基于B-DEM的颗粒聚合体应力计算和破碎路径模拟  

Calculation of stress field and particle breakage paths for granular system based on the combined boundary-discrete element method

作　　者：刘彪 王桥 张宗亮 周伟[3] FENG Y T 彭张振 李蕴升 徐俊[5] 郭凯[5] LIU Biao;WANG Qiao;ZHANG Zong-liang;ZHOU Wei;FENG Y T;PENG Zhang-zhen;LI Yun-sheng;XU Jun;GUO Kai(China Renewable Energy Engineering Institute,Beijing 100120,China;Power China Limited,Beijing 100048,China;School of Water Resources and Hydropower Engineering,Wuhan University,Wuhan,Hubei 430072,China;Faculty of Science and Engineering,Swansea University,Swansea,UK;Jiangsu Jiangdu Water Conservancy Project Management Office,Yangzhou,Jiangsu 225200,China)

机构地区：[1]水电水利规划设计总院,北京100120 [2]中国电力建设集团有限公司,北京100048 [3]武汉大学水利水电学院,湖北武汉430072 [4]斯旺西大学科学与工程学院,英国斯旺西 [5]江苏省江都水利工程管理处,江苏扬州225200

出　　处：《岩土力学》2022年第12期3493-3502,共10页Rock and Soil Mechanics

基　　金：国家自然科学基金(No.52011530193)。

摘　　要：结合边界元法和离散元法,提出一种可以进行计算颗粒内部应力和破碎路径的方法。该方法利用离散元法求解颗粒的相互作用和每个颗粒上的荷载。然后利用边界元法计算颗粒的应力分布,为了实现动态平衡,将颗粒的加速度视为恒定大小的体力。但体力导致边界积分方程中出现域积分,故采用直线积分法将域积分转化为边界积分,以保证边界元法降维的优势。为了提高边界元的计算效率,对于几何形状相似的颗粒,以其中一个颗粒作为模板颗粒,只需要计算模板颗粒在局部坐标系中的系数矩阵,其他相似颗粒可以通过局部和全局坐标系之间的映射获得。在得到应力后,基于Hoek-Brown准则来判断颗粒是否破碎。此外,将破坏路径简化为直线,并采用最小二乘法拟合得到破坏路径。The boundary element method(BEM) and discrete element method(DEM) are combined to calculate the internal stress and breakage paths of brittle granular materials. DEM is exerted to simulate the interaction between particles and the contact forces on each particle. Then, the calculation of the stress distribution inside the particle is conducted using BEM, during this procedure, the non-static or dynamic equilibrium of a particle is taken into consideration via treating the acceleration of particles as constant body force. Meanwhile, the body force leads to a domain integral in boundary integration equation(BIE), to avoid BEM losing the traditional advantage, i.e., dimension reduction, the domain integral is treated by the line integration method(LIM) and transformed into boundary integrals. In order to improve the computational efficiency of BEM, for particles with similar geometric shape, a random particle can be used as the template particle in the granular system, only the calculation of coefficient matrices of the template particle in the local coordinate system is needed, then, coefficient matrices of the rest particles can be obtained by mapping the solutions between the local and global coordinate systems. After the stress field is obtained, the Hoek-Brown criterion is applied to estimate whether particles are “broken” or not. Additionally, the breakage path that is assumed as a straight line can be obtained based on the least-squares fit.

关 键 词：边界元法 离散元法 颗粒材料 破碎路径 

分 类 号：TU452[建筑科学—岩土工程]