Abstract

Serious damage of the Dakai stations with accompanying life and economic loss in the 1995 Hanshin earthquake in Japan[1]clearly shows that the seismic performance assessment of underground structures is of particular importance.In recent years,there has been an increasing tendency in structural design codes and seismic design guidelines to move toward adoption of performance-based design approaches[2].Seismic response prediction and assessment of structures is the one of core contents in the performance-based earthquake engineering.At present,the conventional methods for seismic performance assessment of the underground structures include nonlinear static Pushover analysis[3-5]and incremental dynamic analysis(IDA)[6].However,the pushover method adopts a static approach to analyze a dynamic problem,which fails to capture the dynamic characteristics of the soil-structure interaction system and the uncertainties of the ground motions.The IDA method uses full nonlinear dynamic analyses with its limitations of high computational cost and low efficiency.

The endurance time method(ETM)is an efficient seismic performance evaluation method characterized by developing series of seismic response spectra compatible acceleration time histories whose amplitudes increase with the duration[7-9],as shown in Figure 1.Those endurance acceleration time histories are subsequently used as the input for engineering structures to perform nonlinear dynamic analyses.ETM can effectively capture the entire dynamic response of the structure from elastic to plastic till finally collapse,and can be used as an alternative approach to evaluate the seismic performance of structures.

Figure 1　An ET acceleration function(ETAF)

Figure 2　2 D integrated finite element model of soil-structure interaction system

This paper used Dakai subway station as a case study.Two-dimensional finite element model was established using the open source computer program,OpenSees,considering nonlinear dynamic soil-structure interaction,as shown in Figure 2.The nonlinear beam-column fiber element was employed for the underground structure and four-node plane strain quad element was employed for the soil.The mechanical behavior of concrete and steel was modeled using the Kent-Scott-Park and the Giuffré-Pinto constitutive model,respectively.The mechanical behavior of sand and clay was simulated by using the Pressure Depend Multi Yield material and Pressure Independ Multi Yield material in OpenSees,respectively.The soil domain was truncated at a width of 102 m(6 times of the width),where the lateral boundaries are sufficiently far from the underground structure so as to eliminate the influence of the boundary ef fects on the seismic response of the underground structure.Moreover,horizontal kinematic constraints were introduced to the nodes on two side boundaries to ensure the same horizontal movement of the two nodes at the same burial depth and effectively simulate the shear deformations of the soil layers under upward propagation of inplane waves.

Three endurance time acceleration functions were generated based on the design response spectra of Chinese seismic design code and a set of 15 real ground motion records were selected from the PEER-NGA database.The seismic response of the Dakai subway station subjected to three ETAFs and 15 real ground motions were compared and investigated in this study.

The numerical results show that the responses of endurance time analyses generally fall between the envelopes of the incremental dynamic analyses of 15 real ground motions.The average response of the subway station using ETM is also in good agreement with the average results using IDA,as shown in Figure 3.Besides,the response spectrum corresponding to the fundamental period of the soilstructure interaction system is more preferable than the peak ground acceleration as the seismic intensity measure for the performance evaluation of the underground structures,as shown in Figure 3.Overall,the endurance time analysis provides a new computationally efficient alternative for seismic performance evaluation of the underground structures other than the traditional nonlinear IDA.

Figure 3　Comparison of ETM and IDA results