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

王志亮, 余浪浪. 深部大理岩真三轴力学特性离散元和有限差分耦合分析[J]. 爆炸与冲击. doi: 10.11883/bzycj-2023-0394
引用本文: 王志亮, 余浪浪. 深部大理岩真三轴力学特性离散元和有限差分耦合分析[J]. 爆炸与冲击. doi: 10.11883/bzycj-2023-0394
WANG Zhiliang, YU Langlang. Analysis on true triaxial mechanical properties of deep marble by using a discrete element-finite difference coupling method[J]. Explosion And Shock Waves. doi: 10.11883/bzycj-2023-0394
Citation: WANG Zhiliang, YU Langlang. Analysis on true triaxial mechanical properties of deep marble by using a discrete element-finite difference coupling method[J]. Explosion And Shock Waves. 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
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

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

  • 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。
  • 图  1  颗粒接触模型

    Figure  1.  Particle contact model

    图  2  单元示意图

    Figure  2.  Diagrams of elements

    图  3  耦合边界节点力传递模型

    Figure  3.  Force transfer model of coupling boundary nodes

    图  4  耦合数值模型

    Figure  4.  Modelling for coupling simulation

    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  7  3个测点应力信号记录

    Figure  7.  Recorded stress signals at three measuring points

    图  8  动态应力平衡图

    Figure  8.  Diagram of dynamic stress balance

    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

    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

    图  14  不同时刻的岩样破坏形貌

    Figure  14.  Failure morphologies of rock specimens at different times

    图  15  岩样破坏正视图

    Figure  15.  Front views of failed specimens

    图  16  不同类型裂纹演化曲线

    Figure  16.  Evolution curves of different types of cracks

    图  17  应力与能量时程曲线

    Figure  17.  Curves of stress and energy time histories

    表  1  大理岩细观参数

    Table  1.   Microscopic parameters of marble

    细观参数 描述 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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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

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