New insights into quantifying the stable impact forces of a submarine debris flow on a pipeline

In recent years, many estimation methods have been developed to assess the stable impact forces of a submarine debris flow on a pipeline. However, existing methods cannot fully consider the physically coupled effects of plasticity, inertia, and viscosity of a debris flow within a single framework. This study aims to provide some insights into the estimations of stable impact forces based on the theory of viscoplastic fluid dynamics. Theo-retical analyses of the stable impact forces are performed based on the dimensionless governing equations. Estimation methods for assessing the stable impact forces including drag and lift forces are proposed. The drag and lift forces are expressed in terms of the drag and lift coefficients, which are demonstrated in theory to be functions of the Reynolds number, Oldroyd number, and power index (Approach I). They can be alternative functions of the plastic Reynolds number, modified Oldroyd number, and power index (Approach II). Referring to these two approaches, different sets of empirical formulae of drag and lift coefficients are fitted against the available numerical datasets. The estimation methods proposed in this study will facilitate more reliable as-sessments of the stable impact forces of a debris flow on a pipeline.