非连续变形分析法位移模式改进及工程应用
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摘要
非连续变形分析(DDA)方法适用于解决工程中有较多不连续性界面的力学问题,如节理岩体工程稳定性分析。论文回顾了工程计算中非连续性数值方法的发展历史,以及DDA方法研究现状,详细介绍了该方法的基本原理,讨论了与其他相关数值方法的联系与区别。DDA方法还处在研究发展阶段,其中,为提高块体应力场精度而改进现有块体位移模式是研究的热点方向之一。本文分析了目前就此方面的相关改进方案的不足,提出了采用无网格节点插值块体位移的新思路,成功地实现了无网格法和DDA方法相耦合,并由此扩展了原DDA法的计算功能如分析块体内精确应力场、计算弯曲变形、安全系数计算以及裂纹扩展分析等,具体研究内容如下:
在第二章,介绍了DDA方法基本原理,讨论了其与有限元法、离散元法的联系与区别。
第三章分析了线性位移模式DDA方法的缺点,以及相关改进方法的研究现状,提出了在块体上布置离散节点,引入无网格法中的移动最小二乘法构造位移近似函数。然后,基于能量极值原理推导建立整体平衡方程组,求解插值节点的未知位移向量,进一步可得到各时刻块体精确的应力场、位移场。通过算例分析了其计算特点。
第四章进一步研究基于自然邻接点插值法的DDA方法,对比了其与移动最小二乘法的优劣,表明前者计算效率更高,缺点是需要处理特殊网格生成。第五章分析了采用DDA方法进行边坡极限平衡分析时结果往往过于保守的现象,发现造成这一现象的根本原因在于经典的DDA低估了凝聚力作用。基于此,提出极限平衡分析时保留凝聚力作用可以大大改善评估结果。在此基础上尝试采用了基于强度储备概念的安全系数,计算表明修正后的DDA方法计算滑移型破坏边坡和传统极限平衡方法具有很好的可比性。
第六章研究了块体内的穿裂纹扩展问题,主要借鉴和发展了无网格法在这方面的成果。
最后在第七章利用上述新位移模式DDA方法进行了简单的工程应用。
从第三章到第七章都提供了许多典型的证明算例,表明了方法的可行性。
The Discontinuous Deformation Analysis (DDA) method is suitable for solving engineering problems with many discontinuous interfaces inside the concerned domain, e.g. the stability analysis of fractured rock mass. The history of various discontinuous deformation analysis methods including DDA is stated. The basic theory of DDA is introduced, and the comparisions between DDA and other numerical methods (the finite element methods, the discrete element methods, etc.) are made. Since DDA is still under development, one of concerns is how to improve block displacement functions so that the block stress precision can be improved. Based on the analysis of some related techniques, this dissertation proposes that the meshfree method be unilized to construct the displacement patterns, which can be considered as a technique of coupling DDA with meshfree methods. By the new technique, many new numerical abilities of DDA can be explored such as calculating the precious block stress fields, analyzing the block bending, and imitating the propagation of cracks etc. The detailed works are as follows:
In chapter 2, the DDA theory is stated. The relationship between DDA and other numerical methods is discussed, such as the finite element methods and the discrete element method.
In chapter 3, firstly the defect of linear displacement function is discussed, as well as some related techniques for improving this. Then the displacement interpolation mode based on the meshfree methods is introduced in DDA. By this new mode some interpolative nodes are needed to be scattered in the blocks. According to the principle of the minimum potential, the system of equations is deduced. Through solving the system, the displacements of the nodes are obtained. In this chapter, the Move Least-Square (MLS) technique is adopted to construct the displacement functions and the features are discussed.
Chapter 4 makes an attempt to use an alternative meshfree method to interpolate the displacement, namely the Natural Neighbor Interpolation (NNI). By comparing this with MLS Interpolation, it is founded that the former are more efficient then the latter, but the former may need to adjust the mesh within the blocks.
Those who have some expericences in the stability analysis of slopes by DDA know that DDA in gereral gives too conservative results. In chapter 5, the reason that causes DDA to underestimate the safety factors is analyzed. It is found that this is because the origional DDA ignores the effect of cohesion within the contact interfaces. The origional DDA considers that once slide happens on an interface, the C of the interfaces would be taken zero during the subsequent sliding. While the behavior of the interface might be true, it contradicts the classical limit equlibrium methods. For this reason, by keeping the cohesion force along the sliding surface, the safety factor based on the strength reservation is calculated. Compariosns with the classical limit equilibrium methods have shown that the improved DDA aggress with the classical limit equilibrium methods.
Chapter 6 is devoted to the propagation of cracks in the blocks. The similar techniques in the meshfree methods are utilized and improved.
Finally in chapter 7, the methods proposed in this dissertation are used to solve some engineering problems.
From chapter 3 to 7, many typical numerical examples are presented which testify this new DDA method is feasible.
在第二章,介绍了DDA方法基本原理,讨论了其与有限元法、离散元法的联系与区别。
第三章分析了线性位移模式DDA方法的缺点,以及相关改进方法的研究现状,提出了在块体上布置离散节点,引入无网格法中的移动最小二乘法构造位移近似函数。然后,基于能量极值原理推导建立整体平衡方程组,求解插值节点的未知位移向量,进一步可得到各时刻块体精确的应力场、位移场。通过算例分析了其计算特点。
第四章进一步研究基于自然邻接点插值法的DDA方法,对比了其与移动最小二乘法的优劣,表明前者计算效率更高,缺点是需要处理特殊网格生成。第五章分析了采用DDA方法进行边坡极限平衡分析时结果往往过于保守的现象,发现造成这一现象的根本原因在于经典的DDA低估了凝聚力作用。基于此,提出极限平衡分析时保留凝聚力作用可以大大改善评估结果。在此基础上尝试采用了基于强度储备概念的安全系数,计算表明修正后的DDA方法计算滑移型破坏边坡和传统极限平衡方法具有很好的可比性。
第六章研究了块体内的穿裂纹扩展问题,主要借鉴和发展了无网格法在这方面的成果。
最后在第七章利用上述新位移模式DDA方法进行了简单的工程应用。
从第三章到第七章都提供了许多典型的证明算例,表明了方法的可行性。
The Discontinuous Deformation Analysis (DDA) method is suitable for solving engineering problems with many discontinuous interfaces inside the concerned domain, e.g. the stability analysis of fractured rock mass. The history of various discontinuous deformation analysis methods including DDA is stated. The basic theory of DDA is introduced, and the comparisions between DDA and other numerical methods (the finite element methods, the discrete element methods, etc.) are made. Since DDA is still under development, one of concerns is how to improve block displacement functions so that the block stress precision can be improved. Based on the analysis of some related techniques, this dissertation proposes that the meshfree method be unilized to construct the displacement patterns, which can be considered as a technique of coupling DDA with meshfree methods. By the new technique, many new numerical abilities of DDA can be explored such as calculating the precious block stress fields, analyzing the block bending, and imitating the propagation of cracks etc. The detailed works are as follows:
In chapter 2, the DDA theory is stated. The relationship between DDA and other numerical methods is discussed, such as the finite element methods and the discrete element method.
In chapter 3, firstly the defect of linear displacement function is discussed, as well as some related techniques for improving this. Then the displacement interpolation mode based on the meshfree methods is introduced in DDA. By this new mode some interpolative nodes are needed to be scattered in the blocks. According to the principle of the minimum potential, the system of equations is deduced. Through solving the system, the displacements of the nodes are obtained. In this chapter, the Move Least-Square (MLS) technique is adopted to construct the displacement functions and the features are discussed.
Chapter 4 makes an attempt to use an alternative meshfree method to interpolate the displacement, namely the Natural Neighbor Interpolation (NNI). By comparing this with MLS Interpolation, it is founded that the former are more efficient then the latter, but the former may need to adjust the mesh within the blocks.
Those who have some expericences in the stability analysis of slopes by DDA know that DDA in gereral gives too conservative results. In chapter 5, the reason that causes DDA to underestimate the safety factors is analyzed. It is found that this is because the origional DDA ignores the effect of cohesion within the contact interfaces. The origional DDA considers that once slide happens on an interface, the C of the interfaces would be taken zero during the subsequent sliding. While the behavior of the interface might be true, it contradicts the classical limit equlibrium methods. For this reason, by keeping the cohesion force along the sliding surface, the safety factor based on the strength reservation is calculated. Compariosns with the classical limit equilibrium methods have shown that the improved DDA aggress with the classical limit equilibrium methods.
Chapter 6 is devoted to the propagation of cracks in the blocks. The similar techniques in the meshfree methods are utilized and improved.
Finally in chapter 7, the methods proposed in this dissertation are used to solve some engineering problems.
From chapter 3 to 7, many typical numerical examples are presented which testify this new DDA method is feasible.
引文
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