深基坑工程建模理论与稳定性评判的关键技术研究
|
摘要
基坑工程中的数值仿真存在着许多的技术难题，本文在系统总结基坑工程中存在的关键问题的基础上，从基坑的建模、反分析方法、稳定性分析及临界变形指标几个方面进行了深入研究，提出了相应的解决方法。传统有限元模拟大型深基坑施工时，模型难以真实反映挡墙和支护结构的弯曲变形效应，故其计算结果与实际相差较大，这对工程是不利的。为了在数值模拟方面力求合理地反映基坑工程中复杂结构体系的实际效应，迫切需要建立一种新的数值计算模型，一方面可以提高传统有限元的计算精度，另一方面，既可直接应用于三维实体和中厚度板壳结构又易于与其它带转动自由度的梁单元相容，并且在处理复杂组合结构体时无需引入任何过渡单元就可完成数值实施。本文首先建立了一种新型单元——RH8单元，推导了该单元的确定性有限元及随机有限元列式，建立了基坑的有限元数值模拟的新模型；在此基础上本文对基坑的动态模拟及基坑的稳定性进行了研究。全文的主要内容如下：
1．基于非协调元理论和修正的Reissner泛函中引入独立转动场的变分原理，将转角自由度作为独立自由度，创建了一种新的三维八结点单元——RH8单元，并根据变分原理推导了相应的有限元列式，最后还对其适用性进行了讨论。
2．将本文所建立的单元用于梁、板、块体同时存在的复杂组合结构体系问题当中，讨论了该单元在处理联结问题的优势，通过若干考例验证了该单元在计算组合结构时的合理性。针对大型结构中计算量较大的问题，讨论了提高新型单元计算效率的处理方法。
3．提出了带独立转动自由度的随机变分原理，在此基础上推导了新型单元的随机有限元列式。
4．基于新型单元模式对连续墙、支撑及土体进行模拟，从而建立了基坑施工模拟的新模型，对实际工程应用中该模型存在的问题及解决方法进行了探讨。
5．系统综述了反分析计算方法，对目前反分析中存在的问题进行了总结。针对实际存在的问题，提出了并行进化演化反演算法，采用面向对象的编程思想编制了相应的程序，验证了该算法的有效性。
6．在干扰能量法和超变形法的基础上，提出了基坑稳定评判的广角度综合评判法。同时考虑参数的随机性，以杆件的干扰能量作为功能函数，提出了支撑体系的体系可靠度计算方法，采用可靠度来对基坑的稳定性进行评价。最后还对基坑临界
摘要
变形指标问题进行了探讨。
7.针对国内某一特大型深基坑施工，利用本文方法进行了应力和变形分析、土
层参数反分析、基坑支撑体系的体系可靠度分析，对基坑的安全稳定性进行了评价，
得到合理的研究结果。
关键词:深基坑、建模理论、稳定性、转动自由度、体系可靠度、临界变形指标
For the critical problems in the foundation-pit, the corresponding solutions are indicated from several aspects, i.e. the model of foundation-pit numerical value simulation, back-analysis, stability, critical target of the foundation-pit strain. When the excavation of deep foundation is simulated in three-dimension with isoparametric elements which have eight nodes, the result is difficult to reflect the influence of bending-strain exactly because of the model itself. Therefore the safety of the project is threaten. In order to simulate the excavation more exactly, a model, which can not only improve the precision but also predigest the coupling of the different structure, is urgent to be established. This paper proposes one new elements - RH8 elements(Rotation Hexahedron element of 8 nodes). The determined finite element formula and random finite element formula of the new element is also presented. Then the new model of the foundation which give facilities for the finite element numerical simulation is developed. Ultimately, the dynamic simulation and stability of the foundation is studied. The main contents of the dissertation are as follows:1. Based on the inconsistent element theory and the Reissner variational principle which is modified to the independent rotation fields, the rotation degree is considered as independent degree and a new three-dimensional eight-node element-RH8 element is developed. Then the finite element formula is presented based on the variational principle. Finally this paper discussed the appropriate range of the new element.2. The new element is introduced into the problem of composite structures in which the girder, plate and block exists at the same time. Then this paper discussed the advantages of the elements when dealing with the connect problem. Ultimately, a classical problem calculating connect structures demonstrated the new elements is rational.3. The random variational principle with independent rational degree is proposed. Then on the basis of it, the random finite element formula of the new element is presented.4. This paper simulates the continuous wall, supports and soil mass adopting the new elements. Then it established a new model for simulating the excavation and discussed the existing issues, then gives some advices to this problem.
5. The method of back-analysis and the existing problem is comprehensively summarized. This paper proposed the method of back-analysis with Parallel-Genetic-Algorithm and corresponding program has been validated correctly.6. Based on the Inteference-Energy method and Over-deformation method, the extensive angle method is applied in the judgement of the stability of ground foundation pit. At the same time, considering the uncertainty of the parameters, a system reliability method of the supports whose performance function is the inteference energy is presented. And the stability of the foundation is evaluated based-on the reliability method. Finally this paper bring forward the method to attain the critical target of the strain7. For certain project of deep foundation, stress-deformation analysis, soil parameters back-analysis, system reliability analysis of the support and the evaluation of the stability are done. The result is demonstrated rationally.
1．基于非协调元理论和修正的Reissner泛函中引入独立转动场的变分原理，将转角自由度作为独立自由度，创建了一种新的三维八结点单元——RH8单元，并根据变分原理推导了相应的有限元列式，最后还对其适用性进行了讨论。
2．将本文所建立的单元用于梁、板、块体同时存在的复杂组合结构体系问题当中，讨论了该单元在处理联结问题的优势，通过若干考例验证了该单元在计算组合结构时的合理性。针对大型结构中计算量较大的问题，讨论了提高新型单元计算效率的处理方法。
3．提出了带独立转动自由度的随机变分原理，在此基础上推导了新型单元的随机有限元列式。
4．基于新型单元模式对连续墙、支撑及土体进行模拟，从而建立了基坑施工模拟的新模型，对实际工程应用中该模型存在的问题及解决方法进行了探讨。
5．系统综述了反分析计算方法，对目前反分析中存在的问题进行了总结。针对实际存在的问题，提出了并行进化演化反演算法，采用面向对象的编程思想编制了相应的程序，验证了该算法的有效性。
6．在干扰能量法和超变形法的基础上，提出了基坑稳定评判的广角度综合评判法。同时考虑参数的随机性，以杆件的干扰能量作为功能函数，提出了支撑体系的体系可靠度计算方法，采用可靠度来对基坑的稳定性进行评价。最后还对基坑临界
摘要
变形指标问题进行了探讨。
7.针对国内某一特大型深基坑施工，利用本文方法进行了应力和变形分析、土
层参数反分析、基坑支撑体系的体系可靠度分析，对基坑的安全稳定性进行了评价，
得到合理的研究结果。
关键词:深基坑、建模理论、稳定性、转动自由度、体系可靠度、临界变形指标
For the critical problems in the foundation-pit, the corresponding solutions are indicated from several aspects, i.e. the model of foundation-pit numerical value simulation, back-analysis, stability, critical target of the foundation-pit strain. When the excavation of deep foundation is simulated in three-dimension with isoparametric elements which have eight nodes, the result is difficult to reflect the influence of bending-strain exactly because of the model itself. Therefore the safety of the project is threaten. In order to simulate the excavation more exactly, a model, which can not only improve the precision but also predigest the coupling of the different structure, is urgent to be established. This paper proposes one new elements - RH8 elements(Rotation Hexahedron element of 8 nodes). The determined finite element formula and random finite element formula of the new element is also presented. Then the new model of the foundation which give facilities for the finite element numerical simulation is developed. Ultimately, the dynamic simulation and stability of the foundation is studied. The main contents of the dissertation are as follows:1. Based on the inconsistent element theory and the Reissner variational principle which is modified to the independent rotation fields, the rotation degree is considered as independent degree and a new three-dimensional eight-node element-RH8 element is developed. Then the finite element formula is presented based on the variational principle. Finally this paper discussed the appropriate range of the new element.2. The new element is introduced into the problem of composite structures in which the girder, plate and block exists at the same time. Then this paper discussed the advantages of the elements when dealing with the connect problem. Ultimately, a classical problem calculating connect structures demonstrated the new elements is rational.3. The random variational principle with independent rational degree is proposed. Then on the basis of it, the random finite element formula of the new element is presented.4. This paper simulates the continuous wall, supports and soil mass adopting the new elements. Then it established a new model for simulating the excavation and discussed the existing issues, then gives some advices to this problem.
5. The method of back-analysis and the existing problem is comprehensively summarized. This paper proposed the method of back-analysis with Parallel-Genetic-Algorithm and corresponding program has been validated correctly.6. Based on the Inteference-Energy method and Over-deformation method, the extensive angle method is applied in the judgement of the stability of ground foundation pit. At the same time, considering the uncertainty of the parameters, a system reliability method of the supports whose performance function is the inteference energy is presented. And the stability of the foundation is evaluated based-on the reliability method. Finally this paper bring forward the method to attain the critical target of the strain7. For certain project of deep foundation, stress-deformation analysis, soil parameters back-analysis, system reliability analysis of the support and the evaluation of the stability are done. The result is demonstrated rationally.
引文
1．刘国彬，候学渊，黄院雄．城市基坑工程发展的几点看法．见：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，1999：603～606
2．唐业清．基坑工程事故分析与处理．北京：中国建筑工业出版社，1999
3．顾宝和，周红．基坑工程若干基本问题的讨论—基坑开挖与支护研讨会综述．工程勘察，1997，3：12-17
4．吴京生．高层建筑深基坑工程现状与展望．电力勘测，1998，3：13～19
5．高俊合．深基坑支护结构设计理论研究．河海大学博士学位论文，1998
6．黄宗瑜．基坑支护设计概论(上)．四川建筑，2000，20(1)：51-55
7．黄宗瑜．基坑支护设计概论(下)．四川建筑，2000，20(2)：61-64
8. Beacher G., Need for probabilistic characterization, in Probabilistic Characterization of Soil Properties: Bridge between Theory & Practice, Eds: Bowles D. S. And Ko H.Y., ASCE. NewYork. 1984:1～18.
9．刘宁，郑建青．工程随机力学及可靠性理论中的若干问题(上)．河海大学学报，1999，27 (5)：1～9
10．刘宁．工程随机力学与工程可靠性中的若干问题(下)．河海大学学报，2000，28(1)：1～9
11．李立新，石程云．岩土工程位移反分析方法综述．沈阳建筑工程学院学报，1996，12(3)：354～358
12．余志成，施文华．深基坑支扩设计与施工．北京：中国建筑工业出版社，1997
13．高文华，沈蒲生，彭良忠．基坑工程发展现状与展望．湘潭矿业学院学报，1999，14(4)：67～72
14．陈晓平等．深基坑支护结构的三维杆系有限元分析．岩土力学，2001，22(3)：258～261
15．周军，周瑞忠．深基坑结构计算的有限元方法．福建建筑，2002，2：47～49
16．陆陪毅，刘畅，顾晓鲁．深基坑支护结构支撑系统简化空间分析方法的研究．岩土工程学报，2002，24(4)：471～474
17．高文华，沈蒲生，杨林德．深基坑支护结构内力与变形时空效应分析的程序实现．土木工程学报，2003，36(2)：86～90
18．高文华，杨林德．软土深基坑围护结构变形的三维有限元分析．工程力学，2000，17(2)：134～141
19. Liu K X, Yoag K Y, Lee F H. A Numerical study on 3-D behavior of excavation-support system. Nanjing: Second International Conference on Soft Soil Engineering, 1996: 501-506
20. Charles W W, Simpson N B, Lings M L, et al. Numerical analysis of a multipropped excavation in stiff clay. Canadian Geotechnical Journal, 1998,35:115～130
21．赵海燕，黄金枝．深基坑支护结构变形的三维有限元分析与模拟．上海交通大学学报，2001，35(4)：610～613
22．江苏省长江公路大桥建设指挥部等．润扬长江公路大桥悬索桥南锚碇深基坑排桩冻结工法研究总报告．2003
23. T. J. R. Hughes, W. R. Liu, Nonlinear finite element analysis of shell, Part Ⅰ: three-dimensional shells, Comput. Meth. Appl. Mech. Engng, 1981,26:331～362
24
24. W. Kanoknukulchasi, R. L. Taylor, T. J. R. Hughes, A Large deformation formulation for shell analysis by the finite element method, Comput. Struct, 1981,13: 19～27
25. Astill H.,Impact Loading on Structures with Random Properties. J of Struct Mech. 1972, 1 (1) : 63～67
26. Shinozuka M, Lenoe E. A probabilistic model for spatial distribution of material properties. Fracture Mech. 1976, 8:217～227
27. Cambou B. Application of first-order uncertainty analysis in the finite element method in linear elasticity. In: Proc of 2nd Int Conf on Applications of Statistics and Structural Engineering. Aachen. 1975. 67～87
28. Dendrou B A, Houstis E N. An inference finite element method for field application, Applied Mathematical Modeling. Guildford, Englad. 1978. 49～55
29. Baecher G B, Ingra T S. Stochastic FEM in settlement predictions, J of Geotech Eng. 1981, 107 (2) : 449～463
30. Handa K, Anderson K. Application of finite element methods in statistical analysis of structures. In: Proc 3rd Int Conf on Struct Safety and Reliability. Trondheim, Nroway, Hune. 1981. 409～417
31. Hisada T, Nakagiri S. Stochastic finite element method developed for struct. Safety and reliability. In: Proc. 3rd Int Conf on Struct Safety and Reliability, Trondheim, Norway. 1981. 395～408
32. Nakagiri S, Hisada T. Stochastic finite element method applied to structural analysis with uncertain parameters. In: Proc Int Conf on FEM. Australia. 1982. 206～211
33. Hisada T, Nakagiri S. Role of the stochastic finite element method in struct, safety and reliability, In: Proc 4th Int Conf on Struct Safety and Reliability, Kobe, Japan. 1985. 213～219
34. Shinozuka M, Deodatis G. Response variability of stochastic finite element systems. J of Eng Mech. 1988, 114(3): 499～519.
35. Yamazaki F, Shinozuka M., Dasgupta G. Neumann expansion for stochastic finite element analysis, J. of Eng. Mech., ASCE, 11(8), 1988: 1335～1354.
36. Kiureghian A D, Ke J. Stochastic finite element method in structural reliability, Probabilistic Eng Mech. 1988,3(2):83～91
37．吴世伟，李同春．重力坝最大可能失效模式初探．水利学报，1990，4：36～44
38．李同春，吴世伟．基于三维SFEM的拱坝可靠度分析．工程结构可靠性全国第二届学术交流会议论文集．重庆．1989．114～125
39．刘宁，卓家寿．基于三维弹塑性随机有限元的可靠度计算．水利学报．1996，9：53～62
40．刘宁，卓家寿．三维弹塑性随机有限元迭代计算方法研究．河海大学学报．1996，24(1)：1～8
41. Liu N, Tang W H and Ng C W W. Probabilistic FEM and reliability assessment for strain softening media. Finite Elements in Analysis and Design. 2000 (to appear)
42
42. Takada T. Weighted integral method in stochastic finite element analysis. Prob Eng Mech. 1990, 5(3):146～156
43. Deodatis G. Weighted integral method Ⅰ: stochastic stiffness matrix, J of Eng Mech. 1991, 117(8): 1851～1864
44. Deodatis G, Shinozuka M. Weighted integral method Ⅱ: response variability and reliability, J of Eng Mech. 1991, 117(8): 1865～1877
45. Rajashekhar M R, Ellingwood B R. A new look at the response surface approach for reliability analysis. Struct Safety. 1993,12:205～220
46．吴世伟．结构可靠度分析．北京：交通出版社．1988
47．武清玺，吴世伟，吕泰仁．基于有限元法的重力坝可靠度分析．水利学报，1990，1：39～45
48．吴世伟．拱坝的失效模式与可靠度．河海大学学报．1992，20(2)：88～96
49. Liu N, Wang Y, Wu S W. Reliability analysis of gravity dam with weak layers. In: Proc of Int Symon Application of Computer Methods in Rock Mechanics and Engineering. Xian, P.R. China. 1993. 1265～1270
50．陈虬，刘先斌．随机有限元法及其工程应用．成都：西南交大出版社．1993
51．秦权．随机有限元及其进展Ⅰ：随机场的离散和反应矩的计算．工程力学．1994，11(4)：1～10
52．秦权．随机有限元及其进展Ⅱ：可靠度随机有限元和随机有限元的应用．工程力学．1995，12(1)：1～9
53．刘宁，吕泰仁．随机有限元及其工程应用．力学进展．1995，25(1)：114～126
54．姚耀武，申超．非线性随机有限元法及其在可靠度分析中的应用．岩土工程学报．1996，18(2)：37～46
55．张圣坤．不确定性问题的有限元方法及应用．固体力学学报．1987，8(3)：277～281
56．张汝清，高行山．随机变量的变分原理及有限元法．应用数学和力学．1992，13(5)：383～388
57．龚晓南，钱纯．非线性随机过程的有限元分析．计算结构力学及其应用．1994，11(1)：9～18
58．张晓春，杨挺青，缪协兴．摄动随机有限元法在顺层岩至质边坡可靠性分析中的应用，岩土工程学报．1999，21(1)：71～76
59. Ghanem R and Sponas P D. Stochastic Finite Elements: A Spectral Approach, New York: Springer-Verlag. 1991
60. Liu W K. Variational approach to probabilistic finite elements. J of Eng Mech. 1988, 114 (12): 213～225
61．刘先斌．随机有限元法的误差估计及基于随机场规范展开的有限元法：[学位论文]．成都：西南交通大学．199l
62. Kleiber M, Hien T D. The Stochastic Finite Element Method - Basic Perturbation Technique and Computer Implementation. New York: John Wiley & Sons. 1992
63．刘宁，刘光廷．大体积混凝土结构温度场的随机有限元算法．清华大学学报．1996，36(1)：41～47
64. Liu P L, Kiureghian A D. Finete element reliability of geometrically nonlinear uncertain structures. J of Eng Mech. 1988, 117 (8) : 164～168
65
65. Hisada T, Noguchi H. Development of a nonlinear stochastic FEM and its Application. In:The 5th Int Conf on Struct Safety and Reliability. Australia: Balkema Press. 1989:1097～1104
66. Papadrakakis M, Papadopoulos V. A computationally efficient method for the limit elasto-plastic analysis of space frames, J of Comp Mech. 1995, 16(2): 132～141
67. Schorling Y and Bucher C G. Stability analysis of a geometrically imperfect structure using a random field model, In: Proc ASCE Special Conf, Worcester, MA., ASCE, New York, 1996. 604～607
68. Kavanagh K. and R. W. Clough, Finite element application in the characterization of elastic solids, Int. J. Solids Structure, 1971, Vol. 7, :11～23
69. A. Cividini, L. Jurina and G. Gioda, Some aspects of 'Characterization' problems in geomechanics, Int. J. Rock Mech. Mining Sc., 1981, 18:487～503
70. Hosiya M., Yoshida I., Observation and conditional stochastic FEM, Probabilistic Mechanics and Structural Safety and Reliability, Proceedings of the Specialty Conference of ASCE, New York, NY, USA. 1996:178～181
71. Iding R H., Pister K. S. And Taylor R. L., Identification of nonlinear elastic solids by a finite element method, Computer methods in applied mechanics and engineering, 1974, Vol. 4:121～142
72. Kaiser P, Zou D, Lang P. Stress determination by back-analysis of excavation-induced stress changes, Rock Mechanics and Rock Engineering, 1990, Vol 23, No. 3: 185～200
73．刘维倩，黄光远，穆永科等．岩土工程的位移反分析法．计算结构力学及其应用，1995，12(1)：93～101
74. Swoboda G, lchikawa Y, Dong Q, et al. Back analysis of large geotechnical models. Int J for Numerical and Analytical Methods in Geomechanics, 1999, Vol 23, No. 12: 1455～1472
75．刘怀恒．支护荷载反演及安全度预测．西安矿业学院学报，1991，11(4)：1～8
76. Tanigawa M, Hojo A, Sakurai S. Study of some problems on the back analysis of measured displacements in tunnelling. Proc of the Japan Society of Civil Enginners, Tokyo, 1990:85～93
77．陈子荫．由位移测定值反算流变岩体变形参数及地应力．煤炭学报，1982，7(4)：340～345
78．薛琳．岩体粘弹性力学模型的判别定理与应用．岩土工程学报，1994，16(5)：1～10
79. Giancarlo Gioda & Shunsuke Sakurai, Back analysis procedure for the interpretation of field measurements in geomechanics, Int. J. for numerical and analysis methods in geomechanics, 1987, Vol. 11: 555～583
80. Gioda G, Jurina L. Numerical identification of soil-structure interaction pressures. Int J for Numerical and Analytical Methods in Geomechanics, 1981, (5): 33～56
81. Gordon A. Estimation for stochastic soil models . J of Geotechnical and Geoenvironmental Engineering, 1999, (7): 470～485
82. Karkkainen T, Neittaanmaki P, Nemisto T. Numerical method for nonlinear inverse problem. J of Computational and Applied Mathematics, 1996,74(1-2): 231～244
83. Ledsma A, Gens A, Alonso E. Parameter and variance estimation of geotechnical back analysis using prior information. Int J for Numerical and Analytical Methods in Geomechanics, 1996,20(2): 119～141
84．李皓，唐新军，朱焕春．岩体工程正反耦合位移反分析初探．武汉水利电力大学学报，1997，30(4)：42～45
85．林育梁，樱井春辅．应用模糊有限元法的一种反分析形式．岩土工程学报，1995，17(5)：48～56
86．孙钧，蒋树屏，袁勇等．岩土力学反演问题的随机理论与方法．汕头：汕头大学出版社，1996
87. Sharma M, McBean E, Thomson N. Maximum likelihood method for parameter estimation in linear model with below-detection data. J of Environmental Engineering, 1995,121(11): 776～784
88. Asaoka A, Matsuo M. Bayesian approach to inverse problem in consolidation and its application to settlement predication. Proc 3rd Int Conf on Numerical Methods in Geomechanics, Archen, 1997:732～739
89. Yoshihiko M, Genki Y, Shinobu Y. Inverse analysis by means of the combination of multiplayer neural networks and computational mechanics. Study on learning and estimating process and its application to defect identification, Nippon Kikai Gakkai Ronbunshu, A Hen, 1991,57(540): 1922～1929
90. Zaman M, Hossain M, Faruque M. Creep constitutive modeling of rock salt and evaluation of model parameters using optimization technique. Indian Geotechnical Journal, 1997,27(3): 221～240
91．樊琨，刘宇敏，张艳华．基于人工神经网络的岩土工程力学参数反分析．河海大学学报，1998，26(4)：98～102
92. Bastian A, Gasos J. Type Ⅰ structure identification approach using feed-forward neural networks. Proc of the 1994 IEEE Int conf on Neural Networks, New Jersey, 1994:3256～3260
93. S. Sakurai, Determination of initial stress and mechanics properties of viscoelastic underground medium, Proc. 3rd ISRM Cong. Denver, Ⅱ-B, 1974: 1169-1174
94. Kirsten H A D. Determination of rock mass elastic moduli by back analysis of deformation measurement. In:Proc Symp on Expliration for Rock Eng. Johannesburg, 1976, (11):54-1160
95. Sakurai S., Wasmongkol N., D., Shinji M. Back analysis for determining material characteristics in cut slopes. In: Proc. Int. Symp. on ECRF, Beijing, Science Press, 1986:770-776
96. Sakurai S. Interpretation of the results of displacement measurements in cut slopes. In: Proc. 2nd Int. Symp. on FMGM'87, Kobe, 1987:528-54097. Giancarlo Gioda and Giulio Maiers, Direct search solution of and inverse problem in elastoplastisity: Identification of cohesion, friction angle and in situ stress by pressure tunnel test, Int. J. for numerical methods in Eng., 1980, Vol. 15: 1823-184898. Asaoka A. Observational procedure of settlement prediction. Soils and Foundations, 1978,18(4): 87-10199. Gioda G. A numerical procedure for defining the values of soil parameter affecting consolidation. In: Proc. of the 7th Eroupean Conf. on Soil Mechanics and Foundation Engineering. Design Parameter in Geotechnical Engineering. London: British Geotechnical Socierty, 1979, (1): 169-172100. Maiar G, Jurina L, Podolak K. On model identification problems in rock mechanics. In: Proc Symp on the Geotechnics of Structurally Complex Formations. Capri, 1977,. 257-261101. Kovari K et al. Integrated measuring technique for rock pressure determination. In: Proc Int Conf on Field Measurements in Rock Mechanics. Zurich, 1977, (1):. 533-538102.Beliveau J. G.. Identification of viscous damping in structures from modal information. J. Appl. Mech., 1976,43(2): 335-339.103. Yang L & Sterling R. L., Back analysis of rock tunnel using bounding element method, J. Geo. Eng. Div ASCE, 1989, Vol.115, No. 8: 1163-1169104. Ohkami T., Ichikawa Y., A boundary element method for identifying orthotropic material parameters, Int. J. for Num. And Analy. Method in Geomechanics, 1991, Vol. 15, No. 9: 609-625105. Giancarlo Gioda & Shunsuke Sakurai, Back analysis procedure for the interpretation of field measurements in geomechanics, Int. J. for numerical and analysis methods in geomechanics, 1987, Vol. 11: 555-583106. Gioda G. Some remarks on back analysis and characterization problems. In: Proc 5th Int Conf on Num Meth in Geom. Nagoya, 1985,1.47-61107. MaierG, Gioda G. Optimization methods for parametric identiication of geotechnical system. In: Maitins J Bed. Num Methods in Geom. Boston, 1980,1.65-73108.Aral R. An inverse problem approach to the prediction of Multi-dimensional consolidation behavior. Soil and Foundations, 1984,24(1): 95-108109. Katsuhiko Arai, Hideki Ohta and Tatsuo Yasui, Simple optimization techniques for evaluating deformation module from field observations, Soil parameters estimation, 1982: 107-112110. Masoud Sanayei and Michael J. Saletnik, Parameter estimation of structures from static strain measurements. I: Formulation, J. of Structural Eng., 1996:555-562111. Chang W. C., The application and limitation of extensometer for tunnel monitoring, Rock Mechanics Contributions and challenges, Hustrulid & Johnsons, 1990
96. Sakurai S. Interpretation of the results of displacement measurements in cut slopes. In: Proc. 2nd Int. Symp. on FMGM'87, Kobe, 1987:528-540
97. Giancarlo Gioda and Giulio Maiers, Direct search solution of and inverse problem in elastoplastisity: Identification of cohesion, friction angle and in situ stress by pressure tunnel test, Int. J. for numerical methods in Eng., 1980, Vol. 15: 1823-1848
98. Asaoka A. Observational procedure of settlement prediction. Soils and Foundations, 1978,18(4): 87-101
99. Gioda G. A numerical procedure for defining the values of soil parameter affecting consolidation. In: Proc. of the 7th Eroupean Conf. on Soil Mechanics and Foundation Engineering. Design Parameter in Geotechnical Engineering. London: British Geotechnical Socierty, 1979, (1): 169-172
100. Maiar G, Jurina L, Podolak K. On model identification problems in rock mechanics. In: Proc Symp on the Geotechnics of Structurally Complex Formations. Capri, 1977,. 257-261
101. Kovari K et al. Integrated measuring technique for rock pressure determination. In: Proc Int Conf on Field Measurements in Rock Mechanics. Zurich, 1977, (1):. 533-538
102.Beliveau J. G.. Identification of viscous damping in structures from modal information. J. Appl. Mech., 1976,43(2): 335-339.
103. Yang L & Sterling R. L., Back analysis of rock tunnel using bounding element method, J. Geo. Eng. Div ASCE, 1989, Vol.115, No. 8: 1163-1169
104. Ohkami T., Ichikawa Y., A boundary element method for identifying orthotropic material parameters, Int. J. for Num. And Analy. Method in Geomechanics, 1991, Vol. 15, No. 9: 609-625
105. Giancarlo Gioda & Shunsuke Sakurai, Back analysis procedure for the interpretation of field measurements in geomechanics, Int. J. for numerical and analysis methods in geomechanics, 1987, Vol. 11: 555-583
106. Gioda G. Some remarks on back analysis and characterization problems. In: Proc 5th Int Conf on Num Meth in Geom. Nagoya, 1985,1.47-61
107. MaierG, Gioda G. Optimization methods for parametric identiication of geotechnical system. In: Maitins J Bed. Num Methods in Geom. Boston, 1980,1.65-73
108.Aral R. An inverse problem approach to the prediction of Multi-dimensional consolidation behavior. Soil and Foundations, 1984,24(1): 95-108
109. Katsuhiko Arai, Hideki Ohta and Tatsuo Yasui, Simple optimization techniques for evaluating deformation module from field observations, Soil parameters estimation, 1982: 107-112
110. Masoud Sanayei and Michael J. Saletnik, Parameter estimation of structures from static strain measurements. I: Formulation, J. of Structural Eng., 1996:555-562
111. Chang W. C., The application and limitation of extensometer for tunnel monitoring, Rock Mechanics Contributions and challenges, Hustrulid & Johnsons, 1990
133．刘大鹏．排桩支护结构监测数据的反分析．湖北地矿，2000，14(3)：53～59
134．汪中卫．根据反馈对基坑围护结构内力与变形的反分析．大坝观测与土工测试，1998，22(6)：14～17
135．赵振寰．反分析法在基坑开挖数值分析中的应用．工程勘察，1996，4：1～8
136．朱志伟．深基坑工程土层参数反演及挡墙内力预报．岩土力学，1996，20(4)：63～68
137．朱合华．深基坑工程动态施工反演分析与变形预报．岩土工程学报，1998，20(4)：30～35
138. Eykhoff P. System identification-parameter state estimation, John Wiley & Sons, 1974
139. Ledesma A, Alonso E E. Probabilistic back analysis using a maximum likelihood approach. Proceedings 12th International Conference on Soil MeChanics and Foundation Engineering, Brazil, 1989(2): 849～852
140. Ledesma A, Gens A, Alonso E E. Estimation of parameters in geotechnical back analysis —Ⅰ: Maximum likelihood Approch. Computers & Geotechnique, 1996, 18(1): 1～27
141．袁勇．围岩弹塑性参数反算的极大似然法．工程勘察，1991(5)：5～7
142. Hoshiya M, Yoshida I. Identification of conditional stochastic Gaussian field. J of Engineering Mechanics ASCE, 1996,122(2): 101～108
143. Cividini A, Maier G, Nappi A. Parameter estimation of a static geotechnical model using a Bayes' approach. Int J Rock Mechanics Mining Science & Geotechnical Abstract, 1983, 20(5): 215～226
144. Honjo Y, Liu W T, Soumitra G. Inverse analysis of an embankment on soft clay by extended Bayesian method. Int J for Numerical and Analytical Methods in Geomechanics, 1994(18): 709～734
145. Hoshiya M, Saito E. Structural identification by extended Kalman filter. J of Engineering Mechanics, ASCE, 1984, 110(12): 1757～1770
146. Murakami A, Hasegawa T. Observational prediction of settlement using Kalman filtering theory. Proceedings 5th International Conference on Numerical Method in Geomechanics, Nagoya, 1985
147．蒋树屏．扩张卡尔曼滤波器有限元耦合算法及其隧道工程应用．岩土工程学报，1996(2)：11～19
148．黄宏伟．岩体变形随机预报理论及其在地下工程中的应用．同济大学博士学位论文，1993
149．刘维宁．岩土工程反分析方法的信息论研究．岩石力学与工程学报，1993，12(3)：193～205
150．袁勇，孙钧．岩土工程优化反演的目标函数．岩石力学与工程学报，1994，13(2)：29～37
151. Holland J H. Adaptation in neural and artificial system. Ann Arbor: The University of Michigan Press, 1975
152．周明，孙树栋．遗传算法原理及应用．北京：国防工业出版社，1999
153．李立新，王建党，李造鼎．神经网络模型在非线性位移反分析中的应用．岩土力学，1997，1(2)：62～66
154．李瑞有，李迪，马水山．三峡永久船闸开挖边坡岩体力学参数反分析．长江科学院院报，1998，18(2)：10～13
155．李晓红，靳晓光等．隧道位移智能化反分析及其应用靳地下空间，2001，21(4)：299～304
156．周保生，朱维申．巷道围岩参数的人工神经网络预测．岩土力学，1999，20(1)：22～25
157．冯夏庭，杨成祥．智能岩石力学(2)—参数与模型的智能辨识．岩石力学与工程学报，1999，18(3)：359～362
158．王登刚，刘迎曦等．岩土工程位移反分析的遗传算法．岩石力学与工程学报，2000，19(增)：979～982
159．高玮，郑颖人．岩体参数的进化反演．水利学报，2000(8)：1～5
160．高玮，郑颖人．采用快速遗传算法进行岩土工程反分析．岩土工程学报，2001，23(1)：120～122
161．冯夏庭等．位移反分析的进化神经网络方法研究．岩石力学与工程学报，1999，18(5)：529～533
162．邓建辉，李焯芬，葛修润．BP网络和遗传算法在岩石边坡位移反分析中的应用．岩石力学与工程学报，2001．20(1)：1-5
163．高玮，郑颖人，一种新的岩土工程进化反分析算法，岩石力学与工程学报，2003，22(2)：192～196
164. I. Babuska, T. Scapolia, Benchmark Computation and performance evaluation for a rhombic plate bending problem, Int. J. Meth. Eng.,1989,28:155-181
165. E. Reissner, On the theory of elastic plates, J. Appl. Mech., 1951,18:31-38
166. E. Reissner, The effect of transverse shear deformation on the bending of elastic plates, J. Appl. Mech., 1945,12:67-76
167. R. D. Mindlin, Influence of rotatory inertia and shear inflexural motions of isotropic elastic plates, J. Appl. Mech., 1951,18:31-38
168. E. onate, O. C. Zienkewicg, B. Suarez and R. L. Taylor, A general methodology for deriving shear constraint Reissner-Minddin plate elements, Int. J. Num. Meth. Eng.,1992,33:345-359
169. A. Ibrahimbegoric, Quadrilateral finite elements for analysis of thick and thin plates, Comput. Meth. Appli. Meth. Eng., 1993,110:195-209
170. T. J. R. Hughes and W. R. Liu, Nonlinear finite element analysis of shell, Part Ⅰ: three-dimensional shells, Comput. Meth. Appl. Mech. Engng., 1981,26:331-362
171. W. Kanoknukulchasi, R. L. Taylor and T. J. R. Hughes, A Large deformation formulation for shell analysis by the finite element method, Comput. Struct., 1981,13:19-27
172. E. L. Wilson, R. L. Taylor, W D Doherty and J Ghaboussi. Incompatible displacement models. Numerical and Computer Methods in Structral (ed. S J Fenves et. al.), Academic Press, New York, 1973:43～47
173. R. L. Taylor, P. J. Beresford and E. L. Wilson. A Non-conforming element for stress analysis. Int. J. Num. Meth. In Eng., 1976,10:1211～1219
174. C. C. Wu, M. G. Huang and T. H. H. Plan. Consistency condition and convergence criteria of incompatible element: General formulation of incompatible functions and its application. Computer & Structures, 1987,27:639～644
175．鹿晓阳，史宝军，岑章志，鹿宵力．协调等参元与非协调元的对应性研究．工程力学，2001， 18(1)：36～40
17
176．焦兆平，盛勇，吴长春．内参型非协调元合理位移场的研究．工程力学，1998，15(2)：1～10
177. A. Ibrahimbegovic, R. L. Taylor and E. L. Wilson. A robust quadrilateral membrane finite element with drilling degrees of freedom. Int. J. Num. Meth. In Eng.,1990,30: 445～457
178. A. Ibrahimbegovic, F. Frey. Membrane quadrilateral finite element with rotational degrees of freedom. Engineering Fracture Mechanics, 1992,43(1): 13～24
179. B Irons and S. Ahmad, Techniques of Finite Elements, Ellis Horwood, 1980
180. Allman D J. A compatible triangular element including vertex rotations for plane elasticity analysis. Comput & Struct, 1984, 19:1～8
181. Bergan P G, Felippa C A. A triangular element with rotational degrees of freedom. Comp Meth Appl Mech Eng, 1985, 50:25～69
182. Cook R D. On the Allman triangular and a related quadrilateral element. Comp & Struct, 1986,22:1065～1067
183. Macneal R H, Harder R L. A refined four-noded membrane element with rotational degrees of freedom. Comp & Struct, 1989,28:75～84
184. E. Reissner, A note on variational principles in elasticity, Int. J. Solids Struct., 1965, 1:93～95
185. T. J. R. Hughes and F. Brazzi, On drilling degrees of freedom, Comp. Meth. Appl. Mech. Eng., 1989,27:105～121
186. Hughes T. J. R., Brezzi F., Masud A., Harari I. Finite elements with drilling degrees of freedom: theory and numerical evaluations. In Proceedings of the 5th International Symposium on Numerical Methods in Engineering, Vol. 1. Gruber R., Periaux J., Shaw R. P. (eds). Springer: Berlin, 1989
187．吴长春等．非协调数值分析与杂交元方法．科学出版社，1997
188．龙志飞，岑松．有限元法新论．中国水利水电出版社，2001
189．邵国建．一种新的通用板壳元模式及其应用．河海大学博士学位论文，1997
190. K.S. Surana. Transition finite elements for axi-symmetricstress analysis. Int. J. Num. Meth. Eng, 1980,15:809-832
191. K.S. Surana. Transition finite elements for three-dimensional stress analysis. Int. J. Num. Meth. Eng, 1980,15:991-1020
192．王勖成，邵敏．有限单元法基本原理与数值方法，清华大学出版社，1988
193．曲圣年．组合结构有限元分析德罚单元法，固体力学学报，1982，4：555—559
194．钟万勰．关于组合结构分析程序JIGFEX的设计问题，力学与实践，1979，1：3—4
195．冯康．弹性结构的数学理论，科学出版社，1981
196．J．S．Przemieniesk．Theory of matrix structural analysis，1968．(汪德荣等译校，矩阵结构分析理论，1974)
197. A. Ibrahimbegovic, E. L. Wilson. Thick shell and solid finite elements with independent rotation fields. International Journal for Numerical Methods In Engineering. 31,1991:1393-1414
19
198. Kiureghian A D, Ke J. Stochastic finite element method in structural reliability. Probabilistic Eng Mech. 1988, 3(2): 83～91
199. Baecher G B, Ingra T S. Stochastic FEM in settlement predictions. J of Geotech Eng. 1981, 107:449～463
200. Vanmarcke E, Shinozuka M. Random fields and stochastic finite element method. Struct Safety. 1986, 3:143～166
201．朱位秋，任永坚．基于随机场局部平均的随机有限元法．固体力学学报．1988，4：261～271
202. Zhu W Q, Ren Y J. Wu W Q. Stochastic FEM based on local averages of random vector fields. J Eng Mech. 1992, 118(3): 496～511
203．刘宁．三维可分向量随机场局部平均的三维随机有限元及可靠度计算．水利学报．1995，6：75～82
204. Liu W.K., Besterfield G., Mani A., Probabilistic Finite Element Methods in Nonlinear Dynamics, Computer Methods in Applied Mech. And Engrg., Vol. 57, 1986:61-81
205. Liu W K, Mani A. Random fields finite elements. Int J of Numerical Methods in Eng. 1988, 23(10): 1831～1845
206. Liu X B and Chen Q. The interpolation method of stochastic functions and the stochastic variational principle. In: Proc. of SMIRT12. Germany: Stuttgart. 1993: 243～249
207. ZhuW. Q., Ren Y.J., Wu W. Q., Stochastic FEM based on local average of random vector fields . J. Eng. Mech., 118(3), 1992:496-511
208．刘先斌，随机有限元法的误差估计及基于随机场规范展开的有限元法，西南交通大学硕士学位论文，1991
209. Takada T, Shinozuka M. Local integration method in stochastic finite element analysis. In: Proc Int Conf on Structural Safety and Reliability. 1989: 1072～1080
210. Deodatis G. Bounds on response variability stochastic finite element systems. J of Eng Mech. 1990, 116(3): 565～585
211. Spanos P D, Ghanem R. Stochastic finite element expansion for random media. J of Eng Mech. 1989, 115(5): 1035～1053
212. Ghanem R, Spanos P D. Polynomia chaos in stochastic finite elements. J of Appl Mech. 1990, 57: 197～202
213．刘宁，可靠度随机有限元法及工程应用，水利水电出版社，2000
214. Desai C. S., Zaman M. M., Thin layer element for interfaces and joints. Int. J. Num. And Analy. Meth. In Geomech., 1984,8(1): 19～43
215．殷宗泽，朱弘，许国华．土与结构材料接触面的变形及其数学模拟．岩土工程学报，1994，16(3)：14～22
216．高文华，杨林德，叶为民．板—土三维等厚接触单元模型及其应用．同济大学学报，1999，27(3)：297～300
217．杜景灿等，加权位移反演法确定掩体结构面的力学参数，岩土工程学报，1999，2：209～212
218．束善杭，参数的随机反演方法及其面向对象的程序设计，河海大学硕士论文，2000
219. Eykhoff P., System identification—parameter state estimation, John Wiley & Sons, 1974
220. Ledesma A., Gens A. & Alonso E. E., Probabilistic back analysis using a Maximum likelihood approach, Proc. 12th Lnt. Conf. On Soil Mech. & Foundation Eng., Brazil, 1989:849～852
221. A. Cividini, G. Maier, A. Nappi, Parameter estimation of a static geotechnical model using a Bayes' approach , Int. J. Rock Mech. Min. Sci. & Geomechanics Abstract, 1983,20,5:215～226
222．吕爱钟，蒋斌松著，岩石力学反问题，煤炭工业出版社，1998
223．袁勇，围岩弹塑性参数反算的极大似然法，工程勘察，1991年第五期
224．汪成为等著，面向对象分析、设计及应用，国防工业出版社，1992
225．[美]Dale Rogerson著，杨秀章译，COM技术内幕，清华大学出版社，1999
226．[美]Charlie Calvert著，DELPHI 4编程技术内幕，机械工业出版社，1999
227．王小平等，遗传算法—理论、应用与软件实现，西安交通大学出版社，2002
228．郭志川，排桩冻结法深基坑的动态反分析及其支护结构体系可靠度研究，河海大学博士论文，2003
229．杜建成，黄大寿，胡定，边坡稳定的三维极限平衡分析法，四川大学学报(工程科学版)，2001，33(4)：9～12．
230．李朝国，陆金池，张林等，综合法与超载法在沙牌RCC拱坝坝肩稳定分析中的应用，四川大学学报(工程科学版)，1997．1(3)：64～71．
231．钱向东，复杂基岩稳定分析的弹塑性极限平衡法，河海大学学报，1999，27(6)：16～19．
232．王建仁，张福林，基坑稳定的人工神经网络预测，建筑技术开发，2001，28(2)：10～13．
233．卓家寿，邵国建，陈振雷，工程稳定问题中确定滑坍面、滑向与安全度的干扰能量法，水利学报，1997，8：80～84．
234．邵国建，卓家寿，章青，岩体稳定性分析与评判准则研究，岩石力学与工程学报，2003，25(5)：691～696．
235．高凌．工程稳定问题的干扰能量法，河海大学硕士学位论文，1993．
236．胡强，郭志川，刘宁．深基坑支撑体系可靠度计算研究．河海大学学报，2003，6：674～678
237．吕泰仁等，用几何法求构件得可靠指标。河海大学学报，1988，5：86～93
238．吴世伟，结构可靠度分析。交通出版社，1988．210～211
239．陈志坚，游庆仲，胡应德，江阴大桥北锚沉井地基土邓肯参数的反演及反馈分析，固体力学学报，1999，20(计算力学专辑)：102～106
2．唐业清．基坑工程事故分析与处理．北京：中国建筑工业出版社，1999
3．顾宝和，周红．基坑工程若干基本问题的讨论—基坑开挖与支护研讨会综述．工程勘察，1997，3：12-17
4．吴京生．高层建筑深基坑工程现状与展望．电力勘测，1998，3：13～19
5．高俊合．深基坑支护结构设计理论研究．河海大学博士学位论文，1998
6．黄宗瑜．基坑支护设计概论(上)．四川建筑，2000，20(1)：51-55
7．黄宗瑜．基坑支护设计概论(下)．四川建筑，2000，20(2)：61-64
8. Beacher G., Need for probabilistic characterization, in Probabilistic Characterization of Soil Properties: Bridge between Theory & Practice, Eds: Bowles D. S. And Ko H.Y., ASCE. NewYork. 1984:1～18.
9．刘宁，郑建青．工程随机力学及可靠性理论中的若干问题(上)．河海大学学报，1999，27 (5)：1～9
10．刘宁．工程随机力学与工程可靠性中的若干问题(下)．河海大学学报，2000，28(1)：1～9
11．李立新，石程云．岩土工程位移反分析方法综述．沈阳建筑工程学院学报，1996，12(3)：354～358
12．余志成，施文华．深基坑支扩设计与施工．北京：中国建筑工业出版社，1997
13．高文华，沈蒲生，彭良忠．基坑工程发展现状与展望．湘潭矿业学院学报，1999，14(4)：67～72
14．陈晓平等．深基坑支护结构的三维杆系有限元分析．岩土力学，2001，22(3)：258～261
15．周军，周瑞忠．深基坑结构计算的有限元方法．福建建筑，2002，2：47～49
16．陆陪毅，刘畅，顾晓鲁．深基坑支护结构支撑系统简化空间分析方法的研究．岩土工程学报，2002，24(4)：471～474
17．高文华，沈蒲生，杨林德．深基坑支护结构内力与变形时空效应分析的程序实现．土木工程学报，2003，36(2)：86～90
18．高文华，杨林德．软土深基坑围护结构变形的三维有限元分析．工程力学，2000，17(2)：134～141
19. Liu K X, Yoag K Y, Lee F H. A Numerical study on 3-D behavior of excavation-support system. Nanjing: Second International Conference on Soft Soil Engineering, 1996: 501-506
20. Charles W W, Simpson N B, Lings M L, et al. Numerical analysis of a multipropped excavation in stiff clay. Canadian Geotechnical Journal, 1998,35:115～130
21．赵海燕，黄金枝．深基坑支护结构变形的三维有限元分析与模拟．上海交通大学学报，2001，35(4)：610～613
22．江苏省长江公路大桥建设指挥部等．润扬长江公路大桥悬索桥南锚碇深基坑排桩冻结工法研究总报告．2003
23. T. J. R. Hughes, W. R. Liu, Nonlinear finite element analysis of shell, Part Ⅰ: three-dimensional shells, Comput. Meth. Appl. Mech. Engng, 1981,26:331～362
24
24. W. Kanoknukulchasi, R. L. Taylor, T. J. R. Hughes, A Large deformation formulation for shell analysis by the finite element method, Comput. Struct, 1981,13: 19～27
25. Astill H.,Impact Loading on Structures with Random Properties. J of Struct Mech. 1972, 1 (1) : 63～67
26. Shinozuka M, Lenoe E. A probabilistic model for spatial distribution of material properties. Fracture Mech. 1976, 8:217～227
27. Cambou B. Application of first-order uncertainty analysis in the finite element method in linear elasticity. In: Proc of 2nd Int Conf on Applications of Statistics and Structural Engineering. Aachen. 1975. 67～87
28. Dendrou B A, Houstis E N. An inference finite element method for field application, Applied Mathematical Modeling. Guildford, Englad. 1978. 49～55
29. Baecher G B, Ingra T S. Stochastic FEM in settlement predictions, J of Geotech Eng. 1981, 107 (2) : 449～463
30. Handa K, Anderson K. Application of finite element methods in statistical analysis of structures. In: Proc 3rd Int Conf on Struct Safety and Reliability. Trondheim, Nroway, Hune. 1981. 409～417
31. Hisada T, Nakagiri S. Stochastic finite element method developed for struct. Safety and reliability. In: Proc. 3rd Int Conf on Struct Safety and Reliability, Trondheim, Norway. 1981. 395～408
32. Nakagiri S, Hisada T. Stochastic finite element method applied to structural analysis with uncertain parameters. In: Proc Int Conf on FEM. Australia. 1982. 206～211
33. Hisada T, Nakagiri S. Role of the stochastic finite element method in struct, safety and reliability, In: Proc 4th Int Conf on Struct Safety and Reliability, Kobe, Japan. 1985. 213～219
34. Shinozuka M, Deodatis G. Response variability of stochastic finite element systems. J of Eng Mech. 1988, 114(3): 499～519.
35. Yamazaki F, Shinozuka M., Dasgupta G. Neumann expansion for stochastic finite element analysis, J. of Eng. Mech., ASCE, 11(8), 1988: 1335～1354.
36. Kiureghian A D, Ke J. Stochastic finite element method in structural reliability, Probabilistic Eng Mech. 1988,3(2):83～91
37．吴世伟，李同春．重力坝最大可能失效模式初探．水利学报，1990，4：36～44
38．李同春，吴世伟．基于三维SFEM的拱坝可靠度分析．工程结构可靠性全国第二届学术交流会议论文集．重庆．1989．114～125
39．刘宁，卓家寿．基于三维弹塑性随机有限元的可靠度计算．水利学报．1996，9：53～62
40．刘宁，卓家寿．三维弹塑性随机有限元迭代计算方法研究．河海大学学报．1996，24(1)：1～8
41. Liu N, Tang W H and Ng C W W. Probabilistic FEM and reliability assessment for strain softening media. Finite Elements in Analysis and Design. 2000 (to appear)
42
42. Takada T. Weighted integral method in stochastic finite element analysis. Prob Eng Mech. 1990, 5(3):146～156
43. Deodatis G. Weighted integral method Ⅰ: stochastic stiffness matrix, J of Eng Mech. 1991, 117(8): 1851～1864
44. Deodatis G, Shinozuka M. Weighted integral method Ⅱ: response variability and reliability, J of Eng Mech. 1991, 117(8): 1865～1877
45. Rajashekhar M R, Ellingwood B R. A new look at the response surface approach for reliability analysis. Struct Safety. 1993,12:205～220
46．吴世伟．结构可靠度分析．北京：交通出版社．1988
47．武清玺，吴世伟，吕泰仁．基于有限元法的重力坝可靠度分析．水利学报，1990，1：39～45
48．吴世伟．拱坝的失效模式与可靠度．河海大学学报．1992，20(2)：88～96
49. Liu N, Wang Y, Wu S W. Reliability analysis of gravity dam with weak layers. In: Proc of Int Symon Application of Computer Methods in Rock Mechanics and Engineering. Xian, P.R. China. 1993. 1265～1270
50．陈虬，刘先斌．随机有限元法及其工程应用．成都：西南交大出版社．1993
51．秦权．随机有限元及其进展Ⅰ：随机场的离散和反应矩的计算．工程力学．1994，11(4)：1～10
52．秦权．随机有限元及其进展Ⅱ：可靠度随机有限元和随机有限元的应用．工程力学．1995，12(1)：1～9
53．刘宁，吕泰仁．随机有限元及其工程应用．力学进展．1995，25(1)：114～126
54．姚耀武，申超．非线性随机有限元法及其在可靠度分析中的应用．岩土工程学报．1996，18(2)：37～46
55．张圣坤．不确定性问题的有限元方法及应用．固体力学学报．1987，8(3)：277～281
56．张汝清，高行山．随机变量的变分原理及有限元法．应用数学和力学．1992，13(5)：383～388
57．龚晓南，钱纯．非线性随机过程的有限元分析．计算结构力学及其应用．1994，11(1)：9～18
58．张晓春，杨挺青，缪协兴．摄动随机有限元法在顺层岩至质边坡可靠性分析中的应用，岩土工程学报．1999，21(1)：71～76
59. Ghanem R and Sponas P D. Stochastic Finite Elements: A Spectral Approach, New York: Springer-Verlag. 1991
60. Liu W K. Variational approach to probabilistic finite elements. J of Eng Mech. 1988, 114 (12): 213～225
61．刘先斌．随机有限元法的误差估计及基于随机场规范展开的有限元法：[学位论文]．成都：西南交通大学．199l
62. Kleiber M, Hien T D. The Stochastic Finite Element Method - Basic Perturbation Technique and Computer Implementation. New York: John Wiley & Sons. 1992
63．刘宁，刘光廷．大体积混凝土结构温度场的随机有限元算法．清华大学学报．1996，36(1)：41～47
64. Liu P L, Kiureghian A D. Finete element reliability of geometrically nonlinear uncertain structures. J of Eng Mech. 1988, 117 (8) : 164～168
65
65. Hisada T, Noguchi H. Development of a nonlinear stochastic FEM and its Application. In:The 5th Int Conf on Struct Safety and Reliability. Australia: Balkema Press. 1989:1097～1104
66. Papadrakakis M, Papadopoulos V. A computationally efficient method for the limit elasto-plastic analysis of space frames, J of Comp Mech. 1995, 16(2): 132～141
67. Schorling Y and Bucher C G. Stability analysis of a geometrically imperfect structure using a random field model, In: Proc ASCE Special Conf, Worcester, MA., ASCE, New York, 1996. 604～607
68. Kavanagh K. and R. W. Clough, Finite element application in the characterization of elastic solids, Int. J. Solids Structure, 1971, Vol. 7, :11～23
69. A. Cividini, L. Jurina and G. Gioda, Some aspects of 'Characterization' problems in geomechanics, Int. J. Rock Mech. Mining Sc., 1981, 18:487～503
70. Hosiya M., Yoshida I., Observation and conditional stochastic FEM, Probabilistic Mechanics and Structural Safety and Reliability, Proceedings of the Specialty Conference of ASCE, New York, NY, USA. 1996:178～181
71. Iding R H., Pister K. S. And Taylor R. L., Identification of nonlinear elastic solids by a finite element method, Computer methods in applied mechanics and engineering, 1974, Vol. 4:121～142
72. Kaiser P, Zou D, Lang P. Stress determination by back-analysis of excavation-induced stress changes, Rock Mechanics and Rock Engineering, 1990, Vol 23, No. 3: 185～200
73．刘维倩，黄光远，穆永科等．岩土工程的位移反分析法．计算结构力学及其应用，1995，12(1)：93～101
74. Swoboda G, lchikawa Y, Dong Q, et al. Back analysis of large geotechnical models. Int J for Numerical and Analytical Methods in Geomechanics, 1999, Vol 23, No. 12: 1455～1472
75．刘怀恒．支护荷载反演及安全度预测．西安矿业学院学报，1991，11(4)：1～8
76. Tanigawa M, Hojo A, Sakurai S. Study of some problems on the back analysis of measured displacements in tunnelling. Proc of the Japan Society of Civil Enginners, Tokyo, 1990:85～93
77．陈子荫．由位移测定值反算流变岩体变形参数及地应力．煤炭学报，1982，7(4)：340～345
78．薛琳．岩体粘弹性力学模型的判别定理与应用．岩土工程学报，1994，16(5)：1～10
79. Giancarlo Gioda & Shunsuke Sakurai, Back analysis procedure for the interpretation of field measurements in geomechanics, Int. J. for numerical and analysis methods in geomechanics, 1987, Vol. 11: 555～583
80. Gioda G, Jurina L. Numerical identification of soil-structure interaction pressures. Int J for Numerical and Analytical Methods in Geomechanics, 1981, (5): 33～56
81. Gordon A. Estimation for stochastic soil models . J of Geotechnical and Geoenvironmental Engineering, 1999, (7): 470～485
82. Karkkainen T, Neittaanmaki P, Nemisto T. Numerical method for nonlinear inverse problem. J of Computational and Applied Mathematics, 1996,74(1-2): 231～244
83. Ledsma A, Gens A, Alonso E. Parameter and variance estimation of geotechnical back analysis using prior information. Int J for Numerical and Analytical Methods in Geomechanics, 1996,20(2): 119～141
84．李皓，唐新军，朱焕春．岩体工程正反耦合位移反分析初探．武汉水利电力大学学报，1997，30(4)：42～45
85．林育梁，樱井春辅．应用模糊有限元法的一种反分析形式．岩土工程学报，1995，17(5)：48～56
86．孙钧，蒋树屏，袁勇等．岩土力学反演问题的随机理论与方法．汕头：汕头大学出版社，1996
87. Sharma M, McBean E, Thomson N. Maximum likelihood method for parameter estimation in linear model with below-detection data. J of Environmental Engineering, 1995,121(11): 776～784
88. Asaoka A, Matsuo M. Bayesian approach to inverse problem in consolidation and its application to settlement predication. Proc 3rd Int Conf on Numerical Methods in Geomechanics, Archen, 1997:732～739
89. Yoshihiko M, Genki Y, Shinobu Y. Inverse analysis by means of the combination of multiplayer neural networks and computational mechanics. Study on learning and estimating process and its application to defect identification, Nippon Kikai Gakkai Ronbunshu, A Hen, 1991,57(540): 1922～1929
90. Zaman M, Hossain M, Faruque M. Creep constitutive modeling of rock salt and evaluation of model parameters using optimization technique. Indian Geotechnical Journal, 1997,27(3): 221～240
91．樊琨，刘宇敏，张艳华．基于人工神经网络的岩土工程力学参数反分析．河海大学学报，1998，26(4)：98～102
92. Bastian A, Gasos J. Type Ⅰ structure identification approach using feed-forward neural networks. Proc of the 1994 IEEE Int conf on Neural Networks, New Jersey, 1994:3256～3260
93. S. Sakurai, Determination of initial stress and mechanics properties of viscoelastic underground medium, Proc. 3rd ISRM Cong. Denver, Ⅱ-B, 1974: 1169-1174
94. Kirsten H A D. Determination of rock mass elastic moduli by back analysis of deformation measurement. In:Proc Symp on Expliration for Rock Eng. Johannesburg, 1976, (11):54-1160
95. Sakurai S., Wasmongkol N., D., Shinji M. Back analysis for determining material characteristics in cut slopes. In: Proc. Int. Symp. on ECRF, Beijing, Science Press, 1986:770-776
96. Sakurai S. Interpretation of the results of displacement measurements in cut slopes. In: Proc. 2nd Int. Symp. on FMGM'87, Kobe, 1987:528-54097. Giancarlo Gioda and Giulio Maiers, Direct search solution of and inverse problem in elastoplastisity: Identification of cohesion, friction angle and in situ stress by pressure tunnel test, Int. J. for numerical methods in Eng., 1980, Vol. 15: 1823-184898. Asaoka A. Observational procedure of settlement prediction. Soils and Foundations, 1978,18(4): 87-10199. Gioda G. A numerical procedure for defining the values of soil parameter affecting consolidation. In: Proc. of the 7th Eroupean Conf. on Soil Mechanics and Foundation Engineering. Design Parameter in Geotechnical Engineering. London: British Geotechnical Socierty, 1979, (1): 169-172100. Maiar G, Jurina L, Podolak K. On model identification problems in rock mechanics. In: Proc Symp on the Geotechnics of Structurally Complex Formations. Capri, 1977,. 257-261101. Kovari K et al. Integrated measuring technique for rock pressure determination. In: Proc Int Conf on Field Measurements in Rock Mechanics. Zurich, 1977, (1):. 533-538102.Beliveau J. G.. Identification of viscous damping in structures from modal information. J. Appl. Mech., 1976,43(2): 335-339.103. Yang L & Sterling R. L., Back analysis of rock tunnel using bounding element method, J. Geo. Eng. Div ASCE, 1989, Vol.115, No. 8: 1163-1169104. Ohkami T., Ichikawa Y., A boundary element method for identifying orthotropic material parameters, Int. J. for Num. And Analy. Method in Geomechanics, 1991, Vol. 15, No. 9: 609-625105. Giancarlo Gioda & Shunsuke Sakurai, Back analysis procedure for the interpretation of field measurements in geomechanics, Int. J. for numerical and analysis methods in geomechanics, 1987, Vol. 11: 555-583106. Gioda G. Some remarks on back analysis and characterization problems. In: Proc 5th Int Conf on Num Meth in Geom. Nagoya, 1985,1.47-61107. MaierG, Gioda G. Optimization methods for parametric identiication of geotechnical system. In: Maitins J Bed. Num Methods in Geom. Boston, 1980,1.65-73108.Aral R. An inverse problem approach to the prediction of Multi-dimensional consolidation behavior. Soil and Foundations, 1984,24(1): 95-108109. Katsuhiko Arai, Hideki Ohta and Tatsuo Yasui, Simple optimization techniques for evaluating deformation module from field observations, Soil parameters estimation, 1982: 107-112110. Masoud Sanayei and Michael J. Saletnik, Parameter estimation of structures from static strain measurements. I: Formulation, J. of Structural Eng., 1996:555-562111. Chang W. C., The application and limitation of extensometer for tunnel monitoring, Rock Mechanics Contributions and challenges, Hustrulid & Johnsons, 1990
96. Sakurai S. Interpretation of the results of displacement measurements in cut slopes. In: Proc. 2nd Int. Symp. on FMGM'87, Kobe, 1987:528-540
97. Giancarlo Gioda and Giulio Maiers, Direct search solution of and inverse problem in elastoplastisity: Identification of cohesion, friction angle and in situ stress by pressure tunnel test, Int. J. for numerical methods in Eng., 1980, Vol. 15: 1823-1848
98. Asaoka A. Observational procedure of settlement prediction. Soils and Foundations, 1978,18(4): 87-101
99. Gioda G. A numerical procedure for defining the values of soil parameter affecting consolidation. In: Proc. of the 7th Eroupean Conf. on Soil Mechanics and Foundation Engineering. Design Parameter in Geotechnical Engineering. London: British Geotechnical Socierty, 1979, (1): 169-172
100. Maiar G, Jurina L, Podolak K. On model identification problems in rock mechanics. In: Proc Symp on the Geotechnics of Structurally Complex Formations. Capri, 1977,. 257-261
101. Kovari K et al. Integrated measuring technique for rock pressure determination. In: Proc Int Conf on Field Measurements in Rock Mechanics. Zurich, 1977, (1):. 533-538
102.Beliveau J. G.. Identification of viscous damping in structures from modal information. J. Appl. Mech., 1976,43(2): 335-339.
103. Yang L & Sterling R. L., Back analysis of rock tunnel using bounding element method, J. Geo. Eng. Div ASCE, 1989, Vol.115, No. 8: 1163-1169
104. Ohkami T., Ichikawa Y., A boundary element method for identifying orthotropic material parameters, Int. J. for Num. And Analy. Method in Geomechanics, 1991, Vol. 15, No. 9: 609-625
105. Giancarlo Gioda & Shunsuke Sakurai, Back analysis procedure for the interpretation of field measurements in geomechanics, Int. J. for numerical and analysis methods in geomechanics, 1987, Vol. 11: 555-583
106. Gioda G. Some remarks on back analysis and characterization problems. In: Proc 5th Int Conf on Num Meth in Geom. Nagoya, 1985,1.47-61
107. MaierG, Gioda G. Optimization methods for parametric identiication of geotechnical system. In: Maitins J Bed. Num Methods in Geom. Boston, 1980,1.65-73
108.Aral R. An inverse problem approach to the prediction of Multi-dimensional consolidation behavior. Soil and Foundations, 1984,24(1): 95-108
109. Katsuhiko Arai, Hideki Ohta and Tatsuo Yasui, Simple optimization techniques for evaluating deformation module from field observations, Soil parameters estimation, 1982: 107-112
110. Masoud Sanayei and Michael J. Saletnik, Parameter estimation of structures from static strain measurements. I: Formulation, J. of Structural Eng., 1996:555-562
111. Chang W. C., The application and limitation of extensometer for tunnel monitoring, Rock Mechanics Contributions and challenges, Hustrulid & Johnsons, 1990
133．刘大鹏．排桩支护结构监测数据的反分析．湖北地矿，2000，14(3)：53～59
134．汪中卫．根据反馈对基坑围护结构内力与变形的反分析．大坝观测与土工测试，1998，22(6)：14～17
135．赵振寰．反分析法在基坑开挖数值分析中的应用．工程勘察，1996，4：1～8
136．朱志伟．深基坑工程土层参数反演及挡墙内力预报．岩土力学，1996，20(4)：63～68
137．朱合华．深基坑工程动态施工反演分析与变形预报．岩土工程学报，1998，20(4)：30～35
138. Eykhoff P. System identification-parameter state estimation, John Wiley & Sons, 1974
139. Ledesma A, Alonso E E. Probabilistic back analysis using a maximum likelihood approach. Proceedings 12th International Conference on Soil MeChanics and Foundation Engineering, Brazil, 1989(2): 849～852
140. Ledesma A, Gens A, Alonso E E. Estimation of parameters in geotechnical back analysis —Ⅰ: Maximum likelihood Approch. Computers & Geotechnique, 1996, 18(1): 1～27
141．袁勇．围岩弹塑性参数反算的极大似然法．工程勘察，1991(5)：5～7
142. Hoshiya M, Yoshida I. Identification of conditional stochastic Gaussian field. J of Engineering Mechanics ASCE, 1996,122(2): 101～108
143. Cividini A, Maier G, Nappi A. Parameter estimation of a static geotechnical model using a Bayes' approach. Int J Rock Mechanics Mining Science & Geotechnical Abstract, 1983, 20(5): 215～226
144. Honjo Y, Liu W T, Soumitra G. Inverse analysis of an embankment on soft clay by extended Bayesian method. Int J for Numerical and Analytical Methods in Geomechanics, 1994(18): 709～734
145. Hoshiya M, Saito E. Structural identification by extended Kalman filter. J of Engineering Mechanics, ASCE, 1984, 110(12): 1757～1770
146. Murakami A, Hasegawa T. Observational prediction of settlement using Kalman filtering theory. Proceedings 5th International Conference on Numerical Method in Geomechanics, Nagoya, 1985
147．蒋树屏．扩张卡尔曼滤波器有限元耦合算法及其隧道工程应用．岩土工程学报，1996(2)：11～19
148．黄宏伟．岩体变形随机预报理论及其在地下工程中的应用．同济大学博士学位论文，1993
149．刘维宁．岩土工程反分析方法的信息论研究．岩石力学与工程学报，1993，12(3)：193～205
150．袁勇，孙钧．岩土工程优化反演的目标函数．岩石力学与工程学报，1994，13(2)：29～37
151. Holland J H. Adaptation in neural and artificial system. Ann Arbor: The University of Michigan Press, 1975
152．周明，孙树栋．遗传算法原理及应用．北京：国防工业出版社，1999
153．李立新，王建党，李造鼎．神经网络模型在非线性位移反分析中的应用．岩土力学，1997，1(2)：62～66
154．李瑞有，李迪，马水山．三峡永久船闸开挖边坡岩体力学参数反分析．长江科学院院报，1998，18(2)：10～13
155．李晓红，靳晓光等．隧道位移智能化反分析及其应用靳地下空间，2001，21(4)：299～304
156．周保生，朱维申．巷道围岩参数的人工神经网络预测．岩土力学，1999，20(1)：22～25
157．冯夏庭，杨成祥．智能岩石力学(2)—参数与模型的智能辨识．岩石力学与工程学报，1999，18(3)：359～362
158．王登刚，刘迎曦等．岩土工程位移反分析的遗传算法．岩石力学与工程学报，2000，19(增)：979～982
159．高玮，郑颖人．岩体参数的进化反演．水利学报，2000(8)：1～5
160．高玮，郑颖人．采用快速遗传算法进行岩土工程反分析．岩土工程学报，2001，23(1)：120～122
161．冯夏庭等．位移反分析的进化神经网络方法研究．岩石力学与工程学报，1999，18(5)：529～533
162．邓建辉，李焯芬，葛修润．BP网络和遗传算法在岩石边坡位移反分析中的应用．岩石力学与工程学报，2001．20(1)：1-5
163．高玮，郑颖人，一种新的岩土工程进化反分析算法，岩石力学与工程学报，2003，22(2)：192～196
164. I. Babuska, T. Scapolia, Benchmark Computation and performance evaluation for a rhombic plate bending problem, Int. J. Meth. Eng.,1989,28:155-181
165. E. Reissner, On the theory of elastic plates, J. Appl. Mech., 1951,18:31-38
166. E. Reissner, The effect of transverse shear deformation on the bending of elastic plates, J. Appl. Mech., 1945,12:67-76
167. R. D. Mindlin, Influence of rotatory inertia and shear inflexural motions of isotropic elastic plates, J. Appl. Mech., 1951,18:31-38
168. E. onate, O. C. Zienkewicg, B. Suarez and R. L. Taylor, A general methodology for deriving shear constraint Reissner-Minddin plate elements, Int. J. Num. Meth. Eng.,1992,33:345-359
169. A. Ibrahimbegoric, Quadrilateral finite elements for analysis of thick and thin plates, Comput. Meth. Appli. Meth. Eng., 1993,110:195-209
170. T. J. R. Hughes and W. R. Liu, Nonlinear finite element analysis of shell, Part Ⅰ: three-dimensional shells, Comput. Meth. Appl. Mech. Engng., 1981,26:331-362
171. W. Kanoknukulchasi, R. L. Taylor and T. J. R. Hughes, A Large deformation formulation for shell analysis by the finite element method, Comput. Struct., 1981,13:19-27
172. E. L. Wilson, R. L. Taylor, W D Doherty and J Ghaboussi. Incompatible displacement models. Numerical and Computer Methods in Structral (ed. S J Fenves et. al.), Academic Press, New York, 1973:43～47
173. R. L. Taylor, P. J. Beresford and E. L. Wilson. A Non-conforming element for stress analysis. Int. J. Num. Meth. In Eng., 1976,10:1211～1219
174. C. C. Wu, M. G. Huang and T. H. H. Plan. Consistency condition and convergence criteria of incompatible element: General formulation of incompatible functions and its application. Computer & Structures, 1987,27:639～644
175．鹿晓阳，史宝军，岑章志，鹿宵力．协调等参元与非协调元的对应性研究．工程力学，2001， 18(1)：36～40
17
176．焦兆平，盛勇，吴长春．内参型非协调元合理位移场的研究．工程力学，1998，15(2)：1～10
177. A. Ibrahimbegovic, R. L. Taylor and E. L. Wilson. A robust quadrilateral membrane finite element with drilling degrees of freedom. Int. J. Num. Meth. In Eng.,1990,30: 445～457
178. A. Ibrahimbegovic, F. Frey. Membrane quadrilateral finite element with rotational degrees of freedom. Engineering Fracture Mechanics, 1992,43(1): 13～24
179. B Irons and S. Ahmad, Techniques of Finite Elements, Ellis Horwood, 1980
180. Allman D J. A compatible triangular element including vertex rotations for plane elasticity analysis. Comput & Struct, 1984, 19:1～8
181. Bergan P G, Felippa C A. A triangular element with rotational degrees of freedom. Comp Meth Appl Mech Eng, 1985, 50:25～69
182. Cook R D. On the Allman triangular and a related quadrilateral element. Comp & Struct, 1986,22:1065～1067
183. Macneal R H, Harder R L. A refined four-noded membrane element with rotational degrees of freedom. Comp & Struct, 1989,28:75～84
184. E. Reissner, A note on variational principles in elasticity, Int. J. Solids Struct., 1965, 1:93～95
185. T. J. R. Hughes and F. Brazzi, On drilling degrees of freedom, Comp. Meth. Appl. Mech. Eng., 1989,27:105～121
186. Hughes T. J. R., Brezzi F., Masud A., Harari I. Finite elements with drilling degrees of freedom: theory and numerical evaluations. In Proceedings of the 5th International Symposium on Numerical Methods in Engineering, Vol. 1. Gruber R., Periaux J., Shaw R. P. (eds). Springer: Berlin, 1989
187．吴长春等．非协调数值分析与杂交元方法．科学出版社，1997
188．龙志飞，岑松．有限元法新论．中国水利水电出版社，2001
189．邵国建．一种新的通用板壳元模式及其应用．河海大学博士学位论文，1997
190. K.S. Surana. Transition finite elements for axi-symmetricstress analysis. Int. J. Num. Meth. Eng, 1980,15:809-832
191. K.S. Surana. Transition finite elements for three-dimensional stress analysis. Int. J. Num. Meth. Eng, 1980,15:991-1020
192．王勖成，邵敏．有限单元法基本原理与数值方法，清华大学出版社，1988
193．曲圣年．组合结构有限元分析德罚单元法，固体力学学报，1982，4：555—559
194．钟万勰．关于组合结构分析程序JIGFEX的设计问题，力学与实践，1979，1：3—4
195．冯康．弹性结构的数学理论，科学出版社，1981
196．J．S．Przemieniesk．Theory of matrix structural analysis，1968．(汪德荣等译校，矩阵结构分析理论，1974)
197. A. Ibrahimbegovic, E. L. Wilson. Thick shell and solid finite elements with independent rotation fields. International Journal for Numerical Methods In Engineering. 31,1991:1393-1414
19
198. Kiureghian A D, Ke J. Stochastic finite element method in structural reliability. Probabilistic Eng Mech. 1988, 3(2): 83～91
199. Baecher G B, Ingra T S. Stochastic FEM in settlement predictions. J of Geotech Eng. 1981, 107:449～463
200. Vanmarcke E, Shinozuka M. Random fields and stochastic finite element method. Struct Safety. 1986, 3:143～166
201．朱位秋，任永坚．基于随机场局部平均的随机有限元法．固体力学学报．1988，4：261～271
202. Zhu W Q, Ren Y J. Wu W Q. Stochastic FEM based on local averages of random vector fields. J Eng Mech. 1992, 118(3): 496～511
203．刘宁．三维可分向量随机场局部平均的三维随机有限元及可靠度计算．水利学报．1995，6：75～82
204. Liu W.K., Besterfield G., Mani A., Probabilistic Finite Element Methods in Nonlinear Dynamics, Computer Methods in Applied Mech. And Engrg., Vol. 57, 1986:61-81
205. Liu W K, Mani A. Random fields finite elements. Int J of Numerical Methods in Eng. 1988, 23(10): 1831～1845
206. Liu X B and Chen Q. The interpolation method of stochastic functions and the stochastic variational principle. In: Proc. of SMIRT12. Germany: Stuttgart. 1993: 243～249
207. ZhuW. Q., Ren Y.J., Wu W. Q., Stochastic FEM based on local average of random vector fields . J. Eng. Mech., 118(3), 1992:496-511
208．刘先斌，随机有限元法的误差估计及基于随机场规范展开的有限元法，西南交通大学硕士学位论文，1991
209. Takada T, Shinozuka M. Local integration method in stochastic finite element analysis. In: Proc Int Conf on Structural Safety and Reliability. 1989: 1072～1080
210. Deodatis G. Bounds on response variability stochastic finite element systems. J of Eng Mech. 1990, 116(3): 565～585
211. Spanos P D, Ghanem R. Stochastic finite element expansion for random media. J of Eng Mech. 1989, 115(5): 1035～1053
212. Ghanem R, Spanos P D. Polynomia chaos in stochastic finite elements. J of Appl Mech. 1990, 57: 197～202
213．刘宁，可靠度随机有限元法及工程应用，水利水电出版社，2000
214. Desai C. S., Zaman M. M., Thin layer element for interfaces and joints. Int. J. Num. And Analy. Meth. In Geomech., 1984,8(1): 19～43
215．殷宗泽，朱弘，许国华．土与结构材料接触面的变形及其数学模拟．岩土工程学报，1994，16(3)：14～22
216．高文华，杨林德，叶为民．板—土三维等厚接触单元模型及其应用．同济大学学报，1999，27(3)：297～300
217．杜景灿等，加权位移反演法确定掩体结构面的力学参数，岩土工程学报，1999，2：209～212
218．束善杭，参数的随机反演方法及其面向对象的程序设计，河海大学硕士论文，2000
219. Eykhoff P., System identification—parameter state estimation, John Wiley & Sons, 1974
220. Ledesma A., Gens A. & Alonso E. E., Probabilistic back analysis using a Maximum likelihood approach, Proc. 12th Lnt. Conf. On Soil Mech. & Foundation Eng., Brazil, 1989:849～852
221. A. Cividini, G. Maier, A. Nappi, Parameter estimation of a static geotechnical model using a Bayes' approach , Int. J. Rock Mech. Min. Sci. & Geomechanics Abstract, 1983,20,5:215～226
222．吕爱钟，蒋斌松著，岩石力学反问题，煤炭工业出版社，1998
223．袁勇，围岩弹塑性参数反算的极大似然法，工程勘察，1991年第五期
224．汪成为等著，面向对象分析、设计及应用，国防工业出版社，1992
225．[美]Dale Rogerson著，杨秀章译，COM技术内幕，清华大学出版社，1999
226．[美]Charlie Calvert著，DELPHI 4编程技术内幕，机械工业出版社，1999
227．王小平等，遗传算法—理论、应用与软件实现，西安交通大学出版社，2002
228．郭志川，排桩冻结法深基坑的动态反分析及其支护结构体系可靠度研究，河海大学博士论文，2003
229．杜建成，黄大寿，胡定，边坡稳定的三维极限平衡分析法，四川大学学报(工程科学版)，2001，33(4)：9～12．
230．李朝国，陆金池，张林等，综合法与超载法在沙牌RCC拱坝坝肩稳定分析中的应用，四川大学学报(工程科学版)，1997．1(3)：64～71．
231．钱向东，复杂基岩稳定分析的弹塑性极限平衡法，河海大学学报，1999，27(6)：16～19．
232．王建仁，张福林，基坑稳定的人工神经网络预测，建筑技术开发，2001，28(2)：10～13．
233．卓家寿，邵国建，陈振雷，工程稳定问题中确定滑坍面、滑向与安全度的干扰能量法，水利学报，1997，8：80～84．
234．邵国建，卓家寿，章青，岩体稳定性分析与评判准则研究，岩石力学与工程学报，2003，25(5)：691～696．
235．高凌．工程稳定问题的干扰能量法，河海大学硕士学位论文，1993．
236．胡强，郭志川，刘宁．深基坑支撑体系可靠度计算研究．河海大学学报，2003，6：674～678
237．吕泰仁等，用几何法求构件得可靠指标。河海大学学报，1988，5：86～93
238．吴世伟，结构可靠度分析。交通出版社，1988．210～211
239．陈志坚，游庆仲，胡应德，江阴大桥北锚沉井地基土邓肯参数的反演及反馈分析，固体力学学报，1999，20(计算力学专辑)：102～106
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |