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A. Introduction 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: 1.What are the processes that control pore fluid pressurization and depressurization in response to deformation of the granular skeleton? a.What is the role of fluid compressibility? b.Can liquefaction occur also when drainage is good? c.Can liquefaction occur also when the packing is initially dense? 2.How do variations of pore pressure affect the mechanical strength of the grains skeleton? B. The physics of pore fluid pressure Mass and momentum conservation Lead to a simple equation for the evolution of pore pressure: Diffusion Forcing by granular skeleton deformation Time evolution of pore pressure fluid compressibility porosity permeability fluid viscosity time evolution of porosity pore pressure gradients C. Fully-Coupled grains and fluid model: two phases in two scales The grains dynamics is solved with discrete element Granular Dynamics Algorithm with Hertz-Mindlin contact model The fluid is solved on an Eulerian grid that is superimposed over the grains Model scheme 1.Solve granular dynamics to find position and velocity of grains. 2.Interpolate to the fluid grid 3.Solve the fluid equation (*) to find the pore fluid pressure on the grid. 4.Interpolate P back to the granular level. D. Validation: the law of effective stress P = const Applied Δσ n Boundary free to move Measured Δε Poor correlation between strain and applied stress Good correlation between strain and effective stress 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. Setup of validation simulations E. Simulations setup - constant shear velocity and stress Applied σ n Applied Vsh – constant shear velocity Measure map of pore fluid pressure, P Applied drainage conditions: 1.Undrained, no fluid flux 2.Drained, P=0 Measure dilation and compaction Measure apparent friction F. Viscoelastic behavior of pore pressure The response of pore fluid pressure to grains deformation depends on the Deborah number De>>1 effectively undrained conditions Elastic-like behavior 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-like behavior 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. De<<1 effectively drained conditions Viscous-like behavior Note that β<<1 intense pore pressure response. Fully-coupled undrained simulations show Good correlation between pore pressure and porosity strain Fully-coupled well-drained simulations show Good correlation between pore pressure and porosity strain rate G. Simulation results - Liquefaction with drained conditions Note reduction in the apparent friction below zero. At the same time average P ≈ σ n, leading to the observed loss of shear resistance. Framed letters mark the time when the snapshots in the figure below are taken. 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 σ n. After liquefaction: Percolating stress chains reappear and pore pressure drops. H. Liquefaction potential - LP Based on the analysis of the pore pressure evolution and simulation results, we propose to evaluate the liquefaction potential as I. Conclusions 1.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. 2.When drainage is good (De<<1), the magnitude of pore pressure change depends on the instantaneous strain rate of porosity (viscous-like behavior). 3.When drainage is poor (De >>1), pore pressure response to the overall strain of porosity with respect to the initial configuration (elastic-like behavior). 4.When De≈1 both porosity strain and porosity strain rate are important. 5.Fluid compressibility is important when drainage is poor. Fluid may be considered incompressible when drainage is good. 6.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. 7.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. 8.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: /2009JB Goren, L., E. Aharonov, D. Sparks, and R. Toussaint (2011), The Mechanical Coupling of Fluid-Filled Granular Material Under Shear, Pure Appl. Geophys. Accepted. Liran Goren The Department of Earth Sciences, ETH, Zurich, Switzerland. Einat Aharonov 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. σ n = 2.4 MPa The high pore pressure replaces the stress chains in supporting the external load and causes a complete loss of shear resistance. Based on simulations it is proposed that λ≈0.01 Note that the evolution of P is independent of β De>>1 De<<1 P is the estimated pore pressure that depends on the drainage conditions as expressed by De. σ n is 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.

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