Dynamic Stress-Deformed States of a Circular Tunnel of Small Position Under Harmonic Disturbances

Khamidulla Sagdiyev,Farruh Jalolov,Tulkin Ruziyev,Zafar Boltayev,Uktam Jurayev,D Bazarov

doi:10.1051/e3sconf/202126401028

Abstract

There are many underground tunnels of various shapes located in seismically active areas that need to be protected from seismic impacts. The paper considers the impact of harmonic waves on a cylindrical shell located in a viscoelastic half-plane. The study's main purpose is to determine the stress-strain state of a cylindrical shell when exposed to harmonic waves. The basic equation of viscoelasticity in displacements with the corresponding boundary conditions is obtained. The problem posed is solved in mixed potentials that satisfy the wave equation with complex parameters. The solution is expressed in terms of special Bessel and Hankel functions. As a result of multiple reflections, a system of algebraic equations with complex coefficients is obtained. In the future, this system is solved by the Gauss method with the selection of the main element. The analytical solution is obtained in infinite series, the convergence of which is investigated numerically. The numerical results were obtained using the MATLAB software package. The reliability of the research results is confirmed by good agreement with theoretical and experimental results and those obtained by other authors.

Highlights

To determine the dynamic stress-strain state (SSS) of underground tunnels and pipelines under the influence of seismic loads, various approaches are used [1,2,3]
In the case of a sufficiently extended cavity and the action directed perpendicular to its longitudinal axis, the medium surrounding the cavity and the lining are under plane deformation, and the problem of determining the stress-strain state of the massif and lining is reduced to the plane problem of the dynamic theory of elasticity
It is known that the length of seismic waves λ exceeds the diameters of the cross-sections of the tunnel

Summary

Introduction

To determine the dynamic stress-strain state (SSS) of underground tunnels and pipelines under the influence of seismic loads, various approaches are used [1,2,3]. The first approach, the so-called seismodynamic theory of foundations, was developed [4], which calculates underground tunnels and pipelines. A third approach is the wave theory of the foundation, which is used for calculating underground structures, laid down [11].

Methods

Results

Conclusion