基于D-P准则和西原模型的圆形隧道黏弹-黏塑性解

Viscoelasto-viscoplastic solutions for circular tunnel based on D-P yield criterion and Nishihara model

为了较好地描述圆形隧道开挖后围岩的流变特性,假设围岩本构模型为西原模型,选用Drucker-Prager屈服准则,考虑塑性区的黏性与剪胀特性,推导了圆形隧道开挖后围岩塑性区半径、应力、位移的理论解。当剪胀角ψ=0°时,这些解答转化为体积不变假设下基于Mohr-Coulomb准则和西原模型的黏弹-黏塑性解。通过具体算例,分析了剪胀角对塑性区半径、洞壁位移和应力场的影响。将黏弹-黏塑性位移解和黏弹-塑性位移解进行了对比分析。结果表明:围岩达到稳态之前,剪胀角对应力场和塑性区半径影响较小,对洞壁位移影响较大。稳态围岩的应力场和塑性区半径与剪胀角取值无关。稳态围岩洞壁位移随着剪胀角的增大有较为明显的增加。塑性区的黏性特性对围岩的稳态应力没有影响,对围岩的稳态洞壁位移有较大的影响。剪胀角较大时,应考虑塑性区的黏性,否则会低估稳态围岩洞壁位移。研究结果对实际工程有一定的参考价值。

In order to characterize the rheological properties of surrounding rocks after the excavation of circular tunnel,theoretical solutions of radius,stress and displacement of the plastic zone for surrounding rocks after the excavation of circular tunnel are derived by using the Drucker-Prager yield criterion and considering the viscosity and dilatancy characteristics of plastic zone,assuming the constitutive model of surrounding rocks as the Nishihara model.When the dilatancy angle is 0,the solutions change into viscoelastic-viscoplastic solutions based on the Nishihara model and Mohr-Coulomb criterion under the assumption of constant volume.The effects of dilatancy angle on the radius of plastic zone,tunnel-wall displacement and stress field are analyzed.The solutions for viscoelastic-viscoplastic displacement and viscoelastic-plastic displacement are compared and analyzed.The results show that before the surrounding rock reaches the steady state,the effects of dilatancy angle on the stress field and the radium of plastic zone are relatively smaller while the effects of dilatancy angle on the tunnel-wall displacement is relatively larger.The stress field and the radium of plastic zone for stable surrounding rocks are independent of the value of dilatancy angle,however,the tunnel-wall displacement of steady-state rock increases obviously with the dilatancy angle.When the dilatancy angle is large,the viscosity of plastic zone should be considered;otherwise the tunnel-wall displacement of steady-state surrounding rocks will be underestimated.The research results are of certain reference value for practical engineering.