## Abstract

This study develops a new numerical simulation model for rubble mound failure prediction caused by piping destruction under seepage flows. The piping has been pointed out as a significant cause of breakwater failure during tsunamis. Once boiling and heaving occur on the mound surface, the piping suddenly propagates in the opposite direction of seepage flow. For the seepage failure prediction, a coupled fluid-soil-structure simulator is developed by combining the ISPH for fluid and the DEM for rubble mounds and caisson blocks. The ISPH, a Lagrangian particle method for incompressible fluids, can simulate seepage and violent flows such as tsunamis. The DEM has been applied for discrete particle and rigid body simulations that include discontinuous deformation, as in the rubble mounds failure and large displacement of the caisson block. ISPH-DEM coupling simulations have already been proposed as a technique for multi-phase flows. Still, the technique cannot reproduce the sudden onset of piping from a stable mound. Two simple assumptions are applied to reduce the numerical cost for the fluid-soil-structure simulators of a breakwater structure composed of a rubble mound and the caisson block. Firstly, each rubble is modeled as an idealized spherical DEM particle with the mean diameter of the rubble. The ISPH particle size is assumed to be the same size as the DEM particle. Under these assumptions, the unresolved coupling model between rubble mound particles and fluid, which obtains the interaction through empirical drag force, should be applied. At the same time, the interaction between the fluid and the caisson block is fully resolved with the spatial resolution with the ISPH and DEM particle size. Our new contribution in this paper is how to model the interaction as an unresolved coupling between seepage flow simulated by ISPH and rubble mound particle modeled with DEM. Our original seepage failure experiment is simulated using the proposed ISPH-DEM coupling simulator. We identified the conventional drag force models as the unresolved coupling model are insufficient to initiate the boiling and piping observed in the experiment. It may be due in one part to excessive averaging of flow velocities caused by unresolved coupling. Therefore, Terzaghi’s critical hydraulic gradient is introduced to initiate the boiling and heaving. Unstable DEM particles, judged by Terzaghi’s critical hydraulic gradient, gradually lose their mass to represent unresolved suspended fine rubble mound particles. Our models qualitatively reproduce the sand boiling and backward erosion in the opposite direction of the seepage flow, as shown in the experiment.