Seismodynamics of Pipelines Interacting with the Soil

Abstract

IntroductionThe first investigations focused on the study of the earthquake resistance of underground pipelines were carried out as long ago as [1950][1951][1952][1953][1954][1955][1956][1957][1958][1959][1960]. It was suggested that damage to pipelines is caused chiefly by the action of a seismic wave travelling along the axis of the pipeline [1][2][3].A number of studies describing damage to underground pipelines occurring in the course of earthquakes then appeared. These studies established the degree of damage and specific fault rate of underground pipelines as a function of the occurrence depth, the soil conditions, geometric dimensions, type of joints, and the influence of the pressure of the contents and the quality of the construction. There exist data on the destructions of underground pipelines that pass through active fractures, ruptures in the ground, areas with collapses, cracks, and water-saturated soil [4][5][6][7][8][9].Modeling of interaction in the system "pipe − soil" is one of the major problems of the seismodynamics of underground pipelines. Statement of problemA mathematical model for the case of movement of the points of a rod subjected to the combined action of longitudinal and transverse forces is presented in [10]. A system of equations describing the motion of a linear underground pipeline based on the Hamilton-Ostrogradskii variational principle with arbitrary direction of the seismic wave relative to the axis of the pipeline was obtained in [3,4]. On the basis of certain assumptions [10], the pipeline is modeled in the form of a rod and the displacements are selected as follows:where u 1 and u 2 are the displacements of sections of the pipeline; u and w are longitudinal and transverse displacements; and α 1 is turning angle of a section of pipe.A system of equations describing the oscillations of a rectilinear pipeline that interacts with the surrounding soil in the case of seismic action functioning in an arbitrary direction is presented. A numerical implementation of problems related to the determination of the mode of deformation of a pipeline experiencing seismic movement of the soil is performed.

Vibrations of a Girder on Rigid Supports of Finite Mass Interacting With Soil under Seismic Loads

“…This article aims to study the transverse vibrations of a single-span girder bridge, the pile part of which interacts with the surrounding soil under seismic action Academician T. Rashidov has developed a dynamic theory of seismic resistance of complex systems of underground structures based on considering the difference in strains of a structure and soil [16][17]. Several scientists in our country and abroad have researched the problems of seismic resistance of underground and surface structures interacting with surrounding soil [18][19][20][21][22][23]. To assess the reliability and bearing capacity of road girder bridges on supports, in addition to the moving loads acting on the girder, we should take into account the forces transmitted through the girder supports related to the impact of, for example, seismic waves.…”

Underground polymeric l-shaped pipeline vibrations under seismic effect

“…To derive a system of differential equations of motion with boundary and initial conditions, the Hamilton -Ostrogradsky variational principle was used [16][17][18]  …”

Study of the seismodynamics of spatially located underground pipelines with a nodal connection of non-orthogonal configuration

“…The seismic motion of the Earth's crust contributes to the appearance of substantial horizontal and vertical strains in soil that can lead to accidents in underground pipelines [1][2][3][4].…”