Experiments on Seismic Metamaterials: Molding Surface Waves

Materials engineered at the micro- and nanometer scales have had a tremendous and lasting impact in photonics and phononics. At much larger scales, natural soils civil engineered at decimeter to meter scales may interact with seismic waves when the global properties of the medium are modified, or alternatively thanks to a seismic metamaterial constituted of a mesh of vertical empty inclusions bored in the initial soil. Here, we show the experimental results of a seismic test carried out using seismic waves generated by a monochromatic vibrocompaction probe. Measurements of the particles’ velocities show a modification of the seismic energy distribution in the presence of the metamaterial in agreement with numerical simulations using an approximate plate model. For complex natural materials such as soils, this large-scale experiment was needed to show the practical feasibility of seismic metamaterials and to stress their importance for applications in civil engineering. We anticipate this experiment to be a starting point for smart devices for anthropic and natural vibrations.

Figure 1

Schematics of (a) a seismic wave in an alluvium basin and (b) the seismic testing device cross section in the $x\text{−}z$ plane (see Fig. 3 for a photograph of the experiment).

Figure 2

Simulated dispersion curves [frequency versus Bloch wave number describing the reduced Brillouin zone of vertices $\mathrm{\Gamma }=(0,0)$, $X=(\pi /d,\pi /d)$, $M=(\pi /d,0)$] for a periodic plate of pitch $d=1.73\mathrm{m}$ and thickness 5 m, with inclusions of diameter 0.32 m and density about 1/1000 that of the surrounding medium (soil). The inset shows the plot of flexural wave [i.e., displacement in the $x$-$z$ plane in Fig. 1] intensity for a forcing at 50 Hz (frequency in the second partial stop band along $XM$), which is located as in Fig. 4.

Figure 3

Photograph of the seismic metamaterial experiment from Ménard company (see the Supplemental Material [40] for more photos and a movie [41]). The three dashed perimeters account for the location of sensors [measuring the three components of wave velocity (green area on this photograph)], seismic metamaterial [5 m deep self-stable holes of diameter 0.32 m with center-to-center spacing of 1.73 m (blue area)], and rotating source (a vibrating probe set on a crane) with a horizontal displacement of 0.014 m generating an elastic wave at frequency 50 Hz.

Figure 4

Measurements for a monochromatic source. Experimental results’ map after interpolation between sensors: (a) the difference ($J_2-J_1$) and (b) ratio ($J_2/J_1$, with image magnification on the metamaterial) of the measured energy field (arbitrary units) after ($J_2$) and before ($J_1$) carrying out the boreholes. Note that the dark blue region in panel (b) has 5 times less elastic energy after we carried out the boreholes. Note also the small values of $J_1$ about 10 meters away from the source (viscoelastic soil) make $J_2/J_1$ artificially high on the upper edge of the map, and should be disregarded. Black rectangles symbolize sensors, white circles symbolize the holes, and the red cross symbolizes the source.