基于有序聚类的强度折减法安全系数确定方法
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摘要
为准确获取强度折减法中位移-折减系数关系曲线中的突变点,引入有序聚类分析方法,以确定安全系数。首先介绍了强度折减法,指出了目前确定安全系数的各种失稳判据存在的问题。鉴于系统模式在突变破坏点前后发生了变化,特别是位移和塑性应变急剧增大,尝试用有序聚类分析法找出该突变点。针对常规Fisher最优分割法不适用于渐进趋势,结合"回归类"聚类思想,将拟合的一次多项式作为聚类中心,残差平方和作为回归类直径,建立起新的有序样品回归类聚类方法。利用该法将位移-折减系数序列分为稳定段和失稳段,从而确定突变点,采用对应的折减系数作为系统的安全系数。用该方法对澳大利亚计算机应用协会(ACDAS)的经典边坡考题EX1(a)进行了研究,计算出的安全系数和Flac3D内置强度折减模块(Solen fos)的计算结果一致,证明了方法的可行性。最后,在基础上建立了更方便实用的系统稳定状态的判别式。
In order to accurately obtain the mutation point of displacement-reduction coefficient curve when using shear strength reduction method,the method of orderly clustering analysis is brought in for the safety coefficient determination.First,the strength reduction method and criterions of instability are introduced.In view of the system model changes before and after the mutation breakdown point,especially displacement and plastic strain increase sharply,the orderly clustering analysis is used to find out the mutation point.Since conventional Fisher optimal segmentation is not applicable to the progressive trend sequence,by integrating the regression clustering thought,using fitting a polynomial as clustering center,the sum of squared residuals as regression class diameter,a new orderly regression clustering method is set up.Based on the method,the displacement-reduction coefficient sequence is divided into a stable segment and a buckling segment,therefore the mutation point is able to be ascertained,and the corresponding reduction factor is the safety factor of the system.The typical examination question of EX1(a) from ACDAS is used to prove the feasibility of the method,the result for the method is consistent with that for solve fos method of Flac3D and closes to the standard answer.Finally,a discriminant of the system state is established,it is more convenient and practical.
In order to accurately obtain the mutation point of displacement-reduction coefficient curve when using shear strength reduction method,the method of orderly clustering analysis is brought in for the safety coefficient determination.First,the strength reduction method and criterions of instability are introduced.In view of the system model changes before and after the mutation breakdown point,especially displacement and plastic strain increase sharply,the orderly clustering analysis is used to find out the mutation point.Since conventional Fisher optimal segmentation is not applicable to the progressive trend sequence,by integrating the regression clustering thought,using fitting a polynomial as clustering center,the sum of squared residuals as regression class diameter,a new orderly regression clustering method is set up.Based on the method,the displacement-reduction coefficient sequence is divided into a stable segment and a buckling segment,therefore the mutation point is able to be ascertained,and the corresponding reduction factor is the safety factor of the system.The typical examination question of EX1(a) from ACDAS is used to prove the feasibility of the method,the result for the method is consistent with that for solve fos method of Flac3D and closes to the standard answer.Finally,a discriminant of the system state is established,it is more convenient and practical.
引文
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[9]钟伟,杨宝俊,张智.多项式拟合技术在强噪声地震资料中的应用研究[J].地球物理学进展,2006(1):184-189.Zhong Wei,Yang Baojun,Zhang Zhi.Progress in Geophysics,2006(1):184-189.
[10]陈祖煜.土质边坡稳定分析:原理.方法.程序[M].北京:中国水利水电出版社,2003:364-370.Chen Zuyu.Soil slope stability analysis:Principle method program[M].Beijing:China Water Power Press,2003:364-370.
[11]林杭,曹平,宫凤强.位移突变判据中监测点的位置和位移方式分析[J].岩土工程学报,2007(9):1433-1438.Lin Hang,Cao Ping,Gong Fengqiang.Chinese Journal of Geotechnical Engineering,2007(9):1433-1438.
[2]郑颖人.岩土数值极限分析方法的发展与应用[J].岩石力学与工程学报,2012(7):1297-1316.Zheng Yingren.Chinese Journal of Rock Mechanics and Engineering,2012(7):1297-1316.
[3]刘金龙,栾茂田,赵少飞,等.关于强度折减有限元方法中边坡失稳判据的讨论[J].岩土力学,2005(8):1345-1348.Liu Jinlong,Luan Maotian,Zhao Shaofei,et al.Rock and Soil Mechanics,2005(8):1345-1348.
[4]赵延林,吴启红,王卫军,等.基于突变理论的采空区重叠顶板稳定性强度折减法及应用[J].岩石力学与工程学报,2010(7):1424-1434.Zhao Yanlin,Wu Qihong,Wang Weijun,et al.Chinese Journal of Rock Mechanics and Engineering,2010(7):1424-1434.
[5]李卫东.应用多元统计分析[M].北京:北京大学出版社,2008:142-146.Li Weidong.Applied multivariate statistical analysis[M].Beijing:Peking University Press,2008:142-146.
[6]方开泰.有序样品的一些聚类方法[J].应用数学学报,1982(1):94-101.Fang Kaitai.Acta Mathematicae Applicatae Sinica,1982(1):94-101.
[7]陈远中,陆宝宏,张育德,等.改进的有序聚类分析法提取时间序列转折点[J].水文,2011(1):41-44.Chen Yuanzhong,Lu Baohong,Zhang Yude,et al.Journal of China Hydrology,2011(1):41-44.
[8]马江洪,张文修,梁怡.挖掘回归类的混合模型的可识别性[J].计算机学报,2003(12):1652-1659.Ma Jianghong,Zhang Wenxiu,Liang Yi.Chinese Journal of Computers,2003(12):1652-1659.
[9]钟伟,杨宝俊,张智.多项式拟合技术在强噪声地震资料中的应用研究[J].地球物理学进展,2006(1):184-189.Zhong Wei,Yang Baojun,Zhang Zhi.Progress in Geophysics,2006(1):184-189.
[10]陈祖煜.土质边坡稳定分析:原理.方法.程序[M].北京:中国水利水电出版社,2003:364-370.Chen Zuyu.Soil slope stability analysis:Principle method program[M].Beijing:China Water Power Press,2003:364-370.
[11]林杭,曹平,宫凤强.位移突变判据中监测点的位置和位移方式分析[J].岩土工程学报,2007(9):1433-1438.Lin Hang,Cao Ping,Gong Fengqiang.Chinese Journal of Geotechnical Engineering,2007(9):1433-1438.
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