Can fractals mitigate blast loading?

Fractals are self-similar objects; a shape or pattern made up of an infinitely repeating series of smaller copies of the original. Self-similarity is common in nature – trees, coastlines, shells – and infinitely-repeating fractals possess the interesting characteristic of having finite volume but infinite surface area (hence the 'Coastline Paradox'). Whilst it is not possible to achieve infinite fractal iterations in real-life, pre-fractals (a self-similar structure with a finite number of iterations) have a sufficiently large area:volume ratio to be useful in a number of engineering applications, such as antennae and heat exchangers. The properties of a blast wave are substantially altered after it comes into contact with an obstacle: reflection of the wavefront diverts the blast away from its primary path, and diffraction around the obstacle edge induces vortices and further diverts momentum. This raises an interesting question: can fractals mitigate blast loading? Specifically, does the large area:volume property of pre-fractal obstacles increase the propensity for a blast wave to divert energy away from its original path, thereby mitigating the blast load downstream of the obstacle? This paper details a rigorous experimental study on the blast mitigation of the first three iterations of a Sierpinski carpet subjected to the blast load from PE4 explosives, with downstream, upstream, and on-obstacle pressures directly measured by flush-mounted pressure gauges. The results show that mitigation is enhanced with increasing iteration number, and that the mitigation behaviour of a pre-fractal obstacle is fundamentally different to that of a simple, singular obstacle. This proof-of-concept study opens up the possibility of using natural self-similar structures, such as trees and hedges, for sustainable and less intrusive blast protection in urban environments.