元胞自动机有限元法及其在边坡工程中的应用研究
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摘要
近年来,基于局部作用原理的元胞自动机理论受到广泛关注。它将结构的整体分析变成局部分析,利用结构的自组织平衡特性,通过力的局域间的不平衡传递使结构达到最终的整体平衡。结合有限元,将元胞自动机应用于边坡稳定性分析,弥补极限平衡法只能假定土体为刚塑性体的不足,同时兼有极限平衡法、极限分析法等方法物理概念清晰,计算简便的优点,且不需像其他数值计算(如ANSYS)形成整体刚度矩阵而避免计算内存占用量大、边坡失稳临界状态引起的整体刚度矩阵奇异性、计算不收敛等问题。本文依托于国家杰出青年资金(项目批准号:50625824),主要研究工作如下:
1、基于元胞自动机的局部作用原理,充分利用受力(包括边界条件等)结构的自组织平衡特性,结合弹性有限元基本概念,编制元胞有限元程序和基于MATLAB图形用户界面功能包的元胞自动机有限元用户界面,包括常见的前处理、求解、后处理等模块,以实现参数输入、边界条件加载、计算求解、应力云图查看等功能。
2、应用黄金分割法对边坡滑面圆弧的圆心和滑出点坐标进行搜索,改进传统的圆弧搜索法,提出“平行空间”概念,即将计算域离散成规整的矩形空间,用平行矩阵表示,该平行矩阵的每个元素代表着落在其空间位置的单元号。根据滑面离散点坐标通过该“平行矩阵”找到所属单元,方便计算该点处的应力值。
3、将元胞有限元程序及自编用户界面应用于边坡稳定性分析领域。应用元胞有限元计算得到边坡位移、应力场,结合改进的圆弧滑面搜索法,寻找最危险滑面,并得到相应的安全系数和滑面实际应力分布。开发元胞有限元边坡稳定性分析界面,通过输入计算参数和控制计算精度,查看安全系数、滑面位置及滑面应力分布情况。
4、利用自编的元胞有限元边坡稳定性分析程序,分析不同物理参数(弹性模量、泊松比、粘聚力、摩擦角等)和边坡滑面、安全系数的关系,并和简化Bishop法进行对比验证。
In recent years, cellular automata theory that based on the part effect principle is being paid close attention to broadly, in which the integer analysis of structure is changed into a series of part analysis by using the Properties of self organization. Combination of finite element analysis, the method can be used in slope stability analysis, which not only overcomes the shortcoming of the assumption that soil is rigid-plastic body in limit equilibrium method, but also has the averages of limit equilibrium method and limit analysis method, such as clearing physical concept, simply calculation. Not as the finite element method(such as ANSYS), the cellular automata isn’t need to create global stiffness matrix, that could overcome or circumvent the calculation from the problems, such as stiffness singularity, high memory occupancy rate, and so on, which may be exist when calculating with global stiffness matrix. The paper bases on the National Outstanding Youth funds (No. projects approved: 50625824). And the main research work of this paper is:
1. In this paper, basing on the part effect principle of cellular automata method, making full use of the properties of self-organizing balance of the forced structure (including the boundary conditions, etc.), combining with the basic concepts of elastic finite element, the cellular automata finite element program and user interface are compiled, which including the common pre-processing, solving, post-processing modules, that is based on the meta-package of MATLAB graphical user figures. And it can achieve parameter input, loading boundary conditions, solving calculation, viewing stress cloud.
2. In this paper, the golden section method is applied to find the center and off point coordinates of smooth arc in arc searching, and put forward the concept of "parallel space", that discretizing calculation of regional into rectangular discrete space with a parallel matrix. And each element of the parallel matrix is representative of element number that located in the element’s space, which can be easily calculated stress value of smooth discrete point.
3. In this paper, the program and the user interface are used in the field of slope stability analysis. Using the displacement field and the stress field calculated by cellular automata finite element program and the improved circular slip surface search, the most dangerous sliding surface and the corresponding factor of safety and the actual stress distribution of smooth can be found. And slope stability analysis of the cellular automata finite element program is designed, which can see the safety factor, the location of sliding surface and stress distribution on the sliding surface visibly.
4. In this paper, the relationship between the different physical parameters and the sliding surface slope and safety factor are analyzed by using the slope stability analysis program of cellular automata finite element and simplified Bishop method.
1、基于元胞自动机的局部作用原理,充分利用受力(包括边界条件等)结构的自组织平衡特性,结合弹性有限元基本概念,编制元胞有限元程序和基于MATLAB图形用户界面功能包的元胞自动机有限元用户界面,包括常见的前处理、求解、后处理等模块,以实现参数输入、边界条件加载、计算求解、应力云图查看等功能。
2、应用黄金分割法对边坡滑面圆弧的圆心和滑出点坐标进行搜索,改进传统的圆弧搜索法,提出“平行空间”概念,即将计算域离散成规整的矩形空间,用平行矩阵表示,该平行矩阵的每个元素代表着落在其空间位置的单元号。根据滑面离散点坐标通过该“平行矩阵”找到所属单元,方便计算该点处的应力值。
3、将元胞有限元程序及自编用户界面应用于边坡稳定性分析领域。应用元胞有限元计算得到边坡位移、应力场,结合改进的圆弧滑面搜索法,寻找最危险滑面,并得到相应的安全系数和滑面实际应力分布。开发元胞有限元边坡稳定性分析界面,通过输入计算参数和控制计算精度,查看安全系数、滑面位置及滑面应力分布情况。
4、利用自编的元胞有限元边坡稳定性分析程序,分析不同物理参数(弹性模量、泊松比、粘聚力、摩擦角等)和边坡滑面、安全系数的关系,并和简化Bishop法进行对比验证。
In recent years, cellular automata theory that based on the part effect principle is being paid close attention to broadly, in which the integer analysis of structure is changed into a series of part analysis by using the Properties of self organization. Combination of finite element analysis, the method can be used in slope stability analysis, which not only overcomes the shortcoming of the assumption that soil is rigid-plastic body in limit equilibrium method, but also has the averages of limit equilibrium method and limit analysis method, such as clearing physical concept, simply calculation. Not as the finite element method(such as ANSYS), the cellular automata isn’t need to create global stiffness matrix, that could overcome or circumvent the calculation from the problems, such as stiffness singularity, high memory occupancy rate, and so on, which may be exist when calculating with global stiffness matrix. The paper bases on the National Outstanding Youth funds (No. projects approved: 50625824). And the main research work of this paper is:
1. In this paper, basing on the part effect principle of cellular automata method, making full use of the properties of self-organizing balance of the forced structure (including the boundary conditions, etc.), combining with the basic concepts of elastic finite element, the cellular automata finite element program and user interface are compiled, which including the common pre-processing, solving, post-processing modules, that is based on the meta-package of MATLAB graphical user figures. And it can achieve parameter input, loading boundary conditions, solving calculation, viewing stress cloud.
2. In this paper, the golden section method is applied to find the center and off point coordinates of smooth arc in arc searching, and put forward the concept of "parallel space", that discretizing calculation of regional into rectangular discrete space with a parallel matrix. And each element of the parallel matrix is representative of element number that located in the element’s space, which can be easily calculated stress value of smooth discrete point.
3. In this paper, the program and the user interface are used in the field of slope stability analysis. Using the displacement field and the stress field calculated by cellular automata finite element program and the improved circular slip surface search, the most dangerous sliding surface and the corresponding factor of safety and the actual stress distribution of smooth can be found. And slope stability analysis of the cellular automata finite element program is designed, which can see the safety factor, the location of sliding surface and stress distribution on the sliding surface visibly.
4. In this paper, the relationship between the different physical parameters and the sliding surface slope and safety factor are analyzed by using the slope stability analysis program of cellular automata finite element and simplified Bishop method.
引文
[1]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.
[2]龚晓南.土工计算机分析[M].北京:中国建筑工业出版社,2000.10.
[3]钱家欢,殷宗泽.土工原理与计算[M].北京:水利水电出版社,1994.
[4]赵尚毅,郑颖人等.用有限元强度折减法求边坡稳定安全系数[J].岩土工程学报,2002,24(3): 343-346.
[5]张永兴,王桂林,胡居义等.岩石洞室地基稳定性分析方法与实践[M].北京:科学出版社.2005.
[6]郏建磊.基于强度折减法的均质土坡稳定性研究[D].重庆:重庆大学,2007.
[7]朱凡,胡岱文.土力学[M].重庆:重庆大学出版社,2005.
[8]孙仁博,王天明等.材料力学[M] .北京:中国建筑工业出版社.1995.
[9]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,1978.
[10] Zienkiewicz O.C. Zhu J.Z. The super convergent patch recovery(SPR) and adaptive finite element refinement[J]. Computer Methods in Applied Mechanics and Engineering, 1992,101:207-224.
[11]李育超.基于实际应力状态的土质边坡稳定分析研究[D].杭州:浙江大学,2006.
[12] Fellinius W.Calculation of stability of Earth Dams[C].In Transactions,2nd International Congress of Large Dams,Washington,1936,(4): 445.
[13] Bishop A W.The use of the slip circle in the stability analysis of slopes [J]. Geotechnique,1955,(5): 7~17.
[14] Janbu N.Application of composite slip surface for stability analysis[C].Proceedings of European Conference on Stability of Earth Slopes,Sweden,1954,(3):43~49.
[15] Spencer E.A method of analysis of the stability of embankments assuming parallel interslice forces[J].Geotechnique,1967,17(1): 11-26.
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[22]颜伟.岩石蠕变的FEM和PCA模拟算法研究[D].山东:山东科技大学,2005.
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[29]谭云亮.模拟细观非均质材料破坏演化的物理元胞自动机理论[J].物理学报,2001,50(4):704-709.
[30]谭云亮,周辉等.模拟岩体破坏演化的新途径—物理细胞自动机理论[C],第六次岩石力学与工程学术大会论文,2000.
[31] von Newmann. Theory of self-Reproduction Automata (edited and completed by A. W. Burks) [M]. Urbana, IL : University of lllinois Press 1966.
[32] Montheillet F, Gilormini P. Predicting the mechanical behavior of two-phase materials with cellular automata[J]. Int J Plasticity,1996,12(4): 561~574.
[33] Wolfram S.Cellular automata as models of complexity[J]. Nature,1984: 311(4):419~422.
[34] Sangi D, Stock E A, Bross S. Simulation of self-organised dislocation structures in f.c.c and b.c.c single crystals[J]. Acta Mechanica.1999, 132:93~112.
[35] Bernsdorf J, Durst F, Schafer M. Comparison of cellular au-tomata and finite volue techniques for simulation of incompressible flows in complex geometries[J]. Int J Numer Meth Fluids, 1999, 29:251~264.
[36]王勖成,邵敏.有限单元法基本原理和数值方法(第2版)[M].北京:清华大学出版社,1997.
[37]崔俊芝,梁俊.现代有限元软件方法[M].北京:国防工业出版社,1995:序,122-138.
[38]赵更新.土木工程结构分析程序设计[M].北京:中国水利水电出版社. 2000.
[39] Gurdal Z.and Tatting T.,Cellular automata for design of truss structures with linear and non-linear response[J],Proceedings of the 41st AIAA/ASME/ASCE/AHS/ASC Structure,Structural Dynamics and Materials Conference,Atlanta,GA,April 3~6,2000.
[40] Tatting T.and Gurdal Z., Cellular automata for design of two-dimensional continuum structure[J],8thAIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization,September 6-8,2000.
[41]沈成武,戴诗亮,杨吉新等.平面弹性力学中的细胞自动机方法[J].清华大学学报(自然科学版),2001,41(11): 35~38.
[42]沈成武,唐小兵,杨吉新.平面桁架力学分析的细胞自动机方法初探[J].武汉交通科技大学学报,2000,24(2): 105~108.
[43] MATLAB有限元分析与应用/(德)卡坦著:韩来彬译[M].北京:清华大学出版社,2004.
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[45] Cook, R., Finite Element Modeling for Stress Analysis[M], John Wiley & Sons, 1995.
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[2]龚晓南.土工计算机分析[M].北京:中国建筑工业出版社,2000.10.
[3]钱家欢,殷宗泽.土工原理与计算[M].北京:水利水电出版社,1994.
[4]赵尚毅,郑颖人等.用有限元强度折减法求边坡稳定安全系数[J].岩土工程学报,2002,24(3): 343-346.
[5]张永兴,王桂林,胡居义等.岩石洞室地基稳定性分析方法与实践[M].北京:科学出版社.2005.
[6]郏建磊.基于强度折减法的均质土坡稳定性研究[D].重庆:重庆大学,2007.
[7]朱凡,胡岱文.土力学[M].重庆:重庆大学出版社,2005.
[8]孙仁博,王天明等.材料力学[M] .北京:中国建筑工业出版社.1995.
[9]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,1978.
[10] Zienkiewicz O.C. Zhu J.Z. The super convergent patch recovery(SPR) and adaptive finite element refinement[J]. Computer Methods in Applied Mechanics and Engineering, 1992,101:207-224.
[11]李育超.基于实际应力状态的土质边坡稳定分析研究[D].杭州:浙江大学,2006.
[12] Fellinius W.Calculation of stability of Earth Dams[C].In Transactions,2nd International Congress of Large Dams,Washington,1936,(4): 445.
[13] Bishop A W.The use of the slip circle in the stability analysis of slopes [J]. Geotechnique,1955,(5): 7~17.
[14] Janbu N.Application of composite slip surface for stability analysis[C].Proceedings of European Conference on Stability of Earth Slopes,Sweden,1954,(3):43~49.
[15] Spencer E.A method of analysis of the stability of embankments assuming parallel interslice forces[J].Geotechnique,1967,17(1): 11-26.
[16] Chen Z,Morgenstern N R.Extensions to the generalized method of slices for stability analysis [J].Canadian Geothechniacal Joural,1983,20(1):104~119.
[17]徐秉业.结构塑性极限分析[M].北京:中国建筑工业出版社,1985.
[18]郑颖人,龚晓南.岩土塑性力学基础[M].北京:中国建筑工业出版社,1989.
[19]吕擎峰.土坡稳定分析方法研究[D].南京:河海大学,2005.
[20]李明田.岩石破裂过程数值模拟的格构细胞自动机方法研究[D].武汉:中国科学院武汉岩土力学研究所,2003.
[21]杨吉新.元胞单元法理论研究及程序设计[D].武汉:武汉理工大学,2002.
[22]颜伟.岩石蠕变的FEM和PCA模拟算法研究[D].山东:山东科技大学,2005.
[23] Bak P. and Chao T. Earthquakes as a self-organized critical phenomenon[J]. Geophys. Res., 1989.
[24] Chen K. and Bak P. Self-organized criticality in a crack-propagation model of earthquakes[J]. Phy. Rev.A, 1991,43(2):625-630
[25] Ito K. and Matsuzaki M. Earthquakes as self-organized critical phenomenon[J]. Geophys. Res., 1990,95(135):6853-6860.
[26]郑捷.研究地震和岩石破裂现象的非线性科学方法·非线性科学在地震中的应用[M].北京:地震出版社,1992:45-53.
[27]伊东敬.地震与临界状态[J].国际地震杂志,1990,10:10-26.
[28]刘杰等.基于大陆地震活动特点建立的简化动力学模型—细胞自动机模型[J].地震,1999,19(3):230-238.
[29]谭云亮.模拟细观非均质材料破坏演化的物理元胞自动机理论[J].物理学报,2001,50(4):704-709.
[30]谭云亮,周辉等.模拟岩体破坏演化的新途径—物理细胞自动机理论[C],第六次岩石力学与工程学术大会论文,2000.
[31] von Newmann. Theory of self-Reproduction Automata (edited and completed by A. W. Burks) [M]. Urbana, IL : University of lllinois Press 1966.
[32] Montheillet F, Gilormini P. Predicting the mechanical behavior of two-phase materials with cellular automata[J]. Int J Plasticity,1996,12(4): 561~574.
[33] Wolfram S.Cellular automata as models of complexity[J]. Nature,1984: 311(4):419~422.
[34] Sangi D, Stock E A, Bross S. Simulation of self-organised dislocation structures in f.c.c and b.c.c single crystals[J]. Acta Mechanica.1999, 132:93~112.
[35] Bernsdorf J, Durst F, Schafer M. Comparison of cellular au-tomata and finite volue techniques for simulation of incompressible flows in complex geometries[J]. Int J Numer Meth Fluids, 1999, 29:251~264.
[36]王勖成,邵敏.有限单元法基本原理和数值方法(第2版)[M].北京:清华大学出版社,1997.
[37]崔俊芝,梁俊.现代有限元软件方法[M].北京:国防工业出版社,1995:序,122-138.
[38]赵更新.土木工程结构分析程序设计[M].北京:中国水利水电出版社. 2000.
[39] Gurdal Z.and Tatting T.,Cellular automata for design of truss structures with linear and non-linear response[J],Proceedings of the 41st AIAA/ASME/ASCE/AHS/ASC Structure,Structural Dynamics and Materials Conference,Atlanta,GA,April 3~6,2000.
[40] Tatting T.and Gurdal Z., Cellular automata for design of two-dimensional continuum structure[J],8thAIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization,September 6-8,2000.
[41]沈成武,戴诗亮,杨吉新等.平面弹性力学中的细胞自动机方法[J].清华大学学报(自然科学版),2001,41(11): 35~38.
[42]沈成武,唐小兵,杨吉新.平面桁架力学分析的细胞自动机方法初探[J].武汉交通科技大学学报,2000,24(2): 105~108.
[43] MATLAB有限元分析与应用/(德)卡坦著:韩来彬译[M].北京:清华大学出版社,2004.
[44] Logan, D., A First Course in the finite Element Method Using Algor[J], Second Edition, Brooks/Cole Publishing Company, IPT, 2001.
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