爆炸荷载作用下深埋圆形隧洞的饱和黏弹性土-衬砌系统动力响应

Dynamic responses of system of saturated viscoelastic soil and lining of a deep tunnel under a blasting load

假定土骨架服从标准线性固体黏弹性本构关系,研究了深埋圆形隧洞的饱和黏弹性土-弹性衬砌耦合系统在轴对称爆炸作用下的瞬态动力响应。首先,基于饱和土的Biot模型和衬砌的弹性理论,通过引入势函数和Laplace变换,利用弹性衬砌和饱和黏弹性土界面处的连续性条件以及边界条件,得到饱和黏弹性土体和弹性衬砌位移、应力和孔隙水压力等在Laplace变换域中的解析解。其次,利用Laplace数值Crump逆变换得到耦合系统在时间域的动力响应,数值分析了不同土体模型下土体-衬砌耦合系统的径向位移和环向应力以及土体孔隙水压力等。结果表明:对不同土体模型的土体-衬砌耦合系统,其在爆炸载荷作用下的动力响应性态基本一致,但动力响应的振动周期和幅值等具有明显的差异。同时,对于饱和黏弹性土-弹性衬砌系统,土体黏性参数对土体径向位移和孔隙水压力有明显的影响,但对土体环向应力影响较小。

Assuming that soil skeleton satisfies the constitutive relation of the standard linear viscoelastic solid, the transient dynamic responses of the coupled system of saturated viscoelastic soil-elastic lining of a deep circular tunnel subjected to a blasting load are studied. First, based on the Biot model of the saturated soil and the elasticity theory of the lining, with the boundary conditions as well as the continuity conditions on the interface between the saturated viscoelastic soil and elastic lining, the analytical solutions of the displacements and stresses as well as the pore water pressure of the saturated viscoelastic soil and elastic lining in the Laplace transformed domain are derived by means of the Laplace transform and potential functions. Then, the transient dynamic responses of the coupled system in the time domain are obtained with the Crump numerical inverse Laplace transform, and the radial displacements and circumferential stresses of the soil-lining coupled system as well as the pore water pressures of the saturated soil for different soil models are analyzed numerically. It is shown that, for the soil-lining coupled system with different soil models, their dynamic behaviors are almost the same under the blasting load, whereas their vibration periods and amplitudes are obviously different. Furthermore, for the system of saturated viscoelastic soil-elastic lining, the influences of the viscosity parameters on the soil radial displacement and the pore water pressure are remarkable; while the viscosity parameters have a little influence on the circumferential stress of soil.