基于3D-FSM的预紧力端锚数值模拟及其多核并行化研究

在对传统锚杆荷载传递机制分析的基础上，提出了一种考虑托板、锚杆与岩体相互作用的数值模拟方法：通过Kelvin基本解计算出锚杆集中力对围岩的影响，同时就锚杆自由段与相应岩体两端点的位移差相等建立位移方程，结合先前开发的3D-FSM数值模拟系统中的表面受力平衡方程进行联立求解，利用所得结果可以计算域内任意点的应力及位移变化，形成完整的预紧力端锚边界元数值模拟系统。通过与Flac3D系统模拟对比，验证了该系统的可靠性。为提高运算效率，对该系统进行基于OpenMP的多核并行化改进，给出了改进的基本思路和加速比对比图。由于边界元本身具有建模简单、计算区域大、计算精度高等优点，因此，这种模拟方法有很大的应用价值。

Numerical simulation of pre-tightening force grouted anchor coupled with 3D-FSM and its multi-core parallel computing

A new numerical approach is proposed to simulate bolt supporting by considering interactions among anchor plate, anchor arm and rock based on the analysis of traditional load transfer mechanism of the bolt. The effects of concentrated stress from one bolt on the surrounding rock are investigated by employing analytical integral of Kelvin’s solutions. The displacements equations of the anchor free section and the relative section of drilling holes are established according to the same displacements of them along the axis of anchor arm. Coupled with the previous 3D fictitious stress method (FSM) system, a new boundary element simulation system is formed completely on the partially grouted bolt supporting by considering anchor plate, which can be applied to calculate the stress and displacement of an arbitrary point in the rock after bolting. The reliability of the system has been verified by a comparison of numerical results obtained by a commercial software Flac3D. Meanwhile, a multi-core parallel improvement in terms of OpenMP is conducted to improve the operation efficiency. The principal ideas and the comparison chart of speedups are presented in detail. The system has great application value in the course of advantages of boundary element such as simple modelling, large computable domain and high accuracy.