本論文探討多層飽和含水層系統受靜點載重或點抽水作用時引致之暫態問題。在一般擬三維分析中，土壤之孔隙水壓與變形非耦合化，因此邊界條件設定須以孔隙水壓方式呈現；然現實狀況與條件較為複雜，未必符合擬三維分析之假設與邊界條件形式。本論文依據Biot三維孔彈理論求解耦合之土壤孔隙水壓與變形。利用有限元素數值軟體ABAQUS建立多含水層模型進行暫態分析。靜點載重問題數值分析結果，可以以初始狀態孔隙水壓場及位移場與彈性體集中力問題解析解比較做為驗證，且最終穩態之位移場亦符合彈性體之解。以點抽水問題數值結果，可以以抽水點附近之孔隙水壓穩態值與無窮域點抽水解析解比較做為驗證。並討論非侷限(自由含水層)與侷限(受壓含水層)之孔隙壓力邊界條件，和土層滲透係數k之變化，對於土層孔隙水壓與沉陷量造成之影響。藉以本研究之延伸可更加瞭解載重或抽水引發地層下陷發生之機制。

The research focus on the transient problems of a fully saturated multi-aquifer system subjected to point force or point sink. In the common quasi-three-dimensional analyses, the pore pressure of the soil is uncoupled to the deformation, so that boundary conditions need to be presented in terms of pore pressure. However, the situation in reality could be more complicated. Assumptions of the quasi–three–dimensional analysis and the types of boundary conditions may not be suitable. The research is based on the three-dimensional poroelastic theory of Biot to solve the coupled pore pressure and deformation of the soils. The multi-aquifer transient problems are analyzed by numerical models built using commercial finite element software ABAQUS. Numerical results of the point force problem are verified by the comparison of the initial pore pressure and displacement fields with solutions of an elastic solid subjected to a concentrated load. At long time, the steady displacement also coincide with solutions of elastic solid. Numerical results of the point sink problem are verified by the comparison of the pore pressure at long time near the sink with the steady solution of the infinite aquifer subjected to a point sink. Effects of unconfined and confined pore pressure boundary conditions, and the variation in permeability coefficients in the multi-aquifer system on the pore pressure and the consolidation are discussed. The mechanism of the land subsidence due to loads and pumping can be further understood from the extension of these analyses.

[1] Jacob, C. E., 〝Flow of Groundwater〞 Engineering Hydraulics, ed. H. Rouse. John Wiley & Sons, New York, pp.321-386, 1950
[2] Theis, C. V., 〝The Significance and Nature of the Cone of Depression in Groundwater Bodies〞Economic Geology, vol.33, 1938
[3] 蔡東霖, 〝大區域地下水超抽導致地層下陷模式之發展應用〞 國立交通大學博士論文, 2001
[4] Biot, M. A., 〝General Theory of Three-dimensional Consolidation〞Journal of Applied Physics, vol.12, pp.155-164, 1941
[5] Gibson, R. E. and Mcnamee, J., 〝Displacement Functions and Linear Transforms Applied to Diffusion through Porous Elastic Media〞 Journal of Mechanics and Applied Mathematics, vol. XIII, Pt.1, 1960
[6] Gibson, R. E., Schiffman, R. L. and Pu, S L., 〝Plane Strain and Axially Symmetric Consolidation of a Clay Layer on a Smooth Impervious Base〞 Journal of Mechanics and Applied Mathematics, vol. XXIII, Pt.4, 1970
[7] Vardoulakis, I. and Harnpattanapanich, T., 〝Numerical Laplace-Fourier Transform Inversion Technique for Layered-soil Consolidation Problems: I. Fundamental Solutions and Validation〞 Journal for Numerical and Analytical Methods in Geomechanics, vol.10, pp.347-365, 1986
[8] 洪以璇, 〝多層含水層抽水引起壓密問題之耦合分析〞 國立成功大學碩士論文, 2013
[9] 曾鈞敏, 〝地下水超抽引致地層下陷之三維解析研究〞 國立台灣大學博士論文, 2009
[10] 許琇晴, 〝三維地層下陷之解析研究〞 國立台灣大學碩士論文, 2012
[11] Davies, T. G. and Banerjee, P. K.,〝The Displacement Field due to a Point Load at the Interface of a Two Layer Elastic Half-space〞 Journal Geotechnique 28, No.1, pp43-56, 1978
[12] Barber, J. R., 〝Elasticity〞 Springer Science & Business Media, pp363-374, 2010
[13] 〝ABAQUS 6.14 User’s Manual.〞