前人研究土壤壓密行為通常應用於單層土壤，但是實際上，天然土壤是透過沉降過程形成的，每一層都包含不同性質的土壤。由於天然土壤通常表現出分層，因此分析層狀土壤壓密的過程將能有效瞭解土壤分層壓密的機制。前人研究中利用Terzaghi (1925)及Biot (1941)的飽和土壤壓密沉陷理論模式於單層及多層土壤壓密的研究已具有相當完備的理論以及數值研究。透過Lo et al. (2014)利用孔彈性理論方程式(Lo et al., 2005)並結合線性應力-應變關係式所推導出單層未飽和土壤壓密理論，可以瞭解未飽和土壤壓密與飽和土壤壓密之間的差異及重要性。因此本研究將以Biot (1941)的飽和土壤壓密理論以及Lo et al. (2014)的未飽和土壤壓密理論為基礎，分析上層為未飽和土壤與下層為飽和土壤之層狀土壤壓密行為。
本研究假設雙層土壤間之交界面滿足超額孔隙水壓連續及水流連續之條件下，且邊界條件為土壤表面為透水層與大氣接觸，底層為不透水層之半排水條件與土壤表面和底層均為透水層與大氣接觸之雙邊排水條件，將單層土壤壓密沉陷問題延伸至雙層土壤，探討地層為下層由飽和土壤所組成，上層由未飽和土壤所組成之雙層土壤。假設土壤為上層未飽和砂土，與下層飽和黏土組成，和與之相反的上層未飽和黏土，與下層飽和砂土組成。分別探討邊界條件與上層未飽和部分之初始水飽和度對雙層土壤之超額孔隙流體壓力的消散行為及隨時間變化之土壤總沉陷量之影響。首先將未飽和耦合方程式精確分離為可解析求解之非耦合方程式，再搭配拉普拉斯轉換(Laplace transform)，我們得出了封閉形式的解析解，它解釋了這種兩層系統中可變形固體基質與可壓縮流體之間複雜的交互作用。排水邊界條件的不同影響了超額孔隙流體壓力的消散時間與土壤總沉陷量的大小。由於在上層和下層中存在不同的水飽和度(部分飽和與完全飽和)，因此超額孔隙水壓不會表現出相對於深度的對稱分佈。

Researches often focus on single-layered soil, in fact, natural soils have been created through a sedimentation process and tend to be horizontally layered, consisting of several homogeneous layers, each layer comprising a different soil type with its own distinct properties. Due to natural soils are often layered, each stratum will be subjected to induced fluid pressure gradient or applied compaction stress to produce distinct flow and deformation patterns. Thus, predicting the behavior of layered soils is crucial. To model the behavior of soil consolidation for a two-layered (saturated and unsaturated) soil system, we begin from the incorporation of the one-dimensional consolidation poroelasticity model of porous medium containing a single compressible, viscous fluid studied by Biot (1941), and combine with the expansion of the model presented by Lo et al. (2014) to a double-fluid system. This two-layered soil system consists of a lower soil layer is fully saturated, whereas an upper soil layer is unsaturated. First, the linear transformation that accurately separates our coupled model equations into analytically solvable coordinates is realized.
Next, the boundary value problem involving these governing equations under semi-permeable boundary condition and fully permeable boundary condition are formulated as a typical example, which complies with the physical constraint to ensure the continuity of pore water pressure and pore water flux at the interface. Using the Laplace time transformation, we obtain the closed-form, analytical solution accounting for the complex interaction between compressible interstitial fluids and deformable solid matrix in such a double-layered soil system. Drainage boundary condition indeed influence the development of excess pore air and water pressures along with the time-dependent total soil subsidence. Owing to the existence of different water saturation (full and partial saturations) in the lower saturated layer and upper unsaturated layer, excess pore fluid pressure does not show a symmetric distribution with respect to vertical depth.

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