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基于离散元法的砂石混合体直剪试验结果分析

苏永华 王栋

苏永华, 王栋. 基于离散元法的砂石混合体直剪试验结果分析[J]. 水文地质工程地质, 2021, 48(6): 97-104. doi: 10.16030/j.cnki.issn.1000-3665.202012029
引用本文: 苏永华, 王栋. 基于离散元法的砂石混合体直剪试验结果分析[J]. 水文地质工程地质, 2021, 48(6): 97-104. doi: 10.16030/j.cnki.issn.1000-3665.202012029
SU Yonghua, WANG Dong. An analysis of direct shear test results of sand - gravel mixture based on the discrete element method[J]. Hydrogeology & Engineering Geology, 2021, 48(6): 97-104. doi: 10.16030/j.cnki.issn.1000-3665.202012029
Citation: SU Yonghua, WANG Dong. An analysis of direct shear test results of sand - gravel mixture based on the discrete element method[J]. Hydrogeology & Engineering Geology, 2021, 48(6): 97-104. doi: 10.16030/j.cnki.issn.1000-3665.202012029

基于离散元法的砂石混合体直剪试验结果分析

doi: 10.16030/j.cnki.issn.1000-3665.202012029
基金项目: 国家自然科学基金项目(51878266)
详细信息
    作者简介:

    苏永华(1965-),男,教授,博士,主要从事地下结构和岩土工程研究。E-mail:yong_su1965@126.com

    通讯作者:

    王栋(1995-),男,硕士研究生,主要从事地表塌陷方面研究。E-mail:975662835@qq.com

  • 中图分类号: TU43

An analysis of direct shear test results of sand - gravel mixture based on the discrete element method

  • 摘要: 砂石混合体由力学性质以及结构相差极大的材料组成,其组成的重塑地层易发生塌陷等问题,因此对砂石混合体力学特性的研究具有重要的工程意义。砾石形状是砂砾石力学特性研究的重要属性参数,但采用规则图形对砾石进行描述不能反映出其真实的力学性质,采用数字图像处理技术构建的砾石数据库能反映砾石真实形状并可对特定形状参数进行具体分析。由于砂石混合体的粒径分布较广,采用特征粒径等无法描述整体粒度分布,故本文结合分形理论构建砂石混合体的二重分形结构模型,通过粒度分维值反演出完整的级配分布曲线。考虑到砂石混合体离散型的特点,采用离散元软件进行直剪试验数值模拟并对细观结构进行分析,研究结果表明,砂石混合体一般具有2个粒度分维值:砂粒度分维值和砾石粒度分维值,砂、砾石粒度分维值越接近,抗剪强度和内摩擦角越大;当两者相等时,砂石混合体具有一重分维,此时均一性最好,抗剪强度和内摩擦角最大;轴向系数是形容砾石形状的一个重要参数,随着轴向系数的增加,砾石显示出明显的条状性,在直剪试验中抗转动能力增强、周围接触数量增加,导致抗剪强度和内摩擦角不断增加。
  • 图  1  数字图像处理技术获取边界信息流程示意图

    Figure  1.  Flow chart showing the digital image processing technology to obtain boundary information

    图  2  圆度频率(a)和轴向系数频率(b)分布直方图

    Figure  2.  Distribution histogram of (a) roundness frequency and (b) axial coefficient frequency

    图  3  最大粒径、含石量和砾石粒度分维值的关系

    Figure  3.  Relationship among the maximum grain size, rock content and fractal dimension of gravel size

    图  4  砂(a)和砂石混合体(b)剪应力-剪切位移模拟和实际试验结果对比曲线

    Figure  4.  Shear stress-shear displacement comparison curve between the simulation and actual test results of (a) sand and (b) sand - gravel mixture

    图  5  不同砾石粒度分维值的级配曲线

    Figure  5.  Grading curves of fractal dimension of different gravel sizes

    图  6  300 kPa正应力下不同Dr剪应力-剪切位移曲线

    Figure  6.  Shear stress-shear displacement curves of different Dr under the normal stress of 300 kPa

    图  7  粒度分维差值与内摩擦角关系

    Figure  7.  Relationship between the difference in particle size fractal dimension and the angle of internal friction

    图  8  不同粒度分维差值的位移变化图

    Figure  8.  Displacement change diagram of difference of different fractal dimensions

    图  9  不同轴向系数的砾石

    Figure  9.  Gravel with different axial coefficients

    图  10  不同轴向系数下剪应力峰值-正应力曲线

    Figure  10.  Shear stress peak-normal stress curve under different axial coefficients

    图  11  砾石颗粒旋转角度及周围接触示意图

    Figure  11.  Schematic diagram of rotation angle and surrounding contact of gravel particles

    表  1  基于离散元模拟的直剪试验主要计算参数

    Table  1.   Main computational parameters in DEM simulation of direct shear

    计算参数砾石
    法向刚度kn/(${\rm{N}} \cdot {{\rm{m}}^{ - 1}}$)5×1085×109
    切向刚度ks/(${\rm{N}} \cdot {{\rm{m}}^{ - 1}}$)2×1082×109
    摩擦系数0.50.9
    粒径/mm0.5~5.0>5.0
    下载: 导出CSV

    表  2  不同砾石粒度分维值在直剪试验中获取的相关参数

    Table  2.   Correlation parameters of fractal dimension of different gravel sizes obtained in the direct shear test

    砾石粒度分维值100 kPa200 kPa300 kPa内摩擦角/(°)
    2.4568.57144.84196.0734.06
    2.5065.22147.33209.9735.26
    2.5569.56150.10220.0536.34
    2.6065.22123.23210.7833.99
    2.6564.84112.112195.4832.02
    下载: 导出CSV

    表  3  不同砂粒度分维值在直剪试验中获取的相关参数

    Table  3.   Relevant parameters obtained in the direct shear test of the fractal dimension of different sand particle sizes

    砂粒度分维值100 kPa200 kPa300 kPa内摩擦角/(°)
    2.4565.22143.75175.3132.11
    2.5066.09150.45202.7534.86
    2.5569.57150.10220.0536.34
    2.6068.70135.24203.5334.15
    2.6564.44134.01170.9931.13
    下载: 导出CSV

    表  4  不同轴向系数在直剪试验中获取的强度参数

    Table  4.   Strength parameters obtained in direct shear test with different axial coefficients

    主要参数轴向系数
    S=1.0S =1.4S =1.8
    100 kPa65.3168.9183.95
    200 kPa127.39128.25143.04
    300 kPa174.61184.58211.15
    400 kPa235.34251.42292.50
    内摩擦角/(°)30.7632.1435.92
    相关系数R20.99190.99680.9925
    下载: 导出CSV

    表  5  不同轴向系数下砾石接触数量和旋转角度

    Table  5.   Gravel contact number and rotation angle under different axial coefficients

    轴向系数砾石接触数量砾石平均旋转角度/(°)
    1.015819.43
    1.416568.70
    1.817426.42
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-12-14
  • 修回日期:  2021-02-04
  • 网络出版日期:  2021-09-03
  • 刊出日期:  2021-11-15

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