No abstract

We numerically model two-dimensional systems of granular aggregates confined between two rough walls and demonstrate that at a critical grain volume fraction nu(c) an abrupt rigidity transition occurs. The transition has first-order characteristics, although the elastic constants undergo a second-order transition. Densely packed grains, with a volume fraction nu>nu(c), display an elastic-plastic rheology. Loose packings, with nu

We present results from two-dimensional computer simulations of shearing granular layers, using a discrete element code, and applying a wide range of boundary conditions. We specifically investigate the distribution of shear within the granular layer and find two different modes of localization depending on the applied shear velocity, pressure, and layer thickness: (1) granular layers that develop a persistent shearing boundary region ("fluidlike" behavior) and (2) layers that switch between diffuse deformation and randomly positioned internal shear bands ("solidlike" behavior). The two end-member deformation modes can be found in laboratory experiments performed under low and high confining pressure, respectively. Micromechanical investigation reveals two different statistical distributions of the grain contacts correlating with the two different shearing modes. These results imply that rehological transitions in granular flow modes are linked to quantifiable microtstructural organization.

Abstract. In contrast to the along-axis uniformity observed at the East Pacific Rise (EPR), crustal accretion at the Mid-Atlantic Ridge (MAR) appears to be a highly complex and heterogeneous process. Besides spreading rate, one of the first-order differences between the EPR and the MAR is the much higher degree of ridge segmentation observed in the Atlantic. Circular lows in the mantle Bouguer anomaly (MBA bull' s-eyes) are common at centers of spreading segments of the MAR, suggesting crustal thickness variations of up to 4 km along individual segments. We use a three-dimensional numerical model of mantle flow to examine the effect of ridge segmentation on mantle upwelling and the resulting overall crustal production and along-axis variations in crustal thickness. Mantle flow in our model is driven by both buoyant forces and segmented plate spreading. Various asthenospheric viscosity structures, plate spreading geometries, and mantle potential temperatures are explored. We find that a combination of buoyant mantle flow and three-dimensional melt migration can reproduce crustal thickness variations similar to those inferred from gravity. Buoyant flow gives rise to variations in upwelling velocity at along-axis wavelengths greater than 150 km but does not contribute to short-wavelength variations. However, three-dimensional melt migration may greatly enhance crustal thickness variations along all segments, independent of the wavelength of buoyant upwelling. We present an idealized model, in which melt first rises vertically and then flows along the base of the lithosphere toward the ridge axis, that easily produces crustal thickness variations greater than 4 km. The models also predict that the average crustal thickness should decrease with increasing amount of segmentation and decreasing spreading rate. Therefore the thinner, more heterogeneous crust observed at the MAR may result from the combined effects of slower spreading rate and more pervasive ridge segmentation.

[1] Two-dimensional numerical simulations of shear in a gravity-free layer of circular grains were conducted to illuminate the basic mechanics of shear of granular layers (such as layers of fault gouge). Our simulated granular layers exhibit either stable (steady state) or unstable (stick slip) motion. The transition from steady to stick-slip sliding depends on loading velocity and applied confining stress in a way similar to a simple model of a block on a frictional surface. We investigate the conditions which lead to naturally occurring stick-slip behavior and study in detail the systems behavior prior to and during slip events. Matching our numerical results to a spring block model, the system of grains was found to have bulk static and dynamic coefficients of friction that differ by about 0.1. This differing static and dynamic friction emerged spontaneously, from the collective behavior of grains, and was not prescribed a priori via a frictional rule between grain contacts. Results show that the micromechanics of contact forces is responsible for stick-slip behavior: During the ''stuck'' phase, and in preparation for slip, more and more grain contacts which carry low forces slide, resulting in accelerating internal stress release. When enough of the low-force contacts frictionally slide, the granular layer weakens and losses rigidity, leading to motion of contacts that carry larger forces and large-scale slip. Our results may have implications to the understanding of the stability of gouge layers and are thus related to the underlying physics of earthquakes.

Abstract. 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. Despite the great importance of the coupled mechanics of grains-fluid systems, the basic physics that controls this coupling is far from understood. Fundamental questions that need to be addressed are what are the processes that control pore fluid pressurization and depressurization in response to deformation of the granular skeleton? and how do variations of pore pressure affect the mechanical strength of the grains skeleton? To answer these questions, a formulation for the pore fluid pressure and flow is developed from mass and momentum conservation, and is coupled with a granular dynamics algorithm that solves the grain dynamics, to form a fully coupled model. The pore fluid formulation reveals that the evolution of pore pressure obeys a viscoelastic rheology in response to pore space variations. Elastic-like behavior dominates with undrained conditions and leads to a linear relation between pore pressure and overall volumetric strain. Viscous-like behavior dominates under well drained conditions and leads to a linear relation between pore pressure and volumetric strain rate. Numerical simulations reveal the possibility of liquefaction under drained and initially over-compacted conditions, which were often believed to be resistant to liquefaction. Under such conditions liquefaction occurs during short compactive 1 phases that punctuate the overall dilative trend. In addition, the more established generation of elevated pore pressure under undrained compactive conditions is observed. Simulations also show that during liquefaction events stress chains are detached, the external load becomes completely supported by the pressurized pore fluid, and shear resistance vanishes.

[1] The physics of deformation of fluid-filled granular media controls many geophysical systems, ranging from shear on geological faults to landslides and soil liquefaction. Its great complexity is rooted in the mechanical coupling between two deforming phases: the solid granular network and the fluid-filled pore network. Often deformation of the granular network leads to pore fluid pressure (PP) changes. If the PP rises enough, the fluid-filled granular media may transition from a stress-supporting grain network to a flowing grain-fluid slurry, with an accompanying catastrophic loss of shear strength. Despite its great importance, the mechanisms and parameters controlling PP evolution by granular shear are not well understood. A formulation describing the general physics of pore fluid response to granular media deformation is developed and used to study simple scenarios that lead to PP changes. We focus on the infinitely stiff end-member scenario, where granular deformation is prescribed, and the PP responds to this deformation. This end-member scenario illustrates the two possible modes of pore fluid pressurization: (1) via rapid fluid flow when fluid drainage is good and (2) via pore volume compaction when drainage is poor. In the former case the rate of deformation controls PP evolution, while in the latter case, fluid compressibility is found to be an important parameter and the amount of pressurization is controlled by the overall compaction. The newly suggested fluid-induced mechanism (mechanism 1) may help explain observations of liquefaction of initially compact soils and shear zones.Citation: 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,

No abstract