Abstract
Underground tunnels are vulnerable to terrorists’ bombing attacks, which calls for studies on tunnel’s response to internal explosive loading. In this paper, the dynamic response of a cylindrical tunnel to an ideal centric point explosion was treated as an axisymmetric 2-dimensional problem, in which the tunnel was modeled with a continuous anisotropic shell, while the ground medium’s effect was accounted for with linear elastic Winkler springs and the explosive loading described by a temporal and spatial function. The governing equation of the motion is a fourth-order partial differential equation, for which a numerical method combining finite difference with the implicit Newmark-β method was adopted. This method avoided complicated integral transform and numerical inverse transformation, thus allowing efficient parameter study. The maximum radial displacement was found on the cricle of the center of explosive, where hoop stress is the maximum principal stress. The anisotropy showed little influence on maximum hoop stress. Within the range of ground medium’s modulus, minor influence on maximum hoop stress was incurred. This research may be helpful to hazard assessment and protective design for some critical subway tunnels.
Highlights
In recent years, increased terrorist bombing attacks on subway system have been observed [1,2,3]; the most recent one was the notorious 2017 Saint Petersburg subway bombing [4]
As for theoretical investigation, a tunnel’s response to internal blast loads is generally treated as an axisymmetric plane strain problem, where the blast loading is simplified as uniformly distributed loading which keeps constant along the axial direction, and the tunnel is modeled with continuous isotropic thin shell [18,19,20], but this can hardly be the real case since the explosion could not be a centric infinite line charge detonation
An ideal centric point explosion in a cylindrical thin tunnel was simplified as an axisymmetric 2-dimensional problem, in which the tunnel was modeled with a continuous anisotropic shell, while the surrounding ground medium’s effect was accounted for with linear elastic Winkler springs
Summary
In recent years, increased terrorist bombing attacks on subway system have been observed [1,2,3]; the most recent one was the notorious 2017 Saint Petersburg subway bombing [4]. As for theoretical investigation, a tunnel’s response to internal blast loads is generally treated as an axisymmetric plane strain problem, where the blast loading is simplified as uniformly distributed loading which keeps constant along the axial direction, and the tunnel is modeled with continuous isotropic thin shell [18,19,20], but this can hardly be the real case since the explosion could not be a centric infinite line charge detonation Among those theoretical studies, Gao et al [21] studied a 3D problem of point-source explosion’s effects on a long straight cylindrical tunnel in soil. The method developed in this paper may aid in both blast hazard assessment and protective design for some critical part of subway tunnel systems
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