Dynamic Responses of Layered Viscoelastic Half-Medium with Twin Tunnel Under Harmonic Load

Abstract

Abstract Purpose This paper presents dynamic analysis of layered viscoelastic half medium which includes twin rectangular tunnel under harmonic load. Viscoelastic half medium is considered and modelled with using Kelvin–Voigt viscoelastic model and two dimensional (2-D) continua. Methods The considered problem is solved by using finite element method. The energy expressions of the system are obtained and equation of motion are obtained by using Lagrange procedure. Infinite region far from twin tunnel is modelled by using infinite elements with 8 nodes and finite region is modelled by using 16 nodes finite elements. The dynamic equations for finite and infinite elements are solved by using Newmark-Beta method in time domain. Finite and infinite element models with different layers and twin tunnel are generated and numerical solutions are obtained by using an algorithm by authors. Results In order to achieve verify the used models and methods, some special results are obtained and compared with results from a finite element software. In numerical studies, effects of location of twin tunnel on dynamical responses of the system under harmonic load are obtained in figures and discussed in detail. Dynamic tunnel-medium interaction is discussed in the obtained results. Conclusions The numerical results show that tunnel location plays important role on the dynamic responses of half medium and dynamic responses change significantly with tunnel-medium interaction. In field near to the tunnel, the dynamic responses are more affected. Important practical implication is that computational cost for this kind of problems could be reduced, more realistic results could be obtained and all boundary conditions could be considered by used model with infinite elements. The used model and method are very useful and practical for dynamic analysis of tunnel structures.