Blast Load Response Analysis
Blast Load Response Analysis: Theoretical Foundations
What is Blast Load?
Professor, what is blast load?
It is the pressure load acting on a structure caused by the shock wave (blast wave) generated by an explosion (chemical explosive, gas explosion, etc.). It has a characteristic time waveform: peak pressure → exponential decay → negative pressure.
Friedlander Waveform
Standard approximation formula for blast pressure (modified Friedlander equation):
- $P_s$ — Peak overpressure
- $t_d$ — Positive phase duration
- $b$ — Decay parameter
- $p_0$ — Atmospheric pressure
So it decays exponentially and even becomes negative pressure, right?
There is a positive pressure phase (pushing force) followed by a negative pressure phase (pulling force). For a building wall, it's a repetition of positive pressure (outward) → negative pressure (inward).
Estimating Blast Parameters
Estimate blast parameters using the Kingery-Bulmash equations from ConWep (Conventional Weapons Effects Program):
$Z$ is the scaled distance (m/kg^{1/3}), $R$ is the distance from the source, $W$ is the TNT equivalent mass. Estimate $P_s, t_d, I$ from $Z$.
So the parameters are determined just by the explosive mass and distance?
It's the "Scaling Law" (Hopkinson-Cranz law). The same $Z$ yields the same pressure waveform. TNT 1 kg at 10 m and TNT 1000 kg at 100 m have the same $Z$ and thus the same overpressure.
FEM Setup
Two approaches:
1. Direct input of pressure time history — Apply the pressure from the Friedlander equation as a time function onto structural surfaces. The simplest method.
2. ALE method (Arbitrary Lagrangian-Eulerian) — Solve blast wave propagation using Eulerian mesh and structural deformation using Lagrangian mesh simultaneously. Includes reflection and diffraction.
Is the ALE method more accurate?
The ALE method automatically calculates blast reflection, diffraction, and superposition, so it's more accurate. However, it requires a 3D air mesh and has a high computational cost. For simple shapes, direct pressure input is sufficient.
Summary
Key points:
- Friedlander waveform — Peak overpressure → exponential decay → negative pressure
- Parameter estimation with ConWep (Kingery-Bulmash equations) — $Z = R/W^{1/3}$
- Direct pressure input or ALE method — Choose based on complexity
- LS-DYNA's *LOAD_BLAST_ENHANCED — Automatically calculates ConWep
Explosion Pressure Decays with the Cube of Distance
According to the TNT equivalent scaling law (Hopkinson-Cranz law), the maximum overpressure from an explosion is organized by the ratio Z = R/W^(1/3) of distance R and charge mass W to the 1/3 power. At Z = 1, the maximum overpressure reaches about 0.3 MPa. Brode's equation from 1944 was later refined into the Kingery-Bulmash database (US Army TM5-855-1), which is still adopted in ANSYS Autodyn's ATBLAST function.
Computational Methods for Blast Load Response Analysis
Blast Analysis in LS-DYNA
LS-DYNA has dedicated functions for blast:
```
*LOAD_BLAST_ENHANCED
1, 100., 10., 0., 0., 0., 1, 1.0 $ W=100kg TNT, R=10m
```
Automatically calculates and applies ConWep blast pressure to each surface of the structure. Also automatically considers reflection angles.
It's convenient that ConWep is built-in.
*LOAD_BLAST_ENHANCED automatically calculates reflected pressure from explosive mass, source location, and structural surface orientation. Much lighter than ALE method and sufficiently accurate for many problems.
ALE Method Setup
1. Place Eulerian mesh for air around the structure
2. Define the explosion source with *INITIAL_DETONATION etc.
3. Define the structure with Lagrangian mesh
4. Connect fluid and structure with ALE coupling (*CONSTRAINED_LAGRANGE_IN_SOLID)
Summary
ALE Method Solves Blast-Structure Coupling
In explosion analysis, the ALE (Arbitrary Lagrangian-Eulerian) method is mainstream, treating air/explosives with Eulerian grids and structures with Lagrangian elements. LS-DYNA's ALE multi-material code was developed at LLNL (Lawrence Livermore) in the 1990s; simulating a 1 kg TNT free-field explosion for 5 ms with 1 million nodes takes about 30 minutes on current HPC.
Blast Load Response Analysis in Practice
Blast Analysis in Practice
Used in structural design for defense, petrochemical plants, and counter-terrorism measures.
Application Examples
| Application | Purpose |
|---|---|
| Blast wall design | Shielding from blast. Keep deformation within allowable limits. |
| Building blast-resistant design | Glass breakage, structural response. |
| Vehicle blast resistance | Resistance to IEDs (Improvised Explosive Devices). |
| Plant safety distance | Impact on structures during explosion accidents. |
Practical Checklist
What is UFC 3-340-02?
The US Department of Defense's Structural Design Manual for Blast Loads. Specifies peak pressure, duration, and allowable structural deformation. The world standard for blast-resistant design.
Protection Design Standard is UFC 4-010-01
The US Department of Defense UFC (Unified Facilities Criteria) 4-010-01 is the blast protection design standard for government facilities, specifying standoff distances and structural response limits. The 2012 edition revised after 9/11/2001 requires the Ductility Ratio (μ) of RC slabs to be kept below 10 and explicitly mentions the use of dynamic analysis (SDOF or FEM) for verification.