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  

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

作　　者：刘志钦[1,2] 余东明[3] 

机构地区：[1]河南城建学院土木与材料工程系,平顶山467036 [2]西安建筑科技大学土木工程学院,西安710055 [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,武汉430071

出　　处：《工程力学》2012年第8期289-296,共8页Engineering Mechanics

基　　金：河南省科技攻关重点项目(112102210361)

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。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.

关 键 词：中间主应力 剪胀 强度准则 非关联流动法则 平面应变 

分 类 号：U451.2[建筑科学—桥梁与隧道工程]