A depth-averaged method modeling three-dimensional submarine landslides caused by earthquakes

Depth-averaged method (DAM) is one of the widely used numerical methods to back analyse the post-failure deposits of submarine landslides due to its high efficiency. However, its simplifications of the velocities along the thickness of the slide cannot capture complex behaviours such as shear band propagation. A novel non-averaged method, material point method (MPM), is used to validate the DAM analysis. The runout distances and morphologies of viscous debris flows predicted by the DAM and MPM are compared with those predicted by experiments and computational fluid dynamics analyses. The ranges of the shear strength, viscosity and sensitivity parameters are investigated to determine the feasibility of the DAM. The conventional DAM algorithm specialised for no-slip bases is enhanced to reproduce the phenomenon of block sliding of slides on frictional bases by considering the stability of the front and rear faces. Then, a spreading of horsts and grabens due to shear band propagation is presented with the MPM analysis. Two real cases of submarine landslides, Southern Mediterranean slide and Finneidfjord slide, were back-analysed with the DAM and MPM.

Submarine mudflows, frequently triggered by underwater landslides, lead to substantial debris accumulation stretching over kilometers once the landslide subsides, posing significant risks to vital infrastructure and the potential for triggering tsunamis. As these events are challenging to measure directly, simulation becomes imperative. Furthermore, these simulations must accurately depict the intricate dynamics of mudflow sliding processes, often modeled as viscoplastic fluids, and effectively captured by rheological models like Herschel-Bulkley and Bingham. The potential nonlinearity inherent in the Herschel-Bulkley model adds to the complexity of predicting final runout distances. The governing equations, comprised of a set of partial differential equations, further compound this challenge, making their solution difficult. In this paper, we delve into the numerical simulation of mudflows using the Depth-Averaged Method (DAM), a technique that streamlines the governing equations by integrating the momentum and continuity equations over the depth dimension. The mud descends down a slope with a fixed angle of declination. Employing both the Herschel-Bulkley and Bingham models within the DAM framework, we analyze the final runout distance and explore how various mud parameters - such as density, initial shape, and bed slope angle - affect the resulting deposit length. Using an explicit finite difference scheme to solve the governing equations, we first conducted a validation case to ensure the accuracy of our implementation, followed by a comprehensive comparison of runout distances across simulations, varying mud parameters.