Geoscience Reference
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deformation mechanism for buried pipelines. In this case, the peak ground strain
PGS
a
along thelongitudinal axis
a
of thestructure iscalculated as
PGV
a
κ
PGS
a
=
(18.1)
C
where
PGV
a
isthepeakparticlevelocityalongthe
a
direction,
C
isasuitablemeasureof
wave propagation velocity, and
κ
is a correction parameter to account for maximization
φ
of strain as a function of the angle
formed by the direction of propagation of the plane
wavewithrespecttothelongitudinalaxisofthestructure.Simpletheoreticalderivations,
first reported by Yeh (1974), show that for S-waves
C
=
V
s
,
V
s
being the S-waves prop-
45
◦
.
agation velocity, and
κ
=
2, corresponding to
φ
=
Theappropriateselectionof
and
C
isnotstraightforward,sinceitdependsonthewave
type(P,S,orsurfacewaves),ontheincidenceangleandonthelocalsoilproperties.Fur-
thermore, the available technical guidelines provide some contradictory practical rules.
For example, according to ALA (2001a,b),
C
should be taken as “the apparent propa-
gation velocity for seismic waves (conservatively assumed to be 2km/s)”, while
κ
κ
=
2
for S-waves and
1 otherwise. According to Eurocode 8 Part 4 for buried pipelines
(CEN, 2006),
C
is the “apparent wave speed” and the selection of the wave type shall
be made “based on geophysical considerations”, while it is implicitly assumed
κ
=
1.
A more detailed definition of the above parameters is provided by the French guidelines
AFPS/AFTES (2001), according to which
C
is the apparent wave propagation velocity
that is suggested to be taken as min (1km/s,
V
s
), where
V
s
should be averaged over a
depth equal to the fundamental wavelength, while
κ
=
κ
=
2 to maximize the axial strains
with respect totheincident angle.
Based on the previous indications, the seismic action in a buried pipeline deduced from
theAFPS/AFTESguidelineswouldbeatleasttwotimeslargerthanusingtheALAones,
while a comparison with EC8-Part4 is not straightforward because it implies the arbi-
trary selection of the apparent wave propagation velocity, with values typically ranging
between 2 and 4km/s (seee.g. Abrahamson, 2003).
Therefore, the practical application of eq. (18.1) is subject to numerous, and partly arbi-
trary, assumptions, mainly due to the lack of sound methods for transient ground strain
evaluation and to the lack of a comprehensive set of experimental validations. Referring
to the thorough state-of-art of Zerva (2003), the proper identification of the wave type
andthecorrespondingapparentvelocitymayaccountforoneorderofmagnitudeofvari-
ability in the ground strain estimation, while an additional factor of 2-3 may be due to
spatial incoherence of ground motion (Zerva, 1992).
Besides the proper evaluation of the apparent velocity of wave propagation in eq. (18.1),
a suitable correlation to estimate earthquake-induced transient ground strains should
also account for the different frequency, and hence magnitude, dependence of peak
ground motion parameters and of their possible non-simultaneous occurrence, as will
be shown later in the application to the Duzce case, where
PGS
is carried by late surface
