基于Levy-Mises本构关系及D-P屈服准则的轴对称圆巷理想弹塑性解

如何判断巷道开挖后在无支护反力条件下的围岩弹塑性变形及围岩应力重新分布的力学行为一直是人们研究的重点问题。卡斯特纳方程(Kastner equation)的求解存在以下不足和缺陷：(1) 对支护反力的力学处理存在缺陷，不具有工程实际意义；(2) 塑性区应力求解，没有使用到假设的理想弹塑性材料的塑性本构关系；(3) 塑性区应力求解，没有考虑沿巷道轴向方向的应力的影响。基于增量型本构关系即Levy-Mises关系及D-P屈服准则，对轴对称圆巷进行了理想弹塑性条件的求解。公式计算结果与卡斯特纳方程计算结果和数值模拟计算结果分别进行了对比分析。由于该求解弥补了卡斯特纳方程求解中忽略的3个问题，因此，其结果更具有理论意义和实践价值。

Perfect elastoplastic solution of axisymmetric circular openings in rock mass based on Levy-Mises constitutive relation and D-P yield criterion

How to determine the mechanical behavior of the elastoplastic deformation and stress redistribution in rock mass without supporting reaction after tunnel excavation is the important research problem all the time. The insufficiency and defect existed in the solution of Kastner equation are as follows: (1) there are drawbacks in the mechanical treatment of supporting reaction, which has no practical meaning; (2) in the solution of plastic zone stresses, it takes no advantage of the plastic constitutive relation given by perfect elastoplastic materials; (3) in the solution of plastic zone stresses, the influence of axial stress along tunnel is not taken into account. The perfect elastoplastic solution based on the incremental constitutive relation of plastic mechanics, namely Levy-Mises relationship and D-P yield criterion, is addressed. The present solution is studied with calculation results by Kastner equation and numerical computation. It has more theoretical meaning and practical value, for the present solution, it is able to account for three problems neglected in the solution of Kastner equation.