An equation for estimating the maximum normal strain of buried steel pipes in bend area under propagating waves in sands

The possible vulnerability of pipelines under propagating waves, especially in bend areas, emphasizes the need for much research in this context. Although beam and beam-shell hybrid models are usually used in the studies conducted in this eld, the current study employs a continuum model. To this end, the bent pipe was modeled using shell elements, and suitable boundary conditions were taken into account to simulate the in nite length of the pipe away from the bend. The soil around the pipe was also modeled using 3D elements in compliance with the Mohr-Coulomb rule of behavior. In addition, equivalent boundary conditions were imposed on the boundaries of the soil domain where it is truncated. The properties of the pipe-soil model varied so that they were investigated under seven di erent ground motions, and the maximum axial strain was calculated in the bend area. The e ects of di erent parameters including incidence angle of seismic waves, bend angle, ratio of pipe diameter to wall thickness, and physical properties of soil were also evaluated. Based on the results of analysis and regression, an equation was proposed for estimating the maximum normal strain of the buried pipes in the bend area with good accuracy.