Applicability of 3D Spectral Element Method for Computing Close-Range Underwater Piling Noises

Pile driving is used for constructing foundation supports for offshore structures. Underwater noise, induced by in-water pile driving, could adversely impact marine life near the piling location. Many studies have computed this noise in close ranges by using semi-analytical models and Finite Element Method (FEM) models. This work presents a Spectral Element Method (SEM) wave simulator as an alternative simulation tool to obtain close-range underwater piling noise in complex, fully three-dimensional, axially-asymmetric settings in the time domain for impacting force signals with high-frequency contents (e.g., frequencies greater than 1000Hz). The presented numerical results show that the flexibility of SEM can accommodate the axially-asymmetric geometry of a model, its heterogeneity, and fluid-solid coupling. We showed that there are multiple Mach Cones of different angles in fluid and sediment caused by the difference in wave speeds in fluid, a pile, and sediment. The angles of Mach Cones in our numerical results match those that are theoretically evaluated. A previous work¹⁸ had shown that Mach Cone waves lead to intense amplitudes of underwater piling noise via a FEM simulation in an axis-symmetric setting. Since it modeled sediment as fluid with a larger wave speed than that of water, we examined if our SEM simulation, using solid sediment-fluid coupling, leads to additional Mach Cones. Because this work computes the shear wave in sediment and the downward-propagating shear wave in a pile, we present six Mach Cones in fluid and sediment induced by downward-propagating P- and S-waves in a pile in lieu of two previously-reported Mach Cones in fluid and sediment (modeled as fluid) induced by a downward-propagating P-wave in a pile. We also showed that the amplitudes of the close-range underwater noise are dependent on the cross-sectional geometry of a pile. In addition, when a pile is surrounded by a solid of an axially-asymmetric geometry, waves are reflected from the surface of the surrounding solid back to the fluid so that constructive and destructive interferences of waves take place in the fluid and affect the amplitude of the underwater piling noise.