Stress concentration in parallel fluid-filled underground cylindrical pipes under harmonic and recorded seismic excitation

Abstract

Abstract

This paper investigates the dynamic stress concentration in two parallel underground cylindrical pipes filled with a compressible fluid and subjected to seismic excitation. The pipe-soil–fluid system is described as a coupled boundary-value problem within the plane dynamic theory of elasticity, in which each pipe is modelled as a thick-walled, homogeneous, isotropic, linearly elastic cylinder embedded in an infinite elastic medium and filled with an inviscid compressible fluid. The wave field around the two parallel cylinders is represented in bipolar cylindrical coordinates, and the displacement potentials are expanded in cylindrical wave functions of Bessel and Hankel type. Continuity of displacements and tractions at the outer pipe-soil interface, matching of normal velocity and pressure at the inner pipe–fluid interface, regularity at the pipe axis, and the Sommerfeld radiation condition in the surrounding medium are imposed simultaneously, leading to an infinite system of linear algebraic equations whose unknowns are obtained numerically. The model is first verified under harmonic P-, SV-, and SH-wave excitation; it is then extended to realistic seismic loading through an FFT-based transfer-function procedure, in which the harmonic solution serves as the frequency-domain Green operator. Numerical results show that the maximum dynamic stress concentration coefficient under the incident P-wave reaches 1.76 at d / D = 1.0; the limiting non-resonant distance between pipe centres increases from 5.0 m to 10.0 m as the incidence angle changes from 0° to 90°; and the presence of the internal fluid increases the seismic response by 10-20 %. Time-history analysis with the 1940 El Centro NS and 1966 Tashkent records confirms that these trends persist under realistic broadband ground motion. The novelty of the study lies in the simultaneous treatment of pipe–pipe interaction, internal fluid coupling, multiple incident wave types, and recorded seismic input within a single bipolar-coordinate analytical framework. The results are useful for the seismic design and resilience assessment of multi-line buried pipeline systems.