基于Drucker-Prager屈服准则的圆形巷道围岩弹塑性分析

Elastoplastic analysis of surrounding rock on circular roadway based on Drucker-Prager yield criterion

考虑不同程度的中间主应力对屈服的影响,以Drucker-Prager屈服准则作为巷道围岩的塑性条件,推算出巷道围岩弹塑性区应力、塑性区半径和位移的解析解。研究表明,中间主应力对塑性区半径和位移的大小以及围岩应力的分布均有重要影响,并且验证了中间主应力效应的区间性。用单因素分析法,分别考虑不同内聚力、内摩擦角、原岩应力和支护阻力情况下,塑性区半径和位移的Drucker-Prager准则解、Mohr-Coulomb准则解和统一强度准则解的变化规律并对其进行比较,分析表明:相同条件下,塑性区半径及位移的Drucker-Prager准则解比Mohr-Coulomb准则解和统一强度准则解大,并且在较高内聚力、较低内摩擦角或较低原岩应力情况下Drucker-Prager准则解接近于Mohr-Coulomb准则解。采用Flac3D进行数值模拟,模拟结果与理论分析结果较为吻合。因此,适当的应用Drucker-Prager屈服准则将更能保证工程实践的安全性,更具实践价值。

The Drucker-Prager yield criterion was used as plastic condtion of roadway surrounding rock and by considering different degree of intermediate principal stress on yield effect,the analytical solutions of elastoplastic zone stress,plastic zone radius and displacement were calculated.The studies show that the intermediate principal stress has significant effects on surrounding rock stress distribution,plastic zone radius and displacement.In addition,the interval of effect by intermediate principal stress was verificated.The plastic zone radius and displacement based on Drucker-Prager criterion,Mohr-Coulomb criterion and unified strength criterion were analyzed and compared by using single factor analysis method according to the different cohesive force,internal friction angle,in-situ stress and support resistance.The results show that under the same conditions,the plastic zone radius and displacement based on Drucker-Prager criterion are larger than those based on Mohr-Coulomb criterion and unified strength criterion,and with a large cohesive force,large internal friction angle and low in-situ stress,the plastic zone radius and displacement based on Drucker-Prager criterion are close to those based on Mohr-Coulomb criterion.Solutions of Flac3D numerical simulation and theoretical analysis results coincide with each other.Therefore,the Drucker-Prager yield criterion can ensure the safety of engineering,and it is of more practical values when it is applied properly.