18

Earthquake effects on tunnels

18.1 General remarks

Experience shows that underground structures, especially deep ones, are farless vulnerable to earthquakes than superficial ones. The latter are endangeredby earthquakes due to the fact that the motion of the ground can be amplifiedby the response of the structure to such an extent that the induced strainsdamage the structure. The earthquake waves can also be amplified within softsuperficial strata. In addition, loose water-saturated soil may loose its strength(so-called liquefaction), and this can lead to landslides or failure of foundationsand retaining walls. In contrast, deep buried structures, especially flexibleones, are not expected to oscillate independently of the surrounding ground,i.e. amplification of the ground motion can be excluded. This is manifested bythe relatively low earthquake damage of tunnels.1 Of course, the portals maybe damaged by earthquake-induced landslides. Very revealing on earthquakeeffects is the report of what happened to the driving of a 7 m diameter tunnelin the underground of Los Angeles during the San Fernando M 6.7 earthquakein 1971:2

’The earthquake caused an outage of electrical power that caused thetunnel pumps to stop. Amid the attendant confusion and anxiety, theminers made their way to the locomotive and drove 5 miles out ofthe tunnel in pitch darkness. This means that the rails were not sig-nificantly distorted to cause a derailment. However, Southern PacificRailroad tracks on the surface were distorted and broken.’

Earthquakes can endanger tunnel and other structures if they are buried inloose watersaturated soil that can be liquefied by dynamic excitation. Lique-

1Y.M.A. Hashash, J.J. Hook, B. Schmidt, I. I-Chiag Yao, Seismic design and anal-ysis of underground structures. Tunnelling and Underground Space Technology 16(2001) 247-293

2R.J. Proctor, The San Fernando Tunnel Explosion, California. Engineering Ge-ology 67 (2002) 1-3

338 18 Earthquake effects on tunnels

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

18.2 Imposed deformation

The main loading of deep tunnels results from their deformation, which maybe assumed to be identical with the deformation of the surrounding ground.This assumption implies that the tunnel is infinitely thin and flexible, so thatit can be considered as a material line. The distortion of this line resultscompletely from the wave motion of the embedding continuum. For designpurposes, this motion must be somehow predicted. This is a very difficulttask called seismic hazard analysis. Predictions can be attempted based ondeterministic or probabilistic analysis.3 In either case the results are highlyuncertain but possibly still the best achievable assumption.Assume now that the wave motion is given. We consider harmonic waveswith the circular frequency ω. Non-harmonic waves can be decomposed intoharmonic ones. Let the unit vector l denote the direction of wave propagationand let a be the amplitude of oscillation. Then the displacement u of a pointwith spatial coordinates x is given by the following expressions. Herein, up

denotes the p-wave and us denotes the s-wave displacement vectors.

up = ap l exp

[iω

(t− l · x

cp

)]

us = as × l exp

[iω

(t− l · x

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 thetunnel axis. Then, the earthquake-induced longitudinal strain and the changeof curvature of tunnel can be obtained as:

εmax =ω

ca cos2 α

κmax =(ωc

)2

a cos2 α

3S.L. Kramer, Geotechnical Earthquake Engineering. Prentice Hall, 1996

18.2 Imposed deformation 339

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

θ

sL

Fig. 18.1. Distortion between two rigid tunnel elements