岩土介质三维快速拉格朗日数值分析方法研究

Study on fast lagrangian numerical analysis method for rock and soil medium in 3 dimensions

研究了FLAC3D(fast lagrangian analysis of continua in 3 dimensions)的特点,并与有限单元法作了比较。FLAC3D方法以结点运动方程为支配方程,追踪了介质从受荷到达到平衡状态的过程,而有限元法是根据介质力学平衡方程直接求解,这是二者主要区别。FLAC3D没有采用介质真实的阻尼特性和结点质量,给出的不是介质所经历的真实过程,不能正确反映过程的影响,因此给出的介质应力和变形计算结果的物理意义是不甚明确的。求解过程中的介质振动,是一种噪音,可引起弹塑性介质计算结果误差,而弹性介质的计算结果几乎不受影响。研究指出了FLAC3D方法的优缺点。还通过算例作了四个方面的研究:(1)Drucker-Prager屈服准则与Mohr-Coulomb屈服准则比较;(2)膨胀角取值对计算结果的影响;(3)大变形与小变形对计算结果的影响;(4)精度设置对计算结果的影响。研究表明,Drucker-Prager准则与Mohr-Coulomb准则结果差异颇大;膨胀角取值对结果的影响是敏感和显著的;一般情况下,取小变形模式是合适的,计算精度取10-5是足够的。

The characters of FLAC^3D are studied and compared with finite element method. FLAC^3D method uses node motion equation and traces the medium motion process from being loaded to reaching equilibrium state. While the finite element method solves from mechanical equilibrium equation directly. The above is the basic difference between the two methods. Because FLAC^3D does not use the real medium damping property and node mass, the real process experiencing by the medium is not given and the influence of medium motion process on result cannot be reflected rightly. So the physical meaning of stress and deformation given by FLAC^3D is not very clear. The medium vibration during solving process is a noise rather than a more real simulation to medium mechanical behavior and could cause calculation error for elastoplastic medium. The study shows that FLAC^3D has a very high precision in determining the stress and deformation of elastic medium at equilibrium state and the vibration in solving process almost does not affect the final result. The advantages of FLAC^3D method are that its mathematical operation is simple, and the solving process is convergent, and it is convenient in treating cases of medium large deformation, elastoplastic property, non-associated flow rule, excavation and supporting, etc. compared with finite element method. The defects of FLAC^3D are that its calculation time is long, and the efficiency is low, and in some cases the number of time steps is high amazingly which may result in accumulating error. Studies in four aspects are also made through examples. （1） Comparisons between Drucker-Prager yield criterion and Mohr-Coulomb yield criterion. （2） Influence of dilation angle value on calculation result. （3） Influence of large deformation mode and small deformation mode on calculation result. （4） Influence of calculation precision setting on result.