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

*(English)*Zbl 1385.76012Summary: 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 \(G_{4i}\), \(G_{i4}\), 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.

##### MSC:

76S05 | Flows in porous media; filtration; seepage |

76T99 | Multiphase and multicomponent flows |

45B05 | Fredholm integral equations |

65M38 | Boundary element methods for initial value and initial-boundary value problems involving PDEs |

74L10 | Soil and rock mechanics |

74S15 | Boundary element methods applied to problems in solid mechanics |

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\textit{B. Ding} et al., Appl. Math. Mech., Engl. Ed. 31, No. 9, 1113--1124 (2010; Zbl 1385.76012)

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