Formation of systems of incompact bands parallel to the compression axis in the unconsolidated sedimentary rocks: A model |
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| Authors: | Sh A Mukhamediev D A Ul’kin |
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| Institution: | (1) Sandia National Laboratories, Albuquerque, NM 87123-0751, USA;(2) Department of Civil and Env. Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL, USA;(3) Wallace H. Coulter School of Engineering, Clarkson University, 207 CAMP, Box 5725, Potsdam, NY 13699-5725, USA;(4) Harvard Design & Mapping, 125 Cambridgepark Drive, Cambridge, MA 02140, USA |
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| Abstract: | Uniaxial compression of poorly lithified rocks leads to the formation of thin incompact layers (or bands, in the two-dimensional
case) parallel to the compression axis, which are characterized by increased porosity. The standard model of the formation
of such bands, as well as deformation bands of other types, associates them with the narrow zones of localization of plastic
deformations. In the case of decompaction, it is assumed that transverse tensile deformations are localized within the band,
which cause the band to dilate. Here, the formation of a band of localized deformations is treated as a loss-of-stability
phenomenon. Based on observations, we propose a fundamentally different model of incompact bands formation, according to which
the microdefects in sediment packing (pores) rather than the deformations are localized in the narrow zones. The localization
of pores, which are initially randomly distributed in the medium, occurs as a result of their migration through the geomaterial.
The migration and subsequent localization of pores are driven by a common mechanism, namely, a trend of a system to lower
its total energy (small variations in total energy are equal to the increment of free energy minus the work of external forces).
Migration of a single pore in a granular sedimentary rock is caused by the force f driving the defect. This force was introduced by J. Eshelby (1951; 1970). An important feature of our model is that the formation
of an incompact band here does not have a sense of a loss of stability. Quite the contrary, the formation of incompact bands
is treated as a gradual process spread over time. In this context, the origination of incompact band systems directly follows
from our model itself, without any a priori assumptions postulating the existence of such systems and without any special
tuning of the model parameters. Moreover, based on the proposed model, we can predict the incompact bands to always occur
in the form of systems rather than as individual structures. A single incompact band may only be formed when the force resisting
the pore motion, f
c
, is absent. |
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