彈性波在飽和土壤中之傳波特性

Characteristics of Dilatational Wave Propagation and Attenuation through Fluid-saturated Soils

羅偉誠(Wei-Cheng Lo) ； 葉昭龍(Chao-Lung Yeh) ； 詹錢登(Chyan-Deng Jan)

《農業工程學報》 53卷3期 (2007/09) Pp. 11-21

https://doi.org/10.29974/JTAE.200709.0002

摘要

本文應用Biot(1956a, b)的孔彈性力學理論方程式分析彈性波在飽和含水土壤及空氣佔滿孔隙土壤中之傳波特性。首先探討飽和土壤中固體與孔隙流體之間的應力與應變關係式，其次應用Biot的理論方程式建立彈性波在飽和土壤中之傳波頻率方程式，然後整理三種不同土壤［砂土(sand)、粉土(silt)和黏土(clay)］之相關參數，最後應用傳波頻率方程式探討三種不同頻率（50、100和150Hz）的Biot快速膨脹波（P1波）及Biot慢速膨脹波（P2波）在這些土壤中之傳波速度及傳波衰退係數。結果顯示，在本文所探討的三種不同頻率內，P1波的傳波速度與傳波頻率無明顯之關係，但與土壤和孔隙流體特性有關；P1波在各種飽和含水土壤中的傳波速度之差異不顯著，但在各種由空氣佔滿孔隙之土壤（全乾土壤）中其傳波速度之差異較明顯，而且在前者的速度遠高於在後者的速度；P1波的傳波衰退係數約與傳波頻率兩次方成正比。P2波的傳波速度遠小於P1波的傳波速度，但P2波的傳波衰退係數遠大於P1波的傳波衰退係數，而且前述兩者均與土壤材質有密切之關係；P2波的傳波速度及衰退係數均約與傳波頻率的1/2次方成正比。

關鍵字

彈性波 ； 飽和 ； 土壤特性 ； 傳波速度 ； 衰退係數

並列摘要

The behaviors of dilatational wave propagation and attenuation through three different types of saturated soils (sand, silt, and clay) whose pore spaces are completely occupied either by water or by air were investigated in this study based on the celebrated Biot model equations of poroelasticity. The corresponding frequency equation was first derived and then solved numerically to determine the phase velocity and attenuation coefficient of the Biot fast (P1) and slow (P2) waves at the seismic frequency range of excitation (50, 100 and 150Hz). The results show that the phase velocity of P1 wave is equal to the square root of the ratio of an effective hulk modulus to an effective density of the fluid-containing porous medium, regardless of excitation frequency and pore fluid. It is also found that the phase velocity of the P1 wave does not vary significantly in the water-saturated case whereas the variation is apparent in the air-saturated case. The attenuation coefficient of the P1 wave is approximately proportional to the square of the excitation frequency. In reference to the P2 wave, its attenuation is demonstrated to he greater than that of the P1 wave, but its phase velocity is less than that of the P1 wave. The magnitude of the phase velocity of attenuation coefficient of the P2 wave increases with the square root of the excitation frequency.

並列關鍵字

Dilatational waves ； Saturated ； Soil characteristics ； Wave velocity ； Attenuation coefficient