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基于Drucker-Prager准则的三维应力场下围岩塑性区近似解
  • Title

    Approximate solution of plastic zone in surrounding rock under three-dimensional stress field based on Drucker-Prager strength criterion

  • 作者

    刘洪涛梁嘉璐韩子俊刘勤裕乔钟槿

  • Author

    LIU Hongtao;LIANG Jialu;HAN Zijun;LIU Qinyu;QIAO Zhongjin

  • 单位

    中国矿业大学(北京)能源与矿业学院煤炭行业巷道支护与围岩控制工程研究中心

  • Organization
    School of Energy and Mining Engineering, China University of Mining and Technology-Beijing
    Research Center of Roadway Support and Surrounding Rock Control Engineering in Coal Industry
  • 摘要

    为了研究三维应力场下巷道围岩的稳定性,基于Drucker-Prager准则,以弹塑性力学为理论基础,通过引入轴向应力解推导了三维应力场下的巷道围岩塑性区边界方程,对不同应力场条件下的围岩塑性区形态及尺寸展开分析,对比分析了巷道围岩的内聚力、内摩擦角、泊松比和巷道半径变化的条件下,5种Drucker-Prager系列屈服准则对塑性区形态及尺寸的影响,并基于演化特性提出实际工程意义。结果表明:水平侧压的增减对巷道围岩的塑性区形态影响程度较大,过高或过低的水平侧压会使巷道围岩呈蝶形扩展;轴向侧压的增减对巷道围岩的塑性区形态影响较小,对围岩的塑性区尺寸影响较大,相同水平侧压下,不同轴向侧压会使围岩的塑性区尺寸变化呈碗状发展;内聚力、内摩擦角和巷道半径变化时,不同Drucker-Prager准则下巷道围岩塑性区尺寸变化规律具有一致性,选取不同Drucker-Prager准则会对巷道围岩塑性区的计算结果产生影响。

  • Abstract

    This study proposes to address the stability of roadway surrounding rock under three-dimensional stress field based on the Drucker-Prager criterion and the theory of elastic-plastic mechanics. Specifically, we deduced the boundary equation of plastic zone of roadway surrounding rock under three-dimensional stress field by introducing the axial stress solution, and analyzed the shape and size of plastic zone of surrounding rock under different stress field conditions. We compared the effect of five Drucker-Prager yield criteria on the shape and size of plastic zone under variations of cohesion, internal friction angle, Poisson's ratio and roadway radius in roadway surrounding rock. We then analyzed its implications for engineering practice based on the evolution characteristics. Results show that ① Variations in horizontal stress exerts significant impact on the plastic zone morphology of roadway surrounding rock: too high or too low horizontal stress will lead to a butterfly-shaped expansion in the roadway surrounding rock. ② Variations in axial pressure has little effect on the plastic zone shape of roadway surrounding rock, yet exerts major influence on the plastic zone size of surrounding rock: under the same horizontal stress, different axial stress will lead to a bowl-shaped development in the plastic zone size of surrounding rock. With variations in the cohesion, internal friction angle and roadway radius, we observed consistency in the size variation of plastic zone in roadway surrounding rock under different Drucker-Prager criteria. Therefore, the choice of different Drucker-Prager criteria will affect the calculation results of plastic zone in surrounding rock of roadway.

  • 关键词

    塑性区蝶形破坏Drucker-Prager准则三维应力场巷道支护

  • KeyWords

    plastic zone;butterfly failure;Drucker-Prager criterion;three-dimensional stress field;roadway support

  • 基金项目(Foundation)
    国家自然科学基金(U22A20165,52004289);中央高校基本科研业务费(2022XJNY01)
  • DOI
  • 图表
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    •  
    • Drucker-Prager准则[21]

    图(9) / 表(3)

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