臺灣博碩士論文加值系統

　　軟弱黏土取樣過程所造成之擾動，改變了黏土原本結構，影響其力學性質，影響所及無法依現行一般試驗方法獲取應有之正確強度。過去一些深開挖工程，在循正常設計及施工條件下，卻依然發生失敗案例，檢討眾多災變原因之中，設計參數採用不正確黏土剪力強度是其中重大關鍵因素。因此本文針對取樣擾動對軟弱黏土強度之影響提出研究心得，除了根據學理探討擾動的現象與大小外，更根據實務工程設計需求提出簡易之分析方法。

　　由取樣擾動所衍生的後果加上現有常用的實驗室試驗，並無法有效修正黏土強度偏差。由過去的深開挖隆起破壞案例經驗指出取樣擾動及不當試驗方法導致黏土應有強度誤判。因此本文首先提出一簡易方法用於開挖隆起穩定分析中判斷現地黏土應有的強度。藉此，不但有效運用傳統試驗資料，維持原有工程分析有效便利以外，同時在實際應用上避免採用非常繁複的 試驗方法而可以繼續沿用慣用的試驗方法。

　　為達到有效運用傳統試驗方法的目的，必需藉由提昇試體品質，以獲取可靠試驗成果。因此，現階段有必要探討與試體品質相關之取樣試驗等擾動所造成的影響。由於泛稱擾動之成因不只一端，依個別影響性重要程度考量，本研究內容著重於對軟弱黏土影響最大之取樣貫入擾動上。

　　研究方法以黏土經歷之應變歷史與應變率做為薄管取樣擾動之評估指標。其中，理論方法採用流體動力學推演擾動應變理論，將黏土視為不可壓縮流體。數值方法則應用FLAC程式，解析取樣貫入過程之擾動應變，在分析過程中將土壤模擬為不可壓縮彈性材料，並據此與前項理論結果相互驗證比較。對於基本擾動行為特性而言，兩種研究方法獲致如下結論：(1)薄管取樣最大擾動應變約與取樣器厚徑比成正比；(2)取樣擾動應變率除隨厚徑比增加外，並隨著取樣之速度增大而增加；(3)取樣器刃口形狀影響擾動應變。對於實務工程而言，取樣薄管厚徑比過大、刃口截平及取樣速度過快時，容易導致黏土降伏改變強度，使得實驗結果產生偏差，誤判真實強度。進而錯估設計需求，影響工程安全。

　　降低取樣擾動最直接的方法，可藉由改進目前之取樣器達成。本研究參考各種取樣器之優點，提出一種兼顧工程及經濟價值之新型斜口式取樣器，藉數值試驗確認能有效降低擾動。

　　本文課題由實務問題而來，研究成果回饋於實務應用。透過細密的理論與數值研究過程，將心得以簡便實用的分析方法與取樣器呈現兩項具體成果，盼能改善工程應用上的困境，並緩和對黏土擾動問題的困惑。因此，提供適當的分析方法消弭取樣擾動所偏失的土壤強度，以及研發可以降低取樣擾動的取樣器，成為本文研究對於實際工程應用的兩項貢獻。

誌謝 I
摘要 II
目錄 IV
表目錄 VII
圖目錄 VIII
符號說明 XI

第一章　緒論 1
　　1-1 概說 1
　　1-2 研究動機與目的 2
　　1-3 研究內容與流程 3
　　1-4 本文內容與組織 3

第二章　軟弱黏土深開挖案例檢討與穩定分析 7
　　2-1 概說 7
　　2-2 正常壓密黏土特性 8
　　　　2-2-1 正常壓密黏土強度正規化行為 8
　　　　2-2-2 正常壓密黏土強度異向性特質 8
　　2-3 強度試驗法 9
　　2-4 正常壓密軟弱黏土 強度 13
　　2-5 隆起穩定分析原理 13
　　　　2-5-1上界原理與 強度 14
　　　　2-5-2下界原理與 強度 18
　　　　2-5-3安全係數理論分析法 20
　　2-6安全係數簡易分析法與傳統試驗強度之應用 21
　　2-7案例研究 22
　　2-8結語 28

第三章　軟弱黏土取樣貫入擾動理論研究 40
　　3-1 概說 40
　　3-2 擾動相關研究回顧 40
　　　　3-2-1試體儲存運送及修整擾動 40
　　　　3-2-2解壓擾動 41
　　　　3-2-3貫入擾動 42
　　　　3-2-4文獻回顧結語 43
　　3-3 貫入擾動理論推導 44
　　　　3-3-1應變路徑法與貫入問題 45
　　　　3-3-2錐形貫入器貫入原理 46
　　　　　　3-3-2-1流函數、勢能函數、流速 46
　　　　　　3-3-2-2均勻流 48
　　　　　　3-3-2-3點源 48
　　　　3-3-2-4均勻流與點源疊加 49
　　　　3-3-3筒型貫入器貫入原理 52
　　　　　　3-3-3-1勢能函數 ， 52
　　　　　　3-3-3-2流函數 ， 53
　　　　3-3-4取樣擾動應變及應變率分析 54
　　　　　　3-3-4-1軸向速度 及應變 54
　　　　　　3-3-4-2取樣器厚薄對軸向應變及應變率 之影響 55
　　3-4 結語 59

第四章　取樣擾動數值分析 69
　　4-1 概說 69
　　4-2 數值分析之動機及目的 69
　　4-3 數值分析應用程式 70
　　4-4 數值分析方法與結果分析 71
　　　　4-4-1 數值分析網格，邊界條件及參數 71
　　　　4-4-2 數值分析結果與討論 72

第五章　採用斜口式薄管改善取樣擾動之研究 85
　　5-1 概說 85
　　5-2 取樣薄管設計原理 85
　　5-3 斜口式取樣薄管設計及分析 88
　　5-4 分析結果與討論 89

第六章　結論與建議 97
　　6-1 結論 97
　　6-2 建議 100

附錄A 不排水強度分析法 101
附錄B 取樣擾動理論分析基礎及適用範圍檢討 102
附錄C 流體模式理論分析之座標系統 104
附錄D 薄壁圓筒型取樣器模擬 108
附錄E 採用線彈性材料模擬取樣管中心軟弱黏土行為 109

參考文獻 113
作者簡歷 124
學術著作目錄 125

1.劉泉枝，「台北盆地凝聚性土壤之不排水剪力強度與孔隙壓力參數」，中國土木水利工程學刊，第三卷，第三期，第267-270頁 (1991)。

2. 蔡錦松，「軟弱地盤深開挖工程之案例探討—台北基河路經驗」，地工技術雜誌，第45期，第5-12頁 (1994)。

3. 蔡錦松，「軟弱地盤深開挖穩定之分析—台北基河路經驗」，地工 技術雜誌，第45期，第13-22頁 (1994)。

4. Adam, J. I., & Radakrishna, H. S., “Loss of Strength due to Sampling in a Glacial Lake Deposit,” Proceedings of a Symposium on Sampling of Soil and Rock, STP 483, pp.109-120. Detroit: American Society for Testing and Materials (1971).

5. Arthur, J. R. F., and Phillips, A. B., “Homogeneous and Layered Sand in Triaxial Compression, ” Geotechnique, Vol.25, No.4, pp.799-815 (1975).

6. Atkinson, J. H., Foundations and Slopes : An Introduction to Applications of Critical State of Soil Mechanics, McGraw-Hill (UK), Berkshire, U.K., (1980).

7. Atkinson et al., “Influence of Laboratory Sample Preparation Procedures on the Strength and Stiffness of Intact Bothkennar Soil Recovered Using the Laval Sampler,” Geotechnique Vol.42, No.2 pp.349-354 (1992).

8. Brinch-Hansen, J., and Gibson, R. E., “Undrained Shear Strengths of Anisotropically Consolidated Clays,” Geotechnique, London, England, Vol.1, No.3, pp. 189-204 (1949).

9. Bjerrum, L., and Eide, O., “Stability of Strutted Excavations in Clay,” Geotechnique, Vol.6, No.1, pp. 32-47 (1956).

10.Bishop et al., “Theory of Indendation and Hardness Tests, ”Proceedings of the Physical Society of London, Vol.57, Part3, No.SM11, pp.147-159(1945).

11. Bishop, A.W., and Bjerrum, L., “The Relevance of the Triaxial Test to the Solution of Stability Problems, ” Proceedings of ASCE Special Conference on Shear Strength of Cohesive Soils , Boulder, pp.437-501 (1960).

12. Brooker, E. W., and Ireland, H. O., “Earth Pressure at Rest Related to Stress History, ” Canadian Geotechnical Journal, Vol.2, No.1, pp. 1-15 (1965).

13. Bjerrum, L., “Problems of Soil Mechanics and Construction on Soft Clays:SOA Report,” Proceedings of the 8th International Conference on Soil Mechanics and Foundation Engineerings, Moscow, U.S.S.R., Vol.3, pp.111-159 (1973).

14. Berre, T., and Bjerrum, L., “Shear Strength of Normally Consolidated Clays,” Proceedings of the 8th International Conference on Soil Mechanics and Foundation Engineerings, Moscow, U.S.S.R, Vol. 1, No. 1, pp. 39-49 (1973).

15. Bowles, J. E., Foundation Analysis and Design, McGraw-Hill, U.S.A., pp.35 (1977).

16. Baligh, M. M., “Strain Path Method,” ASCE, Journal of Geotecnhnical Engineering, Vol.111, No.9, pp.1108-1136 (1985).

17. Baligh, M. M., “Undrained Deep Penetration, Ⅰ: Shear Stresses.” Geotechnique, London, England, Vol.36(4), pp.471-485 (1986a).

18. Baligh, M. M., “Undrained Deep Penetration, Ⅱ: Pore Pressures.” Geotechnique, London, England, Vol.36(4), pp.487-501 (1986b).

19. Baligh, M. M., Azzouz, A. S., & Chin, C. T., “Disturbance due to “Ideal” Tube Sampling,” Journal of Geotechnical Engineering, ASCE, Vol.113, No.7, pp.739-757 (1987).

20. Chadwick, P. “The Quasi-Static Expansion of Spherical Cavity in Metals and Ideal Soils,” Quarterly Journal of Mechanics and Applied Mathematics, Vol.12, Part1, pp.52-71.(1959).

21. Casagrande, A., and Carrillo, N., “Surfaces Shear Failure of Anisotropic Materials, in Contribution to Soil Mechanics 1941-1953, ” Boston Society of Civil Engineering, Boston, Mass., (1944).

22. Casagrande, A., and Rutledge, P.C., “Cooperative Triaxial Shear Research,” Waterways Experiment Station, Vicksburg, MS. (1947).

23. Casagrande, A., and Wilson, S. D., “Testing Equipment Techniques and Errors,: Moderators Report, Session 2, ” Proceedings of the Research Conference on Shear Strength of Cohesive Soils, ASCE, pp.1123-1130 (1960).

24. Currie, I. G., Fundamental Mechanics of Fluids, McGraw-Hill, Inc. New York , N. Y.(1974).

25. Clough, G. W., and Hansen, L. A., “Clay Anisotropy and Braced Wall Behavior,” Journal of the Geotechnical Engineering Division, ASCE, Vol.107, No.7, pp.893-913 (1981).

26. Chin, C. T., and Baligh, M. M., “Deformations and Strains due to Open-Ended Pile Installation in Saturated Clays,” Research Report R83017, Order No.757, Deptartment of Civil Engineering, Massachusetts Institute of Technology, Cambridge, Mass. (1983).

27. Clayton, C. R. I., Hight, D. W., & Hopper, R. J., “Progressive Destructuring of Bothkennar Clay,” Geotechnique , Vol.42, No.2, pp. 219-239 (1992).

28. Clayton,C.R.I., Matthews, M.C. and Simons, N. E., Site Ivestigation, London. Blackwell.(1995).

29. Clayton, C. R. I., Siddique, A., and Hopper, R. J., “Effects of Sampler Design on Tube Sampling Disturbance-Numerical and Analytical Investigations,” Geotechnique , Vol. 48, No. 6, pp. 847-867 (1998).

30. Davis, E.M., and Poulos, H.G., “Laboratory Investigations of the Effects of Sampling, ”Civil Engineering Transactions of the Institution of Engineers, Australia, Vol.CE9, No.1, pp.86-949 (1967).

31. D’Applonia, D. J., Discussion of, “Bearing Capacity of Anisotropic Cohesive Soil,” Journal of the Soil Mechannics and Foundation Engineerings Division, ASCE, Vol.98, No.1, pp.126-132 (1972).

32. Graham, J., & Lau, S.L.-K., “Influence of Stress Release Disturbance, Storage, and Reconsolidation Procedures on the Shore Behaviour of Reconstituted Underwater Clay,” Geotechnique , Vol.38, No.2, pp. 279-300 (1988).

33. Hvorslev, M.H., “Subsurface Exploration and Sampling of Soils for Civil Engineering Purposes, ”Waterways Experiment Station, Vicksburg, Mississippi, 521p (1949).

34. Henkel, D. J., “The Shear Strength of Saturated Remolded Clays,” Proceedings of ASCE Special Conference On Shear Strength of Cohesive Soils,Boulder, pp.533-554 (1960).

35. Hight, D. W., Gens, A., & Jardine, R. J., “Evaluation of Geotechnical Parameters from Triaxial Tests on Offshore Clay,” Proceedings of the International Conference on Offshore Site Investigation, Society for Underwater Technology, London, pp.253-268 (1985).

36. Hight et al., “Disturbance of the Bothkennar Clay prior to Laboratory Testing, ” Geotechnique Vol.42 No.2, pp.199-217 (1992).

37. Hight, D. W., “A Review of Sampling Effects in Clay and Sands,” Offshore Site Investigation of Foundation Behavior, Society for Underwater Technology, London, Vol. 28, pp.115-146 (1993).

38.Hashash, Y. M. A., and Whittle, A. J., “ Ground Movement Prediction for Deep Excavations in Soft Clay,” Journal of Geotechnical Engineering, ASCE, Vol.122, No.6, pp.474-486 (1996).

39. International Society for Soil Mechanics and Foundation Engineering. Report of the Subcommittee on Problems and Practices of Soil Sampling. Proceedings of the 6th International Conference on Soil Mechanics and Foundation Engineerings, Montreal 3, appendix II, pp.64-71 (1965).

40. ITASCA Consulting Group, Inc., FLAC:Fast Lagrangian Analysis of Continua, Version 3.2, Vol. 1~3, Minnesota (1993).

41. ITASCA Consulting Group, Inc., FLAC3D:Fast Lagrangian Analysis of Continua in 3D dimensions, Version 2.0, Vol. 1~6, Minnesota (1997).

42.Jamiolkowski, M., Ladd, C. C., Germaine, J. T., and Lancellotta, R., “New Developments in Field and Laboratory Testing of Soils:Theme Lecture 2,” Proceedings of the 8th International Conference on Soil Mechanics Foundation Engineerings, San Francisco, Vol.1, pp.57-153 (1985).

43. Kallstenius, T., “Mechanical Disturbances in Clay Samples Taken with Piston Samplers,” Proceedings of the Royal Swedish Geotechnical Institute, No.16, 1-75 (1958).

44. Kallstenius, T., “Studies on Clay Samples Taken with Piston Sampler, ” Proceedings of the Royal Swedish Geotechnical Institute, Stockholm , No.21 210p (1963).

45. Kallstenius, T., “Secondary Mechanical Disturbance; Effects in Cohesive Soil Samples, ” Proceedings of the Special Session on Quality in Soil Sampling, 4th Asian Conference of International Society for Soil Mechanics and Foundation Engineerings, Bangkok, pp.30-39 (1971).

46. Kenney, T. C. and Folkes, D.J., “Mechanical Properties of Soft Soils, ” State-of-The-Art Report to Session 2, 32nd Canadian Geotechnical Conference, Quebec, p.51. (1979).

47. Kavadas, M., “Non-Linear Consolidation around Driven Piles in Clays,” Thesis Presented to the Massachusetts Institute of Technology, at, Mass., in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy.(1982).

48. Kirpatrick, W. M., & Khan, A. J., “The Reaction of Clays to Sampling Stress Relief,” Geotechnique, Vol.34, No.1, pp.29-42. (1984).

49. Koutsoftas, D. C., and Ladd, C. C., “Design Strengths for an Offshore Clay,” Journal of Geotechnical Engineering, ASCE, Vol.111, No.3, pp. 337-355 (1985).

50. Leonards, G. A., Engineering Properties of Soils, McGraw-Hill, Book Company, New York, U.S.A., (1962).

51. Ladd, C. C., and Lambe, T. W., “The Strength of“Undisturbed”Clay Determined from Undrained Tests, ” Laboratory Shear Testing of Soils (STP361), ASTM, Philadelphia Pa., pp.342-371 (1963).

52. Lo, K. Y., “ Stability of Slopes in Anistropic Soils,” Journal of the Soil Mechannics and Foundation Division, ASCE, Vol.91, No.4, pp. 85-106 (1965).

53. Ladd , C. C., and Varallyay, J.,“The Influence of Stress System on the Behavior of Saturated Clays During Undrained Shear, ” Research Report R65-11 No.177, Deptartment of Civil Engineering, M.I.T., Cambridge, Massachusetts (1965).

54. Lambe, T. W., and Whitman, R. V., Soil Mechannics, 1st Ed., John Wiley and Sons, Inc., New York, N.Y., (1969).

55. Lang, J.G., “Forces on an Open-Drive Sampler in Stiff Clay, ” Proceedings of the Special Session on Quality in Soil Sampling, 4th Asian Conference of International Society for Soil Mechanics and Foundation Engineerings, Bangkok,pp.21-29(1971).

56. Ladd, C. C., Bovee, R. B., Edgers L., and Rixner, J. J., “Consolidated-Undrained Plane Strain Shear Test on Boston Blue Clay,” Research Report. R71-13, No.273, Department of Civil Engineering, Massachusetts (1971).

57. La Rochelle, P., “Discussion on the State-of-the-Art Report to session 4, “Proplems of Soil Mechanics and Construction on Soft Clays, ”by Bjerrum, L., ” Proceedings of the 8th International Conference on Soil Mechanics and Foundation Engineerings, Vol. 4.2, pp.102-108(1973).

58. Ladd, C. C., and Foott, R., “New Design Procedure for Stability of Soft Clays,” Journal of the Geotechnical Engineering Division, ASCE, Vol. 100, No.GT7, pp.763-786 (1974).

59. Ladanyi, B. “Use of the Static Penetration Test in Frozen Soils, ” Canadian Geotechnical Journal, Vol. 13, No.2 pp.95-110(1976).

60. Ladd, C. C., Foott, R., Ishihara, K., Schlosser, F., and Poulos, H. G., “Stress-Deformation and Strength Characteristics,” Proceedings of the 9th International Conference on Soil Mechanics and Foundation Engineering, Tokyo, Vol.2, pp.421-494 (1977).

61. Lefebvre G., and Poulin, C., “A New Method of Sampling in Sensitive Clay,” Canadian Geotechnical Journal, Vol.16, No.1, pp.226-233 (1979).

62. Levadoux, J. N., “Pore Pressures in Clays due to Cone Penetration.” Thesis Presented to the Massachusetts Institute of Technology, at Cambridge, Mass., in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy, 573 Pages (1980).

63. Levadoux,J.N., and Baligh, M.M., “Pore Pressure during Cone Penetration, ” Research Report R80-15, order No.666, Deptartment of Civil Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, 310pages (1980).

64. La Rochelle, P., Sarrailh, J., Tavenas, F., Roy, M., & Leroueil, S., “Causes of Sampling Disturbance and Design of a New Sampler for Sensitive Soils,” Canadian Geotechnical Journal, Vol.18 No.1, pp.52-66 (1981).

65. Lefebvre, G., Ladd, C. C., Mesri, G., and Tavenas, F., “Report of the Testing Subcommittee,” Committee of Specialists on Sensitive Clay on the NBR Complex, SEBJ, Montreal, Canada, Annexe I. (1983).

66. Leroueil, S., & Vaughan, P. R., “The General and Congruent Effects of Structure in Natural Soils and Weak rocks, ” Geotechnique Vol.40, No.3, pp.467-488 (1990).

67. Ladd, C. C., “ Stability Evaluation during Staged Construction,” Journal of Geotechnical Engineering, ASCE, Vol.117, No.4, pp.540-615 (1991).

68. Milovic, D.M., “Effect of Sampling on Some Loess Characteristics, ” Proceedings of the Special Session on Quality in Soil Sampling, 4th Asian Conference. of International Society for Soil Mechanics and Foundation Engineering, Bangkok, pp.17-20 (1971).

69. Mitachi, T., and Kitago, S., “Undrained Triaxial and Plane Strain Behavior of Saturated Remolded Clay,” Soils and Foundations, Vol.20, No.1, pp.12-28 (1980).

70. Mayne, P. W., “Cam-Clay Predictions of Undrained Strength,” Journal of Geotechnical Engineering Division, ASCE, Vol.106, No.11, pp.1219-1242 (1980).

71. Morrison, M., “In Situ Measurements on a Model Pile in Clay, ” Thesis Presented to the Massachusetts Institute of Technology, at, Mass., in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy.(1984).

72. Mayne, P. W., “Stress Anisotropy Effects on Clay Strength,” Journal of Geotechnical Engineering, ASCE, Vol.111, No.3, pp.356-366 (1985).

73. Noorany, I., and Seed, H.B., “In Situ Strength Characteristics of Soft Clays, ”Journal of the Soil Mechanics and Foundations Division, Proceedings of the American Society of Civil Engineers, Vol.91, No. SM2, pp.49-80 (1965).

74. Nakase, A., and Kamei, T., “Undrained Shear Strength Anisotropy of Normally Consolidated Cohesive Soils,” Soils and Foundations, Vol.23, No.1, pp. 91-101 (1983).

75. Otter, J. R. H., Cassel, A. C., and Hobbs, R. E., “Dynamic Relaxation,” Proceedings of the Institution of Civil Engineerings, Vol. 35, London, pp.633-656 (1967).

76. Okumura, T., “The Variation of Mechanical Properties of Clay Samples Depending on its Degree of Disturbance, ” Proceedings of the Special Session on Quality in Soil Sampling, 4th Asian Conference of International Society for Soil Mechanics and Foundation Engineerings, Bangkok, pp.73-81(1971).

77. O’Rourke, T. D., “Base Stability and Ground Movement Prediction for Excavations in Soft Clay,” Journal of Geotechnical Engineering, ASCE, Vol.122, No.6, pp.474- 486 (1992).

78. Parry, R.G.H., “Triaxial Compression and Extension Tests on Remolded Saturated Clay, ” Geotechnique, Vol.10, No.4, pp.166-180(1960).

79. Peck, R. B., “Deep Excavations and Tunneling in Soft Ground,” Proceedings of the 7th International Conference on Soil Mechanics and Foundations Engineerings, State of-the-Art Volume (1969).

80. Rennie, I. A., “The Structure and Directional Stress-Strain Behaviour of Consolidated Kaolin,” ph.D. Thesis, University of Strathclyde (1972).

81. Recommendations for Design of Building Foundations, Architectural Institute of Japan, Tokyo, Japan (1974).

82. Sangrey, D.A., “Normalized Design Procedures in Sensitive Clays,” Journal of Geotechnical Engineering Division, ASCE, vol.10, No. GT11, pp.1181-1187 (1975).

83. Schmertmann, J.H., “Discussion on “Effect of Sample Disturbance on the Strength of a Clay, ” Transactions of the American Society for Civil Engineers, Vol.121, pp.940-950 (1956).

84. Skeptmon, A. W., and Sowa, V. A., “The Behavior of Saturated Clays During Sampling and Testing,” Geotechnique, Vol.13, No.4, pp. 269-290 (1963).

85. Schjetne, K., “The Measurement of Pore Pressure During Sampling ,” Proceedings of Special Session on Quality in Soil Sampling,4th Asian Conference of International Society for Soil Mechanics and Foundation Engineerings, Bangkok, pp.12-16 (1971).

86. Su, S. F., and Liao, H. J., “Base Stabiliy of Deep Excavation in Anisotropic Soft Clay,” Journal of Geotechnical Engineering, ASCE, Vol.124, No.9, pp. 809-819 (1998).

87. Siddique et al., “Disturbance due to Tube Sampling in Castal Soils, ” Journal of Geotechnical and Geoenvironmental Engineering, Vol.126, No.6 pp.568-575 (2000).

88. Terzaghi, K., Theoretical Soil Mechanics, John Wiley and Sons. New York, N. Y. (1943 ).

89. Terzaghi, K., and Peck, R. B., Soil Mechanics in Engineering Practice, 2nd Ed., Jone Wiley & Sons. (1948).

90. Tavenas, F., & Leroueil, S., “Discussion,” Proceedings of the 11th International Conference on Soil Mechanics and Foundations Engineering, San Francisco 5, pp2693-2694 (1985).

91. Vesic, A. S., “Expansion of Cavities in Infinite Soil Mass,” Journal of the Soil Mechanics and Foundations Division, ASCE, Vol.98, No. SM3, Mar., pp.265-290(1972).

92. Vaid, Y. P., and Campanella, R. G., “Triaxial and Plane Strain Behavior of Natural Clay,” Journal of Geotechnical Engineering Division, ASCE, Vol.100, No.3, pp.207-224 (1974).

93. Vivatrat, V., “Cone Penetration in Clays, ” Thesis Presented to the Massachusetts Institute of Technology, at, Mass., in Partial Fulfillment of the Requirements for the Degree of Doctor of Science, 427 pages.(1978).

94. Watson, G. N., “Theory of Bessel Functions,” Cambridge University Press, pp.388 (1922).

95. Weinstein, A., “On Axially Symmeretric Flows,” Quarter Journal of Applied Mathmatics, Vol.5, No.4, pp.419-423 (1946).

96. White, F. M., Fluid Mechanics, McGraw-Hill, Inc. New York (1994).