深部大理岩真三轴力学特性离散元和有限差分耦合分析

王志亮; 余浪浪

doi:10.11883/bzycj-2023-0394

深部大理岩真三轴力学特性离散元和有限差分耦合分析

doi: 10.11883/bzycj-2023-0394

合肥工业大学土木与水利工程学院，安徽合肥 230009

基金项目: 国家自然科学基金（12272119，U1965101）

详细信息

作者简介:
王志亮（1969－　），男，博士，教授，博士生导师，cvewzL@hfut.edu.cn

中图分类号: O347
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- 文章访问数: 47
- HTML全文浏览量: 9
- PDF下载量: 13
- 被引次数: 0
出版历程
- 收稿日期: 2023-10-30
- 修回日期: 2024-03-18
- 网络出版日期: 2024-03-26

Analysis on true triaxial mechanical properties of deep marble by using a discrete element-finite difference coupling method

School of Civil and Hydraulic Engineering, Hefei University of Technology, Hefei, 230009, Anhui, China

摘要

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值（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，垂直于冲击方向的围压（下称“侧向压力”）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，大理岩破坏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。
- 深部大理岩 /
- 真三轴条件 /
- 力学特性 /
- 破碎特征 /
- 耦合分析
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 impact simulation of three-dimensional split Hopkinson pressure bar (SHPB) test were numerically validated. Finally, an in-depth analysis was conducted on the stress-strain response, fracture characteristics, and energy evolution mechanism of marble under true triaxial stress environment. It has 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 specimen, while the confining pressure perpendicular to the impact direction (lateral pressure hereafter) 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 specimen. Under true triaxial dynamic compression, the failure specimens are mainly characterized by tensile cracks, accounting for over 80% of the total number of cracks. The specimen 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.
- deep marble /
- true triaxial condition /
- mechanical properties /
- fragmentation characteristics /
- coupling analysis

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图 1 颗粒接触模型

Figure 1. Particle contact model

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图 2 单元示意图

Figure 2. Diagrams of elements

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图 3 耦合边界节点力传递模型

Figure 3. Force transfer model of coupling boundary nodes

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图 4 耦合数值模型

Figure 4. Modelling for coupling simulation

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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

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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

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图 7 3个测点应力信号记录

Figure 7. Recorded stress signals at three measuring points

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图 8 动态应力平衡图

Figure 8. Diagram of dynamic stress balance

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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 under different incident pressures

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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

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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

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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

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图 13 不同入射应力下大理岩试样内部声发射事件数和应力-应变曲线关系

Figure 13. Number of acoustic emission events in specimens and stress-strain curves under different incident stresses

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图 14 不同时刻的岩样破坏形貌

Figure 14. Failure morphologies of rock specimens at different times

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图 15 岩样破坏正视图

Figure 15. Front views of failed specimens

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图 16 不同类型裂纹演化曲线

Figure 16. Evolution curves of different types of cracks

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图 17 应力与能量时程曲线

Figure 17. Curves of stress and energy time histories

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表 1 大理岩细观参数

Table 1. Microscopic parameters of marble

细观参数	描述	标定值
R_min/mm	最小颗粒半径	0.9
R_max/R_min	最大、最小颗粒半径比	1.4
E_c/GPa	颗粒接触模量	30
k_n/k_s	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	颗粒摩擦系数	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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