How forest can protect buildings from earthquakes

How forests can protect buildings from earthquakes

Buildings in the future could be isolated from earthquakes by being placed behind rows of trees. That’s according to physicists in France, who have shown that certain seismic waves, known as Love waves (see mathematic calculations and definition on internet), could be diverted away from the Earth’s surface as they pass through a forest containing trees of a certain height. The forest acts like a metamaterial – an artificial structure usually used to steer electromagnetic radiation around objects.

Best known for their use as invisibility cloaks, metamaterials are made from large arrays of tiny resonators that manipulate light and other electromagnetic waves in unnatural ways. In recent years, however, the mathematics underlying metamaterials have also been applied to other kinds of radiation, including seismic waves. The idea here is to use arrays of suitably-sized objects either below or above ground – holes or posts of some kind – to divert seismic waves around vulnerable buildings.

Whereas passive isolation typically targets a building’s resonant frequency, seismic cloaks could, in principle, be broadband, according to Sébastien Guenneau of the Fresnel Institute in Marseille . This, he says, would allow extensions to be added to buildings and could be used to protect historical monuments that cannot be altered. Guenneau was part of a team that demonstrated the basic principle of such “seismic cloaks” in 2012 by drilling a 2D grid of 5 m-deep boreholes into top soil and measuring the grid’s effect on acoustic waves generated close by.

The researchers found that just a couple of rows of boreholes could reflect around half of the wave energy back towards the source. A few years later, however, another group, which included Guenneau and Phillippe Roux from the University of Grenoble, showed that nature could do a similar job. They showed that a small pine forest in Grenoble could reflect most of the energy within certain frequency bands of “Rayleigh waves”, which travel just under the surface and are generated by the wind and vibrations from nearby road works.

Love the feeling

Now Guenneau – along with Agnès Maurel of the Langevin Institute in Paris and Jean-Jacques Marigo of the Ecole Polytechnique in Saclay – has shown theoretically that forests should also be able to shield against Love waves. Like Rayleigh waves, these waves travel just below ground and are generated when seismic waves travelling away from an earthquake’s epicentre reach the Earth’s surface. But, whereas Rayleigh waves have both a horizontal and vertical motion, Love waves – which can severely damage a building’s foundations – cause a side-to-side, purely horizontal shaking.

Guenneau and co-workers have found that, like Rayleigh waves, Love waves should set up vibrations in tree trunks. They have identified a new kind of wave that they dub a “spoof Love wave” generated when a seismic wave propagates along wooded ground, whose top soil yields lower shear velocities than does the bulk. This wave is mathematically analogous to an electromagnetic wave known as a “spoof plasmon”, which can propagate along a metal surface studded with metallic pillars – the ground playing the role of the air above the surface while the trees stand in for the pillars.

The researchers considered what would happen when Love waves approach a forest containing rows of progressively shorter trees. They worked out that the resulting spoof Love waves would propagate through the forest until they reach the row containing trees of just the right height. The waves would then set the trees shaking and so turn them into secondary sources that dissipate most of the vibrational energy downwards through the Earth. Conversely, they found that when Love waves approach a forest with progressively taller trees, the seismic energy should largely reflect back to where it came from.

The group also found that trees foliage should affect passing seismic waves, changing the height of a resonating tree for a given wave frequency. “The striking effect of foliage might also lead to revised models of Rayleigh waves in forests,” says Maurel.

Life-saving

As to the practical potential of “arboreal shielding”, Guenneau points out that a five to 10-storey building resonates at no more than about 10 Hz. At that frequency, he says, trees would only have to be 10–15 m tall to resonate with Love waves, while they would need to be a whopping 50–75 m to protect against Rayleigh waves. He therefore envisages trees preventing horizontal shaking, while conventional techniques continue to guard against vertical motion. “Forests could halve the work of civil engineers,” he says.

To show that their idea works in practice, Guenneau and colleagues hope to persuade Roux to investigate Love waves when he starts new experiments in Grenoble, possibly in the autumn. To support their case, the trio first plan to take part in a small lab test involving ultrasonic waves and micron-sized piezoelectric “trees”.

Ping Sheng from the Hong Kong University of Science and Technology, who studies acoustic metamaterials, warns that the proposal would need trees with specific heights usually not found in nature. As such, he argues, the idea would have greater appeal if it could be applied to a more realistic forest. “That would indeed be interesting,” he says.