Keywords: seismic analysis, soil-structure interaction, lined tunnels, transmitting boundaries, hyperbolic, damping.

Dynamic soil-structure interaction (DSSI) has great importance, especially when a seismic problem is studied. However, in many studies, no soil-structure interaction analysis is made [1], estimating stresses on structures using the maximum free-field strains expected. This approximation can be applied for flexible structures (pipes). However, this assumption is not valid for stiffer structures such as tunnels [2].

In this paper, DSSI is studied, considering the problem of a circular monolithic lined tunnel, inside of a horizontally infinite stratum, resting on rigid bedrock, and subjected to seismic loads, using several numerical codes: FLUSH-Plus [3], FLAC [4], ABAQUS/Explicit [5], and ESES [6]. This last numerical code demonstrated that it is the most adapted code to predict efforts in underground structures under seismic loads. Moreover, numerical models to study a DSSI problem should be adapted with an appropriate internal soil damping (hysteretic damping instead Rayleigh damping), and a hyperbolic or pseudo-hyperbolic soil model.

The numerical results are validated using the analytical models of St. John and Zahrah [7], Wang [8], Penzien [9], and Bobet [10], leading to the conclusion that Wang and Bobet models reproduce a better trend of liner stresses resulting from the soil-liner stiffness ratio. For applying analytical models, maximum shear strain resulting from the seismic action has to be calculated. However, the estimation of the maximum shear strain as the ratio of maximum particle velocity and elastic shear-wave velocity, results in excessive maximum shear strain values, comparing these to those resulting from a free-field analysis. Also, hyperbolic and pseudo-hyperbolic soil models can lead to very different estimation of the maximum shear strain, because the second soil model uses the equivalent linear method (EQLM [3]) to reduce stiffness and increase damping with the greater shear strain in an iterative process. This proves less accurate than hyperbolic soil models defined in time-domain codes.

1

G.P. Kouretzis, G.D. Bouckovalas, Ch.J. Gantes, "3-D shell analysis of cylindrical underground structures under seismic shear (S) wave action", Soil Dynamics and Earthquake Engineering, 26(10), 909-921, 2006. doi:10.1016/j.soildyn.2006.02.002

2

I.V. Constantopoulos, J.T. Motherwell, J.R. Hall Jr., "Dynamic analysis of tunnels", Proceedings of the 3rd International Conference on Numerical Methods in Geomechanics, Aachen, 1979.

3

J. Lysmer, T. Udaka, C.F. Tsai, H.B. Seed, "FLUSH. A computer program for approximate 3-D analysis of soil structure interaction problems", College of Engineering, University of California, Berkeley, UCB/EERC-75/30, 1975.

4

P. Cundall, "FLAC, v.5.00. User's Manual", Itasca Consulting Group, 2005.

5

Hibbit, Karlsson and Sorensen Inc., "ABAQUS/Explicit User's Manual v.6.7.5", 2008.

6

A.L. Sánchez-Merino, "Análisis Sísmico de Dobles Túneles", Ph.D. Thesis, Universidad Carlos III de Madrid, 2009.

7

C.M. St. John, T.F. Zahrah, "Aseismic design of underground structures", Tunnelling and Underground Space Technology, 2(2), 165-197, 1987. doi:10.1016/0886-7798(87)90011-3

8

J.N. Wang, "Seismic design of tunnels: A simple state-of-the-art design approach", Monograph 7, Parsons Brinckerhoff Quade & Douglas Inc., New York, 1993.

9

J. Penzien, "Seismically induced racking of tunnel linings", Earthquake Engineering and Structural Dynamics, 29, 683-691, 2000. doi:10.1002/(SICI)1096-9845(200005)29:5<683::AID-EQE932>3.3.CO;2-T

10

A. Bobet, "Effect of pore water pressure on tunnel support during static and seismic loading", Tunneling and Underground Space Technology, 18(4), 377-393, 2003. doi:10.1016/S0886-7798(03)00008-7

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