三维块体离散元可变形计算方法研究

RESEARCH ON DEFORMABLE CALCULATION METHOD BASED ON THREE-DIMENSIONAL BLOCK DISCRETE ELEMENT

在三维刚性块体离散元的基础上,研究可变形块体离散元方法,并编制相应的可变形块体离散元程序。该方法把块体单元看作弹性体,并对其划分有限元网格,对每个可变形单元的计算是假设在力边界条件下求解可变形单元的节点位移;可变形块体之间力和位移的传递是通过构筑的节理单元实现的,节理单元反应岩土工程中实际节理的变形性质和强度特征,结构面破坏前,体现了连续介质计算方法的特点,结构面如果发生破坏,预设节理处的节理单元直接转变化为法向和切向弹簧,体现了离散元计算方法的特点。另外,节理单元有实际的厚度,可以根据实际节理的性质确定计算参数,这一点也体现出了对刚性块体离散元方法的改进。与刚性块体离散元方法比较,该方法可以反映岩体变形性质,如泊松效应、三维岩体中的真实波速,它还可以模拟结构面的破坏演化过程;与有限元方法比较,它可以更好地描述岩体中节理的特征,允许单元有较大的位移;相对于以前的可变性离散元方法,它既克服了有限差分格式带来计算上的复杂,又建立在三维模型的基础上,为有关岩土工程的数值分析提供了一个可行的数值方法。

Deformable block discrete element model is studied on the basis of three-dimensional rigid block discrete element method,and corresponding program is developed for this method. Each block element is considered as an elastic body,and finite element grids are generated. Each node displacement in the deformable block is calculated under the condition of force boundary. Jointed elements are constructed to transfer the force and displacement between adjacent deformable blocks. Jointed elements in the method can represent practical joint characteristics and strength in rock engineering. This method reflects the characteristics of continuous calculative method before breakage of structural plane. If the structural plane is broken,the jointed element will change into the normal and shear springs at the preset joint. So it also reflects the characteristics of discontinuous calculation method. In addition,the jointed element has certain thickness,so the calculative parameter can be determined by those of the actual joint. It embodies the improvement to rigid block discrete element method. Compared with rigid block discrete element method,this method can reflect the deformable character of rock,such as Poisson′s effect of rock mass and the propagation velocity of stress wave in three-dimensional rock mass. Compared with finite element method(FEM),it presents the jointed characteristics of rock mass more sufficient than FEM,and allows large displacement of element. Moreover,it can simulate the failure evolution process of the structural surface. Compared with the former discrete element model of deformable bodies,it overcomes the complicated calculation induced by finite difference method and is also three-dimensional discrete element model. So it provides an available numerical analytical method for geotechnical engineering.