飽和土壤沉陷受重力影響下之孔彈性理論

Poroelastic Theory of Consolidation for Saturated Soil Incorporating Gravitational Body Forces

趙南傑(Nan-Chieh Chao) ； 鄧教弘(Jiao-Hong Deng) ； 程士豪(Shih-Hao Cheng) ； 王常勉(Chang-Mien Wang) ； 羅偉誠(Wei-Cheng Lo)

《農業工程學報》 65卷1期 (2019/03) Pp. 46-56

https://doi.org/10.29974/JTAE.201903_65(1).0004

摘要

土壤壓密沉陷是一種由土壤受外力因素影響導致孔隙介質及內含流體產生形變進而造成土壤體積減少的現象；本研究將以Lo et al.（2005）所推導出的多孔隙介質中含有兩相非混和、可壓縮且具有黏滯性流體之孔彈性理論方程式為基礎，並考慮密度及孔隙率的微小變化量重新推導出具重力影響之質量守恆及動量守恆方程式，並使兩方程式耦合推導出三維具重力影響之孔彈性土壤壓密沉陷理論；本研究將利用顯式有限差分法求解一維垂直方向下考慮雙邊排水的飽和土壤受固定載重影響所產生壓密沉陷情形，之後將其結果與前人所提出之一維飽和或受固定載重壓密沉陷理論之解析解結果進行比較驗證，發展一維孔彈性土壤壓密沉陷數值模式，根據研究結果發現在不考慮重力影響下的超額孔隙水壓結果中，壓力分布呈上下對稱之形式，而在考慮重力影響後，超額孔隙水壓呈不對稱分布，由上述本研究之成果可證明重力影響在壓密沉陷中是不可忽視的重要因素。

關鍵字

孔彈性理論 ； 飽和土壤壓密 ； 重力

並列摘要

Soil consolidation is a transient process by which soil volume is decreased due to the coupling between deformation of a porous medium and interstitial fluid flows. The effect of body force has been conventionally ignored in the consolidation theory of poroelasticity for saturated soils. The objective of this research is to develop the consolidation theory of poroelasticity for saturated soil which incorporates provided with gravitational body forces. In this research, based on the poroelastic theory of consolidation developed by Lo et al. (2005), the gravity effect is well taken into account in the diffusion equation that feature the excess pore water pressure as dependent variables, thus leading to additional first-order time-derivative terms. Considering a one-dimensional condition with external loads, numerical methods will be used to solve those equations with consolidation problem. The comparisons of the results with body forces and without body forces reveal that variations in the excess pore water pressure due to the existence of body forces increase with soil depth and more total settlement is induced when body forces is considered.

並列關鍵字

Poroelasticity ； Consolidation for Saturated soil ； Gravitational body forces