Seminar in Applied Mathematics

Brian Hayes Department of Mathematical Sciences Stevens Institute of Technology Two problems in granular flow: Liquefaction of soils and transient behavior in dry granular flows Monday, November 29, 1999 3:00pm Morton 105

Abstract:   We focus on two phenomena in granular flows: liquefaction of soils and transient behavior in dry granular flows. The latter topic applies to the flow of bulk solids in silos and hoppers. Both topics concern time-dependent flows, governed by mathematical equations that are ill-posed. In each case, this ill-posedness is thought to be responsible for destructive physical effects. Numerical and analytical studies of models for both phenomena will be presented. Liquefaction describes the liquid-like behavior of a loose, saturated soil which has been subjected to a cyclic disturbance. During earthquakes, seismic waves can trigger liquefaction, leading to large-scale structural damage. In fact, extensive damage to San Francisco's Marina district in the October, 1989 earthquake is attributed to liquefaction. We discuss a hypoplastic model for propagating shear waves in a saturated soil and describe the results of two problems with periodic boundary disturbances. In the velocity-control problem, stress and velocity are found to saturate outside of a boundary layer. This asymptotic stress has a discontinuous, fractal dependence on the boundary data. The stress-control problem has a similar structure, except that the asymptotic stress now varies smoothly with the boundary data. We mention current studies aimed at resolving this discrepancy, as well as extensions of the model. The design of industrial silos and hoppers is based almost entirely on steady-state solutions of governing equations. In many cases, actual time-dependent flows do not achieve these states, resulting in financial loss from reduced or inconsistent outflow, or even in collapse of structures. In order to understand how granular flows proceed from initial conditions to steady-states (or, possibly, to periodic states or even singularities), we study an elastoplastic model which shares two key properties with the full system of granular flow. Specifically, the model is linearly ill-posed, yet has well-defined steady-state solutions. For a physically relevant boundary value problem, we construct these steady solutions, then describe numerical results for the model. In some cases, solutions pass through violent transients before converging to the steady-state. In other cases, the steady solution either does not exist or is not attained, and a growing velocity jump appears.

Refreshments immediately following the talk. For additional information contact Patrick Miller  or Yi Li.