基于分数阶损伤蠕变模型的圆形隧洞黏弹塑性解

Visco-elastoplastic Solutions for Circular Tunnel Based on a Fractional Derivative Damage Creep Model

深埋隧洞围岩变形是一个与时间相关的复杂力学过程.为了描述这一过程,首先基于分数阶理论,提出一个新的非线性蠕变损伤本构模型.然后基于该模型,并引入Hoke-Brown屈服准则,推导出深埋条件下圆形隧洞围岩位移的黏弹塑性解析解.最后,以锦屏二级水电站辅助洞为工程实例,对解析解的有效性进行验证,并分析了流变参数对流变位移的影响.研究结果表明:1)分数阶蠕变损伤本构可以较好的描述岩石蠕变全过程,即衰减蠕变、常速蠕变及加速蠕变过程.2)随着模型中分数阶阶次及损伤因子量值的增加,围岩的蠕变变形更为明显.3)解析曲线与现场实测位移平均值曲线在量值与形态上均吻合较好,验证了解析解的有效性.

The deformation of deep buried tunnel is a complicated time-evolving process.To reflect this process,a novel nonlinear damage creep model based on fractional derivative was put forward,and the analytical solution regarding the visco-elastoplastic deformation for circular tunnel was derived by combing this creep model and Hoke-Brown plastic criterion.Then,the auxiliary tunnel of Jinping II hydropower station was chosen as an example to validate the analytical solution,and the influence of the creep parameters on the creep deformation was also revealed.The research shows that:1) The novel creep model can well describe the three creep stage,that is,the decay,constant,and accelerated creep stage in turn.2) The creep deform has a positive proportion to the magnitude of fractional orders and damage factor;3) The shape of creep curves and the corresponding values between test result and analytical solution are well consistent with each other.