PREDICTION OF BLAST LOADINGS ON BUILDINGS

Transcription

1 PREDICTION OF BLAST LOADINGS ON BUILDINGS Assoc. Prof. PhD, Marin LUPOAE Miliary Technical Academy, George Cosbuc 9-49, Buchares, Romania Absrac: To deermine he effecs of a vehicle bomb explosion on a building involves he compuing of blas loadings. In engineering calculaions his blas loading has he form of pressure-ime variaion and in order o deermine his funcion i have o compue he parameers of he shock wave. Then he pressure-ime variaion should be simplified o have a simple shape as o be easily inegraed ino various schemes for calculaion. This paper presens a comprehensive overview of differen equaions o esimae blas parameers and o model he blas wave as a riangular pulse. Empirical relaions and numerical simulaions are presened and he resuls obained are discussed and compared. 1. Inroducion In recen years occurred more prominen idea of proecing buildings (especially public ones) agains vehicle bomb aacks. The main poin of such proecion is o increase he sandoff disance. Even in hese circumsances appears he necessiy of deermining he blas loadings and effecs on buildings [1], [], [] in order o esimae he damage or o design he srucure o wihsand he deonaion of a cerain explosive charge. In deermining he loads and he effecs of an explosion on a building should be considered explosive charge-building configuraion. Thus, i is possible o have he following cases: i) conac deonaion; ii) near deonaion and iii) burs away from he srucure, Fig. 1. Fig. 1 Explosion ypes The conac deonaion appears when he explosive charge is in conac wih he elemen or a a disance less han he disance of deonaion producs acion (approximaely en radius of explosive charge). The main effec produced on a building by his ype of explosion is a local effec agains consrucion elemens. A global effec in his case can be obained if he explosive charge is large enough o iniiae he collapse of he srucure. Near deonaion case is righ near he conac deonaion, beyond he limi of he deonaion producs limis of

2 acion, bu he main effec produced on srucure is sill a local one. This laer case can in urn be divided in hree cases depending on he configuraion of he explosive charge- srucure-ground surface: free-air burs, air burs and surface burs [4]. A. Free Air Burs Explosion An explosion, which occurs in free air, produces an iniial oupu whose shock wave propagaes away from he cener of he deonaion, sriking he srucure wihou inermediae amplificaion of is wave. Fig. Free air burs explosion [4] As he inciden wave moves radially away from he cener of he explosion, i will impac wih he srucure, and, upon impac, he iniial wave (pressure and impulse) is reinforced and refleced. The refleced pressure pulse of figure is ypical for infinie plane reflecors. When he shock wave impinges on a surface oriened so ha line which describes he pah of ravel of he wave is normal o he surface, hen he poin of iniial conac is said o susain he maximum (normal refleced) pressure and impulse. B. Air Burs Explosion The air burs environmen is produced by deonaions which occur above he ground surface and a a disance away from he proecive srucure so ha he iniial shock wave, propagaing away from he explosion, impinges on he ground surface prior o arrival a he srucure. An air burs is limied o an explosion which occurs a wo o hree imes he heigh of a one or wo-sory building. Fig. Air burs [4]

3 As he shock wave coninues o propagae ouward along he ground surface, a fron known as he Mach fron is formed by he ineracion of he iniial wave (inciden wave) and he refleced wave. This refleced wave is he resul of he reinforcemen of he inciden wave by he ground surface, fig.. The pressure-ime variaion of he Mach fron is similar o ha of he inciden wave excep ha he magniude of he blas parameers are somewha larger. The heigh of he Mach fron increases as he wave propagaes away from he cener of he deonaion. This increase in heigh is referred o as he pah of he riple poin and is formed by he inersecion of he iniial, refleced, and Mach waves. A proeced srucure is considered o be subjeced o a plane wave (uniform pressure) when he heigh of he riple poin exceeds he heigh of he srucure. If he heigh of he riple poin does no exend above he heigh of he srucure, hen he magniude of he applied loads will vary wih he heigh of he poin being considered. Above he riple poin, he pressure-ime variaion consiss of an ineracion of he inciden and refleced inciden wave pressures resuling in a pressure-ime variaion differen from ha of he Mach inciden wave pressures. The magniude of pressures above he riple poin is smaller han ha of he Mach fron. In mos pracical design siuaions, he locaion of he deonaion will be far enough away from he srucure so as no o produce his pressure variaion. An excepion may exis for mulisory buildings even hough hese buildings are usually locaed a very low-pressure ranges where he riple poin is high. C. Surface Burs Explosion A surface burs explosion will occur when he deonaion is locaed close o or on he ground so ha he iniial shock is amplified a he poin of deonaion due o he ground reflecions. Fig. 4 Surface burs (Hemispherical blas) A charge locaed on or very near he ground surface is considered o be a surface burs. The iniial wave of he explosion is refleced and reinforced by he ground surface o produce a refleced wave. Unlike he air burs, he refleced wave merges wih he inciden wave a he poin of deonaion o form a single wave, similar in naure o he mach wave of he air burs bu essenially hemispherical in shape (Fig. 4). A comparison of he parameers of surface burs wih hose of free-air indicae ha, a a given disance from a deonaion of he same weigh of explosive, all of he parameers of he surface burs environmen are larger han hose for he free-air environmen. As for he case of air burss, proeced srucures subjeced o he explosive oupu of a surface burs will usually be locaed in he pressure range where he plane wave (Fig. 4) concep can be applied.

4 This paper discusses how o deermine he loads produced on a building by a vehicle bomb explosion (he hird siuaion of he hird case: explosion near he ground). Afer compleing he empirical equaions which can be used o deermine he variaion in ime of he inciden and refleced overpressure, a case sudy was used o exemplify he deermining of he equivalen load produced in a specific siuaion (deonaion of 450 kg TNT a 10 m sand-off disance o building).. Relaions o deermine pressure ime hisory and impulse In engineering calculaions, he blas loadings on a building are simulaed using pressureime variaion. This pressure ime hisory, figure 5 is furher simplified by modeling his funcion as a riangular pulse characerized by peak refleced overpressure and he refleced impulse. To define peak refleced overpressure and impulse i has o deermine firs he parameers of inciden shock wave. Pressure Posiive phase Negaive phase Posiive impulse Ambien pressure Negaive impulse Fig. 5 Pressure-ime hisory Parameers needed o fully define he shock wave are: peak posiive overpressure, p f ; impulse for posiive phase I p and posiive phase duraion, p ; arrival ime, s ms and wave form parameer, b. In his paper he effec of negaive pressure phase of he blas wave was negligible. The mos commonly used relaion o describe pressure ime variaion is modified Friedlander equaion: P ( ) P p 0 f 1 p e b where: Po is he amospheric pressure..1 Peak overpressure p Time Henrych [5] deermined he following equaions for peak overpressure compuing: p f, [bar] for 0.05 Z Z Z Z Z () p f Z Z Z [bar] for 0. Z 1. () p f Z Z Z [bar] for 0.1 Z 10. (4) Kinney and Grahm [6], based on he analysis of large experimenal daa, presened he following equaion o deermine he peak posiive overpressure: (1)

5 Z bar. (5) p f P0, Z Z Z Sadovskiy [7] used he following equaion: p f [MPa]. (6) Z Z Z Kingery and Bulmash [8] proposed for compuing he peak overpressure he following polynomial equaion: p Exp( A B ln Z C ln Z D ln Z E ln Z 4 f [kpa], (7) where consans A, B, C, D and E are presened in Table 1. In all he above equaions, Z is he scaled disance: R Z, [m/kg 1/ ], [8] 1/ W where R is he sand-off disance in m and W is he charge weigh in kg. Table 1 Consans for polynomial equaions of Kingery and Bulmash o deermine peak overpressure [8] Range, Z (m/kg 1/ ) A B C D E , A comparison of he all above menioned equaions is presened in Fig. 6. I can be seen ha he curves obained using equaions proposed by Kinney and Kingery are almos idenical for small scaled disances, bu he differences beween he peak overpressures are increased as he scaled disance is increased (almos 50% for Z =10). Fig. 6 Variaion of peak overpressure wih scaled disance Fig. 7 Variaion of posiive phase duraion wih scaled disance. Posiive phase duraion The posiive phase duraion is he ime beween he ime of he passing shock fron and he end of he posiive pressure phase.

6 According Henrych [5] posiive phase duraion can be compued using his equaion: 1/ 4 p W ( Z 0.64 Z 0.19 Z 0.05 Z ),[ms] for 0.05 Z 9) Also, Sadovskiy [7] proposed he following relaion: 6 p B W R, [ms] (10) where B is beween 1.0 and 1.5. Kinney and Grahm [6] presened he following equaion o compue posiive phase duraion: 10 Z ,54 1 / [ms] (11) p W, 6 Z Z Z ,0 0,74 6,9 Kingery and Bulmash [8] polynomial equaion can also be used o compue he posiive phase duraion funcion of scaled disance. Graphical represenaion of relaions describing he posiive phase duraion is shown in Fig. 7. Noe ha he graphical represenaion of equaions (9), (10) and (11), shown in Fig. 7, was made wihou aking ino accoun he amoun of explosives.. Impulse For a blas wave he posiive impulse represen he area under he posiive phase of pressureime curve. An empirical equaion is presened by Kinney and Grahm [6]: I A 0,067 Z Z 1 0, Z 1 1,55 4, (bar*ms) (1) To compue posiive impulse Sadovkiy [7] proposed he following relaion: 1/ W I 00,(Pa*s) (1) R Equaion proposed by Held [9] is similar o he Sadovskiy relaion and has he form: 1/ W I 00,(Pa*s) R (14) Anoher possibiliy for deermining he impulse is o use he polynomial equaion of Kingery and Bulmash [8]..4 Wave form parameer Table Parameers for inciden and normal refleced waves (W = 450 kg TNT, R = 10m) Mehod Z, (m/kg 1/ ) s, (ms) p, (ms) Δp f, (kpa) *Δp r, (kpa) I i, (kpa*ms ) **I r, (kpa*ms ) Kinney 6, Kingery 5, b

7 This parameer describes he way of how decay pressure-ime funcion and also is an adjusable facor so overpressure-ime relaion provide suiable values of blas impulse. The relaion beween blas impulse and he wave form parameer can be obained by inegraion of he following equaion [6]: I A p s pd p (15) where s and p f p e b b are above defined. b.4 Refleced overpressure In order o deermine he refleced overpressure i can be used he following equaions: for normal reflecion: Py k 1 k 1 P P r x (16) Py Py k 1 k 1 Px for oblique reflecion: k M r ( k 1) Pr Py (17) k 1 where, Py is he pressure in disurbed medium afer passage of he inciden shock, P x is he amospheric pressure, M r is Mach number for refleced shock and k is he raio beween hea capaciies. Parameers for disurbed medium afer passage of inciden and refleced shock waves can be compued using seady flow counerpar of normal or oblique reflecion [6].. Case sudy To compare he parameers of shock wave compued using all above empirical equaion an explosive charge of 450 kg TNT a a sand-off disance of 10 m was considered. The amoun of explosive charge corresponds o a vehicle bomb aack (sedan vehicle) and he sand-off disance of 10 m was chosen in accordance wih minimum defended sand-off disances in order o respec he medium ISC level of proecion for reinforced concree consrucion [6]. Because only Kinney and Kinegery mehods include equaions necessary o deermine all parameers for inciden and refleced shock wave, i was compared pressure-ime variaions obained by hese wo mehods. Parameers for inciden and normal refleced waves are presened in Table and pressureime variaions are shown in Fig. 8. Noe ha he zero pressure, in Fig. 8 and 9, corresponds o he amospheric pressure. I can be seen ha boh he peak overpressure and impulse calculaed wih he Kingery s mehod are higher han hose calculaed wih he Kinney s mehod for he surface burs. The difference is abou 5% for pressure and 40% for impulse.

8 Fig. 8 Pressure ime variaion for 450 kg TNT and disance of 10 m Fig. 9 Pressure and impulse for inciden and normal refleced wave In hese condiions i will be used he Kingery s equaions o deermine pressure-ime variaion. A comparison beween inciden and refleced overpressures and impulses, for surface burs, is presened in Fig. 9. To esablish equivalen riangular pulse i can be used he following relaion: b p p p p _ echiv p f d p f 1 e d (18) s p _ echiv s s p where lef erm represens area under equivalen riangular line passing hrough poins (, s ) and (0, p _ echiv ), and righ erm represens area under pressure-ime curve, which is acually he blas impulse. The parameer _ is he riangular phase duraion for equivalen load and i can be ieraive compued. The iniial value of p echiv p _ echiv p f is equal wih p and hen i will be decreased unil he value of lef erm of equaion (18) will be equal wih he value of blas impulse (he righ erm of he same equaion). The equivalen riangular pulse can be seen in Fig. 10. This equivalen load was deermined by using he peak overpressure and he value of impulse, bu modifying he posiive phase duraion. Fig. 10 Triangular blas wave profile for inciden and normal refleced wave

9 4. Numerical simulaions The goal of he simulaions is o analyze he blas effecs on a building associaed wih he deonaion of a bare 450 kg, spherical charge of TNT, 1.5 m above a rigid surface (he same condiions like in case sudy). For his i was used he Auodyn sofware. The Auodyn is a compuer code used o simulae he response of solids, fluids and gases o high speed and exreme loadings. The dimensions of he building (m x 6m x 10 m) were chosen arbirarily only o see he effecs of he blas and o compare he analyical and numerical resuls. The comparison beween Kingery and Auodyn values for normal refleced pressure when he explosive charge is deonaed a 1.5m from rigid surface (hemispherical surface burs) is presened in Fig 11. The same comparison is done for he case when explosive charge is deonaed a.0 m from he ground (air burs), Fig. 1. As i can be seen in Fig. 11, he peak pressures from Kingery and Auodyn are approximaely he same (.5% difference), bu he impulse is differen. To avoid he Mach sem and obain he normal refleced pressure a he direc disance, he explosive charge was deonaion a a m o ground surface, Fig. 14. In his case he inciden shock wave impinges on he surface of he building before he wave refleced by he ground his he building. The pressure-ime curve raced based on Kinney parameers for inciden and normal refleced wave was added in Fig. 11 and 1 o compare wih Kingery and Auodyn resuls. Fig. 11 Normal refleced pressure for hemispherical surface burs Fig. 1 Normal refleced pressure for air burs 5. Conclusions To calculae blas loads on a building i has o deermine he refleced pressure-ime variaion and he value of refleced blas impulse. In his respec he inciden shock wave parameers need o be compued firs. Thus, empirical equaions by various auhors have been examined o calculae he parameers of he shock wave. The resuls showed ha only Kinney and Grahm mehod and respecively Kingery și Bulmash mehod provide equaions o compue all blas wave parameers. There are differences beween peak values of inciden overpressure compued wih Kinney and Kingery equaions: 0% for scaled disances less han 1. m/kg 1/ and up o 50% for scaled disances of 10 m/kg 1/. Noe ha Kinney mehod uses only an equaion o compue peak overpressure no maer of heigh of burs. According wih case sudy, i was showed ha for Z greaer han 1 m/kg 1/ he peak and decay of refleced overpressure in ime compued wih Kinney mehod are much closer o Kingery resuls for air burs (4% difference) han Kingery resuls for surface burs (49%). Based on he pressure-ime variaion (inciden or refleced) i was compued and drawn he equivalen riangular pulse, keeping he maximum overpressure and impulse value, bu

10 modifying he posiive phase duraion. This equivalen blas load can be furher used o compue he srucural response under blas loadings. Explosive charge Explosive charge Fig. 1 Hemispherical surface burs (heigh of burs 1.5m) Fig. 14 Air burs (heigh of burs.0m) References [1] Goel M. D., Masagar V.A., Gupa A., Marburg S., An Abridged Review of Blas Wave Parameers, Defence Science Journal, Vol. 6, No. 5, pp , 007. [] Larcher M., Simulaion of he Effecs of an Air Blas Wave, Technical Repor JRC417, European Commission- IPSC,007 [] Remennikov A.M., A Review of Mehods for Predicing Bomb Blas Effecs on Buildings, Journal of Balefield Technology, Vol. 6, No., pp. 5-10, 00 [4] U.S. Deparmen of he Army, Srucures o Resis he Effecs of Accidenal Explosions, Technical Manual 5-100, Nov [5] Henrych J., The dynamics of explosion and is use, Elsevier, Amserdam, [6] Kinney G.F., Grahm, K.J., Explosive shocks in air. Springer, Berlin, [7] Sadovskiy, M.A. Mechanical effecs of air shockwaves from explosions according o experimens, In Sadovskiy M.A. Seleced works: Geophysics and physics of explosion. Nauka Press, Moscow, 004. [8] Kingery, C.N. Bulmash G., Airblas parameers from TNT spherical air burs and hemispherical surface burs. US Army ARDC, Ballisics Research Laboraory, Aberdeen Proving Ground, Maryland, USA, Technical Repor ARBRLTR- 0555, April [9] Held M., Blas waves in free air, Prop. Exp. Pyro., Vol. 8, No. 1, pp. 1-8, 198. [10] *** Ineragency Securiy Commiee (ISC), ISC Securiy Design Crieria for New Federal Office Buildings and Major Modernizaion Projecs, Washingon, DC., 004