Modelling the Brittle Rock Failure by the Quaternion-based Bonded-Particle Model in DEM

This research investigates brittle rock failure using a quaternion-based bonded-particle model within the discrete element method (DEM). Unit quaternions represent particle spatial rotations, enabling the computation of relative displacements and bonding forces. Validation is achieved through uniaxial compression tests, yielding good agreement with established experimental data. Findings reveal that stress oscillation, uniaxial compression strength, and failure patterns in solids are predominantly influenced by the loading strain rate. Increasing strain rates lead to intensified oscillations in the strain-stress curve due to force wave interactions and solid deformation inertia. A quasi-static loading condition with minimal stress oscillation is attainable only at very low loading strain rates. Brittle failure initiates with the nucleation of internal damage, forming interconnected failure planes that grow in area with increasing loading strain rates, ultimately transforming the failure pattern from localized damage to complete fragmentation.

本研究旨在探讨脆性岩石的失效现象，通过在离散元法（DEM）框架内运用基于四元数的绑定粒子模型进行探究。单位四元数用于表征粒子在空间中的旋转，从而实现相对位移和结合力的计算。验证过程通过单轴压缩实验完成，结果显示与已建立的实验数据具有良好的一致性。研究结果表明，应力振荡、单轴压缩强度以及固体的失效模式主要受加载应变率的影响。随着应变率的增加，由于力波相互作用和固体变形惯性，应变-应力曲线中的振荡现象愈发显著。仅在极低的加载应变率下，方可实现应力振荡极小的准静态加载条件。脆性失效始于内部损伤的成核，形成相互连接的失效平面，随着加载应变率的增加，这些平面面积逐渐扩大，最终将失效模式从局部损伤转变为完全破碎。