地層下陷泛指地面向下沉陷的垂直地表變形，其發生常伴隨許多的災害，如地下水資源涵蓄能力降低、海水倒灌、土壤鹽化及防洪效益降低等，這些災害將會對流域水土資源造成相當大的損失，以往在從事土壤壓密的研究通常以Terzaghi (1925)及Biot (1941)的理論作為主要的依據，然而在土壤壓密理論的研究中重力所造成的影響往往是被忽略的，僅有部分的相關文獻指出當土壤受外力產生壓密沉陷時，土壤在較軟或厚度較厚的情況重力的影響較為顯著，因此若能將重力對土壤壓密的影響也考量進去，應更能符合土壤壓密實際的情況，進而使其物理機制更為完善。
本研究應用Lo et al. (2005)利用多相連體力學(continuum theory of mixtures)所推導出的孔隙介質中含有兩相非混合、可壓縮且具有黏滯性流體之孔彈性理論模式為基礎，並考慮質量密度及孔隙率的微小變化量，重新推導出三維具重力影響之土壤壓密沉陷理論；在考慮一維情況下，本研究利用顯式有限差分法進行求解，透由此數值模式可得到在一維垂直方向下考慮雙邊排水的飽和土壤受固定載重作用所產生的壓密沉陷情形，之後將其結果與前人所提出的壓密沉陷理論之解析解進行比較與驗證，並探討重力對於不同質地之土壤在壓密沉陷的影響。
由結果發現在相同土壤條件下，考慮重力影響時會使土壤產生額外的壓密沉陷量，以及造成超額孔隙水壓的消散較慢，且隨著土體深度增加，重力的影響會越顯著，而在比較不同土壤性質中的結果可發現，當土壤在質地越軟或越厚的情況下，重力的影響會越顯著，最後雖然考慮重力的影響會使土體產生額外的沉陷量或延遲超額孔隙水壓的消散，但若要比較不同土壤在壓密沉陷的差異則還是以本身的土壤性質為主。

In recent years, land subsidence has caused many disasters in the coastal and alluvial fan of Taiwan. For example, it has caused seawater intrusion, soil salinization, and reduced groundwater storage capacity. Relevant research on land subsidence is mainly divided into two types: field surveys and theoretical analyses. Soil consolidation plays an important role in theoretical analysis; however, in references to soil consolidation theory, the effect of gravity is often ignored.
In the current study, we apply the consolidation theory of poroelasticity developed by Lo et al. (2005) to illustrate the effect of gravity on one-dimensional consolidation of saturated soils, and use the finite difference scheme to develop a numerical solution for excess pore water pressure and consolidation settlement under constant loading.
The numerical results show that, when the effect of gravity is included, more total settlement will occur, and the dissipation of excess pore water pressure will be slower and asymmetrical. Also, as the depth of the soil increases, the effect of gravity on the excess pore water pressure will be more significant.

[1] Beresnev, I.A., Johnson, P.A., “Elastic-wave stimulation of oil production: a review of methods and results”, Geophysics, Vol. 59, No. 6, pp. 1000-1017, 1994.
[2] Biot, M.A., General theory of three-dimensional consolidation,“Journal of Applied Physics”, Vol. 12, No. 2, pp. 155-164, 1941.
[3] Biot, M.A., Theory of propagation of elastic waves in a fluid-saturated porous solid, I. Low-frequency range, II. Higher frequency range, J.Acoust.Soc.Am., Vol. 28, No. 2, pp. 168-191, 1956.
[4] Biot, M.A., Willis, D.G., The elastic coefficients of the theory of consolidation, J. Appl, Mech., Vol. 24, pp. 594-601, 1957.
[5] Biot, M.A., Mechanics of deformation and acoustic propagation in porous media, J.Appl.Phys., Vol. 33, No. 4, pp.1482-1498, 1962.
[6] Borja, R.I., Liu X, White J.A., Multiphysics hillslope processes triggering landslides, Acta Geotech., Vol. 7, pp. 261–269, 2012.
[7] Cowin, S.C., Bone poroelasticity, J Biomech., Vol. 32, pp. 218–238, 1999.
[8] Das, B.M., Advanced Soil Mechanics, Taylor and Francis, Philadelphia, Pa, 1997.
[9] Girsang, C.H., A numerical investigation of the seismic response of the aggregate pier foundation system, Master Thesis, Department of Civil Engineering, University of Virginia, Blacksburg, 2001.
[10] Gibson, R.E., Robert, L.S., Kenneth, W.C., The theory of one-dimensional consolidation of saturated clays. II. Finite nonlinear consolidation of thick homogeneous layers, Can 10, Geotech J, Vol. 18, No. 2, pp. 280-293, 1981.
[11] Gutierrez, M.S., and R. W. Lewis., Coupling of fluid flow and deformation in underground formations, Journal of Engineering Mechanics, Vol. 128, pp. 779-787, 2002.
[12] G. W. Gee and D. Or, “Particle-Size Analysis,” In: J. H. Dane and G. C. Topp, Ed., Methods of Soil Analysis, Part 4, Physical Methods, SSSA Book Series 5, SSSA, Madison, pp. 255-294, 2002.
[13] Lo, W.C., Sposito, G., and Majer, E.,“Wave propagation through elastic porous media containing two immiscible fluids,”Water Resour. Res., Vol. 41, W02025, 2005.
[14] Lo, W.C., Yeh, C.L., and Tsai, C.T.,“Effect of soil texture on the propagation and attenuation of acoustic wave at unsaturated conditions,”J. Hydrology, Vol. 338, pp. 273-284, 2007.
[15] Lo, W.C., Sposito, G., and Chu, H.,“Poroelastic theory of consolidation in unsaturated soils,”Vadose Zone J, Vol. 13, No. 5, 2014.
[16] Lo, W.C., Chao, N.C., Chen, C.H., Lee J.W., “Poroelastic Theory of Consolidation in Unsaturated Soils Incorporating Gravitational Body Forces,”Adv Water Resour., Vol. 106, pp. 121-131, 2017.
[17] Mei, C.C., “Gravity effects in consolidation of layer of soft soil,”J Eng Mech., Vol. 111, No. 8, pp. 1038-1047, 1985.
[18] Ng, A.K.L., and J.C. Small, Use of coupled finite element analysis in unsaturated soil problems, International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 24, pp. 73-94, 2000.
[19] Oka, F.,T. Adachi, and Y. Okano, Two-dimensional consolidation analysis using an elasto-viscoplastic constitutive equation, International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 10, pp. 1-16, 1986.
[20] Rice, J.R., Cleary, M.P., “Some basic stress diffusion solutions for fluid-saturated porous media with compressible constituents”,Rev Geophys Space Phys., Vol. 14, pp. 227–241, 1976.
[21] Rawls, W.J., Ahuja, J.R., Brakensiek, D.L., Estimating soil hydraulic properties from soils data. In: Proceedings of Workshop on Indirect Methods for Estimating the Hydraulic Properties of Unsaturated Soils. Riverside, CA, pp. 329–341, 1992.
[22] Roberts PM, Sharma A, Uddameri V, Monagle M, Dale DE, Steck LK. Enhanced DNAPL transport in a sand core during dynamic stress stimulation, Envir, Eng, Sci., Vol. 18, No. 2, pp. 67-79, 2001.
[23] Selvadurai APS, Suvorov AP. Thermo-Poroelasticity and Geomechanics. Cambridge University Press, Cambridge, 2017.
[24] Terzaghi, K., Erdbaumechanik auf bodenphysikalischer grundlage, 1925.
[25] Terzaghi K. Theoretical soil mechanics. New York: John Wiley & Sons, 1943.
[26] Tuncay, K., Kambham, K., Corapcioglu, M., “Self-weight subsidence of saturated soft porous media,” J. Eng. Mech, Vol. 124, No. 6, pp. 630–638, 1998.
[27] Tsai, T.L., Chang, K.C., Huang, L.H.,“Body force effect on consolidation of porous elastic media due to pumping,” J Chin Inst Eng, Vol. 29, No. 1, pp. 75–82, 2006.
[28] Tseng, C.M., Tsai, T.L., Huang, L.H.,“Effects of body force on transient poroelastic consolidation due to groundwater pumping,”Environ Geol, Vol. 54, No. 7, pp. 1507-1516, 2008.
[29] Verruijt, A., “Approximations of cyclic pore pressure caused by sea waves in a poro-elastic half-plane”In:Pande,G.N.,Zienkiewicz, O.S.(Eds.), Soil mechanics-Transient and cyclic loads, Wiley, New York, pp. 37-51, 1982.
[30] Wang, K., and E. E. Davis, Theory for the propagation of tidally induced pore pressure variations in layered subseafloor formations, Journal of Geophysical Research,Vol. 101 (B5), pp. 11483-11496, 1996.
[31] Wang HF. Theory of Linear Poroelasticity with Applications to Geomechanics and Hydrogeology. Princeton University Press, Princeton; 2000.
[32] 徐啟洋，應用孔彈性理論分析單層週期性載重下之飽和土壤壓密行為，國立成功大學水利及海洋工程研究所碩士論文，2014。