Theory of Plastic Sand Flow with Fluid Pressure Effect
Publication: Journal of Engineering Mechanics
Volume 131, Issue 9
Abstract
Fundamental principles of elastic–plastic mechanics of soils and rocks are given on the base of the original publications. The solid friction and dilatancy effects are included in the nonstandard form of nonassociative rule of plastic flow. The resulting hyperbolic system of equations is represented for a plane case. The slip surfaces are assumed to be jump tangential discontinuities of a velocity field. The possibility of limit equilibrium at slip surfaces is accounted for. The attempts to account for grain rotations, permitting study of slip surface structure, are discussed. The Biot–Frenkel model of interpenetrating continua is developed for plastic flow of porous saturated matrix. In this case the solid matrix state is determined by the effective stresses and pore pressure diffusion happens in plastically flowing matrix. To illustrate the theory possibilities, solutions for failure and mass sand flow, driven by the pore pressure gradient, are selected. They are important especially for oil/gas reservoirs with a weak matrix, typical for offshore geology.
Get full access to this article
View all available purchase options and get full access to this article.
References
Biot, M. A. (1973). “Nonlinear and semilinear rheology of porous solids.” J. Geophys. Res., 78(23), 4924–4937.
Brulin, O., and Hjalmars, S. (1981). “Linear grade-consistent micropolar theory.” Int. J. Eng. Sci., 19(12), 1731–1738.
Chambon, R., Desrues, J., and Vardoulakis, I., eds. (1994). Localizations and bifurcation theory for soils and rocks. Balkema, Rotterdam, The Netherlands.
Cosserat, E., and Cosserat, F. (1909). Theorie des corps deformables, Hermann, Paris.
Davis, E. H. (1968). “Theories of plasticity and failure of soil masses.” Soil mechanics: Selected topics, I. K. Lee, ed., Butterworths, London, 341–380.
De Borst, R., and Van der Geissen, E., eds. (1998). Material instabilities in solids, Wiley, Chichester, England.
Drucker, D. C., and Prager, W. (1952). “Soil mechanics and plastic analysis or limit design.” Q. Appl. Math., 10(1), 157–165.
Economides, M. J., and Nolte, K. G., eds. (2000). Reservoir stimulation, 3rd Ed., Wiley, Chichester, U.K.
Garagash, I. A. (1996). “Microdeformations of preliminary stressed discrete geophysical medium.” Proc. Russ. Acad. Sci. (DAN), 347(1), 95–98.
Garagash, I. A., and Nikolaevskiy, V. N. (1994). “Limit Equilibrium conditions of fragmented rock masses in macro- and micro-scale.” Proc. Russ. Acad. Sci. (DAN), 338(5), 675–679.
Grafutko, S. B., and Nikolaevskiy, V. N. (1998). “Problem of the sand production in a producing well.” Fluid Dyn., 33(5), 745–752.
Hansen, B. (1958). “Line ruptures regarded as a narrow rupture zones. Basic equations based on kinematic, considerations.” Proc., Conf. on Earth Pressure Problems, Brussels, Belgium, Vol. 1, 39–48.
Kapustyanskiy, S. M., and Nikolaevskiy, V. N. (2001). “The self-similar problem of the transfer of sand from a bed into a well.” J. Appl. Math. Mech., 65(5), 845–854.
Kapustyanskiy, S. M., Nikolaevskiy, V. N., and Schmidt, J. H. (2003). “Elasticoplastic model of sludge injection into a weak water-pressurized reservoir.” Fluid Dyn., 38(2), 293–302.
Krylov, A. L., Mazur, N. G., Nikolaevskiy, V. N., and El’, G. A. (1993). “Gradient-consistent non-linear model of the generation of ultrasound in the propagation of seismic waves.” J. Appl. Math. Mech., 57(6), 1057–1066.
Labuz, J. F., Dai, S.-T., and Papamichos, E. (1996). “Plane-strain compression of rock-like materials.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 33(6), 573–584.
Mroz, Z. (1963). “Non-associated flow laws in plasticity.” J. Mec., 2(1), 21–42.
Muhlhaus, H.-B., and Vardoulakis, I. (1987). “The thickness of shear bands in granular materials.” Geotechnique, 37, 271–268.
Nadai, A. (1963). Theory of flow and fracture of solids, Vol. 2, McGraw-Hill, New York.
Nikolaevskiy, V. N., Basniev, K. S., Gorbunov, A. T., and Zotov, G. A. (1970). Mechanics of porous saturated media, Nedra, Moscow.
Nikolaevskii, V. N. (1971). “Governing equations of plastic deformation of a granular medium.” J. Appl. Math. Mech., 35(6), 1017–1029.
Nikolaevskij, V. N. (1990). Mechanics of porous and fractured media, World Scientific, Singapore.
Nikolaevskiy, V. N. (1996). Geomechanics and fluidodynamics with applications to reservoir engineering, Kluwer Academic, Dordrecht, The Netherlands.
Nikolaevskiy, V. N., Kuznetzov, A. S., and Bellindir, E. N. (1991). “Mathematical dilatancy theory and conditions at strong discontinuities.” Int. J. Eng. Sci., 29(11), 1375–1389.
Papamichos, E., and Malmanger, E. M. (2001). “A sand-erosion model for volumetric sand prediction in a North Sea reservoir.” SPE Reservoir Eval. Eng., 4(1), 44–50.
Revuzhenko, A. F., Stazhevskiy, S. E., and Shemyakin, E. I. (1974). “On mechanism of granulated material deformation under big shears.” Phys.-Techn. Problems of Mineral Deposits Development, No. 3, 130–133.
Reynolds, O. (1885). “On the dilatancy of media composed of rigid particles in contact.” Philos. Mag., 20(127), 469–481.
Rice, J. R. (1975). “On the stability of hardening for saturated rock masses.” J. Geophys. Res., 80, 1531–1536.
Roodhart, L. P., Fokker, P. A., Davis, D. R., Shlyapobersky, J., and Wong, G. K. (1994). “Frac & Pack stimulation: Application, design and field experience from the Gulf of Mexico to Borneo.” JPT, 46(3), 230–238.
Rudnicky, J. W., and Rice, J. R. (1975). “Conditions for localization of deformation, in pressure sensitive dilatant materials.” J. Mech. Phys. Solids, 23(6), 371–394.
Schofield, A., and Wroth, P. (1968). Critical state soil mechanics, McGraw-Hill, London.
Stephanov, Yu. P. (2002). “Localization of deformation and failure in geomaterials. Numerical modeling.” Phys. Mesomech., 5(5), 107–118.
Tejchman, J., and Wu, W. (1993). “Numerical study on shear band patterning in a Cosserat continuum.” Acta Mech., 99, 61–74.
Wong, G. K., Kapustyanskiy, S. M., Nikolaevskiy, V. N., and Shlyapobersky, J. V. (2002). “Elastic-plastic calculations of mechanical damage in a well vicinity.” Mech. Solids, 1, 121–135.
Information & Authors
Information
Published In
Copyright
© 2005 ASCE.
History
Received: Oct 7, 2003
Accepted: Jul 29, 2004
Published online: Sep 1, 2005
Published in print: Sep 2005
Notes
Note. Associate Editor: Alexander H.-D. Cheng
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.