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107 action plays a critical role in the evaluation of the effect of seis- mic loading for both flexible and rigid culverts and pipes. A unified evaluation procedure is developed in this chapter to provide a rational and reliable means for seismic evaluations as well as realistic design for buried culvert and pipe structures. 9.3.1 Ground Shaking Ground shaking refers to the vibration of the ground pro- duced by seismic waves propagating through the earth's crust. The area experiencing this shaking may cover hundreds of square miles in the vicinity of the fault rupture. The intensity of the shaking attenuates with distance from the fault rupture. Ground shaking motions are composed of two different types of seismic waves, each with two subtypes: Body waves travel within the earth's material. They may be either longitudinal compressional (P-) waves or transverse shear (S-) waves, and they can travel in any direction in the ground. Surface waves travel along the earth's surface. They may be Figure 9-2. Ovaling and racking deformations. either Rayleigh waves or Love waves. The axial and curvature deformations are induced by com- As stable ground is deformed by the traveling waves, any ponents of seismic waves that propagate along the culvert or culverts or pipelines in the ground also will be deformed. The pipeline axis. Figure 9-1 shows the idealized representations of shaking or wave traveling induced ground deformations are axial and curvature deformations. The general behavior of the called transient ground deformations. linear structure is similar to that of an elastic beam subject to When subject to transient ground deformations, the re- deformations or strains imposed by the surrounding ground. sponse of a buried linear culvert or pipe structure can be de- Current design and analysis methodologies for pipeline scribed in terms of three principal types of deformations: systems were developed typically for long, linear structures. (1) axial deformations, (2) curvature deformations (refers The principal failure modes for long, continuous pipeline struc- to Figure 9-1), and (3) ovaling (for circular cross section) or tures consist of (1) rupture due to axial tension (or pull out for racking (for rectangular cross section) deformations (refers jointed segmented pipelines), and (2) local bucking (wrinkling) to Figure 9-2). due to axial compression and flexural failure. If the pipelines are buried at shallow depth, continuous pipelines in com- pression also can exhibit beam-buckling behavior (that is, global bucking with upward buckling deflections). If the axial stiffness of the structures is large, such as that for a large sec- tional concrete pipe, then the buckling potential in the longi- tudinal direction is small for both local buckling and global buckling. The general failure criteria for the above-mentioned potential failure modes have been documented by previous studies (O'Rourke and Liu, 1996). It should be noted, however, that typical culvert structures for transportation applications are generally of limited length. For this condition, it is in general unlikely to develop signifi- cant transient axial/curvature deformations along the culvert structures. The potential failure modes mentioned above are not likely to take place during the earthquake. The main focus of this chapter will not be on the effects of axial/curvature de- formations. Instead, the scope of this chapter will concentrate Figure 9-1. Axial and curvature deformations. on transverse deformations of culverts and pipes.