the atmospheric pressure.
The most widely accepted method to estimate the peak overpressure is by using the Kingery and Bulmash (1984). These are the standard curves that were employed in the UFC 3–340–01 (2002) for the reference manual of blast resistant design of structures. The manual provides various formulations for the calculation of blast parameters in both spherical (free air bursts) and hemispherical pressure waves (surface bursts). They also provide the values of the incident and reflected pressures as well as of all other blast parameters. Their proposed blast parameters are valid for the stand- off distances from 0.05 m to 40 m.
iii) Idealized blast wave equation
The pressure wave variation with time can be characterized by the Friedlander’s blast wave shown in Figure 3.4 and the equation as follows:
( ) 1 d
bt t
s so
d
P t P t e
t
(3.7)
where
Pso is the peak overpressure, ‘b’ is a decay coefficient of the waveform, td is the positive phase duration, and ‘t’ is the time elapsed, measured from the instant of blast arrival. The decay coefficient ‘b’ can be calculated through a non-linear fitting of an experimental pressure time curve over its positive phase, is the ambient pressure and is the time of arrival of the shock front. Impulse is an important blast parameter of the blast wave pulse. It is the total force applied on a structure due to the blast per unit area. It is defined as the area under the overpressure-time curve of Figure 3.4. The impulse is classified into positive and negative , based on the relevant phase of the blast wave time history. During the blast analysis for the structural collapse as failure criteria, it was considered the positive phase impulse is more prominent than its negative counterpart.' t
d'
' P
o' ' ' t
a i
s
is( )
A a
A
t t
s s
t
i P t dt
(3.8)Figure 3.4 Ideal blast wave pressure-time history
iv) Reflected pressure (Pr)
When a blast wave interacts with the target, the generated pressure pattern will be different than the idealized time history shown in Figure 3.4. As the blast wave moves through space, there will be decay in the peak pressure and decrease in the speed which surrounds every object/structure that lies within the blast range. Further, the blast wave comes in contact with a rigid surface, and the pressure reflected has a larger magnitude than that of incident peak pressure
Pso , can be seen in Figure 3.4. The reason behind the rise in the reflected wave is due to the nature of the propagation of blast through the air. The blast wave travels along with the air particles and collides with the surface upon the arrival. In an ideal linear-elastic case, the particles may bounce back freely that leads to a reflected pressure equal to the incident pressure, and thus the surface would experience a magnification of the acting pressure. For a strong intensity blast wave, a non-linear phenomenon case, the reflection of these particles is prevented by subsequent air particles that are transferred and results in higher magnitude and intensity in the reflected pressure.The acting pressure acting on the contact surface of the target structure experiences higher incident pressure, and this pressure should be considered while designing the blast-resistant structure. The reflected pressure decreases with the increase in the angle of incidence 'α', can be seen in Figure 3.5. The minimum value of reflected pressure is equal to the incident pressure, which was induced on the target surface perpendicular to the shock front when 'α' is equal to 90°. A peak incident pressure is also termed as peak side-on overpressure as it is equal to the reflected pressure on the target surface that is parallel to the direction of the blast wave.
The maximum reflected pressure acts on a target surface (building) when the angle of incidence 'α' becomes zero. A schematic showing the angle of incidence and reflected
time [t=ms]
Incident pressure [P(t)]
Triangular blast wave profile for negative phase
Very low Low Medium High
LowMediumHigh
Very high Frequency Frequency distribution of various structural loads
Amplitude
Acoustic Seismic
Blast
Machine vibration
wind
pressure can be seen in Figure 3.5. Therefore the value of maximum reflected pressure is given by Kingery and Bulmash (1984),
4 7
2 7
so o
r so
so o
P P
P P
P P
(3.9)
where,
Pso is the incident peak overpressure and
Po is the ambient pressure.Figure 3.5 Angle of incidence and reflected pressure (Karlos and Solomos 2013) v) Dynamic pressure (q)
The blast wave generated through the air travels with a speed more significant than the speed of sound and decreases continuously due to the propagation. The air behind the shock front of the blast wave travels in the same direction of the wind with a smaller velocity. The generated winds from the blast wave are responsible for loading on the target surface for the whole positive phase duration. The produced pressure is referred as dynamic or drag pressure . It has an initial peak value , which is lesser than the incident or reflected pressures for both small and medium overpressures which attenuates eventually. Both the incident and reflected pressures last for a very short duration, usually less than one second, whereas the dynamic pressure may last for longer periods up to 2-3 seconds (Karlos and Solomos 2013). This dynamic pressure depends on the density of the air and the wind velocity released from the shock front of the blast wave, which is influenced by the peak incident overpressure. Its effectiveness depends on the drag coefficient and the orientation of the target surface with respect to the propagation of blast wind direction. Due to security issues in conducting the blast experiments in an academic institution, a shock tube testing facility is developed as a part of research work at Indian Institute of Technology Guwahati. A shock tube is a good research tool which can produce a substantial magnitude of pressure waves that can mitigate the blast pressure magnitude. The shock
( )
q t
q
otube testing facility is employed in the current dissertation to conduct the shock and impact testing experiments. The fundamentals of the shock wave is discussed in the succeeding sections. Furthermore, the calibration of the shock tube and its characterisation is emphasized in the subsequent sections.