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非均一性斜坡落石运动轨迹

陈泰江 章广成 向欣

陈泰江, 章广成, 向欣. 非均一性斜坡落石运动轨迹[J]. 地质科技通报, 2021, 40(4): 196-203, 213. doi: 10.19509/j.cnki.dzkq.2021.0413
引用本文: 陈泰江, 章广成, 向欣. 非均一性斜坡落石运动轨迹[J]. 地质科技通报, 2021, 40(4): 196-203, 213. doi: 10.19509/j.cnki.dzkq.2021.0413
Chen Taijiang, Zhang Guangcheng, Xiang Xin. Trajectory of rockfall on the uniform slope[J]. Bulletin of Geological Science and Technology, 2021, 40(4): 196-203, 213. doi: 10.19509/j.cnki.dzkq.2021.0413
Citation: Chen Taijiang, Zhang Guangcheng, Xiang Xin. Trajectory of rockfall on the uniform slope[J]. Bulletin of Geological Science and Technology, 2021, 40(4): 196-203, 213. doi: 10.19509/j.cnki.dzkq.2021.0413

非均一性斜坡落石运动轨迹

doi: 10.19509/j.cnki.dzkq.2021.0413
基金项目: 

国家重点研发计划 2018YFC1505306

国家自然科学基金项目 41877263

详细信息
    作者简介:

    陈泰江(1995-), 男, 现正攻读土木工程专业博士学位, 主要从事岩土工程力学方面的研究工作。E-mail: Chendjiang@cug.edu.cn

    通讯作者:

    章广成(1980-), 男, 教授, 博士生导师, 主要从事岩土体稳定性评价与防治方面的教学与研究工作。E-mail: zhangguangc@foxmail.com

  • 中图分类号: P642.21

Trajectory of rockfall on the uniform slope

  • 摘要: 现有的落石运动轨迹研究均将斜坡视为半无限均匀的坡面,而实际的工况下,坡面由不均一材料组成。根据落石不同的运动模式,将坡面简化为多层岩土体材料的结构形式,在滚动阶段,基于Hertz接触理论得到落石在不同坡面条件下运动特征,并给出坡面分层条件下落石切向摩擦系数的计算公式,在碰撞阶段,基于能量守恒定理,采用准静态接触力学理论得到法向恢复系数公式,理论推导得到任意层厚岩土体材料坡面条件下落石法向和切向恢复系数的解析解,然后求解得到碰撞后落石运动参数,并根据碰撞后落石的速度及回弹量关系,给出碰撞后落石运动模式转换的判别条件,最后结合运动学定理,得到3种运动模式任意分层坡面条件落石的运动轨迹,将理论公式应用于某山区落石运动轨迹预测,验证了理论公式的适用性和有效性。

     

  • 图 1  单一坡面条件下落石滚动模式[23]

    Figure 1.  Rockfall rolling mode under single slope

    图 2  分层坡面条件下落石滚动模式

    Figure 2.  Rockfall rolling mode under layered slope

    图 3  落石抛体运动模式

    Figure 3.  Movement mode of rockfall projectile

    图 4  碰撞过程计算模型[23]

    Figure 4.  Calculation model of collision process

    图 5  分层坡面下落石碰撞过程图

    Figure 5.  Collision process diagram of rockfall under the layered slope

    图 6  研究区边坡图

    Figure 6.  Slope of the study area

    图 7  危岩体WYT2形态图

    Qcol.崩积物;C1b.下石炭统大塘组砂岩

    Figure 7.  WYT2 morphology of dangerous rock mass

    图 8  落石运动轨迹计算模型

    Figure 8.  Calculation model of the rockfall trajectory

    图 9  落石运动轨迹

    Figure 9.  Rockfall trajectory

    图 10  落石运动能量包络线图

    Figure 10.  Energy envelope diagram of rockfall motion

    表  1  滚动摩擦系数[24]

    Table  1.   Rolling friction coefficient

    坡面特征 滚动摩擦系数
    光滑岩面、混凝土表面 0.40~0.60
    块石堆积坡面 0.55~0.70
    密实碎石堆积坡面、硬土坡面 0.55~0.85
    松散碎石坡面、软土坡面 0.50~0.85
    下载: 导出CSV

    表  2  落石运动计算参数

    Table  2.   Calculation parameters of rockfall movement

    材料 ρ/(g·cm-3) E/MPa υ μ
    落石 2.05 22 000 0.22 -
    堆积物 - 46 0.30 0.6
    灰岩 - 280 0.28 0.5
    下载: 导出CSV

    表  3  落石运动碰撞点速度

    Table  3.   Rockfall velocity of the point

    碰撞点 碰撞前速度/(m·s-1) 碰撞后速度/(m·s-1)
    q1 36.3 13.5
    P1 36.3 13.6
    P2 17.1 12.8
    P3 13.9 10.9
    P4 11.3 10.0
    下载: 导出CSV
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  • 收稿日期:  2020-10-10

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