**by M. O'Rourke**

*This article presents research resulting from NCEER's Lifeline Project. Comments and
questions should be directed to Michael O'Rourke, Rensselaer Polytechnic Institute, at
(518) 276-6933; or email: orourm@rpi.edu.*

For buried pipelines, seismic impacts can be classified as being either due to wave propagation (i.e., transient strain and curvature in the ground due to traveling wave effects) or permanent ground deformation (i.e., landslides, liquefaction-induced lateral spread, etc.). There have been some events where pipe damage has been due only to wave propagation. One example is damage in Mexico City occasioned by the 1985 Michoacan earthquake. More typically, pipeline damage is due to a combination of hazards. This was the case in the 1906 San Francisco event and more recently in the 1994 Northridge event.

Herein the seismic behavior and response of buried pipelines subject to wave propagation (WP) are reviewed. Specifically, empirical relations for estimating WP damage, procedures for quantifying the WP hazard and methods for determining response parameters of interest are presented.

**Empirical Damage Relations**

Often the first step in the seismic upgrade of a pipeline system is an evaluation of the likely amounts of damage in the existing system due to potential future earthquakes. For buried pipelines, empirical correlations between observed seismic damage (typically repairs per unit length of pipe) and some measure of ground motion are typically used. For example, based upon data from four U.S. and two Mexican events, O'Rourke and Ayala (1993) prepared a plot, shown in figure 1, of wave propagation damage rate versus peak ground velocity. This figure applies to cast-iron, concrete, prestressed concrete and asbestos cement pipe.

**Wave Propagation Hazard**

For the analysis and design of buried pipelines, the effects of seismic wave
propagations are typically characterized by the induced ground strain and curvature.
Newmark (1967) developed a simplified procedure to estimate the ground strain. He
considered a simple traveling wave with a constant wave shape. That is, on an absolute
time scale, the acceleration, velocity and displacement time histories of two points along
the propagation path are assumed to differ only by a time lag, which is a function of the
separation distance between the two points and the speed of the seismic wave. For such a
case, he showed that the maximum ground strain *E _{g}* (tension and
compression) in the direction of wave propagation is given by:

(1)

where *V _{m}* is the maximum horizontal ground velocity in the direction
of wave propagation and

Similarly, the maximum ground curvature, *k _{g}*, is given by:

(2)

where *A _{m}* is the maximum ground acceleration perpendicular to the
direction of wave propagation.

These two relations for ground strain and curvature along the direction of wave
propagation are relatively straightforward. The ground motion parameters *V _{m}*
and

**Propagation Velocity**

In terms of propagation velocity, two types of seismic waves are considered: body waves and surface waves. Body waves propagate through earth, while surface waves travel along the ground surface. The body waves (P-waves and S-waves) are generated by seismic faulting, while for the simplest case, surface waves (L-waves and R-waves) are generated by the reflection and refraction of body waves at the ground surface.

**Body Waves**

For body waves, only S-waves are typically considered since they carry more energy and
tend to generate larger ground motion than P-waves. For vertically incident S-waves, the
apparent propagation velocity is infinity. However, there is typically a small angle of
incidence in the vertical plane leading to non-zero horizontal ground strain. O'Rourke et
al. (1982) have studied the apparent horizontal propagation velocity, *C*, for body
waves utilizing a ground motion intensity tensor, for evaluating the angle of incidence of
S-waves. The apparent propagation velocity for S-waves is then given by:

(3)

where * _{s}*
is the incidence angle of S-waves with respect to the vertical and

Event | Focal Depth (km) |
Epicentral Distance (km) |
C (km/s) |
Method for Calculating C |
---|---|---|---|---|

Japan 1/23/68 |
80 | 54 | 2.9 | (1) |

Japan 7/1/68 |
50 | 30 | 2.6 | (1) |

Japan 5/9/74 |
10 | 140 | 5.3 | (1) |

Japan 7/8/74 |
40 | 161 | 2.6 | (1) |

Japan 8/4/74 |
50 | 54 | 4.4 | (1) |

San Fernando 2/9/71 |
13 | 29 to 44 | 2.1 | (2) |

Imperial Valley 10/15/79 |
Shallow | 6 to 57 | 3.8 | (2) |

Imperial Valley 10/15/79 |
Shallow | 6 to 93 | 3.7 | (3) |

(1) Cross-correlation for array with common time | ||||

(2) Ground motion intexsity tensor (median value) | ||||

(3) Epicentral distance vs. initial S-wave travel time | ||||

Table 1: Summary of Apparent Horizontal Propagation Velocities |

Table 1 shows results by the ground motion intensity method for the 1971 San Fernando and the 1979 Imperial Valley events as well as values for other events from more direct techniques. Note that the apparent propagation velocity for S-waves ranged from 2.1 to 5.3 km/sec with an average of about 3.4 km/sec.

**Surface Waves**

For surface waves, only R-waves are typically considered since L-waves generate bending
strains in buried pipelines which, particularly for moderate pipe diameters, are
significantly less than axial strain induced by R-waves. R-waves cause the ground
particles to move in a retrograde ellipse within a vertical plane. The horizontal
component of the ground motions for R-waves is parallel to the propagation path and thus
will generate axial strain in a pipe lying parallel to the direction of wave propagation.
Since R-waves always travel parallel to the ground surface, the phase velocity of the
R-waves, *C _{ph}*, is the apparent propagation velocity.

The phase velocity is a function of the variation of the shear wave velocity with
depth, and, unlike body waves, is also a function of frequency. For R-waves, the
wavelength , frequency *f *and
the phase velocity *C _{ph}* are interrelated by:

(4)

The variation with frequency is typically quantified by a dispersion curve. For example, O'Rourke et al. (1984) developed a simple procedure for determining the dispersion curve for layered soil profiles in which the shear wave velocity increases with depth. Figure 2 shows a comparison of the exact dispersion curve for the two layers over a half space soil profile and the approximate curve based on the O'Rourke et al. (1984) approach.

**Response of Continuous Pipe**

Simplified procedures for assessing continuous pipe response due to wave propagation assume that pipeline inertia terms are small and may be neglected. Experimental evidence from Japan as well as analytical studies (Shinozuka and Koike, 1979) indicate that this is a reasonable engineering approximation.

Hence, for low levels of seismic excitation, the pipe strain is essentially equal to the ground strain. However, for higher levels of seismic excitation, slippage of the pipe-soil interface results in pipe strain being a function of both ground strain as well as length over which friction forces at the soil-pipe interface exist.

For example, O'Rourke and ElHmadi (1988) developed an analysis procedure to estimate maximum pipe strain for R-wave excitation. This procedure compares axial strain in the soil to the strain in a continuous pipeline due to soil friction along its length. It is assumed that the soil strain is due to R-waves propagating along the pipe axis. The soil strain is a decreasing function of separation distance or wavelength. The pipe strain due to the friction at the pipe-soil interface is an increasing function of separation distance or wavelength. At a particular separation distance (that is, for a particular wavelength), the friction strain matches the soil strain. The unique strain then becomes an estimate of the peak strain induced in a continuous pipeline as shown in figure 3.

Subsequently, O'Rourke and Ayala (1990) applied this procedure to a welded steel water pipeline in Mexico City which suffered local buckling failure due to the 1985 Michoacan earthquake. Note that this case history is one of the few instances of wave propagation damage to corrosion-free steel pipe with modern (arc-welded) joints. The procedure correctly estimated the distance between failure locations. In addition, the estimated pipe stress was very close to (within 4%) the expected pipe failure stress.

**Response of Segmented Pipe**

For a long straight run of segmented pipe, the ground strain is accomplished by a
combination of pipe strain and relative axial displacement (expansion/contraction) at pipe
joints. Since the overall axial stiffness for segments is typically much larger than the
joints, ground strain results primarily in relative displacement of the joints. As a first
approximation, the maximum joint movement *U* is:

(5)

where *L _{o}* is the pipe segment and

Although equation (5) holds on average, it is not useful in predicting damage since it assumes uniform behavior from joint to joint. In reality, even relatively heavy damage to buried pipe corresponds to only one in 500 or one in 1000 joints requiring repair (i.e., not every joint).

ElHmadi and O'Rourke (1990) developed a more realistic approach by considering the actual variation in joint properties from joint to joint.

A quasistatic approximation to the seismic wave propagation environment is modeled by displacing the base of soil spring sliders in the longitudinal direction. A simplified Monte Carlo simulation technique is used to establish the probability density function for the relative joint displacement. As shown in figure 4, although the average joint behavior is reasonably estimated by equation 5, one in every 1000 (0.1% probability of exceedence) has a much larger relative displacement.

Subsequently, O'Rourke and Bouabid (1996) applied this approach to concrete pipe damage in Mexico City due to the 1985 Michoacan event. The procedure correctly identified the predominant failure mode (telescopic crushing at the joints) and provided a "ball park" estimate of the damage ratio (estimated damage ratio of 0.3 to 0.5 repairs per kilometer compared to observed value of 0.2 repairs per kilometer).

**References**

*ElHmadi, K. and O'Rourke, M.J., (1990), "Seismic Damage to Segmented Buried
Pipelines," Earthquake Engineering and Structural Dynamics, Vol. 19, pp. 529-539, May
1990.*

*Newmark, N.M., (1967), "Problems in Wave Propagation in Soil and Rocks,"
Proceedings of International Symposium on Wave Propagation and Dynamic Properties of Earth
Materials, Albuquerque, NM, pp. 7-26.*

*O'Rourke, M. and Bouabid, J., (1996), "Analytical Damage Estimates for Concrete
Pipelines," paper no. 346, 11th World Conference on Earthquake Engineering, Acapulco,
Mexico.*

*O'Rourke, M.J. and Ayala, G., (1990), "Seismic Damage to Pipeline: Case
Study," Journal of Transportation Engineering, ASCE, Vol. 116, No. 2, pp. 123-134,
March/April, 1990.*

*O'Rourke, M.J. and Ayala, G., (1993), "Pipeline Damage Due to Wave
Propagation," Journal of Geotechnical Engineering, ASCE, Vol. 119, No. 9, September
1993.*

*O'Rourke, M.J. et al., (1984), "Horizontal Soil Strain Due to Seismic
Waves," Journal of Geotechnical Engineering, Vol. 110, No. 9, pp. 1173-1187,
September 1984.*

*O'Rourke, M.J., Bloom, M.C., and Dobry, R., (1982), "Apparent Propagation
Velocity of Body Waves," Earthquake Engineering and Structural Dynamics, Vol. 10, pp.
283-294.*

*O'Rourke, M.J. and ElHmadi, K.E., (1988), "Analysis of Continuous Buried
Pipelines for Seismic Wave Effects," Earthquake Engineering and Structural Dynamics,
Vol. 16, pp. 917-929.*

*Shinozuka, M. and Koike, T., (1979), "Estimation of Structural Strains in
Underground Lifeline Pipes," PVP-34, ASME.*

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