台灣位於環太平洋火山地震帶，每年發生的地震不勝其數，台灣的土層條件也屬易發生液化的區域，而且地震所造成的建築物損害也有很大的一部分是土壤液化所造成，因此一直以來土壤液化是一個被重視的課題之一。
本研究以非線性能量消散原理的觀點出發，藉由反覆三軸試驗推算遲滯圈液化能量，並提出二元一次方程式來描述能量與孔隙水壓力比之間的關係，再以類神經網路訓練並模擬遲滯圈液化能量，配合現地鑽探資料推算能量式安全係數，再以統計方法推算液化機率。
本研究經比較Seed法（1997）推算出的安全係數，本研究以能量法原理推估之結果準確率較高，且結果顯示土壤試體內條件較地震的外部條件影響較大，當現地點位之初始液化能量越高或點位離震央越遠，土壤越不易液化；當能量式安全係數大於1.055時，其液化機率小於40％，屬相對安全之地區。

Taiwan is located in the Circum-Pacific Seismic Belt. The earthquakes happened very often. In addition, the stratum in southwestern Taiwan is also prone to the liquefaction induced by earthquake. Many buildings damaged during the earthquake, caused by the soil liquefaction. Therefore, soil liquefaction has been an important issue in the research related to the geotechnical seismology.

Based on the principle of non-linear energy, the energy for generating the soil liquefaction obtained from the cyclic traxial test is calculated from the hysteresis. The dual linear equation of the relationship between the energy and the pore water ratio is established. The neural network technique is need to simulate the liquefaction energy of hysteresis loop. The energy-based safety factor is calculated by using the energy and the drilling data, and the probability of liquefaction can be established by using statistics.

The energy-based safety factor of soil liquefaction developed by this study is more accurate than the safety factor which was established by Seed in 1997. As the stratum with a higher initial energy to liquefaction as with the higher distance away to the epicenter, the less possibility to generate the liquefaction. When the energy-based safety factors are greater than 1, the probability of liquefaction will be less than 40% and the areas is relatively safe.

1. 古志生，「CPT土壤分類及液化評估之研究」國立成功大學土木工程研究所博士論文，2001。
2. 李雅芬，「基於可靠度理論之土壤液化機率評估法之研究」，國立成功大學土木工程研究所博士論文，2007。
3. 亞新工程顧問股份有限公司，「土壤液化評估與處理對策研擬─第一期計畫（彰化員林鎮、大村鄉、社頭鄉）總報告」，2000。
4. 周政宏「神經網路-理論與實務」，松崗電腦圖書資料公司，台北，1996。
5. 施政杰，「能量式液化評估模式之研究」，國立成功大學土木工程研究所碩士論文，2003。
6. 施慶煌，「低塑性粉質砂土之原狀與重模試體動態性質之探討」，國立成功大學土木工程研究所碩士論文，2009。
7. 施繼揚，「遲滯圈能量原理應用於液化潛勢評估模式之建置」，國立成功大學土木工程研究所碩士論文，2009。
8. 胡玉城，「暢談類神經網路」，倚天資訊，1992。
9. 范恩碩，「以九二一集集地震案例套討細粒料對液化潛能評估之影響」，國立成功大學土木工程研究所碩士論文，2004。
10. 秦中天、陳皆儒、孫介文、王劍虹，「大地工程規範的新趨勢－可靠度分析」，岩盤工程研討會論文集，2004。
11. 張孝德、蘇木春，「機器學習-類神經網路、模糊系統以及基因演算法則」，全華科技，2003。
12. 張益騰，「類神經網路結合非線性能量消散原理應用於土壤液化潛能評估之研究，」國立成功大學土木工程研究所碩士論文，2010。
13. 張浼珣，「初步液化潛能分區法之研究」，國立成功大學土木工程研究所碩士論文，2005。
14. 張斐章，張麗秋，黃浩倫，「類神經網路理論與實務」，東華書局，台北，2003。
15. 張朝盛，「土壤液化潛能之類神經網路分析」，國立交通大學土木工程研究所碩士論文，2000。
16. 張舜孔，「類神經網路應用於阿里山公路邊坡破壞因子之分析研究」，2003。
17. 張維哲，「土壤取樣方式對低塑性粉土值砂動態性質探討」，國立成功學土木工程研究所碩士論文，2010。
18. 陳俶季，「土壤液化潛能之風險評估」，地工技術雜誌，第38期，第5~16頁，1992。
19. 陳景文，「CPT資料在液化危害度估之應用」，國科會計畫，2002。
20. 陳順宇，「多變量分析」，華泰書局，2000。
21. 陳毓山，「螞蟻演算法最佳化倒傳遞類神經網路於土層剪力波速評估之研究」，國立台灣大學土木工程研究所碩士論文，2003。
22. 陳嘉謙，「飽和砂土等向及非等向壓密不排水三軸試驗力學特性之研究」，長榮大學土地管理與開發學系研究所碩士論文，2008。
23. 彭成麒，「貫入試驗之倒傳遞類神經網路與頻散曲線之有線差分法評估地盤剪力波速」，國立台灣大學土木工程研究所碩士論文，2002。
24. 焦李成，「神經網路系統理論」儒林圖書股份有限公司，1991。
25. 辜炳寰，「類神經網路於土壤液化評估之應用」，國立成功大學土木工程研究所碩士論文，2002。
26. 葉怡成，「類神經網路模式應用與實作」，儒林圖書，2000。
27. 劉晉宏，「基因演算法自動演化類神經網路應用於飽和砂土不排水三軸應力－應變行為之模擬」，長榮大學土地管理與開發學系研究所碩士論文，2009。
28. 蔡維倫，「地震能量於液化評估準則建立之應用」，國立成功大學土木工程研究所碩士論文，2002。
29. 賴聖耀、林炳森、李豐博、謝明志，「荷式錐貫入試驗與液化可靠度之相關研究」，土木水利，第十六卷，第二期，第43-60頁，1989。
30. 鍾永琪，「屏東地區土層液化潛能評估」，國立成功大學土木工程學系碩論文，2002。
31. 羅建民，「剪力波速評估土壤液化潛能－模糊類神經網路」，國立台灣大學土木工程研究所碩士論文，2003。
32. 羅華強，「類神經網路-MATLAB的應用」，高立圖書，2005。
33. AlKahatib, M., “Liquefaction Assessment by Strain Energy Approach,” Ph.D. thesis, Wayne State University, p. 212 ,1994.
34. Baziar, M.H. and Jafarian, Y., ”Assessment of Liquefaction Triggering Using Strain Energy Concept and ANN Model: Capacity Energy,” Soil Dynamics and Earthquake Engineering 27, pp. 1056-1072 ,2007.
35. Berrill, J.B. and Davis R.O., “Energy Disssipation and Seismic Liquefaction of Sands: Revised Model”, JSSMFE Soil and Foundations Vol. 25, No.2, pp. 106-118, 1985.
36. Brune, J.N., "Tectonic Stress and The Spectra of Seismic Shear Waves," J. Geophys.Res.75, pp. 4997-5009,1970.
37. Casagrande, A., “Characteristics of Cohesionless Soil Affecting the Stability of Slope and Earth Fills,” Journal of the Boston Society of Civil Engineering, reprinted in Contributions to Soil Mechanics, Boston Society of Civil Engineering, pp. 257-276,1936.
38. Chen, Y.R., “ Behavior of a Fine Sand in Triaxial, Torsional and Rotational Shear Tests,” Ph.D. Dissertation, Department of Civil and Environmental Engineering, University of California, Davis, USA,1995.
39. Chen, Y.R., Hsieh, S.C., Chen, J.W. and Shih, C.C., ”Energy-based Probabilistic Evaluation of Soil Liquefaction,” Soil Dynamics and Earthquake Engineering 25, pp. 55-68,2005.
40. Cybenko G., “Approximation by Superpositions of a Sigmoidal Function,” Urbana: University of Illinois,1989.
41. Davis, R.O. and Berrill J.B., “Energy Dissipation and Seismic Liquefaction in Sands,” Earthquake Engineering and Structure Dynamics, Vol. 10, pp. 59-68,1982.
42. Davis, R.O. and Berrill J.B., “Pore Pressure and Dissipated Energy in Earthquake-Field Verification,” Journal of Geotechnical Engineering,ASCE, Vol. 127, No.3, March （2001）.
43. Dobry, R., Ladd, R.S., Yokel, F.Y., Chung, R.M., and Powell, D., “Prediction of Pore Water Pressure Buildup and Liquefaction of Sands During Earthquake by the Cyclic Strain Method,” NBS Building Science Seriess138, US Department of Commerce, pp. 152 ,1982.
44. Garson, G.D., ”Interpreting Neural Network Connection Weights,” AI Expert, 6（7）, pp. 47-51,1991.
45. Geller, R.J., "Scaling Relations for Earthquake Source Parameters and Magnitudes," Bull. Seism. Soc. Am., 66 , pp. 1501-1523,1976.
46. Goh, A.T.C., ”Back-propagation Neural Networks for Modeling Complex Systems,” Artificial Intelligence in Engineering , pp. 143-151,1995.
47. Green R.A., Mitchell J.K., Polito C.P., “Energy-based excess pore pressure generation model for cohesionless soils,” In: Proceedings of the John Booker memorial symposium, Sydney, Australia, A.A. Balkema Publishers, pp. 383-390,2000.
48. Green, R.A., “Energy-based evaluation and Remediation of Liquefiable soils,” Ph.D. thesis, Civil Engineering, Virginia Polytechnic Institute and State Univ,2001.
49. Gutenberg, B. and Richter, C.F., “Magnitude and Energy of Earthquakes, ” Ann. Geofis., 9, pp. 1-15,1956.
50. Hall, W.J. and McCabe, S.L., ”Current Design Spectra: Background and Limitations, Earthquake Hazards and the Design of Constructed Facilities in the Eastern United States,” Annals of the New York Academy of Sciences, pp. 222-233,1989.
51. herif, M.A., Ishibashi, I., and Tsuchiga, C., “Saturated Effects on Initial Soil Liquefaction,” Journal of the Geotechnical Engineering Division, ASCE Vol. 103, No. 8, pp. 914-917,1977.
52. Holland, J. H., “Adaptation in Natural and Artificial Systems,” second ed. Cambridge: MIT Press, MA. ,1992.
53. Idriss, I.M., and Seed, H.B., ”Seismic Response of Horizontal Layers,” Journal of the Soil Mechanics and Foundations Divion, pp. 1003-1031,1968.
54. Ishihara, K., and Tadatsu, H., “Effects of Over-consolidation k0 Conditions on the Liquefaction Characteristics of Sands,” Soils and Foundations, Vol. 19, No. 4, pp. 59-68 ,1979.
55. Ishihara, K., Sodekawa, M., and Tanaka, Y., “Effect of Over consolidation on Liquefaction Characteristic of Sand Containing Fine”, Dynamic Geotechnical Test, American Society for Testing and Materials,pp. 246-264 ,1978.
56. Iwasaki, T., “Soil Liquefaction Study in Japan: State-of-the-Art,” Soil Dynamics and Earthquake Engineering, Vol. 5, No. 1 ,1986.
57. Iwasaki, T., Tatsouoka, F., and Takagi, Y., “Shear Moduli of Sand Under Cyclic Torsional Shear Loading,” Soils and Foundations, Vol. 18, No. 14, pp. 1-18,1978.
58. Juang C.H., Lu C.C., and Hwang J.H.,” Assessing probability of surface manifestation of liquefaction at a given site in a given exposure time using CPTU,” Engineering Geology 104, pp.223-231, 2009.
59. Juang, C.H., and Caroline J, Chen, “A Rational Method for Development of Limit State for Liquefaction Evaluation Based on Shear Wave Velocity Measurements,” Int. J. Numer. Anal. Meth. Geomech., 24, 1-27,2000.
60. Juang, C.H., and Caroline J, Chen, ”CPT-Based Liquefaction Evaluation Using Artificial Neural Networks,” Computer-Aided Civil and Infractructure Engineering Vol. 14,pp.221-229,1999.
61. Juang C.H., Caroline J. Chen, and Jiang T., “Probabilistic Framework for Liquefaction by Shear Wave Velocity,” Journal of Geotechnical and Geoenvironmental Engineering, 2001.
62. Juang C.H., and David Kun Li, “Assessment of liquefaction hazards in Charleston quadrangle, South Carolina,” Engineering Geology 92, pp. 59-72, 2007.
63. Juang C.H., Jiang T., and Ronald D. Andrus, ”Assess Probability-based Methods for Liquefaction Potential Evaluation,” Journal of Geotechnical and Geoenvironmental Engineering, July 2002.
64. Juang C.H., Sunny Ye Fang, Eng Hui Khor, “First-Order Reliability Method for Probabilistic Liquefaction Triggering Analysis Using CPT,” Journal of Geotechnical and Geoenvironmental Engineering, 2006.
65. Juang C.H., Susan Hui Yang, and Haiming Yuan, ”Model Uncertainty of Shear Wave Velocity-Based Method for Liquefaction Potential Evaluation,” Journal of Geotechnical and Geoenvironmental Engineering, 2005
66. Kramer, S.L., Geotechnical Earthquake Engineering, Prentice Hall Publishing, Upper Saddle River, NJ, p. 653,1996.
67. Kutter, B.L., Chen, Y.R., and Shen, C.K., “Triaxial and torsional shear test results for sand, Contract Report to Naval Civil Engineering Laboratory,” Report No. CR94.003-SHR, Naval Facilities Engineering Service Center, Port Hueneme, CA, USA, 1994.
68. Ku C.S., Lee D.H., Juang C.H., and Wu J.H., “Evaluation of Soil Liquefaction in the Chi-Chi, Taiwan Earthquake Using CPT Data,” Special issue on soil liquefaction Soil Dynamics and Earthquake Engineering, 2003.
69. Law, K.T., Cao, Y.L., and He, G.N., “An Energy Approach for Assessing Seismic Liquefaction Potential,” Canadian Geotechnical Journal, 27（3）, pp. 320-329,1990.
70. Lee D.H., Juang C.H., Ku C.S., “Liquefaction performance of soils at the site of a partially completed ground improvement project during the 1999 Chi-Chi earthquake in Taiwan,” Can Geotech. J. Vol. 38, pp. 1241-1253,2001.
71. Lee, M.K.W. and Finn, W.D.L. ,“Dynamic Effective Stress Response Analysis of Soil Deposits with Energy Transmitting Boundary Including Assessment of Liquefaction Potential,” Soil Mechanics Series No. 38, University of British Columbia, Vancouver, Canda ,1978.
72. Lee. Y.F., Chi Y.Y., Juang C.H., Lee D.H. “Annual probability and return period of soil liquefaction in Yuanlin, Taiwan attributed to Chelungpu Fault and Changhua Fault,” Engineering Geology 114, pp. 343-353, 2010.
73. Liao, S. C. and Whitman, R. V., “Overburden Correction Factors for SPT in Sand”, Journal of Geotechnical Engineering, ASCE, Vol. 112, No. GT3, pp. 373 -377, 1986.
74. Mulilis, J.P., Mori, K., Seed, H.B., and Chan, C.K., “Resistance to Liquefaction Due to Sustained Pressure,” Journal of the Geotechnical Engineering Division, ASCE, Vol. 103, No. GT7, pp. 793-797 ,1977.
75. Nemat-Nasser, S. and Shokooh, A., “A Unified Approach Densification and Liquefaction of Cohesionless Sand in Cyclic Shearing,” Canadian Geotech. J. 16, pp. 659-678 ,1979.
76. Ostadan, F., Deng, N.,and Arango, I., “Energy-Based Method for Liquefaction Potential Evaluation,” Phase I-Feasibility Study, U.S. Department of Commerce, Technology Administration, National Institute of Standards and Technology, Building and Fire Research Laboratory, August ,1996.
77. Peck, R. B., Hanson, W. E. and Thornburn, T. H., “Foundation Engineering,” Wiley , New York,1974.
78. Randall, M.J., "The Spectral Theory of Seismic Sources," Bull. Seism. Soc. Am., 63, pp. 1133-1144,1973.
79. Rumelhart D.E., Hinton, G.E., Williams, R.J., “Learning internal representation by error propagation,” in Parallel Distributed Processing, D. E. Rumelhart and McClelland （Eds）, MIT, Press, Cambridge, MA, Vol. 1, pp.318-362, 1986.
80. Schofield, A. and Wroth, P., “Critical State Soil Mechanics,” McGraw-Hill Book Company, New York, pp. 310,1968.
81. Seed, H.B., Idriss, I.M., Makdisi, F. and Banerji, N., “Representation of Irregular Stress Time Histories by Equivalent Uniform Stress Series in Liquefaction Analysis”, EERC Report 75-29, Earthquake Engineering Research Center, University of California, Berkeley, 1975.
82. Seed, H.B., Tokimatsu, K., Harder, L.F. and Chung, R.M., “Influence of SPT Procedures in Soil Liquefaction Resistance Evaluations”, Journal of Geotechnical Engineering, ASCE, Vol. 111, No. 12, pp. 1425-1445,1985.
83. Seed, H.B. Peacock, ”Test Procedure for Measuring Soil Liquefaction Characteristics,” Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 97, No. SM8, pp. 1099-1119 ,1971.
84. Seed, H.B., and Idriss, I.M., “Simplified Procedure for Evaluating Soil Liquefaction Potential,” Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 97, No. SM8, pp. 1249-1273,1971.
85. Seed, H.B., Tokimatsu, K., Harder, L.F., and Chung, R.M., “The Influence of SPT Procedure in Soil Liquefaction Resistance Evaluation,” Report No. EERC 84-15, Earthquake Research Center, University of California, Berkeley, California ,1984.
86. Simcock, K.J., Davis,R.O., Berrill, J.B., and Mullenger, G., “Cyclic Triaxial Tests with Continuous Measurement of Dissipated Energy,” Geotechnical Testing Journal, 6（1）, pp. 35-39,1983.
87. Streeter, V.L., Wylie, E.B., and Richart, F.E., “Soil Motion Computations by Characteristic Methods,” ASCE National Structural Engineering Conference, San Francisco ,1973.
88. Tokimatsu, K., and Yoshimi, Y., “Empirical Correlation of Soil Liquefaction Based on SPT N-Value and Fines Content,” Soils and Foundations, JSSMFE, Vol. 23, No. 4, pp. 56-74 ,1983.
89. Trifunac, M.D., “Empirical Criteria for Liquefaction in Sands via Standard Penetration Tests and Seismic Wave Energy,” Soil Dynamics and Earthquake Engineering, Vol. 14, pp,419-426 ,1995.
90. Youd, T. L., and Idriss, I. M., “Liquefaction Resistance of Solils: Summary Report from the 1996 NCCER and 1998 NCCER/NSF Workshops on Evaluation of Liquefaction Resistance of Soils,” Journal of Geotechnical and Geoenviromental Engineering, April, pp. 297-313,2001.