复合地基固结与变形的计算理论及数值分析
|
摘要
复合地基工后沉降是复合地基设计必需考虑的重要内容之一，对其如何合理地进行计算已逐渐成为工程界所关注的问题，但有关研究至今尚不多见。本文从解析计算和有限元分析两方面着手对复合地基固结与变形问题展开了较全面、深入的研究。主要研究工作如下：
1．在对若干试验结果分析的基础上，提出了刚性基础下复合地基桩侧摩阻力分布形状的假定，然后基于总应力法分析了单桩复合地基中桩体和桩间土的沉降变形，并编制了相应的计算程序。
2．基于Biot理论，分别对在桩顶受外荷载作用和桩土共同受外荷载作用的情况下考虑桩土相互作用的单桩复合地基固结问题建立了基本方程和求解条件，并在Laplace变换域和Hankel变换域内得到了土体和桩体的变形解答。
3．编制了可以进行平面应变、轴对称以及三维情况下复合地基固结与变形分析的有限元程序。该程序对土体可采用弹性、非线性弹性、弹塑性等多种本构模型并可考虑基础筏板、垫层等复杂条件。同时通过多种算例对该程序进行了验证。
4．在假定复合地基桩土间竖向和切向变形协调、应力平衡以及复合元模型的平均固结度与单桩轴对称复合地基的平均固结度相等的条件下，用有效应力分析法建立了三维复合有限元模型，提出了基于此模型的复合地基固结变形分析有限元法。该法无需将桩单元和土单元分别进行网格剖分，从而能极大地减少有限元分析的工作量，特别是对于群桩复合地基固结分析，其优势更为突出。
5．用编制的有限元程序对单桩、群桩复合地基的固结变形性状进行了大量的计算分析，阐述了弱排水桩也能加速地基固结的机理，提出了将强排水桩成层复合地基固结简化为均质单层复合地基固结的计算方法，并通过工程实例分析说明了该程序在实际中的应用。
本文工作较全面地揭示了复合地基固结性状，并为复合地基工后沉降的计算提供了新的理论和技术支持，从而丰富和完善了复合地基变形计算理论和技术。
The settlement induced by consolidation of composite foundation is one of the important items that must be considered in design of such foundation, and its reasonable evaluation has been becoming a problem deeply concerned by engineers. However, the relevant study was rarely reported. In this dissertation, the consolidation and deformation problem of composite foundation was studied both by analytical method and by FEM. The main work includes:
1. On the basis of analyzing data from several field tests, assumption was proposed for the distribution of side friction along column under rigid raft, and settlements of column and soil in the composite foundation with single column were analyzed by totally stress method. The corresponding computer program was developed at the same time.
2. Based on Biot's theory, the basic equations and solution conditions were established for the consolidation problem of the composite foundation with single column considering soil-column interactions when load was applied on the top of column only or applied on the top of both column and soil, and the solution for deformations of soil and column were obtained in the forms of Laplace and Hankel transformation.
3. Computer program was developed by FEM that can be used to perform consolidation and deformation analyses of composite ground for plane strain, axial symmetry and three-dimensional conditions, in which, the soil model can be linear elastic, non-linear elastic or elasto-plastic, and complicate factors such as raft, cushion et al. can be taken into consideration. Meanwhile, the program was verified by many examples.
4. By assuming that distortion is coordinative and stress is in equilibrium at the interfaces of columns and soil in composite foundation and that the average consolidation degree in composite model was equal to the one in composite foundation, a three-dimensional composite model was established by effective stress analysis method. The corresponding finite element method is then developed for consolidation analysis of composite foundation. This method is advantaged by no need to distinguish column and soil and thus raises greatly the efficiency of FEM analysis, especially in consolidation analysis of composite foundation with columns group.
5. The consolidation behavior of composite foundation with single column or with columns group was analyzed extensively by the computer program developed, and the mechanism that the column with low permeability can also accelerate the consolidation of soil was illustrated. Moreover, a simplified method was proposed for consolidation analysis of layered composite foundation with column of high permeability. Finally, a case study was made to show the practical application of this computer program.
The work presented herein not only reveals the consolidation behavior of composite foundation, but also provides new theory and technique support for the computation of settlement induced by consolidation of composite foundation, and thus makes the computation theory for the settlement of composite foundation more perfect.
1．在对若干试验结果分析的基础上，提出了刚性基础下复合地基桩侧摩阻力分布形状的假定，然后基于总应力法分析了单桩复合地基中桩体和桩间土的沉降变形，并编制了相应的计算程序。
2．基于Biot理论，分别对在桩顶受外荷载作用和桩土共同受外荷载作用的情况下考虑桩土相互作用的单桩复合地基固结问题建立了基本方程和求解条件，并在Laplace变换域和Hankel变换域内得到了土体和桩体的变形解答。
3．编制了可以进行平面应变、轴对称以及三维情况下复合地基固结与变形分析的有限元程序。该程序对土体可采用弹性、非线性弹性、弹塑性等多种本构模型并可考虑基础筏板、垫层等复杂条件。同时通过多种算例对该程序进行了验证。
4．在假定复合地基桩土间竖向和切向变形协调、应力平衡以及复合元模型的平均固结度与单桩轴对称复合地基的平均固结度相等的条件下，用有效应力分析法建立了三维复合有限元模型，提出了基于此模型的复合地基固结变形分析有限元法。该法无需将桩单元和土单元分别进行网格剖分，从而能极大地减少有限元分析的工作量，特别是对于群桩复合地基固结分析，其优势更为突出。
5．用编制的有限元程序对单桩、群桩复合地基的固结变形性状进行了大量的计算分析，阐述了弱排水桩也能加速地基固结的机理，提出了将强排水桩成层复合地基固结简化为均质单层复合地基固结的计算方法，并通过工程实例分析说明了该程序在实际中的应用。
本文工作较全面地揭示了复合地基固结性状，并为复合地基工后沉降的计算提供了新的理论和技术支持，从而丰富和完善了复合地基变形计算理论和技术。
The settlement induced by consolidation of composite foundation is one of the important items that must be considered in design of such foundation, and its reasonable evaluation has been becoming a problem deeply concerned by engineers. However, the relevant study was rarely reported. In this dissertation, the consolidation and deformation problem of composite foundation was studied both by analytical method and by FEM. The main work includes:
1. On the basis of analyzing data from several field tests, assumption was proposed for the distribution of side friction along column under rigid raft, and settlements of column and soil in the composite foundation with single column were analyzed by totally stress method. The corresponding computer program was developed at the same time.
2. Based on Biot's theory, the basic equations and solution conditions were established for the consolidation problem of the composite foundation with single column considering soil-column interactions when load was applied on the top of column only or applied on the top of both column and soil, and the solution for deformations of soil and column were obtained in the forms of Laplace and Hankel transformation.
3. Computer program was developed by FEM that can be used to perform consolidation and deformation analyses of composite ground for plane strain, axial symmetry and three-dimensional conditions, in which, the soil model can be linear elastic, non-linear elastic or elasto-plastic, and complicate factors such as raft, cushion et al. can be taken into consideration. Meanwhile, the program was verified by many examples.
4. By assuming that distortion is coordinative and stress is in equilibrium at the interfaces of columns and soil in composite foundation and that the average consolidation degree in composite model was equal to the one in composite foundation, a three-dimensional composite model was established by effective stress analysis method. The corresponding finite element method is then developed for consolidation analysis of composite foundation. This method is advantaged by no need to distinguish column and soil and thus raises greatly the efficiency of FEM analysis, especially in consolidation analysis of composite foundation with columns group.
5. The consolidation behavior of composite foundation with single column or with columns group was analyzed extensively by the computer program developed, and the mechanism that the column with low permeability can also accelerate the consolidation of soil was illustrated. Moreover, a simplified method was proposed for consolidation analysis of layered composite foundation with column of high permeability. Finally, a case study was made to show the practical application of this computer program.
The work presented herein not only reveals the consolidation behavior of composite foundation, but also provides new theory and technique support for the computation of settlement induced by consolidation of composite foundation, and thus makes the computation theory for the settlement of composite foundation more perfect.
引文
1. Adachi T, Oka F, Tange Y. Finite element of two dimensional consolidation using, an elasto-viscoplastic constitutive equation. Proc. 4th Int. Conf. Numerical Methods on Geomechanics, 1982: 287-296.
2. Al-Khafaji Z A, Craig W H. Drainage and reinforcement of soft clay tank foundation by sand columns. Geotechnique, 2000,50(6): 709-713.
3. Almeida M.S.S. Britto A.M. Parry R.H.G. Numerical modeling of centrifuged embankment on soft clay. Can. Geotech. J., 1986, 23:103-114.
4. Al-Tabbaa A. Excess pore pressure during consolidation and swelling with radial drainage. Geotechnique, 1995,45(4): 701-707.
5. Al-Tabbaa A, Muir Wood D. Horizontal drainage during consolidation: insights gained from analyses of a simple problem. Geotechnique, 1991,41(4): 571-585.
6. Balaam N, Booker J. Analysis of rigid rafts supported by granular piles. I. J. Num. Anal. Meth. Geomech., 1981(5): 379-403.
7. Balaam N, Booker J. Effect of stone column yield on settlement of rigid foundation in stabilized clay. I. J. Num. Anal. Meth. Geomech., 1985(3): 331-351.
8. Biot M A. General theory of three-dimensional consolidation. J. Appl. Physics, 1941, (12): 155-164.
9. Broms B, Boman P. Lime columns-A new foundation method. Journal of The Geotechnical Engineering Division, ASCE, 1979, 105(GT4):539-556.
10. Canetta G, Nova R. A numerical method for the analysis of ground improved by columnar inclusion. Computers and Geotechnics, 1989, 7:99-114.
11. Chai J C, Norihiko Miura. Investigation of factors affecting vertical drains behavior. Journal of Geotechnical and Geoenvironmental Engineering. 1999,125(3): 216-226.
12. Charles J A, Watts K S. Compressibility of soft clay reinforcement with granular columns. Proceedings of The Eighth European Conference of Soils Mechanics and Foundation Engineering. 1983:347-352.
13. Cheung Y K, Lee P P K & Xie K H. Some remarks on two and three dimensional consolidation analysis of sand-drained ground. Computers and Geotechnics, 1991,12:73-87.
14. Christian J T, Boehmer J W. Plain strain consolidation by finite elements. Proc. Of ASCE, 1970, SM4: 1435-1457.
15. Christian J T, Boehmer J W. Consolidation of a layer under a strip load. Proc. of ASCE, 1972, SM7: 693-707.
16. Davis E H, Poulos H G. Rate of settlement under two- and three-dimensional conditions. Geotechnique, 1972,22(1): 95-114.
17. Duncan J M, Chang C Y. Non-linear analysis of stress and strain in soils. J. Soil Mech. Div. ASCE, 1970:1629-1653.
18. Geddes G. Stress in foundation soils due to vertical subsurface loading. Geotechnique, 1966, 16(3).
19. Han Jie, Ye Shu-Lin. Simplified method for consolidation rate of stone column reinforced foundations. Journal of Geotechnical and Geoenvironmental Engineering. 2001,127(7): 597-603.
20. Hansbo S, Jamiolkowski M, Kok L. Consolidation by vertical drains. Geotechnique, 1981, 31(1): 45-66.
21. Hwang C T, Morgenstern N R, Murray D W. Application of the finite element method to consolidation problems. Application of The Finite Element Method in Geotechnical Engineering. Mississippi: Vicksburg, 1972, Vol2: 739-760.
22. John D. Mckinley. Coupled consolidation of a solid, infinite cylinder using a Terzaghi formulation. Computer and Geotechnics, 1998, 23:193-204.
23. Juran I, Guermazi A. settlement response of soft soils reinforced by compacted sand columns. Journal of Geotechnical Engineering, 1988,114(8): 930-943.
24. Karunaratne G P, Tan S A, Lee S L. Analysis of flexible drains in Changi reclamation. Can. Geotech. J. 1989, 26:401-417.
25. Kezdi A. The bearing capacity of pile and pile groups. Proc. 4th ICSMFE, London, Vol (2), 1957.
26. Lewis R W, Roberts G K, Zienkiewicz O C. A non-linear flow and deformation analysis of consolidated problems. Proc. 2nd Int. Conf. Numerical Methods on Geomechanics, 1976:1106- 1118.
27. Magnan J P, Humbert P, Belkeziz A, Mouratidis A. Finite element analysis of soil consolidation, with special reference to the case of strain hardening elasto-plastic stress-strain models. Proc. 4th Int. Conf. Numerical Methods on Geomechanics, 1982: 327-336.
28. Majorana C, Mazzalai P, Odorizzi S. Prediction of the settlement of steel petroleum tanks resting on stone columns reinforcement soil. Proceedings of The Eighth European Conference of Soils Mechanics and Foundation Engineering. 1983:271-274.
29. Manoharan N, Dasgupta S P. Consolidation analysis of elasto-plastic soil. Computers and Structures, 1995,54(6): 1005-1021.
30. Mindlin R D. Force at a point in the interior of a semi-infinite solid. J. Appl. Phys., 1936, 7(5).
31. Onoue A. Consolidation by vertical drains taking well resistance and swear into consolidation. Soils and foundations, 1988, 28(4): 165-174.
32. Oka F, Adachi T, Okano Y. Two-dimensional consolidation analysis using an elasto-viscoplastic constitutive equation. Int. J. Numer. Anal. Meth. Geomech, 1986, 10:1-16.
33. Parbaha A., Pradhan T.B.S., Kishida T. Static response of fly ash columnar improved ground. Can.
Geotech. J., 2001,38:276-286.
34. Poulous H G, Davis E H. Pile foundation analysis and design. John Wiley and Sons, New York, 1980.
35. Priebe H J. The design of vibro replacement. Ground Engng.1995, 28(10): 31-37.
36. Randolph M F, Wroth C P. Analysis of deformation of vertically loaded piles. ASCE, 1978, 104(GT12): 1465-1488.
37. Richter T. Nonlinear consolidation models for finite element computations. Proc. 3rd Int. Conf. Numerical Methods on Geomechanics, 1979:181-190.
38. Sainz J A, Sagaseta C. Plane strain consolidation of elasto-plastic soft clays. Proc. 4th Int. Conf. Numerical Methods on Geomechanics, 1982: 373-381.
39. Sandhu R S, Wilson E L. Finite element analysis of seepage in elastic media. J. Engg. Mech. Div., ASCE proc., 1969, No.Em3: 641.
40. Schweiger H F, Pande G N. Numerical a analysis of a road embankment constructed on soft clay stabilized with stone column. Proc. Num. Method in Geomechanics. Rotterdam: Balkema, 1988, 1329-1333.
41. Seed H B, Reese L C. The action of soft clay along friction piles. Transaction, ASCE, 1957:731-754.
42. Siriwardane H J, Desai C S. Two numerical schemes for nonlinear consolidation. Int. J. Numer. Meth. Engng, 1981, 17:405-426.
43. Shahu J T, Madhav M R, Hayashi S. Analysis of soft ground-granular pile-granular mat system. Computer and Geotechnics, 2000, 27:45-62.
44. Taiebat H A, Carter J P. A semi-analysis finite element method for three-dimensional consolidation analysis. Computer and Geotechnics, 2001, 28:55-78.
45. Takashi Matsumoto. Finite element analysis of immediate and consolidation deformation based on effectives stress principle. Soils and Foundations, 1976,16(4): 23-34.
46. Tamotsu Matsui, Nobuharu Abe. Multi-dimensional elasto-plastic consolidation analysis by finite element method. Soils and Foundations, Vol21, No 1, 1981:79-95.
47. Tang X W, Onitsuka K. Rigorous solutions of vertical drains considering radial and vertical flow under equal condition. 31 st Annual Conference of Japanese Geotechnical Society. 1996:633-634.
48. Tang X W. A study for consolidation of ground with drain system. Japan Saga: Saga University, 1998.
49. Tang X W, Onitsuka K. Analytical solution of consolidation of double-layered ground with vertical drains. Proceedings of 52nd Annual Conference of JSCE. 1997:350-351.
50. Tang X W. A study for consolidation of ground with vertical drain system. PH.D. Dissertation, Saga University, Japan, 1998.
51. Xie K H, Gao P, Xie X Y. Consolidation theory for soft clays reinforced by cement or granular columns. Computer Method and Advances in Geomechanics, 2001 ,Rotterdam: Balkema, 1263-1268.
52. Xie K H, Pan Q Y, Zeng G X. & Zhu X R. Prediction versus performance on the behavior of soft clay
ground improved by vertical drains. Proc. of Symposium on versus Performance in Geotechnical Engrg. Bangkok, 1993:105-113.
53. Xie K H, Xu, Y, Wang K H. Consolidation analysis of composite ground beneath expressway by 3D FEM. Proc. of 3rd Int. Symposium on 3D Finite Element for Pavement Analysis, Design and Resaerch. Rotterdam: Balkema, 2002:197-207.
54. Yoshikuni H. Design and control of construction in the vertical drain method. Gihoudou Tokyo, 1979.
55. Yoshikuni H, Nakanodo H. Consolidation of soils by vertical drain wells with finite permeability. Soils and Foundations, 1974, 14(2): 35-46.
56. Zaman M, Gopalasingam A, Laguros J G. Consolidation settlement of bridge approach foundation. J. Geotech. Engng, ASCE, 1991,117:219-240.
57. Zeng G X, Xie K H & Shi Z Y. Consolidation analysis of sand-drained ground by FEM. Proc. 8th ARCSMFE. Kyoto, 1987, Vol. 1: 139-142.
58．佐滕悟．基础桩支持力学结构(日)．土工技术，1965，20(1)：1-5．
59．艾尔斯著．微分方程原理及题解．北京：晓园出版社，1993．
60．艾智勇，杨敏．广义Mindlin解在多层地基单桩分析中的应用．土木工程学报，2001，34(2)：89-95．
61．曹明葆，王德纯．用应力路径法分析路堤的稳定性．土木工程学报，1988，21(1)．
62．陈光敬．成层横观各向同性地基的解析法分析及其工程应用．上海：同济大学博士论文，1998．
63．陈明中，龚晓南，严平．单桩沉降的一种解析解法．水利学报，2000，Vol(8)：70-74．
64．池跃君，宋二祥，陈肇元．刚性桩复合地基竖向承载特性分析．工程力学，2003，20(4)：9-14．
65．池跃君，宋二祥，金淮，高文新．素混凝土桩复合地基荷载传递机理的试验研究．工业建筑．2001，31(4)：39-42．
66．段继伟．柔性桩复合地基的数值分析．杭州：浙江大学博士论文，1993．
67．段继伟．单桩带台复合地基的有限元分析．地基处理，1994，5(2)：5-12．
68．宫全美．基于Mindlin位移解的群桩沉降计算．地下空间，2001，21(3)：167-172．
69．龚晓南．软土地基固结有限元分析．杭州：浙江大学硕士论文，1981．
70．龚晓南．复合地基．杭州：浙江大学出版社，1992：138-151．
71．顾洪，李启涛，胡键．粉喷桩荷载传递特性原位试验研究．水利水电科技进展，1988，18(5)：42-43．
72．顾尧章，金波．轴对称荷载下多层地基的Biot固结及其变形．工程力学，1992，9(3)：81-94．
73．郭本宏．数学物理方法．山西：山西高校联合出版社，1992．
74．韩杰，叶书麟．考虑井阻和涂抹作用碎石桩复合地基固结度计算．第三届全国地基处理学术讨论会论文集，杭州：浙江大学出版社，1992a：351-358．
75．韩杰，叶书麟．碎石桩复合地基的有限元分析．岩土工程学报，vol．14，supplement，1992b：13-19．
76．韩煊，李宁．复合地基中群桩相互作用机理的数值试验研究．土木工程学报，1999，32(4)：75-80．
77．金振奋，陈仁朋，凌道盛，陈云敏．群桩地基中应力及变形规律数值分析．工业建筑，2001，31(10)：37-42．
78．李静文．联合应用Boussinesq和Mindlin解求桩土复合地基中的应力及其沉降．地基处理，1993，4(4)：15-21．
79．李宁，韩煊．复合地基中褥垫层作用机理研究．岩土力学，2000，21(1)：10-15．
80．李小青，薛林华，黄文涛．复合地基承载特性的数值分析研究．探矿工程，2002(5)：7-9．
81．粱义聪，周常春，邓安福，刘典湘．竖直荷载下群桩受力变形特性弹塑性分析．地下空间，2001，21(2)：81-86．
82．刘和元，刘松玉．超长水泥土搅拌桩复合地基性状研究．东南大学学报，1999，29(2)：63-69．
83．刘兴旺，谢康和，潘秋元，曾国熙．竖向排水地基粘弹性固结解析理论．土木工程学报，1998，31(1)：10-19．
84．刘蕴华，张乃良．数学物理方程及其应用．南京：河海大学出版社，1994．
85．陆贻杰，周国钧．搅拌桩复合地基模型试验及三维有限元分析．岩土工程学报，1989，11(5)：86-91．
86．马克生，龚晓南．模量随深度变化的单桩沉降．工业建筑．2000，30(1)：66-67．
87．南京工学院数学教研组．数学物理方程与特殊函数(第二版)．北京：高等教育出版社，1982．
88．钱家欢主编．土力学．南京：河海大学出版社，1995．
89．钱家欢，殷宗泽．土工原理与计算(第二版)．北京：中国水利水电出版社，1996．
90．秦建庆，叶观宝，费涵昌．Mindlin解在水泥土桩复合地基变形中的应用．岩土工程技术，2000(1)：17-20．
91．沈珠江．用有限单元法计算软土地基的固结变形．水利水运科技情报，1977，Nol：7-15．
92．施建勇，邹坚．深层搅拌桩复合地基沉降计算理论研究．岩土力学，2002，23(3)：309-320．
93．孙志东．层状地基中单桩沉降分析．江苏建筑，1995(4)：30-32．
94．王国体，王志亮．单桩侧摩擦阻力曲线的推求与拟合．合肥工业大学学报，2000，23(2)：205-209．
95．王建华，陆建飞，沈为平．Biot固结理论在单桩负摩擦研究中的应用．岩土工程学报，2000，22(5)：590-593．
96．王瑞春，谢康和．变荷载下竖向排水井地基粘弹性固结沉降解析解．土木工程学报，2001a，34(6)：93-99．
97．王瑞春，谢康和．考虑应力集中效应的散体材料桩复合地基固结解析分析．科技通报，2001b，17(5)：26-31．
98．王瑞春，谢康和．双层散体材料桩复合地基固结解析理论．岩土工程学报，2001c，23(4)：418-421．
99．王瑞春．竖井地基和散体材料桩复合地基固结解析研究．杭州：浙江大学，2001d．
100．王瑞春，谢康和，关山海．变化荷载下散体材料桩复合地基固结解析解．浙江大学学报(工学版)，2002，36(1)：12-16．
101．王士杰，张梅，张吉占．对Mindlin解求地基附加应力的进一步探讨．第八届土力学及岩土工程学术会议论文集，北京：万国学术出版社，1999：247-250．
102．吴永红．碎石桩复合地基的弹塑性有限元分析．首届全国岩土力学与工程青年工作者学术讨
论会论文集．杭州：浙江大学出版社，1992：514-517．
103．吴永红，顾晓鲁．桩基加固软土地基的有限元分析．第三届全国地基处理学术讨论会论文集．杭州：浙江大学出版社，1992：538-541．
104．谢康和．砂井地基：固结理论、数值分析与优化设计．杭州：浙江大学博士学位论文，1987．
105．谢康和．复合地基固结理论研究现状与发展．地基处理，1993，4(3)：1-14．
106．谢康和．双层地基一维固结理论与应用．岩土工程学报，1994，16(5)：24-35．
107．谢康和．土工有限元分析理论与程序．杭州：浙江大学研究生系列教材(内部实用)，1999．
108．谢康和，曾国熙．等应变条件下的砂井地基固结解析理论．岩土工程学报，1989，11(2)：3-17．
109．谢康和，周健．岩土工程有限元分析理论与应用．北京：科学出版社，2002．
110．徐洋．复合双层地基的概念及应用．兰州：第七届全国地基处理学术会议，2002a：502-506．
111．徐洋，谢康和，梁仕华．复合地基的平面应力扩散效应．土木工程学报，2002b，35(2)：57-60．
112．杨从军．长短桩复合地基沉降计算．杭州：浙江大学硕士论文，2002．
113．杨敏，艾智勇．多层地基内部作用竖向集中力时的广义Mindlin课题解．第八届土力学及岩土工程学术会议论文集，北京：万国学术出版社，1999：243-246．
114．杨涛．复合地基沉降计算理论、位移反分析模型和二灰土桩软基加固试验研究．南京：河海大学博士学位论文，1997．
115．杨涛，殷宗泽．复合地基沉降的复合本构有限元分析．岩土力学，1998，19(2)：19-25．
116．殷宗泽，徐鸿江，朱泽民．饱和粘土平面固结问题有限单元法．华东水利学院学报，1978，No1：71-79．
117．袁聚云，赵锡宏．竖向均布荷载作用在地基内部时的土中应力公式．上海力学，1995，16(3)：213-222．
118．曾国熙，谢康和，朱向荣等．竖向排水固结理论研究的若干进展．见：《曾国熙教授科技论文选集》编委会．曾国熙教授科技论文选集．北京：中国建筑工业出版社，1997：126-139．
119．张捷，韩杰，叶书麟．水泥土桩复合地基的固结特性分析．第七届全国土力学及基础工程学术研讨会议论文集，北京：中国建筑工业出版社，1994：542-545．
120．章胜南，卞守中，汪友平．深层水泥搅拌桩复合地基沉降计算的探讨．第三届全国地基处理学术讨论会论文集，杭州：浙江大学出版社，1992：106-109．
121．章胜南，周荣祥．承台下桩的荷载传递规律研究．工业建筑，1999，29(7)：35-40．
122．张曙光，谢康和，潘秋元，施淑群．条形荷载下搅拌桩复合地基的固结特性．第三届全国地基处理学术讨论会论文集，浙江大学出版社，1992：162-165．
123．张小平，顾强生．粉煤灰桩的现场试验研究．工程勘查，2000(1)：51-53．
124．张小平，俞仲泉．用Mindlin解推求复合地基中附加应力的计算公式．河海大学学报，1999，27(2)：35-39．
125．张雁，黄强．半刚性桩复合地基性状分析，岩土工程学报，1993，15(2)：86-93．
126．张延军．FEM-EFGM耦合法分析砂井地基的固结变形．岩土力学与工程学报，2003，22(9)：
1542-1546．
127．张英，沈苾文，余寅春．单桩复合地基承载性状的数值模拟与研究．浙江水利科技，2002(3)：55-57．
128．赵维炳．广义Voigt模型模拟的饱和土体轴对称固结理论解．河海大学学报，1988，16(5)：47-56．
129．赵维炳，施建勇．软土的固结与流变．南京：河海大学出版社，1996．
130．郑俊杰，刘志刚，吴世明．石灰桩复合地基的固结分析．华中理工大学学报，28(5)，2000：111-113．
131．周履，范赋群．复合材料力学．北京：高等教育出版社，1991．
132．朱百里，沈珠江．计算土力学．上海：上海科学技术出版社，1990．
133．朱伯芳．有限单元法原理与应用．北京：中国水利水电出版社，1998．
2. Al-Khafaji Z A, Craig W H. Drainage and reinforcement of soft clay tank foundation by sand columns. Geotechnique, 2000,50(6): 709-713.
3. Almeida M.S.S. Britto A.M. Parry R.H.G. Numerical modeling of centrifuged embankment on soft clay. Can. Geotech. J., 1986, 23:103-114.
4. Al-Tabbaa A. Excess pore pressure during consolidation and swelling with radial drainage. Geotechnique, 1995,45(4): 701-707.
5. Al-Tabbaa A, Muir Wood D. Horizontal drainage during consolidation: insights gained from analyses of a simple problem. Geotechnique, 1991,41(4): 571-585.
6. Balaam N, Booker J. Analysis of rigid rafts supported by granular piles. I. J. Num. Anal. Meth. Geomech., 1981(5): 379-403.
7. Balaam N, Booker J. Effect of stone column yield on settlement of rigid foundation in stabilized clay. I. J. Num. Anal. Meth. Geomech., 1985(3): 331-351.
8. Biot M A. General theory of three-dimensional consolidation. J. Appl. Physics, 1941, (12): 155-164.
9. Broms B, Boman P. Lime columns-A new foundation method. Journal of The Geotechnical Engineering Division, ASCE, 1979, 105(GT4):539-556.
10. Canetta G, Nova R. A numerical method for the analysis of ground improved by columnar inclusion. Computers and Geotechnics, 1989, 7:99-114.
11. Chai J C, Norihiko Miura. Investigation of factors affecting vertical drains behavior. Journal of Geotechnical and Geoenvironmental Engineering. 1999,125(3): 216-226.
12. Charles J A, Watts K S. Compressibility of soft clay reinforcement with granular columns. Proceedings of The Eighth European Conference of Soils Mechanics and Foundation Engineering. 1983:347-352.
13. Cheung Y K, Lee P P K & Xie K H. Some remarks on two and three dimensional consolidation analysis of sand-drained ground. Computers and Geotechnics, 1991,12:73-87.
14. Christian J T, Boehmer J W. Plain strain consolidation by finite elements. Proc. Of ASCE, 1970, SM4: 1435-1457.
15. Christian J T, Boehmer J W. Consolidation of a layer under a strip load. Proc. of ASCE, 1972, SM7: 693-707.
16. Davis E H, Poulos H G. Rate of settlement under two- and three-dimensional conditions. Geotechnique, 1972,22(1): 95-114.
17. Duncan J M, Chang C Y. Non-linear analysis of stress and strain in soils. J. Soil Mech. Div. ASCE, 1970:1629-1653.
18. Geddes G. Stress in foundation soils due to vertical subsurface loading. Geotechnique, 1966, 16(3).
19. Han Jie, Ye Shu-Lin. Simplified method for consolidation rate of stone column reinforced foundations. Journal of Geotechnical and Geoenvironmental Engineering. 2001,127(7): 597-603.
20. Hansbo S, Jamiolkowski M, Kok L. Consolidation by vertical drains. Geotechnique, 1981, 31(1): 45-66.
21. Hwang C T, Morgenstern N R, Murray D W. Application of the finite element method to consolidation problems. Application of The Finite Element Method in Geotechnical Engineering. Mississippi: Vicksburg, 1972, Vol2: 739-760.
22. John D. Mckinley. Coupled consolidation of a solid, infinite cylinder using a Terzaghi formulation. Computer and Geotechnics, 1998, 23:193-204.
23. Juran I, Guermazi A. settlement response of soft soils reinforced by compacted sand columns. Journal of Geotechnical Engineering, 1988,114(8): 930-943.
24. Karunaratne G P, Tan S A, Lee S L. Analysis of flexible drains in Changi reclamation. Can. Geotech. J. 1989, 26:401-417.
25. Kezdi A. The bearing capacity of pile and pile groups. Proc. 4th ICSMFE, London, Vol (2), 1957.
26. Lewis R W, Roberts G K, Zienkiewicz O C. A non-linear flow and deformation analysis of consolidated problems. Proc. 2nd Int. Conf. Numerical Methods on Geomechanics, 1976:1106- 1118.
27. Magnan J P, Humbert P, Belkeziz A, Mouratidis A. Finite element analysis of soil consolidation, with special reference to the case of strain hardening elasto-plastic stress-strain models. Proc. 4th Int. Conf. Numerical Methods on Geomechanics, 1982: 327-336.
28. Majorana C, Mazzalai P, Odorizzi S. Prediction of the settlement of steel petroleum tanks resting on stone columns reinforcement soil. Proceedings of The Eighth European Conference of Soils Mechanics and Foundation Engineering. 1983:271-274.
29. Manoharan N, Dasgupta S P. Consolidation analysis of elasto-plastic soil. Computers and Structures, 1995,54(6): 1005-1021.
30. Mindlin R D. Force at a point in the interior of a semi-infinite solid. J. Appl. Phys., 1936, 7(5).
31. Onoue A. Consolidation by vertical drains taking well resistance and swear into consolidation. Soils and foundations, 1988, 28(4): 165-174.
32. Oka F, Adachi T, Okano Y. Two-dimensional consolidation analysis using an elasto-viscoplastic constitutive equation. Int. J. Numer. Anal. Meth. Geomech, 1986, 10:1-16.
33. Parbaha A., Pradhan T.B.S., Kishida T. Static response of fly ash columnar improved ground. Can.
Geotech. J., 2001,38:276-286.
34. Poulous H G, Davis E H. Pile foundation analysis and design. John Wiley and Sons, New York, 1980.
35. Priebe H J. The design of vibro replacement. Ground Engng.1995, 28(10): 31-37.
36. Randolph M F, Wroth C P. Analysis of deformation of vertically loaded piles. ASCE, 1978, 104(GT12): 1465-1488.
37. Richter T. Nonlinear consolidation models for finite element computations. Proc. 3rd Int. Conf. Numerical Methods on Geomechanics, 1979:181-190.
38. Sainz J A, Sagaseta C. Plane strain consolidation of elasto-plastic soft clays. Proc. 4th Int. Conf. Numerical Methods on Geomechanics, 1982: 373-381.
39. Sandhu R S, Wilson E L. Finite element analysis of seepage in elastic media. J. Engg. Mech. Div., ASCE proc., 1969, No.Em3: 641.
40. Schweiger H F, Pande G N. Numerical a analysis of a road embankment constructed on soft clay stabilized with stone column. Proc. Num. Method in Geomechanics. Rotterdam: Balkema, 1988, 1329-1333.
41. Seed H B, Reese L C. The action of soft clay along friction piles. Transaction, ASCE, 1957:731-754.
42. Siriwardane H J, Desai C S. Two numerical schemes for nonlinear consolidation. Int. J. Numer. Meth. Engng, 1981, 17:405-426.
43. Shahu J T, Madhav M R, Hayashi S. Analysis of soft ground-granular pile-granular mat system. Computer and Geotechnics, 2000, 27:45-62.
44. Taiebat H A, Carter J P. A semi-analysis finite element method for three-dimensional consolidation analysis. Computer and Geotechnics, 2001, 28:55-78.
45. Takashi Matsumoto. Finite element analysis of immediate and consolidation deformation based on effectives stress principle. Soils and Foundations, 1976,16(4): 23-34.
46. Tamotsu Matsui, Nobuharu Abe. Multi-dimensional elasto-plastic consolidation analysis by finite element method. Soils and Foundations, Vol21, No 1, 1981:79-95.
47. Tang X W, Onitsuka K. Rigorous solutions of vertical drains considering radial and vertical flow under equal condition. 31 st Annual Conference of Japanese Geotechnical Society. 1996:633-634.
48. Tang X W. A study for consolidation of ground with drain system. Japan Saga: Saga University, 1998.
49. Tang X W, Onitsuka K. Analytical solution of consolidation of double-layered ground with vertical drains. Proceedings of 52nd Annual Conference of JSCE. 1997:350-351.
50. Tang X W. A study for consolidation of ground with vertical drain system. PH.D. Dissertation, Saga University, Japan, 1998.
51. Xie K H, Gao P, Xie X Y. Consolidation theory for soft clays reinforced by cement or granular columns. Computer Method and Advances in Geomechanics, 2001 ,Rotterdam: Balkema, 1263-1268.
52. Xie K H, Pan Q Y, Zeng G X. & Zhu X R. Prediction versus performance on the behavior of soft clay
ground improved by vertical drains. Proc. of Symposium on versus Performance in Geotechnical Engrg. Bangkok, 1993:105-113.
53. Xie K H, Xu, Y, Wang K H. Consolidation analysis of composite ground beneath expressway by 3D FEM. Proc. of 3rd Int. Symposium on 3D Finite Element for Pavement Analysis, Design and Resaerch. Rotterdam: Balkema, 2002:197-207.
54. Yoshikuni H. Design and control of construction in the vertical drain method. Gihoudou Tokyo, 1979.
55. Yoshikuni H, Nakanodo H. Consolidation of soils by vertical drain wells with finite permeability. Soils and Foundations, 1974, 14(2): 35-46.
56. Zaman M, Gopalasingam A, Laguros J G. Consolidation settlement of bridge approach foundation. J. Geotech. Engng, ASCE, 1991,117:219-240.
57. Zeng G X, Xie K H & Shi Z Y. Consolidation analysis of sand-drained ground by FEM. Proc. 8th ARCSMFE. Kyoto, 1987, Vol. 1: 139-142.
58．佐滕悟．基础桩支持力学结构(日)．土工技术，1965，20(1)：1-5．
59．艾尔斯著．微分方程原理及题解．北京：晓园出版社，1993．
60．艾智勇，杨敏．广义Mindlin解在多层地基单桩分析中的应用．土木工程学报，2001，34(2)：89-95．
61．曹明葆，王德纯．用应力路径法分析路堤的稳定性．土木工程学报，1988，21(1)．
62．陈光敬．成层横观各向同性地基的解析法分析及其工程应用．上海：同济大学博士论文，1998．
63．陈明中，龚晓南，严平．单桩沉降的一种解析解法．水利学报，2000，Vol(8)：70-74．
64．池跃君，宋二祥，陈肇元．刚性桩复合地基竖向承载特性分析．工程力学，2003，20(4)：9-14．
65．池跃君，宋二祥，金淮，高文新．素混凝土桩复合地基荷载传递机理的试验研究．工业建筑．2001，31(4)：39-42．
66．段继伟．柔性桩复合地基的数值分析．杭州：浙江大学博士论文，1993．
67．段继伟．单桩带台复合地基的有限元分析．地基处理，1994，5(2)：5-12．
68．宫全美．基于Mindlin位移解的群桩沉降计算．地下空间，2001，21(3)：167-172．
69．龚晓南．软土地基固结有限元分析．杭州：浙江大学硕士论文，1981．
70．龚晓南．复合地基．杭州：浙江大学出版社，1992：138-151．
71．顾洪，李启涛，胡键．粉喷桩荷载传递特性原位试验研究．水利水电科技进展，1988，18(5)：42-43．
72．顾尧章，金波．轴对称荷载下多层地基的Biot固结及其变形．工程力学，1992，9(3)：81-94．
73．郭本宏．数学物理方法．山西：山西高校联合出版社，1992．
74．韩杰，叶书麟．考虑井阻和涂抹作用碎石桩复合地基固结度计算．第三届全国地基处理学术讨论会论文集，杭州：浙江大学出版社，1992a：351-358．
75．韩杰，叶书麟．碎石桩复合地基的有限元分析．岩土工程学报，vol．14，supplement，1992b：13-19．
76．韩煊，李宁．复合地基中群桩相互作用机理的数值试验研究．土木工程学报，1999，32(4)：75-80．
77．金振奋，陈仁朋，凌道盛，陈云敏．群桩地基中应力及变形规律数值分析．工业建筑，2001，31(10)：37-42．
78．李静文．联合应用Boussinesq和Mindlin解求桩土复合地基中的应力及其沉降．地基处理，1993，4(4)：15-21．
79．李宁，韩煊．复合地基中褥垫层作用机理研究．岩土力学，2000，21(1)：10-15．
80．李小青，薛林华，黄文涛．复合地基承载特性的数值分析研究．探矿工程，2002(5)：7-9．
81．粱义聪，周常春，邓安福，刘典湘．竖直荷载下群桩受力变形特性弹塑性分析．地下空间，2001，21(2)：81-86．
82．刘和元，刘松玉．超长水泥土搅拌桩复合地基性状研究．东南大学学报，1999，29(2)：63-69．
83．刘兴旺，谢康和，潘秋元，曾国熙．竖向排水地基粘弹性固结解析理论．土木工程学报，1998，31(1)：10-19．
84．刘蕴华，张乃良．数学物理方程及其应用．南京：河海大学出版社，1994．
85．陆贻杰，周国钧．搅拌桩复合地基模型试验及三维有限元分析．岩土工程学报，1989，11(5)：86-91．
86．马克生，龚晓南．模量随深度变化的单桩沉降．工业建筑．2000，30(1)：66-67．
87．南京工学院数学教研组．数学物理方程与特殊函数(第二版)．北京：高等教育出版社，1982．
88．钱家欢主编．土力学．南京：河海大学出版社，1995．
89．钱家欢，殷宗泽．土工原理与计算(第二版)．北京：中国水利水电出版社，1996．
90．秦建庆，叶观宝，费涵昌．Mindlin解在水泥土桩复合地基变形中的应用．岩土工程技术，2000(1)：17-20．
91．沈珠江．用有限单元法计算软土地基的固结变形．水利水运科技情报，1977，Nol：7-15．
92．施建勇，邹坚．深层搅拌桩复合地基沉降计算理论研究．岩土力学，2002，23(3)：309-320．
93．孙志东．层状地基中单桩沉降分析．江苏建筑，1995(4)：30-32．
94．王国体，王志亮．单桩侧摩擦阻力曲线的推求与拟合．合肥工业大学学报，2000，23(2)：205-209．
95．王建华，陆建飞，沈为平．Biot固结理论在单桩负摩擦研究中的应用．岩土工程学报，2000，22(5)：590-593．
96．王瑞春，谢康和．变荷载下竖向排水井地基粘弹性固结沉降解析解．土木工程学报，2001a，34(6)：93-99．
97．王瑞春，谢康和．考虑应力集中效应的散体材料桩复合地基固结解析分析．科技通报，2001b，17(5)：26-31．
98．王瑞春，谢康和．双层散体材料桩复合地基固结解析理论．岩土工程学报，2001c，23(4)：418-421．
99．王瑞春．竖井地基和散体材料桩复合地基固结解析研究．杭州：浙江大学，2001d．
100．王瑞春，谢康和，关山海．变化荷载下散体材料桩复合地基固结解析解．浙江大学学报(工学版)，2002，36(1)：12-16．
101．王士杰，张梅，张吉占．对Mindlin解求地基附加应力的进一步探讨．第八届土力学及岩土工程学术会议论文集，北京：万国学术出版社，1999：247-250．
102．吴永红．碎石桩复合地基的弹塑性有限元分析．首届全国岩土力学与工程青年工作者学术讨
论会论文集．杭州：浙江大学出版社，1992：514-517．
103．吴永红，顾晓鲁．桩基加固软土地基的有限元分析．第三届全国地基处理学术讨论会论文集．杭州：浙江大学出版社，1992：538-541．
104．谢康和．砂井地基：固结理论、数值分析与优化设计．杭州：浙江大学博士学位论文，1987．
105．谢康和．复合地基固结理论研究现状与发展．地基处理，1993，4(3)：1-14．
106．谢康和．双层地基一维固结理论与应用．岩土工程学报，1994，16(5)：24-35．
107．谢康和．土工有限元分析理论与程序．杭州：浙江大学研究生系列教材(内部实用)，1999．
108．谢康和，曾国熙．等应变条件下的砂井地基固结解析理论．岩土工程学报，1989，11(2)：3-17．
109．谢康和，周健．岩土工程有限元分析理论与应用．北京：科学出版社，2002．
110．徐洋．复合双层地基的概念及应用．兰州：第七届全国地基处理学术会议，2002a：502-506．
111．徐洋，谢康和，梁仕华．复合地基的平面应力扩散效应．土木工程学报，2002b，35(2)：57-60．
112．杨从军．长短桩复合地基沉降计算．杭州：浙江大学硕士论文，2002．
113．杨敏，艾智勇．多层地基内部作用竖向集中力时的广义Mindlin课题解．第八届土力学及岩土工程学术会议论文集，北京：万国学术出版社，1999：243-246．
114．杨涛．复合地基沉降计算理论、位移反分析模型和二灰土桩软基加固试验研究．南京：河海大学博士学位论文，1997．
115．杨涛，殷宗泽．复合地基沉降的复合本构有限元分析．岩土力学，1998，19(2)：19-25．
116．殷宗泽，徐鸿江，朱泽民．饱和粘土平面固结问题有限单元法．华东水利学院学报，1978，No1：71-79．
117．袁聚云，赵锡宏．竖向均布荷载作用在地基内部时的土中应力公式．上海力学，1995，16(3)：213-222．
118．曾国熙，谢康和，朱向荣等．竖向排水固结理论研究的若干进展．见：《曾国熙教授科技论文选集》编委会．曾国熙教授科技论文选集．北京：中国建筑工业出版社，1997：126-139．
119．张捷，韩杰，叶书麟．水泥土桩复合地基的固结特性分析．第七届全国土力学及基础工程学术研讨会议论文集，北京：中国建筑工业出版社，1994：542-545．
120．章胜南，卞守中，汪友平．深层水泥搅拌桩复合地基沉降计算的探讨．第三届全国地基处理学术讨论会论文集，杭州：浙江大学出版社，1992：106-109．
121．章胜南，周荣祥．承台下桩的荷载传递规律研究．工业建筑，1999，29(7)：35-40．
122．张曙光，谢康和，潘秋元，施淑群．条形荷载下搅拌桩复合地基的固结特性．第三届全国地基处理学术讨论会论文集，浙江大学出版社，1992：162-165．
123．张小平，顾强生．粉煤灰桩的现场试验研究．工程勘查，2000(1)：51-53．
124．张小平，俞仲泉．用Mindlin解推求复合地基中附加应力的计算公式．河海大学学报，1999，27(2)：35-39．
125．张雁，黄强．半刚性桩复合地基性状分析，岩土工程学报，1993，15(2)：86-93．
126．张延军．FEM-EFGM耦合法分析砂井地基的固结变形．岩土力学与工程学报，2003，22(9)：
1542-1546．
127．张英，沈苾文，余寅春．单桩复合地基承载性状的数值模拟与研究．浙江水利科技，2002(3)：55-57．
128．赵维炳．广义Voigt模型模拟的饱和土体轴对称固结理论解．河海大学学报，1988，16(5)：47-56．
129．赵维炳，施建勇．软土的固结与流变．南京：河海大学出版社，1996．
130．郑俊杰，刘志刚，吴世明．石灰桩复合地基的固结分析．华中理工大学学报，28(5)，2000：111-113．
131．周履，范赋群．复合材料力学．北京：高等教育出版社，1991．
132．朱百里，沈珠江．计算土力学．上海：上海科学技术出版社，1990．
133．朱伯芳．有限单元法原理与应用．北京：中国水利水电出版社，1998．