Earthquake Effects On Tunnels

18 Earthquake effects on tunnels

18.1 General remarks Experience shows that underground structures, especially deep ones, are far less vulnerable to earthquakes than superficial ones. The latter are endangered by earthquakes due to the fact that the motion of the ground can be amplified by the response of the structure to such an extent that the induced strains damage the structure. The earthquake waves can also be amplified within soft superficial strata. In addition, loose water-saturated soil may loose its strength (so-called liquefaction), and this can lead to landslides or failure of foundations and retaining walls. In contrast, deep buried structures, especially flexible ones, are not expected to oscillate independently of the surrounding ground, i.e. amplification of the ground motion can be excluded. This is manifested by the relatively low earthquake damage of tunnels.1 Of course, the portals may be damaged by earthquake-induced landslides. Very revealing on earthquake effects is the report of what happened to the driving of a 7 m diameter tunnel in the underground of Los Angeles during the San Fernando M 6.7 earthquake in 1971:2 ’The earthquake caused an outage of electrical power that caused the tunnel pumps to stop. Amid the attendant confusion and anxiety, the miners made their way to the locomotive and drove 5 miles out of the tunnel in pitch darkness. This means that the rails were not significantly distorted to cause a derailment. However, Southern Pacific Railroad tracks on the surface were distorted and broken.’ Earthquakes can endanger tunnel and other structures if they are buried in loose watersaturated soil that can be liquefied by dynamic excitation. Lique1

Y.M.A. Hashash, J.J. Hook, B. Schmidt, I. I-Chiag Yao, Seismic design and analysis of underground structures. Tunnelling and Underground Space Technology 16 (2001) 247-293 2 R.J. Proctor, The San Fernando Tunnel Explosion, California. Engineering Geology 67 (2002) 1-3

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18 Earthquake effects on tunnels

faction implies a drastic loss of shear strength, the consequence of which can be large displacements of structures. Countermeasures are stone columns or soil improvement by densification or grouting. A point of concern is when a tunnel has to cross an active fault. In this case, the tunnel cross section can be enlarged to accommodate the expected displacement. The latter, however, can hardly be predicted nor can it be easily judged whether a fault is active or not.

18.2 Imposed deformation The main loading of deep tunnels results from their deformation, which may be assumed to be identical with the deformation of the surrounding ground. This assumption implies that the tunnel is infinitely thin and flexible, so that it can be considered as a material line. The distortion of this line results completely from the wave motion of the embedding continuum. For design purposes, this motion must be somehow predicted. This is a very difficult task called seismic hazard analysis. Predictions can be attempted based on deterministic or probabilistic analysis.3 In either case the results are highly uncertain but possibly still the best achievable assumption. Assume now that the wave motion is given. We consider harmonic waves with the circular frequency ω. Non-harmonic waves can be decomposed into harmonic ones. Let the unit vector l denote the direction of wave propagation and let a be the amplitude of oscillation. Then the displacement u of a point with spatial coordinates x is given by the following expressions. Herein, up denotes the p-wave and us denotes the s-wave displacement vectors. 

  l·x up = ap l exp iω t − cp    l·x us = as × l exp iω t − cs cp , cs , ap and as are the corresponding propagation speeds and amplitudes, respectively. Let t be the unit tangential vector at a particular point P of the tunnel axis. Then, the earthquake-induced longitudinal strain and the change of curvature of tunnel can be obtained as: ω a cos2 α c  ω 2 = a cos2 α c

εmax = κmax 3

S.L. Kramer, Geotechnical Earthquake Engineering. Prentice Hall, 1996

18.2 Imposed deformation

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with α being the angle between l and t (see Appendix G). Thus, a joint between two rigid tunnel elements will suffer the elongation s = Lε and the rotation ϑ = κL (Fig. 18.1). Herein, L is the length of each tunnel element.

L s θ

Fig. 18.1. Distortion between two rigid tunnel elements