M. Zaiser1 and E.C. Aifantis2
1Laboratory of Mechanics and Materials, Aristotle University of Thessaloniki, GR 54124, Thessaloniki, Greece
2permanent address: Center for Materials Science and Engineering and School of Engineering and Electronics, Institute for Materials and Processes, The University of Edinburgh, Edinburgh, EH93JL, UK
2also: Center for the Mechanics of Material Instabilities and Manufacturing Processes, Michigan Tech. Houghton, MI 49931, USA
Preliminary Considerations on Slab Avalanche Release by Using a Gradient Model for a Random Medium

The problem of slab avalanche release is investigated by employing a gradient model for shear band formation and slip avalanches earlier advanced by Aifantis and co-workers [1-4]. The model is based on the hypothesis of a non-monotonous variation of the local shear strength with the slip displacement and a gradient approximation of the internal slab stress represented by screw dislocations and their image fields. A shear band propagation criterion or a slope failure condition is derived which resembles those earlier obtained by Palmer and Rice [5] and McClung [6] by using J-integral and energy considerations. Then disorder is introduced by allowing for random spatial variations in the peak strength which is assumed to obey a Weibull distribution. A cellular automaton simulation is used. It turns out that the probabilistic distribution of critical stresses for slope failure can be approximated by a Gaussian. The local strength fluctuations may have a dramatic knock-down effect on the failure strength of a slope. The nature of the critical flaw is studied to conclude that the damage distribution can be described as a random fractal set with a characteristic fractal dimension. Precursors to failure in the form of bursts are considered and the implications for slope stability predictions are discussed.

References
  1. E.C. Aifantis, On the microstructural origin of certain inelastic models, Transactions of ASME, J. Engng. Mat. Tech. 106, 326-330 (1984).
  2. E.C. Aifantis, The Physics of plastic deformation, Int. J. Plasticity 3, 211-247 (1987).
  3. H.M. Zbib and E.C. Aifantis, On the structure and width of shear bands, Scripta Met. 22, 703-708 (1988).
  4. M. Zaiser and E. C. Aifantis, Avalanches and Slip Patterning in Plastic Deformation, J. Mech. Beh. Mat. (in press).
  5. A.C. Palmer J.R. and Rice, The growth of slip surfaces in the progressive failure of over-consolidated clay, Proc. Roy. Soc. Lond. A 332, 527-548 (1973).
  6. D.M. McClung, Shear fracture precipitated by strain softening as a mechanism of dry slab avalanche release, J. Geophys. Res. 84, 3519-3526 (1979). [see also: D.M. McClung, Fracture mechanical models of dry slab avalanche release, J. Geophys. Res. 86, 10783-10790 (1981).]
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