Response of a circular tunnel embedded in saturated soil to a series of equidistant moving loads

The dynamic response of an infinitely long circular tunnel embedded in the saturated soil to a series of equidistant moving loads (SEML) is investigated in this study. The saturated soil surrounding the tunnel is described by Biot’s theory. Two scalar potentials and one vector potential are introduc...

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Bibliographic Details
Published in:Acta mechanica 2017-10, Vol.228 (10), p.3675-3693
Main Authors: Lu, Jian-Fei, Ding, Jiang-Jiang, Fan, Zeng, Li, Min-Hao
Format: Article
Language:English
Subjects:
Circularity
Classical and Continuum Physics
Computer simulation
Control
Critical velocity
Dynamic response
Dynamical Systems
Engineering
Engineering Thermodynamics
Fourier transforms
Heat and Mass Transfer
Helmholtz equations
Load
Moving loads
Numerical analysis
Original Paper
Saturated soils
Soil dynamics
Soil investigations
Soils
Solid Mechanics
Theoretical and Applied Mechanics
Tunnels
Vibration
Wavelengths
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Summary:The dynamic response of an infinitely long circular tunnel embedded in the saturated soil to a series of equidistant moving loads (SEML) is investigated in this study. The saturated soil surrounding the tunnel is described by Biot’s theory. Two scalar potentials and one vector potential are introduced to represent the displacement of the solid skeleton and the pore pressure. Based on Biot’s theory, the Helmholtz equations for the potentials are derived using the Fourier transform method. Performing the Fourier transform with respect to the longitudinal coordinate on the Helmholtz equations gives the frequency–wavenumber domain general solutions for the potentials. With the general solutions and the boundary conditions along the tunnel surface, the solution for the circular tunnel subjected to a single moving load (SML) is obtained. Superposition of the solutions for SMLs gives the representation for the response of the tunnel to a SEML, with which the resonance and cancelation conditions for the SEML are derived. Numerical simulations suggest that for the circular infinite tunnel there is a critical velocity. When the load moves with the critical velocity, the frequency domain response of the tunnel exhibits some dominant peak. Further, for a SEML moving with the critical velocity, the resonance and cancelation phenomena in the time domain may occur when the aforementioned resonance and cancelation conditions are fulfilled.
ISSN:0001-5970
1619-6937
DOI:10.1007/s00707-017-1893-5