混合多位移模式的非连续变形分析法研究

An analysis of discontinuous deformation with mixed multiple deformation modes

传统的非连续变形分析法(DDA)法采用简单的线性位移模式计算效率高,描述大块体的高阶多项式位移模式在一定程度保留了该特点,并提高了计算精度。近年来流行的耦合有限元、自然单元的DDA法实质上是引入相应的插值形函数构成块体位移函数,计算相对低效,但具有计算更精细、更容易施加边界条件等优点。为结合传统DDA法与DDA耦合法各自的优点,建立了一种同时利用传统DDA法线性位移模式与耦合型DDA法非线性位移模式的混合法。该方法非线性模式主要针对大块体,采用了自然单元插值,缘于其具有一定无网格特征,且效率比有限元高。建立了混合模式下的整体矩阵并推导出接触等因素刚度子矩阵和荷载子向量的具体表达式。该方法建模更加方便合理,计算精度、效率介于线性模式的传统DDA法和非线性位移模式的耦合法之间。通过基本算例验证了混合法的有效性,并给出了节理围岩-隧道衬砌整体分析模型的计算结果,体现了新方法的优越性。

The traditional discontinuous deformation analysis（DDA） has high efficiency by adopting simple linear displacement mode, and the high-order polynomial displacement mode of the large blocks retains the characteristics and improves the calculation accuracy. The recently developed DDAs coupling FEM or natural element method（NEM） is a kind of the DDA models that use the FEM or NEM shape functions to construct block displacement functions, and has the properties of interpolation and high precision, and displacement boundary conditions can be directly imposed. However, these methods are less efficient than the original DDA. To combine the advantages of the traditional DDA and the DDA coupling method, a hybrid method is established for the linear displacement mode and the coupled DDA using the traditional DDA. In this method, the nonlinear model is mainly used for large blocks, and the natural element interpolation is adopted with certain characteristics of non-grid, and the efficiency is higher than that of the finite element method. The integral matrix of the mixed mode is developed and the expressions of the contact and other factors such as the stiffness sub-matrix and the load subvector are derived. The computation efficiency and precision of the new DDA is between the linear DDA and the DDAs coupling FEM or NEM. Some basic examples are provided to verify the new DDA; and the calculation results of the overall analysis of jointed surrounding rock-tunnel lining are given, showing the superiority of the new method.