A semi-analytical model for estimating seismic behavior of buried steel pipes at bend point under propagating waves

A buried pipe extends over long distances and passes through soils with different properties. In the event of an earthquake, the same pipe experiences a variable ground motion along its length. At bends, geometrically a more complicated problem exists where seismic waves propagating in a certain direction affect pipe before and after bend differently. Studying these different effects is the subject of this paper. Two variants for modeling of pipe, a beam model and a beam-shell hybrid model are examined. The surrounding soil is modeled with the conventional springs in both models. A suitable boundary condition is introduced at the ends of the system to simulate the far field. Effects of angle of incidence in the horizontal and vertical planes, angle of pipe bend, soil type, diameter to thickness ratio, and burial depth ratio on pipe strains at bend are examined thoroughly. It is concluded that extensional strains are highest at bends and these strains increase with the angle of incidence with the vertical axis. The pipe strains attain their peaks when pipe bend is around $135^{circ }$ and exceed the elastic limit in certain cases especially in stiffer soils, but remain below the rupture limit. Then equations for predicting the seismic response of the buried pipe at bend are developed using the analytical data calculated above and regression analysis. It is shown that these semi-analytical equations predict the response with very good accuracy saving much time and effort.