In many natural granular systems, the interstitial pores are filled with a fluid. Deformation of this two-phase system is complex, is 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 liquidlike rheology from a solidlike region.
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We thank K. J. Måløy, Y. H. Hatzor, V. Vidal, J. C. Géminard, E. G. Flekkøy, E. Altshuler, A. Batista-Leyra, and G. Sanchez-Colina for interesting discussions. S.B.-Z. acknowledges the support of Institut Français d'Israël and Campus France for the Chateaubriand Fellowship, as well as the University of Strasbourg. S.B.-Z. and E.A. are grateful for the support of ISF Grant No. 197/17. S.P. acknowledges Grant No. 19-21114Y from the Czech Science Foundation (GA CR). R.T. acknowledges the support of the INSU ALEAS program, of the LIA France-Norway D-FFRACT, IPGS, and of the ITN FlowTrans, funding from the European Union's Seventh Framework Programme for research under Grant Agreement No. 316889.
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