Abstract

Empirical predictions of discharge rates for dry non-cohesive grains are commonly based on the Beverloo law (Chem Eng Sci 15:260–269, 1961). The present work extends this practical configuration to submerged and cohesive cases to investigate the flow behavior of granular media with applications in the geophysical process of sinkhole formation. The analysis of the hydrostatic collapse of soil in the presence of underground conduits is performed with a 2D GPU-parallelized simulation coupling the lattice Boltzmann method and the discrete element method to describe the fluid and the solid phases, respectively. The discharge rate of a large submerged granular sample is analyzed by varying orifice sizes and inter-particle cohesion strengths. For the submerged cohesionless case, we first study the revisited Beverloo relationship that includes the terminal velocity of a single falling particle in the fluid, proposed in the experimental work of Wilson et al. (Pap Phys 1307: 2812, 2014). We consistently take into account the interstitial fluid with an effective orifice size smaller than in the dry case. Then, the additional contribution of grain cohesion is examined. Our main finding is that the empirical prediction remains valid provided that the orifice cutoff increases with cohesion. Finally, the evolution of fluid pressure during the discharge, at the vicinity of the orifice, is studied and favorably compared with the recent experimental study of Guo et al. (Granul Matter 19(3): 1–8, 2017). By considering the pressure drop around the orifice as a driven-term, we succeed in predicting the solid flow rate with a similar Beverloo approach.

Graphic abstract

中文翻译：

---

浸没粘性颗粒物排放的DEM–LBM数值模拟

摘要

干燥的非粘性谷物的排放速率的经验预测通常基于贝弗鲁定律（Chem Eng Sci 15：260–269，1961）。本工作将这种实际构型扩展到淹没和粘性的情况下，以研究粒状介质的流动行为及其在下陷形成的地球物理过程中的应用。在地下管道存在的情况下，对土壤的静水坍塌进行了分析，方法是使用二维GPU并行模拟，分别结合格子Boltzmann方法和离散元素方法来描述流体相和固相。通过改变孔口尺寸和颗粒间的内聚强度来分析大型浸没颗粒样品的排放速率。对于水下无内聚的情况，我们首先研究了威尔逊等人的实验工作中提出的重新探讨的贝弗鲁关系，该关系包括流体中单个下落颗粒的终速度。（Pap Phys 1307：2812，2014）。我们始终考虑有效孔口尺寸小于干燥情况下的组织液。然后，检查了晶粒内聚力的其他贡献。我们的主要发现是，只要孔口截断随着内聚力的增加而增加，经验预测仍然有效。最后，对孔附近的排放过程中流体压力的变化进行了研究，并与最近的Guo等人的实验研究进行了比较。（Granul Matter 19（3）：2017年1月8日）。通过将孔口周围的压降视为驱动项，

图形摘要