Advances in Civil Engineering

Volume 2019, Article ID 9650294, 17 pages

https://doi.org/10.1155/2019/9650294

## Vertical Seismic Effect on the Seismic Fragility of Large-Space Underground Structures

^{1}State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China^{2}Department of Structural Engineering and Disaster Reduction, Tongji University, Shanghai 200092, China

Correspondence should be addressed to Qingjun Chen; nc.ude.ijgnot@jqnehc

Received 18 February 2019; Revised 16 March 2019; Accepted 18 March 2019; Published 7 April 2019

Academic Editor: Rosario Montuori

Copyright © 2019 Zhiming He and Qingjun Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The measured vertical peak ground acceleration was larger than the horizontal peak ground acceleration. It is essential to consider the vertical seismic effect in seismic fragility evaluation of large-space underground structures. In this research, an approach is presented to construct fragility curves of large-space underground structures considering the vertical seismic effect. In seismic capacity, the soil-underground structure pushover analysis method which considers the vertical seismic loading is used to obtain the capacity curve of central columns. The thresholds of performance levels are quantified through a load-drift backbone curve model. In seismic demand, it is evaluated through incremental dynamic analysis (IDA) method under the excitation of horizontal and vertical acceleration, and the soil-structure-interaction and ground motion characteristics are also considered. The IDA results are compared in terms of peak ground acceleration and peak ground velocity. To construct the fragility curves, the evolutions of performance index versus the increasing earthquake intensity are performed, considering related uncertainties. The result indicates that if we ignore the vertical seismic effect to the fragility assessment of large-space underground structures, the exceedance probabilities of damage of large-space underground structures will be underestimated, which will result in an unfavorable assessment result.

#### 1. Introduction

Large-space underground structures such as subway stations, commercial streets, and parking lots are wildly used urban construction measures. These structures can suffer severe damage under strong ground shaking [1, 2]. Especially for shallow embedded structures in soft soil, their susceptibility to damage can be increased, due to ground strain and velocity along with acceleration increase when approaching the ground surface [3, 4]. In addition, for some early built large-space underground structures, they are facing a high potential risk of seismic damage due to without properly considering seismic design. Consequently, to ensure the seismic safety of large-space underground structures, especially in seismic prone areas, the seismic fragility assessment is introduced to large-space underground structures by different researchers.

So far, the seismic fragility studies related to large-space underground structures are conducted in different perspectives. Li et al. [5] used the pushover analysis method applicable for underground structures to investigate the vulnerability of Daikai subway station. In this process, the seismic demand calculated from pushover analysis method cannot consider the soil-structure-interaction and the frequency characters of ground motion. Liu et al. [6] investigated the vulnerability of Daikai subway station based on the full dynamic numerical analysis. The performance levels thresholds of aboveground structures were directly applied to underground subway station. Due to the geometric feature and the character which underground structures are buried and restrained by surrounding soil [7, 8], their seismic behavior and performance are highly distinct. Then, Huh et al. [9] investigated the vulnerability of a shallow double story underground RC box structure based on the ground response acceleration method. The performance levels thresholds of structures were defined through the pushover analysis method. In addition, the studies investigated by Castaldo et al. [10, 11] have demonstrated that the existing underground structure can cause a not neglectable increase in the seismic vulnerability of the nearby aboveground R.C structure due to the deep excavation-induced foundations’ displacement.

The present fragility studies of large-space underground structures only consider the horizontal seismic loading. However, there are sufficient evidences to prove that the vertical seismic effect cannot be neglected. For instance, the measured vertical peak ground acceleration was larger than the horizontal peak ground acceleration in the 1995 Kobe earthquake [12]. In the 1994 Northridge earthquake [13], the peak vertical acceleration value of near-field motion reached 1.19 g, and the ratio of vertical-to-horizontal peak ground acceleration exceeded 1.5, significantly greater than 2/3. In addition, it has been proved that the contribution of vertical earthquake component is one of the major factors to the failure of the structure [7, 8, 14–16]. Both Parra-Montesinos [7] and Iida et al. [12] verified that the high axial load induced by the vertical component of ground motion can increase the axial compression ratio and reduce the ductility of central column of large-space underground structures, which is one of the most important factors of collapsing. Study of Nakamura et al. [16] demonstrated that the vertical ground motion caused the compression-bending failure of central columns. An et al. [8] stated that ductility of central column under high compression ratio which was induced by vertical vibration can decrease obviously. Although the vertical component of ground motion was introduced to seismic analysis of large-space underground structures, the existing studies still have not provide the solutions to consider the influence of the vertical seismic effect quantitatively in seismic fragility analysis.

Along these lines, this paper presents a seismic fragility analysis approach for large-space underground structures, which account for the vertical seismic effect. In seismic capacity, the soil-underground structure pushover analysis method which considers the vertical seismic loading is applied to obtain the performance index thresholds. In seismic demand, it is evaluated through incremental dynamic analysis method under the excitation of horizontal and vertical acceleration, the soil-structure-interaction and ground motion characteristics are also considered. To construct the fragility curves, the evolutions of performance index versus the increasing earthquake intensity are performed, considering related uncertainties.

#### 2. Methodology

##### 2.1. Overview of the Proposed Method for Deriving Fragility Curve

The proposed method is based on pushover analysis and incremental dynamic analysis of large-space underground structures, considering the vertical seismic effect, which is described in Figure 1. As the performance levels thresholds of large-space underground structures are not yet documented, one of the crucial tasks in this study is to obtain the thresholds. The existing seismic damage and failure mechanism of typical large-space underground structures demonstrate that central columns are the weakest position of the structure [12, 17]. Therefore, the seismic capacity of the entire structure can be represented by the seismic capacity of the central column. In order to obtain the capacity curve of the central column which can be used to quantify the thresholds of performance levels, the soil-underground structure pushover analysis method [18] is adopted. Because the seismic response of the soil-underground structure system is mainly controlled by the fundamental mode, the inverted triangular distribution that decreases linearly with depth is used for the distribution of body force [18]. This distribution is easy to obtain without ground response analysis, so is more practical than the other types of force distributions. But it should be noted that this pushover analysis method only considering the horizontal seismic loading. To consider the vertical seismic effect, the uniform vertical acceleration distribution [19] is added to the soil-underground structure system as vertical body force distribution, as shown in Figure 2. The influence of the vertical component of ground motion is often introduced by the ratio ( is the peak vertical acceleration and is the peak horizontal acceleration). As many design codes use an average ratio of 2/3 [20], the inputted vertical acceleration is scaled to 2/3 to the inputted horizontal acceleration, and both seismic accelerations are monotonically increasing simultaneously. The pushover analysis procedure is presented as the following sequence of steps:(1)Establish the soil-underground structure analysis model(2)Gravity response analysis: perform the static response of the soil-underground structure analysis model according to the gravity load(3)Pushover analysis: based on the gravity response analysis result, conduct the pushover analysis by monotonically increasing forces using the inverted triangular distribution and uniform vertical acceleration distribution until structure collapse(4)Record data of each analytical step and obtain the capacity curves of the central column