基于三剪能量理论的巷道围岩弹塑性分析

针对弹塑性圆形巷道，应用三剪能量屈服准则，理论推导了塑性区半径、应力及径向位移公式，在塑性区半径公式的基础上，应用Mohr-Coulomb准则，进一步推导了破裂区应力及位移公式；通过具体算例，分析了不同影响因素对塑性区半径的影响。实例表明：原岩应力、黏聚力、支护反力、围岩应力对塑性区半径有一定影响。原岩应力及支护反力均随塑性区半径的增大而增大，但支护反力对塑性区半径的影响变化不大，当增大到一定程度时，半径将保持不变；黏聚力随塑性区半径的增大而降低；围岩应力随塑性区半径的增大而增大，当半径达到塑性区半径时，切向应力将保持不变，其值为原岩应力值，而径向应力在一定范围内仍将保持递增，但递增率减小，一直到原岩应力值；对比于单剪条件（Mohr-Coulomb准则），得出了三剪能量准则条件下的巷道围岩弹塑性公式比Mohr-Coulomb准则条件更为准确的结论。

Elasto-plastic analysis on surrounding rock based on triple shear energy theory

According to elasto plastic circle roadway，using triple shear energy yield criterion，formulas of plastic zone radius，stress and radial displacement were derived.Furthermore，based on plastic zone radius formula，using Mohr Coulomb criterion，stress and radial displacement formulas were deduced in fractured zone.By practical calculation example gave，the influence on plastic zone radius in different affecting factors was analyzed.The example analysis demonstrates that rock stress，cohesion，supporting force and surrounding rock stress have some effect on plastic zone radius.Rock stress and supporting force increases with plastic zone radius，however，when supporting force having little influence increases to a certain extent，the radius keep unchanged；cohesion decrees with radius increasing；surrounding rock stress is also increased，tangential stress will remain unchanged while reaching the radius，its value is rock stress，but radial stress keep increasing in a certain range and the increasing rate decreases，until rock stress；elasto plastic formula of roadway in triple shear energy yield criterion is more accurate than in Mohr Coulomb criterion.