恒载作用下轴对称圆巷围岩的流变变形方程求解

建立围岩-支护相互作用流变变形机制的数学力学模型是解决岩石地下工程支护问题的有效途径，其关键问题是，在围岩产生流变变形的过程中支护是如何对围岩进行作用的。根据基于Levy-Mises本构关系及D-P屈服准则的轴对称圆巷的理想弹塑性解、一维蠕变曲线的等时曲线相似的假设以及三维流变试验结果，推导出了原岩应力和被动支护反力均为恒载，且巷道围岩为三维应力状态下的蠕变方程及轴对称圆巷围岩的非线性黏弹塑性流变变形计算公式。与前人的工作相比，文中推导的公式中含有对围岩流变变形起决定作用的2个参数，即原岩应力 和岩石材料的单轴塑性屈服应力 ，因此公式推导的理论基础更加完备、可信度更高。

Solving equation of rheological deformation in axisymmetric round well under dead load

Setting up the mathematical mechanical model of rheological deformation mechanism under the interaction between surrounding rock and support is an efficient way to solve the support problem in the underground rock engineering. How support affects it is the key problem in the process of rheological behavior of surrounding rock. According to the ideal elastoplastic solution of axisymmetric round well based on Levy-Mises model and D-P yield criterion, the assumption that all the tautochrones of one-dimensional creep curves are similar, and the results of three-dimensional rheological test, the creep equation of that primary rock stress and passive supporting force are constant; in the same time, surrounding rock is under 3D stresses is derived; and the formula for rheological deformation of nonlinear viscoelastic plasticity in axisymmetric round well is also proposed. Comparing to the works made by previous researchers, there are two parameters in the formula derived, initial rock stress and the uniaxial plastic yield stress of rock, which play decisive roles in the process of rheological deformation, for this reason, the theoretical foundation of the formula derived is more complete and credible.