二维颗粒非连续变形分析粘结算法改进

2D Particle-based Discontinuous Deformation Analysis with Improved Bond Model

非连续变形分析(DDA)采用隐式格式,使用位移作为未知数,通过势能最小原理建立平衡方程将块体间的接触问题与块体本身的变形统一到方程中,具有理论推导严密、计算精度高等特点。基于颗粒的DDA方法在模拟砂土、岩石破坏等方面有独特的优势,并逐渐得到重视。为了模拟岩石破坏,需要引入粘结算法来描述连续介质的变形特征,而合理的粘结算法能够更好地模拟颗粒间的胶结作用。在二维颗粒DDA的框架下,建立了一种新的粘结模型。该粘结模型由法向粘结、切向粘结和转动粘结三部分组成,除了能抵抗颗粒间的嵌入和滑移外,还能抵抗颗粒间的相互转动。并在该模型的基础上,建立了相应的粘结破坏准则。最后基于Matlab模拟了岩石的单轴压缩和直剪实验,通过与实验结果对比验证了模型的准确性和有效性。

Discontinuous deformation analysis( DDA),using the implicit formation and using the displacement as the arguments,set up the equilibrium equation by minimizing the potential energy. The contact problem between the blocks and the deformation of the blocks itself are unified into the equation,which has strict theoretical deduction and high calculation precision,etc. Particle-based DDA has its unique advantages in simulating the failure of sandy soil and rock materials,and thus has been increasingly received attention. In order to simulate the process of rock failure,bonding algorithm between particles is necessary to describe the deformation characteristics of continuous medium. A reasonable bonding algorithm should better represent the cementation between particles. In the framework of 2 D particle-based DDA,a new bonding model is established,which is composed of a normal,a tangential and a rotational spring. The new bonding model can resist not only normal penetration and tangential slip as has been done in the literature,but also relative rotation. On the basis of the model,the corresponding bond failure criterion is established for judging. Several numerical examples,such as the uniaxial compression and direct shear test are calculated to demonstrate the effectiveness of the proposed model by using Matlab.