基于随机力学的盐岩地下储气库可靠性分析
|
摘要
利用深部盐岩洞穴进行能源地下储备是国际上广泛认可的能源储备方式,我国盐岩能源地下储库群大规模兴建已经开始。由于近30年,国外盐岩地下油气储库灾难性事故时有发生,因此开展盐岩地下油气储库的可靠性分析工作尤为重要。本文在国家重点基础研究发展计划(973课题)—《油气储库群运营中的灾变风险评估与调控机制》的支持下,以江苏金坛盐岩地下储气库为工程背景,开展了以下工作：
(1)通过收集、整理国内外大量能源地下储备库的事故资料,辨识出了影响盐岩地下储库规划设计、施工、运营各阶段的安全性的主要风险因子；针对主要风险因子,建立了盐岩地下储气库材料参数的随机有限元模型,以及盐岩弹性模量的随机场模型,探讨了在不同模型下盐岩地下储气库的可靠度；
(2)从储气库的稳定性、密闭性和可用性角度出发,总结了14种盐岩地下储气库的可能失效模式；并针对以下3种主要失效模式：顶底板受拉破坏、泥岩夹层与盐岩交界面层面滑动、腔壁片帮破坏,计算出了5条储气库渐进失效路径,及其各失效路径的发展方向及深度；讨论了在上述失效模式下盐岩地下储气库的体系可靠度。
本文的结论对实际工程中工程监测、安全防护提供了一定的理论参考价值,为工作人员采取相应措施,避免事故发生提供参考。
It is wdiely recognized that storing energy in the rock salt cavern in the world, large-scale construction for underground salt-rock storage group have already begun. Because last 30 years, catastrophic accidents of foreign underground salt-rock storages occurred frequently, carrying out reliability analysis work for underground salt-rock storages is particularly important. So under the support of National Key Basic Development Plan(973 subject)-(Risk assessment of catastrophe and regulation mechanism for soil and gas storage in the operation process》, and getting underground salt-rock storage in Jintan of Jiangsu province as the engineering background, the content is presented as follows:
(1) Through the collection and neatening large underground energy carven at home and abroad, identify major risk factors, affecting the rock salt underground storage safety in the state of planning design、construction and operation; In the light of main risk factor, built underground gas storage stochastic finite element model of material parameters, and the salt elastic modulus random field model, discusses the reliability in different model of underground storage;
(2) From the stability、leakproofness and usability of the gas storage, summarized the 14 species of failure mode of underground gas storage; To the three kinds of main failure modes:tensile destruction in the roof and floor of the storage’the interface sliding between mudstone interlayer and rock salt、wall caving on the wall of the storage, calculated the 5 gradual failure paths of the gas storage, and the development direction、depth of failure paths; Discussed system reliability of the underground gas storage under the 3 failure modes.
The conclusion provided some theoretical reference value to the actual engineering project monitoring and security protection, provide the reference for workers to take some measures to avoid the accidents.
(1)通过收集、整理国内外大量能源地下储备库的事故资料,辨识出了影响盐岩地下储库规划设计、施工、运营各阶段的安全性的主要风险因子；针对主要风险因子,建立了盐岩地下储气库材料参数的随机有限元模型,以及盐岩弹性模量的随机场模型,探讨了在不同模型下盐岩地下储气库的可靠度；
(2)从储气库的稳定性、密闭性和可用性角度出发,总结了14种盐岩地下储气库的可能失效模式；并针对以下3种主要失效模式：顶底板受拉破坏、泥岩夹层与盐岩交界面层面滑动、腔壁片帮破坏,计算出了5条储气库渐进失效路径,及其各失效路径的发展方向及深度；讨论了在上述失效模式下盐岩地下储气库的体系可靠度。
本文的结论对实际工程中工程监测、安全防护提供了一定的理论参考价值,为工作人员采取相应措施,避免事故发生提供参考。
It is wdiely recognized that storing energy in the rock salt cavern in the world, large-scale construction for underground salt-rock storage group have already begun. Because last 30 years, catastrophic accidents of foreign underground salt-rock storages occurred frequently, carrying out reliability analysis work for underground salt-rock storages is particularly important. So under the support of National Key Basic Development Plan(973 subject)-(Risk assessment of catastrophe and regulation mechanism for soil and gas storage in the operation process》, and getting underground salt-rock storage in Jintan of Jiangsu province as the engineering background, the content is presented as follows:
(1) Through the collection and neatening large underground energy carven at home and abroad, identify major risk factors, affecting the rock salt underground storage safety in the state of planning design、construction and operation; In the light of main risk factor, built underground gas storage stochastic finite element model of material parameters, and the salt elastic modulus random field model, discusses the reliability in different model of underground storage;
(2) From the stability、leakproofness and usability of the gas storage, summarized the 14 species of failure mode of underground gas storage; To the three kinds of main failure modes:tensile destruction in the roof and floor of the storage’the interface sliding between mudstone interlayer and rock salt、wall caving on the wall of the storage, calculated the 5 gradual failure paths of the gas storage, and the development direction、depth of failure paths; Discussed system reliability of the underground gas storage under the 3 failure modes.
The conclusion provided some theoretical reference value to the actual engineering project monitoring and security protection, provide the reference for workers to take some measures to avoid the accidents.
引文
[1]杨春和.梁卫国,魏东吼等.中国盐岩能源地下储存可行性研究[J].岩石力学与工程学报,2005,24(24)：4409-4417
[2]杨春和.深部盐岩层地下石油储备中的基础性研究-国家自然科学基金资助项目结题报告[R].2008.12
[3]康永尚,徐宝华,徐显生.中国天然气战略储备的需求和对策[J].天然气工业，2006.26(10)：133-136
[4]陈卫忠,杨建平,伍国军等.低渗透性介质渗透性试验研究.岩石力学与工程学报,2008,27(2)：236-243.
[5]吴文,杨春和,侯正猛等.盐岩中能源(石油和天然气)地下储存力学问题研究现状及其进展[J].岩石力学与工程学报,2005,24(增2)：5561-5568.
[6]卻保平,赵阳升,赵延林等.层状盐岩储存长期运行腔体围岩流变破坏及渗透现象研究[J].岩土力学,2008,29(增)：241-246
[7]J. C. Stormont. In situ gas permeability measurements to delineate damage in rock salt[J]. Int. J. Rock Mech. Min. Sci.1997,34(7):1055-1064
[8]J. C. Stormont., DAEMEN J J K. Laboratory study of gas permeability changes in rock salt during deformation[J]. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr.,1999,29(4):325-342
[9]Hunsche U & Albrecht H. Results of true tri-axial strength tests on rock salt. Engineering fracture mechanics 35(4/5),1990:867-877
[10]Werner Skrotzki. An estimate of the brittle to ductile transition in salt [A]. Langer, The mechanical behavior of salt proceedings of the first conference[C]. Clausthal, trans tech publications,1984:381-388
[11]Hunsche U. Determination of the dilatancy boundary and damage up to failure for four types of rock salt at different stress geometries[A]. Langer, The mechanical behavior of salt proceedings of the second conference[C]. Clausthal, trans tech publications,1996:163-174
[12]Hunsche U. Fracture experiments on cubic rock salt samples[A]. Langer, The mechanical behavior of salt proceedings of the first conference[C]. Clausthal, trans tech publications,1984:169-179
[13]Dawson E. M., Cundall P. A. Cosserat plasticity for modeling layered rock. In:Proceedings of the ISRM Regional Conference on Fractured and Jointed Rock Masses. Berkeley, California: Lawrence Berkeley Laboratory,1992,269-276.
[14]Cunddall P.1978. Explicit finite difference method in geomechanics[J]. Desai C. Numerical Methods in Geomichanics:132-150
[15]Iordache M M, Willamb K.1998. Localized failure analysis in elastoplastic cosserat continua[M].Comput. Methods Appl. Mech. Engng.,151:559-586
[16]Chikhaoui M., La zone des diapirs en Tunisie:cadre structural, e'volution ge'odynamique de la segmentation me'so ce'nozoRque et ge'ome'trie des corps triasiques. The'se Doct. Es Sciences. Universite'de Tunis El Manar.2002, (323pp.).
[17]Chikhaoui, M. Sucession distension compression dans Iesillon tunisien, secteur de Nebeur-El Kef, ro^ le des extrusions triasiques pre'coce lors des serrages alpins. The'se Doct. Universite'de Nice, France.1988, (143 pp.).
[18]Adhikary D. P., Dyskin A. V. A Continuum model of layered rock masses with non^associative joint plasticity. International Journal for Numerical and Analytical Methods in Geomechanics,1998,22(4):245～261
[19]刘俊,黄铭,葛修润Cosserat理论的应变能定理及解的唯一性[J].岩石力学与工程学报,2003,22[3]：343-346
[20]佘成学,熊文林,陈胜宏.层状岩体的弹粘塑性Cosserat介质理论及其工程应用[J].水利学报,1996, (4):10-174
[21]Cosserat E., Cosserat F. Theorie des corps deformables. Hermann:Paris,1909.
[22]张强勇,刘德军,贾超等.盐岩油气储库介质地质力学模型相似材料的研制[J].岩土力学,2009,30(12)：3581-3586
[23]梁卫国,赵阳升.盐岩力学特性的试验研究[J].岩石力学与工程学报,2004,23(3)：391-394
[24]Aubertin M, An up to now version of SUVIC-D for modeling the behavior of salt[A]. In:The Mechanical Behavior of salt. Proc,4th conf. Trans. Tech, Publ.[C]. Clausthal-Zellerfeld:[s.n.], 1998:205-220.
[25]Lux K H, Duesterloh U, Bertram J, et al. Abschlubrticht zum BMBF-Forschungs-vorhaben 02C00922[R]. Claustha:Professor fur Deponietechnik u. Geomechanik der TU,1997.
[26]姜德义,任松,刘新荣.岩盐溶腔顶板稳定性突变理论分析.岩土力学,2005,26(7)：1099-1103.
[27]杨春和,陈锋,曾义金.盐岩蠕变损伤本构关系研究[J].岩石力学与工程学报,2002(11)：1602-1604.
[28]Yang Chunhe, Daeman JJK, Yin Jianhua. Experimental investigation of creep behavior of salt rock[J].International Journal of Rock Mechanics and Mining Science,2000,36(2):336-341.
[29]杨春和,殷建华,DaemanJJK盐岩应力松弛效应的研究[J].岩石力学与工程学报,1999,18(3)：262-265.
[30]Rokahr R, Staudtmeister K. the assessment of the stability of a cavern field in bedded salt with the help of the new hannover dimensioning concept[A]. Ghoreychi M, Berest Jr P, Langer M. Proceedings of 3rd Conf. Mech. Beh. Of Salt. Clausthal-Zellerfeld:Trans. Tech. Pub1.:534-544
[31]贾超,张强勇,张宁等.盐岩地下储气库风险分级机制初探[J].岩土力学.2009,30(12)：3621-3626
[32]杨强,刘耀儒等.能源储备地下库群稳定性与连锁破坏分析[J].岩土力学,2009,30(12)：3553-3561
[33]余海龙,谭学术,鲜学福等.盐岩溶腔稳定性模型试验研究[J]矿山压力与顶板管理,1995,3/4：156-159
[34]刘新荣,余海龙,姜德义等.盐岩顶板复合岩石力学性质试验研究[J]重庆建筑大学学报,2004,26(3)31-35
[35]任松,姜德义,杨春和.盐穴储气库破坏后地表沉陷规律数值模拟研究[J].岩土力学.2009,30(12)：3595-3601
[36]刘宁.可靠度随机有限元法及其工程应用[M].中国水利水电出版社,2001.
[37]Vanmarcke E. Random field:Analysis and synthesis[M]. Cambrige:MIT Press,1983
[38]Nowak, A.S., Lind,N.C. Practical code calibration procedures[M] National Research Council of Canada,1980
[39]赵国藩.结构可靠度理论[M].中国建筑工业出版社,2005.
[40]Alfredo H-S. Ang and Wilson H. Tang. Probability concepts in engineering planning and design[M] John Wiley & Sons, Volume 1,1975, Volume 2,1984
[41]Hak-Fong Ma and A.H-S. Ang. Reliability analysis of redundant ductile structural system[A]University of Illinois at Urbana-Champaign.1981
[42]R.M.Bennett and A.H-S.Ang. Investigation of methods for structural system reliability[A]University of Illinois at Urbana-Champaign,1983
[43]吕泰仁,吴世伟.用儿何法求构件可靠指标[J]河海大学学报,1988.5
[44]叶军,吴世伟.蒙特卡洛法在结构可靠度分析中的应用[J]河海大学学报,1988,5
[45]武清玺,吕泰仁,吴世伟.变量相关时结构可靠指标的计算[J]高校应用数学学报,1987.9
[46]Murotsu Y, Okada H, Taguchi K, Grimmeit M, Yonezawa M[J]. Automatic generation of stochastically dominant failure modes of frame structures. Structural Safety,1984,2:17-25.
[47]Melhers R E, Tang L K[J]. Dominant failure modes in stochastic structural systems[J]. Structural Safety,1984,2:127-143.
[48]Tang L K, Melhers R E[J]. Dominant mechanisms in stochastic plastic frames[J]. Reliability Engineering,1987,18:101-115.
[49]Ma H F, Ang A H S. Reliability analysis of redundant ductile structural system[M]n: Research Report. Urban-Champaign:University of Illinois,1981.
[50]Moses E. System reliability development in structural engineering[J]. Structural Safety,1982, 1(1):3-13.
[51]Feng Y S. Enumerating significant failure modes of a structural system by using criterion methods. Comput. and Struct.,1988,130(5):1153-1157.
[52]李宏.框架结构失效机构的自动产生与体系可靠度[D].南京：河海大学,1990.
[53]吴世伟,李同春.重力坝最大可能失效模式初探[J].水利学报1990.4:36-44(WU Shi-wei, LI
[54]吴世伟,李同春,张思俊.拱坝的失效模式与可靠度[J].河海大学学报.1992,20(2)：
[55]Mostyn GR,Li KS. Probabilistic slope analysis-state-of-play [A].In:Li KS, Lo S-CR,eds. Probabilistic methods in geotechnical engineering:Proceedings of the Conference on Probabilistic methods in geotechnical engineering [C].Rotterdam.Balkema,1993:89-120
[56]Spanos P D. Ghanem R. Stochastic finite element expansion for random media[J] Journal of Engineering Mechanics,1989,115(5):1035-1053
[57]钟文华.岩土参数随机场特性及最优估计研究[D].河北工业大学硕士学位论文,2002
[58]Bucher C. Structural Reliability and Stochastic Finite Elements[R]. NAFEMS Seminar, Use of Stochastics in FEM Analyses, Wiesbaden, Germany,2003
[59]朱位秋,任永坚.随机场的局部平均与随机有限元[J].航空学报,1986,7(6)：604-611
[60]朱位秋.随机振动[M].北京：科学出版社,1992
[61]冷伍明,赵善瑞.士工参数不确定性的计算分析[J].岩土工程学报,1995,17(2)：68-74
[62]徐斌,王大通,高大钊.用相关函数法求静探曲线相关距离的探讨[J].岩土力学,1998,19(1)：55-59
[63]韩宪军.弹模随机场对地下洞室可靠度计算结果的影响[J].西安科技大学学报,2007,27(2)：214-217
[64]刘润,闫澍旺.渤海湾地基土随机场特性及可靠度分析[J].岩土工程学报,2004,26(4)：464-467
[65]胡小荣,唐春安.邹正盛.岩土力学参数随机场的离散研究[J].岩士工程学报,1999,21(4)：450-455
[66]杨怀.考虑坝基材料参数随机场的重力坝可靠度计算[D].河海大学硕士学位论文,2006
[2]杨春和.深部盐岩层地下石油储备中的基础性研究-国家自然科学基金资助项目结题报告[R].2008.12
[3]康永尚,徐宝华,徐显生.中国天然气战略储备的需求和对策[J].天然气工业，2006.26(10)：133-136
[4]陈卫忠,杨建平,伍国军等.低渗透性介质渗透性试验研究.岩石力学与工程学报,2008,27(2)：236-243.
[5]吴文,杨春和,侯正猛等.盐岩中能源(石油和天然气)地下储存力学问题研究现状及其进展[J].岩石力学与工程学报,2005,24(增2)：5561-5568.
[6]卻保平,赵阳升,赵延林等.层状盐岩储存长期运行腔体围岩流变破坏及渗透现象研究[J].岩土力学,2008,29(增)：241-246
[7]J. C. Stormont. In situ gas permeability measurements to delineate damage in rock salt[J]. Int. J. Rock Mech. Min. Sci.1997,34(7):1055-1064
[8]J. C. Stormont., DAEMEN J J K. Laboratory study of gas permeability changes in rock salt during deformation[J]. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr.,1999,29(4):325-342
[9]Hunsche U & Albrecht H. Results of true tri-axial strength tests on rock salt. Engineering fracture mechanics 35(4/5),1990:867-877
[10]Werner Skrotzki. An estimate of the brittle to ductile transition in salt [A]. Langer, The mechanical behavior of salt proceedings of the first conference[C]. Clausthal, trans tech publications,1984:381-388
[11]Hunsche U. Determination of the dilatancy boundary and damage up to failure for four types of rock salt at different stress geometries[A]. Langer, The mechanical behavior of salt proceedings of the second conference[C]. Clausthal, trans tech publications,1996:163-174
[12]Hunsche U. Fracture experiments on cubic rock salt samples[A]. Langer, The mechanical behavior of salt proceedings of the first conference[C]. Clausthal, trans tech publications,1984:169-179
[13]Dawson E. M., Cundall P. A. Cosserat plasticity for modeling layered rock. In:Proceedings of the ISRM Regional Conference on Fractured and Jointed Rock Masses. Berkeley, California: Lawrence Berkeley Laboratory,1992,269-276.
[14]Cunddall P.1978. Explicit finite difference method in geomechanics[J]. Desai C. Numerical Methods in Geomichanics:132-150
[15]Iordache M M, Willamb K.1998. Localized failure analysis in elastoplastic cosserat continua[M].Comput. Methods Appl. Mech. Engng.,151:559-586
[16]Chikhaoui M., La zone des diapirs en Tunisie:cadre structural, e'volution ge'odynamique de la segmentation me'so ce'nozoRque et ge'ome'trie des corps triasiques. The'se Doct. Es Sciences. Universite'de Tunis El Manar.2002, (323pp.).
[17]Chikhaoui, M. Sucession distension compression dans Iesillon tunisien, secteur de Nebeur-El Kef, ro^ le des extrusions triasiques pre'coce lors des serrages alpins. The'se Doct. Universite'de Nice, France.1988, (143 pp.).
[18]Adhikary D. P., Dyskin A. V. A Continuum model of layered rock masses with non^associative joint plasticity. International Journal for Numerical and Analytical Methods in Geomechanics,1998,22(4):245～261
[19]刘俊,黄铭,葛修润Cosserat理论的应变能定理及解的唯一性[J].岩石力学与工程学报,2003,22[3]：343-346
[20]佘成学,熊文林,陈胜宏.层状岩体的弹粘塑性Cosserat介质理论及其工程应用[J].水利学报,1996, (4):10-174
[21]Cosserat E., Cosserat F. Theorie des corps deformables. Hermann:Paris,1909.
[22]张强勇,刘德军,贾超等.盐岩油气储库介质地质力学模型相似材料的研制[J].岩土力学,2009,30(12)：3581-3586
[23]梁卫国,赵阳升.盐岩力学特性的试验研究[J].岩石力学与工程学报,2004,23(3)：391-394
[24]Aubertin M, An up to now version of SUVIC-D for modeling the behavior of salt[A]. In:The Mechanical Behavior of salt. Proc,4th conf. Trans. Tech, Publ.[C]. Clausthal-Zellerfeld:[s.n.], 1998:205-220.
[25]Lux K H, Duesterloh U, Bertram J, et al. Abschlubrticht zum BMBF-Forschungs-vorhaben 02C00922[R]. Claustha:Professor fur Deponietechnik u. Geomechanik der TU,1997.
[26]姜德义,任松,刘新荣.岩盐溶腔顶板稳定性突变理论分析.岩土力学,2005,26(7)：1099-1103.
[27]杨春和,陈锋,曾义金.盐岩蠕变损伤本构关系研究[J].岩石力学与工程学报,2002(11)：1602-1604.
[28]Yang Chunhe, Daeman JJK, Yin Jianhua. Experimental investigation of creep behavior of salt rock[J].International Journal of Rock Mechanics and Mining Science,2000,36(2):336-341.
[29]杨春和,殷建华,DaemanJJK盐岩应力松弛效应的研究[J].岩石力学与工程学报,1999,18(3)：262-265.
[30]Rokahr R, Staudtmeister K. the assessment of the stability of a cavern field in bedded salt with the help of the new hannover dimensioning concept[A]. Ghoreychi M, Berest Jr P, Langer M. Proceedings of 3rd Conf. Mech. Beh. Of Salt. Clausthal-Zellerfeld:Trans. Tech. Pub1.:534-544
[31]贾超,张强勇,张宁等.盐岩地下储气库风险分级机制初探[J].岩土力学.2009,30(12)：3621-3626
[32]杨强,刘耀儒等.能源储备地下库群稳定性与连锁破坏分析[J].岩土力学,2009,30(12)：3553-3561
[33]余海龙,谭学术,鲜学福等.盐岩溶腔稳定性模型试验研究[J]矿山压力与顶板管理,1995,3/4：156-159
[34]刘新荣,余海龙,姜德义等.盐岩顶板复合岩石力学性质试验研究[J]重庆建筑大学学报,2004,26(3)31-35
[35]任松,姜德义,杨春和.盐穴储气库破坏后地表沉陷规律数值模拟研究[J].岩土力学.2009,30(12)：3595-3601
[36]刘宁.可靠度随机有限元法及其工程应用[M].中国水利水电出版社,2001.
[37]Vanmarcke E. Random field:Analysis and synthesis[M]. Cambrige:MIT Press,1983
[38]Nowak, A.S., Lind,N.C. Practical code calibration procedures[M] National Research Council of Canada,1980
[39]赵国藩.结构可靠度理论[M].中国建筑工业出版社,2005.
[40]Alfredo H-S. Ang and Wilson H. Tang. Probability concepts in engineering planning and design[M] John Wiley & Sons, Volume 1,1975, Volume 2,1984
[41]Hak-Fong Ma and A.H-S. Ang. Reliability analysis of redundant ductile structural system[A]University of Illinois at Urbana-Champaign.1981
[42]R.M.Bennett and A.H-S.Ang. Investigation of methods for structural system reliability[A]University of Illinois at Urbana-Champaign,1983
[43]吕泰仁,吴世伟.用儿何法求构件可靠指标[J]河海大学学报,1988.5
[44]叶军,吴世伟.蒙特卡洛法在结构可靠度分析中的应用[J]河海大学学报,1988,5
[45]武清玺,吕泰仁,吴世伟.变量相关时结构可靠指标的计算[J]高校应用数学学报,1987.9
[46]Murotsu Y, Okada H, Taguchi K, Grimmeit M, Yonezawa M[J]. Automatic generation of stochastically dominant failure modes of frame structures. Structural Safety,1984,2:17-25.
[47]Melhers R E, Tang L K[J]. Dominant failure modes in stochastic structural systems[J]. Structural Safety,1984,2:127-143.
[48]Tang L K, Melhers R E[J]. Dominant mechanisms in stochastic plastic frames[J]. Reliability Engineering,1987,18:101-115.
[49]Ma H F, Ang A H S. Reliability analysis of redundant ductile structural system[M]n: Research Report. Urban-Champaign:University of Illinois,1981.
[50]Moses E. System reliability development in structural engineering[J]. Structural Safety,1982, 1(1):3-13.
[51]Feng Y S. Enumerating significant failure modes of a structural system by using criterion methods. Comput. and Struct.,1988,130(5):1153-1157.
[52]李宏.框架结构失效机构的自动产生与体系可靠度[D].南京：河海大学,1990.
[53]吴世伟,李同春.重力坝最大可能失效模式初探[J].水利学报1990.4:36-44(WU Shi-wei, LI
[54]吴世伟,李同春,张思俊.拱坝的失效模式与可靠度[J].河海大学学报.1992,20(2)：
[55]Mostyn GR,Li KS. Probabilistic slope analysis-state-of-play [A].In:Li KS, Lo S-CR,eds. Probabilistic methods in geotechnical engineering:Proceedings of the Conference on Probabilistic methods in geotechnical engineering [C].Rotterdam.Balkema,1993:89-120
[56]Spanos P D. Ghanem R. Stochastic finite element expansion for random media[J] Journal of Engineering Mechanics,1989,115(5):1035-1053
[57]钟文华.岩土参数随机场特性及最优估计研究[D].河北工业大学硕士学位论文,2002
[58]Bucher C. Structural Reliability and Stochastic Finite Elements[R]. NAFEMS Seminar, Use of Stochastics in FEM Analyses, Wiesbaden, Germany,2003
[59]朱位秋,任永坚.随机场的局部平均与随机有限元[J].航空学报,1986,7(6)：604-611
[60]朱位秋.随机振动[M].北京：科学出版社,1992
[61]冷伍明,赵善瑞.士工参数不确定性的计算分析[J].岩土工程学报,1995,17(2)：68-74
[62]徐斌,王大通,高大钊.用相关函数法求静探曲线相关距离的探讨[J].岩土力学,1998,19(1)：55-59
[63]韩宪军.弹模随机场对地下洞室可靠度计算结果的影响[J].西安科技大学学报,2007,27(2)：214-217
[64]刘润,闫澍旺.渤海湾地基土随机场特性及可靠度分析[J].岩土工程学报,2004,26(4)：464-467
[65]胡小荣,唐春安.邹正盛.岩土力学参数随机场的离散研究[J].岩士工程学报,1999,21(4)：450-455
[66]杨怀.考虑坝基材料参数随机场的重力坝可靠度计算[D].河海大学硕士学位论文,2006