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Typus
BauernOpfer
Bearbeiter
Graf Isolan
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Untersuchte Arbeit:
Seite: 5, Zeilen: 1-18
Quelle: Schanz and Diebels 2003
Seite(n): 214, Zeilen: 1-17, 21-23
[Based on the work of von Terzaghi, a theoretical] description of porous materials saturated by a viscous fluid was presented by Biot [16, 15]. This was the starting point of Biot’s theory of poroelasticity. In the following years, Biot extended his theory to anisotropic cases [17] and also to poroviscoelasticity [18]. The dynamic extension of Biot’s theory was published in 1956 in two papers, one covering the low frequency range [20] and the other one covering the high frequency range [21]. One of the significant findings in these papers was the identification of three different wave types for a 3-d continuum, namely two compressional waves and one shear wave. The additional compressional wave is also known as the slow wave and has been experimentally confirmed [124]. In Biot’s original approach, a fully saturated material was assumed. The extension to a nearly saturated (partially saturated) poroelastic solid was presented by Vardoulakis and Beskos [162].

Based on the work of Fillunger [77], a different approach, the Theory of Porous Media has been developed. This theory is based on the axioms of continuum theories of mixtures [161, 24] extended by the concept of volume fractions by Bowen [25, 26] and by the research group of Ehlers [54, 63, 65, 64, 57]. Thus, the Theory of Porous Media proceeds from the assumption of immiscible and superimposed continua with internal interactions. Remarks on the equivalence of both theories are found in the work of Bowen [26], Ehlers and Kubik [66] and Schanz and Diebels [149]. In all these publications, linear versions of both theories are compared and, finally, the equivalence can only be shown if Biot’s apparent mass density is set to zero.


[15] Biot, M.A.: Consolidation settlement under a rectangular load distribution. Journal of Applied Physics, 12, 426–430, 1941.

[16] Biot, M.A.: General Theory of Three-Dimensional Consolidation. Journal of Applied Physics, 12, 155–164, 1941.

[17] Biot, M.A.: Theory of Elasticity and Consolidation for a Porous Anisotropic Solid. Journal of Applied Physics, 26, 182–185, 1955.

[18] Biot, M.A.: Theory of Deformation of a Porous Viscoelastic Anisotropic Solid. Journal of Applied Physics, 27(5), 459–467, 1956.

[20] Biot, M.A.: Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid.I. Low-Frequency Range. Journal of the Acoustical Society of America, 28(2), 168–178, 1956.

[21] Biot, M.A.: Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid.II. Higher Frequency Range. Journal of the Acoustical Society of America, 28(2), 179–191, 1956.

[24] Bowen, R.M.: Theory of Mixtures. In Continuum Physics. (Eringen, A.C., Ed.), Vol. III, Acadenic Press, New York, 1–127, 1976.

[25] Bowen, R.M.: Incompressible Porous Media Models by use of the Theory of Mixtures. International Journal of Engineering Science, 18, 1129–1148, 1980.

[26] Bowen, R.M.: Compressible Porous Media Models by use of the Theory of Mixtures. International Journal of Engineering Science, 20(6), 697–735, 1982.

[54] de Boer, R.; Ehlers, W.: Theorie der Mehrkomponentenkontinua mit Anwendungen auf bodenmechanische Probleme, Teil I. Forschungsbericht aus dem Fachbereich Bauwesen 40, Universität - GH Essen, 1986.

[57] Diebels, S.: Mikropolare Zweiphasenmodelle: Formulierung auf der Basis der Theorie Poröser Medien. Bericht Nr. II-4, Universität Stuttgart, Institut für Mechanik, Lehrstuhl II, 2000.

[63] Ehlers, W.: Poröse Medien – ein kontinuumsmechanisches Modell auf der Basis der Mischungstheorie. Forschungsbericht aus dem Fachbereich Bauwesen 47, Universität - GH Essen, 1989.

[64] Ehlers,W.: Compressible, Incompressible and Hybrid Two-phase Models in Porous Media Theories. ASME: AMD-Vol., 158, 25–38, 1993.

[65] Ehlers, W.: Constitutive Equations for Granular Materials in Geomechanical Context. In Continuum Mechanics in Environmental Sciences and Geophysics. (Hutter, K., Ed.), CISM Courses and Lecture Notes, No. 337, Springer-Verlag, Wien, 313–402, 1993.

[66] Ehlers, W.; Kubik, J.: On Finite Dynamic Equations for Fluid-Saturated Porous Media. Acta Mechanica, 105, 101–117, 1994.

[77] Fillunger, P.: Der Auftrieb von Talsperren, Teil I-III. Österr. Wochenschrift für den öffentlichen Baudienst, 532–570, 1913.

[124] Plona, T.J.: Observation of a Second Bulk Compressional Wave in Porous Medium at Ultrasonic Frequencies. Applied Physics Letters, 36(4), 259–261, 1980.

[149] Schanz, M.; Diebels, S.: A Comparative Study of Biot’s Theory and the Linear Theory of Porous Media for Wave Propagation Problems. Acta Mechanica, 161(3-4), 213–235, 2003.

[161] Truesdell, C.; Toupin, R.A.: The Classical Field Theories. In Handbuch der Physik. (Flügge, S., Ed.), Vol. III/1, Springer-Verlag, Berlin, 226–793, 1960.

[162] Vardoulakis, I.; Beskos, D.E.: Dynamic Behavior of Nearly Saturated Porous Media. Mechanics of Composite Materials, 5, 87–108, 1986.

Based on the work of von Terzaghi, a theoretical description of porous materials saturated by a viscous fluid was presented by Biot [6]. This was the starting point of the theory of poroelasticity or the BT. In the following years, Biot extended his theory to anisotropic cases [7] and also to poroviscoelasticity [8]. The dynamic extension of Biot’s theory was published in 1956 in two papers, one covering the low frequency range [9] and the other one covering the high frequency range [10]. One of the significant findings in these papers was the identification of three different wave types for a 3-d continuum, namely two compressional waves and one shear wave. The additional compressional wave is also known as the slow wave and has been experimentally confirmed [11]. In Biot’s original approach a fully saturated material was assumed. The extension to a nearly saturated (partially saturated) poroelastic solid was presented by Vardoulakis and Beskos [12].

On the other hand, based on the work of Fillunger, a different approach, namely the Theory of Porous Media, has been developed. This theory is based on the axioms of continuum theories of mixtures [13], [14] extended by the concept of volume fractions by Bowen [15], [16] and others [17]–[21]. Thus, the TPM proceeds from the assumption of immiscible and superimposed continua with internal interactions.

Remarks on the equivalence of both theories are found in the work of Bowen [16]. [...] Furthermore, Ehlers and Kubik [22] compared and discussed the linear versions of both theories claiming that they are equivalent if Biot’s apparent mass density is assumed to be zero.


[4] Fillunger, P.: Der Auftrieb von Talsperren, Teil I-III. Österr. Wochenschrift für den öffentlichen Baudienst. 7, 532–510 (1913).

[6] Biot, M. A.: General theory of three-dimensional consolidation. J. Appl. Phys. 12, 155–164 (1941).

[7] Biot, M. A.: Theory of elasticity and consolidation for a porous anisotropic solid. J. Appl. Phys. 26, 182–185 (l955).

[8] Biot, M. A.: Theory of deformation of a porous viscoelastic anisotropic solid. J. Appl. Phys. 27, 459–467 (1956).

[9] Biot, M. A.: Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Lowfrequency range. J. Acoust. Soc. America 28, 168–178 (1956).

[10] Biot, M. A.: Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range. J. Acoust. Soc. America 28, 179–191 (1956).

[11] Plona, T. J.: Observation of a second bulk compressional wave in porous medium at ultrasonic frequencies. Appl. Phys. Letters 36, 259–261 (1980).

[12] Vardoulakis, I., Beskos, D. E.: Dynamic behavior of nearly saturated porous media. Mech. Comp. Mater. 5, 87–108 (1986).

[13] Truesdell, C., Toupin, R. A.: The classical field theories. In: Handbuch der Physik (Flügge, S., ed.), vol. III/1, pp. 226–793. Berlin: Springer 1960.

[14] Bowen, R. M.: Theory of mixtures. In: Continuum physics (Eringen, A. C., ed.), vol. III, pp. 1–127. New York: Academic press 1976.

[15] Bowen, R. M.: Incompressible porous media models by use of the theory of mixtures. Int. J. Engng Sci. 18, 1129–1148 (1980).

[16] Bowen, R. M.: Compressible porous media models by use of the theory of mixtures. Int. J. Engng Sci. 20, 697–735 (1982).

[17] de Boer, R., Ehlers, W.: Theorie der Mehrkomponentenkontinua mit Anwendungen auf bodenmechanische Probleme, Teil I. Forschungsbericht aus dem Fachbereich Bauwesen 40, Universität – GH Essen, 1986.

[18] Ehlers, W.: Poröse Medien – ein kontinuumsmechanisches Modell auf der Basis der Mischungstheorie. Forschungsbericht aus dem Fachbereich Bauwesen 47, Universität – GH Essen, 1989.

[19] Ehlers, W.: Constitutive equations for granular materials in geomechanical context. In: Continuum mechanics in environmental sciences and geophysics (Hutter, K., ed.). CISM Courses and Lecture Notes, No. 337, pp. 313–402 Wien: Springer 1993.

[20] Ehlers, W.: Compressible, incompressible and hybrid two-phase models in porous media theories. ASME: AMD-Vol. 158, 25–38 (1993).

[21] Diebels, S.: Mikropolare Zweiphasenmodelle: Formulierung auf der Basis der Theorie Poröser Medien. Bericht Nr. II-4, Universität Stuttgart, Institut für Mechanik, Lehrstuhl II, 2000.

[22] Ehlers, W., Kubik, J.: On finite dynamic equations for fluid-saturated porous media. Acta Mech. 105, 101–117 (1994).

Anmerkungen

Mostly identical with all but one of the literary references just having been copied. Nothing has been marked as a citation. The source is mentioned in passing.

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(Graf Isolan) Schumann

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