基于双屈服面模型的圆形软岩巷道围岩变形弹塑性解

软岩巷道过大的径向位移对煤矿生产有较大影响。基于双屈服面模型,利用某种泥岩材料的常规三轴实验数据,分别拟合了以第一、第三塑性主应变(ε_1~p,ε_3~p)为硬化参量的加载面,根据对完全加载假设的验证,推导了此泥岩材料的非关联流动法则,得到了围岩塑性区范围和径向位移的解。研究结果表明:该泥岩材料的2个加载面形式为二次函数,各项系数均可表示为ε_1~p或ε_3~p的一次函数,由此确定塑性应变增量分量的大小;推导出的非关联流动法则中含有常数项,其原因为:在加载过程中,会先达到以ε_3~p为硬化参量的加载面,当ε_1~p恰好为0时,ε_3~p即为该常数的值;考虑了岩石的非线性应变软化特征,排除了"人为假定流动法则"等主观因素的干扰,求解了塑性区范围和径向位移的解析解,得到了在一定地应力和该岩性条件下二者与开挖半径的线性拟合公式。

Elasto plastic solution of deformation in circular soft rock tunnel based on double yield surface model

The radial displacement of the soft rock roadway has great influence on the coal mine production.Based on double yield surface model，using the conventional triaxial test data of a mudstone，the loading surfaces which were expressed by the first and the third main plastic strain(εp1，εp3) as the hardening parameter were fitted.According to the verified hypothesis of complete loading，the non associated flow rule of the mudstone material was derived，and the surrounding rock plastic zone scope and radial displacement solution were obtained.The results show that:① the form of two loading surfaces of the mudstone material are quadratic function，and the coefficients can be expressed as a linear function of εp1 or εp3，and the value of the plastic strain increment component is determined.② the derived non associated flow law contains a constant term，the reason is that in the process of loading，it will first reach the loading surface of the εp3，when εp1 happens to be 0，εp3 is the value of the constant.③ in this paper，the authors consider the rock characteristics of strain nonlinear softening，rule out the subjective cognition of “assumed flow rule” and others，get the analytical solution of the range of plastic zone and radial displacement，obtain the linear fitting formula between the range of plastic zone，radial displacement and excavation radius under the condition of constant stress.