Numerical Simulation of Dynamic Response of an Existing Subway Station Subjected to Internal Blast Loading

In order to design and retrofit a subway station to resist an internal blast, the distribution of blast loading and its effects on structures should be investigated firstly. In this paper, the behavior of a typical subway station subjected to different internal blast Ioadings was analyzed. It briefly introduced the geometric characteristics and material constitutive model of an existing two-layer and three-span frame subway station. Then three cases of different explosive charges were consid- ered to analyze the dynamic responses of the structure. Finally, the maximum principal stress, dis- placement and velocity of the columns in the three cases were obtained and discussed. It con- cluded that the responses of the columns are sensitive to the charge of explosive and the distance from the detonation. It＇s also found that the stairs between the two layers have significant effects on the distribution of the maximum principal stress of the columns in the upper layer. The explicit dynamic nonlinear finite element software ANSYS/LS-DYNA was used in this study.

NUMERICAL ANALYSIS OF THE DYNAMICAL BEHAVIOR OF THE EQUATION OF J-J TYPE

In this paper, we have analysed the dynamical behavior of the Josephson Junction equation bynumerical computation and the theory of dynamical systems. As 0<β<2:1+ε, and ρis not sufficientlylarge, we observed the intermittent chaotic behavior and the period-doubling chaotic behavior in whichpeople are very interested recently. This implies the for some β(0<β<2:1+ε), the dynamicalbehavior of the J-J equation is rather complex.

Nonlinear Response of Tunnel Portal under Earthquake Waves with Different Vibration Directions

Tunnel portal sections often suffer serious damage in strong earthquake events.Earthquake waves may propagate in different directions,producing various dynamic responses in the tunnel portal.Based on the Galongla tunnel,which is located in a seismic region of China,three-dimensional seismic analysis is conducted to investigate the dynamic response of a tunnel portal subjected to earthquake waves with different vibration directions.In order to simulate the mechanic behavior of slope rock effectively,an elastoplastic damage model is adopted and applied to ABAQUS software by a self-compiled user material(UMAT)subroutine.Moreover,the seismic wave input method for tunnel portal is established to realize the seismic input under vertically incident earthquake waves with different vibration directions,e.g.,S waves with a vibration direction perpendicular or parallel to the tunnel axis and P waves with a vibration direction perpendicular to the tunnel axis.The numerical results indicate that the seismic response and damage mechanisms of the tunnel portal section are related to the vibration direction of the earthquake waves.For vertically incident S waves running perpendicular to the tunnel axis,the hoop tensile strain at the spandrel and arch foot and the hoop shear strain at the vault and arch bottom are the main contributors to the plastic damage of the tunnel.The strain is initially concentrated around the tunnel foot and spandrel,before shifting to the tunnel vault and bottom farther away from the tunnel entrance.For vertically incident S waves running parallel to the tunnel axis,very large hoop shear strain and plastic damage appear at the tunnel haunches.This strain first increases and then decreases with distance from the tunnel entrance.For vertically incident P waves running perpendicular to the tunnel axis,the maximum damage factor of the slope rock and the maximum plastic strain of the tunnel are significantly lower than for S waves.Moreover,with increasing distance from the tunnel entrance,the plastic damage to the tunnel lining rapidly decreases.

Effect of frequency and flexibility ratio on the seismic response of deep tunnels

Two-dimensional dynamic numerical analyses have been conducted,using FLAC 7.0,to evaluate the seismic response of underground structures located far from the seismic source,placed in either linear-elastic or nonlinear elastoplastic ground.The interaction between the ground and deep circular tunnels with a tied interface is considered.For the simulations,it is assumed that the liner remains in its elastic regime,and plane strain conditions apply to any cross section perpendicular to the tunnel axis.An elastoplastic constitutive model is implemented in FLAC to simulate the nonlinear ground.The effect of input frequency and relative stiffness between the liner and the ground,on the seismic response of tunnels,is evaluated.The response is studied in terms of distortions normalized with respect to those of the free field,and load demand(axial forces and bending moments)in the liner.In all cases,i.e.for linear-elastic and nonlinear ground models,the results show negligible effect of the input frequency on the distortions of the cross section,for input frequencies smaller than 5 Hz;that is for ratios between the wave length and the tunnel opening(k=D)larger than ten for linear-elastic and nine for nonlinear ground.Larger normalized distortions are obtained for the nonlinear than for the linear-elastic ground,for the same relative stiffness,with differences increasing as the tunnel becomes more flexible,or when the amplitude of the dynamic input shear stress increases.It has been found that normalized distortions for the nonlinear ground do not follow a unique relationship,as it happens for the linear-elastic ground,but increase as the amplitude of the dynamic input increases.The loading in the liner decreases as the structure becomes more flexible with respect to the ground,and is smaller for a tunnel placed in a stiffer nonlinear ground than in a softer nonlinear ground,for the same flexibility ratio.