Analysis on true triaxial mechanical properties of deep marbleby using a discrete element-finite difference coupling method
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摘要: 为了研究深部大理岩的动态力学特性，首先基于离散元PFC (particle flow code)和有限差分FLAC (fast Lagrangian analysis of continua)耦合法，对大理岩的细观参数进行标定。接着，对三维分离式霍普金森压杆（split Hopkinson pressure bar, SHPB）冲击模拟中的动态应力平衡条件及均匀性假设进行数值验证。最后，对真三轴应力环境下大理岩的应力-应变响应、破碎特征及能量演化机理等问题进行深入分析。结果表明：基于PFC-FLAC耦合理论的真三轴SHPB试验数值结果满足应力均匀性假设，模拟得到的应力-应变曲线与室内试验数据高度一致。峰值应力、峰值应变随着冲击方向上预压（下称“轴向压力”）的增大呈下降趋势。在轴向压力相同时，试样峰值应力增幅随入射应力的提高逐渐变小；当入射应力固定时，轴向压力对试样峰值应力有削弱作用，垂直于冲击方向的侧压则会提升试样的抗压强度。加载过程中声发射事件爆发期整体上发生在应力峰后段，并在此阶段试样内形成较明显的宏观破碎带。在真三轴动态压缩下，大理岩试样主要以拉伸裂纹居多，在总裂纹数中占比超过80%。试样从加载至破坏的过程伴随有能量的变化，达到应力峰值点时试样的应变储能达到极限，之后转化为以耗散能为主、颗粒动能等为辅的能量形式。Abstract: To study the dynamic mechanical properties of deep marble, the micro parameters of deep marble were calibrated based on the coupling method of discrete element (particle flow code, PFC) and finite difference (fast Lagrangian analysis of continua, FLAC). Then, the dynamic stress equilibrium condition and uniformity assumption in the simulated three-dimensional split Hopkinson pressure bar (SHPB) test are numerically validated. Finally, an in-depth analysis is conducted on the stress-strain response, fracture characteristics, and energy evolution mechanism of marble under true triaxial stress environment. It is found that the numerical results of the true triaxial SHPB test based on the PFC-FLAC coupling theory satisfy the assumption of stress uniformity, and the simulated stress-strain curves are highly consistent with the measured ones. Peak stress and peak strain decrease with the increase of pre-pressure in the impact direction (axial pressure hereafter). At the same axial pressure, the peak stress gradually drops down with the increase of incident stress; when the incident stress is fixed, the axial pressure weakens the peak stress of the sample, while the lateral pressure perpendicular to the impact direction increases the compressive strength. During the loading process, the outbreak period of acoustic emission events generally occurs in the post-peak stage, and during this stage, a relatively obvious macroscopic fracture zone is formed within the sample. Under a true triaxial dynamic compression, the samples are mainly characterized by tensile cracks, accounting for over 80% of the total number of cracks. The sample undergoes energy changes from loading to failure. At the peak stress point, the strain energy storage reaches its limit, which is then transformed into an energy form dominated by dissipated energy and supplemented by particle kinetic energy. The relevant conclusions have important guiding significance for the study of the dynamic characteristics of deep marble and the long-term stability evaluation of deep rock engineering.
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Key words:
- deep marble /
- true triaxial condition /
- mechanical property /
- fragmentation shape /
- coupling analysis
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图 5 不同压缩条件下试件的应力-应变曲线对比
Figure 5. Comparison of stress-strain curves of specimens under different compression conditions
图 6 不同压缩条件下试件的破碎形态对比
Figure 6. Comparison of failure modes of specimens under different compression conditions
图 9 不同轴压试样在不同入射应力下的应力-应变曲线
Figure 9. Stress-strain curves of the specimens in different axial compression states (σ1, 5 MPa, 10 MPa) under different incident pressures
图 10 三轴围压(0 MPa, 5 MPa, 10 MPa)试样在3种入射应力下的应变时程曲线
Figure 10. Strain-time histories of specimens in triaxial compression (0 MPa, 5 MPa, 10 MPa) under three different incident pressures
图 11 不同入射压力下试样的峰值应力和峰值应变随轴压的变化
Figure 11. Vairations of peak stresses and peak strains of specimens under different incident pressures with axial pressure
图 12 不同方向预压力对岩样峰值强度的影响
Figure 12. Effect of pre-pressures in different directions on the peak strength of specimens
图 13 不同入射应力下大理岩试样内部声发射事件数量和应力-应变曲线关系
Figure 13. Numbers of acoustic emission events in specimens and stress-strain curves under different incident stresses
表 1 大理岩细观参数
Table 1. Microscopic parameters of marble
细观参数 含义 标定值 Rmin/mm 最小颗粒半径 0.9 Rmax/Rmin 最大、最小颗粒半径比 1.4 Ec/GPa 颗粒接触模量 30 kn/ks 颗粒刚度比 1.5 ${ \overline{{E}_{\mathrm{c}}}} $/GPa 平行黏结接触模量 10 $ {\overline{{k}_{\mathrm{n}}}/\overline{{k}_{\mathrm{s}}}} $ 平行黏结刚度比 1.5 μ 颗粒摩擦因数 0.5 ${ \overline{{\sigma }_{\mathrm{c}}}} $/MPa 黏结法向强度 70 ${ \overline{{\tau }_{\mathrm{c}}} }$/MPa 黏结切向强度 44 λ 黏结半径乘子 1 
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