Compaction front and pore fluid pressurization in horizontally shaken drained granular layers

Abstract

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.

A thermodynamical model for paleomagnetism in Earth’s crust

“…• m) from equation (8f) for any w ∈ W 1,∞ (I×Ω) with w(T) = 0, and eventually also (8) with the boundary and initial conditions (17) and (33) has a weak solution (v, E, R, m, u, θ) according Definition 1 and every such solution also satisfies the mechanical-energy balance (26) and conserves the total energy in the sense (27).…”

“…This means here the test of equation (40a) by v k ετ while using also equation (40b) tested by S k ετ = ϕ E (E k ετ , m k ετ ), then the test (40c) by R k ετ , the inclusion (40d) by µ 0 r k ετ , (40e) by (u k ετ −u k−1 ετ )/τ , and (40f) by 1. We thus obtain an energy-like inequality for the time-discrete approximation corresponding to equation (27), but in contrast to equation (27), we treat the non-convex terms ω ε and ϕ ε "on the right-hand side".…”

“…ετ and an "ε-cancelation" of the dissipative terms. We thus obtain an analogue of the total energy balance (27) except that an ε-part of the dissipation still remains:…”

“…The non-convexity of the stored energy for θ < θ c now makes no problem and testing by ∂ ∂t m ε can be performed as in the time-continuous variant in equation (22). Due to the factor 1−ε in equation (44e), we obtain the total energy balance (27) for ε-solution with "ε-part" of the dissipative heat source "on the left-hand side" like in equation (54) which is now to be neglected for obtaining uniform estimates with respect to ε > 0. Thus, we obtain the inequality: Using the Young and the Gronwall inequalities, we obtain the a-priori estimates uniform with respect to ε > 0:…”

Sink versus tilt penetration into shaken dry granular matter: The role of the foundation

“…Liquefaction in the ground may be triggered dynamically by waves emitted during earthquakes, generating cyclic shear stresses that lead to the gradual build-up of pore water pressure [5,6]. The shaking produced by seismic events is a trigger for extensive liquefaction, as was observed recently in Belgium [7].…”