Fundamental and Applied Problems in Granular Flow Michael Shearer/David Schaeffer This project focuses on three aspects of the flow of granular materials: an investigation of fluctuations, flows and stresses in industrial silos, and liquefaction of soils. The various issues will be addressed using an interdisciplinary approach involving analysis, computation and experiment. The latter two parts will also involve input from industrial and geotechnical experts. Details of each subproject follow. Subproject 1, fluctuations in sheared granular materials: Recent work has shown that fluctuations of forces and to some extent velocities can be very large for moderate scale systems. The experimental part of this project will provide additional quantitative characterizations of these fluctuations for modest scale slowly sheared systems. In addition, new experiments will be constructed of a Couette type that will probe force fluctuations on larger length and time scales. These experiments will be integrated into ongoing work to model force fluctuations by lattice type models, and computations using novel hybrid molecular dynamics and finite element codes. Subproject 2, flow in industrial silos: In collaboration with engineers at the firm Jenike and Johanson, Inc. the co-PI's of this project will analyze flows in a spatial region that corresponds to the shape of a typical hopper. This analysis will be based both on Coulomb materials and on critical state soil mechanics (CSSM). Some of the aspects under study will include an investigation of the relationship between CSSM and Coulomb models, shock and rarefaction wave solutions, boundary value problems for hopper flow, and stability of such solutions. An important application is the design of flow corrective devices. Subproject 3, liquefaction of soils: This phenomenon corresponds to the abrupt loss of load-bearing capacity of a loose, water-saturated soil, possibly leading to a massive landslide. Real world s oil failure/liquefaction will be investigated in collaboration with G. Gudehus and his associates. This project will combine experiments, mathematical analysis, computer simulation and industrial/geotechnical expertise to better understand the flow of granular materials. The area of study is of considerable importance to technical processes involving all types of granular materials, including but by no means limited to chemical process industries, and to the handling of coal, ores, food grains, and pharmaceuticals. Many aspects of the above processes are not fully understood, leading in some cases to enormous financial losses. Also under consideration are geotechnical issues such as the stability of embankments, as well as the stability of soils under earthquake conditions. The project will involve the application of existing theories for granular materials to such fundamental problems as flows in hoppers and stability of soils in landfills. New models will be developed in order to take into account some important aspects of granular flows such as fluctuations of forces. Recent experiments in this lab have shown that fluctuations, which are not accounted for in existing models, can be very strong and may well be necessary to provide safe and reliable design criteria for industrial devices involving granular flows. The models will be tightly linked to the experimental data, on the one hand, and, on the other hand, will be the basis of computer solutions for relevant technical problems.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Deborah Lockhart
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North Carolina State University Raleigh
United States
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