Shape optimized inclined single and double wall wave barriers for ground vibration mitigation

Stiff wave barriers are capable of reducing the transmission of ground vibrations. Most designs consist of a single vertical wall, although double walls are also being considered. This paper investigates the shape optimization (position, inclination, length and thickness) of these topologies in a two-dimensional setting, for a point source and a point receiver placed symmetrically with respect to the design domain. Three types of sources are studied: a single-frequency source, a broadband source and a harmonic source within a given frequency range. An economical constraint on the maximum material use is considered. A multi-region BEM methodology is used for evaluating the objective function and its gradient. Analytical expressions are presented for the sensitivities, providing a very effective simulation tool for this type of problem. It is found that significant improvement can be achieved by repositioning and inclining the walls when compared to the reference cases. It is also found that optimized double wall barriers outperform single wall barriers. The improvement is insignificant for sources which generate Rayleigh wavelengths similar to the design domain depth, but it greatly increases as frequency increases and the penetration depth decreases.