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Lecture 16

Blast Waves

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Terrorist bombing attack has substantially increased recently

throughout the world. Thousands of people have been killed since1980s in the terrorist bombing, and many more injured. As a

results, more and more research effort has been paid on

protecting structures and occupants from blast loads

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Accidental Explosion

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Blast Damage

Earthquake damage

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Explosion in air results in a shock wave that propagates away from

the center of explosion

Surface

explosionAir explosion

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At any point in free air away from the explosion center, the

pressure generated from explosion has the shape

t

Ps0

ta tr

t0+ t0

-

ta arrival time, tr rise time (very small, usually zero)

t0+ - positive phase duration, t0

- negative phase duration

Ps0 Peak overpressure (measured from ambient pressure)

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Blast induced overpressure and shock wave propagation in air

have been intensively studied. Many empirical formulae areavailable to predict Ps0 in free air.

For example, from Brode Numerical solution of spherical blast

waves,

)/(

1010),/(019.085.5455.1975.0

/10),/(17.6

3/1

3

202320

20

2

30

kgmW

RZ

kp/cmP.cmkpZZZ

P

cmkpPcmkpZ

P

SS

SS

=

++=

+=

Zis the scaled distance,R is the stand-off distance in meters(distance between explosion center and the target) andWis the

equivalent TNT charge weight in kg, kp is a force unit,

1kp=9.80665N, and 1kp/cm2=9.80665x104 Pa

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Empirical formulae by Henrych The dynamics of explosion and

its use

10Z1)/(288.305.4662.0

1Z0.3)/(1324.23262.01938.6

3.005.0)/(00625.03572.05397.50717.14

2

320

2

320

2

4320

++=

+=

++=

cmkp

ZZZ

P

cmkpZZZ

P

ZcmkpZZZZ

P

S

S

S

Because of the unstable nature of explosives, the various formulae

from different authors to estimate blast pressure vary when thescaled distance is small (

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If a shock wave impinges on a rigid surface oriented at an angle to

the direction of the wave, a reflected pressure is instantlydeveloped on the surface. The pressure acting on the surface is

raised to an value exceeding Ps0.

The peak reflected pressure Pr is a function Ps0 and the anglebetween rigid surface and the shock wave front, .

In engineering application, ta is not important, and tr is usually

neglected because it is very small. The idealized pressure

distribution is as

Pr

Ps0

t0+ t0++t0

-

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There are also some formulae to estimate shock wave reflection.

For example, from The dynamic of explosions and its use byHenrych, it has

)/(2.7

148 2

0

0

2

0 cmkpPPPP

S

SSr

++=

This formula corresponds to the ideal case with normal shock

wave incidence. From this formula, the ratio Cra=Pr/Ps0 is in the

range of 2 to 8.

It should be noted that the shock wave reflection could be very

complicated. For example, if air ionizes and dissociates as shock

strength increases, the reflection coefficient Cra=Pr/Ps0 could be

as high as 20.

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In practice, Ps0 and Prare usually obtained by field blast test. Ps0 can

now be quite reliably predicted using numerical method. Pr isrelatively difficult to be determined. It depends on many factors

such as the incident angle, shock wave intensity, and structure

configuration, etc.

The most popularly used method to estimate blast pressure is the

US Design Codes, such as TM-5-1300, TM-5-863, DOE-1126,

etc. They use the same charts to estimate blast loads on structures.

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Other Parameters of Importance

1. Positive phase duration t0+

2. Impulse of the incident wave, is, and the reflected wave, ir.

3. Positive wave lengthLw (length at a given distance from the

detonation which at a particular instant is experiencing positive

pressures.

4. Shock wave velocity, U.

5. Arrival time ta

.

6. Dynamic pressure q0.

7. Empirical reflection factor Cra=Pr/Ps0.

++ ++

==00

)(,)(0tt

trr

tt

tss

a

a

a

a

dttPidttPi

Lw

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Dynamic pressure q0 is the force acting on a structure associated

with a plane shock wave. It depends on both the peak values and

the pressure time variation of the incident pressures. Dynamic

pressure is associated with the wind induced by blast wave. It

also depends on the air density.

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Scaled Distance Z = R/W^(1/3)

Figure 2-7. Positive phase shock wave parameters for aspherical TNT explosion in free air at sea level

0.1 1.0 10 100.001

.01

0.1

1.0

10

100

1000

10000

1.E+5

Pr, psiPso, psiIr, psi-ms/lb^(1/3)Is, psi-ms/lb^(1/3)ta, ms/lb^(1/3)to, ms/lb^(1/3)U, ft/ms

Lw, ft/lb^(1/3)

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Unit Conversion

1 lb =4.448 N, 1ft=0.3048 m, 1ft=12 in, 1 in=2.54 cm

Psi=lb/in2 1kg=2.2lb, 1 psi=6894 Pa

Conversion factors (TNT equivalence) for some high explosives

Explosives TNT equivalent Explosives TNT equivalent

Amcol 0.586 Nitroglycerine 1.481

Baronai 1.051 PETN 1.282

Comp B 1.148 Octol 0.994

RDX 1.185 Pencolite 1.129

Explosive D 0.740 Picric Acid 0.926

HMX 1.256 Silver Acid 0.419Lead Azide 0.340 Tetryl 1.000

Lead Styphnace 0.423 Torpex 1.667

Mercury fulminace 0.395 Tritonai 1.693

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Example

Estimate the peak overpressure Ps0, positive phase duration t0+,

arrival time ta and impulse is for a 25 kg RDX explosion at 5 m in

free air.

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2 Surface Explosion

Charge is located on or very near the ground surface. The initialshock wave is reflected and reinforced by ground surface to

produce a reflected wave. Unlike the airblast, the reflected wave

and incident wave merges at the point of detonation to form asingle wave. Because ground surface reflection intensifies the

shock wave, at the same scaled distanceR/W1/3, the surface

explosion generates larger pressures than free-air explosion.

R

R

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Scaled Distance Z = R/W^(1/3)

Figure 2-15. Positive phase shock wave parameters for ahemispherical TNT explosion on the surface at sea level

0.1 1.0 10 100.001

.01

0.1

1.0

10

100

1000

10000

1.E+5

1.E+6

Pr, psiPso, psiIr, psi-ms/lb^(1/3)Is, psi-ms/lb^(1/3)ta, ms/lb^(1/3)to, ms/lb^(1/3)U, ft/ms

Lw, ft/lb^(1/3)

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Example

Estimate the peak pressure Ps0, positive phase duration t0+, arrival

time ta and impulse is at 5 m from a 25 kg RDX explosion on

ground surface,

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Blast wavestructure interaction

Blast wave encountering a solid surface will reflect from and

diffract around it

Incidence Ps0

Wave frontReflection P

r

Solidsurface

incidence angle

R

reflection angle

Reflection coefficient Cra=Pr/Ps0, For zero incidence (=0.0), it has

)/(2.7

148 2

0

020 cmkpP

PPP

S

SSr

+

+=

Cra is between 2 and 8 according to this formula. However, Prof up

to 20 times Ps0 have also been measured, as discussed above.

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Note:

1) For a given Ps0, there exists a value of above which thisreflection process does not occur. Instead Mach Reflection

takes place.

2) There exists a value above which Pr is greater than the Prgenerated for head-on (=0) reflection. For air, this criticalangle is 3923 (also depending on Ps0)

3) For a given Ps0, there exists a value that Cra is a minimum.

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Depending on the stand-off distance and the building height, the

blast pressure may not be uniformly distributed on the building.

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Mach Reflection

When an explosion occurs in air above the structure such that no

amplification of the shock occurs between the explosion and the

structure.

As shown, when air blast wave reaches the ground surface, a

reflection occurs. The interaction between the incident and reflected

pressure wave results in a formation of a Mach stem. The Mach stem

propagates normal to the surface and terminates in a triple point, at

some distance above the ground. This triple point is the conjunctionof the Mach stem, the reflected wave and the incident wave.

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Note:

1) The pressure and hence the positive phase impulse in the Mach

stem is larger than the corresponding incident wave quantities.

2) These quantities will also be greater than those produced by a

surface charge. In other words, for an explosion above the

ground, the intensity of the blast wave in the Mach stem is

greater at a given horizontal distance than if the explosion

occurs on the ground.3) If the charge is positioned directly on the ground, the Mach

stem does not form and the blast wave travels along the ground.

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If the height of the structure is lower than the triple point, the

pressure wave acting on the structure is a plane wave, and thestructure is under uniform blast load.

The pressure acting on the structure is calculated using the

distance R between the explosion center and the point on theground surface, as shown.

R

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Example

A spherical charge of TNT equivalent weight of 20 kg is positioned5 m above the midspan of a 6 m long simply supported beam as

shown. Determine the peak reflected pressure Prat midspan and at

the beam ends.

5m

20kg

6m