BLAST EFFECTS MODELLING IN A PASSENGER BUS

L. K. Antanovskii1, A. M. Remennikov2

1Defence Science and Technology Organisation, PO Box 1500 (190 EOP), Edinburgh,

SA 5111, Australia; 2School of Civil, Mining and Environmental Engineering,

Faculty of Engineering, University of Wollongong, Wollongong, NSW 2522,

Australia

ABSTRACT

This paper presents a methodology for the assessment of the blast environment inside and outside of a passenger

bus due to an internal explosive detonation. It addresses the mathematical modelling and Computational Fluid

Dynamics (CFD) simulation of blast wave propagation in the bus taking into account the effect of venting due to

progressive breakage of glass windows and doors. The pressure-impulse diagrams, traditionally used as criteria

for the failure of glazing elements, are encoded by a dynamic equation for accumulated damage. The bus

windows and doors are modelled using special frangible elements and removed from the computational domain

once the accumulated damage reaches a threshold value. Three-dimensional numerical simulations are used to

carry out parametric studies of the influence of the strength of bus windows on the blast pressure-time histories

at various locations inside and outside the bus. As is expected, weaker windows better protect the bus passengers

and the driver at sufficiently large stand-off distances from the explosive charge but make people outside the bus

more vulnerable, particularly when the effects of window fragmentation are included. Using the proposed

methodology, the critical explosive charges for the selected passenger bus designs can be determined.

Experimental data from an instrumented live fire bus blast is included to validate the CFD overpressure

predictions and to illustrate the actual failure of glazing elements.

INTRODUCTION

Blast effects inside a passenger bus strongly depend on the bus geometry due to multiple

reflections of shock waves, and on the times of breakage of windows and doors that cause

venting. To a first approximation the deformation of the bus hull can be neglected as it is a

much slower process compared to blast propagation, and hence has secondary influence on

peak over-pressure and impulse. This assumption allows one to employ a simplified model for

blast effects modelling by assuming that the bus hull is rigid whereas windows and doors are

fragile and of zero thickness. A mathematical model for the failure mechanism of glazing

elements has been proposed which employs the concept of accumulated damage [2]. A

glazing element fails when the accumulated damage, whose rate of change in time is defined

by a dynamic equation, reaches some critical value. Note that, strictly speaking, the traditional

failure criterion based on the pressure-impulse (P-I) diagrams cannot be used when shock

waves have multiple pulses due to reflections in a confined environment. In fact, the proposed

failure model contains two parameters estimated from the corresponding P-I diagram, namely,

from the pressure and impulse asymptotes, and therefore can be considered as a way to extend

the P-I diagram approach to include the damage effects due to shock waves with multiple

pulses.

This identified accumulated damage/failure model is incorporated in DSTO’s computational

fluid dynamics (CFD) software DBLAST, which employs a conservative Godunov-type

scheme with an exact Riemann solver for blast propagation, coupled with dynamically

changing geometry due to the failure of window elements. DBLAST outputs pressure time

history at specified gauge points, saves pressure and temperature in each cell at specified

times, and automatically generates a MATLAB script for post-processing. A graphical user

interface for pre-processing of target and charge geometries has also been developed.

Numerical CFD simulation of the blast effects from an external explosive charge on a

deformable bus have been conducted at [7]. Risk analyses of explosions in public transport

systems based on a fluid-structure interaction modelling have been previously undertaken and

are presented in [6].

MODEL OVERVIEW

The mathematical model for the accumulated damage/failure method consists of gas

dynamics equations [4] governing the propagation of shock waves in polytropic gas (the

properties of air and detonation products are not distinguished). The windows and doors of a

public bus respond to blast loading at discrete times when the accumulated damage

governed by the damage accumulation equation

0,max *pppdt

d

(1)

exceeds some threshold value * . Here *p is the cut-off overpressure, and p denote

pressure at both sides of the window or door. Note that the accumulated damage is

implicitly defined from the postulated expression for its rate, and has the dimension of

impulse.

To the first approximation, the parameters *p and * can be estimated from existing

pressure-impulse (P-I) diagrams for specific element materials/geometries. The pressure

asymptote of a P-I diagram can be identified with *p and the impulse asymptote with *

provided that the shock wave is strong enough with respect to the cut-off overpressure.

Indeed, it is conceivable that if the pressure does not exceed the value of the horizontal

pressure asymptote, there is no failure irrespective of impulse; therefore this value has the

meaning of *p . Similarly, if impulse is less than the value of the vertical impulse asymptote,

there is no failure irrespective of the peak overpressure. Clearly, the magnitude of impulse is

close to the accumulated damage for sufficiently high blast pressure compared to *p , and

therefore this value can be identified with * [2].

This simplified accumulated damage model is essentially a way to encode a P-I diagram when

shock waves are composed of multiple shock pulses from which it is difficult to extract a

single peak pressure and impulse.

The numerical model involves simultaneous solution of the gas dynamics and accumulated

damage equations. The computational domain changes dynamically at discrete instances of

time whenever a window or door fails. Currently this model does not account for the effects

of fragmentation on the target element under consideration.

SCENARIO DESCRIPTON

The pre-blast image of the passenger bus Mercedes MK 2-1 used in the instrumented live fire

experiments is shown in Figure 1. A spherical charge equivalent to 4.55 kg of trinitrotoluene

(TNT) explosive was placed on the second seat, towards the aisle, on the nearside of the bus

67 cm away from the left-hand wall. Two pressure gauges were installed; gauge B1 on bus

floor with sensor face towards the bus roof and gauge B2 on rear bus wall with sensor

pointing forward down the bus aisle.

Figure 1: Passenger bus (Mercedes MK 2-1).

The bus geometry used for the DBLAST simulation is shown in Figure 2. The origin of the

Cartesian coordinate system is selected at the left front lower corner of the bus. In this

coordinate system the spherical charge is located at point C = (4.4 m, 0.7 m, 0.7 m) and the

identified pressure gauge points at B1 = (8.4 m, 1.2 m, 0.05 m) and B2 = (10.67 m, 1.2 m, 0.67

m), respectively.

Figure 2: The passenger bus geometry.

SIMULATION RESULTS

The described scenario was numerically simulated by DBLAST for three window types:

infinite window strength, 10 mm thick window, and no window. P-I diagrams were generated

for the window dimensions and thicknesses, which were then used to estimate the cut-off

pressure and critical damage as shown in Table 1.

Table 1: Model parameters.

Glazing element type Cut-off pressure *p (kPa) Critical damage * (kPa ms)

100 cm x 95 cm windows 12.99 121

130 cm x 95 cm windows 10.116 119

Rear window 8.305 118

Driver’s windscreen 38.444 539

Front and back doors 8.531 133

The pressure time history at the two gauge points is shown in Figure 3. As expected the

pressure levels at B1 and B2 for the infinite strength windows are significantly higher than

those in the breakable window (or no window) bus model, and the shock wave arrival time is

shorter than for the other two cases. However, interestingly there is very little difference in

pressure/time histories for the breakable window and no window bus models.

Figure 3: Pressure time history at the gauge points.

The later result also indicates that the blast pressure loads exhibited outside the bus will be

roughly the same irrespective of whether breakable windows are installed or not. Of course,

breakable windows will be more dangerous for personnel outside the bus because of flying

glass fragments.

Pressure contours for the bus model with 10mm glass windows are shown for increasing

times in Figures 4a-4d. It is seen that the pressure contours have complex pattern due to

multiple reflections of the shock waves from the bus walls and seats. For the current

simulation the windows nearest to the charge are broken within 1ms (Figure 4a), and the

driver’s windscreen starts to fail at t = 6 ms (Figure 4d). At failure the windows in DBLAST

are removed from the model and shown as empty window frames.

Figure 4a: Pressure contours in a horizontal cross-section at t = 0.8 ms.

Figure 4b: Pressure contours in a vertical cross-section at t = 1.6 ms.

Figure 4c: Pressure contours in a vertical cross-section at t = 2.6 ms.

Figure 4d: Pressure contours in a vertical cross-section at t = 6 ms.

The time history of the accumulated damage normalised by the critical damage level for the

driver’s windscreen is shown in Figure 5. The predicted time of failure of the windscreen is

approximately 6 ms.

Figure 5: The accumulated damage time history of the driver’s windscreen.

QUALITATIVE COMPARISON WITH A LIVE FIRE EXPERIMENT

The still images of video recording from the actual bus test are shown in Figure 6. It can be

seen that the nearest window to the explosive charge is broken almost immediately (within 1

ms) after explosive initiation, whereas the driver’s windscreen fails at approximately t = 7 ms.

These window failure times are seen to be in good agreement with the predicted values.

Figure 6: Live fire images at t = 1 ms and t = 7 ms after the blast, respectively.

The experimental pressure time records for gauge points B1 and B2 exhibited significant

electronic noise superimposed on the pressure/time measurements i.e. low signal-to-noise

ratio. Signal filtering applied to the pressure gauge records using MATLAB resulted in the

plots shown in Figure 7, (blue measurements). Even with this filtering there are still visible

spikes which are believed to be due to fragment/debris impacts on the pressure gauges as well

as general noise due to bus floor and wall vibration being transferred to the gauges through

the gauge mounts. The predicted pressure/time histories at B1 and B2 are shown as the red

lines in Figure 7.

Figure 7: Measured pressure time history (blue line) at the gauge points B1 and B2 compared

with simulation (red line) for 10 mm glass window. NB: The recorded pressure measurements

have been filtered to reduce extraneous noise.

Discrepancies in the experimental and numerical pressure time histories are thought to be due

to the simplifying assumption of the rigidness of the bus hull. In reality the elastic waves

generated by the explosive charge within the bus structure are thought to be capable of

significantly influencing the gauges.

ASSESSMENT OF THE EFFECTS OF BLAST ON THE BUS PASSENGERS

Human tolerance to low level pressure loading is relatively high. For higher shock levels the

position and orientation of a person on the bus (standing, sitting, face-on or side-on) relative

to the blast front and direction, as well as the steepness of the pressure front, are significant

factors in the level of sustained injuries. Past incidents have also demonstrated that human

body blast tolerance depends on both the peak blast pressure as well as the shock duration.

Conventional attacks on public transport such as buses and trains are generally characterised

by fast-rising air blasts of short duration (3-5 ms), and personnel pressure tolerance for short-

duration loads is significantly higher than that for long-duration blast loads.

Detonation of an explosive device causes injuries in four categories:

1. Primary blast injury results from the envelopment of the body in the over-pressurised

wave. Body surface and internal organs are rapidly distorted because the body

contains highly compressible tissues (air-containing organs) that undergo rapid

volume change. Blast lung injury and perforation of the middle ear are most common

in this category.

2. Secondary blast injury is caused by impact on the body from flying debris and bomb

fragments.

3. Tertiary blast injury results from whole-body acceleration of a victim’s body caused

by the blast wind.

4. Burns effects which are termed quaternary blast injury.

Injuries caused by suicide bombing attacks are characterised by a lethal combination of blast

injury, multiple penetrating wounds from shrapnel and debris, which cause extensive soft

tissue damage, and to a more limited extent burns [1, 3]. Most deaths due to explosive events

on buses and in semi-confined spaces are caused by the blast effects [5, 8].

Based on currently available data [9], an estimate of a human’s response to fast rising

pressures of short duration is presented in Figure 8 for close-range detonation of explosive

devices with up to 20 kg TNT equivalence. The threshold and severe lung damage pressure

levels are 200 to 270 kPa and above 550 kPa, respectively, while the threshold for lethality

due to lung damage is approximately 700 to 820 kPa.

Figure 8: Nomogram for estimating human response to close-range detonation of small

explosive devices ≤ 20 kg.

A direct relationship exists between the percentage of ruptured eardrums and maximum

pressure, i.e. 50 percent of eardrum rupture at a pressure of about 100 kPa for fast rising

pressures, while the threshold of eardrum rupture is about 70 kPa. It should be noted that the

pressures used in human tolerance assessments are the maximum effective pressures, that is,

the highest of either the incident or the reflected pressure. The type of pressure will depend

upon the orientation of the individual relative to the blast as well as the proximity of reflecting

surfaces.

Since the bus interior represents a complex geometry with multiple reflecting surfaces, the

assessment of the effects of blast on the bus passengers is performed by utilising the results of

CFD simulations discussed above to determine the maximum effective pressures at various

locations around the bus interior. Figure 9 presents the contours of maximum effective

pressures inside the bus recorded at the horizontal array of target points for a height of 1.5 m

above the bus floor. The peak pressure contours for two threat scenarios (1.0 kg TNT and 4.5

kg TNT) have been mapped onto the critical pressures associated with failures of critical

human organs and probabilities of lethality to produce a useful tool for the rapid assessment

of the vulnerability of passengers to explosions occurring inside public buses.

Figure 9: Contours of maximum effective pressures for assessment of effects of blast on the

bus passengers: (a) 4.5 kg TNT explosive device; (b) 1 kg TNT explosive device. NB: Refer

to Figure 8 for details on damage levels 1 – 9.

The following observations made from contour plots in Figure 9 may be of interest in the

context of this paper.

1. A zone of near 100 percent lethality can be identified. For the threat based on a 4.5 kg

TNT charge, this zone extends about 2 m from the centre of blast. For a 1 kg TNT

explosive device, zone of near 100 percent lethality is about 0.5 m from the centre of

blast.

2. Failure of the bus doors plays an important role in the enhancement of probability of

survival. Internal bus zones directly in front of the doors show significantly lower

risks of lethality.

3. The driver screen acts as a reflecting surface increasing the risk of lethality for the

passengers sitting or standing directly behind the bus driver.

4. The comparison of contour plots in Figures 9 (a) and (b) demonstrates that the severity

of blast injuries associated with a 1-kg TNT explosive device is significantly lower

than that for a 4.5-kg TNT explosive device. Hence, the proposed methodology can be

used to determine a critical explosive charge level for the selected passenger bus

design. This information can be used for designing measures aimed at mitigation of

blast injuries to bus passengers.

DISCUSSION

A methodology for the assessment of the blast environment inside a passenger bus subjected

to an internal explosion is presented. The predicted blast pressures are generated using high

fidelity three-dimensional Computational Fluid Dynamics numerical simulations. The concept

of accumulated damage appears to be quite useful in the modelling of complex blast

environments when multi-pulse shock waves are expected. It is worthwhile noting that the

normalised accumulated damage applied in the same fashion to vulnerable components, such

as humans, can be used for casualty damage level estimation including the probability of kill.

The reported numerical simulations are partially validated against the results from a live fire

test. It is demonstrated that the predicted values for the failure times of some bus windows are

in good agreement with the experiments. However, due to extraneous noise levels the

pressure time histories at the selected gauges show only quantitative agreement. This result is

likely due to the strong effect of shattering of the bus structure causing elastic waves,

travelling at a higher speed than that of the shock waves, to interfere with the pressure gauge

records.

The proposed methodology also provides a means for predicting response of humans inside

public buses. Explosions in confined spaces are typically associated with a higher incidence

of primary blast injuries. Utilising the proposed relationships for human response due to

close-range detonations, rapid assessment of the vulnerability of bus passengers in various

threat scenarios can be undertaken.

The modelling of fragment ejection/projection from broken windows and other structural

elements resulting from an explosive event will be the subject of a future paper.

ACKNOWLEDGEMENTS

The live fire exercise was conducted by the NSW Police with instrumentation support

provided by DSTO. The authors would like to acknowledge Peter Ray (NSW Police) and the

DSTO team (Phil Winter, Sergiy Kravchuk, Shaun Lavelle, Edmond Almond, Shaun

McCormack, Trevor Delaney and Jared Freundt) for conducting the trial. Grateful thanks are

to Norbert Burman for valuable comments, discussion and support.

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