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.

中文翻译：

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使用未解决的 ISPH-DEM 耦合方法进行防波堤渗流破坏预测，该耦合方法丰富了 Terzaghi 临界水力梯度

本研究开发了一种新的数值模拟模型，用于预测渗流下管道破坏引起的碎石堆破坏。管道已被指出是海啸期间防波堤失效的重要原因。一旦土丘表面发生沸腾和隆起，管道突然向与渗流相反的方向传播。对于渗流破坏预测，通过结合流体的 ISPH 和碎石堆和沉箱块的 DEM，开发了耦合的流体-土-结构模拟器。ISPH 是一种用于不可压缩流体的拉格朗日粒子法，可以模拟渗流和海啸等剧烈流动。DEM 已应用于离散粒子和刚体模拟，包括不连续变形，如瓦砾堆破坏和沉箱块的大位移。ISPH-DEM 耦合模拟已经被提议作为多相流的一种技术。尽管如此，该技术仍无法重现从稳定的土丘突然开始的管道。应用两个简单的假设来降低由碎石堆和沉箱组成的防波堤结构的流土结构模拟器的数值成本。首先，每个碎石被建模为具有碎石平均直径的理想化球形 DEM 粒子。假定 ISPH 粒子大小与 DEM 粒子大小相同。在这些假设下，应该应用未解决的碎石堆颗粒与流体之间的耦合模型，该模型通过经验拖曳力获得相互作用。同时，流体与沉箱块之间的相互作用通过 ISPH 和 DEM 粒径的空间分辨率得到完全解决。我们在本文中的新贡献是如何将相互作用建模为 ISPH 模拟的渗流与 DEM 模拟的碎石堆粒子之间未解决的耦合。我们最初的渗流破坏实验是使用建议的 ISPH-DEM 耦合模拟器进行模拟的。我们确定了传统的阻力模型，因为未解决的耦合模型不足以引发实验中观察到的沸腾和管道。一方面可能是由于未解决的耦合导致流速过度平均。因此，Terzaghi 的临界水力梯度被引入以引发沸腾和起伏。不稳定的 DEM 粒子，由 Terzaghi 的临界水力梯度判断，逐渐失去质量以表示未解决的悬浮细碎石堆颗粒。我们的模型定性地再现了渗流相反方向的沙子沸腾和向后侵蚀，如实验所示。