Reflection, blast waves

Both scaling laws apply to reflected blast wave parameters, as well as side-on parameters. (Note that, if charge weight W is used instead of energy E, these parameters have dimensions.)... 

The Hopkinson-Cranz scaling law described earlier applies to scaling of reflected blast wave parameters just as well as it does to side-on waves. That is, all reflected blast data taken under the same atmospheric conditions for the same type of explosive source can be reduced to a common base for comparison and prediction. Sachs law for reflected waves fails close to high explosive blast sources but it does apply beyond about ten charge radii. 

On the loaded side of a slab subjected to an intense reflected blast wave, a region of the slab will fail if the intensity of the compressive wave transmitted into the slab exceeds the dynamic compressive strength of the material. For an intense wave striking a thin concrete slab, the failure region can extend through the slab, and a sizeable area turned to rubble which can fall or be ejected from the slab. For a thicker slab or localized loaded area, spherical divergence of the stress wave can cause it to decay in amplitude within the slab so that only part of the loaded face side is crushed by direct compression. 

Figures 3.5 and 3.6 are based on free air bursts—for a grotmd or near ground level explosion, the energy is multiplied by a factor of two to account for the reflected blast wave.

The forces on a structure associated with a blast wave resulting from an external detonation are dependent upon the peak values and the pressure-time variation of the incident and dynamic wind pressure action, including characteristics of the reflected blast wave caused by interaction with the structure.28... 

B.E. Gelfand, A.M. Bartenev, S.P. Medvedev, A.N. Polenov, H. Gronig, M. Lenartz, Specific features of incident and reflected blast waves. Shock Waves 4(2), 137-157 (1994)... 

Figure 10.21 illustrates the change in the Kp value with distance for a reflected blast wave (curve 1) and an incident blast wave (curve 2) for Ef = 46 MJ/kg. Figure 10.22 presents similar relations for the TNT impulse equivalent Kp Comparison between parameters of incident, reflected and rarefaction waves resulting from gas detonations and HE charge explosions shows that the similarity... 

For a damage diagram of a reflected blast wave from a gas detonation, the following empirical relation can be used ... 

In summary, an object s blast loading has two components. The first is a transient pressure distribution induced by the overpressure of the blast wave. This component of blast loading is determined primarily by reflection and lateral rarefaction of the reflected overpressure. The height and duration of reflected overpressure are determined by the peak side-on overpressure of the blast wave and the lateral dimensions of the object, respectively. The Blast loading of objects with substantial... 

The pressure vessel under consideration in this subsection is spherical and is located far from surfaces that might reflect the shock wave. Furthermore, it is assumed that the vessel will fracture into many massless fragments, that the energy required to mpture the vessel is negligible, and that the gas inside the vessel behaves as an ideal gas. The first consequence of these assumptions is that the blast wave is perfectly spherical, thus permitting the use of one-dimensional calculations. Second, all energy stored in the compressed gas is available to drive the blast wave. Certain equations can then be derived in combination with the assumption of ideal gas behavior. 

For BLEVEs or pressure vessel bursts that take place far from reflecting surfaces, the above method may be used if a few modifications are made. The blast wave does not reflect on the ground. Thus, the available energy E is spread over twice the volume of air. Therefore, instead of using Eq. (6.3.15), calculate the energy with... 

The curves in Figure B-1 represent primarily the transient nature of blast waves. They do not represent the interaction effects of blast waves and structures, such as multiple reflections and shielding due to the presence of other structures. 

If the body is near a surface against which the blast wave can reflect (Figures C-2C and C-2D), the pressure P acting on the body equals the reflected pressure... 

In general, a reflected shock wave of 55 psi on a human for 400 milliseconds would be just about the tolerance limit [41] (see Table 7-25B). For a more detailed discussion of blast scaling and overpressure, see Ref [40]. 

Figure 7-44 shows the sequence of events involved in diffraction of a blast wave about a circular cylinder (Bishop and Rowe 1967). In these figures the shock fronts are shown as thick lines and their direction of movement by arrows normal to the shock front. In Figure 1.13a, the incident shock / and reflected shock Rare joined to the cylinder surface by a Mach stem M. R is now much weaker and is omitted in succeeding figures. 

Blast wave (Overpressure and negative phase pressure relative to atmospheric condition) Diffraction loading—forces on a structure resulting from the direct and reflected overpressure... 

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

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

Barricades can reduce peak overpressures and impulses behind the barricades, but reflections on obstacles may amplify blast waves behind barricades. 

This keynote paper gives a general discussion of blast waves developed by high explosive detonations, their effects on structures and people, and risk assessment methods. The properties of free-field waves and normally and obliquely reflected waves are reviewed. Diffraction around block shapes and slender obstacles is covered next. Blast and gas pressures from explosions within vented structures are sumnarized. 

The ideal side-on parameters almost never represent the actual pressure loading applied to structures or targets following an explosion. So a number of other properties are defined to either more closely approximate real blast loads or to provide upper limits for such loads. (The processes of reflection and diffraction will be discussed later.) Properties of free-field blast waves other than side-on pressure which can be important in structural loading ares... 

Normal Reflection. An upper limit to blast loads is obtained if one interposes an infinite, rigid wall in front of the wave, and reflects the wave normally. 

Diffraction. When a blast wave encounters a finite obstacle, it is partially reflected but also diffracts around the obstacle. This process is described here. 

In preparing this figure, the authors of Ref. 28 assumed no wave attenuation through the wall thickness H, so Pr and ir are the normally reflected blast loading parameters on the loaded side of the wall or slab. 

When using Figure 26 to predict blast wave properties for conditions other than bare, spherical TNT detonated away from a reflecting surface and at sea level ambient conditions, suggested adjustments are as follows ... 

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