Abstract
A mathematical model of elastoplastic rock deformation, under which brittle failure and shear slippages occur on the microscopic level and cataclastic flow on the macrolevel, is formulated. Since the model allows for the motion of a fluid in the pore space with its own velocity, the only applicable representation is the Eulerian representation with the Cauchy stress tensor. Naturally, the data of the rheological tests of rock samples correspond to their Lagrange representation. The problem is solved in terms of the current deformation of the material, i.e., the methodology of Mark Wilkins [Wilkins et al., 1973] applied in the adequate numerical solutions is used. The constructed model agrees with the general rules of the nonholonomic theory of plasticity, which indicates that the current parameters of the geological material depend on the path of loading. The yield surface consists of the generalized Drucker-Prager section, which corresponds to macro-slip, and the closing (at elevated pressure) cap-curve. The crushing effect corresponds to the moment when the figurative point of Mohr’s plane attains the cap-curve. The kinematics is based on nonassociative flow rules and is constructed by the summation of the known experimental data for sands and sandstones. The computer calculations of homogeneous states closely correspond to the basic types of the tests of fluid-saturated sandstone. It turned out that the rotational movements in the problems considered are so small that the corrections according to Oldroyd (which are necessary for making the formulas consistent with the theory of finite deformations) can be ignored. The changes in the coefficient of side thrust (the side pressure) appearing in the course of irreversible rock deformation are found, and the levels of crushing are evaluated.
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Original Russian Text © S.M. Kapustyanskii, V.N. Nikolaevskii, A.G. Zhilenkov, 2010, published in Fizika Zemli, 2010, No. 12, pp. 82–93.
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Kapustyanskii, S.M., Nikolaevskii, V.N. & Zhilenkov, A.G. Nonholonomic model of deformation of highly porous sandstone under its internal crushing. Izv., Phys. Solid Earth 46, 1095–1104 (2010). https://doi.org/10.1134/S1069351310120062
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DOI: https://doi.org/10.1134/S1069351310120062