砂土孔隙中兩相流體特性對不透水薄層下地震表面波傳遞影響之剖析

Effect of Pore Fluid Mixtures on Seismic Surface Wave Propagation through Sand beneath a Sealed-Pore Thin Surface

陳由聖(Yu-Sheng Chen) ； 羅偉誠(Wei-Cheng Lo) ； 呂珍謀(Jan-Mou Leu)

《農業工程學報》 56卷4期 (2010/12) Pp. 11-26

https://doi.org/10.29974/JTAE.201012.0002

摘要

本文旨在探討三種非混合流體系統（空氣－水，空氣－油及油－水）對雷利表面波相速度及衰退係數之影響。利用未飽和孔隙介質之孔彈性理論，我們推導出雷利表面波相速度及衰減係數的解析三次冪次擴散(dispersion)方程式。我們數值模擬此三次；冪次方程式，求得三個雷利表面波（依其波速大至小表示爲R1、R2和R3波）分別在上述三種非混合流體系統之林肯砂土中且在不同潤濕流體飽和度下之相速度及衰退係數。震盪頻率以接近地震波之低頻率範圍1~100Hz爲例。
數值模擬結果顯示：在三種非混合流體系統中，R1波之相速度約佔剪力波相速度之93%~96%。R1波之衰退係數在空氣－水流體系統及空氣－油流體系統中，與孔隙中兩流體密度差及相對運動相關。然而R1波之衰退係數在油－水流體系統中主要與有效動力剪力黏滯性有關。R2波及R3波分別與P2波及P3波之相速度(Lo et al., 2005)之趨勢非當相近，推論R2波及R3波之相速度分別受流體與固體相間反相(out-of-phase)運動（如同P2波）及受毛細壓力（如同P3波）所影響。R2波衰退係數如同P2波，隨有效動力剪力黏滯性之增加而增加，係與流體黏性愈大流動速度減少相關。R3波之衰退係數在油－水流體系統中最大，在空氣－水流體系統中最小，但此三種非混合流體系統中之三個R3波衰退係數值彼此間差異並不大。

關鍵字

孔彈性 ； 雷利表面波 ； 不透水

並列摘要

The present study investigates the effect of pore fluid mixtures on surface wave propagation and attenuation along an impermeable boundary. A derived cubic polynomial dispersion equation depicts the relationship between wave number and excitation frequency. As the excitation frequency (1-100 Hz) is stipulated, the dispersion equation can be numerically solved via Matlab to determine the phase speed and attenuation coefficient of Rayleigh waves in Lincoln sand permeated by three different fluid mixtures (air-water, aft-oil and oil-water). Numerical results show the existence of three different Rayleigh waves, which are designated as the R1, R2, and R3 waves in descending magnitude of phase speed.
The R1 wave phase speed wan found to be approximately 93-96% of the shear wave speed within relative fluid saturation of 1 to 99%. The R1 wave attenuation coefficients in both air-water and air-oil systems are dependent on the difference between the two fluid densities and the relative motion between the solid and fluid phases. However, the R1 wave attenuation coefficient in the oil-water system depends on effective dynamic viscosity. The R2 and R3 wave phase speeds possess similar patterns to those of the P2 and P3 waves found in Lo et al. (2005). This implies the out-of-phase motion between the solid and fluid phases influences R2 wave phase speed and capillary pressure affects R3 wave phase speed. Similar to the P2 wave, the R2 wave attenuation coefficient is positively correlated to effective dynamic viscosity. The R3 wave attenuation coefficient in an oil-water system is highest among the three fluid mixtures, but the difference in trivial.

並列關鍵字

Poroelasticity ； Rayleigh surface wave ； Impermeability