Emergence of seismic metamaterials: Current state and future perspectives

International audienceFollowing the advent of electromagnetic metamaterials, researchers working in wave physics have translated concepts of engineered media to acoustics, elastodynamics and diffusion processes. In elastodynamics, seismic metamaterials have emerged in the last decade for soft soils structured at the meter scale, and have been tested with full-scale experiments on holey soils. Born in the soil, seismic metamaterials have emerged from the field of tuned-resonators buried in the soil, around building's foundations or near the soil-structure interface as local seismic isolators. Forests of trees have been interpreted as above-surface resonators, and coined natural seismic metamaterials. We first review some advances made in seismic metamaterials and dress an inventory of which material parameters can be achieved and which cannot, from the effective medium theory perspective. We envision future developments of large scale auxetic metamaterials for building's foundations, above surface resonators for seismic protection and metamaterial-like transformed urbanism at the city scale

Role of nanophotonics in the birth of seismic megastructures

International audienceThe discovery of photonic crystals 30 years ago in conjunction with research advances in plasmonics and metamaterials, has inspired the concept of decameter scale metasurfaces, coined seismic metamaterials for an enhanced control of surface (Love and Rayleigh) and bulk (shear and pressure) elastodynamic waves. These powerful mathematical tools of coordinate transforms, effective medium and Floquet-Bloch theories which have revolutionized nanophotonics, can be translated in the language of civil engineering and geophysics. Experiments on seismic metamaterials made of buried elements in the soil demonstrate that the fore mentioned tools make a possible novel description of complex phenomena of soil-structure interaction during a seismic disturbance. But the concepts are already moving to more futuristic concepts and the same notions developed for structured soils are now used to examine the effects of buildings viewed as above surface resonators in megastructures such as metacities. But this perspective of future should not make us forget the heritage of the ancient peoples. Indeed, we finally point out the striking similarity between an invisible cloak design and the architecture of some ancient megastructures as the antique Gallo-Roman theaters and amphitheatres

Experimental evidence of auxetic features in seismic metamaterials: Ellipticity of seismic Rayleigh waves for subsurface architectured ground with holes

This paper describes auxetic features of an array of boreholes in a sedimentary soil when a seismic wave passes through. This is a collaboration between Stephane Brule at the Menard company and Stefan Enoch and Sebastien Guenneau at Institut Fresnel.Structured soils with regular meshes of metric size holes implemented in first ten meters of the ground have been theoretically and experimentally tested under seismic disturbance this last decade. Structured soils with rigid inclusions embedded in a substratum have been also recently developed. The influence of these inclusions in the ground can be characterized in different ways: redistribution of energy within the network with focusing effects for seismic metamaterials, wave reflection, frequency filtering, reduction of the amplitude of seismic signal energy, etc. Here we first provide some time-domain analysis of the flat lens effect in conjunction with some form of external cloaking of Rayleigh waves and then we experimentally show the effect of a finite mesh of cylindrical holes on the ellipticity of the surface Rayleigh waves at the level of the Earth's surface. Orbital diagrams in time domain are drawn for the surface particle's velocity in vertical (x, z) and horizontal (x, y) planes. These results enable us to observe that the mesh of holes locally creates a tilt of the axes of the ellipse and changes the direction of particle movement. Interestingly, changes of Rayleigh waves ellipticity can be interpreted as changes of an effective Poisson ratio. However, the proximity of the source is also important to explain the shape of the ellipses. We analyze these observations in terms of wave mode conversions inside the mesh and we propose to broaden the discussion on the complexity of seismic wave phenomena in structured soils such as soils foundations and on the coupling effects specific to the soil-structure interaction

Controlling seismic elastic surface waves via interacting structures

International audienceWe present some recent research advances on controlling elastic surface waves in thin and thick plates, this is aimed at understanding the seismic wave trajectories in soils structured with buildings. We show the influence of building interactions on surface and body waves when a significant proportion of soil is replaced by inclusions with different densities and Lamécoefficients acting as building foundation, raising the question of the effective dynamic properties of these smart soils. One of our objectives is to improve the control of seismic waves by taking into consideration the in-plane twisting motion of local helical resonators

Control of Rayleigh-like waves in thick plate Willis metamaterials

International audienceRecent advances in control of anthropic seismic sources in structured soil led us to explore interactions of elastic waves propagating in plates (with soil parameters) structured with concrete pillars buried in the soil. Pillars are 2 m in diameter, 30 m in depth and the plate is 50 m in thickness. We study the frequency range 5 to 10 Hz, for which Rayleigh wave wavelengths are smaller than the plate thickness. This frequency range is compatible with frequency ranges of particular interest in earthquake engineering. It is demonstrated in this paper that two seismic cloaks’ configurations allow for an unprecedented flow of elastodynamic energy associated with Rayleigh surface waves. The first cloak design is inspired by some approximation of ideal cloaks’ parameters within the framework of thin plate theory. The second, more accomplished but more involved, cloak design is deduced from a geometric transform in the full Navier equations that preserves the symmetry of the elasticity tensor but leads to Willis’ equations, well approximated by a homogenization procedure, as corroborated by numerical simulations. The two cloaks’s designs are strickingly different, and the superior efficiency of the second type of cloak emphasizes the necessity for rigour in transposition of existing cloaks’s designs in thin plates to the geophysics setting. Importantly, we focus our attention on geometric transforms applied to thick plates, which is an intermediate case between thin plates and semi-infinite media, not studied previously. Cloaking efficiency (reduction of the disturbance of the wave wavefront and its amplitude behind an obstacle) and protection (reduction of the wave amplitude within the center of the cloak) are studied for ideal and approximated cloaks’ parameters. These results represent a preliminary step towards designs of seismic cloaks for surface Rayleigh waves propagating in sedimentary soils structured with concrete pillars

Métamatériaux pour la protection sismique

National audienceLes physiciens des ondes élaborent des modèles théoriques et numériques pour un contrôle accru de la lumière dans des matériaux structurés à l’échelle nanométrique et s’en inspirent pour contrôler les ondes mécaniques de Rayleigh dans des sols structurés à l’échelle métrique, avec des trous dans un sol ou des arbres en surface savamment agencés. Un transfert de paradigme s’opère entre les métamatériaux électromagnétiques pour la photonique et les métamatériaux sismiques pour le génie civil

Seismic Defence Structures

A seismic wave shield for protecting an area from seismic vibrations and a method of shielding an area from seismic waves by installing a seismic wave shield. The seismic wave shield comprises a set of columns embedded in regolith and in contact with bedrock. There is a material contrast between a material forming the columns and the regolith