عنوان مقاله [English]
In this paper, the seismic response of Tabriz subway tunnel line 2, located in the high seismic activity area in the northwest of Iran, was studied by using the two-dimensional finite difference program FLAC 7.0. The dynamic time history analyses of the coupled tunnel-soil system were carried out under plane strain conditions. The tunnel lining is made of segments of precast concrete with a thickness of 0.35 m and length of 1.50 m installed behind the shield of the earth pressure balance TBM. In the study area of the path, the type of the soil is mostly GM and SM, and the water level is approximately 10 m under the ground surface. By considering the location of Tabriz subway tunnels that are close to the Tabriz north fault, the characteristics of three near-field earthquakes, Kocaeli, Kobe, and Chi-Chi, were used for the numerical analysis.
In this study, the tunnel was meshed by linear elements, whereas the soil was modeled with quadratic plane-strain elements. The linear elastic model was assumed for the tunnel behavior, while the combined hysteretic total-stress constitutive model (UBCHYST) was used to model the soil behavior. This constitutive model simulates nonlinear cyclic behavior containing degradation of shear modulus with shear strain and strain-dependent damping ratio. Modulus degradation and damping curves proposed by Darendeli were used for calibrating the UBCHYST model parameters.
Based on the sensitive analysis, the width and height of the model were selected 80 m and 50 m, respectively. The free-field boundary was assigned to the lateral boundaries so that it supplies similar conditions to that of an infinite model. The interaction effects of soil-lining were also taken into account by applying interface elements. In addition, in dynamic analyses, seismic ground motions related to the shear waves were applied to the base of the models as a function of time.
Generally, the model analysis was conducted in three phases. First, the soil elements were loaded under a geostatic condition to obtain the natural steady state. These values were used as initial stress for the next calculations. Then, the concrete lining was placed in the soil, the interface properties were applied and thus, the model was analyzed again. In the static analysis, the soil-lining system was under gravity loading only, the base boundary was fixed in all directions and the side boundaries were fixed in the x-direction. Finally, the seismic analysis was carried out.
According to the performed analyses, the natural frequencies of the soil layers and the soil-tunnel system were obtained 3.50 and 3.46 Hz, respectively. Therefore, the existence of the tunnel inside the soil decreases the natural frequency of the system. Also, the ratio of calculated acceleration at the different depths to the base acceleration along the tunnel is generally larger than one, which indicates the tendency of the model to amplify the base signal moving toward the ground surface.
The Kobe earthquake with two peak ground accelerations (PGA=0.175g and 0.35g) was chosen as the input seismic load applied to the model base for evaluating the impact of the earthquake maximum amplitude. According to the analysis results, by increasing the earthquake maximum amplitude, the ground surface settlement increase as well. In addition, dynamic axial force and bending moment caused in the lining tunnel increase by increasing peak ground acceleration and ground surface displacement during earthquake. It should be noted that a dependence of the increment of bending moment and axial force on the ground surface settlement was observed. Also, at the end of the analysis, the residual axial force remaining in the lining is the same for both earthquakes.
In order to study the effects of earthquake frequency content, acceleration time history of three earthquakes (Kocaeli, Kobe, and Chi-Chi) with different predominate period (1.40, 0.16 and 0.93sec, respectively) and the constant PGA (0.35g) were applied to the model. Based on the analysis results, for a given PGA, not only decreasing the predominate frequency of earthquake has the effect on increasing of internal forces, but also other earthquake characteristics such as ground displacement and energy density of earthquake have their own effects. Furthermore, large residual values were observed after each earthquake for dynamic bending moments because of cumulative strains during the earthquake, but smaller residual values were observed after each earthquake for the dynamic axial forces. Moreover, the peak values of the dynamic bending moment are shown near the crown and the shoulders of the tunnel.