Evaluation of the Dynamic Response of Tunnels under the Effect of Surface Blast; Case Study: Line 7 of Tehran Metro

In a case study, behavior of an underground-railway tunnel of the Tehran metro subjected to tremendous explosive load was explored by numerical analysis. Blast wave propagation in the soil is studied by effective stress analysis in PLAXIS 2D finite element code. To assure reliability of the code in performing a robust dynamic calculation, Lamb Problem was modeled by the code and results were compared with analytical solutions, which was satisfactory. Due to the significant effect of the soil type and layering on the dynamic response of the buried structures in an explosive loading, care was taken in the study to resemble the real soil layering, relying on the available geotechnical investigations in the area. Based on the available data and also semi-empirical relations, HS Small soil model was calibrated to resemble soil behavior. In this regard, five parameters of density, elastic modulus, Poisson’s ratio, damping ration and layer thickness were carefully defined for each layer. Semi-empirical relationships were used to calculate soil dynamic shear modulus, which were larger than the static shear modulus. HS Small model has the ability to resemble the cyclic behavior of the soil by applying Masing’s rules in a load-unload-reload cycle. PLAXIS updates the stiffness matrix of the soil mass at each step of the analysis according to the strain and deformations that have been created in the soil, which increases the precision of the calculations. In this study, the Unified Facilities Criteria (UFC 3-340-03) manual was used to calculate the blast pressure. The weight of TNT explosive (charge weight) was considered 510 pounds (230 weight) in this regard. The type of explosion is assumed as an unconfined explosion, i.e., a surface burst. According to the UFC 3-340-03, the graph of changes of explosive pressure with time which is presented as a triangular pulse in the time domain, was defined in applied to the model geometry in the finite element code. Appropriate mesh dimensions relative to the transmitted wave-length in the numerical simulation play an important role in the precision of the results. Consequently, the frequency content of the pressure-time signal was probed in the frequency domain using the Fourier transform technique. To reduce the reflection of the waves from the model boundaries, viscous absorbent boundaries were defined in the model, as well as enlarging the model dimensions to reduce unwanted and unreal reflections from the boundaries of the model as much as possible.
After careful definition of the model geometry and loadings, both static and dynamic calculations were performed. The former simulated the construction of the underground tunnel, and the latter simulated the surface burst after tunnel construction, ignoring the crater caused by the explosion on the surface. The results show that the peak stress at the crown and bottom of the tunnel decreases as the soil density of the first layer increases, irrespective of static or dynamic values of the soil modulus. However, the stress values corresponding to the static parameters are greater than those of dynamic parameters. This comparison shows that if the static shear modulus values are preferred, the tunnel should be designed regarding larger stresses, which is not economical. Despite the decreasing effect of the first layer density on the stress magnitudes, the increase of the density of the second layer -that surrounds the tunnel- increases the stresses at the crown and bottom of the tunnel. The results also revealed that the effect of Poisson’s ratio of the soil on the tunnel's stresses are very small, but with the increase in the damping ratio, the amount of stress in the tunnel crown decreases dramatically. As the soil layers thicknesses increase, stress at the crown of tunnel decreases. These findings are useful to plan a safer design for crowded subway stations, regarding proper soil layering and properties