基于离散颗粒模型的岩体结构面动-静态刚度系数对比的数值模拟研究

周剑 王彦兵 张路青 金永军 涂新斌

周剑, 王彦兵, 张路青, 等. 2021. 基于离散颗粒模型的岩体结构面动-静态刚度系数对比的数值模拟研究[J]. 工程地质学报, 29(1): 25-33. doi: 10.13544/j.cnki.jeg.2020-387
引用本文: 周剑, 王彦兵, 张路青, 等. 2021. 基于离散颗粒模型的岩体结构面动-静态刚度系数对比的数值模拟研究[J]. 工程地质学报, 29(1): 25-33. doi: 10.13544/j.cnki.jeg.2020-387
Zhou Jian, Wang Yanbing, Zhang Luqing, et al. 2021. Numerical study on dynamic-static stiffness coefficient of rock fractures based on discrete particle model[J]. Journal of Engineering Geology, 29(1): 25-33. doi: 10.13544/j.cnki.jeg.2020-387
Citation: Zhou Jian, Wang Yanbing, Zhang Luqing, et al. 2021. Numerical study on dynamic-static stiffness coefficient of rock fractures based on discrete particle model[J]. Journal of Engineering Geology, 29(1): 25-33. doi: 10.13544/j.cnki.jeg.2020-387

基于离散颗粒模型的岩体结构面动-静态刚度系数对比的数值模拟研究

doi: 10.13544/j.cnki.jeg.2020-387
基金项目: 

国家自然科学基金面上项目 41972287

国家自然科学基金面上项目 41672321

国家自然科学基金青年科学基金项目 41502307

详细信息
    作者简介:

    周剑(1985-),男,博士,副研究员,主要从事工程地质方面的研究工作. E-mail: zhoujian@bjut.edu.cn

  • 中图分类号: P642.13

NUMERICAL STUDY ON DYNAMIC-STATIC STIFFNESS COEFFICIENT OF ROCK FRACTURES BASED ON DISCRETE PARTICLE MODEL

Funds: 

the National Natural Science Foundation of China 41972287

the National Natural Science Foundation of China 41672321

the National Natural Science Foundation of China 41502307

  • 摘要: 岩体工程计算分析中结构面刚度系数是至关重要的力学参数,计算分析的精度和可靠程度与这个参数密不可分,结构面刚度系数取值仍然是一个难点。岩体中应力波传播至结构面处将会发生反射和透射现象,利用应力波透射系数可反演结构面动态刚度系数。本文从细观力学角度运用颗粒离散元方法,开发分段线性接触模型及应力波吸收边界模型,开展宏观岩体中应力波传播的模拟,结合准静态压缩试验模拟,研究了较为平直的岩体结构面分别在不同正应力条件下的动、静态刚度系数的变化特征。模拟结果表明:(1)利用C++语言开发的分段线性接触模型很好地实现了结构面非线性变形特征的模拟;(2)基于颗粒离散元方法能够准确地反映岩体中应力波传播规律,应力波通过不同刚度结构面的透射系数与理论解一致;(3)在离散颗粒模型中加入黏滞吸收边界条件很好地实现了在有限尺寸模型中远场应力波传播模拟;(4)在岩体模型中结构面接触部位运用分段线性接触模型,通过模拟应力波传播与单轴压缩试验分别获得了一致性较好的结构面动、静态刚度系数,结构面动/静态刚度系数之比值约为1.0。本文对岩体中结构面刚度的测试和取值具有重要的指导意义。
  • 图  1  分段线性接触模型示意图

    Figure  1.  Schematic diagram of multistage linear contact model

    图  2  颗粒按六边形组合方式构建的计算模型(含一条结构面)

    Figure  2.  The model containing a fracture in the middle assembled by particles in the hexagon way with particles

    图  3  结构面法向压力随变形的关系曲线

    Figure  3.  The curve of normal force with deformation of a fracture

    图  4  颗粒呈矩形排列的颗粒流模型

    Figure  4.  Particle flow model for rectangular array of particles

    图  5  应力波通过两种不同刚度结构面的透反射图

    a. Kn=0.6;b. Kn=1.0

    Figure  5.  Transmission and reflection diagrams of stress waves passing through fractures with different stiffness

    图  6  应力波透射系数随结构面归一化刚度系数变化的曲线

    Figure  6.  The curves of the transmission coefficient of stress wave under various normalized fracture stiffnesses

    图  7  颗粒随机排列组合的PFC2D模型

    Figure  7.  PFC model assembled by random particles

    图  8  图 7所示模型中结构面归一化Kn=1.0时透反射应力波曲线

    Figure  8.  Transmission and reflection stress wave curves for normalized Kn=1.0 in the model shown in Fig. 7

    图  9  应力波穿过颗粒随机的PFC模型中结构面的透射系数

    Figure  9.  Transmission coefficient of stress wave passing through the fracture in a PFC model assembled by random particles

    图  10  建立含结构面岩体的颗粒流模型的步骤

    Figure  10.  Steps for establishing PFC model of rock mass with a fracture

    图  11  结构面数值模型法向应力-相对位移曲线

    Figure  11.  Stress-displacement curve of the numerical fracture

    图  12  结构面法向刚度与变形量的关系曲线

    Figure  12.  The curve of normal stiffness of a fracture varying its deformation

    图  13  不同压应力下应力波通过结构面后的透反射波

    a.压应力为10 MPa;b.压应力为100 MPa;c.压应力为200 MPa

    Figure  13.  Transmission and reflection waves of stress waves passing through the structural plane under different compressive stresses

    图  14  不同压应力作用下结构面动静态法向刚度变化曲线

    Figure  14.  Dynamic and static normal stiffness curves of structural surfaces under different compressive stresses

    表  1  图 7所示模型中的微观参数

    Table  1.   Microscopic parameters in the model shown in Fig. 7

    颗粒密度/kg·m-3 颗粒半径/mm 颗粒半径比 接触模量Ec/GPa 平行黏结模量Ec/GPa
    2650 0.02 1.6 30 30
    接触刚度比kn/ks 平行黏结刚度比kn/ks 法向黏结强度及标准差(σ±δσ)/MPa 黏结强度比σn/σs 摩擦系数μ
    1.0 1.0 100±20 1 0.5
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  • 收稿日期:  2020-07-15
  • 修回日期:  2020-11-18
  • 刊出日期:  2021-02-01

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