红沿河核电站人工边坡可靠性分析
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摘要
边坡工程是最常见的工程形式之一,随着我国城乡建设规模不断扩大,工程建设中人工边坡工程越来越多,工程的复杂程度也随之增加。做好边坡工程防护,防范在建建筑边坡工程质量安全事故,防止在施工过程中诱发滑坡、崩塌等地质灾害等工作显得日益重要。
边坡与人类生产生活息息相关,在全国乃至全球范围内,边坡失稳事故频繁发生,对人类社会经济发展产生了极大的影响。因此,边坡稳定性分析作为岩土工程的一个分支,占有极其重要的地位。东岗联合泵房位于辽宁省瓦房店市东岗镇,泵房基坑开挖形成的人工边坡坡高达31m,文中采用改进的响应面法和蒙特卡洛法对东岗联合泵房边坡进行了稳定性分析与计算,为工程设计提供了依据。
本文首先介绍了边坡稳定可靠度计算方法及相关的数理统计理论。通过室内试验和工程类比,采用统计方法得出了岩土体物理力学参数。边坡按1:1.5的坡度开挖,针对饱水和地震两种工况,对边坡整体稳定可靠度进行了计算。计算过程通过改进的响应面法和蒙特卡洛法两种途径,并得到近于一致的结论。文中还针对岩土体不同物理力学参数对边坡整体稳定可靠度影响的敏感性作了进一步的探讨,为后续研究奠定基础。
In the four geological disasters, the hazard of land sliding goes after that of earthquake and volcano, but comes before debris flow. However, considering the frequency and distribution area of land sliding, the hazard to human being caused by land sliding is more serious than any other geological disasters. Since 1950s, we have had a great progress in studying land sliding, and obtained abundant practical experience in prevention of land sliding, thus the loss declined a lot. However, due to the needs of the development of economy, a great deal of human projects were constructed from land to sea, from plane to mountain areas which cause the change of the nature environment and make new land sliding disaster more than nature land sliding.
Hongyanhe Nuclear power station locates in hilly country which is high in north and low in south. From South to Forth, the land has three terraces with the elevation of 3m, 8m, and 20m. In the process of digging of foundation ditch, a 30m artificial slope is generated which influent the construction of the project and the safety of the workers’lives. Because of the reasons above, it plays a typical important role to do the research of reliability analysis of stability of artificial slope in the foundation ditch of pump room of Hongyanhe Nuclear Power station.
Currently, the analysis method of evaluation of slope stability can divides into qualitative analysis ways and quantitative analysis ways. Qualitative analysis ways include Geological Analysis method, Geological Engineering Analogue method, graphical method, and Slope stability expert system, etc. in practice, Quantitative analysis ways are more widely used which can also be divided into certainty analysis methods and uncertainty analysis methods. In certainty analysis methods, the factors such as the parameters of rock or soil mass, structure model of slope, which can influence the slope stability, are considered as certain parameters. Based on these certain parameters, the evaluation of slope stability are performed in some certain ways: Slice method including Fellenius method, Bishop method, Janbu method, Morgenstern-Price method, residual thrust method, and Sarma method, etc; Numerical method including Finite Element method, Boundary Element method, and Distinct Element method, etc. In uncertainty methods, the factors influence the slope stability are regarded as the probability function in a certain probability distribution which is more closed to the the practical condition. The uncertainty methods include Grey theory method, BP neural network method, fuzzy comprehensive evaluation method, etc.
Reliability analysis of slope stability is one of the uncertainty analysis methods, which include Monte-Carlo Method, Reliability index method, statistical moment method, and Stochastic Finite Element method, etc. Response surface method is a new reliability analysis way introduced into Geotechnical engineering in recent 10 years, before which, the method has been widely used in biology, chemistry industry, machinery, and so on. Combining the response surface method with other methods listed above can make the process of solution simple with a clear thinking and high precision to satisfy the needs of geotechnical engineering.
The soils of the artificial slope of foundation pitch in pump room are weathered sand, strongly weathered granite, medium weather granite from the top to the bottom. The boundaries of the strata were obtained by drilling and the grade of the slope is 1:1.5. Due to the lack of the initial data, there may be some error when determine the distribution of the physical-mechanical parameters and characteristic parameters. Because of this, a lot of literatures are read to choose plenty of mechanical parameters of strongly weathered granite who has the similar Young’s modulus, Poisson ratio and weather condition. Probability distribution and characteristic parameters of every mechanical parameter are obtained by mathematically statistic method, which can provide a solid foundation to reliability analysis of slope stability.
In this paper, response surface method is combined with Morgenstern-Price method to become the improved response surface method. The idea is that: substitute M-P method for Finite Element Method in response surface method and introduce the concept of factor of safety to response surface method. Complex process of solution of stress and strain in finite element method is replaced by the calculation of factor of safety. When the factor of safety is less than 1.0, the slope can be considered as destroyed. In this paper, the Slope module in the software Geostudio and M-P method are used in calculating of the factor of safety. The iterative process in reliability index method is applied in calculation of reliability index with the state function of quadratic fitting response surface function. Because fitting of response surface function, iterative calculation of reliability index, and multi fitting and iteration of response surface function are involved in the whole calculation, Matlab programming is used and satisfied results are obtained.
In this paper, sensibility analysis of mechanical parameters to the reliability analysis of slope stability is also studied. Unit weight, cohesion, and internal friction angle are considered as the variable of the reliability analysis. A series of reliability index are obtained when coefficients of variation of two of the variables are fixed and the last one changes in a certain law. And then the coefficient of variation-reliability index chart is generated to get the sensibility of every parameter to the reliability of the slope stability.
Conventional slope stability analysis ways do not consider the random of the parameters which, however, is considered in reliability analysis. The improved response surface method applied in this paper has a clear thinking and the results have a little error compared with the results of Monte-Carlo method. At last, some advices about research direction and advantages are given.
边坡与人类生产生活息息相关,在全国乃至全球范围内,边坡失稳事故频繁发生,对人类社会经济发展产生了极大的影响。因此,边坡稳定性分析作为岩土工程的一个分支,占有极其重要的地位。东岗联合泵房位于辽宁省瓦房店市东岗镇,泵房基坑开挖形成的人工边坡坡高达31m,文中采用改进的响应面法和蒙特卡洛法对东岗联合泵房边坡进行了稳定性分析与计算,为工程设计提供了依据。
本文首先介绍了边坡稳定可靠度计算方法及相关的数理统计理论。通过室内试验和工程类比,采用统计方法得出了岩土体物理力学参数。边坡按1:1.5的坡度开挖,针对饱水和地震两种工况,对边坡整体稳定可靠度进行了计算。计算过程通过改进的响应面法和蒙特卡洛法两种途径,并得到近于一致的结论。文中还针对岩土体不同物理力学参数对边坡整体稳定可靠度影响的敏感性作了进一步的探讨,为后续研究奠定基础。
In the four geological disasters, the hazard of land sliding goes after that of earthquake and volcano, but comes before debris flow. However, considering the frequency and distribution area of land sliding, the hazard to human being caused by land sliding is more serious than any other geological disasters. Since 1950s, we have had a great progress in studying land sliding, and obtained abundant practical experience in prevention of land sliding, thus the loss declined a lot. However, due to the needs of the development of economy, a great deal of human projects were constructed from land to sea, from plane to mountain areas which cause the change of the nature environment and make new land sliding disaster more than nature land sliding.
Hongyanhe Nuclear power station locates in hilly country which is high in north and low in south. From South to Forth, the land has three terraces with the elevation of 3m, 8m, and 20m. In the process of digging of foundation ditch, a 30m artificial slope is generated which influent the construction of the project and the safety of the workers’lives. Because of the reasons above, it plays a typical important role to do the research of reliability analysis of stability of artificial slope in the foundation ditch of pump room of Hongyanhe Nuclear Power station.
Currently, the analysis method of evaluation of slope stability can divides into qualitative analysis ways and quantitative analysis ways. Qualitative analysis ways include Geological Analysis method, Geological Engineering Analogue method, graphical method, and Slope stability expert system, etc. in practice, Quantitative analysis ways are more widely used which can also be divided into certainty analysis methods and uncertainty analysis methods. In certainty analysis methods, the factors such as the parameters of rock or soil mass, structure model of slope, which can influence the slope stability, are considered as certain parameters. Based on these certain parameters, the evaluation of slope stability are performed in some certain ways: Slice method including Fellenius method, Bishop method, Janbu method, Morgenstern-Price method, residual thrust method, and Sarma method, etc; Numerical method including Finite Element method, Boundary Element method, and Distinct Element method, etc. In uncertainty methods, the factors influence the slope stability are regarded as the probability function in a certain probability distribution which is more closed to the the practical condition. The uncertainty methods include Grey theory method, BP neural network method, fuzzy comprehensive evaluation method, etc.
Reliability analysis of slope stability is one of the uncertainty analysis methods, which include Monte-Carlo Method, Reliability index method, statistical moment method, and Stochastic Finite Element method, etc. Response surface method is a new reliability analysis way introduced into Geotechnical engineering in recent 10 years, before which, the method has been widely used in biology, chemistry industry, machinery, and so on. Combining the response surface method with other methods listed above can make the process of solution simple with a clear thinking and high precision to satisfy the needs of geotechnical engineering.
The soils of the artificial slope of foundation pitch in pump room are weathered sand, strongly weathered granite, medium weather granite from the top to the bottom. The boundaries of the strata were obtained by drilling and the grade of the slope is 1:1.5. Due to the lack of the initial data, there may be some error when determine the distribution of the physical-mechanical parameters and characteristic parameters. Because of this, a lot of literatures are read to choose plenty of mechanical parameters of strongly weathered granite who has the similar Young’s modulus, Poisson ratio and weather condition. Probability distribution and characteristic parameters of every mechanical parameter are obtained by mathematically statistic method, which can provide a solid foundation to reliability analysis of slope stability.
In this paper, response surface method is combined with Morgenstern-Price method to become the improved response surface method. The idea is that: substitute M-P method for Finite Element Method in response surface method and introduce the concept of factor of safety to response surface method. Complex process of solution of stress and strain in finite element method is replaced by the calculation of factor of safety. When the factor of safety is less than 1.0, the slope can be considered as destroyed. In this paper, the Slope module in the software Geostudio and M-P method are used in calculating of the factor of safety. The iterative process in reliability index method is applied in calculation of reliability index with the state function of quadratic fitting response surface function. Because fitting of response surface function, iterative calculation of reliability index, and multi fitting and iteration of response surface function are involved in the whole calculation, Matlab programming is used and satisfied results are obtained.
In this paper, sensibility analysis of mechanical parameters to the reliability analysis of slope stability is also studied. Unit weight, cohesion, and internal friction angle are considered as the variable of the reliability analysis. A series of reliability index are obtained when coefficients of variation of two of the variables are fixed and the last one changes in a certain law. And then the coefficient of variation-reliability index chart is generated to get the sensibility of every parameter to the reliability of the slope stability.
Conventional slope stability analysis ways do not consider the random of the parameters which, however, is considered in reliability analysis. The improved response surface method applied in this paper has a clear thinking and the results have a little error compared with the results of Monte-Carlo method. At last, some advices about research direction and advantages are given.
引文
[1]徐邦栋,滑坡分析与防治[M],北京:中国铁道出版社,2001.
[2]赵明阶,何光春,王多垠,边坡工程处治技术[M],北京:人民交通出版社,2003,10:20~22
[3]高大钊,土力学可靠性原理[M],北京:中国建筑工业出版社,1989.
[4]王家臣,边坡工程随机分析原理[M],北京:煤炭工业出版社,1996,2.
[5] W.费兰纽斯著,陈愈炯译,土坡稳定的精力计算[M],北京:水利出版社,1957.
[6] Bishop A W. The use of the slip circle in the stability analysis of slopes[J], Geotechnique, 1965.15(1): 79~93.
[7] Sarma S K. Stability analysis of embankments and slope. Geotechnique,1973, 23(3): 423~433.
[8] M orgenstern N. Price V E, The analysis of the stability of general slip surfaces, Geotechnique,1965. 15(1): 79~93.
[9]陈祖煜,土质边坡稳定分析——原理·方法·程序[M],北京:水利水电出版社,2003,1.
[10]李玉起,黄志全,王凤群, GeoStudio软件在堤防边坡稳定计算中的应用[J],东北水利水电, 2007(2): 3~5.
[11] J.H.Fergiger,数值方法在工程中的应用[M],北京:机械工业出版社,1990,11.
[12]魏兆正,边界单元法及工程应用[M],大连:大连理工大学出版社,1990,12:2~3.
[13]夏元友,李梅,边坡稳定性评价方法研究及发展趋势[J],岩石力学与工程学报,2002,21(7).
[14]崔政权,李宁,边坡工程——理论与实践最新发展[M],北京:中国水利水电出版社,1999: 208~245.
[15]魏安,蒋爵光,铁路岩石边坡稳定性分类的逐步判别分析[J],西南交通大学报,1991,2:49~55.
[16]孙君实,条分法的数值分析[J],岩土工程学报,1984,6(2).
[17]程桦,孙钧,三峡船闸及高边坡非线性大变形数值分析[J],岩土力学,1998,19(4).
[18]陈昌富,袁玲红,龚晓南,边坡稳定性评价T-S型模糊神经网络模型[J],工程力学,2002.
[19]冷伍明,基础工程可靠度分析与设计理论[M],长沙:中南大学出版社,2000.
[20]祝玉学,边坡可靠性分析[M],北京:冶金工业出版社,1993,4:136~297.
[21] Lumb P, The variability of natural soils, Canadian Geotechnical Journal, 1966,3: 74~79.
[22] Vanmarcke E. H. Probability modeling of soil profile[J], Journal of Geotechnical Engineering Division, ASCE, 1977, 103: 1227~1245.
[23] Tang W. H.著,冷伍明译,土性参数的概率特性处理原则[J], Bridge Between Theory and Practice, Edited by David S. B.,ect., ASCE, New York, 1984.
[24] Vanmarecke E. H., Reliability of Earth Slope[J], ASCE, V.103, GT11, 1977.
[25] Amren Der Kiureghian, Taleen Dakessian. Multiple design points in first and second-order reliability[J], Stureutral Safety, 1998, (20):37~49.
[26] Kim S, Na S, Response surface method using vector projected sampling points[J], Structural Safety, 1997, 19(1): 3~19.
[27]包承纲,谈岩土工程概率分析法中的若干基本问题[J],岩土工程学报, 1989, 11(4):94~97.
[28]高大钊,地基土力学性质指标的可靠性分析与取值[J],同济大学学报, 1985, 4:59~68.
[29]祝玉学,鲁兆明,露天边坡可靠性分析的随机有限元法[J],有色金属, 1992, 44(1).
[30]陈祖煜,张广文,关于“土坡稳定可靠度分析”一文的讨论[J],岩土工程学报, 1995, 17(6).
[31]罗文强,张倬元,黄润秋,王士天,斜坡系统可靠性分析研究[J],地学前缘, 2008, 7(增刊): 105~111.
[32]谭晓慧,王建国,刘新荣,改进的响应面法及其在可靠度分析中的应用[J],岩石力学与工程学报, 2005, 24(增2).
[33]姚参林,蒙特卡洛非线性反演方法及应用[M],北京:冶金工业出版社,1997,9.
[34]张建中,蒙特卡洛方法[J],数学的实践与认识,1974,01.
[35]高雷阜, Monte-Carlo理论与优化方法的研究[J],辽宁工程技术大学学报,2006,21(3).
[36]杨自强,魏公毅,产生伪随机数的若干新方法[J],数值计算与计算机应用,2001,22(3).
[37]杨自强,魏公毅,常见随机数发生器的缺陷及组合随机数发生器的理论与实践[J],数理统计与管理, 2001,20(1):45~51.
[38]李红文,解伟,张保伟,刘云,工程结构可靠度分析的一次二阶矩计算法研究[J],甘肃科技, 2007, 23(3).
[39]杨伟军,赵传智,土木工程可靠度理论与设计[M],北京:人民交通出版社, 1998.
[40]吴世伟,结构可靠度理论与应用状况[J],华水科技情报, 1985,01.
[41] G.E.P. Box, K.B. Wilson, On the Experimental Attainment of Optimum Conditions(with Discussion)[J], Journal of Royal Statistical Society, 1951,B13:1~45.
[42]王延克,基于响应面法的汽车悬架系统优化设计[D],西南交通大学, 2009.
[43]平芮巾,孙谧,刘均忠,王跃军,郝建华,张胜军,响应面法优化海洋细菌MP-2酯酶发酵条件[J],应用与环境生物学报, 2008, 14(4):548~552.
[44] Bueher C G, Bourgund U. A fast and effieient response surface approach for struetural reliability problems, Structural Safety, 1990, 7:57~66.
[45]袁荫棠,概率论与数理统计[M],北京:中国人民大学出版社, 1985, 12.
[46]高惠漩,统计计算,北京:北京大学出版社, 1995, 12.
[47]王常明,土力学[M],长春:吉林大学出版社, 2002,12:153~160.
[48]张天宝,土坡稳定分析和土工建筑物的边坡设计[M],成都:成都科技大学出版社, 1987,9:83~90.
[49]龙驭球,高等学校教材:有限元法概论(上册)(第二版)[M],北京:高等教育出版社, 1978,6:1~4.
[50]沈养中,李桐栋,工程结构有限元计算[M],北京:科学出版社, 2001,8: 2~4.
[51]水利水电科学研究院等,岩石力学参数手册[M],北京:中国水利水电出版社, 1991, 5.
[52]黄志全,姜彤,刘汉东,李华晔,工程岩体抗剪强度参数的可靠度分析[J],华北水利水电学院学报, 2004, 25(2):36~38.
[53]刘春,黄麦岭磷矿边坡岩体抗剪强度参数的随机-模糊法取值研究[J],岩石力学与工程学报, 2005, 24(5):653~656.
[54]赵建军,王思敬,尚彦军,丘中琦,全风化花岗岩抗剪强度影响因素分析[J],岩土力学,2005, 26(4):624~628.
[55]田野,三峡工程岩石力学参数研究[J],长江科学院院报, 1992, 29:72~76.
[56]光耀华,岩质高边坡稳定分析中的抗剪强度参数的概率统计方法[J],广西科学, 1995, 2(1):65~72.
[57]郑阿奇, MATLAB实用教程[M],北京:电子工业出版社, 2004, 6.
[58]周建兴, MATLAB从入门到精通[M],北京:人民邮电出版社, 2008, 11.
[59]董宏志,辽宁红沿河核电厂一期工程核岛泵房基坑稳定性研究[D],长春:吉林大学建设工程学院, 2008, 6.
[60]赵明华,曾昭宇,苏永华,改进响应面法及其在倾斜荷载桩可靠度分析中的应用[J],岩土力学, 2007, 28(12): 2539~2548.
[61]徐军,郑颖人,响应面重构的若干方法研究及其在可靠度分析中的应用[J],计算力学学报, 2002, 19(2): 217~221.
[2]赵明阶,何光春,王多垠,边坡工程处治技术[M],北京:人民交通出版社,2003,10:20~22
[3]高大钊,土力学可靠性原理[M],北京:中国建筑工业出版社,1989.
[4]王家臣,边坡工程随机分析原理[M],北京:煤炭工业出版社,1996,2.
[5] W.费兰纽斯著,陈愈炯译,土坡稳定的精力计算[M],北京:水利出版社,1957.
[6] Bishop A W. The use of the slip circle in the stability analysis of slopes[J], Geotechnique, 1965.15(1): 79~93.
[7] Sarma S K. Stability analysis of embankments and slope. Geotechnique,1973, 23(3): 423~433.
[8] M orgenstern N. Price V E, The analysis of the stability of general slip surfaces, Geotechnique,1965. 15(1): 79~93.
[9]陈祖煜,土质边坡稳定分析——原理·方法·程序[M],北京:水利水电出版社,2003,1.
[10]李玉起,黄志全,王凤群, GeoStudio软件在堤防边坡稳定计算中的应用[J],东北水利水电, 2007(2): 3~5.
[11] J.H.Fergiger,数值方法在工程中的应用[M],北京:机械工业出版社,1990,11.
[12]魏兆正,边界单元法及工程应用[M],大连:大连理工大学出版社,1990,12:2~3.
[13]夏元友,李梅,边坡稳定性评价方法研究及发展趋势[J],岩石力学与工程学报,2002,21(7).
[14]崔政权,李宁,边坡工程——理论与实践最新发展[M],北京:中国水利水电出版社,1999: 208~245.
[15]魏安,蒋爵光,铁路岩石边坡稳定性分类的逐步判别分析[J],西南交通大学报,1991,2:49~55.
[16]孙君实,条分法的数值分析[J],岩土工程学报,1984,6(2).
[17]程桦,孙钧,三峡船闸及高边坡非线性大变形数值分析[J],岩土力学,1998,19(4).
[18]陈昌富,袁玲红,龚晓南,边坡稳定性评价T-S型模糊神经网络模型[J],工程力学,2002.
[19]冷伍明,基础工程可靠度分析与设计理论[M],长沙:中南大学出版社,2000.
[20]祝玉学,边坡可靠性分析[M],北京:冶金工业出版社,1993,4:136~297.
[21] Lumb P, The variability of natural soils, Canadian Geotechnical Journal, 1966,3: 74~79.
[22] Vanmarcke E. H. Probability modeling of soil profile[J], Journal of Geotechnical Engineering Division, ASCE, 1977, 103: 1227~1245.
[23] Tang W. H.著,冷伍明译,土性参数的概率特性处理原则[J], Bridge Between Theory and Practice, Edited by David S. B.,ect., ASCE, New York, 1984.
[24] Vanmarecke E. H., Reliability of Earth Slope[J], ASCE, V.103, GT11, 1977.
[25] Amren Der Kiureghian, Taleen Dakessian. Multiple design points in first and second-order reliability[J], Stureutral Safety, 1998, (20):37~49.
[26] Kim S, Na S, Response surface method using vector projected sampling points[J], Structural Safety, 1997, 19(1): 3~19.
[27]包承纲,谈岩土工程概率分析法中的若干基本问题[J],岩土工程学报, 1989, 11(4):94~97.
[28]高大钊,地基土力学性质指标的可靠性分析与取值[J],同济大学学报, 1985, 4:59~68.
[29]祝玉学,鲁兆明,露天边坡可靠性分析的随机有限元法[J],有色金属, 1992, 44(1).
[30]陈祖煜,张广文,关于“土坡稳定可靠度分析”一文的讨论[J],岩土工程学报, 1995, 17(6).
[31]罗文强,张倬元,黄润秋,王士天,斜坡系统可靠性分析研究[J],地学前缘, 2008, 7(增刊): 105~111.
[32]谭晓慧,王建国,刘新荣,改进的响应面法及其在可靠度分析中的应用[J],岩石力学与工程学报, 2005, 24(增2).
[33]姚参林,蒙特卡洛非线性反演方法及应用[M],北京:冶金工业出版社,1997,9.
[34]张建中,蒙特卡洛方法[J],数学的实践与认识,1974,01.
[35]高雷阜, Monte-Carlo理论与优化方法的研究[J],辽宁工程技术大学学报,2006,21(3).
[36]杨自强,魏公毅,产生伪随机数的若干新方法[J],数值计算与计算机应用,2001,22(3).
[37]杨自强,魏公毅,常见随机数发生器的缺陷及组合随机数发生器的理论与实践[J],数理统计与管理, 2001,20(1):45~51.
[38]李红文,解伟,张保伟,刘云,工程结构可靠度分析的一次二阶矩计算法研究[J],甘肃科技, 2007, 23(3).
[39]杨伟军,赵传智,土木工程可靠度理论与设计[M],北京:人民交通出版社, 1998.
[40]吴世伟,结构可靠度理论与应用状况[J],华水科技情报, 1985,01.
[41] G.E.P. Box, K.B. Wilson, On the Experimental Attainment of Optimum Conditions(with Discussion)[J], Journal of Royal Statistical Society, 1951,B13:1~45.
[42]王延克,基于响应面法的汽车悬架系统优化设计[D],西南交通大学, 2009.
[43]平芮巾,孙谧,刘均忠,王跃军,郝建华,张胜军,响应面法优化海洋细菌MP-2酯酶发酵条件[J],应用与环境生物学报, 2008, 14(4):548~552.
[44] Bueher C G, Bourgund U. A fast and effieient response surface approach for struetural reliability problems, Structural Safety, 1990, 7:57~66.
[45]袁荫棠,概率论与数理统计[M],北京:中国人民大学出版社, 1985, 12.
[46]高惠漩,统计计算,北京:北京大学出版社, 1995, 12.
[47]王常明,土力学[M],长春:吉林大学出版社, 2002,12:153~160.
[48]张天宝,土坡稳定分析和土工建筑物的边坡设计[M],成都:成都科技大学出版社, 1987,9:83~90.
[49]龙驭球,高等学校教材:有限元法概论(上册)(第二版)[M],北京:高等教育出版社, 1978,6:1~4.
[50]沈养中,李桐栋,工程结构有限元计算[M],北京:科学出版社, 2001,8: 2~4.
[51]水利水电科学研究院等,岩石力学参数手册[M],北京:中国水利水电出版社, 1991, 5.
[52]黄志全,姜彤,刘汉东,李华晔,工程岩体抗剪强度参数的可靠度分析[J],华北水利水电学院学报, 2004, 25(2):36~38.
[53]刘春,黄麦岭磷矿边坡岩体抗剪强度参数的随机-模糊法取值研究[J],岩石力学与工程学报, 2005, 24(5):653~656.
[54]赵建军,王思敬,尚彦军,丘中琦,全风化花岗岩抗剪强度影响因素分析[J],岩土力学,2005, 26(4):624~628.
[55]田野,三峡工程岩石力学参数研究[J],长江科学院院报, 1992, 29:72~76.
[56]光耀华,岩质高边坡稳定分析中的抗剪强度参数的概率统计方法[J],广西科学, 1995, 2(1):65~72.
[57]郑阿奇, MATLAB实用教程[M],北京:电子工业出版社, 2004, 6.
[58]周建兴, MATLAB从入门到精通[M],北京:人民邮电出版社, 2008, 11.
[59]董宏志,辽宁红沿河核电厂一期工程核岛泵房基坑稳定性研究[D],长春:吉林大学建设工程学院, 2008, 6.
[60]赵明华,曾昭宇,苏永华,改进响应面法及其在倾斜荷载桩可靠度分析中的应用[J],岩土力学, 2007, 28(12): 2539~2548.
[61]徐军,郑颖人,响应面重构的若干方法研究及其在可靠度分析中的应用[J],计算力学学报, 2002, 19(2): 217~221.