圆形隧洞围岩应力松弛效应解析理论

Analytic theory about stress relaxation effects of rock around circular tunnel

为了深化效应的理论认识,建立圆隧围岩应力松弛效应理论模型,采用经典应力松弛模型计算围岩三维应力场,探讨应力松弛模型及其流变参数的敏感性.结果表明:采用Burgers模型与西原模型均能充分反映围岩应力松弛效应,围岩三向应力均随时间推移而迅速降低直至稳定于某一平衡状态;在应力松弛初期,环向应力下降的速度明显大于轴向应力与径向应力;围岩三向应力收敛值均随Burgers模型Kelvin体切向模量的增大而增大,Kelvin体黏滞系数的影响贯穿于应力松弛全过程;西原模型Kelvin体黏滞系数影响下围岩应力收敛值一致,应力松弛过程呈现非线性非完全衰减特征,应力松弛时间尺度随着Kelvin体剪切模量增大而增大,显著区别于Burgers模型下围岩应力松弛规律.

The theoretical model of stress relaxation effect of rock around a circular tunnel was established in order to deepen the theoretical understanding of effect. The classical stress relaxation models were utilized to calculate three-dimensional stress distribution. The sensitivity analysis of the different stress relaxation models and the related rheological parameters was conducted. Resuls show that surrounding rock stress declines rapidly and ultimately stables at a balanced state with the time elapses. The Burgers model and the Nishihara model can fully reflect the rock stress relaxation effects. The descent rate of the hoop stress, prior to the stress relaxation, is significantly greater than that of the axial stress and the radial stress. The convergence value of stress relaxation in three directions increases with increasing the shear modulus of the Kelvin unit of the Burgers model, and the effect of the viscous coefficient runs through the whole process of stress relaxation. The convergence value of stress relaxation is consistent under the effects of the viscous coefficient of the Kelvin unit of the Nishihara model. The process of stress relaxation presents a nonlinear and non-complete attenuation feature, and stress relaxation time scale increases with an increase in the shear modulus of Kelvin uni t, which is significantly different from the stress relaxation law of surrounding rock under the Burgers model.