A numerical study on the motional modes of acoustic waves in an elastic porous medium containing two immiscible fluids

• Main Authors: Yu-HanSu, 蘇郁涵
• Other Authors: Wei-Cheng Lo
• Format: Others
• Language: zh-TW
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/38519383234369871268

碩士 === 國立成功大學 === 水利及海洋工程學系專班 === 98 === Numerical simulations of dilatational waves in an elastic porous medium containing two immiscible viscous compressible fluids indicate that three types of wave occur（P1, P2 and P3）, but the modes of dilatory motion corresponding to the three waves remain uncharacterized as functions of relative saturation. In this paper, we address this problem by deriving normal coordinates for the three dilatational waves based on the general poroelasticity equations of Lo et al. 2005. The normal coordinates provide a theoretical foundation with which to characterize the motional modes in terms of six connecting coefficients（X1?X6）that depend in a well defined way on inertial drag, viscous drag, and elasticity properties. Using numerical calculations of six connecting coefficients for eleven unconsolidated soil, we confirm that the dilatational wave whose speed is greatest corresponds to the motional mode in which the solid framework and the two pore fluids always move in phase, regardless of water saturation, in agreement with the classic Biot theory of the fast compressional wave in a water-saturated porous medium. For the wave which propagates second fastest that the solid framework moves in phase with water, but out of phase with air?Mode（III）?, if the water saturation is below some critical value, whereas the solid framework moves out of phase with both pore fluids?Mode（IV）?above this water saturation. The transition from Mode（III）to Mode（IV）corresponds to that between the capillarity-dominated region of the water retention curve and the region reflecting air-entry conditions near full water saturation. Mode（IV） corresponds exactly to the slow compressional wave in classic Biot theory, whereas the Mode（III） is possible only in a two-fluid system undergoing capillary pressure fluctuations. For the wave which has the smallest speed that water saturation more than some critical value, the dilatational mode is dominated by the motions of the two pore fluids, which are out of phase, a result that is consistent with the proposition that this wave is caused by capillary pressure fluctuations.