球颗粒DDA云计算模式及程序研究

The discontinuous deformation analysis (DDA) method has inherent advantages when it is employed to simulate the large displacement and fracturing process of rock masses. The bottleneck of this method is that the computational scale is small, and the efficiency is low. This study is based on the mature commercial cloud computing platform, and develop the parallel spherical discontinuous deformation analysis and its cloud computing model. By applying theoretical analysis, algorithm formulation, programming and test verification, this project supposes to perform study on the following aspects: the 3D spherical DDA algorithm which can be used to simulate the fracturing process and coupling effect of mechanical, temperature, and seepage of rock masses; effective contact search algorithm, criterion of contact convergence, contact model; parallel computation technique, including the storage method of sparse matrix and parallel iterative solution method of equations; parallel framework and dynamic scheduling method in cloud; developing the parallel 3D spherical DDA program in cloud computing platform. Verification and validation will be done by means of classic benchmarking problems, laboratory tests and practical engineering problems. The objective of this research is to achieve the simulation analysis of failure process of large-scale rock engineering. Besides, this research will help to promote application of the cloud computing in rock engineering.

非连续变形分析（DDA）方法在模拟岩体的大位移和破碎过程时具有天然的优势。然而该方法的瓶颈在于求解问题的规模不能太大、计算效率也不高。本项目基于成熟的商业云计算平台，研究并行的三维球颗粒DDA方法及其云计算模式。拟采用理论分析、算法推演和编程、试验验证等手段，研究如下内容：能够模拟岩体三维破裂过程及耦合应力、温度、渗流效应的三维球颗粒DDA算法；三维球颗粒DDA方法中的高效接触搜索算法、接触收敛准则和接触模型；三维球颗粒DDA方法的并行计算技术，包括稀疏矩阵存储方式和方程组并行迭代求解技术；云环境中并行执行的计算框架和动态并行作业调度方法；开发基于云计算平台的三维球颗粒DDA并行程序。采用多种手段对程序进行调试和验证。最终实现对大型岩体工程的破坏失稳过程的快速精确模拟，并推动云计算在岩体工程中的应用。

基于完备的接触约束表征和严格的收敛分析，非连续计算方法（DDA）在分析岩体的非连续大变形及破裂全过程具有理论优势和广泛的应用前景，但是其隐式计算方案需要较大的大计算量，制约了现有程序的计算规模和计算效率，阻碍了其在工程尺度的应用。针对以上问题，本项目从简化接触计算和提高分析效率的角度出发在以下方面发展了球颗粒的DDA方法，包括三维球颗粒DDA方法中的球-球、球-面、球-棱接触模型、高效的并行接触搜索算法、代替开合迭代判断的最大位移判断准则；模拟岩体三维破裂过程、热-力耦合、水-力耦合效应的三维球颗粒DDA算法；基于MPI和OpenMP的三维球颗粒DDA并行计算技术，包括并行接触搜索算法和方程组并行迭代求解技术；云环境中并行执行的计算框架和动态并行作业调度方法。基于云平台开发了一套球颗粒DDA计算软件，经过了基础碰撞、斜面摩擦、自由落体等经典算例验证、断裂分析模块经过了相似材料模型试验的校核与验证，在工程应用尺度探索了多个应用案例。云计算程序计算规模可增大至十万颗粒数量级，在52进程算例测试中可获得23.3倍加速比。项目验证了云计算方法的可行性，颗粒系统计算规模的扩大和计算效率的提升将进一步推动云计算和DDA方法在岩体工程中的应用。