台灣位處於地震帶上，頻繁的地震所造成的土壤液化是無法避免的。但是，土壤液化會使得土壤強度減少，造成支撐建築物和橋梁的能力降低，導致他們傾斜或滑動因而被破壞。本論文之主要目的是發展三維有限元素方法並用於模擬液化土壤受力後之行為。所發展之有限元素程式是採用Zienkiewnicz等人所推導之流固耦合系統理論做為控制方程式; 使用Newmark法求解微分方程; 土壤之非線性行為遵循帽蓋模式，為非線性彈塑性分析。並使用有限元素程式建立簡單之液化土壤模型計算例題，其分析之結果與前人之研究結果相當符合，因此本程式之正確性應可證明。由於此領域之研究內容相當廣泛複雜，本論文僅有初步分析之結果，其更進一步之研究持續進行中。

Taiwan is located at the intersection of the Philippines Sea Plate and the Euraisian Plate, where are part of the circum-Pacific volcano and seismic zone. The soil liquefaction caused by frequent earthquake thus cannot be avoided. When liquefaction occurs, the strength of the soil decreases, and the ability of a soil deposit to support foundations for buildings and bridges is reduced. That can cause them to tilt or slide and this movement can cause destruction of structures. The main purpose of this study is to establish the three dimensional finite element program, which can be used to analyze the behavior of soil liquefaction under seismic loads. The governing equation implemented in the program is coupled soil skeleton and pore fluid interaction, which were derived by Zienkiewicz et al; use Newmark method of numerical integration to solve differential equations; and the nonlinear soil behavior is represented by the nonlinear kinematic cap model based on classic theory of elastoplasticity. This study builds the fundamental model of soil liquefaction to analyze examples by the finite element program. The results are similar to the other thesis. Therefore, the program is validated and it is able to successfully analyze the system that coupled soil and water. This study only presented with initial achievement on soil liquefaction because the content of this field is quite extensive and complex, and further analysis will be continued.

[1] Bhattacharya S., Hyodo M., Goda K., Tazoh T. and Taylor C. A. (2011), “Liquefaction of soil in the Tokyo Bay area from the 2011 Tohoku (Japan) earthquake”, Soil Dynamics and Earthquake Engineering, 31(11) pp.1618-1628.
[2] Bignell J. and LaFave J. (2010), “Analytical fragility analysis of southern Illinois wall pier supported highway bridges”, Earthquake Engineering & Structural Dynamics, 39(7) pp.709-729.
[3] Bottari C., Carveni P., Sacca C., Copat B. and Iaria G. (2010), “Analysis of Earthquake Damage to Ancient Buildings on the San Raineri Peninsula, Messina, Sicily”, Bulletin of the Seismological Society of America, 100(5A) pp.2067-2079.
[4] Bradley B. A., Cubrinovski M., Dhakal R. P. and MacRae G. A. (2010), “Probabilistic seismic performance and loss assessment of a bridge-foundation-soil system”, Soil Dynamics and Earthquake Engineering, 30(5) pp.395-411.
[5] Chen, W. F. and Baladi, G. Y. (1985), “Soil Plasticity: Theory and Inplementation”, Elsevier Science Publishers B. V., Amsterdam, 238~239 pp.
[6] Cheng Z. and Jeremic B. (2009), “Numerical modeling and simulation of pile in liquefiable soil”, Soil Dynamics and Earthquake Engineering, 29(11-12) pp.1405-1416.
[7] Claypool, G. E., Milkov A. V., Lee Y.-J., Torres M. E., Borowski W. S. and Tomaru H. Microbial methane generation and gas transport in shallow sediments of an accretionary complex, southern Hydrate Ridge (ODP Leg 204), offshore Oregon, USA. Proc. Ocean Drilling Progr. Sci. Results 204. http://www-odp.tamu.edu/publications/204_SR/113/113.htm. Cited on June 13th, 2013
[8] DiMaggio F.L and Sandler I.S. (1971), “Material model for granular soils”, New York, Journal of the Engineering Mechanics Division, Vol. 97, No. 3, May/June, pp. 935-950.
[9] FAO, Soil Permeability. In FAO Training Series – Soil. Web site: ftp://ftp.fao.org/FI/CDrom/FAO_Training/FAO_Training/General/x6706e/x6706e09.htm. Cited on June 13th, 2013.
[10] Gao X., Ling X. Z., Tang L. and Xu P. J. (2011), “Soil-pile-bridge structure interaction in liquefying ground using shake table testing”, Soil Dynamics and Earthquake Engineering, 31(7) pp.1009-1017.
[11] Huang Y. and Jiang X. M. (2010), “Field-observed phenomena of seismic liquefaction and subsidence during the 2008 Wenchuan earthquake in China”, Natural Hazards, 54(3) pp.839-850.
[12] Huang Y., Yashima A., Sawada K. and Zhang F. (2008), “Numerical assessment of the seismic response of an earth embankment on liquefiable soils”, Bulletin of Engineering Geology and the Environment, 67(1) pp.31-39.
[13] Huang Y., Yashima A., Sawada K. and Zhang F. (2009), “A case study of seismic response of earth embankment foundation on liquefiable soils”, Journal of Central South University of Technology, 16(6) pp.994-1000.
[14] Huang Y., Zhang W. J., Mao W. W. and Jin C. (2011), “Flow analysis of liquefied soils based on smoothed particle hydrodynamics”, Natural Hazards, 59(3) pp.1547-1560.
[15] Jefferies, Mike; Been, Ken (2006). “Soil Liquefaction: A Critical State Approach”, Taylor & Francis
[16] Ju S. H. (2013), “A Deconvolution Scheme for Determination of Seismic Loads in Finite-Element Analyses”, Bulletin of the Seismological Society of America, 103(1) pp.258-267.
[17] Juang C. H., Yuan H. M., Li D. K., Yang S. H. and Christopher R. A. (2005), “Estimating severity of liquefaction-induced damage near foundation”, Soil Dynamics and Earthquake Engineering, 25(5) pp.403-411.
[18] Khoei A. R., Azami A. R. and Haeri S. M. (2004), “Implementation of plasticity based models in dynamic analysis of earth and rockfill dams: A comparison of Pastor-Zienkiewicz and cap models”, Computers and Geotechnics, 31(5) pp.385-410.
[19] Katona, M. G. and Mulert, M. A. (1984), “A Viscoplastic Cap Model for Soil and Rock.” Mechanics of Engineering Materials, John Wiley & Sons Ltd., pp. 335~350.
[20] Ling H. I., Sun L., Liu H., Mohri Y. and Kawabata T. (2008), “Finite element analysis of pipe buried in saturated soil deposit subject to earthquake loading”, Journal of Earthquake and Tsunami, 2(1) pp.1-17.
[21] Ling H. I., Sun L., Liu H., Mohri Y. and Kawabata T. (2008), “Finite element analysis of pipe buried in saturated soil deposit subject to earthquake loading”, Journal of Earthquake and Tsunami, 2(1) pp.1-17.
[22] Liyanapathirana D. S. and Poulos H. G. (2010), “Analysis of pile behaviour in liquefying sloping ground”, Computers and Geotechnics, 37(1-2) pp.115-124.
[23] Lopez-Caballero F. and Farahmand-Razavi A. M. (2008), “Numerical simulation of liquefaction effects on seismic SSI”, Soil Dynamics and Earthquake Engineering, 28(2) pp.85-98.
[24] Mondal G. and Rai D. C. (2008), “Performance of harbour structures in Andaman Islands during 2004 Sumatra earthquake”, Engineering Structures, 30(1) pp.174-182.
[25] Naranjo J. A. and Clavero J. E. (2005), “A rare case of grass flow induced by the M8.4 Arequipa earthquake, June 2001, in the Altiplano of Northern Chile”, Quaternary Research, 64(2) pp.242-248.
[26] Newmark N. M. (1959), “A method of computation for structural dynamics”, Journal of Engineering Mechanics, ASCE, 85 (EM3) pp.67-94.
[27] Noda T., Asaoka A. and Nakano M. (2008), “Soil-Water Coupled Finite Deformation Analysis Based on a Rate-Type Equation of Motion Incorporating the Sys Cam-Clay Model”, Soils and Foundations, 48(6) pp.771-790.
[28] Onoue A., Yasuda S., Toyota H., Inotsume T., Kiku H., Yamada S., Hosaka Y., Tsukamoto Y., Towhata I., Wakai A. and Ugai K. (2011), “Review of Topographic and Soil Conditions for Liquefaction-Related Damage Induced by the 2007 Off Mid-Niigata Earthquake”, Soils and Foundations, 51(3) pp.533-548.
[29] Papathanassiou G., Seggis K. and Pavlides S. (2011), “Evaluating earthquake-induced liquefaction in the urban area of Larissa, Greece”, Bulletin of Engineering Geology and the Environment, 70(1) pp.79-88.
[30] Poran, C. J. and Rodriguez, J. (1992). “A finite element analysis of impact behavior of sand”. Soils and Foundations, Vol. 32, No. 4, pp. 68-80.
[31] Rahmani A. and Pak A. (2012), “Dynamic behavior of pile foundations under cyclic loading in liquefiable soils”, Computers and Geotechnics, 40 pp.114-126.
[32] Ravichandran N., Machmer B., Krishnapillai H. and Meguro K. (2010), “Micro-scale modeling of saturated sandy soil behavior subjected to cyclic loading”, Soil Dynamics and Earthquake Engineering, 30(11) pp.1212-1225.
[33] Struckmeier V. (2007), “A computational model for seismically induced liquefaction”, Mechanik-Zentrum der Techn. Univ..
[34] Taiebat H. A. and Carter J. P. (2000), “A semi-empirical method for the liquefaction analysis of offshore foundations”, International Journal for Numerical and Analytical Methods in Geomechanics, 24(13) pp.991-1011.
[35] Takahashi A., Sugita H. and Tanimoto S. (2010), “Forces acting on bridge abutments over liquefied ground”, Soil Dynamics and Earthquake Engineering, 30(3) pp.146-156.
[36] Uzuoka R., Sento N., Kazama M., Zhang F., Yashima A. and Oka F. (2007), “Three-dimensional numerical simulation of earthquake damage to group-piles in a liquefied ground”, Soil Dynamics and Earthquake Engineering, 27(5) pp.395-413.
[37] Wu G. X. (2001), “Earthquake-induced deformation analyses of the Upper San Fernando Dam under the 1971 San Fernando Earthquake”, Canadian Geotechnical Journal, 38(1) pp.1-15.
[38] Zhang J., Huo Y., Brandenberg S. J. and Kashighandi P. (2008), “Effects of structural characterizations on fragility functions of bridges subject to seismic shaking and lateral spreading”, Earthquake Engineering and Engineering Vibration, 7(4) pp.369-382.
[39] Zienkiewicz O. C. and Shiomi T. (1984), “Dynamic Behavior of Saturated Porous-Media - the Generalized Biot Formulation and Its Numerical-Solution”, International Journal for Numerical and Analytical Methods in Geomechanics, 8(1) pp.71-96.
[40] Zienkiewicz O. C., Taylor R. L., and Zhu J. Z. (2000), “The Finite Element Method: Its Basis and Fundamentals: Its Basis and Fundamentals.” Fifth edition, Butterworth-Heinemann.
[41] 李建和 (1998) , 「加勁式連續壁之三維有限元素分析」 , 碩士論文 , 國立成功大學土木工程研究所結構工程組。