In many natural granular systems, the interstitial pores are filled with a fluid. Deformation of this two-phase system is complex, highly coupled, and depends on the initial and boundary conditions. Here we study granular compaction and fluid flow in a saturated, horizontally shaken, unconfined granular layer, where the fluid is free to flow in and out of the layer through the free upper surface during shaking (i.e., drained boundary condition). The geometry, boundary conditions and parameters are chosen to resemble a shallow soil layer, subjected to horizontal cyclic acceleration simulating that of an earthquake. We develop a theory and conduct coupled discrete element and fluid numerical simulations. Theoretical and simulation results show that under drained conditions and above a critical acceleration, the grain layer compacts at a rate governed by the fluid flow parameters of permeability and viscosity, and is independent of the shaking parameters of frequency and acceleration. A compaction front develops, swiping upward through the system. Above the front, compaction occurs and the fluid becomes pressurized. Pressure gradients drive fluid seepage upward and out of the compacting layer while supporting the granular skeleton. The rate of compaction and the interstitial fluid pressure gradient coevolve until fluid seepage forces balance solid contact forces and grain contacts disappear. As an outcome, the imposed shear waves are not transmitted and the region is liquefied. Below the compaction front (i.e., after its passage), the grains are well compacted, and shaking is transmitted upward. We conclude that the drained condition for the interstitial pore fluid is a critical ingredient for the formation of an upward moving compaction front, which separates a granular region that exhibits a liquid-like rheology from a solid-like region.

中文翻译：

---

水平振动排干的颗粒层中的压实前沿和孔隙流体增压

在许多天然颗粒系统中，间隙孔充满了流体。该两相系统的变形是复杂的，高度耦合的，并且取决于初始条件和边界条件。在这里，我们研究了在水平振动的无限制饱和饱和颗粒层中的颗粒压实和流体流动，其中在振动过程中（即排水边界条件），流体通过自由上表面自由流入和流出层。选择几何形状，边界条件和参数，使其类似于浅土层，并经受模拟地震加速度的水平循环加速度。我们开发了一种理论，并进行了离散元和流体耦合数值模拟。理论和仿真结果表明，在排水条件下以及高于临界加速度的情况下，颗粒层的压实速率受渗透率和粘度的流体参数控制，并且与频率和加速度的振动参数无关。产生压实前缘，向上滑动整个系统。在前部上方，发生压实，并且流体受压。压力梯度在支撑颗粒骨架的同时，驱使流体向上渗出并从压实层中流出。压实速率和间隙流体压力梯度共同发展，直到流体渗流力平衡固体接触力并且颗粒接触消失为止。结果，所施加的剪切波不被传输并且该区域被液化。在压实前沿下方（即，在其通过之后），晶粒被很好地压实，并且振动向上传递。