Seismic Analysis of Infinite Aboveground Pipeline
Considering Hydrodynamic Pressure
Jong Seung Kim
This paper presents a seismic analysis scheme for the infinite aboveground pipeline considering hydrodynamic pressure inside it. The infinite aboveground pipeline is modeled by continuous Euler-Bernoulli beam which is a periodic structure. Dynamic pressure of the fluid inside the pipeline is determined by Housner's fluid-modeling method for the rectangular tank and recommendations of a Study Group of the New Zealand National Society for Earthquake Engineering. In the earthquake ground motion there are two mutually perpendicular horizontal components and vertical one. Generally, stresses in a pipeline produced by vertical ground shaking are relatively small and the primary analysis concerns are horizontal bending deformations. Earthquake ground motion varies both in amplitude and phase propagating through the crust.
For efficient analyses of periodic structures, transfer matrix approach is adopted. Transfer matrix for one single-bay beam is derived taking into account hydrodynamic pressure. One single-bay element is a substructure of the infinite aboveground pipeline. Seismic response of a specific support is represented by displacement of each support and responses of the boundary supports. Since state vector cannot be solved directly due to the numerical instability of the transfer matrix, wave vector is first obtained by the wave-propagation approach using transformation matrix. From the wave number response function and the power spectral density function of the ground motion, the power spectral density function and the root mean square value of the seismic response can be determined.
The validity of this paper is demonstrated through examples of the infinite aboveground pipeline.
Periodic structure, wave number, transfer matrix, state vector, wave-propagation approach, wave vector, hydrodynamic pressure, power spectral density function