Introduction to Protective Structures: What Does a Wall See from an Explosion?

1. The blast wave

An explosion releases a large amount of energy in a very short time, compressing the surrounding air into a shock wave that travels outward. When the wave reaches a point, the pressure jumps almost instantly to a peak, falls rapidly, and for a while drops below atmospheric (the positive and negative phases). The aim of protective design is to build structures that can carry, or limit the effect of, this brief but very intense load: shelters, critical facilities, buildings with industrial explosion risks.

2. Scaled distance: a single number

The Hopkinson–Cranz scaling law makes it possible to compare explosions of different sizes with one parameter:

where R is the distance (m) and W the TNT-equivalent charge mass (kg). At the same Z the peak pressure is the same, whatever the charge. An 800 kg charge at 20 m, for example, produces the same effect as a 100 kg charge at 10 m: the cube root of 800 is exactly twice that of 100. The site's engine gives Z = 2.154 and the same peak pressure (174.9 kPa) for both.

3. The power of distance

For a 100 kg TNT-equivalent charge, computed with the site's engine:

When the distance grows from 5 m to 40 m — eight times — the peak incident pressure falls by a factor of about 70. Pressure drops not linearly but much faster. That is why the first and cheapest measure in protective design is to increase the standoff between a possible explosion point and the structure: perimeter walls, barriers and vehicle-approach control. Where distance cannot be gained the structure must be hardened, which is far more expensive.

4. Reflection: why a wall sees more

When the wave strikes a wall head-on it reflects, and the reflected wave superimposes on the incident one. The reflected pressure P_r on the wall is much larger than the incident pressure P_so. Their ratio is the reflection coefficient, C_r = P_r/P_so. For an ideal gas the Rankine–Hugoniot relations give C_r ≈ 2 for weak shocks and C_r → 8 for very strong ones. In the 5 m row of the table, C_r = 5.28: the wall sees more than five times the incident pressure.

Protective design is therefore based on reflected, not incident, pressure. Reflection behaves differently when the wave arrives obliquely; that case is covered by the site's oblique reflection tool.

5. Limits of the calculation

The numbers here are a starting point; the site's engine states its own limits explicitly:

• Peak-pressure relation: the engine uses the closed-form relation of Kinney and Graham (1985). It is not the Kingery–Bulmash curves of UFC 3-340-02, but a published relation that represents free-air burst data well within its documented range.
• Reflection coefficient: computed under the ideal-gas assumption. In the engine's own audit it was compared with the real-gas data of UFC 3-340-02 Figure 2-193: up to about 1400 kPa (200 psi) the difference is below 1%; at higher pressures the ideal-gas value falls below the real value, on the unconservative side.
• TNT equivalence is not a single constant. There are different factors for pressure and impulse, and they vary with scaled distance. A calculation should always state which basis it uses.
• Ground reflection: for bursts near the ground the wave also reflects from the ground and spreads hemispherically, which increases the effect of the same charge.

6. Protective-structures articles on this site

1. PRT-01 — How deep does a projectile go into concrete? (Young's relations)
2. PRT-02 — Why are thin layers permeable?
3. PRT-03 — From projectile to equipment: the ground-shock chain