A History of Research and a Review of Recent Developments

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Blast loads in tunnels and shafts 109 For end on bursts (i.e. in line with the entrance to the tunnel), Ē was given by Ē=K e (W 2/3 /A)(p 0 /p i ) 0.4 , (5.24) where W=charge weight, p0=atmospheric pressure Ke=0.586 if W is in kilograms and A in square metres, or Ke=3.72 if W is in pounds and A in square feet. For side-on bursts, in which the charge explodes at a lateral distance from the entrance to the tunnel, E¯ was given tentatively as Ē=K s (W 2/3 /A)(p 0 /p i ) 0.8 , (5.25) where Ks=2.26 for W in kilograms and A in square metres, or 14.4 for W in pounds and A in square feet, but further experimental work was said to be needed to confirm this. These equations were stated by the author to be valid within the following ranges: 1
110 Structural loading from local explosions enable extremely complex systems with up to 1000 branches to be analysed for a very wide range of inlet geometries and bomb orientations. Codes of this type can be used, for example, to model the effect of shock waves in the ducting system of aircraft or ship structures, and are valuable tools in analysing the strength of such structures under attack by terrorist explosive devices. Most of the codes are marketed by the developers, and a comparison of their capabilities is beyond the purpose of this book. However, one code which was commissioned by the US Army Corps of Engineers, Omaha District, and written at the University of Nevada, has been described in some detail by Fashbaugh [5.15]. The code, which can be used on a PC computer, enables the shock propagation in ducting systems (SPIDS) to be calculated sequentially. The shock propagation in a main duct, for example, is calculated and the time history of pressures and temperatures is stored on a computer file. This file then specifies pressures and temperatures at the inlet of a branch duct from which the shock propagation in the duct can be deduced. This procedure can be repeated for large numbers of branches—up to ten for each specific duct. There are limitations, one of which is that reflected shock waves from branch ducts into main ducts are not accounted for; neither are shock wave losses as the wave passes the entrance to a branch duct. Simulation is achieved by evaluating flow losses from a point s just outside the duct entrance to a point e inside the entrance, using the collected results of many experimental programmes. The duct entrance static pressure p e is related to the pressure outside the duct, p s, by the relationship where p te/p ts is the stagnation pressure ratio, given by (5.28) (5.29) T e and T s are static temperatures at points e and s; T te and T ts are stagnation temperatures. A(1) and A(2) are empirical coefficients that depend on the entrance geometry and position of the explosion, and M s is the flow Mach number outside the duct. The shock wave attenuation due to internal friction in the ducting is represented by a friction factor, given in terms of (h/D) 1/2 , as discussed earlier, where h is the average wall protrusion height and D is the duct diameter. Fashbaugh used the equation t=0.016+0.00491(h/D) 1/2 +0.258(h/D), (5.30) and for a side-on entrance A(1)=1.1398, A(2)=1.24. The linear relationship between p te/p ts and M s from experiments is shown in Figure 5.15. The code has been shown to give good agreement with tests for the decay of shock pressure with distance along a duct, and for the effects of a sudden increase in the cross-sectional area of a duct.
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EXPLOSIVE LOADING OF ENGINEERING ST
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Explosive Loading of Engineering St
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Contents Preface vii Acknowledgemen
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Preface A long time ago I walked ov
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Acknowledgements The reports from w
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xii Notation m mass of projectile m
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xiv Notation Q work done during exp
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Introduction Explosions can threate
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Introduction xix Bertram Hopkinson
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Introduction xxi in the seventeenth
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Introduction xxiii own versions of
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Introduction xxv indoor shelters an
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Introduction xxvii explosions/ stru
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Introduction xxix particularly dama
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Introduction xxxi but the feeling i
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2 The nature of explosions propelli
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4 The nature of explosions or rathe
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6 The nature of explosions ogive, a
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8 The nature of explosions mass, an
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10 The nature of explosions Figure
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12 4 lb cylinders, TNT, 3.75 lb sph
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14 The nature of explosions As Figu
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16 The nature of explosions of the
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18 1.4 THE DECAY OF INSTANTANEOUS O
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20 The nature of explosions Figure
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22 The nature of explosions where I
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24 sometimes written in psi as The
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26 The nature of explosions 1.20 Ki
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28 The detonation of explosive char
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50 Figure 2.18 Radius/time curve of
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54 and 50%, rather than by a factor
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Page 92 and 93: 3 Propellant, dust, gas and vapour
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Page 96 and 97: Gas explosions 63 reported by Palme
Page 98 and 99: Gas explosions 65 workings in very
Page 100 and 101: Vapour cloud explosions 67 the leak
Page 102 and 103: References 69 in Los Angeles Harbou
Page 104 and 105: 4 Structural loading from distant e
Page 106 and 107: Uniformly distributed pressures 73
Page 108 and 109: Table 4.1 Loading/time relationship
Page 110 and 111: Loading/time relationships 77 overp
Page 112 and 113: Loading/time relationships 79 side
Page 114 and 115: Loads on underground structures 81
Page 120 and 121: Loads on underwater structures 87 c
Page 122: References 89 4.12 Allgood, J. (197
Page 125 and 126: 92 Structural loading from local ex
Page 131 and 132: 98 The general empirical equation f
Page 133 and 134: 100 Structural loading from local e
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Page 145 and 146: 112 Figure 5.16 Relationship betwee
Page 153 and 154: 120 Pressure measurement and blast
Page 175 and 176: 142 Penetration and fragmentation r
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Page 181 and 182: 148 Penetration and fragmentation T
Page 183 and 184: 152 Penetration and fragmentation F
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Page 191 and 192: 158 Figure 7.16 Penetration simulat
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160 Penetration and fragmentation F
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162 Penetration and fragmentation b
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164 Table 7.1 Penetration and fragm
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166 Penetration and fragmentation w
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168 Penetration and fragmentation I
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170 Penetration and fragmentation l
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172 Penetration and fragmentation w
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174 Penetration and fragmentation p
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176 Penetration and fragmentation o
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178 Penetration and fragmentation o
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180 Penetration and fragmentation 7
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182 Penetration and fragmentation 7
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184 The effects of explosive loadin
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188 Table 8.1 It is worth noting th
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200 Table 8.5 The effects of explos
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216 Response, safety and evolution
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224 In the log-normal distribution
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230 Cole, R.H. 46, 48, 53, 55, 99 C
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232 Petry 143 Philip, E.B. 13, 14,
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Subject index Aircraft damage 207 A
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A History of Research and a Review of Recent Developments

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