孔彈性力學理論已經在工程應用上廣泛地被認為可以精確地分析兩種非混合流體在孔隙介質中複雜力學機制的有效解析方法。然而，因為孔彈性力學理論其偏微分方程式中所含之慣性阻力項、黏滯阻力項和應力項皆為互相互制（coupling）。因此，除非在特定情況下，否則無法求得孔彈性理論其封閉形態（closed-form）之穩態解析解。本文利用有限差分法將兩個流體系統的孔彈性力學理論內偏微分方程式之互制項加以離散化，以進一步數值模擬分析彈性波在未飽和孔隙介質之傳波行為。
本文探討彈性波在拘限含水層傳遞時之應力的變化，經由有限差分數值模擬後，可以求得總壓力與兩個孔隙流體相壓力值。文中發現在我們模擬的傳波頻率的變化下（1 Hz、5 Hz、10 Hz），當頻率越大，隨著距離越遠則彈性波衰退程度也越大（頻率在1 Hz的彈性波隨著距離的傳遞，衰減的能量就比頻率為10 Hz來的小）；在起始孔隙流體飽和度的變化下（ = 0.1、0.2、0.3、0.4、0.5），衰退係數隨著飽和度越大而越大（飽和度0.1之衰退係數比飽和度0.5小）。

Poroelasticity theory has long been regarded as an effective method to analyze complex mechanics of two immiscible fluids in an elastic porous medium in a precise way. However, the resulting partial differential equations in the theory of poroelasticity intrinsically take on a coupled form in the terms pertinent to inertial drag, viscous damping, and applied stress. Therefore, the closed-form analytical solution cannot be solved except in specific cases. The present study analyzes the characteristics of wave propagation of elastic waves in an unsaturated porous medium by discretizing the coupled equations using the Finite Difference Method.
A numerical study was performed to determine the induced total pressure and the pore fluid pressures due to elastic wave propagation and attenuation through unsaturated porous media in a confined area caused by a harmonic excitation. Our numerical simulation indicates that under the excitation frequencies we examined (1, 5, and 10Hz), the attenuation is found to increase with an increase in distance and excitation frequency. In reference to initial non-wetting water saturation ( = 0.1, 0.2, 0.3, 0.4, and 0.5), it is shown to be positively related to the attenuation.

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