Analytical modelling of the steady flow of a submarine slide and consequent loading on a pipeline

Abstract

This paper considers a simple one-dimensional model of a submarine slide at a steady state. From equilibrium relations, the distributions of shear stress, velocity and strain rate across the slide thickness are determined analytically for two rate-dependent soil strength models. Previous work has demonstrated that the increase in shear strength with strain rate can be adequately described using a power law or a logarithmic law model. The analytical solutions obtained with these models are compared with the ones available for a viscoplastic fluid of the Bingham or Herschel–Bulkley types. The influence of the rheological parameters, the slope angle and the slide thickness on the flow and deformation characteristics is analysed for each model. The derived analytical solutions can be viewed as representing a particular position within a slide at a given instant in time. They can be used in conjunction with numerical modelling of the entire slide to provide some insights into the flow pattern, and into the parameter sensitivity. These solutions are also applicable to determination of the loading on a pipeline that is oriented across the path of the slide. They are used to illustrate the relative contributions of the soil strength and the inertial drag, as well as the influence of the vertical position of the pipeline within the slide.