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pressure-sensitive material Rice (1975) has shown that homogeneous undrained deformation is
unstable in the sense that small spatial nonuniformities grow exponentially in time when the
localization condition is met in terms of drained response. Hence, if the localization condition is
met in terms of the drained response before being met in terms of the undrained response, the
latter is irrelevant. However, the condition for localization during undrained response may be
met before or after the condition is met for drained response depending on the nature of the
pressure sensitivity of yield and inelastic volume change.
For a wide class of rate-independent elastic - plastic material models with inelastic volume
change and pressure-sensitivity, the form of the constitutive relation for undrained response is
identical to that for drained response (Rudnicki, 2000). For the special case of elastically
incompressible solid and fluid constituents, a good approximation for soils, the undrained
response is pressure insensitive and inelastically incompressible even if the drained response is
not. As a consequence of this form invariance, the localization condition for undrained
deformation can be determined directly from the result for drained deformation by making
appropriate substitutions. We have compared the localization conditions for drained and
undrained conditions for a range of parameters describing the elastic compressibility of solid and
fluid constituents, inelastic volume change, and dependence of the yield stress on mean normal
stress. For undrained conditions, both the value of the critical hardening modulus for localization
and the band angle depend on the parameters describing the poroelastic response. A particularly
interesting case occurs when the inelastic volume deformation is compactive and the pressure
sensitivity is positive. Such conditions may occur near the transition of a cap-like yield surface to
a frictional yield surface and, thus, are relevant to compaction band (or compactive shear band)
formation. For such cases, the localization condition for undrained response is met before that for
drained response.
References
Besuelle, P. and J. W. Rudnicki, Localization: Shear Bands and Compaction Bands, Chapter V in
Mechanics of Fluid Saturated Rocks, eds. Y. Gueguen and M. Bouteca, pp. 219-321, Vol. 89,
International Geophysics Series, Academic Press, London, 2004.
Rice, J. R., On the stability of dilatant hardening for saturated rock masses, J. Geophys. Res.,
Vol. 80 (11) 1531-1536, 1975.
Rudnicki, J. W., Diffusive Instabilities in Dilating and Compacting Geomaterials, in Multiscale
Fracture and Deformation in Materials and Structures- The James R. Rice 60th Anniversary
Volume, eds, T.-J. Chuang and J. W. Rudnicki, pp. 159-182, Kluwer Academic, Dordrecht, 2000.
Rudnicki, J. W., S. Tembe and T.-F Wong (2006), EOS, Transactions of the American
Geophysical Union, Fall Meeting Supplement (Abstract T43A-1633).
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Rudnicki, J. W. Final Report: Approaches to Some of the Outstanding Problems of Heterogeneous Compactive Deformation of Geomaterials, report, January 2, 2013; Evanston, Illinois. (https://digital.library.unt.edu/ark:/67531/metadc844819/m1/4/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.