Numerical investigation of leaky modes in helical structural waveguides embedded into a solid medium

Helical multi-wire cables are widely used in bridges (suspended or prestressed) and anchored retaining wall constructions. Such structures can be damaged or degraded due to corrosion and fatigue. Non destructive evaluation techniques are required to reveal defects inside cable structures. Among these numerous techniques, elastic guided waves are of potential interest owing to their ability to propagate over long distances. However in civil engineering, cables are often buried or grouted in large solid media that can be considered as unbounded. Waves can strongly attenuate along the guide axis due to the energy leakage into the surrounding medium, which reduces the propagating distance. This energy leakage can be enhanced in helical structures, which further complicates their inspection. Searching modes with low attenuation becomes necessary. The goal of this work is to propose a numerical approach to compute modes in embedded helical structures, combining the so-called semi analytical finite element method and a radial perfectly matched layer technique. Two types of radial perfectly matched layer, centered and off-centered, are considered. Both are implemented in a twisting coordinate system which preserves translational invariance. The centered configuration is validated thanks to the twisted cylinder test case. The effect of twist on the eigenspectrum is briefly discussed. Then, an embedded helical wire of circular cross-section is considered. The off-centered configuration is shown to give the same results as the centered one. The effect of twist on modal attenuation is investigated. Finally, computations are performed for a seven-wire strand embedded into concrete, widely used in civil engineering cables.