A quasi-analytic model of the underwater sound signal from impact driving of an offshore semi-infinite pile

A quasi-analytic model is derived for the underwater sound signal radiated when an offshore pile is struck on its face by a hammer. The pile is modelled as a semi-infinite cylindrical shell of an elastic solid. The impact generates a pulse of vibration that travels down the pile at the longitudinal sound-speed. At a given distance below the pile face, the radial displacement after the peak has arrived decreases exponentially with time. There are two coupled equations of motion for the axial and radial displacements. A closed form expression is derived for the radiated sound pressure (which is proportional to the radial acceleration) in terms of the Poisson ratio and Young Modulus of the pile material, the hammer velocity, contact area between hammer and pile, pile radius, hammer mass, the pile longitudinal sound-speed, and the sound-speed and density of the external medium. This model is applied to a published scenario for which the radiated sound pressure had been computed using a Finite Element Model, but is found to produce a different result. Some assumptions used in the model are identified that may explain the difference.