公路隧道施工监测及围岩稳定性概率分析方法研究
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摘要
隧道施工监控量测是隧道施工安全与质量的基础,通过现场施工监测可以有效地掌握围岩和支护在施工过程中的力学动态及稳定程度,为评价和修改初期支护参数、力学分析及二次衬砌施作时间提供信息依据;通过信息反馈及预测预报来优化施工组织设计,指导现场施工,确保隧道施工的安全与质量以及工程项目的社会、经济和环境效益。
本文以张家界阳和至黄龙洞公路梨子坪隧道施工监测为依托,首先,深入分析了影响公路隧道围岩稳定性的主要因素,对张家界阳和至黄龙洞公路梨子坪隧道围岩进行了详细分级。其次,从现代岩体力学理论出发,利用围岩-支护结构相互作用机理,对公路隧道施工阶段围岩稳定性监测的力学机制进行了较深入研究,得出了隧道二次衬砌施作最佳时段的判断方法。然后,通过张家界阳和至黄龙洞公路梨子坪隧道施工监测,针对不同级别围岩的变形量、变形稳定时间、变形速率进行了深入分析和总结,获得了一些有益的结论,并将其应用于梨子坪隧道施工监控,保证了该工程的安全与顺利进展。最后,在隧道围岩稳定性概率分析方面,本文针对地下结构变形控制原理,建立了正常使用情况下基于变形准则的隧道稳定性可靠度方程,并提出了其差分求解方法;利用本文所研究的方法,具体分析了某隧道围岩基于变形正常使用的稳定性可靠度,并将计算所得结论与蒙特卡洛模拟计算结果进行了对比,两者精度相当,说明本文方法是有效的,可以用于实际工程分析。
Tunnel construction monitoring is the base of security and quality of tunnel contruction. Through construction monitoring, development of mechanics and degree of stability of surrounding rock and supporting on construction process can be commanded effectively. Information gist is offered for estimating and modifying parameters of earlier supporting and mechanics analysis, as well as the time of secondary lining construction. Through the feedback of information and forecasting, the design of construction organization is optimized, locale contruction is guided and the security and quality of tunnel construction is insured, which is socially, economically and environmentally beneficial.
This paper is based on the construction monitoring of Liziping tunnel from Yanghe to Huanglongdong on Zhangjiajie area. At first, the paper will analyze the main ingredient at lengty which influenced the stability of road tunnel surrounding rock and classify the surrounding rock of Liziping tunnel detailedly. Secondly, starting with the theory of modern rock mass mechanics, using the mechanism of the interaction of surrounding rock and supporting.The mechanics mechanism of monitoring of stability of road tunnel surrounding rock is studied deeply. And the best period time of secondary lining construction is educed. And then, through contruction monitoring of Liziping tunnel, the value of deformation, the stabilization time of deformation and velocity of deformation of defferent class surrounding rock are analyzed and summarized. Some useful conclusions are acquired which is applied to construction monitoring of Liziping tunnel, to ensure the security and headway. Finally, on the aspect of reliability analysis of tunnel surrounding rock, aimed at the deformation control theory of underground structure, the reliability equation of tunnel structure in normal use is established which based on deformation criteria, and different method is derived from it. With the method studied on this paper, the reliability in normal use of a tunnel surrounding rock is analyzed which based on deformation criteria. And the computed conclusion is contrasted with the result which computed by Monte Carlo simulation. The precision is close to Monte Carlo, so the method of this paper is effective, and it could be used to analyze the engineering practice.
本文以张家界阳和至黄龙洞公路梨子坪隧道施工监测为依托,首先,深入分析了影响公路隧道围岩稳定性的主要因素,对张家界阳和至黄龙洞公路梨子坪隧道围岩进行了详细分级。其次,从现代岩体力学理论出发,利用围岩-支护结构相互作用机理,对公路隧道施工阶段围岩稳定性监测的力学机制进行了较深入研究,得出了隧道二次衬砌施作最佳时段的判断方法。然后,通过张家界阳和至黄龙洞公路梨子坪隧道施工监测,针对不同级别围岩的变形量、变形稳定时间、变形速率进行了深入分析和总结,获得了一些有益的结论,并将其应用于梨子坪隧道施工监控,保证了该工程的安全与顺利进展。最后,在隧道围岩稳定性概率分析方面,本文针对地下结构变形控制原理,建立了正常使用情况下基于变形准则的隧道稳定性可靠度方程,并提出了其差分求解方法;利用本文所研究的方法,具体分析了某隧道围岩基于变形正常使用的稳定性可靠度,并将计算所得结论与蒙特卡洛模拟计算结果进行了对比,两者精度相当,说明本文方法是有效的,可以用于实际工程分析。
Tunnel construction monitoring is the base of security and quality of tunnel contruction. Through construction monitoring, development of mechanics and degree of stability of surrounding rock and supporting on construction process can be commanded effectively. Information gist is offered for estimating and modifying parameters of earlier supporting and mechanics analysis, as well as the time of secondary lining construction. Through the feedback of information and forecasting, the design of construction organization is optimized, locale contruction is guided and the security and quality of tunnel construction is insured, which is socially, economically and environmentally beneficial.
This paper is based on the construction monitoring of Liziping tunnel from Yanghe to Huanglongdong on Zhangjiajie area. At first, the paper will analyze the main ingredient at lengty which influenced the stability of road tunnel surrounding rock and classify the surrounding rock of Liziping tunnel detailedly. Secondly, starting with the theory of modern rock mass mechanics, using the mechanism of the interaction of surrounding rock and supporting.The mechanics mechanism of monitoring of stability of road tunnel surrounding rock is studied deeply. And the best period time of secondary lining construction is educed. And then, through contruction monitoring of Liziping tunnel, the value of deformation, the stabilization time of deformation and velocity of deformation of defferent class surrounding rock are analyzed and summarized. Some useful conclusions are acquired which is applied to construction monitoring of Liziping tunnel, to ensure the security and headway. Finally, on the aspect of reliability analysis of tunnel surrounding rock, aimed at the deformation control theory of underground structure, the reliability equation of tunnel structure in normal use is established which based on deformation criteria, and different method is derived from it. With the method studied on this paper, the reliability in normal use of a tunnel surrounding rock is analyzed which based on deformation criteria. And the computed conclusion is contrasted with the result which computed by Monte Carlo simulation. The precision is close to Monte Carlo, so the method of this paper is effective, and it could be used to analyze the engineering practice.
引文
[1] 李晓红. 隧道新奥法及其量测技术. 北京: 科学出版社, 2001, 10-32
[2] 陈建平, 朱首军. 新奥法的实质与存在的问题. 河港工程, 2002, 12(1): 34-36
[3] 朱乐辉, 郑金科, 伊雪辉. 旦架哨隧道监控量测与信息化施工. 公路, 2002, 2(6): 24-26
[4] 吉小明, 赵中旺. 隧道监测和信息反馈中的计算模型优化问题. 地下空间, 1997, 17(2): 104-108
[5] 黄宏伟. 城市隧道与地下结构工程的发展与展望. 地下空间, 2001, 21(4): 311-317
[6] Iannacchione A T, Dolinar D R. Compton C S. Controlling roof beam failures from high horizontal stresses in underground stone mines. In: the 17th Int. Conference on Ground Control in Mining Morgantown. West Virginia University, 1998, 102-112
[7] King G C, Stein R S, Lin J. Static stress changes and the triggering of earthquakes. Bulletin of the Seismological Society of America, 1994, 84(3): 935-953
[8] Muller L. Removing the misconception on the new Austrian Tunneling Method. tunnels & tunneling, 1978, (10): 29-32
[9] 文献江. 四联拱隧道施工技术. 西部探矿工程, 2000, 16(3): 51-52
[10] Lee R, Chang C L. Some Properties of Fuzzy Logic. Inf.and Control. 1971, 17(19): 413-417
[11] 苏永华, 赵明华, 刘晓明. 岩体分类的二元相对模糊评判法. 岩体力学与工程学报, 2006, 25(5): 1049-1055
[12] Singh B, Goel R K. Rock Mass Classification. A Practical Approach in Civil Engineering. Holland: Elsevier, 1999, 267
[13] 徐万鹏. 隧道位移监测新方法的可行性探索. 铁道工程学报, 2000, 2(2): 65-68
[14] Stein R S. Stress triggering of the 1994 M=6.7 Northridge, California, earthquake by its predecessors. Science, 1994, 278(265): 1432-1435
[15] 中华人民共和国水利部. 工程岩体分级标准 GB50218-94. 北京: 中国计划出版社, 1995, 1-20
[16] 中华人民共和国交通部. 中华人民共和国行业标准, 公路隧道设计规范 JTGD70-2004. 人民交通出版社, 2004, 23-45
[17] 黑龙江公路勘察设计院. 阳和至黄龙洞公路隧道工程. 哈尔滨市: 黑龙江公路勘察设计院, 2006, 1-132
[18] 金丰年. 考虑时间效应的围岩特征曲线. 岩石力学与工程学报,1997, 18(4): 334-353
[19] 徐林生, 王晓雯. 东门关隧道围岩变形特征及其影响因素分析. 公路交通技术, 2004, 6(4): 88-90, 96
[20] 杨会军. 复杂条件下隧道围岩变形特征. 铁道工程学报, 2006, 12(1): 57-60
[21] 孙兆远, 焦苍, 罗琼. 不同工法开挖超大断面隧道引起围岩变形机理分析. 铁道建筑, 2006, 8(9): 35-37
[22] 李晓红, 王宏图, 贾剑青. 隧道及地下工程围岩稳定性及可靠性分析的极限位移判别. 岩土力学, 2005, 26(6): 850-854
[23] Schubert W, Moritz B. Controllable ductile support system for tunnels in squeezing rock. Sonderdruck aus Felsbau, 1998, 16(4): 224-227
[24] 靳晓光, 李春晓, 沈军辉. 二郎山公路隧道围岩变形影响因素研究. 地质灾害与环境保护, 2000, 11(7): 58-62
[25] 徐林生. 阳宗隧道围岩变形的神经网络技术预测. 重庆交通学院院报, 2006, 25(3): 32-35
[26] Villy A, Kontogianni S, Stiros C. Induced deformation during tunnel excavation: evidence from geodetic monitoring. Engineering Geology, 2005, 344(79): 115-126
[27] Kaiser P. Deformation monitoring for stability assessment of underground openings. Compressive Rock Engineering, 1993(4): 607-630
[28] Kontogianni V A, Tzortzis A, Stiros S C. Deformation and failure of the Tymfristos tunnel. Journal Geotechnical Engineering, ASCE, 2004, 130(10): 1004-1013
[29] Schubert W, Steindorfer A. Selective displacements monitoring during tunnel excavation. Felsbau, 1996, 14(2): 93-97
[30] Kontogianni V, Stiros S. Predictions and observations convergence in shallow tunnels: case histories in Greece. Engineering Geology, 2002, 63(3): 333-345
[31] 李晓红, 夏彬伟, 康勇. 通渝隧道围岩收敛位移量测实践. 重庆大学学报(自然科学版), 2005, 28(1): 131-134
[32] 赵明阶, 徐容, 许锡宾. 岩溶地区全断面开挖隧道围岩变形规律及其监测. 同济大学学报(自然科学版), 2004, 32(7): 866-871
[33] 王金庄, 康建荣, 吴立新. 煤矿覆岩离层注浆减缓地表沉降机理与应用探讨.中国矿业大学学报, 1999, 28(4): 331-334
[34] 刘绍堂. 隧道施工期间的变形监测技术. 地下空间与工程学报, 2006, 2(8): 1346-1348, 1359
[35] Alfredo H, Ang S, Tang W H. Probability concepts in Engineering planning and Design Volume Ⅱ-Decision. New York: Elsevier Science Ltd, 1990.
[36] 柳厚祥, 方风华. 预埋多点位移计现场确定围岩松动圈的方法研究. 矿冶工程, 2006, 26 (1): 1-4
[37] 北京奥多尔投资研究中心. 风险不确定性与秩序. 北京: 中国财政经济出版社, 2001, 15-23
[38] 李旺, 夏建波. 锚杆支护参数对围岩稳定性的影响. 陕西煤炭, 2007(3): 45-46
[39] 王春风. 金融市场奉献管理. 天津: 天津大学出版社, 2001, 1-15
[40] 黄俊, 张顶立. 地铁暗挖隧道上覆地层大变形规律分析. 岩土力学, 2004, 25(8): 1288-1292, 1301
[41] 陈建勋, 马建秦. 隧道工程试验监测技术. 北京: 人民交通出版社, 2005, 26-78
[42] 李世煇. 隧道支护设计新论(第一版). 北京: 科学出版社, 1999, 97-106
[43] Ching S C. Numerical and analytical moding for granulates. In: the 9th International Conference for Computer Mtethod and Advances in Geomechanics. Netherlands, 1997, 105-114
[44] 刘佑荣, 唐辉明. 岩体力学. 武汉: 中国地质大学出版社, 1999, 88-109
[45] 李世辉. 隧道围岩稳定性系统分析. 北京: 中国铁道出版社, 1991, 1-23
[46] 朱永全. 隧道稳定性位移判别准则. 中国铁道科学, 2001, 22(6): 80-83
[47] 贺建民, 戴小平, 郭磊. 隧道围岩稳定性及安全性分析的位移判别方法. 矿业安全与环保, 2001, 28(5): 36-37, 45
[48] 张勇, 张子新, 华安增. 高速公路隧道的围岩变形特征. 中南公路工程 , 2001, 26(3): 12-14
[49] 中华人民共和国行业标准.公路隧道施工技术规范 JTJ 024-94. 人民交通出版社, 1994, 1-20
[50] 朱沛富, 五莹军. 围岩稳定性预测在隧道(洞)施工中的应用. 铁道建筑技术, 1999, 17(6): 23-25
[51] 原国家冶金工业局. 锚杆喷射混凝土支护技术规范 GB50086-2001. 北京: 中国计划出版社,2001,12-24
[52] 赵明华, 陈兆, 苏永华. 基于变形准则的隧道围岩稳定性概率分析. 矿冶工程, 2008, 2(2): 1-5
[53] Jia P, Tang C A. Numerical study on failure mechanism of tunnel in jointed rock mass, Tunnel. Underg.Technol. 2007, 9(1): 1-8
[54] Eberhardt E. Numerical modelling of three-dimension stress rotation ahead of an advancing tunnel face. International Journal of Rock Mechanics and Mining Sciences, 2001, 38(4): 499-518
[55] Melchers R E. Structural reliability analysis and prediction (Second edition). New York: John Wiley & Sons, 1999, 15-28
[56] 贡金鑫. 工程可靠度计算方法(第一版). 大连: 大连理工大学出版社, 2003, 1-349
[57] Hasofer A M, Lind N C. Excat and inviariant second-momrnt code format. Journal of Engineering Mechanics, 1974, 1000(1): 111-121
[58] Box G E P, Wilson K B. On the experimental attainment of optimum condition. J. of the Royal Stat Sociaety. Series B. 1951, 13(1):1-34
[59] Wong F S. Slope reliability and response surface method. Journal of Geotechnical Engineering, ASCE, 1985, 11(1): 32-53
[60] Bucher C G, Bourgrund U. A fast and efficient response surface approach for structural reliability problrms. Structural Safety, 1990, 7(1): 45-51
[61] 苏永华, 蒋德松, 赵明华. 松软围岩隧道结构稳定可靠性估计. 湖南大学学报, 2006, 33(2): 10-14
[62] 李志业, 曾艳华. 地下结构设计原理与方法. 成都: 西南交通大学出版社, 2005, 304-310
[63] 苏永华, 赵明华, 刘晓明. 响应面方法在边坡稳定可靠度分析中的应用. 岩石力学与工程学报, 2006, 25(7): 1417-1425
[64] 桂劲松, 康海贵. 结构可靠度分析的响应面法及其 Matlab 实现. 计算力学学报, 2004, 21(6): 683-688
[65] 赵国藩. 工程结构可靠性理论及其应用. 大连: 大连理工大学出版社, 1996, 12(2): 145-148
[66] 赵云贵 . 结构可靠度的四阶矩分析法 . 大连理工大学学报, 1992, 32(4): 455-459
[67] 佟晓利. 改进的 Rosenbluth 方法及其在结构可靠度分析中的应用. 大连理工大学学报, 1997, 37(3): 316-321
[68] 苏永华, 赵明华, 张月英. 利用差分计算基于 Spencer 分析模式的边坡稳定可靠度. 岩石力学与工程学报, 2006, 25(1): 2750-2756
[69] 张小庆, 康海贵, 王复明. 求解隐式功能函数可靠度的一种新方法. 大连理工大学学报, 2003, 43(5): 650-654
[70] 王星华, 汤国璋, 汪亦元, 巢万里. 多年冻土隧道开挖稳定性分析. 矿冶工程, 2006, 26(3): 2-14, 18
[2] 陈建平, 朱首军. 新奥法的实质与存在的问题. 河港工程, 2002, 12(1): 34-36
[3] 朱乐辉, 郑金科, 伊雪辉. 旦架哨隧道监控量测与信息化施工. 公路, 2002, 2(6): 24-26
[4] 吉小明, 赵中旺. 隧道监测和信息反馈中的计算模型优化问题. 地下空间, 1997, 17(2): 104-108
[5] 黄宏伟. 城市隧道与地下结构工程的发展与展望. 地下空间, 2001, 21(4): 311-317
[6] Iannacchione A T, Dolinar D R. Compton C S. Controlling roof beam failures from high horizontal stresses in underground stone mines. In: the 17th Int. Conference on Ground Control in Mining Morgantown. West Virginia University, 1998, 102-112
[7] King G C, Stein R S, Lin J. Static stress changes and the triggering of earthquakes. Bulletin of the Seismological Society of America, 1994, 84(3): 935-953
[8] Muller L. Removing the misconception on the new Austrian Tunneling Method. tunnels & tunneling, 1978, (10): 29-32
[9] 文献江. 四联拱隧道施工技术. 西部探矿工程, 2000, 16(3): 51-52
[10] Lee R, Chang C L. Some Properties of Fuzzy Logic. Inf.and Control. 1971, 17(19): 413-417
[11] 苏永华, 赵明华, 刘晓明. 岩体分类的二元相对模糊评判法. 岩体力学与工程学报, 2006, 25(5): 1049-1055
[12] Singh B, Goel R K. Rock Mass Classification. A Practical Approach in Civil Engineering. Holland: Elsevier, 1999, 267
[13] 徐万鹏. 隧道位移监测新方法的可行性探索. 铁道工程学报, 2000, 2(2): 65-68
[14] Stein R S. Stress triggering of the 1994 M=6.7 Northridge, California, earthquake by its predecessors. Science, 1994, 278(265): 1432-1435
[15] 中华人民共和国水利部. 工程岩体分级标准 GB50218-94. 北京: 中国计划出版社, 1995, 1-20
[16] 中华人民共和国交通部. 中华人民共和国行业标准, 公路隧道设计规范 JTGD70-2004. 人民交通出版社, 2004, 23-45
[17] 黑龙江公路勘察设计院. 阳和至黄龙洞公路隧道工程. 哈尔滨市: 黑龙江公路勘察设计院, 2006, 1-132
[18] 金丰年. 考虑时间效应的围岩特征曲线. 岩石力学与工程学报,1997, 18(4): 334-353
[19] 徐林生, 王晓雯. 东门关隧道围岩变形特征及其影响因素分析. 公路交通技术, 2004, 6(4): 88-90, 96
[20] 杨会军. 复杂条件下隧道围岩变形特征. 铁道工程学报, 2006, 12(1): 57-60
[21] 孙兆远, 焦苍, 罗琼. 不同工法开挖超大断面隧道引起围岩变形机理分析. 铁道建筑, 2006, 8(9): 35-37
[22] 李晓红, 王宏图, 贾剑青. 隧道及地下工程围岩稳定性及可靠性分析的极限位移判别. 岩土力学, 2005, 26(6): 850-854
[23] Schubert W, Moritz B. Controllable ductile support system for tunnels in squeezing rock. Sonderdruck aus Felsbau, 1998, 16(4): 224-227
[24] 靳晓光, 李春晓, 沈军辉. 二郎山公路隧道围岩变形影响因素研究. 地质灾害与环境保护, 2000, 11(7): 58-62
[25] 徐林生. 阳宗隧道围岩变形的神经网络技术预测. 重庆交通学院院报, 2006, 25(3): 32-35
[26] Villy A, Kontogianni S, Stiros C. Induced deformation during tunnel excavation: evidence from geodetic monitoring. Engineering Geology, 2005, 344(79): 115-126
[27] Kaiser P. Deformation monitoring for stability assessment of underground openings. Compressive Rock Engineering, 1993(4): 607-630
[28] Kontogianni V A, Tzortzis A, Stiros S C. Deformation and failure of the Tymfristos tunnel. Journal Geotechnical Engineering, ASCE, 2004, 130(10): 1004-1013
[29] Schubert W, Steindorfer A. Selective displacements monitoring during tunnel excavation. Felsbau, 1996, 14(2): 93-97
[30] Kontogianni V, Stiros S. Predictions and observations convergence in shallow tunnels: case histories in Greece. Engineering Geology, 2002, 63(3): 333-345
[31] 李晓红, 夏彬伟, 康勇. 通渝隧道围岩收敛位移量测实践. 重庆大学学报(自然科学版), 2005, 28(1): 131-134
[32] 赵明阶, 徐容, 许锡宾. 岩溶地区全断面开挖隧道围岩变形规律及其监测. 同济大学学报(自然科学版), 2004, 32(7): 866-871
[33] 王金庄, 康建荣, 吴立新. 煤矿覆岩离层注浆减缓地表沉降机理与应用探讨.中国矿业大学学报, 1999, 28(4): 331-334
[34] 刘绍堂. 隧道施工期间的变形监测技术. 地下空间与工程学报, 2006, 2(8): 1346-1348, 1359
[35] Alfredo H, Ang S, Tang W H. Probability concepts in Engineering planning and Design Volume Ⅱ-Decision. New York: Elsevier Science Ltd, 1990.
[36] 柳厚祥, 方风华. 预埋多点位移计现场确定围岩松动圈的方法研究. 矿冶工程, 2006, 26 (1): 1-4
[37] 北京奥多尔投资研究中心. 风险不确定性与秩序. 北京: 中国财政经济出版社, 2001, 15-23
[38] 李旺, 夏建波. 锚杆支护参数对围岩稳定性的影响. 陕西煤炭, 2007(3): 45-46
[39] 王春风. 金融市场奉献管理. 天津: 天津大学出版社, 2001, 1-15
[40] 黄俊, 张顶立. 地铁暗挖隧道上覆地层大变形规律分析. 岩土力学, 2004, 25(8): 1288-1292, 1301
[41] 陈建勋, 马建秦. 隧道工程试验监测技术. 北京: 人民交通出版社, 2005, 26-78
[42] 李世煇. 隧道支护设计新论(第一版). 北京: 科学出版社, 1999, 97-106
[43] Ching S C. Numerical and analytical moding for granulates. In: the 9th International Conference for Computer Mtethod and Advances in Geomechanics. Netherlands, 1997, 105-114
[44] 刘佑荣, 唐辉明. 岩体力学. 武汉: 中国地质大学出版社, 1999, 88-109
[45] 李世辉. 隧道围岩稳定性系统分析. 北京: 中国铁道出版社, 1991, 1-23
[46] 朱永全. 隧道稳定性位移判别准则. 中国铁道科学, 2001, 22(6): 80-83
[47] 贺建民, 戴小平, 郭磊. 隧道围岩稳定性及安全性分析的位移判别方法. 矿业安全与环保, 2001, 28(5): 36-37, 45
[48] 张勇, 张子新, 华安增. 高速公路隧道的围岩变形特征. 中南公路工程 , 2001, 26(3): 12-14
[49] 中华人民共和国行业标准.公路隧道施工技术规范 JTJ 024-94. 人民交通出版社, 1994, 1-20
[50] 朱沛富, 五莹军. 围岩稳定性预测在隧道(洞)施工中的应用. 铁道建筑技术, 1999, 17(6): 23-25
[51] 原国家冶金工业局. 锚杆喷射混凝土支护技术规范 GB50086-2001. 北京: 中国计划出版社,2001,12-24
[52] 赵明华, 陈兆, 苏永华. 基于变形准则的隧道围岩稳定性概率分析. 矿冶工程, 2008, 2(2): 1-5
[53] Jia P, Tang C A. Numerical study on failure mechanism of tunnel in jointed rock mass, Tunnel. Underg.Technol. 2007, 9(1): 1-8
[54] Eberhardt E. Numerical modelling of three-dimension stress rotation ahead of an advancing tunnel face. International Journal of Rock Mechanics and Mining Sciences, 2001, 38(4): 499-518
[55] Melchers R E. Structural reliability analysis and prediction (Second edition). New York: John Wiley & Sons, 1999, 15-28
[56] 贡金鑫. 工程可靠度计算方法(第一版). 大连: 大连理工大学出版社, 2003, 1-349
[57] Hasofer A M, Lind N C. Excat and inviariant second-momrnt code format. Journal of Engineering Mechanics, 1974, 1000(1): 111-121
[58] Box G E P, Wilson K B. On the experimental attainment of optimum condition. J. of the Royal Stat Sociaety. Series B. 1951, 13(1):1-34
[59] Wong F S. Slope reliability and response surface method. Journal of Geotechnical Engineering, ASCE, 1985, 11(1): 32-53
[60] Bucher C G, Bourgrund U. A fast and efficient response surface approach for structural reliability problrms. Structural Safety, 1990, 7(1): 45-51
[61] 苏永华, 蒋德松, 赵明华. 松软围岩隧道结构稳定可靠性估计. 湖南大学学报, 2006, 33(2): 10-14
[62] 李志业, 曾艳华. 地下结构设计原理与方法. 成都: 西南交通大学出版社, 2005, 304-310
[63] 苏永华, 赵明华, 刘晓明. 响应面方法在边坡稳定可靠度分析中的应用. 岩石力学与工程学报, 2006, 25(7): 1417-1425
[64] 桂劲松, 康海贵. 结构可靠度分析的响应面法及其 Matlab 实现. 计算力学学报, 2004, 21(6): 683-688
[65] 赵国藩. 工程结构可靠性理论及其应用. 大连: 大连理工大学出版社, 1996, 12(2): 145-148
[66] 赵云贵 . 结构可靠度的四阶矩分析法 . 大连理工大学学报, 1992, 32(4): 455-459
[67] 佟晓利. 改进的 Rosenbluth 方法及其在结构可靠度分析中的应用. 大连理工大学学报, 1997, 37(3): 316-321
[68] 苏永华, 赵明华, 张月英. 利用差分计算基于 Spencer 分析模式的边坡稳定可靠度. 岩石力学与工程学报, 2006, 25(1): 2750-2756
[69] 张小庆, 康海贵, 王复明. 求解隐式功能函数可靠度的一种新方法. 大连理工大学学报, 2003, 43(5): 650-654
[70] 王星华, 汤国璋, 汪亦元, 巢万里. 多年冻土隧道开挖稳定性分析. 矿冶工程, 2006, 26(3): 2-14, 18