臺灣博碩士論文加值系統

土壤液化是大地工程領域所關切的重要議題，如何正確的判斷場址液化與否乃是專家及學者所追求的目標。過去數十年所發展的土壤液化評估方法多以現地試驗資料所發展的簡易經驗法為主，且目前國內、外所採行之規範以及工程實務上亦多引用該法所發展之經驗公式。然而地震機制及土層特性具有高度不確定性，不易選擇適當的經驗公式來進行迴歸分析，因此各專家學者仍試圖找出較傳統經驗公式更為合理簡便且更加準確判斷土壤液化的分析模式。
隨著科技的進步，人工智慧(Artificial Intelligence, AI)已成為現今熱門科技研究及發展的電腦應用技術之一，簡單的說，它是利用電腦技術去模擬人類腦部思考運作，使電腦懂得自行分析及理解事物的一種科技應用技術。人工智慧的研究在70年代末期，專家系統(Expert System)發展時期達到高峰，之後由於技術上逐漸陷入瓶頸而陷入低潮。到了90年代中期，技術上逐漸有所突破，尤其是機器學習(Machine Learning)與模糊邏輯(Fuzzy Logic)資訊處理方法的發明，引起人們對人工智慧的廣泛注意與憧憬。因此AI又成為一門國際間競相投入的研究題材。
機器學習(Machine Learning)算是人工智慧領域最受關注的一支，目前應用範疇相當廣泛，而且已經成功的應用在文字、語音及影像辨識系統上。在大地工程領域方面，藉由能模擬人類思維與學習功能的機器學習理論，例如人工類神經網路(Artificial Neural-Networks, ANN)及支持向量機 (Support Vector Machine, SVM) 對於土壤液化這種高度非線性問題，均展現出相當優越的分析處理能力，許多學者研究亦證明此一技術對於處理土壤液化問題是一強而有力的工具，其優越性明顯高於傳統經驗評估法。因此本研究以機器學習理論為主要研究方法，針對目前應用較廣之ANN 及SVM等方法進行探索，期能建立快速及高準確率之視窗化液化評估模式，做為工程設計以及防災規劃之參考。
研究結果發現ANN及SVM所表現之液化分類正確率均優於傳統之簡易經驗法，其中又以SVM高達98.3 % 之分類正確率最為出色。SVM具有嚴格的統計理論基礎及處理高度非線性問題之能力，經證實可以應用在工程實務上，因此本研究發展一套以SVM 理論為基礎的液化評估程式LA-SVM (Liquefaction Assessment based on SVM)，它是建構在MATLAB/GUI (Graphical User Interface) 環境下的視窗作業系統。這個LA-SVM簡易視窗環境提供一個直覺、友善的操作介面，使用者不需任何圖表、公式及操作手冊，只須操作滑鼠游標點選視窗選項及輸入訓練資料及參數範圍即可迅速得到預測資料之分類結果及預測正確率。這套LA-SVM程式使得液化評估變得非常簡單，並且可以得到極高的準確率，值得後續之推廣及應用。

Soil liquefaction is a vital topic of concern in the field of geotechnical engineering. Experts and scholars in this field seek methods to correctly determine whether liquefaction will occur at a site. The methods developed over the past several decades for evaluating soil liquefaction primarily involve simple empirical methods using in situ test data. Moreover, the current specifications and engineering practices adopted both domestically and internationally reference empirical formulae developed through these simple empirical methods. However, the great uncertainties inherent in earthquake mechanisms and soil properties complicate the selection of a suitable empirical formula for conducting regression analysis. Therefore, experts and scholars have attempted to discover an analytical method that is simpler, more reasonable, and better able to accurately determine soil liquefaction than traditional empirical formulae.
With technological advances, artificial intelligence (AI) has become a popular topic in modern technological research and the development of computer applications technology. In a word, AI is an application of information technology that uses computing technology to simulate the thought processes of the human brain, thereby allowing a computer to conduct analyses and classification autonomously. Research into AI began in the 1950s and reached a peak at the end of the 1970s with the development of the Expert System. After this point, AI research met with certain obstacles and progressed slowly until the mid-1990s when several technological breakthroughs occurred. In particular, the invention of information processing methods such as machine learning and fuzzy logic incited widespread attention and excitement concerning AI. Artificial intelligence once again became a research topic of great interest in the international community.
Among the branches of AI, machine learning receives the most attention. It currently demonstrates extensive applications, and has already been implemented successfully in word, voice, and image recognition systems. Applications of machine learning theory-for example, artificial neural networks (ANN) and support vector machines (SVM)—can simulate human thought and learning functions. These applications are advantageous for analytical processing of highly nonlinear relationships observed in geotechnical engineering domains such as soil liquefaction. Several scholars have confirmed that this technology is a powerful tool for handling liquefaction issues and is superior to traditional empirical assessment methods. Therefore, this study employs machine learning theory as a primary research tool to investigate the wider applications of current ANN and SVM methods. The study establishes a rapid and highly precise liquefaction evaluation model for Windows, which can serve as a reference for engineering design as well as disaster prevention and planning.
The results of this study show that ANN and SVM surpass traditional simple empirical methods because of their accuracy in classifying liquefaction. Of the 2 methods, SVM is the most remarkable; it demonstrates a superior classification accuracy of 98.3%. SVM have proved to achieve good generalization performance and can be used as a practical tool for the prediction of soil liquefaction. Consequently, this study develops a Liquefaction Assessment program based on SVM (LA-SVM) that is constructed within a MATLAB/GUI (Graphical User Interface) Windows environment. This simple Windows-based LA-SVM provides an intuitive and user-friendly interface that obviates the use of graphs, formulae, or operating manuals. The user need only select items in Windows and enter training data and ranges to rapidly obtain classification results for forecast data and prediction accuracy. This LA-SVM program simplifies liquefaction assessment and achieves high accuracy rates, and should be promoted for further application.

摘要 i
ABSTRACT iii
誌 謝 vi
TABLE OF CONTENTS vii
LIST OF TABLES x
LIST OF FIGURES xi
CHAPTER 1 Introduction 1
1.1 Motivation 1
1.2 Objectives and Approach 3
1.3 The Organization of the Thesis 5
CHAPTER 2 Literature Review 7
2.1 Overview of Liquefaction 7
2.1.1 Definition 7
2.1.2 Mechanism of Soil Liquefaction 8
2.1.3 Liquefaction Assessment Method 9
2.2 Traditional empirical Methods 10
2.2.1 SPT-based Method 10
2.2.2 CPT-based method 14
2.3 Artificial Intelligence 15
2.3.1 Artificial Neural Network 17
2.3.2 Support Vector Machine 20
CHAPTER 3 Liquefaction Assessment by Using MADM method 31
3.1 Introduction 31
3.2 Geological Condition 32
3.3 Liquefaction Potential Evaluation Method 33
3.4 Liquefaction Evaluation during Chi-Chi Earthquake 35
3.5 Simple Additive Weighting method 39
3.5.1 Criteria 40
3.5.2 Normalized Performance Value 41
3.5.3 Mean of Performance Value 42
3.5.4 Sequence of Decision-Making 42
3.6 Summary 45

CHAPTER 4 CPT-Based Artificial Neutral Network in Liquefaction Assessment 52
4.1 Introduction 52
4.2 Elements of Analysis 54
4.2.1 Fuzzy Logic 54
4.2.2 Subtractive Clustering 56
4.3 Fuzzy Neural System 59
4.3.1 Establishment of Fuzzy Rule 59
4.3.2 Neural Network 61
4.4 Data Set and Preprocessing 65
4.5 Determination of Neurons in Sub-Network 67
4.5.1 Effective Radius of Optimized Subtractive Clustering 68
4.5.2 Adopted α-cut 69
4.6 Analysis Results 69
4.7 Summary 72
CHAPTER 5 CPT-Based Simplified Liquefaction Assessment by using Fuzzy-Neural Network 87
5.1 Introduction 87
5.2 Limit State 89
5.3 Modeling of Field Liquefaction Records 91
5.4 Determination of Limit State Function 92
5.5 Summary 96
CHAPTER 6 Applying Support Vector Machine for Liquefaction Assessment 100
6.1 Introduction 100
6.2 Overview of Support Vector Machine 101
6.2.1 Linear SVM 101
6.2.2 Linear inseparable SVM 104
6.2.3 Nonlinear inseparable SVM 106
6.3 Cross-Validation 107
6.4 Grid Search 108
6.5 Performance Evaluation 109
6.6 Summary 112


CHAPTER 7 Conclusions 117
7.1 Performance Comparison of SVM and ANN 117
7.2 Applications of SVM Classification 118
7.3 Conclusion 120
References 123

1. Agrawal, G., Chameau, J.L. and Bourdeau, P.L., “Assessing the Liquefaction Susceptibility at a Site Based on Information from Penetrating Test,” Artificial neural networks for civil engineers: Fundamentals and applications. New York: ASSE, pp.185-214 (1997).

2. Arulanandan, K., Yogachandran, C., Meegoda, N.J., Ying, L. and Zhauji, S., “Comparison of the SPT, CPT, SV and electrical methods of evaluating earthquake induced liquefaction susceptibility in Ying Kou City during the Haicheng Earthquake,” Proc., Use of In Situ Tests in Geotechnical Engineering, Geotech. Spec. Publ. No. 6, ASCE, pp. 389-415 (1986).

3. Baziar, M.H. and Nilipour, N., “Evaluation of liquefaction potential using neural-networks and CPT results,” Soil Dynamics and Earthquake Engineering, Vol. 23, No. 7, pp. 631-636 (2003).

4. Bennett, M.J., McLaughlin, P.V., Sarmiento, J.S. and Youd, T.L., Geotechnical investigation of liquefaction sites, Imperial Valley, California. Open-File Rep. No. 84-252, U.S. Geological Survey, Menlo Park, California (1984).

5. Bennett, M.J., “Liquefaction analysis of the 1971 ground failure at the San Fernando Valley Juvenile Hall,” California. Bull. Assoc. of Engng. Geologists, Vol. 26, No. 2, pp. 209-226 (1989).

6. Bennett, M.J. and Tinsley, J.C.III., “Geotechnical data from surface and subsurface samples outside of and within liquefaction-related ground failures caused by the October 17, 1989,” Loma Prieta Earthquake, Santa Cruz and Monterey Counties, California. Open-File Rep. No. 95-663, US. Geological Survey, Menlo Park, California (1995).

7. Bezdek, J.C. Fuzzy Mathematics in pattern classification. Ph. D. Dissertation, Cornell University, Ithaca, N.Y. (1973).

8. Bierschwale, J.G. and Stokoe, K.H.II., “Analytical evaluation of liquefaction potential of sands subjected to the 1981 Westmorland Earthquake,” Journal of Geotechnical Engineering, Rep. No.GR-84-15, Univ. of Texas at Austin, Tex. (1984).

9. Boulanger, R.W., Mejia, L.H. and Idriss, I.M., “Liquefaction at Moss Landing during Loma Prieta earthquake,” Journal of Geotechnical and Geoenvironmental Engineering, Vol. 23, No. 5, pp. 453-467 (1997).

10. Boser, B.E., Guyon, I.M., and Vapnik, V.N., “A training algorithm for optimal margin classiers,” In Proceedings of the 5th Annual Workshop on Computational Learning Theory, pp. 144-152. ACM Press, (1992).

11. Bradley, P.S. and Mangasarian, O.L. Feature selection via concave minimization andsupport vector machines. In J. Shavlik, editor, Machine Learning Proceedings of the Fifteenth International Conference(ICML '98), San Francisco, California, pp. 82-90 (1998).

12. Chang, C.C. and Lin, C.J., LIBSVM: a library for support vector machines, software available at http://www.csie.ntu. edu.tw/~cjlin /libsvm. (2001).

13. Chern, S.G., Hu, R F., Chang, Y.J. and Tsai, I.F., “Fuzz-ART Neural Networks for Predicting Chi-Chi Earthquake Induced Liquefaction in Yuan-Lin Area,” Journal of Marine Science and Technology, Vol. 10, No. 1, pp. 21-32 (2002).

14. Chen J.W. and Chen C.Y., “A fuzzy methodology for evaluation of the liquefaction potential,” Microcomputers in Civil Engineering. Vol.12, No. 3, pp. 193-204 (1997).

15. Chern, S.G., Lee, C.Y. and Wang, C.C., “CPT-Based Liquefaction Assessment by Using Fuzzy-Neural Network,” Journal of Marine Science and Technology, Vol. 16, No. 2, pp. 139-148 (2008).

16. Chern, S.G. and Lee, C.Y., “CPT-Based Simplified Liquefaction Assessment by Using Fuzzy-Neural Network,” Journal of Marine Science and Technology, Vol. 17, No. 4, pp. 326-331 (2009).

17. Chiu, S.L., “Fuzzy model identification based on cluster estimation,” Journal of Intelligent and Fuzzy System, Vol. 2, pp. 267-278 (1994).

18. Cortes, C. and Vapnik, V., “Support vector networks,” Machine Learning, Vol. 20, pp. 273- 297 (1995).
19. Faruto and Liyang, LIBSVM-faruto Uliti- mate Version, a toolbox with implement for support vector machine based on libsvm, software available at http://www. matlabsky.com (2011).

20. Fletcher, R., Practical methods of optimization, 2nd edition, Wiley, Chichester, New York, (1987).

21. Fletcher, T., Support vector machine explained, Technical report, www.cs.ucl.ac.uk/staff/T.Fletcher/, (2009).

22. Goh, A.T.C., “Seismic liquefaction potential assessed by neural networks,” Journal of Geotechnical Engineering, ASCE, Vol. 120, No. 9, pp. 1467-1480 (1994).

23. Goh, A.T.C., “Neural network modeling of CPT seismic liquefaction data,” Journal of Geotechnical Engineering, ASCE, Vol. 122, No. 1, pp. 70-73 (1996).

24. Goh, A.T.C. and Goh, S.H., “Support Vector Machines: Their Use in Geotechnical Engineering as Illustrated using Seismic Liquefaction Data, ” Computer and Geotechnics, Vol.34, pp. 410-421(2007).

25. Gunn, S.R., Support Vector Machines for Classification and Regression, Technical Report, University of Southampton, (1998).

26. Hwang, C.L. and Yoon, K., Multiple Attribute Decision Making- Methods and Applications, Springer-Verlag, New York, pp. 99-103 (1981).

27. Hopfield, J.J. and Tank, D.W., “Neural computation of decision in optimization problems,” Biological Cybernetics, Vol. 52, pp. 141-152 (1985).

28. Hsu, C.W. and Lin, C.J., “A simple decomposition method for support vector Machine, ”Machine Learning, Vol. 46, pp.219-314 (2002)

29. Hsu, C.W., Chang, C.C. and Lin, C.J., A Practical Guide to Support Vector Classification, Available: http://www.csie.ntu.edu.tw/~cjlin/papers/guide/guide. pdf. Taipei, (2010).

30. Huang, Z., Chen, H., Hsu, C.J., Chen, W.H. and Wu, S., “Credit rating analysis with support vector machines and neural networks: a market comparative study. Decision Support Systems, Vol. 37, No. 4, pp. 543-558 (2004).

31. Idriss, I.M. and Boulanger, R.W., “Semi-empirical Procedures for Evaluating Liquefaction Potential During Earthquakes,” Proceedings of the 11th ICSDEE & 3rd ICEGE, pp 32 – 56, (2004).

32. Iwasaki, T., Tatsuoka, F. and Yasuda, S., “A practical Method for Assessing Soil Liquefaction Potential Based on Case Studies at Various Sites in Japan,” Proceedings of the 2nd International Conference Microzonation Safer Construction Research Application, Vol. 2, pp. 885-896 (1978).

33. Iwasaki, T., Arakawa, T. and Tokida, K., “Simplified Procedures for Assessing Soil Liquefaction During Earthquakes,” Soil Dynamics and Earthquake Engineering Conference Southampton, pp. 925-939 (1982).

34. Ishihara, K. and Yoshimi, M., “Evaluation of Settlement in Sand Deposits Following Liquefaction During Earthquakes,” Soils and Foundations, Vol. 32, No.1, pp. 173-188 (1992).

35. Japan Road Association (JRA), Specifications for Highway Bridges, Part V: Seismic Design [in Japan] (1996).

36. JSCE, Earthquake Resistant Design for Civil Engineering Structure, Earth Structure and Foundation in Japan, Japan Society of Civil Engineering (1977).

37. Juang, C.H. and Chen, C.J., “CPT-Based liquefaction evaluation using artificial neural networks,” Computer-Aided Civil and Infrastructure Engng.,Vol. 14, No. 3, pp. 221-229 (1999).

38. Juang, C.H., Chen, C.J. and Tien, Y.M., “Appraising cone penetration test based liquefaction resistance evaluation methods: Artificial neural networks approach, ”Journal of Canadian Geotechnical, Vol. 36, No. 3, pp. 443-454 (1999).

39. Juang, C.H. and Chen, C.J., “A rational method for development of limit state for liquefaction evaluation based on shear wave velocity data,” International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 24, pp. 1-27, (2000).

40. Juang, C.H., Chen, C.J. and Jiang, T., “Probabilistic framework for liquefaction potential by shear wave velocity,” Journal of Geotechnical and Geoenvironmental Engineering, Vol. 127, No. 8, pp. 670-678 (2001).

41. Juang, C.H., Haiming, Y., Lee, D.H. and Ku, C.S., “Assessing CPT-based methods for liquefaction with emphasis on the cases from the Chi-Chi, Taiwan, Earthquake,” Soil Dynamics and Earthquake Engineering, Vol. 22, pp. 241–258 (2002).

42. Juang, C.H., Yuan, H.M., Lee, D.H. and Lin, P.S., “Simplified cone penetration test-based method for evaluating liquefaction resistance of soils,” Journal of Geotechnical and Geoenvironmental Engineering, Vol. 129, No. 1, pp. 66-80 (2003).

43. Kayen, R.E., Mitchell, J.K., Lodge, A., Seed, R.B., Nishio, S. and Coutinho, R., “Evaluation of SPT-, CPT-, and shear wave-based methods for liquefaction potential assessment using Loma Prieta data,” Proc., 4th Japan-U.S. Workshop on Earthquake Resistant Design of Lifeline Facilities and Countermeasures for Soil Liquefaction, M. Hamada and T.D. O’Rouke, eds., State Univ. of New York at Buffalo, N.Y., 177-204 (1992).

44. Kayen, R.E., Mitchell J.K., Seed, R.B. and Nishio, S., Soil liquefaction in the east bay during the earthquake. The Loma Prieta, California, Earthquake of October 17, 1989: Liquefaction, T.L. Holzer, ed., U.S. Government Printing Office, Washington D.C., B61-B86 (1998).

45. Ku, C.S., Lee, D.H. and Wu, J.H., “Evaluation of soil liquefaction in the Chi-Chi, Taiwan earthquake using CPT,” Soil Dynamics and Earthquake Engineering, Vol. 24, 659-673 (2004).

46. Lee, C.Y. and Chern, S.G.,” CPT-Based Liquefaction Assessment by Using Support Vector Machine,” 22nd International Offshore and Polar Engineering Conference, Greece, Rhodes, ISOPE, (3/13/2012 accepted).

47. Lee, C.Y. and Chern, S.G.,” Application of a Support Vector Machine on Liquefaction Assessment,” Journal of Marine Science and Technology, (5/18/2012 accepted).

48. Lee, D. H., Juang, C. H. and 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,” Canadian Geotechnical Journal, Vol. 38, No. 6, pp. 1241–1253 (2001).

49. Liao, S.C.C., Veneziano, D. and Whitman, R.V., “Regression models for evaluating liquefaction probability,” Journal of Geotechnical Engineering, Vol. 114, No. 4, pp. 389-411 (1988).

50. Lin, G.F., Chen, G.R., Huang, P.Y. and Chou, Y.C., “Support Vector Machine-based Models for Hourly Reservoir Inflow Forecasting During Typhoon-warning Periods,” Journal of Hydrology, Vol. 372, No. 1-4, pp. 17-29 (2009).

51. Lin, M.L., Ueng, T.S., Chen, M.H. and Huang, S.C., “A Preliminary Study on Evaluation of Liquefaction Potential of Yuen-Lin Area,” Proceedings of International Workshop on Annual Commemoration of Chi-Chi Earthquake, Vol. III-Geot. Aspect, NCREE, Taipei, pp. 74-82 (2000).

52. Lunne, T., Robertson, P.K. and Powell, J. J. M., Cone penetration testing , Blackie Academic and professional, London. (1997)

53. MacCrimmon, K.R., Decision Making Among Multiple-Attribute Alternatives: A Survey and Consolidated Approach, RAND Memorandum, RM-4823-ARPA (1968).

54. MMA. Soil liquefaction assessment and remediation study, phase I (Yuanlin, Dachun, and Shetou), summary report and appendixes. Taipei, Taiwan: Moh and Associates (MAA) Inc; (2000). [in Chinese].

55. MMA. Soil liquefaction investigation in Nantou and Wufeng areas. Taipei, Taiwan: Moh and Associates (MAA) Inc; (2000). [in Chinese].

56. NCREE, Reconnaissance Report of the Geotechnical Hazard caused by Chi-Chi Earthquake, National Center for Research on Earthquake Engineering, Taipei, Taiwan (1999).

57. Olsen, R.S., “Cyclic liquefaction based on the cone penetrometer test,” In Proceedings of the 1996 NCEER Workshop on Evaluation of Liquefaction Resistance of Soil. NCEER-97-0022, pp. 225-75 (1997).

58. Platt, J. Sequential minimal optimization: A fast algorithm for training support vector machines. http://www.research.microsoft.com/~jplatt/smo.html.

59. Rahman, M.S. and Wang, J., “Fuzzy Neural Network Models for Liquefaction Prediction,” Soil Dynamics and Earthquake Engng., Vol. 22, pp. 685- 694 (2002).

60. Robertson, P.K. and Campanella, R.G., Guidelines for use, Interpretation and application of the CPT and CPTU. UBC, Soil Mechanics Series No.105, Civil Eng. Dept., Vancouver, B.C., V6T 1W5, Canada (1986).

61. Robertson, P.K. and Wride, C.E., “Cyclic liquefaction and its evaluation based on SPT and CPT, ” In Proceedings of the NCEER Workshop on Evaluation of Liquefaction Resistance of Soils, Tech. Rep. No. NCEER-97-0022 (1997).

62. Robertson, P.K. and Wride, C.E., “Evaluating Cyclic liquefaction Potential of Sands using the Cone Penetration Test, ” Canadian Geotechnical Journal, NRC, Vol.35, pp. 442-459 (1998).

63. Samui, P. and Sitharam, T.G., “Machine learning modeling for predicting soil liquefaction susceptibility,” Journal of Natural Hazard and Earth System Science, Vol. 11, pp. 1-9 (2011).

64. Seed, H.B. and Idriss, I.M.,“ Simplified Procedure for Evaluating Soil Liquefaction Potential,” Journal of Soil Mechanics Found. Division, ASCE, Vol. 97, No. SM9, pp. 1249-1273 (1971).

65. Seed, H.B., “Soil liquefaction and cyclic mobility evaluation for level ground during earthquake,” ASCE, Journal of the Geotechnical Engineering Division, Vol. 105, No. GT2, pp. 201-255(1979).

66. Seed, H.B., Tokimatsu, K. and Harder, L.F., “Influence of SPT Procedure In Soil Liquefaction Resistance Evaluations,” Journal of Geotechnical Engineering, ASCE, Vol. 109, No. 3, pp. 458-482 (1983).

67. Seed, H.B., Tokimatsu, K., Harder, L.F. and Chung, R.M., “Influence of SPT Procedure on Soil Liquefaction Resistance Evaluations,” Journal of Geotechnical Engineering, ASCE, Vol. 111, No. 12, pp. 1425-1445 (1985).

68. Shibata, T. and Teparaksa, W., “Evaluation of liquefaction potential of soils using cone penetration tests,” Soils and Foundations, Vol. 28, No. 2, pp. 49–60 (1988).

69. Stark, T.D. and Olson, S.M., “Liquefaction resistance using CPT and field case histories,” Journal of Geotechnical Engineering, Vol. 121, No. 12, pp. 856–869 (1995).

70. Sterlin, P., Overfitting Prevention with Cross-Validation, Paris, (2007).

71. Suykens, J.A.K. et al., Least Squares Support Vector Machines. World Scientific, Singapore. (2002).

72. Tinsley, J.C. III, Egan, J.A., Kayen, R.E., Bennett, M.J., Kropp, A. and Holzer, T.L. Strong ground and failure, appendix: Maps and descriptions of liquefaction and associated effects. The Loma Prieta, California, Earthquake of October 17, 1989: Liquefaction, T.L. Holzer, ed., U.S. Government Printing Office, Washington, D.C., B287-B314 (1998).

73. Tokimatsu, K. and Yoshimi, Y., “Empirical Correlation of Soil Liquefaction Based on SPT-N Value and Fines Contents,” Soil and Foundations, Vol. 23, No. 4, pp. 56-74 (1983).

74. Tokimatsu, K. and Uchida, A., “Correlation between Liquefaction Resistance and Shear Wave Velocity,” Soil and Foundations, Vol. 30, No. 2, pp. 33-42 (1990).

75. Toprak, S., Holzer, T.L., Bennett, M.J. and Tinsley, J.C. III. , “CPT- and SPT-based probabilistic assessment of liquefaction,” Proc., 7th U.S.-Japan Workshop on Earthquake Resistant Design of Lifeline Facilities and Counter measures against Liquefaction, Seattle, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, N.Y., pp. 69-86 (1999).

76. Tuttle, M., Law, K.T., Seeber, L. and Jacob, K., “Liquefaction and ground failure induced by the 1988 Saguenay, Quebec, Earthquake,” Canadian Geotech. J., Ottawa, Canada, Vol. 27, No.5, pp. 580-589 (1990).

77. U.S. Geological Survey (USGS). Effectof Loma Prieta Earthquake on the Marina District, San Francisco, CA. Open-File Rep. No. 90-253, U.S. Geological Survey, Menlo Park, California (1990).

78. Wang, J. and Rahman, M.S., “A neural network model for liquefaction-induced horizontal ground displacement,” Soil Dyn Earthquake Engng., Vol. 18, pp. 555-568 (1999).

79. Vapnik, V.N., The nature of statistical learning theory, Springer -Verlag, New York, (1995).

80. Vapnik, V.N., Statistical Learning Theory, New York: Wiley, (1995).

81. Vincent, P. and Bengio, Y., “Kernel matching pursuit,” Machining. Learning, Vol. 48, pp. 165–187 (2002).

82. Wayne, A.C., Donald, O.D., Jeffrey, P.B. and Hassen, H. Direct measurement of liquefaction potential in soils of Monterey County, California. The Loma Prieta, California, Earthquake of October 17, 1989: Liquefaction, T. L. Holzer, ed., U.S. Government Printing Office, Washington, D.C., B181-B208 (1998).

83. Yager, R.R. and Filev, D.P. Approximate clustering via the mountain method. Tech. Report #MII-1305, Machine Intelligence Institute, Iona College, New Rochelle, NY. Also to appear in IEEE Trans. On Systems, Man & Cybernetics (1992).

84. Youd, T.L., Idriss. I.M., Andrus, R.D., Arango, I., Castro, G., Christian, J.T., Dobry, R., Finn, W.D.L., Harder, L.F., Hynes, M.E., Ishihara, K., Koester, J.P. Liao, S.C., Marcuson III, W.F., Martin, G.R., Mitchell, J.K., Moriwaki, Y., Power, M.S., Roberston, P.K., Seed, R.B. and Stoke II, K.H., “Liquefaction resistance of soils: summary report from 1996 NCEER and 1998 NCEER/NSF workshops on evaluation of liquefaction resistance of soils,” Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 127, No. 10, pp.817-833 (2001).

85. Zadeh, L. A. “Fuzzy Sets,” Information and Control, Vol. 8, pp. 338-353 (1965).