A. Introduction

1. The Mechanical Coupling of Fluid-Filled Granular Material Under Shear G. Simulation results - Liquefaction with drained conditions Applied Δσn Boundary free to move P = const Measure dilation and compaction Note reduction in the apparent friction below zero.At the same time average P ≈ σn, leading to the observed loss of shear resistance.Framed letters mark the time when the snapshots in the figure below are taken. Liran Goren The Department of Earth Sciences, ETH, Zurich, Switzerland. (liran.goren@erdw.ethz.ch) EinatAharonov Institute of Earth Sciences, Hebrew University, Givat Ram, Jerusalem, Israel. David Sparks Department of Geology and Geophysics, Texas A&M University, College Station, Texas, USA. Renaud Toussaint Institut de Physique du Globe (IPGS), CNRS and University of Strasbourg (EOST), Strasbourg, France. Measured Δε σn = 2.4 MPa A. Introduction D. Validation: the law of effective stress • Background • The coupled mechanics of fluid-filled granular media controls the physics of many Earth systems such as saturated soils, fault gouge, and landslide shear zones. It is well established that when the pore fluid pressure rises, the shear resistance of fluid-filled granular systems decreases, and as a result catastrophic events such as soil liquefaction, earthquakes, and accelerating landslides may be triggered. Alternatively, when the pore pressure drops, the shear resistance of these geosystems increases. • The questions that are addressed in this work: • What are the processes that control pore fluid pressurization and depressurization in response to deformation of the granular skeleton? • What is the role of fluid compressibility? • Can liquefaction occur also when drainage is good? • Can liquefaction occur also when the packing is initially dense? • How do variations of pore pressure affect the mechanical strength of the grains skeleton? Setup of validation simulations 1. The model reproduces correctly the law of effective stress. 2. The law of effective stress may be viewed as the macroscopic manifestation of microscopic gradients of pore pressure. Good correlation between strain and effective stress Snapshots of the grain system and the corresponding pore pressure map before, during and after the liquefaction event circled in the figure above. Before liquefaction: stress chains support the external load, and the pore pressure is lower than hydrostatic. During liquefaction: stress chains disappear and the pore pressure increases throughout the system. In most places P surpasses σn.After liquefaction: Percolating stress chains reappear and pore pressure drops. Poor correlation between strain and applied stress E. Simulations setup - constant shear velocity and stress Applied Vsh – constant shear velocity Applied σn Measure map of pore fluid pressure, P The high pore pressure replaces the stress chains in supporting the external load and causes a complete loss of shear resistance. Measure apparent friction B. The physics of pore fluid pressure Mass and momentum conservation Lead to a simple equation for the evolution of pore pressure: • Applied drainage conditions: • Undrained, no fluid flux • Drained, P=0 H. Liquefaction potential - LP Based on the analysis of the pore pressure evolution and simulation results, we propose to evaluate the liquefaction potential as Forcing by granular skeleton deformation Time evolution of pore pressure Diffusion P is the estimated pore pressure that depends on the drainage conditions as expressed by De. σnis the applied normal stress. λ is a statistical factor that expresses the chances of generating high pore pressure, P, in large enough zone to completely detach a layer of stress chains during an applied shear strain. λ may be thought of as representing empirical measures such as the number of shear cycles needed for liquefaction. time evolution of porosity F. Viscoelastic behavior of pore pressure fluid compressibility The response of pore fluid pressure to grains deformation depends on the Deborah number fluid viscosity porosity pore pressure gradients permeability De<<1  effectively drained conditions Viscous-like behavior De>>1effectively undrained conditions Elastic-like behavior Based on simulations it is proposed that λ≈0.01 C. Fully-Coupled grains and fluid model: two phases in two scales Note that β<<1 intense pore pressure response. Note that the evolution of P is independent of β I. Conclusions • The evolution of pore pressure is controlled by the ratio of pore pressure diffusion time scale to grains deformation time scale as expressed by the Deborah number, De. • When drainage is good (De<<1), the magnitude of pore pressure change depends on the instantaneous strain rate of porosity (viscous-like behavior). • When drainage is poor (De >>1), pore pressure response to the overall strain of porosity with respect to the initial configuration (elastic-like behavior). • When De≈1 both porosity strain and porosity strain rate are important. • Fluid compressibility is important when drainage is poor. Fluid may be considered incompressible when drainage is good. • Pressurization and liquefaction may also occur in initially densely-packed layers as long as drainage is good. This occurs during short and rapid compaction episodes that punctuate the dilative trend – a new mechanism for liquefaction. • Liquefaction occurs when pore pressure rises to the value of the applied normal stress in large enough zones. The force exerted by fluid pressure gradients across the grains counter-balance the solid stresses, and thus acts to detach stress chains and separate previously contacting grains. Shear is then accommodated within the pressurized fluid phase. • A scheme is proposed for the evaluation of liquefaction potential based on the system parameters and drainage conditions. • References: • Goren, L., E. Aharonov, D. Sparks, and R. Toussaint (2010), Pore pressure evolution in deforming granular material: A general formulation and the infinitely stiff approximation, J. Geophys. Res., 115, B09216, doi:10.1029/2009JB007191. • Goren, L., E. Aharonov, D. Sparks, and R. Toussaint (2011), The Mechanical Coupling of Fluid-Filled Granular Material Under Shear, Pure Appl. Geophys. Accepted. The grains dynamics is solved with discrete element Granular Dynamics Algorithm with Hertz-Mindlin contact model Pore Pressure evolution depends on the overall strain of porosity  Elastic-like behavior. The classical mechanism of liquefaction where the pore pressure rises upon compaction of loose packing when drainage is poor. Pore Pressure evolution depends on the strain-rate of porosityViscous-likebehavior New mechanism of liquefaction where the pore pressure depends on the instantaneous rate of change of porosity and it has no memory of initial pore space liquefaction may occur in an initial dense packing during short and rapid compaction events punctuating the overall dilative trend. Model scheme Solve granular dynamics to find position and velocity of grains. Interpolate to the fluid grid Solve the fluid equation (*) to find the pore fluid pressure on the grid. Interpolate P back to the granular level. The fluid is solved on an Euleriangrid that is superimposed over the grains Fully-coupled well-drained simulations show Fully-coupled undrained simulations show De<<1 De>>1 Good correlation between pore pressure and porosity strain Good correlation between pore pressure and porosity strain rate