类岩石材料颗粒流模型的细观参数标定方法研究——半解析查表法(SLT)

    缪露莉, 刘新荣, 傅晏, 周小涵, 郭雪岩

    缪露莉, 刘新荣, 傅晏, 周小涵, 郭雪岩. 类岩石材料颗粒流模型的细观参数标定方法研究——半解析查表法(SLT)[J]. 岩土工程学报, 2025, 47(6): 1259-1269. DOI: 10.11779/CJGE20231229
    引用本文: 缪露莉, 刘新荣, 傅晏, 周小涵, 郭雪岩. 类岩石材料颗粒流模型的细观参数标定方法研究——半解析查表法(SLT)[J]. 岩土工程学报, 2025, 47(6): 1259-1269. DOI: 10.11779/CJGE20231229
    MIAO Luli, LIU Xinrong, FU Yan, ZHOU Xiaohan, GUO Xueyan. Calibration method for microscopic parameters in particle flow code models for rock-like materials: semi-analytical lookup table approach[J]. Chinese Journal of Geotechnical Engineering, 2025, 47(6): 1259-1269. DOI: 10.11779/CJGE20231229
    Citation: MIAO Luli, LIU Xinrong, FU Yan, ZHOU Xiaohan, GUO Xueyan. Calibration method for microscopic parameters in particle flow code models for rock-like materials: semi-analytical lookup table approach[J]. Chinese Journal of Geotechnical Engineering, 2025, 47(6): 1259-1269. DOI: 10.11779/CJGE20231229

    类岩石材料颗粒流模型的细观参数标定方法研究——半解析查表法(SLT)  English Version

    基金项目: 

    国家自然科学基金项目 41972266

    国家自然科学基金项目 52074042

    详细信息
      作者简介:

      缪露莉(1991—),女,博士研究生,主要从事岩土工程与离散元等方面的研究工作。E-mail: MiaoGeo@outlook.com

    • 中图分类号: TU43

    Calibration method for microscopic parameters in particle flow code models for rock-like materials: semi-analytical lookup table approach

    • 摘要: 为了研究类岩石材料颗粒流模型的细观参数标定方法,基于CBM模型,首先进行了理论推导,而后基于大量的数值模拟获得了理论关系式中系数的拟合值,最终形成半解析查表法。研究表明:接触黏结的强度比对数值试件的细观破坏模式有重要影响;代表性单元体与实际颗粒流模型具有相同的宏、细观参数变化规律,且各系数的理论值与拟合值基本相符;单轴抗压强度、黏聚力与接触黏结强度的较小值min(σcn,τcs)呈较好的线性相关;细观参数的标定是具有明确的先后顺序的。最后通过标定砂岩的细观参数来证实半解析查表法是能够用于快速的完成参数标定的。
      Abstract: The calibration method for microscopic parameters in particle flow code (PFC) models of rock materials is investigated based on the contact bond model. Firstly, theoretical deductions of the selected representative unit are made, and the fitting coefficients in the theoretical relationship are obatined through extensive numerical simulations. Finally, the semi-analytic lookup table (SLT) method is established. The researches show that the ratio of contact bond strength has a significant impact on the micro-failure mode of numerical specimens. The representative unit has the same macro-microscopic parameter variation law as the actual PFC models, and the theoretical values of each coefficient are generally consistent with the fitted values. The uniaxial compressive strength and cohesion are linearly correlated with the smaller value between the two contact bond strengths. The calibration of microscopic parameters has a clear sequence. Lastly, the calibration of microscopic parameters for sandstone confirms that the SLT method can achieve a rapid parameter calibration.
    • 图  1   二粒径-四颗粒单元体的几何形态

      Figure  1.   Geometric morphology of units with four granules

      图  2   代表性单元体

      Figure  2.   Representative unit

      图  3   拉伸条件下均质模型及其基本单元的受力情况

      Figure  3.   Force analysis of homogeneous model and its basic unit under tensile conditions

      图  4   拉伸条件下基本单元的内力分析及变形特性

      Figure  4.   Analysis of internal forces and deformation characteristics of basic unit under tensile conditions

      图  5   拉伸条件下基本单元的内力分布规律及变形特性

      Figure  5.   Distribution of internal forces and deformation characteristics of unit under tensile conditions

      图  6   单轴压缩条件下基本单元的内力分布规律及变形特性

      Figure  6.   Distribution of internal forces and deformation characteristics of unit under uniaxial compression conditions

      图  7   简单剪切条件下基本单元的内力分布规律及变形特性

      Figure  7.   Distribution of internal forces and deformation characteristics of unit under simple shear conditions

      图  8   标准化效应的Pareto图

      Figure  8.   Pareto charts of standardization effects

      图  9   数值试件模型

      Figure  9.   Numerical models

      图  10   单轴抗压强度fc与细观接触强度的关系(方案C)

      Figure  10.   Relationship between fc and contact bond strength (Plan C)

      图  11   单轴抗压强度vs刚度比kn/ks(方案D)

      Figure  11.   Uniaxial compressive strengths vs. stiffness ratios (Plan D)

      图  12   单轴抗压强度与摩擦系数及接触模量的关系(方案E,F)

      Figure  12.   Relationship among fc, Ec and μ (Plan E, F)

      图  13   接触模量Ec与杨氏模量E、泊松比ν的的关系(方案F)

      Figure  13.   Relationship among Ec, E and ν (Plan F)

      图  14   黏聚力与细观强度的关系(方案G)

      Figure  14.   Relationship between c and contact bond strecngth

      图  15   宏观摩擦系数tanφ vs接触摩擦系数μ(方案H)

      Figure  15.   tanφ vs μ (Plan H)

      图  16   SLT法的具体步骤

      Figure  16.   Specific steps of SLT method

      表  1   均质模型的几何参数

      Table  1   Geometric parameters of homogeneous model

      Rmax/Rmin θ 颗粒配位数N
      小颗粒 大颗粒 平均值
      (1, 2+1) (30°, 45°) 4 6 5(5a+5b)/(5a+5b)(2ab+a+b)(2ab+a+b)
      下载: 导出CSV

      表  2   颗粒流材料的破坏模式

      Table  2   Failure modes of PFC materials

      序号 判据 τcs/σcn < 判据 τcs/σcn > 判据
      破坏模式 宏观强度与细观参数关系式 破坏模式 宏观强度与细观参数关系式
      1 2tanθkk+1 拉致剪裂 σtx=τcsRRmsin2θ 拉致拉裂 σtx=σcnRR(2cotθ+4tanθkk+1)
      2 Rmax2Rmincosθm1 拉致剪裂 σty=τcsRR2mcos2θ 拉致拉裂 σty=σcn(1RR)(1cosθ+1cos3θ(kk+tan2θ))
      3 RmaxRmin1cosθ(kk1) 压致剪裂 fcx=τcsRR(2+cos2θ(kk+1)) 压致拉裂 fcx=σcn(1RR)(cosθsin2θ+2cosθsin2θ(kk1))
      4 压致剪裂 fcy=τcsRR(4tan2θ+2(kk+1))
      5 2RminRmax(1+sin2θ)kkcosθ 剪致剪裂 τmax=τcs(1RR)ncosθ 剪致拉裂 τmax=2σcnRRnncos2θ
      下载: 导出CSV

      表  3   细观参数取值表

      Table  3   Values of microscopic parameters

      细观参数 试验常量取值
      几何参数 最小粒径Rmin/mm 0.2
      粒径比Rmax/Rmin 1.67
      细观强度参数 接触法向黏结强度σcn/MPa 20
      接触切向黏结强度τcs/MPa 20/50
      颗粒摩擦系数μ 1.7
      细观刚度参数 刚度比kn/ks 3.5
      颗粒接触模量Ec/GPa 10
      下载: 导出CSV

      表  4   拟合系数KBKD

      Table  4   Fitting coefficients KB and KD

      系数 Rmin/
      mm
      Rmax/Rmin
      1 2 3 4 5 6 7 8
      KB 0.1 0.609 0.768 0.997 1.090 1.086 1.368 2.015 2.568
      0.15 0.589 0.861 1.137 1.271 1.303 1.317 1.616 2.044
      0.2 0.602 0.817 0.987 1.270 1.583 1.949 2.559 1.983
      0.25 0.737 0.970 0.953 1.213 1.734 2.099 1.926 1.870
      0.3 0.677 0.779 1.120 1.386 1.612 1.692 2.198 2.054
      0.35 0.633 0.839 1.183 1.348 1.988 1.478 1.877 2.008
      0.4 0.541 1.064 1.155 1.247 1.948 1.795 2.155 2.698
      系数 Rmin/ Rmax/Rmin
      mm 1.2 1.67 2 3 4 5 6 7
      KD 0.1 1.320 1.414 1.677 2.175 2.216 2.960 3.443 3.894
      0.15 1.234 1.444 1.614 2.009 2.099 2.698 3.260 3.751
      0.2 1.308 1.425 1.622 1.971 2.450 2.630 3.204
      0.3 1.479 1.479 1.605 2.067 2.330
      0.4 1.186 1.425 1.527 1.844
      0.5 1.267 1.475 1.542
      下载: 导出CSV

      表  5   方案B的拟合结果

      Table  5   Fitting results of Plan B

      Rmin/
      mm
      拟合结果 Rmax/Rmin 拟合结果 Rmax/Rmin
      1.67 2 3 4 1.67 2 3 4
      0.1 aD 1.3 1.47 1.83 cD 0.78 0.73 0.62
      bD 0.65 0.85 1.07 dD 1.54 1.01 0.62
      R2 0.961 0.86 0.85 R2 0.92 0.93 0.72
      0.15 aD 1.32 1.39 1.78 1.83 cD 0.61
      bD 0.48 0.62 0.97 1.26 dD 0.57
      R2 0.89 0.74 0.98 0.99 R2 0.94
      0.2 aD 1.27 1.41 2.16 cD 0.76 0.70
      bD 0.67 0.76 1.19 dD 1.14 0.67
      R2 0.99 0.92 1 R2 0.99 1.00
      0.3 aD 1.41 1.77 2.1 cD 0.71 0.61 0.55
      bD 0.89 1.03 1.17 dD 0.77 0.55 0.26
      R2 0.92 0.9 0.99 R2 0.97 0.81 1.00
      0.4 aD 1.26 1.36 1.61 cD 0.76 0.68
      bD 0.71 0.65 0.99 dD 1.05 1.06
      R2 0.99 0.92 0.99 R2 0.99 0.88
      0.5 aD 1.34 1.32 cD 0.77 0.70 0.57
      bD 0.66 0.92 dD 0.92 0.89 0.42
      R2 0.94 0.96 R2 0.87 0.96 0.99
      下载: 导出CSV

      表  6   拟合系数的理论值与模拟值

      Table  6   Theoretical and simulated ranges of fitting coefficients

      试验类型 系数 理论值范围 拟合值范围
      直接拉伸试验 aD 2~3.46 1.26~2.16
      bD 2.31~4 0.48~1.26
      cD 1.15~1.41 0.55~0.78
      dD 0.33~1 0.26~1.54
      单轴压缩试验 aU 1.41~3.46 1.11~1.93
      bU 5.67~9.24 1.01~2.53
      cU 1.33~4 1.74~7.17
      dU 1~3 0.08~0.77
      eU 0.33~1.04 0.25~0.86
      fU 0.77~2 2.02~4.5
      gU 0.33~1 1.95~3.45
      hU 1~3 1.698~2.21
      下载: 导出CSV

      表  7   单轴抗压强度的拟合结果(方案C)

      Table  7   Fitting results of uniaxial compressive strength (Plan C)

      τcs/σcn 拟合结果
      a b R2
      0.25~0.428 0.0398 1.7570 0.999
      0.5~0.714 0.1392 1.4726 0.999
      1 a+b=1.388 0.997
      1.4~2 1.591 -0.0740 0.998
      2.33~5 1.549 -0.0318 0.999
      6~14 1.419 -0.0010 1
      下载: 导出CSV

      表  8   方案D单轴抗压强度拟合结果

      Table  8   Fitting results of uniaxial compressive strength (Plan D)

      τcs/σcn Rmax/Rmin Rmin/mm 式(13)
      cU dU R2
      0.5 1.67 0.2 2.949 0.331 0.95
      2 0.15 3.924 0.165 0.88
      2 0.3 3.377 0.251 0.98
      3 0.1 4.333 0.331 0.99
      4 0.15 4.696 0.589 0.91
      5 0.15 7.170 0.267 0.87
      1 1.2 0.1 2.435 0.081 0.99
      1.2 0.4 1.736 0.342 0.99
      1.67 0.3 2.358 0.270 0.98
      1.67 0.5 2.735 0.098 0.99
      2 0.1 3.907 0.283 0.99
      2 0.3 2.302 0.395 0.86
      2 0.4 2.689 0.244 0.98
      3 0.1 3.464 0.200 0.98
      3 0.4 2.941 0.358 0.98
      4 0.1 4.628 0.350 0.93
      4 0.2 5.166 0.147 0.98
      5 0.1 5.526 0.140 1.00
      5 0.15 4.638 0.617 0.91
      6 0.15 6.239 0.330 1.00
      6 0.2 4.615 0.767 0.99
      7 0.15 7.654 0.485 0.99
      τcs/σcn Rmax/Rmin Rmin/mm 式(12)
      aU bU R2
      2 1.67 0.2 1.932 1.007 0.99
      2 0.15 1.723 1.077 0.71
      2 0.3 1.461 2.190 0.72
      3 0.1 1.210 2.186 0.83
      3 0.15 1.482 1.047 0.99
      3 0.2 1.116 2.301 1.00
      3 0.3 1.133 2.529 0.99
      下载: 导出CSV

      表  9   拟合参数KE及其拟合优度R2

      Table  9   Fitting coefficient KE and its goodness of fit R2

      颗粒几何参数 拟合参数及R2
      Rmax/Rmin Rmin/mm KE R2
      1.67 0.1 1.5596 0.9945
      0.2 1.5052 0.9938
      2 0.15 1.6553 0.9947
      0.3 1.632 0.9939
      3 0.1 2.272 0.99
      0.3 2.0795 0.9921
      4 0.15 2.5885 0.9938
      0.2 2.4767 0.9889
      下载: 导出CSV

      表  10   方案D中弹性模量的拟合系数及其拟合优度R2

      Table  10   Fitting coefficient of elastic modulus and its goodness of fit R2(Plan D)

      颗粒几何参数 拟合参数及R2
      Rmax/Rmin Rmin/mm eU fU gU R2
      1.2 0.15 0.339 2.201 2.616 0.999
      0.2 0.294 2.565 3.086 0.998
      0.3 0.295 2.579 3.174 0.997
      0.4 0.295 2.629 3.446 0.999
      0.5 0.314 2.026 2.507 0.981
      1 0.254 2.634 3.360 0.996
      1.67 0.1 0.436 2.271 2.414 0.998
      0.15 0.352 2.815 3.063 0.996
      0.2 0.385 2.411 2.573 0.992
      0.3 0.329 2.931 3.214 0.992
      2 0.1 0.460 2.567 2.374 0.998
      0.15 0.423 2.617 2.508 0.997
      0.2 0.422 2.453 2.274 0.998
      0.4 0.365 3.090 3.207 0.991
      3 0.1 0.541 3.387 2.518 0.996
      0.15 0.581 2.770 2.184 0.973
      0.2 0.466 3.776 2.827 0.996
      0.3 0.557 2.865 2.176 0.981
      4 0.1 0.672 3.854 2.186 0.996
      0.15 0.641 4.311 2.758 0.993
      0.2 0.701 3.387 1.955 0.993
      0.3 0.662 3.610 2.270 0.988
      5 0.1 0.864 4.030 2.428 0.953
      0.15 0.788 4.547 2.394 0.989
      下载: 导出CSV

      表  11   方案D中泊松比的拟合系数hU及其R2(方案D)

      Table  11   Fitting coefficient hU and its goodness of fit R2(Plan D)

      Rmin/mm 强度比 Rmax/Rmin
      1.2 1.67 2 3 4 5 6
      0.1 0.5 1.960
      1 2.127 2.210 2.017 1.916 1.906 1.980 2.050
      2 2.161 2.125 1.987 2.015 2.125
      0.15 0.5 2.039 2.054 2.027
      1 1.982 1.914 1.960 1.94 1.962 1.981 1.933
      2 2.026 1.987 1.983 2.096 2.052
      0.2 0.5 1.987
      1 1.933 1.896 1.871 2.019 1.766 1.804 2.104
      2 1.948 1.983 2.093 1.964 1.910
      0.3 0.5 2.055
      1 1.901 1.851 1.916 1.858 1.883
      2 2.001 1.938 1.953 1.935
      0.4 0.5
      1 1.822 1.941 1.904 1.698
      2 2.016 2.072
      0.5 0.5
      1 1.788 1.851 1.874
      2 1.909 1.991
      下载: 导出CSV

      表  12   系数ab

      Table  12   Fitting coefficients a and b

      切法向强度比 拟合公式:c =σcn×(a+b×τcs/σcn)
      a b R2
      0.25~0.428 0.013 0.551 0.997
      0.5~0.714 0.005 0.516 0.991
      1 a+b=0.414 0.998
      1.4~2 0.474 -0.035 0.999
      2.33~5 0.412 0.004 0.991
      6~14 0.426 -0.002 0.996
      下载: 导出CSV

      表  13   系数bScSdS的拟合结果(方案H)

      Table  13   Fitting results of coefficients bS, cS and dS (Plan H)

      颗粒几何参数 拟合系数及R2
      Rmin /mm Rmax/Rmin bS cS dS R2
      0.15 1.67 0.6482 0.8027 2.1002 0.639
      0.2 2 0.6644 0.1074 0.4247 0.723
      0.3 3 0.8122 0.9226 2.3140 0.968
      下载: 导出CSV

      表  14   砂岩的力学特性及细观参数的选取

      Table  14   Mechanical properties of sandstone and selection of microscopic parameters

      细观参数取值 巴西试验 单轴压缩试验 三轴试验强度/MPa
      Rmin/
      mm
      Rmax/
      Rmin
      σcn/
      MPa
      ks/kn Ec/
      GPa
      τcs/
      MPa
      µ σt/MPa fc/MPa E/GPa ν 围压1 MPa 围压6 MPa
      误差 误差 误差 误差 误差 误差
      砂岩 5.99 64 9.195 0.226 71.89 95.45
      1号 0.2 2 34.896 2.172 14.165 69.792 1.7 4.77 -20.4 50.69 -20.8 9.005 -2.1 0.239 +5.8
      2号 0.2 2 51.235 2.172 14.165 51.235 1.7 6.96 +16.2 60.35 -5.7 9.005 -2.1 0.239 +5.8
      3号 0. 2 2 45 2.172 14.165 90 1.7 6.58 +9.8 67.31 +5.2 8.972 -2.4 0.234 +3.5 72.55 +0.9 91.18 -4.5
      下载: 导出CSV
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    • 收稿日期:  2023-12-14
    • 网络出版日期:  2024-12-05
    • 刊出日期:  2025-05-31

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