土工结构有限单元法分析
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摘要
关于提高有限元法解的精度和稳定性问题受到不少学者的重视。
本文以Biot固结理论为基础,研究了固结过程中的时步自适应问题。用基本原理推导出时步控制公式,从而全面控制应力和孔隙压力场。研究结果有助于准确模拟应力应变的发展,对粘土心墙土石坝等建筑物的设计及施工有重要意义。
土石坝工程运行时经常受到地震的动力作用。本文以Blot动力固结理论为基础,应用改进的数值解法来求解动力方程。并且通过液化判断标准来估计土石坝的动力稳定性。
本文还结合作者的一些认识,介绍目前动力分析的研究状态和最新的进展,对相关问题的研究提出一些看法。
本文主要内容有:
(1) 采用Biot固结理论,建立了时步自适应方式。
(2) 研究了土体的动力性质。
(3) 研究了土石坝动力分析方法,应用改进数值Hilber-Hughes-Taylor-a来求解动力方程。
(4) 讨论了液化现象和液化发生过程,并从提出液化发生的条件。
(5) 用Fortran语言开发了应用程序。
(6) 应用上面建立的理论与研究分析了越南的Dakyen土石坝。
The accuracy and stabilility of a problem solved by FE method is concerned and taken in to account by many researchers.In this thesis, the adaptive time step is used in FEM for analysing consolidation problems and dynamic problems. The key points discussed in detail are listed as follows:In order to improve the numerical accuracy and stabilility, based on Biot's consolidation theory the adaptive time step algorithm is introduced. The method is to estimate local and global errors of stress state and pore pressure. By the link between errors and time step length the time step adaptivity strategy has been proposed.This study can provide well understanding of development of the relation between stress and strain by time. Furthermore the study will be very useful for the design and construction of dams with earth core wall. Earth dam is usually subject to earthquake action. Based on Biot's consolidation theory the dynamic analysis technique is introduced for solving dynamic consolidation problems, then the liquefaction criteria is used to estimate the seismic stability. The study will be very useful for the design and construction of earth dam.Beside all the works listed above, base on the author's knowledge, the state of the art and the recent development in dynamic FEM analysis are discussed systematically. Some reviews on the topic will be given, It is desired that this work should contribute to researchers in keeping abreast of the new developements and trends in dynamic FEM problems. The thesis is organized as follows:First, the FEM on soil consolidation problems is introduced .From the result of study, the adaptive time step algorithm is presented.Secondly, discuss on dynamic analysis problem is conducted , the
attention is paid to the earthquake .Thirdly, dynamic analysis method on local material dam is dicussed and Hilber-Hughes-Taylor-a method is applied for solving dynamic equation.Fourthly, discuss on the liquefaction is presented.Fifthly, based on Fortran languge the computation program is developed for solving consolidation problems and dynamic problem in geotechnical structures.Finally, Dakyen's local material dam is studied using the above theory and program
本文以Biot固结理论为基础,研究了固结过程中的时步自适应问题。用基本原理推导出时步控制公式,从而全面控制应力和孔隙压力场。研究结果有助于准确模拟应力应变的发展,对粘土心墙土石坝等建筑物的设计及施工有重要意义。
土石坝工程运行时经常受到地震的动力作用。本文以Blot动力固结理论为基础,应用改进的数值解法来求解动力方程。并且通过液化判断标准来估计土石坝的动力稳定性。
本文还结合作者的一些认识,介绍目前动力分析的研究状态和最新的进展,对相关问题的研究提出一些看法。
本文主要内容有:
(1) 采用Biot固结理论,建立了时步自适应方式。
(2) 研究了土体的动力性质。
(3) 研究了土石坝动力分析方法,应用改进数值Hilber-Hughes-Taylor-a来求解动力方程。
(4) 讨论了液化现象和液化发生过程,并从提出液化发生的条件。
(5) 用Fortran语言开发了应用程序。
(6) 应用上面建立的理论与研究分析了越南的Dakyen土石坝。
The accuracy and stabilility of a problem solved by FE method is concerned and taken in to account by many researchers.In this thesis, the adaptive time step is used in FEM for analysing consolidation problems and dynamic problems. The key points discussed in detail are listed as follows:In order to improve the numerical accuracy and stabilility, based on Biot's consolidation theory the adaptive time step algorithm is introduced. The method is to estimate local and global errors of stress state and pore pressure. By the link between errors and time step length the time step adaptivity strategy has been proposed.This study can provide well understanding of development of the relation between stress and strain by time. Furthermore the study will be very useful for the design and construction of dams with earth core wall. Earth dam is usually subject to earthquake action. Based on Biot's consolidation theory the dynamic analysis technique is introduced for solving dynamic consolidation problems, then the liquefaction criteria is used to estimate the seismic stability. The study will be very useful for the design and construction of earth dam.Beside all the works listed above, base on the author's knowledge, the state of the art and the recent development in dynamic FEM analysis are discussed systematically. Some reviews on the topic will be given, It is desired that this work should contribute to researchers in keeping abreast of the new developements and trends in dynamic FEM problems. The thesis is organized as follows:First, the FEM on soil consolidation problems is introduced .From the result of study, the adaptive time step algorithm is presented.Secondly, discuss on dynamic analysis problem is conducted , the
attention is paid to the earthquake .Thirdly, dynamic analysis method on local material dam is dicussed and Hilber-Hughes-Taylor-a method is applied for solving dynamic equation.Fourthly, discuss on the liquefaction is presented.Fifthly, based on Fortran languge the computation program is developed for solving consolidation problems and dynamic problem in geotechnical structures.Finally, Dakyen's local material dam is studied using the above theory and program
引文
[1] Dams and Development-The report of the Wold commission on Dams-November 2000.
[2] E.W.Brand & R.P.Brenner. Soft clay engineering. Elserier Scientific Publishing Compomy, Amsterdam, 1981.
[3] 库克著.有限元分析的概念和应用.第二版.程耿东等译.北京:科学出版社.1989。
[4] 王勖成,劭敏.有限元法原理.北京:京华大学出版社,1995。
[5] 徐芝纶.弹性力学(上册).北京:高等教育出版社,1995。
[6] 陈胜宏.高坝复杂岩石地基及岩石高边坡稳定分析.北京:中国水利水电出版社,2001。
[7] Cundall P.A.Formulation of Three-dimensional Distinct Element Model, Part Ⅰ, A Sheme to Dectect and Represent Contact in System Composed of Many Polyherdral Blocks. Int. J. Rock Mech. Min.Sci.Geomech.Abstr. 1988,25(3): 107-116.
[8] Hart R.,Cundall P.A.&Lemos J. Formulation of three-dimensional Distinct Element Model, Part Ⅱ, Mechanical Calculation of a System Composed of May Polyhedral Blocks. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 1988, 25(3): 117-125.
[9] Shi G.H.& Goodman R.E. Two Dimensional Discontinuous Analysis, Int.J.Num.Anal. Methods Goemech., 1985, 9: 541-556.
[10] Shi G.H.& Goodman R.E. Generalization of Two-dimensional Discontinuous Analysis for Forward Modeling, Int.J.Num.Anal.Methods Geomech. 1989,13: 359-380.
[11] ITASCA Consulting Group, Inc.In:FLAC 3.3 User's Manual,1996.
[12] 寇晓东,周维恒.无单元法追踪结构开裂[C].岩土力学新计算方法讲义,中国科学院武汉岩土力学研究所,1999.10:45-72。
[13] 王水林.数值流形方法及其应用[C].岩土力学新计算方法讲义,中国科学院武汉岩土力学研究所,1999,10:178-207。
[14] Courant.R, Variational Method for the Solution of Problems of Equibrium and Vibrations, Bull.Am.Math.Soc, 1943, 49.
[15] 孔宪京,韩国成.土石坝与地基震反应分析的波动.剪切梁法。大连理工大学学报,1994,34(2)。
[16] Chen S.H, Adaptive FEM analysis for Two-dimension unconfined seepage problems, J of Hydrodynamic, ser.B,1996,19(1):66-66
[17] Chen S.H, Chen S.F, Three dimensional hexahedron mesh generation for rock engineering, Geoecology and computers, Proceedings of the Third Int.Conf.on Advance of Com.Meth.in Geotech.And Geoenviron.Eng.2000:203-206.
[18] 陈胜宏,王劲松,张君禄.水工结构的弹塑性自适应有限元分析,岩土力学,1996,(2):57-68。
[19] 郑建辉,熊文林.复杂区域自适应三角形网格全自动生成方法.岩土力学,1994,15(2):43-54。
[20] Murry, R.T. Development in Two- and Three-Dimentional Consolidation Theory, Development in Soil Mechanics, 1978.
[21] 陈胜宏.高坝复杂岩石基及岩石高边坡稳定分析.中国水利水电出版社,2001。
[22] Zienkiewicz O C, Zhu J Z. A simple error estimator and adaptive procedure for practical enginerring analysis. Int.J.Num.Meth.Eng.1987,24(2):337-357.
[23] Britto.A.M & Gunn.M.J. Critical state soil mechanics via finite elements. University of Bristol, 1980.
[24] Steven L. Kramer. Geotechnical earthquake engineering. University of Washington. 1996.
[25] 汝乃华,牛运光.大坝:事故与安全·土石坝.中国水利水电出版社.2001。
[26] 黄文熙。沙基和沙坡的液化研究.水利水电技术.1959(15)。
[27] 黄文熙。沙基和沙波的液化研究.水工建设的结构力学与岩土力学问题.黄文熙论文选集.北京:水利水电出版社.1984:252～256.
[28] 陈伟庆,孔书祥.土力学.中国铁道出版社.北京:2002.
[29] Richart. F.E, Woods. Jr. R., D Hall. J.R. Vibrations of soils and foundations. The University of Michigan, Ann Arbor, Michigan.
[30] Hardin,B.O. and Black,W.L. Vibration modulus of normally consolidated clay. J of the Soil Mechanics and Foundations Division, ASCE, 1968.94(SM2): 353～369.
[31] Martin,G.R, Finn,W.D.L, and Sees,H.B. Fondamentals of liquefaction under cyclic loading. Journal of the Geotechnical Engineering Division, ASCE, 1975. 101(GTS): 423～438。
[32] Martin,P.P, and Sees,H.B. MASH- A computer program for the nolinear analysis of vertically propagating shear waves in horizontally layered soil depoisits. Report No. UCB/EERC-78/23, Earthquake Engineering Research Center, University of California, Beckeley, California.
[33] Seed, H.B. and Idriss,I.M. Soil modului and damping factors for danamic reponse analyses. Report EERC 70-10, Eathquake engineering Reseach center, University of California, Berkeley. 1970.
[34] Gutenberg.B. and Richter, C.F. Seismicity of the Earth and Related Phenomena, Princeton University Press, Princeton, New Jersey. 1954.
[35] Richter.C.F. Elementary Seismology, W.H.Freeman, San Francisco. 1958.
[36] Bulle.K.E. The Earth's Density, Chapman&Hall, London. 1975.
[37] Bath.M.. Introduction to seismology, Birkhauser, Boston. 1979.
[38] Gubbins.D. Seismology and Plate Tectonics, University Press, Cambridge. 1990.
[39] Lay,T. and Wallace,T.C. Modern Global Seismology. Academi Press. San Diego.1995.
[40] Bolt.B.A. Earthquakes, W.H. NewYork. 1993
[41] 龚晓南.土工计算机分析.中国建筑工业出版社,1999.
[42] Biot M.A.General theory of Three Dimensional Consolidation. J.App.Physis, 1941.12: 155～162.
[43] Brinkgereve.R.B.J. Plaxis B.V., Netherlands and P.A. Vermeer. University of Stuttgart. Finite Element code for Soil and Rock Analyses. 1998
[44] Roscoe, K.H and Pooroshasb, H.B. A foundamental principle of similarity in model tests for earth pressure problems. Proceedings, 2nd Asian Regional Conference on Soil Mechanics, Tokyo, 1963.1: 134-140.
[45] Been, K and Jeffries,M.G A state parameter for sands . Geotechnique, 1985.35(2): 99-112.
[46] Sladen. J.A. Problems with interpretation of sand state from cone penetration test. Geotechnique. 1985.139(2): 323-332.
[47] Yu.H.S. State parameter from self-boring pressuremeter tests in sand . Journal of Geotechnical Engineering. 1994.120(12): 2118-2135,
[48] Konrad. J.M. Interpretation of flat plate dilatometer tests in sand in terms of the state parameter. Geotechnique. 1988.38(2):263~278o
[49] Been.K , Crooks. J.H.A , Becker.D.E and Jeffries.M.G The cone penetration test in sands. Part I: State parameter interpretation. Geotechnique. 1986.36(2): 239-249.
[50] Been.K , Crooks.J.H.A, Becker.D.E and Jeffries.M.G The cone penetration test in sands. Part II: General inference of state . Geotechnique .1986. 37(3):285-300.
[51] lsihara.K. Liquefaction and flow failure during earthquake. Geotechnique. 1993.43(3): 351-415.
[52] Koppejan.A.W. Wamelan.B.M and Wenberg.L.J. Coastal flowslides in the Dutch province of Zeeland. Proceedings, 2nd International Conference on soil mechanics and foundation engineering. 1948.5: 89-96.
[53] Andersen.A and Bjerrum.L. Slides in subaqueous slopes in loose sand and silt. Publication81. Norwegian Geotechnical institute. Publication 8 . Oslo. 1968. 1-9.
[54] Bjerrum.L. Subaqueous slope failures in Norwegian fjords. Publication 88. NorwegianGeotechnical Institute. Olso. 1971
[55] Kramer.S.L . Triggering of liquefaction flow slides in coastal soil deposits. Engineering Geoloqy. 1988.26(1) 17-31.
[56] Jakobsen.B. The landslide at suite on the Gota River. Proceedings 5. Royal Swedish geotechnical institute. Stockholm. 1952.
[57] Fellenius.B. The landslide at Guntorp. Geotechnique. Vo 5. No 1.1953.120-125.
[58] Brooms.B and Bennermark.H. Free discussion. Froceedings. Geotechnical conference. Vol 2 Oslo. Norway. 1967.118-120.
[59] Hryciw.R.D. Small- strain-shear modulus of soil by dilatometer. Journal of Geotechnical Engineering. ASCE. 1990.116(ll):1700-1716o
[60] Conlon.R. Landslide at Toulnustouc Rive. Quebec. Canadaian geotechnical journal. 1966.3(3): 113-144.
[61] Seed.H.B and Lee.K.L. Lequefaction of saturated sand during cyclic loading. Juornal ogf the Soil mechanics and foundations division. ASCE.1966.92(6): 105-134.
[62] Kramer.S.L and Seed .H.B. Inititiation of soil liquefaction under static loading condition. Journal of Geotechnical Engineering. ASCE.. 1988.114(4).412~430
[63] Hanzawa.H, Itoh.Y and Suzuki.K. Shear characteristics of a quick sand in the Arabian gulf. Soil and foundations . 1979.19(4): 1-15.
[64] Vaid.Y.P and Chern.J.C. Effect static shear on resistance of liquefaction. Soil and foundations. 1983.23(1): 47-60.
[65] Vaid.Y.P and Chern.J.C. Cyclic and monotonic undrained response of staturated sands. Advances in the art of testing soils under cyclic conditions. ASCE. New York. 1985: 120~147.
[66] SladenJ.A. D'Hollander.R.D and Krahn. The liquefaction of sands, a collapse surface approach. Canadian geotechnical journal. 1985. 22 (4): 564-578.
[67] Alarcon-Guzman.A, A.Leonards.G.A and Chanmeau.J.L. Underained monotonic and cyclic strength of sands . Journal of geotechnical engineering.ASCE. 1988.114 (10) :1089~1108.
[68] Youd.T.L. Mapping earthquake-induced liquefaction and associated ground failure. Proceedings, geologic and hydrologic hazards training program. Open file report 84-760, US.geological survey, Menlo park, California. 1984. 210-232.
[69] Finn.W.D.L. Analisys of post-liquefaction deformations in soils structures. Proceedings,H.Botton sedd memorial symposisum. University of California, Berkeley. 1990.2: 291-312.
[70] Seed.R.B . Dickenson.S.E. Reimer.M.F . Bray.J.D . Sitar.N . Mitchell. J.K . Idriss.I.M . Kayen.R.E . Kropp.A . Harder.L.F and Power.M.S . Preliminary report on the principal geotechnical aspects of the October 17,1989 Loma Prieta earthquake. Report UCB/EERC-90/05, Earthquake Enginerring Research Centre, University of California, Becrkeley. 1990 .
[2] E.W.Brand & R.P.Brenner. Soft clay engineering. Elserier Scientific Publishing Compomy, Amsterdam, 1981.
[3] 库克著.有限元分析的概念和应用.第二版.程耿东等译.北京:科学出版社.1989。
[4] 王勖成,劭敏.有限元法原理.北京:京华大学出版社,1995。
[5] 徐芝纶.弹性力学(上册).北京:高等教育出版社,1995。
[6] 陈胜宏.高坝复杂岩石地基及岩石高边坡稳定分析.北京:中国水利水电出版社,2001。
[7] Cundall P.A.Formulation of Three-dimensional Distinct Element Model, Part Ⅰ, A Sheme to Dectect and Represent Contact in System Composed of Many Polyherdral Blocks. Int. J. Rock Mech. Min.Sci.Geomech.Abstr. 1988,25(3): 107-116.
[8] Hart R.,Cundall P.A.&Lemos J. Formulation of three-dimensional Distinct Element Model, Part Ⅱ, Mechanical Calculation of a System Composed of May Polyhedral Blocks. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 1988, 25(3): 117-125.
[9] Shi G.H.& Goodman R.E. Two Dimensional Discontinuous Analysis, Int.J.Num.Anal. Methods Goemech., 1985, 9: 541-556.
[10] Shi G.H.& Goodman R.E. Generalization of Two-dimensional Discontinuous Analysis for Forward Modeling, Int.J.Num.Anal.Methods Geomech. 1989,13: 359-380.
[11] ITASCA Consulting Group, Inc.In:FLAC 3.3 User's Manual,1996.
[12] 寇晓东,周维恒.无单元法追踪结构开裂[C].岩土力学新计算方法讲义,中国科学院武汉岩土力学研究所,1999.10:45-72。
[13] 王水林.数值流形方法及其应用[C].岩土力学新计算方法讲义,中国科学院武汉岩土力学研究所,1999,10:178-207。
[14] Courant.R, Variational Method for the Solution of Problems of Equibrium and Vibrations, Bull.Am.Math.Soc, 1943, 49.
[15] 孔宪京,韩国成.土石坝与地基震反应分析的波动.剪切梁法。大连理工大学学报,1994,34(2)。
[16] Chen S.H, Adaptive FEM analysis for Two-dimension unconfined seepage problems, J of Hydrodynamic, ser.B,1996,19(1):66-66
[17] Chen S.H, Chen S.F, Three dimensional hexahedron mesh generation for rock engineering, Geoecology and computers, Proceedings of the Third Int.Conf.on Advance of Com.Meth.in Geotech.And Geoenviron.Eng.2000:203-206.
[18] 陈胜宏,王劲松,张君禄.水工结构的弹塑性自适应有限元分析,岩土力学,1996,(2):57-68。
[19] 郑建辉,熊文林.复杂区域自适应三角形网格全自动生成方法.岩土力学,1994,15(2):43-54。
[20] Murry, R.T. Development in Two- and Three-Dimentional Consolidation Theory, Development in Soil Mechanics, 1978.
[21] 陈胜宏.高坝复杂岩石基及岩石高边坡稳定分析.中国水利水电出版社,2001。
[22] Zienkiewicz O C, Zhu J Z. A simple error estimator and adaptive procedure for practical enginerring analysis. Int.J.Num.Meth.Eng.1987,24(2):337-357.
[23] Britto.A.M & Gunn.M.J. Critical state soil mechanics via finite elements. University of Bristol, 1980.
[24] Steven L. Kramer. Geotechnical earthquake engineering. University of Washington. 1996.
[25] 汝乃华,牛运光.大坝:事故与安全·土石坝.中国水利水电出版社.2001。
[26] 黄文熙。沙基和沙坡的液化研究.水利水电技术.1959(15)。
[27] 黄文熙。沙基和沙波的液化研究.水工建设的结构力学与岩土力学问题.黄文熙论文选集.北京:水利水电出版社.1984:252～256.
[28] 陈伟庆,孔书祥.土力学.中国铁道出版社.北京:2002.
[29] Richart. F.E, Woods. Jr. R., D Hall. J.R. Vibrations of soils and foundations. The University of Michigan, Ann Arbor, Michigan.
[30] Hardin,B.O. and Black,W.L. Vibration modulus of normally consolidated clay. J of the Soil Mechanics and Foundations Division, ASCE, 1968.94(SM2): 353～369.
[31] Martin,G.R, Finn,W.D.L, and Sees,H.B. Fondamentals of liquefaction under cyclic loading. Journal of the Geotechnical Engineering Division, ASCE, 1975. 101(GTS): 423～438。
[32] Martin,P.P, and Sees,H.B. MASH- A computer program for the nolinear analysis of vertically propagating shear waves in horizontally layered soil depoisits. Report No. UCB/EERC-78/23, Earthquake Engineering Research Center, University of California, Beckeley, California.
[33] Seed, H.B. and Idriss,I.M. Soil modului and damping factors for danamic reponse analyses. Report EERC 70-10, Eathquake engineering Reseach center, University of California, Berkeley. 1970.
[34] Gutenberg.B. and Richter, C.F. Seismicity of the Earth and Related Phenomena, Princeton University Press, Princeton, New Jersey. 1954.
[35] Richter.C.F. Elementary Seismology, W.H.Freeman, San Francisco. 1958.
[36] Bulle.K.E. The Earth's Density, Chapman&Hall, London. 1975.
[37] Bath.M.. Introduction to seismology, Birkhauser, Boston. 1979.
[38] Gubbins.D. Seismology and Plate Tectonics, University Press, Cambridge. 1990.
[39] Lay,T. and Wallace,T.C. Modern Global Seismology. Academi Press. San Diego.1995.
[40] Bolt.B.A. Earthquakes, W.H. NewYork. 1993
[41] 龚晓南.土工计算机分析.中国建筑工业出版社,1999.
[42] Biot M.A.General theory of Three Dimensional Consolidation. J.App.Physis, 1941.12: 155～162.
[43] Brinkgereve.R.B.J. Plaxis B.V., Netherlands and P.A. Vermeer. University of Stuttgart. Finite Element code for Soil and Rock Analyses. 1998
[44] Roscoe, K.H and Pooroshasb, H.B. A foundamental principle of similarity in model tests for earth pressure problems. Proceedings, 2nd Asian Regional Conference on Soil Mechanics, Tokyo, 1963.1: 134-140.
[45] Been, K and Jeffries,M.G A state parameter for sands . Geotechnique, 1985.35(2): 99-112.
[46] Sladen. J.A. Problems with interpretation of sand state from cone penetration test. Geotechnique. 1985.139(2): 323-332.
[47] Yu.H.S. State parameter from self-boring pressuremeter tests in sand . Journal of Geotechnical Engineering. 1994.120(12): 2118-2135,
[48] Konrad. J.M. Interpretation of flat plate dilatometer tests in sand in terms of the state parameter. Geotechnique. 1988.38(2):263~278o
[49] Been.K , Crooks. J.H.A , Becker.D.E and Jeffries.M.G The cone penetration test in sands. Part I: State parameter interpretation. Geotechnique. 1986.36(2): 239-249.
[50] Been.K , Crooks.J.H.A, Becker.D.E and Jeffries.M.G The cone penetration test in sands. Part II: General inference of state . Geotechnique .1986. 37(3):285-300.
[51] lsihara.K. Liquefaction and flow failure during earthquake. Geotechnique. 1993.43(3): 351-415.
[52] Koppejan.A.W. Wamelan.B.M and Wenberg.L.J. Coastal flowslides in the Dutch province of Zeeland. Proceedings, 2nd International Conference on soil mechanics and foundation engineering. 1948.5: 89-96.
[53] Andersen.A and Bjerrum.L. Slides in subaqueous slopes in loose sand and silt. Publication81. Norwegian Geotechnical institute. Publication 8 . Oslo. 1968. 1-9.
[54] Bjerrum.L. Subaqueous slope failures in Norwegian fjords. Publication 88. NorwegianGeotechnical Institute. Olso. 1971
[55] Kramer.S.L . Triggering of liquefaction flow slides in coastal soil deposits. Engineering Geoloqy. 1988.26(1) 17-31.
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