Blast Waves and How They Interact With-J R Army Med Corps-2001-Cullis-16-26

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    ABSTRACTThe paper defines and describes blastwaves, their interaction with a structure

    and its subsequent response. Explosionsgenerate blast waves, which need not be

    due to explosives. A blast wave consistsof two parts: a shock wave and a blastwind. The paper explains how shock

    waves are formed and their basicproperties. The physics of blast waves is

    non-linear and therefore non-intuitive.

    To understand how an explosiongenerates a blast wave a numerical

    modelling computer code, called ahydrocode has to be employed. This is briefly explained and the cAst Eulerian

    hydrocode is used to illustrate theformation and propagation of the blast

    wave generated by a 1 kg sphere of TNTexplosive detonated 1 m above theground. The paper concludes with a

    discussion of the response of a structureto a blast wave and shows that this

    response is governed by the structuresnatural frequency of vibrationcompared to the duration of the blast

    wave.The basic concepts introduced areillustrated in a second simulation that

    introduces two structures into the blastfield of the TNT charge.

    IntroductionIn both the military and civilian worlds, blastwaves and their interactions with a structureneed to be understood. Explosions formblast waves. These explosions can be eitherdeliberate or accidental. Deliberateexplosions can include demolition charges,

    weapon systems and improvised explosivedevices. Accidental explosions can resultfrom the ignition of gas clouds andinflammable liquids and chemicals due tofire or the failure of pressurised containers.In all cases the effects of the blast wavesproduced need to be quantified, particularlyin respect of injuries to personnel.

    A blast wave is formed by a sudden releaseof energy.The source of the energy release isnot important. However, for many materials,particularly explosives, the very high rate of the energy release generates a tremendouspower source. It is this power source that is

    responsible for the catastrophic damageoften associated with an explosive.

    The generation, development andpropagation of blast waves are governed bythe non-linear* physics that describes shockwaves. In the case of an explosive, its’detonation properties define the propertiesof the blast wave. In the military scenario,blast waves created by explosive charges arethe major concern. In this paper, therefore,the detonation of 1kg of TNT is used to

    illustrate the main features of a blast waveinteracting with structures – the ground andspherical objects.

    Since blast waves are non-linear theresponse of a structure can also be highlynon-linear. As will be discussed below thecharacteristics of an explosion, which havethe most influence on structural response,are its peak pressure, impulse, and overallshape. The elastic-plastic strength andnatural period of oscillation of the structurebeing loaded then determines the type of interaction and the response.

    Before discussing blast waves, it is useful tounderstand the size and scope of the energysources that generate blast waves and thenon-linear physics that results. This hasimportant consequences for the properties of blast waves and their propagation. Thedriving mechanism is the shock wave and abasic understanding of their formation andbehaviour is essential for those interested inblast waves and their interaction withstructures, including personnel.

    Explosions and ExplosivesAn explosion is the phenomenon that results

    from a sudden release of energy. The sourceof the energy release may come fromexplosives such as gunpowder or TNT, froma chemical explosion, from wheat flour dust,from pressurized steam in a boiler, from amechanical explosion or from anuncontrolled nuclear transformation.

    Explosions are thus not restricted tochemical explosions. For example, a steamboiler may explode because of the heatenergy which has been put into the water inthe boiler. The thermal energy, however, isnot intrinsic to the water, and water is not anexplosive. The greatest steam explosion in

    Dr IG CullisPhD BA AMIP

    DERA FellowTechnical LeaderNumerical Modelling

    Defence Research andEvaluation Agency,Fort Halstead,Sevenoaks,Kent,TN14 7BP

     J R Army Med Cor ps 2001; 147: 16-26 

    Blast Waves and How They Interact With


    IG Cullis

    *Imagine hanging a mass on the end of a wire.As we add more mass the wire stretches. If we add twice the mass the wirestretches by twice as much. Remove the mass and the wire returns to its former length.This is a linear process. If, however,the mass added exceeds the strength of the wire then it becomes plastic and continuously stretches until it breaks.This is anon-linear process.

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    history was the famous Krakatoa volcanicexplosion of 27 August 1883. It was causedby the sudden vaporization of an estimated 1cubic mile of ocean water when a volcanoruptured and spilled a great mass of moltenlava into the ocean. The blast wave washeard at a distance of 3000 miles. It hasbeen estimated that this great explosioninvolved an energy release possibly

    equivalent to more than 5 billion tons of TNT.The energy release must be a sudden one,

    rapid enough to cause a localisation of energy. This localised energy is thendissipated by a blast wave, propulsion of fragments and surrounding material, and inmany cases thermal radiation.

    An explosive is defined as a material whichis capable of producing an explosion by itsown energy. All explosives possess this singleattribute. All explosives produce heat andnearly all produce gas. The gas is theprimary mechanism by which an explosive

    does work on its surroundings.High performance explosives possess the

    ability to release their energy over a verysmall time period.The energy release rate isgoverned by the Detonation Velocity, whichfor high performance explosives is of order8mm/µs (millimetres per microsecond), or8km/s. This should be compared to thespeed of sound in air at 0.33mm/µs,0.33km/s. The importance of the speed of energy release can be illustrated bycomparing the energy released by burningcoal and the high performance explosive

    TNT – coal has greater available energy(Table 1).

    Table 1: Comparison of energy release of coal and TNT 

    1 kg Coal 1 kgTNT

    Energy Available 24 MJ 4 MJTime to Release the Energy 2000s 10 µsPower Source 12 KW 400,000 KW

    Thus 1 kg of TNT, in terms of its power,is equivalent to 400 power stationsgenerating at 1000 MW for the same fewmicroseconds.This is equivalent to the totalelectricity generating capability of the

    United States in 1979.A sheet of TNT explosive 20m square

    operates at a power level equal to all thepower the earth receives from the sun. Closeto a detonating explosive therefore, there can

    be a significant thermal radiation dose,which can result in an additional damagemechanism.

    In terms of its ability to do work on itssurroundings through the gaseous products,1 kg of TNT has an energy potential of 7MJ,almost twice its chemical energy.

    With these perspectives in mind, it isreadily apparent why relatively small

    amounts of explosives can cause suchcatastrophic damage.

    Shock wavesA disturbance in a medium travels at thelocal speed of sound in that medium. In air,under normal conditions, a disturbance (e.g.a sound wave) travels with a speed of 330m/s. In a metal, however, the same soundwave will travel with a speed of 5000 m/s.The speed of sound is a function of the localpressure and temperature. Therefore, if thepressure or temperature increases, the speedof sound also increases. This has a dramatic

    influence on the propagation of a pressurepulse of arbitrary shape and finite amplitudethrough the medium. Consider an idealisedtriangular pulse as shown in Figure 1A. Sinceeach individual portion of the pulse has adifferent pressure, the local sound speed foreach portion is different.Thus each region of the pulse travels with this local sound speed.The higher-pressure regions thus move fasterthan the preceding lower pressure regions.They catch up with these slower movingregions and the wave profile becomessteeper, as shown in Figure 1B. This process

    continues until in the limit, a sharpdiscontinuity is formed, Figure 1C. This iscalled a shock wave.The velocity of a shockwave is supersonic relative to the undisturbedmedium into which it is travelling. Examplesof shock waves in air include the sonic boomfrom a supersonic aircraft and the ‘bang’ onehears when a balloon is burst or an explosivecharge detonated.A shock wave is an integralpart of a blast wave and heralds its approach.

    From the perspective of an observer at restin the undisturbed medium, the arrival of ashock wave is characterised by an abruptacceleration, a sudden jump in pressure and

    density and a local rise in temperature.As a shock wave is supersonic compared to

    the local sound speed in the surroundingmedium it is often convenient to describe itby a quantity called the   MACH Number.

    IG Cullis 17  

     Fig 1. Development of a ShockWave from an Initial Pressure Distribution in Air.

         p     r     e     s     s     u     r     e

    Direction of travel

    A. initial pulse B. intermediate C. final shock phase

         e   e e

         p     r     e     s     s     u     r     e

         p     r     e     s     s     u     r     e

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    The Mach Number (M) is the ratio of theshock speed to the local speed of sound,usually under ambient conditions.

    Shock waves undergo reflection fromsurfaces in the same way as sound or lightwaves. However, unlike sound waves, wheretheir effect on the properties of the mediumis negligible, shock waves change the

    medium through which they are travelling.Their reflection from a surface is thereforevery complex and non-intuitive. Shock wavesexhibit three kinds of reflection phenomena:• Normal reflection associated with head-on

    impact with a non yielding surface;• Oblique reflection associated with a small

    angle of incidence with a surface;• Mach stem formation, a spurt-type effect

    associated with angles of incidence with asurface near grazing incidence.In the case of a normally reflecting sound

    wave from a rigid surface, the pressuredoubles on reflection. However in the case of shock waves the reflected pressure is a non-linear function of the Mach number (M) of the incident shock wave. Thus if we considera sound wave to be a very weak shock we cansay for low Mach numbers (M ~ 1) thereflection coefficient (the ratio of thereflected to the incident pressure) is 2. Forvery strong shock waves in air, the theoreticalupper limit of the reflection coefficient is 8.

    In the case of oblique reflection, theincident shock wave impinges upon a surfacewith a small angle of incidence and a shockwave is reflected back into the flow, Figure 2.

    In this respect they resemble sound waves.However, in general, unlike a sound wave theangle of reflection does not equal the angle of incidence.

    A shock front impinging on a surface neargrazing incidence does not reflect directly, butis deflected so that it spurts along the surface.As the angle of incidence increases andexceeds 40º the flow travels parallel to thesurface with the shock front perpendicular tothe surface.This is called a Mach Stem.Thissurface shock extends from the surface outinto the flow until it connects with a line of intersection between the incident shock andthe reflected shock. The reflected shock isthus detached from the surface.This is shownschematically in Figure 2.

    This Mach stem regime, as will be shownbelow, is very important in the behaviour of blast waves. The most important feature isthe direction of the blast wind behind it,which is parallel to the surface and travellingwith a much higher velocity than in theincident wave.

    This brief overview of shock waves and

    their behaviour is essential for anunderstanding of the formation andbehaviour of blast waves. Given the non-linearity of their behaviour, their interactionwith a structure can have quite dramaticconsequences, particularly in the case of personnel vulnerability.

    DetonationAn explosive is a chemical compound thathas energy locked up within its moleculesand molecular bonds. When these chemicalbonds are broken, energy is released since

    the solid explosive has a higher energy thanthe gaseous products produced by thereaction. The reaction is said to beexothermic. The reaction rate for suchchemical reactions is an exponentialfunction of temperature. Therefore if thetemperature of the local surroundingsincreases, the rate of production of heatincreases exponentially. This is much fasterthan the heat loss to the surroundingmaterial, through heat conduction, which islinear. As the temperature rises there comesa point where heat evolution becomes thedominant process and rapid acceleration of 

    the chemical decomposition reactionoccurs.

    A pressure wave associated with thischemical reaction is created, whichpropagates out into the explosive. Thepressure wave compresses the explosive andheats it up, as do the hot gases generated bythe ch emical reaction. The highertemperature then increases the rate at whichthe chemical reactions occur, which drivesthe pressure wave even faster. This ‘run-away’ process continues with the pressurewave becoming steeper and steeper until it

    suddenly assumes a step condition, wherethe pressure, density and temperaturesuddenly jump from the initial state to acompressed state. As described above, thisjump is just another example of a shockwave. The resultant heating of the solidexplosive caused by the shock wave initiatesthe chemical reaction almost immediately.The reaction zone in which the chemicaldecomposition occurs is then physicallylocated at the shock front and supports anddrives it. The shock front travels at asupersonic velocity with respect to theunreacted explosive. For a high

    performance explosive, the reaction zone isless than 1mm thick.

    A shock wave driven by a chemicalreaction is called a detonation wave. It issupersonic with respect to the unreacted, or

    18 Blast Waves

     Fig 2. The Oblique Reflection and Mach Stem Regimes for Reflected ShockWaves.

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    undetonated, explosive.When initiated by adetonator the detonation wave is formedwithin a few microseconds and over adistance of about 2-10mm.

    For a high performance explosive, thedetonation velocity is typically of order8km/s. At the front of the detonation wavethe pressure is about 20-30GPa, (200 – 300

    kbar, where 1 kbar is 1000 timesatmospheric pressure). The temperature inthe gaseous products immediately behind itcan reach 7000ºC.

    Formation and propagation of  blast wavesTo illustrate the blast wave generated by anexplosion it is useful to consider the blastwave generated by 1 kg of TNT highexplosive 50 cm above the ground.The shockwaves produced can therefore be expected tobe strong and governed by the non-linear

    physics associated with their formation andpropagation. The linear physics of acousticsis inadequate to understand the resultantexplosion.

    To provide a detailed description of thephysics of blast waves, we have to employsophisticated numerical modellingtechniques contained in a   Hydrocode. Thename hydrocode is used because they werefirst used to solve problems inhydrodynamics.

    HydrocodesIn its simplest form a hydrocode represents

    the problem within a numerical mesh anduses the physical properties of the materialsin the problem to solve the conservation laws

    of mass momentum and energy (Newton’sLaws) in each of the cells within thenumerical mesh. This process calculates thepressure, energy, density and velocity of theflow field and advances the solution by asmall time-step, of order one hundredth of amicrosecond. By repeating this process manythousands of times, the explosive event is

    advanced in time.There are two main numerical methods

    depending on the way in which thenumerical mesh is defined. If the numericalcell is defined as being embedded in thematerial and deforming with it, then thesimulation is a  LAGRANGE simulation. If,however, the mesh is fixed in space andmaterial moves through it, then thesimulation is a  EULERIAN simulation.

    The Lagrange approach is generally usedfor problems with little significantdeformation where material interfaces are

    important e.g. structural deformation. TheEuler approach is generally used forproblems characterised by significantmaterial deformation and flow e.g. blast waveformation and propagation.

    The Theoretical Modelling andHydrocode Development group within theGuns and Warheads Department at DERAFort Halstead has undertaken significantresearch over the past 20 years into thedevelopment and application of thesenumerical techniques to a wide range of problems in detonics and penetrationmechanics. Central to this research is the

    integration of these simulations with small-scale controlled and highly instrumentedexperiments. This serves to validate thenumerical and material models.

    These modelling techniques have beenassembled into a numerical toolbox calledcAst (Computational Applied Science andTechnology) to provide researchers, of anybackground, access to state of the artmodelling capabilities.

     Free Field ExplosionsThe Euler module within cAst has been

    employed to simulate the detonation of the 1kg TNT charge, whose diameter is 11 cm,and the formation of the blast wave, itsdevelopment and subsequent interactionwith the ground. Initially however, the chargecan be considered to be a free field charge.

    When a high performance explosive isdetonated in air, the high pressure, hightemperature detonation wave impinges onthe explosive-air interface. The arrival of thedetonation wave at the surface of the chargegenerates a shock wave in the air. Becauseair, a gas, is highly compressible, a thin layeris compressed by the detonation wave to a

    very high density, pressure and temperature.This temperature can reach 10000ºC.

    The effects of this on the surrounding aircan be understood from the hydrocodesimulation. To assist this process an array of 

    IG Cullis 19  

     Fig 3. Pressure fields at 20µs (left) and at 10µs (right)

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    fixed data collection points, called stationsand equivalent to experimental pressuregauges, were positioned within the ‘air’represented by the numerical mesh. Eachstation records the properties of the blast asa function of time. The stations in this blastsimulation were positioned in a line though

    the centre of the charge and parallel to theground. Their positions were equi-spacedbetween 10 cm and 3.5 m from the centre of the charge.

    Immediately after the detonation of thecharge there is a hot high pressure volume of explosive product gases surrounded by a thinvery hot layer of air. The particle velocity of the product gases and the air can be as highas 2.5km/s.

    The initial 11 cm diameter sphere, nowtransformed into high pressure gases, rapidlyexpands into a sphere 13.5 cm in diameter,

    4.5 µs after the detonation wave reaches thesurface and 10 µs after the initial detonation.By 20 µs (after the ignition of the explosive)its diameter is 24 cm, as illustrated by thepressure fields shown in Figure 3 (10µs onthe right and 20µs on the left).

    At 10 µs the maximum pressure in the airis 120 bar but over 45,000 bar in theexplosive products. Air has a density of 1.2kg/m3 and an ambient sound speed of 330m/s. Because of its low density, it is rapidlyaccelerated by the shock wave. In addition,its high compressibility implies that thesound speed is also a strong function of 

    pressure – i.e. the air shock propagates with ahigh velocity.

    Initially therefore, the thin layer of hotcompressed air remains attached to theexplosive products, because the velocity of 

    the product surface is supersonic withrespect to the stationary air.

    As the explosive products expand however,they cool down and their pressure, density,temperature and velocity fall. As a rule of thumb, for every doubling of their volume,their pressure falls by an order of magnitude.Once their velocity becomes sub-sonic with

    respect to the air, the shocked air layerdetaches from the product cloud.The time ittakes to do this is a function of the explosiveand the charge size.

    For our charge this process is well-advanced 100µs after detonation, as shown inFigure 4. The orange ‘rim’ around theproducts is the heated air layer (A).The blackline, with the regularly spaced protuberancesis the interface between the air layer and theexplosive products (B). Its shape reflects theturbulent mixing of the products and the air.

    Most explosives have a chemicalcomposition that is ‘oxygen negative’, i.e. theproducts formed by the detonation have notfully reacted with the oxygen in the air. Asthey mix they can continue to burn andrelease further energy. TNT is one of themost oxygen negative compositions andreleases almost as much energy through thisafterburning process as is released in theinitial detonation. As will be explained belowthis can have a significant effect on the blasteffects of a charge.

    Thus, an observer close to the explosionwill experience a high-pressure shock wavefollowed by a high-speed wind of decaying

    pressure due to the moving air and explosiveproducts. This combination is called the blast wave.

    We can see this process in the stationpressure histories, shown in Figure 5.

    20 Blast Waves

     Fig 4. Pressure field at 100µs.

    The histories shown in the figure are forthe stations 10, 20, 30 and 40 cm from thecentre of the charge.The time axis extends to200 µs.The pressure axis extends to 2.6 x 108

     Fig 5. Pressure time histories for 1 kg spherical charge ofTNT at 10, 20, 30(left) and 40 cm (r ight) from the charge centre.

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    dynes/cm2 i.e. 257 atmospheres.The first history, 10 cm from the charge,

    shows the air shock, pressure about 170 bar(A), arriving at 15 µs followed at 30 µs (B) bythe explosive products, which have a muchhigher pressure of 257 atmospheres and alonger duration than the air shock.

    The subsequent histories show a

    broadening of the blast wave as the air shockmoves away from the products.The pressureinitially falls quite rapidly and then moregradually as the wave expands away from thecharge.The air shock, at the head of the blastwave, is clearly visible in all of the pressurehistories. It reaches the second station, 20 cmfrom the centre of the charge, at 42 µs afterdetonation. The explosive products can stillbe distinguished in the pressure record (C),but their pressure has fallen dramatically.

    The blast wave reaches the remaining twostations at 70 µs and 117 µs respectively.Although the products reach these gaugepositions, their pressure is so low comparedto the air, that they do not make a significantcontribution to the blast wave, in terms of pressure.

    This process continues until at largerdistances the blast wave simply consists of the air shock and high-speed movement of air, since the products fall further and furtherbehind it. At large distances from the chargeit is the expansion of the shock wave and therapidly moving air behind it that constitutethe blast wave.The rapidly moving air behindthe shock front is often referred to as the

     blast wind.Close to the explosive charge, the thermal

    output (discussed in the section onexplosives and explosions) is likely to igniteany surrounding combustible material. Theblast wave will at the same time rapidly

    IG Cullis 21

    accelerate and disperse it.In addition of course there is a transitory

    temperature rise associated with the passageof the air shock, which close to largeexplosions can be significant. Due to theirreversible nature of the shock process, thereis also a permanent temperature changewhich can effect equipment and personnel.

    Ground EffectsThe discussion so far has concerned aspherical charge detonated in free field, i.e.the charge is far removed from an object orthe ground. In reality, the ground and/or anobject close by almost always has aninfluence on the propagation of a blast wave.

    In the next simulation, the charge is 50 cmabove the ground. The blast wave impactsthe ground at about 200 µs (equivalent to anaverage blast wave velocity of 2000 m/s). Atthis point the shock front is approximately 6cm ahead of the products. On impact withthe ground the shock wave is reflected backinto the products and the surrounding air.This acts to reinforce the blast pressure.Thereflected pressure from the ground cantherefore be between 2 and 8 times theincident pressure.

    The propagation of the reflected shockwave through the fireball and the air shock isshown in Figure 6 in the pressure fields at276 µs (left) (labelled A) and 500 µs (right)(labelled B). Notice how the reflected shocktravels faster through the products thanthrough the shocked air (C). This is because

    the temperature of the products is higherthan the surrounding air and the speed of sound is therefore greater.This effect is evenmore pronounced for explosives that havesignificant afterburning, since they are at ahigher temperature.

    Also visible in the figure is the earlyformation and development of the Machstem.The figure shows the triple point and itstrajectory, (labelled D), idealised in Figure 2.

    The figure also shows the effect thereflected shock has on the product fireball.The particle velocity, initially directedtowards the ground is now reversed by thereflected shock. The fireball thus begins torise.

    The blast wave continues to propagateaway from the explosion, with the reflectedshock wave, because of its higher pressureand velocity, gradually overtaking it. Theblast pressure fields at 900µs and 1.2ms areshown in Figure 7 and at 4ms in Figure 8.

    By this time the reflected wave accounts forabout two-thirds of the blast field. For anobserver far enough away from theexplosion, the total measured blast wave isthis reflected wave. Notice also how the

    product cloud has rolled up into the classic‘mushroom’ shape as it ascends into theatmosphere. This is a direct consequence of the processes described above and thereflected shock wave from the ground. Fig 6. Pressure fields at 276µs (left) and 500µs (r ight) for a 1 kg spherical TNT Charge.

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    The effect of the reflected shock on anobserver 1m away from the centre of thecharge and 50 cm above the ground is shownin the pressure history in Figure 9 (left).Thehistory shows the arrival of the initial blastwave, with a shock pressure of 8.8atmospheres, at 520 µs (labelled A) followedat 900 µs by the reflected shock wave fromthe ground (labelled B).This has the effect of raising the blast pressure, at this timeinterval, from 1.7 atmospheres to 3.4atmospheres; i.e. the reflected shock doublesthe pressure.

    The pressure record also shows anadditional feature due to the dynamics of theblast wind. The moving air and explosiveproducts behind the shock front, thatconstitute the blast wind, continue to expandand their pressure therefore falls. The inertiain the flow however, means that the gasesover-expand. The pressure falls below

    atmospheric, i.e. there is a ‘negative’ relativepressure phase associated with the tail of theblast wave (labelled C). This is clearly shownin Figure 9 (left) and has duration, at thispoint, of almost twice the initial positivephase. This negative pressure regime acts tofirst slow and then reverse the direction of the blast wind. Although the magnitude of the pressure in the negative phase is muchless than that in the initial shock, its effectson a damaged structure can be quitesignificant.

    For an observer 2 m from the centre of thecharge and 50 cm above the ground, theground reflection has overtaken the initialblast wave. The observer, only ‘sees’ thereflected wave. This is demonstrated in thepressure history at this point, Figure 9(right). Notice that the negative phase is wellestablished at 4 ms after detonation.

    The above discussion has centred on acharge detonated above the ground.A chargedetonated on the ground, will not produce areflected shock or Mach stem. An observer

    will experience a blast wave characteristic of a free field charge. Thus the blast wave is astrong function of position and the obstaclesin the path between the observer and thecharge. Reflected waves can significantlyincrease the shock pressure and the blastwind. Thus an observer, depending on theirposition relative to the charge, mayexperience a blast wave that consists of asingle shock wave, two shock waves or asingle stronger reflected shock wave. Eachscenario will also have an associated blastwind with it. It also explains why personnelclose to a charge are often less seriouslyinjured compared to those further away.

    Having defined and explained the essentialfeatures of blast wave formation, propagationand development illustrated by thedetonation of a 1 kg spherical charge ofTNT,

    22 Blast Waves

     Fig 9. Pressure-time histories for observers 50cm above the ground for a 1kg spherical charge of TNT. Figure 9 (left):Observer 1m from charge; Figure 9 (right):Observer 2m from the charge.

     Fig 7. Pressure fields at 900 µs (left) and 1.2 ms (right) for a 1 kg spher ical TNT Charge.   Fig 8. Blast Pressure Field at 4ms after detonation of a 1kg spherical charge

    of TNT 50 cm above the ground.

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    we can now consider how such a waveinteracts with a structure.

    Interaction of a blast wave witha structureThe blast wave from an explosion interactswith a structure by coupling energy from theblast flow field into the structure.This causesthe structure to deform to an extentdependent upon the strength of the blastwave and the properties of the structure.

    The characteristics of an explosive blastwave that have the most influence on thestructural response are its peak pressure,impulse and overall shape.The strength andnatural period of oscillation of the structurebeing loaded then determine the type of interaction and the response.

    Unlike the case of the ground (considereda rigid surface) the blast wave impactingupon a structure will result in a shock wave

    being propagated through the structure aswell as being reflected from it. The strengthof the reflected and transmitted shock wavesdepends upon the material properties of thestructure and its geometry and of course theincident blast wave. In addition, if thestructure has internal spaces e.g. a building,or contains internal components e.g. thehuman chest, then the transmitted shock caninduce quite dramatic and counter intuitiveresponses in these components.

    When a blast wave strikes a structure thepressure loading that results is composed of 

    two components. The first is the reflectedshock pressure, which as described above canbe significantly higher than the incidentshock pressure. The second is the pressuredeveloped by stopping or slowing down theblast wind.

    To understand some of these effects it isuseful to consider a simple pendulum, e.g. aswing or a weight on a string. Left to swingon its own it will have a natural frequency. If we try to force it to swing at a differentfrequency, then its response will depend onthis forcing frequency. Frequencies close toits natural frequency will generate a largeamplitude response in the pendulum.Frequencies far removed from its naturalfrequency will, however, generate a smallamplitude response.

    In addition, the time over which the forceis applied i.e. the impulse, its direction andthe point it is applied in the oscillationperiod, all control the finally observedamplitude. Thus a small force applied inphase with the pendulum can produce largeamplitudes compared to a large force brieflyapplied out of phase with the pendulum.

    A real structure, such as a building or a

    human, behaves in a very similar way, exceptthat in this case the structure has to berepresented by a large number of pendulaeach with a different natural frequency. Thenatural response of the structure is thus

    described by a number of modes of vibrationeach with a characteristic frequency. Theresponse of the structure then depends uponhow the blast wave couples energy into eachof these modes of vibration.

    We can also represent the blast wave as aseries of pendula of different frequencies andamplitudes. As the blast wave develops and

    changes its shape, its natural frequencydistribution will also change. Using thisanalogy we can begin to understand howenergy is coupled to the matching modes of the structure and why the structural responsewill vary with distance from the explosion.

    The overall shape of a blast wave may bequalitatively defined in terms of its rise timeat the shock front,Tr and the duration of theblast wind, Td. The response then dependson how these characteristic times comparewith the natural period of the structure T.

    There are four categories of response that

    are defined by this relationship:Category A:   If the duration of the blastwave is short compared with the structuresperiod of oscillation, the loading is partlyabsorbed by the structure’s inertia, thusreducing the structural deformation.

    Category B:   If the duration of the blastwave is long compared with the structure’speriod of oscillation and has a long rise time,the structure experiences a load, which iseffectively quasi-static. Here quasi-staticmeans the pressure varies very slowly andcould be approximated by an averageconstant value. The deformation is then the

    same as that produced by an equivalent staticload.

    Category C:   If the duration of the blastwave is long compared with the structure’speriod of oscillation and has a short rise time,then the structure experiences adeformation, which is greater than thatcaused by an equivalent static load.

    Category D:   If the duration of the blastwave is roughly equal to the structure’speriod of oscillation and the rise time isabout half its duration, the structure’sresponse may again exceed that caused by

    the equivalent static load.One can now once again understand howdistance from an explosion can alter theobserved damage and why perversely objectsand personnel close to an explosion oftensuffer less damage and injury than thosefurther away from the explosion.

    The relative importance of pressure andimpulse in determining the structuralresponse depends on whether the blast waveloading of the structure is ‘impulsive’ or‘quasi-static’.

    Category A is termed impulsive, i.e. it isthe impulse within the blast wave that

    determines the structure’s response.Categories B & C are termed quasi-static

    loading, i.e. it is the pressure of the blastshock wave that determines the structure’sresponse.

    IG Cullis 23

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    Category D is part impulsive and partquasi-static and pressure and impulsedetermine the structure’s response.

    In general the sharper the rise time of theshock wave, the greater the structuralresponse. Explosive blast waves with steeprise times are generated by high performanceexplosives such as TNT, HMX, RDX etc.

    Combustible gases such as hydrogen orliquids such as petrol generate explosive blastwaves with shallow rise times.

    From this discussion above it can berecognised that a given level of structuralresponse or damage can result from eitherpressure, impulse or a combination of both.The actual mechanism will depend uponthe explosion source and the distance fromit.

    This naturally leads to the very usefulconcept of the Iso-damage curve, the locusof explosions, which give the same structuralresponse, or level of damage.

    An example is shown in Figure 10. Pointsthat lie on the left of the diagram (i.e. thosewith high impulse and low pressure)represent impulsive explosions and pointsthat lie on the right of the curve (i.e. lowimpulse and high pressure) represent quasi-static explosions. Points in-betweenrepresent explosions, which are partimpulsive and part quasi-static.

    The curves predicting the probability of blast lung injury to personnel take this form.

    Internal damage mechanisms

    The discussion so far has assumed that thestructure is represented by a singlefundamental period of oscillation. As waspointed out above, many structures arecomplex and include components or internalstructures that have very different oscillationperiods. For example, the period of oscillation of the human thoracic wall is verydifferent from that of say, alveolar septa, orsolid viscera.Whilst the gross deformation of 

    the external structure may load andcompress these internal components, thetransmitted shock from the incident blastwave can often cause more severe levels of damage. In many cases the materialproperties of the external structure can act toenhance these internal shock levels andhence damage.

    To illustrate some of these effects, wereturn to our 1kg spherical charge of TNT,detonated in free field, i.e. without theground being present. We position twostructures, diametrically opposite each other,90 cm from the charge centre.The structuresconsist of 35cm diameter spheresconstructed from layers of materials. At thecentre of each is a 10cm diameter air space.This space is surrounded by a 10cm thicklayer of water, which in turn is surrounded,by a 8cm layer of a material with a density10% greater than the water (“unprotected”).The second structure, however, also has a3cm thick outer casing made from steel(“protected”). One could consider theseobjects to be constructed of biologicalmaterials. At this standoff from the chargethe blast wave reaches the structures at about300 µs, Figure 11.

    Although the air shock (A) has separatedfrom the product cloud (B), the products stillmake a significant contribution to the blastwave loading.When the blast wave strikes thestructures it effectively ‘wraps’ itself aroundthem. In our example this process is notcompleted until 900µs after detonation, 600

    µs after the arrival of the blast wave, as shownin Figure 12. The product cloud has beenslowed and deformed by its impact with thestructures and is beginning to flow laterally(C). The impact of the products with theunprotected structure has also deformed anddamaged it.

    The figure graphically illustrates anadditional feature of the interaction of a blastwave with a structure, namely its ability to

    24 Blast Waves

     Fig 11. Initial Blast Wave Pressure Loading of unprotected (bottom) and  protected (top) structures.

     Fig 10. ISO-DAMAGE cur ve

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    load all parts of the structure. Unlike animpact scenario, e.g. due to a projectile,where the loading is applied at the initialpoint of contact, a blast wave can load therear of a structure long after the initialloading.

    The reflected shock waves generated by thestructures can be seen propagating away

    from them in Figure 12 at 900 µs. Theymodify the incident blast field. Observersclose to the structures will therefore,experience a complex pressure loading andblast wind. Furthermore, when the shockwaves enveloping the structure, meet at theopposite pole there is a strong pressureenhancement, because the flow is effectivelystagnated, Figure 12 (D). The resultantloading in the structures can also beobserved in the figure.

    In terms of the internal response, thedifferent material speeds of sound imply that

    the shock waves developed by the impact of the blast wave propagate at differentvelocities through them. The protectedstructure, because of the steel case, producesa stronger reflected blast wave. Theconfinement also results in higher and moreuniform pressures within the internalcomponents.

    Internal elements of the structure willrespond differently to these effects. This canlead to relative motion between them withconsequent shearing and tearing atinterfaces. Most materials, includingbiological materials, are relatively weak in

    shear and therefore readily fail under shearloading conditions.

    The pressure field shown in the Figure 12highlights high-pressure regions at theopposite poles of both spherical structures,

    quite marked in the case of the protectedstructure. In the latter case there is also amarked spherical pressure gradient acrossthe water layer, i.e. the water and the airspace are being effectively squeezed.

    In biological systems, this will lead toinjuries such as bowel contusions.

    The response of a structure is thus a

    complex problem. Intuitively obviousdamage mechanisms, e.g. quasi-staticpressure, in fact often do not represent themajor cause of observed structural failure.The dynamic processes associated withmaterial acceleration and high relativevelocities are often far more effective. In thecase of large structures, different parts mayrespond in different ways. It is therefore, vitalthat the important damage mechanisms areidentified and understood.

    In protecting a structure from blast, allpossible damage mechanisms have to beconsidered and ranked. It is often the highfrequency components induced by the blastwave that have to be effectively removed – this is the case with primary blast lung injury.It must be recognised, however, that aninappropriate combination of materials in aprotection scheme can enhance rather thandampen the damaging frequencycomponents.

    ConclusionsThis paper has described how an explosiondue to a sudden release of energy forms blastwaves. The blast wave is composed of two

    parts, the initial shock wave and the blastwind.The shock wave results when we try todrive a disturbance supersonically in amedium. A shock wave modifies theproperties of the medium through which it istravelling.The resulting non-linear behaviourmeans that reflection of a shock wave is alsonon-linear. Significant pressureenhancements can be generated on reflectionand for angles above 40º a Mach stem isproduced.

    The detonation of a 1 kg spherical chargeof TNT has been simulated, using a Eulerian

    hydrocode  cAst

    , to illustrate the formation,development and propagation of blast waves.Numerical simulation is a powerful tool forunderstanding blast waves and theirinteraction with a structure.

    The interaction of the blast wave with theground has been shown to lead to itssignificant enhancement. An observerpositioned at different distances from theexplosion will experience very different blastwaves, with characteristically differentpressures, blast winds and durations.

    The interaction of a blast wave with astructure has been shown to be a complex

    process that is dependent upon its naturalfrequencies.The subsequent response can beimpulsive, quasi-static or a combination of both, dependent upon the explosion sourceand the stand off distance.The same level of 

    IG Cullis 25  

     Fig 12. Blast Wave Pressure Loading at 900µs of unprotected (bottom) and protected(top)structures.

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    damage can, therefore, be created bydifferent loading regimes. This naturallyleads to the concept of an iso-damage curvefor a structure.

    The phenomena associated with theinteraction of a blast wave with a structurehave been illustrated with a simplehydrocode simulation. The ability of a blast

    wave to load all parts of a structure has beenshown to be crucial in describing the overall

    structural response. An understanding of thedamage mechanisms is important if vulnerability and protection of a structure,particularly personnel, is required.

    Simple intuitive ideas on structuralprotection can lead to significantly increasedlevels of damage. This occurs because highfrequency components of the loading are

    often enhanced by an inappropriate selectionof materials.

    26 Blast Waves

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    IG Cullis

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