模拟节理岩体破裂过程的三维球-杆单元DDA方法研究

The mechanical analysis of rock masses fracturing process in three dimensions is important and difficult. Numerical methods, such as the discontinuous deformation analysis (DDA), play a very important role on this aspect. Since the contact issue associated with the spherical DDA method is very simple, the spherical DDA method has many advantages on three-dimensional mechanical analysis. Based on the three-dimensional spherical DDA method, the applicant of this project has proposed a 3D-SDDARF numerical model in his PhD thesis. After a double springs-particles bonding algorithm and cracking algorithm have been implemented in this model, the fracturing process of jointed rock masses can be simulated. The disadvantage in using the double springs-particles bonding algorithm is that it cannot constrain the relative rotation between two spheres. The main purpose of this research is to propose a three-dimensional sphere-beam element DDA numerical model, which can be used to overcome this disadvantage, so that the brittle failure of rock masses can be simulated more accurately. By applying theoretical analysis, algorithm deduction, visual programming and test verification, this project supposes to perform study on the following aspects: (1) deducing a three-dimensional unequal spheres random packing algorithm, to provide calculation model for the sphere-beam element DDA method; (2) deducing a sphere-beam bonding algorithm and cracking algorithm, to realize that the spheres are bonded by the beams within the structure of three-dimensional spherical DDA method, and to build a failure criteria for the beams; (3) developing visual computing platform and test verification for the program, to provide an all new simulating tool for three-dimensional fracturing analysis of jointed rock masses.

岩体三维破裂过程的力学分析是岩体断裂研究的重点和难点，非连续变形分析（DDA）等数值方法在此方面发挥着重要作用。球颗粒DDA方法由于接触问题简单，在三维力学分析中具有很多优势。基于三维球颗粒DDA方法，项目申请人在其博士论文中提出了3D-SDDARF数值模型，利用双弹簧-颗粒粘结算法和开裂算法实现了节理岩体破裂过程的模拟。本研究拟提出三维球-杆单元DDA数值模型，目的在于弥补双弹簧-颗粒粘结算法不能约束球体相对旋转的缺陷，更精确地模拟岩体的脆性破坏。拟采用理论分析、算法推演、可视化编程和试验验证等手段，研究内容为：（1）推演三维非等径球颗粒随机堆积算法，为球-杆单元DDA方法提供计算模型；（2）推导球-杆粘结算法和开裂算法，在三维球颗粒DDA方法框架内实现圆杆对球颗粒的粘接，并建立圆杆的破坏判据；（3）开发可视化计算平台并对程序进行试验验证，为节理岩体的三维破裂分析提供一个全新的模拟工具。

为形成拥有完全知识产权的节理岩体三维破裂分析软件，本课题通过理论分析、算法推演、程序编制和试验验证手段，形成了三维非等径球颗粒随机堆积算法及其相应计算程序，构建了球-杆-球DDA（SBSDDA）数值模型并进行了初步试验验证，基于Qt平台开发了独立于所有商业软件的计算程序。项目资助发表SCI论文3篇，培养已毕业本科生1名，在读硕士研究生1名。项目投入经费22万元，支出16.7912万元，各项支出基本与预算相符。剩余经费5.2088万元，计划用于本项目研究后续支出。