Importance of sign conventions on analytical solutions to the wave-induced cyclic response of a poro-elastic seabed

Abstract

This paper discusses the influence of different sign conventions for strains and stresses, i.e. the solid mechanics sign convention and the soil mechanics sign convention, on the form of governing partial differential equations (the static equilibrium equations and the continuity equation) used to describe the wave-induced cyclic response of a poro-elastic seabed due to propagation of a sinusoidal surface water-wave. Some selected analytical solutions, obtained by different authors and published in specialist literature in the form of complex functions describing the wave-induced pore-fluid pressure, effective normal stress and shear stress oscillations in the seabed, have been analysed and compared with each other mainly with respect to different sign conventions for stains and stresses and also with regard to different orientations of the positive vertical axis of the two-dimensional coordinate system and different directions of surface water-wave propagation. The performed analyses of the analytical solutions has indicated many inaccuracies, or even evident errors and exemplary mistakes of wrong-signed values of basic wave-induced response parameters (the shear stress in particular), thereby disqualifying these solutions and their final equations from practical engineering applications. Most of the mistakes found in the literature must be linked to authors’ lack of understanding and consistency in an uniform application of a certain sign convention for strains and stresses in the soil matrix at both stages of mathematical formulation of the governing problem and correct interpretation of equations of the final analytical solution. The present paper, based mostly on a thorough literature review, ought to draw attention and arouse interest among coastal scientists and engineers in proper identification and use of the existing analytical solutions to the wave-induced cyclic seabed response – solutions which differ very often in the applied sign convention for stresses in the soil matrix.