Numerical Modelling of Runout and Velocity for Slide-Induced Submarine Density Flows: A Building Block of an Integrated Geohazards Assessment for Deepwater Developments
Authors: Spinewine Benoit , Rensonnet Delphine , Clare Michael , Capart Herve , De Thier Thibaud , Dan-unterseh Gabriela 
Published: May 2013

Abstract
We present a numerical model developed to rationally predict the trajectory, the run-out distance and frontal velocity of pulsed submarine mass gravity flows, and illustrate how it forms an essential building block of an integrated geohazards assessment for deep offshore pipeline and cable developments. The model is inspired from Center-of-Mass approaches initially proposed for pulsed snow avalanches, but specifically adapted to the treatment of submarine sediment density flows. We outline how the modeling approach fits into the broader classes of possible modeling strategies and discuss the implications in terms of CPU requirements for field applications. The model relies on simple mass and momentum balance relations for the frontal part of the sediment density flow, with additional terms accounting e.g. for ambient mixing, sediment detrainment or added mass. Depending on the sediment type various rheologies and friction relations can be adopted. Herein we consider a shear resistance derived from a Herschel-Bulkley rheology and a Chezy-type entraining shear relation.
The model may be used to predict the spatial and temporal development of a sediment density flow from inception to runout on a full 3D bathymetry. Because it writes as a system of ordinary (rather than partial) differential equations, it is solved efficiently and is more amenable to repeated simulations than depth-integrated Finite Element models which may rapidly become CPU-prohibitive for field applications. The approach is therefore advantageously used at the stage of a geohazards risk assessment, during which many distinct scenarios may need to be evaluated. The sensitivity of model outputs to differing trigger locations, failed volumes corresponding to e.g. a design seismic scenario, and soil parameters, can be readily investigated, and model outputs possibly combined into an integrated map of maximum velocities and runout distances. These parameters allow estimating the magnitude and duration of forces impacting on submarine pipelines and cables, which can then be used as inputs for a verification of structural integrity based on a pipe/soil interaction model.
The adequacy of the approach is first tested on small-scale laboratory experiments of pulsed debris flows down a slope, including documented experiments from the literature previously used for validation purposes. Then, its application at field scale is illustrated for a hypothetical case of a localized slope failure on the steep flank of a sloping submarine canyon.
We illustrate the typical force signal imposed on a pipeline from recent laboratory experiments on debris flows impacting an instrumented pipe section. We then outline how the outputs of the flow modeling exercise may provide input for a quantitative assessment of potential damage and displacement endured by a submarine pipeline laid along a prescribed route. Impact forces estimated from the simulated conditions of the density flow upon impact are fed into a 3D finite element software modeling the structural response of the pipeline, using adequate pipe-soil interaction parameters and lay conditions.