考虑中间主应力和剪胀特性的深埋圆巷弹塑性应力位移解

刘志钦, 余东明

刘志钦, 余东明. 考虑中间主应力和剪胀特性的深埋圆巷弹塑性应力位移解[J]. 工程力学, 2012, 29(8): 289-296. DOI: 10.6052/j.issn.1000-4750.2011.08.0511
引用本文: 刘志钦, 余东明. 考虑中间主应力和剪胀特性的深埋圆巷弹塑性应力位移解[J]. 工程力学, 2012, 29(8): 289-296. DOI: 10.6052/j.issn.1000-4750.2011.08.0511
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LIU Zhi-qin, YU Dong-ming. ELASTOPLASTIC STRESS AND DISPLACEMENT ANALYTICAL SOLUTIONS TO DEEP-BURIED CIRCULAR TUNNELS CONSIDERING INTERMEDIATE PRINCIPAL STRESS AND DILATANCY[J]. Engineering Mechanics, 2012, 29(8): 289-296. DOI: 10.6052/j.issn.1000-4750.2011.08.0511
Citation: LIU Zhi-qin, YU Dong-ming. ELASTOPLASTIC STRESS AND DISPLACEMENT ANALYTICAL SOLUTIONS TO DEEP-BURIED CIRCULAR TUNNELS CONSIDERING INTERMEDIATE PRINCIPAL STRESS AND DILATANCY[J]. Engineering Mechanics, 2012, 29(8): 289-296. DOI: 10.6052/j.issn.1000-4750.2011.08.0511
shu

考虑中间主应力和剪胀特性的深埋圆巷弹塑性应力位移解

  • 1.

    河南城建学院土木与材料工程系

  • 2.

    西安建筑科技大学土木工程学院

  • 3.

    中国科学院武汉岩土力学研究所 岩土力学与工程国家重点实验室

基金项目: 河南省科技攻关重点项目(112102210361)
详细信息
    作者简介:

    刘志钦(1968―)，女，河南平顶山人，副教授，博士，从事工程力学、结构工程的教学与研究(E-mail: lzq68@hncj.edu.cn).

    通讯作者:

    余东明(1980―)，男，安徽六安人，博士，从事公路路基工程研究(E-mail: yudm80@163.com).

  • 中图分类号: U451+.2

ELASTOPLASTIC STRESS AND DISPLACEMENT ANALYTICAL SOLUTIONS TO DEEP-BURIED CIRCULAR TUNNELS CONSIDERING INTERMEDIATE PRINCIPAL STRESS AND DILATANCY

  • 1.

    Department of Civil and Material Engineering, Henan Uinversity of Urban Construction

  • 2.

    School of Civil Engineering, Xi’an University of Architecture and Technology

  • 3.

    State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences

摘要

    摘要
  • 摘要: 平面应变条件下的深埋圆形巷道问题一般忽略中间主应力的影响，但这会与塑性区围岩的实际情况产生较大差异。为了充分考虑中间主应力对深埋圆形巷道的影响，基于平面应变假设与非关联流动法则将Mohr-Coulomb准则精确匹配为Drucker-Prager准则，在此基础上推导了考虑剪胀特性的理想弹塑性材料在塑性阶段的中间主应力表达式，中间主应力与剪胀角密切相关；根据所得的中间主应力表达式结合非关联流动法则，不引入任何假设，得出深埋圆巷塑性区由于剪胀角而发生体变的关系式；进一步推导了考虑中间主应力和剪胀特性的深埋圆形巷道塑性区应力位移解析式，其中径向应力、切向应力及塑性区半径的表达式与卡斯特奈(Kastner)解完全一致，但卡斯特奈(Kastner)解无法得出中间主应力，而新的位移解析式则与以往的文献完全不同；经与以往文献的位移理论解比较分析知，新的位移解答更加合理。因此考虑中间主应力和剪胀特性的解答为深埋圆形巷道的计算与设计提供一定的理论基础。
    Abstract: The influence of intermediate principal stress was usually ignored for the problem of a deep-buried circular tunnel under plane strain condition, which would lead to significant difference from the actual conditions of surrounding rocks in plastic areas. To consider the influence of intermediate principal stress on deep-buried circular tunnels, plane strain hypothesis and non-associated flow rule were adopted while Mohr-Coulomb strength criterion was precisely matched to Drucker-Prager strength criterion. The analytical expression of intermediate principal stress in plastic state for the perfect elastoplastic material with dilatancy was derived from Drucker-Prager strength criterion. The intermediate principal stress was closely relative to the dilation angle. By combining the analytical expression and non-associated flow rule, any other hypothesis need not to be introduced and the expression on volume dilatancy due to the dilation angle in plastic area could be obtained. Furthermore, the analytical expressions of the displacement and stress in plastic area for a deep-buried circular tunnel considering intermediate principal stress and dilatancy can also be obtained. In the expressions, the radial stress, the circumferential stress and the radius of plastic area have the same form as the solutions of Kastner. But the form of intermediate principal could not be given in solutions of Kastner and the new analytical expression of the displacement was entirely different from other literatures. Compared with the theoretic solutions of the displacement in other literatures, it shows the new solutions of the displacement are more reasonable. The solutions considering intermediate principal stress and dilatancy could therefore provide reasonable theoretic basis for the calculation and design of a deep-buried circular tunnel.
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出版历程
  • 收稿日期:  2011-08-07
  • 修回日期:  2011-12-11

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