基于Voronoi多边形离散的DDA方法模拟岩石破坏

Simulation of rock failure by Voronoi-based discontinuous deformation analysis

非连续变形分析(DDA)方法是为模拟可变形离散块体系统而提出的一种隐式离散元方法。考虑到真实岩石的细观晶粒结构更加接近于Voronoi多边形,将建立基于Voronoi多边形离散形式的DDA方法,并将其与基于三角形离散的DDA方法进行对比分析。首先研究不同子块体尺寸对材料弹性参数的影响,并对比2种离散方法在子块体数和接触对数量上的差异。通过模拟单轴压缩、巴西劈裂、带孔圆盘劈裂以及Kalthoff-Winkler冲击等试验,对比分析2种离散形式对岩石宏观参数、破坏形式以及裂纹扩展路径的影响。同时,为了减小网格的依赖性,考虑了3种程度的随机离散网格对结果的影响。结果表明,过于规则的网格离散形式会导致不合理的破坏形式,过于随机的网格离散形式可能导致结果离散性偏大,收敛性变差,而一定程度的随机性则是必要的;基于Voronoi多边形离散形式的DDA方法能够有效地模拟岩石的破坏过程;相比三角形离散,基于Voronoi多边形离散的DDA方法具有更高的计算效率,能得到更高的弹性模量、抗压、抗拉强度和更加真实的压拉比,且裂纹扩展路径也更接近于岩石的沿晶断裂。

Discontinuous deformation analysis(DDA) is an implicit discrete element method for simulating deformable discrete block systems. Since the meso-grain structure of rocks is similar to Voronoi polygons,this paper will study the rock failure simulation with DDA using Voronoi discretizations,and compare its performance with DDA using triangle discretizations. The influence of the sub-block size on the elastic parameters of the material is studied,and the numbers of sub-blocks and the contact pairs using these two discretizations are compared. By simulating the uniaxial compression test,Brazilian test,Brazilian test with an eccentric circular hole and KalthoffWinkler impact experiment,the influences of these two types of discretizations on rock macroscopic parameters,failure modes and crack propagation paths are analyzed. Meanwhile,in order to reduce mesh-dependence,the influence of the randomness of the discretizations on the simulation results is discussed. The results show that an overly regular discretization will lead to an unreasonable failure pattern,while an overly random discretisation may lead to more disperse results and also worse convergence. That is to say,a proper degree of randomness is necessary for such simulations. It is also shown that DDA with Voronoi discretizations can effectively simulate the failure process of rocks,and that, in comparison with the triangle model,the Voronoi model leads to greater computational efficiency,higher elastic modulus,higher compression strength,higher tensile strength and more realistic compression-tensile ratio,and the crack propagation path is similar to the inter-granular fracture of the rock.