Filtration in cohesive soils : mathematical model

• Autorzy: Schaefer R. , Sędziwy S.
• Języki publikacji: EN

Abstrakty

EN

The paper discusses the physical basis of the process of filtration of water in a case of very low velocities and presents the mathematical model of the process, based on a new constitutive formula. The existence and uniqueness of a weak solution to the resulting nonhomogeneous initial boundary-value problem is then proven.

Słowa kluczowe

EN

mathematical model; filtration; boundary value

PL

model matematyczny; filtracja; wartość brzegowa

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 1999
• Tom: Vol. 6, No. 1
• Strony: 1--13
• Opis fizyczny: Bibliogr. 23 poz., il., tab., wykr.

Twórcy

autor

Schaefer R.

• Jagiellonian University, Institute of Computer Science, ul. Nawojki 11, 30-072 Cracow, Poland

autor

Sędziwy S.

• Jagiellonian University, Institute of Computer Science, ul. Nawojki 11, 30-072 Cracow, Poland

Bibliografia

• [1] L.A. Aylmore, J.P. Quirk. Domain of turbostatic structure of clays. Nature 187: 1046, 1960.
• [2] J. Bear. Dynamics of Fluids in Porous Media. Elsevier, New York, 1972.
• [3] R.N. Chowdury. Ground water flow obeying non-Darcy laws. Wolloungong Univ. 3: 13-22, 1974.
• [4] W. Van Engelhardt, W.L.M. Tun. The flow of fluids through sandstones. Illinois State Geol. Survey Circ 195, 1955.
• [5] H. Gajewski, K. Groger, K. Zacharias. Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen [Russian translation]. Akad. Verl. Berlin, 1974.
• [6] H. Gong. Sur la constitution de la charge électrique á la surface d'un électrolyte. Ann. Phys., Paris 1910, Sér. h, 457—468.
• [7] B. Grabowska-Olszewska. The Technology of Testing Cohesive Soils [in Polish]. Wydawnictwo Geologiczne, Warszawa, 1990.
• [8] S. Hansbo. Consolidation in clay with special reference to influence of vertical sand drains. In: Swed. Geotech. Inst. Proc, Proc. No. 18, Stockholm 1960.
• [9] T.W. Lambe. The structure of compacted clay. J. Soil Mech. Found. Div. 84, 1958.
• [10] Li Sung Ping. Measuring electrically low velocity of water in soil. Soil Sci. 95: 410-413, 1962.
• [11] J.L. Lions. Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires. Dunod Paris, 1969.
• [12] V.P. Michailov. Differential Equations in Partial Derivatives [in Russian]. Nauka, Moscow, 1983.
• [13] R. Schaefer. Numerical modeling of the prelinear fitration [in Polish]. Rozprawy Habilitacyjne UJ 213, 1991.
• [14] R. Schaefer, S. Migórski, H. Telega. Mathematical and computational aspects of inverse problems for nonlinear filtration process. Proc. II Int. Symp. on Inverse Problems in Eng. Mech ISIP ’94, Paris, 403-409, 1994.
• [15] R. Schaefer, S. Sędziwy. Filtration in cohesive soils: modelling and solving. In: K. Morgan et al. eds., Finite Elements in Fluids, New trends and applications, Vol II, 887-891, 1993.
• [16] R. Schaefer, S. Sędziwy. Semivariational numerical model of prelinear filtration with the special emphasis to nonlinear sources. Computer Assisted Mechanics and Engineering Sciences 3: 83-96, 1996.
• [17] D. Swartzendruber. The applicability of Darcy’s law. Soil. Sci. Am. Proc. 32: 11-18, 1968.
• [18] D. Swartzendruber. Modification of Darcy’s Law for the flow of water in soils. Soil. Sci. 93: 23-29, 1961.
• [19] O. Stern. Wechselseitige Adsorption von Kolloiden. Zeitsch. Elektrochem. 48(12): 508-516, 1924.
• [20] H. Telega. Distributed Algorithms and Hierarchic Optimization for Solving Parameter Inverse Problems. Universitas Jagiellonica Acta Scientarium Litterarumque, Schedae Informaticae 8: 7-28, 1998.
• [21] M.G. Vernandiev, V.M. Jentov. Hydrodynamic Theory of Filtration of Abnormal Liquids [in Russian]. Nauka, Moscow, 1975.
• [22] A. Veruit. Generation and Dissipation of Pore — Vater Pressures. Finite Elements in Geomechanics. John Wiley, N. York, 1979.
• [23] W. Wolski et al. Full-scale faliure test on a stage-constructed tests fill on organic soils. Report Swedish Geotechnical Institute, Linkohoping 32, 1998.