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Wave-induced stresses and pore pressures in sloping seabeds. (English) Zbl 0761.73091

Summary: By using the Mellin transform, a general solution is obtained for the total stresses and pore pressure distribution in an infinite wedge under fairly general conditions of loading. The results for the particular case in which each surface is subjected to static sinusoidal pressures are given in an explicit form. The infinite integrals can be evaluated by numerical integration methods. This analytical method is verified by different cases. The results of this study could be used to determine to total stresses and pore pressures induced by a wave on a sloping seabed.

MSC:

74L05 Geophysical solid mechanics
74J10 Bulk waves in solid mechanics
44A15 Special integral transforms (Legendre, Hilbert, etc.)
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[1] and , Théorie de l’Élasticité, Branger, Paris, 1961.
[2] Fillunger, Z. Math. Phys. 60 pp 275– (1912)
[3] Putnam, Am. Geophys. Union 30 pp 349– (1949) · doi:10.1029/TR030i003p00349
[4] Liu, J. Coastal Eng. 1 pp 135– (1977)
[5] Sleath, J. Hydraul. Div. ASCE 96 pp 367– (1970)
[6] Moshagen, J. Waterways, Harbors Coastal Eng. Div. ASCE 101 pp 49– (1975)
[7] Prevost, J. Waterways, Harbors Coastal Eng. Div. ASCE 101 pp 464– (1975)
[8] Foundation of Solid Mechanics, Prentice-Hall, Englewood Cliffs, NJ, 1965, pp. 195-197.
[9] ’Seabed instability from waves’, Proc. 10th Ann. Offshore Technology Conf. Vol. 1, Houston, TX, 1978, pp. 1819-1824.
[10] Madsen, Géotechnique 28 pp 377– (1978)
[11] Biot, J. Appl. Phys. 12 pp 155– (1941)
[12] ’Comportement d’un massif sous-marin sous l’action de la houle: formulation et traitement umérique du probleme’, Report of CERMES for PMVN, No. 405, 1989.
[13] Gatmiri, Géotechnique 40 pp 15– (1990)
[14] and , Méthodes de la Théorie des Fonctions d’une Variable Complexe, MIR, Moscow, 1972.
[15] and , ’Méthodes de la Théorie Mathématique de l’Élasticité, Vols 1 and 2’, MIR, Moscow, 1984.
[16] Tranter, Q. J. Mech. Appl. Math. 1 pp 125– (1947)
[17] Love, Phil. Trans. R. Soc. Lond. Ser. A 228 pp 389– (1929)
[18] Liu, J. Hydraul. Div. ASCE 99 pp 2263– (1973)
[19] and , Transformations Intégrales et Calcul Opérationnel, MIR, Moscow, 1978.
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