Lamb’s integral formulas of two-phase saturated medium for soil dynamic with drainage

• Published in: Applied mathematics and mechanics 2010-09, Vol.31 (9), p.1113-1124
• Main Authors: Ding, Bo-yang, Dang, Gai-hong, Yuan, Jin-hua
• Format: Article
• Language: English
• Subjects: Applications of Mathematics; Classical Mechanics; Drainage; Dynamics; Fluid- and Aerodynamics; Green's functions; Integrals; Lamb; Mathematical analysis; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Partial Differential Equations; Saturated soils; Soil (material)
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-010-1347-9

When dynamic force is applied to a saturated porous soil, drainage is common. In this paper, the saturated porous soil with a two-phase saturated medium is simulated, and Lamb’s integral formulas with drainage and stress formulas for a two-phase saturated medium are given based on Biot’s equation and Betti’s theorem (the reciprocal theorem). According to the basic solution to Biot’s equation, Green’s function G ij and three terms of Green’s function G 4 i , G i 4 , and G 44 of a two-phase saturated medium subject to a concentrated force on a spherical coordinate are presented. The displacement field with drainage, the magnitude of drainage, and the pore pressure of the center explosion source are obtained in computation. The results of the classical Sharpe’s solutions and the solutions of the two-phase saturated medium that decays to a single-phase medium are compared. Good agreement is observed.