APPENDIX A

Explosion and Fire Phenomenaand Effects

Potential explosion phenomena include vapor cloud explosions (VCEs),confined explosions, condensed-phase explosions, exothermic chemicalreactions, boiling liquid expanding vapor explosions (BLEVEs)7 and pres-sure-volume (PV) ruptures. Potential fire phenomena include flash fires,pool fires, jet fires, and fireballs. Guidelines for evaluating the charac-teristics of VCEs, BLEVEs, and flash fires are provided in another CCPSpublication (Ref. 5). The basic principles from Reference 5 for evaluatingcharacteristics of these phenomena are briefly summarized in this appen-dix. In addition, the basic principles for evaluating characteristics of theother explosion and fire phenomena listed above are briefly summarized,and references for detailed evaluation of characteristics are provided.

A.1. Explosion and Fire Phenomena

All Explosions

An explosion may be defined as a phenomenon where a blast (pressure orshock) wave is generated in air by a rapid release of energy. This energymay have originally been stored in the system in a variety of forms (e.g.,nuclear, chemical, electrical, or pressure energy). To be considered explo-sive, the release of energy must be rapid enough and concentrated enoughto produce a pressure wave that can be heard. The resulting blast wave islargely responsible for the damage that was caused (Ref. 84). Buildings maybe damaged and people may be injured by the blast wave, with additionalindirect effects from missile generation, crater formation, ground shock,and fire. Generally, as the blast wave travels farther away from the centerof the explosion it loses energy, so the magnitude of overpressure and othereffects experienced as a result of the blast wave decreases as the distanceincreases from the explosion source. The decay of overpressure is roughly

inversely proportional to the separation distance to the third power (theHopkinson-Cranz "Cube Root" scaling law). As a blast wave strikes a surface,pressure increases because of a process called reflection. Similarly, as a blastwave propagates through a congested region, it is possible for the pressuresto be focused such that local regions of increased pressure may exist.

For process plants, an important distinction to be made for an explo-sion caused by the release of chemical energy is whether it may becharacterized as a deflagration or a detonation. The difference between adeflagration and detonation is the mechanism whereby energy required toactivate the explosive reaction is transferred from reacted to unreactedmaterial.

In a deflagration, the mechanism for propagation of the explosionreaction into the unburned material is by heat and mass transfer. Materialsurrounding an initial exploding site is heated above its autoignitiontemperature, allowing the reaction to propagate. Transfer of energy by thesemeans is a relatively slow process, always at propagation rates that are lessthan the speed of sound in the unreacted material.

In a detonation, the mechanism for propagation of the explosion is byshock compressive heating. Detonation proceeds very rapidly because ofthe rapid transmission of the mechanical forces involved. Detonationpropagation velocities are always greater than the speed of sound.

The overpressure characteristics of deflagrations and detonations as afunction of time are very different (Ref. 85). Typical overpressure profilesare compared in Figures A. Ia and A. Ib. For a given explosion energy,deflagrations are generally characterized by a gradual increase to peakoverpressure with long durations, followed by a gradual decrease in over-pressure. This wave form is generally referred to as a pressure wave.Detonations are characterized by a very rapid rise to peak overpressurefollowed by a steady decrease of overpressure to form the more idealizedshock front.

Even though these blast pressure waves are initially different shapes,they will both eventually develop a shock front as explained below. Devel-opment of a shock front is illustrated in Figure A. 2. Figure A.2a shows apressure pulse of arbitrarily chosen initial configuration. Each portion ofthis pulse moves outward at its own speed. The higher-pressure portionsof the pulse correspond to higher temperatures and hence also to greaterspeeds. The high-pressure portion moves faster than any preceding low-pressure portion of the pulse. As a result, the wave front becomes progres-sively steeper, as shown in Figure A.2b. In time, a discontinuity known asa shock front is developed, as shown in Figure A.2c. For a detonation, theshock front, as shown in Figures A. Ib and A.2c, develops very rapidly atdistances relatively close to the explosion source. For a deflagration, theshock wave, as shown in Figure A.2c, forms more slowly and may not bedeveloped until it is a significant distance from the center of the explosionor, in some cases for weak deflagrations, not before the blast wave decaysto an acoustic (sound wave) magnitude.

Deflagration

Detonation

time

time

Figure A.1. Pressure vs. time curves resulting from a deflagration (Fig. A.1a) anda detonation (Fig. A. 1b).

Direction of TravelDirection of Travel

Direction of Travel

Figure A.2. Development of explosive shock.

pre

ssure

pre

ssure

Pres

sure

Pres

sure

Pres

sure

Vapor Cloud ExplosionsA vapor cloud explosion (VCE) results from the ignition of a flammablemixture of vapor, gas, aerosol, or mist, in which flame speeds accelerate tosufficiently high velocities to produce significant overpressure (Ref. 21).VCEs are generally associated with the release of a sufficient quantity offlammable gas or vaporizing (flashing) liquid from a storage tank, processor transport vessel, or piping system. In general, five conditions must bemet before a VCE with damaging overpressure can occur (Refs. 5 and 85):

1. The released material must be flammable and at suitable conditionsto form a vapor cloud. Some portion of the resulting cloud mustmix with air such that concentrations are within the flammablerange for the material.

2. An ignition source is needed to initiate the explosion. The presenceof an ignition source should always be assumed, because explosionsand fires have occurred where no obvious ignition source could beidentified. Higher-energy ignition sources can lead to a more severeexplosion than do lower-energy sources.

3. Ignition of the flammable vapor cloud must be delayed until a cloudof sufficient size has formed. If ignition occurs as the flammablematerial is escaping, a large fire, jet flame, or fireball might occur,but a VCE is unlikely. The probability of explosion rather than fireincreases with the size of the cloud, since the quantity of themixture within the flammable range increases. Paradoxically, plantsafety measures that eliminate sources of ignition can be contribu-tors to the formation of very large flammable vapor clouds with thepotential for very severe explosions.

4. Turbulence is required for the flame front to accelerate to the speedsrequired for a VCE; otherwise, a flash fire will result. This turbu-lence is typically formed by the interaction between the flame frontand obstacles such as process structures or equipment. Turbulencealso results from material released explosively or via pressure jets.The blast effects produced by VCEs can vary greatly and are stronglydependent on flame speed. In most cases, the mode of flamepropagation is deflagration. Under extraordinary conditions, a deto-nation with more severe blast effects might occur. In the absenceof turbulence, under laminar or near-laminar conditions, flamespeeds are too low to produce significant blast overpressure. In sucha case, the cloud will merely burn as a flash fire.

5. Confinement of the cloud by obstacles can result in rapid increases inpressure during combustion. Conversely, absence of confining obsta-cles allows unlimited outward expansion of the cloud during combus-tion, limiting the pressure increases. Unconfined clouds usually willnot generate sufficient flame speeds to result in overpressure effects.The degree of confinement in process plants, with their congestedequipment layout and built-up structures, is generally high (Ref. 16).

Factors affecting the probability, magnitude, and effect of a VCEinclude (Refs. 16 and 86):

• Amount of flammable material in the cloud, within an area wherethere are objects that will induce turbulence and create a degree ofconfinement

• Degree of cloud mixing (cloud composition)• Reactivity of flammable material (affects explosion severity; highly

reactive materials increase the likelihood of a fireball transition toa VCE)

• Fundamen tal burning velocity• Energy of ignition source• Release conditions (high-pressure releases generate greater turbu-

lence than do low-pressure releases)• Presence of obstacles, or confinement, or other turbulence-enhanc-

ing mechanisms• Cloud configuration (some incidents have exhibited directional

blast effects)• Wind speed and direction

The factors that dominate the development of pressure in VCEs arethe presence of obstacles enhancing turbulence, the degree of confinement,and the reactivity of the unburned material (Refs. 5 and 16).

Bursting Pressure Vessels, Physical Explosions, and BLEVEsWhen a vessel containing pressurized gas bursts, a shock wave propagatesaway from the surface of the vessel. This shock wave may create overpres-sure effects strong enough to cause damage or injury. In addition, thebursting vessel can form a number of fragments moving away from thevessel at relatively high velocity. These fragments may also cause damageor injury. Mechanisms that can result in vessels being overpressurizedinclude deflagration of flammable gases or runaway chemical reactions.Alternatively, vessels may fail because of faulty construction or corrosion,or may become overstressed from mistreatment. Another failure mode canoccur if the vessel is subjected to external fire, causing the unwettedsurfaces to overheat, weaken, and fail.

Vessel ruptures can also occur when a higher-temperature liquid orsolid is combined with a cooler low boiling liquid, transferring sufficientheat from the hotter material to the colder material such that the coldermaterial rapidly vaporizes. No chemical reactions are involved; instead, theexplosion occurs because the cooler liquid expands as it is converted tovapor, creating high pressures. These are called physical explosions. Acommon example is a steam explosion, which occurs when liquid water isaccidentally introduced into a process vessel operating at an elevatedtemperature. If the hotter material is above the superheat limit temperatureof the evaporating liquid, initial confinement by a vessel is not required tocreate an explosion pressure wave.

A BLEVE results from catastrophic failure of a vessel containing a liquidat a temperature significantly above its boiling point at normal atmosphericpressure. When the vessel fails, the liquid can evaporate very rapidly(explosive evaporation). The rapidly expanding vapor compresses the sur-rounding air, creating a blast pressure wave. Also, as the vessel fails,fragmenting may occur. These vessel fragments can be propelled a signifi-cant distance at high initial velocities. BLEVEs are commonly associatedwith releases of pressurized flammable liquids from vessels as a conse-quence of an external fire. Such BLEVEs can produce thermal radiationeffects from a fireball, as well as blast and missile effects.

Condensed-Phase ExplosionsCondensed-phase systems (solids and liquids) that have a high heat ofdecomposition may be capable of detonating. These materials are routinelyfound in the explosive or munitions industry but can also be found in thechemical process industry. Examples include some organic peroxides,acetylenic compounds, and nitration mixtures. In addition, this hazard canoccur in processes if some unwanted and highly sensitive substance isaccidentally allowed to concentrate (Ref. 64). Blast and fragment effectsfrom such explosions may be evaluated by estimating the energy releasedin an explosion of an equivalent mass of TNT.

A 1.2. Fires

Fires result from combustion, an exothermic chemical reaction in whichoxidation takes place. Three essential requirements for combustion exist:oxidizing agent (e.g., oxygen), combustible material (i.e., fuel), and ignitionsource. If any of these three requirements is missing, combustion will notoccur. Generally, the activation energy required to initiate the combustionreaction is initially supplied by the ignition source. After initial ignition,the combustion reaction releases sufficient energy to sustain the reactionwithout an external ignition source.

The type of fire that occurs in a particular situation depends on severalfactors (i.e., the form of the combustible material, the degree of mixingbetween the material and air, the location of the combustible material, andthe nature of the release of the material). Section 2.1 describes flash fires,pool fires, jet fires, and fireballs.

Heat is transferred from a fire by three methods: conduction, convec-tion, and radiation. Conduction is the mechanism by which heat istransferred from one body to another by direct contact between the two.Convection involves the transfer of heat by a circulating medium—eithera gas or a liquid. Radiation is a form of energy traveling across a space orthrough a material as electromagnetic waves.

In the case of small fires (e.g., a candle), most of the heat leaves theflame by vertical convection. However, larger fires release about equalamounts of radiative and connective energy. Radiated energy is potentially

the most damaging to buildings because a stationary surface (such as a wallor roof) near the fire will absorb most of the radiation incident on it, whilemost of the convected energy flows past the surface as it moves away withthe gas stream. Most of the radiant heat from flames originates from sootin the flames, which glows when heated to flame temperature. Clean-burn-ing flames, such as those from natural gas or hydrogen, emit smalleramounts of radiant heat. Radiant energy travels in straight lines and isabsorbed by suspended particles such as smoke and by unsymmetricalmolecules in the atmosphere (e.g., water vapor and carbon dioxide). Thisexplains why mists or water sprays effectively attenuate thermal radiation.

A.2. Evaluating Characteristics of Explosions and Fires

The characteristics of explosions and fires that determine consequences topeople and buildings are identified and briefly described in this section.Also, the basic principles used in quantifying these characteristics aredescribed. References on detailed methods of evaluating explosion and firecharacteristics are also provided. A basic reference is CCPS's Guidelinesfor Evaluating the Characteristics of Vapor Cloud Explosions, Flash Fires,and BLEVEs (Rd. 5).

A.2.1. Explosions

Buildings in process plants may sustain structural damage from blastoverpressure and fragments from an explosion. Cratering and ground shockresulting from explosions can be important considerations for buriedtargets (e.g., pipelines), but for aboveground targets the effects are normallysmall compared to those of the blast pressure wave.

Evaluating Overpressure and Impulse CharacteristicsAs discussed in Section A.I, explosions generate a pressure wave thatpropagates outward from the explosion source. The peak value of the over-pressure, positive phase duration, and the resulting impulse are the pre-dominant parameters that determine the destructiveness of an explosion.

Extensive data are available for evaluating blast wave characteristics asa function of distance from explosion source and of explosion size, ex-pressed as weight of TNT (Refs. 7, 54, 64, and 70). Figure A.3 shows anexample of such data taken from Reference 7, Volume II.

Condensed-phase Explosions. Data such as those shown in Figure A.3can be used for condensed-phase explosions. For many materials, explosivestrengths in terms of %TNT are well established (Ref. 54). For thesematerials, the weight of material, W, is adjusted by the %TNT for thematerial. Blast wave characteristic data can then be obtained from relation-ships such as that shown in Figure A.3.

PSO - Peak Positive Pressure, psiPr = Peak Positive Normal Reflected Pressure, psiis /W1/3 = Scaled Unit Positve Incident Impulse, psi - ms/ib1/3

ir /W1/3 = Scaled Unit Positve Normal Reflected Impulse, psi - ms/ib1/3

tA/W V3 = Scaled Time of Arrival of Blast Wave, ms/lb1/3

VW 1/3 = Scaled Positive Duration of Positive Phase, ms/lb1/3

u = Shock Front Velocity.ft/ms

W = Charge Weight, lbs

IVW1/3 = Scaled Wave Length of Positive Phase, ft/lb1/3

R = Distance from Explosion, ft

Figure A.3. Positive phase shock wave parameters for a hemispherical TNT explo-sion on the surface at sea level (Ref. 7).

Scaled Distance Z=R/W1/3

Vapor Cloud Explosions. Blast wave data such as in Figure A. 3 have notbeen developed for VCEs. However, because of the volume of data available,a TNT equivalence method for predicting VCE overpressures and durationis often used. Establishing TNT equivalency is much more difficult and lessreliable for VCEs than for condensed-phase explosions. In the TNT equiva-lence approach, the blast effects from VCEs are correlated with those fromequivalent explosive charges of TNT as a means of quantifying the severityof explosions (Ref. 88). Many organizations use variations of this approach.

In TNT equivalence methods, the equivalent weight of TNT repre-senting the VCE, WTNT/ *s expressed as:

WfHfTNT = OC_L_L

^TNT

whereWf = weight of fuel involved [lbm (kg)]Hf = heat of combustion of fuel [ft • lbf (J/kg)]HTNT = TNT detonation energy [ft - lbf (J/kg)] = 4.52 MJ/kg(Xe = TNT equivalency based on energy

Differences in the approach by various organizations are in: (1) portionof fuel included, (2) TNT equivalency (also called yield or efficiency), (3)TNT blast data, and (4) TNT blast energy. Normally, only a smallproportion of the heat of combustion of the fuel involved in an explosionappears as energy in the shock wave. It is therefore assumed that only acertain proportion (usually 1%-10% based upon energy) of the fuel releasedcontributes to the explosion. This mass of fuel is converted to an equivalentmass of TNT, taking into account the combustion energy of the fuel andthe detonation energy of TNT. Overpressures are determined from TNTblast curves, which have been well established from experimental data(Figure A.3). Reference 5 gives detailed information on using the TNTequivalence method.

The TNT equivalence method is used because: (1) it is easy to use, (2)it requires limited assumptions for determining the initial spill size andTNT equivalency, and (3) data on damage generated at given distances byhigh explosives are well known and widely available. The method does haveserious limitations and deficiencies (Ref. 16), including: (1) TNT equiva-lency is not clearly defined, (2) blast wave characteristics from TNT arevery different from those for a VCE (TNT produces a shorter-duration andhigher overpressure blast wave than does a VCE for the same energy), and(3) blast attenuation differs between TNT and a VCE (the TNT methodoverpredicts near-field effects and underpredicts far-field effects, which hascaused incident investigators to overestimate the TNT equivalence ofVCEs when based on far-field blast damage such as glass breakage). Theuse of different TNT equivalencies in the near and far fields can overcomethe modeling deficiency described in item 3 (Ref. 5).

Because of the deficiencies of the TNT equivalence model for repre-senting a VCE, additional methods for evaluating VCEs have been pro-posed. These methods address a major feature of gas explosions notconsidered by TNT equivalence methods; namely, the blast source is nota point, and blast strength varies over the extent of the blast source. Suchmethods, grouped as those based on fuel-air charge blast, are covered inReference 5. Basic principles of the Multienergy method (Ref. 88) and theBaker-Strehlow method (Ref. 64) are briefly discussed below.

For VCEs, observations indicate that little correlation exists betweenthe quantity of fuel and the equivalent weight of TNT required to simulateits blast effects. For VCEs, blast effects are determined primarily by the sizeand nature of partially confined and obstructed regions within the cloud.

The Multienergy method recognizes these principles for VCE blastmodeling, emphasizing the influence of obstacles and partial confinementof the cloud. The incident is modeled by dividing the vapor cloud intovolumes according to their degree of obstruction/confinement. An explo-sion strength index, varying from 1 to 10, is assigned to each volume. Thepartly confined and/or obstructed volumes of a cloud will be major blastsources. The unconfined and unobstructed volume of the gas cloud willburn without contributing significantly to the main blast (Ref. 16). Anexplosion strength value of 1 represents a very weak explosion due to avirtually unobstructed or unconfined cloud, whereas a value of 10 repre-sents a detonation. An explosion strength of 7 would correspond to a verystrong explosion caused by a highly congested area such as within a denseprocess block or a bank of pipes. Potential sources of strong blast include:(1) extended spatial configuration of objects such as process equipment inchemical plants or refineries and stacks of crates or pallets, (2) spacesbetween extended parallel planes (e.g., those beneath closely parked carsin parking lots and open buildings such as multistory parking garages), (3)spaces within tube-like structures (e.g., tunnels, bridges, corridors, sewagesystems, and culverts), and (4) an intensely turbulent fuel-air mixture ina jet resulting from release at high pressure.

Each volume of the subdivided cloud is modeled as a hemispherical,stoichiometric, fuel-air charge with an appropriately assigned explosionstrength. The major determining factor for the initial blast strength is thedegree of confinement and obstruction. Plots of scaled overpressure andexplosion duration as a function of scaled distance and explosion strength(Figures A.4 and A.5) enable blast effects to be predicted. Again, refer toReference 5 for more information. See Figure A. 5 for definition of the scaledaxis variables.

The Baker-Strehlow method (Refs. 5, 64, and 89) for VCE blastmodeling uses numerical and experimental data relating the structure ofblast waves generated by constant velocity and accelerating flames propa-gating in a spherical geometry. These data are expressed by plots ofdimensionless overpressure and positive impulse as a function of energy-scaled distance from the cloud center. Application of the Baker-Strehlow

Figure A.4. Scaled overpressure versus energy-scaled distance by Multienergymethod (Ref. 5).

method requires estimation of maximum flame speed attained and equiva-lent energy of the explosion.

Maximum flame speed attained is a function of confinement, obstacledensity, fuel reactivity, and ignition intensity. The maximum flame speedthat will be achieved with a particular combination of confinement,obstacles, fuel reactivity, and ignition source is estimated (Ref. 5). Energyrepresents the heat that is released by that portion of the cloud contributingto the blast wave. Any of the following methods of calculating vapor cloud

combustion energy-scaled distance (R)

dim

ensi

onle

ss m

axim

um 's

ide

on' o

verp

ress

ure

(AP

g)

Figure A.5. Scaled duration versus energy-scaled distance toy Multienergy method(Ref. 5).

explosive energy are applicable to the Baker-Strehlow method: (1) estimat-ing the volume within each congested region, multiplying fuel mass by heatof combustion in that region, and treating each congested region withinthe flammable portion of the cloud as a separate blast source, (2) estimatingtotal release of flammable material within a reasonable amount of timeand multiplying by the heat of combustion and an efficiency factor, and (3)estimating the amount of material within flammable limits (usually bydispersion modeling) and multiplying by the heat of combustion.

BLEVEs and Bursting Pressure Vessels. In Reference 5, three methodsfor calculating values of the blast wave parameters of pressure vessel burstsand BLEVEs are presented. The choice of method depends on the phase ofvessel contents (i.e., liquid, vapor or nonideal gas, and ideal gas) and thedistance to the blast wave "target/' For PV ruptures, the first methodincludes the following steps:

P0 * atmospheric pressureC0 * atmospheric sound speedE B amount of combustion energyR0 * charge radius

time

combustion energy-scaled distance (R)

dim

ensi

onle

ss p

ositi

ve p

hase

dur

atio

n (t

+)

1. Collect data on vessel internal pressure, ambient pressure, volumeof gas-filled space, ratio of specific heats of the gas, distance fromvessel to target, and shape of vessel.

2. Calculate the energy of compressed gas.

3. Evaluate scaled distance from actual distance, energy, and ambientpressure.

4. Check scaled distance region, as different methods apply in near-and far-field regions.

5. Determine scaled side-on pressure as a function of scaled range fromempirical curves.

6. Determine scaled positive impulse as a function of scaled distancefrom empirical curves.

7. Adjust scaled pressure and impulse for geometry effects.

8. Evaluate actual side-on pressure and positive impulse.

9. Check resulting pressure against initial vessel pressure and makeadjustments, if necessary.

The second and third methods include enhancements to the basicmethod described above for different parameters. The second methodrepresents refinements for blast wave characteristics in the near field of thevessel. The third method specifically addresses explosively flashing liquidsand pressure vessel bursts with vapor or nonideal gas.

Fragment CharacteristicsIn addition to the blast pressure wave, explosions can also create fragments.Characteristics of fragments to be used in consequence evaluation includetheir number, shape, velocity, and trajectory. A BLEVE or bursting pressurevessel can produce fragments that fly away from the explosion source.These primary fragments, which are part of the original vessel, are hazard-ous and may result in injuries to people and damage to structures. Also, ablast wave from a condensed-phase explosion, VCE, or BLEVE may pickup and hurl objects (projectiles) because of the blast wind by the associatedblast wave propagation. The effects of fragments resulting from a BLEVEor bursting pressure vessel are considered in detail in References 5 and 64.Specifically, methods for calculating the number, range, and velocity offragments are discussed in depth. A good approximation for the velocityattained by blast wind projectiles is available by using the impulse-momen-tum exchange theory (Ref. 84).

For explosions inside vessels, the initial velocity of the projectiles canbe estimated, for example, by predicting what fraction of the availableenergy is transferred from the expanding fluid to the fragments (Ref. 84).Energy available from an explosion within a vessel will be divided betweenwork to propagate cracks to cause rupture, kinetic energy of fragments,energy in the shock wave (some but not all of which can do work; i.e., cause

damage), heat in products, and plastic strain energy in fragments. Anothermethod for evaluating the initial velocity of projectiles involves a step-by-step analysis of the momentum transfer from the fluid escaping throughcracks in between the projectiles to the projectiles themselves. For brittlevessels, or in the case of detonations, severe fragmentation is possible,while for ductile vessels, a limited number of fragments will be generated(generally less than 10).

The velocity of fragments from a pipeline will be greater than that froman isolated vessel at the same conditions because of the replacement of gasloss by flow from the intact pipe (Ref. 84). The influence of drag and lifton the fragment may significantly affect its range and velocity such thatthe velocity with which it strikes an object can be markedly different fromits initial velocity. Neglecting such aerodynamic effects is likely to lead toa serious underestimation of the velocity with which fragments impact aparticular object.

A.2.2. Jet Fires: Direct Contact and Conduction

Released heat is transmitted to the surroundings by convection and ther-mal radiation. For large fires, thermal radiation is the main hazard and cancause severe burns to people and secondary fires to nearby structures. Twomethods or models used to describe the radiation from a fire are the pointsource model and the surface-emitter model, or solid flame model, whichare discussed in detail in Reference 5.

Reference 5 also provides discussion of a flash fire thermal radiationmodel and means of estimating fireball size and duration along with afireball radiation model. Additional material on fireball modeling may befound in References 63 and 90. Reference 33 provides information onmodeling pool fires. In particular, the flame height above the pool surfaceand the angle of tilt of the flame from the vertical as a function of windvelocity and direction may be estimated from Reference 33. References 33and 91 provide methods of calculating the flame length and diameter of aturbulent gas jet burning in still air.

A.3. Effects of Explosion on Buildings

Following an explosion, a blast propagates through the air outward fromthe explosion source (Figure A.6). Depending on the nature of the explo-sion, the blast wave can be a shock wave with instantaneous rise to thepeak overpressure or a pressure wave with a more gradual rise time. Theblast wave produces diffraction and drag load on structures in its path.

The diffraction loading process on buildings can be illustrated byconsidering a rectangular structure with one side (called the front of thestructure in subsequent discussion) facing the explosion, as shown inFigure A.7. The blast wave is generally assumed to be a plane wave (the

Figure A.7. Blast wave striking a closed rectangular structure.

blast wave front is sufficiently large compared to dimensions of thestructure) with the blast front perpendicular to the surface of the ground(explosion initiated near the ground surface), as shown in Figure A.6.Figures A. 8 and A. 9 illustrate the behavior of a blast wave striking thisstructure.

When the blast wave with a shock front strikes the front of the structure(Figures A.8a and A.9a), the overpressure rises to a value in excess of thepeak overpressure in the incident blast wave. This increased overpressureis called the reflected overpressure and is a function of the peak side-onoverpressure.

The blast wave then bends (or diffracts) around the structure, exertingpressures on the sides and roof and finally on the back face (Figures A.8b

S = f-or H whichever is smaller

Side

Back face

Front face

Top (roof)

Figure A.6. Blast wave propagation along ground surface to location of structures.

Ground surface

Structure

Assumed planewave front

Ground reflected wave

and A.9b). The structure is thus engulfed in the high pressure of the blastwave. Because the reflected pressure on the front face is greater than thepressure above and to the sides, the reflected pressure cannot be main-tained, and it soon decays to the incident overpressure. The decay time ofthe reflected pressure is roughly that required for a rarefaction wave tosweep from the edges of the front face to the center of this face and backto the edges. The decay time may be approximated by 3S/C7, where S is thestagnation distance (Figure A.7) and U is the shock front velocity.

The reflected pressure wave amplitude and impulse for shock wavesassociated with detonations are well documented, as shown in Figure A. 3(Ref. 7, Volume II). Less information is available on reflected overpressureand impulse resulting from deflagration pressure waves. Reference 67documents approaches for evaluating reflected overpressure from weakerblast pressure waves. Forbes (Ref. 71) suggests the following approximaterelation to model the more complex relations in Reference 64:

P1XP8 = 2 + 0.05(P8) for O < P8 < 20 psi (1.4 bar)

where Pr is peak reflected pressure and P8 is peak incident side-on pressure.Reference 64 recommends assuming that the ratio of reflected impulse toincident impulse is the same as the ratio of reflected pressure to incidentpressure. Note that the above relation is a conservative estimate of reflectedpressure for VCEs, since in most cases the VCE blast waves may not becharacterized by an ideal shock front. The reflection process for a nonidealblast wave or pressure wave is not well understood, but it is unlikely thatsuch blast waves are fully reflected by the "front" wall of a building.

Figure A.8. Blast wave and structure—elevation view.

Shock frontVortices

Diffractedshockfront

Shock front

Vortices

Incidentshock front Shock front

VortexRarefactionwaveReflectedshockfront

Roof

Back

wal

l

Fron

t wal

l

Figure A.9. Blast wave and structure—plan view.

However, it is normal practice in blast-resistant design to assume conser-vatively that the VCE blast wave is fully reflected from the front wall as anideal shock.

The pressures on the sides and roof of the structure build up to theincident overpressure as the blast wave traverses the structure. Travelingbehind the blast wave front there is a short period of low pressure causedby a vortex formed at the front edge during the diffraction process (FiguresA.8c and A.9c). After the vortex has passed, the pressure returns essentiallyto that in the incident blast wave. The air flow causes some reduction inthe loading to the sides and roof, because the drag pressure has a negativevalue for these surfaces.

When the blast wave reaches the rear of the structure, it diffractsaround the edges and travels across the back surface (Figures A.8d andA.9d). The pressure takes a certain rise time to reach roughly a steady-statevalue equal to the sum of the overpressure and the drag pressure, the latteragain having a negative value for the back surface.

incidentshock front

End wallBa

ck w

all

Fron

t wal

l

End wall

Vortex

Rarefactionwave

Reflected "shock front

Shock front

Shock frontVorticesShock front

Diffractedshock front

Vortices

Also important to consider is the net horizontal diffraction loading onthe entire structure, corresponding to the loading on the front face minusthat on the back face. The net horizontal loading during the diffractionprocess is high because the pressure on the front face is initially the reflectedpressure, and no loading has reached the back face. When the diffractionprocess is complete, the overpressure loading on the front and back facesis essentially equal, and the net horizontal loading is then relatively small.Because the time required to complete the diffraction process depends onthe size of the structure, rather than on the positive-phase duration of theincident blast wave, the net horizontal loading impulse is greater for largestructures than for small ones.

In summary, an explosion causes overpressure and drag pressures onbuildings and other structures. The overpressure produces the largest loadson the side of buildings facing the explosion because of reflection and lesserloads on the roof and other sides. Drag pressures produce loads on slenderstructures such as stacks and towers. These loads cause buildings and otherstructures to deform, and if deformations are sufficiently large, damage andfailure can result.