Analytical model for the sound pressure waveform radiated underwater when an offshore steel pipe pile is driven with an impact hammer

An analytical model has been developed for the pressure waveform radiated underwater when an offshore steel pipe pile is struck by a hammer. The model is based on the coupled equations of motion for axial and radial vibration of a thin shell and yields frequency-dependent phase velocity and attenuation of these vibrations. A harmonic solution is obtained for the radiated sound pressure, using Junger and Feit’s “Transform formulation of the pressure field of cylindrical radiators”, which uses a Fourier Transform over vertical wavenumber. The model is applied to a comprehensively described measurement of a 6-tonne hammer driving a pile 32 m long and 76-cm in diameter. The pressure waveforms at horizontal range 12 m are examined at two mid-water hydrophone depths. The correlations between the model waveforms and the measured waveforms are high. For the main positive and negative peaks, the present model yields an average Peak-SPL of 219 dB re 1 μPa, which is 2 dB higher than the average of the corresponding measurements. Possible causes of this small difference are discussed.