Seismic risk assessment for oil and gas pipelines - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 688

25.6.1 Wave propagation strain
Pioneering work by Newmark (1967) still serves as the basis for estimating
strains in pipelines arising from wave propagation. The Newmark approach
has been incorporated, with minor modifi cations, into many guideline docu-
ments (ASCE, 1984; ALA, 2001a; Honegger and Nyman, 2004). The basic
formulation of the Newmark approach for shear waves is provided in Equa-
tion 25.1:

V
C

ε = [25.1]

α

where

ε = axial pipe strain,

V = peak horizontal ground velocity,

C = apparent shear wave propagation velocity (inverse of slowness between

earthquake source and site),

α = coeffi cient dependent upon the incidence of the wave with the pipeline

(2 for strain in a pipeline from shear waves, 1 for ground strain).

The inverse of the apparent propagation velocity (1/ C in Equation 25.1)
is termed 'slowness' in seismology and is often noted by the variable ' p '.
Tables of slowness are available in regions where detailed earthquake loca-
tion studies have been undertaken and the value generally ranges from
0.2 s/km to 0.5 s/km. If such tables are not available, it is conservative to
adopt the propagation velocity in bedrock at depth for the apparent propa-
gation velocity. More detailed discussion of the phenomenon of wave prop-
agation is provided in Litehiser et al. (1987). Litehiser et al. (1987) note two
important fi ndings with respect to the application of Equation 25.1. There
is a potential for amplifi cation of strain associated with surface soil layers
compared with rock of approximately 1.5 to 2. There is also the possibility
of further increased amplifi cation, on the order of two times as great as the
above, when the shear response of the surface soil layers is closer to being
linear (i.e., for small ground motions) as opposed to an amplifi cation on
order of 1.5 when the soil response is nonlinear (i.e., for large ground
motions).
The two fi ndings from Litehiser et al. (1987) are consistent with Paolucci
and Smerzini (2008) who determined variations of maximum ground strain
for weak to moderate ground motions (most of the data from sites with
peak horizontal ground velocities far less than 30 cm/s and peak ground
accelerations less than 0.4 g ) that were two to three times greater than what
would be obtained assuming an inverse slowness of 2000 m/s.
Based upon Equation 25.1, it is clear that wave propagation strains are
exceedingly small. Considering the largest ground velocities recorded are