Virtual hybrid simulation method for underground structures subjected to seismic loadings

https://doi.org/10.1016/j.tust.2021.103831Get rights and content

Highlights

  • Virtual hybrid simulation framework is established based on OpenSees and OpenFresco.

  • Nonlinear features of the soil-structure system are captured during emulation.

  • The Daikai station is applied to validate the effectiveness of the framework.

  • Two substructure schemes are presented under different levels of earthquake motion.

Abstract

Current knowledge on seismic analysis of underground structures is limited to analytical solutions, numerical methods and scaled model tests. Virtual hybrid simulation (VHS) is an efficient and economical analysis method that combines numerical approaches and experiment methods while taking the advantages of both. In this study, a VHS method employing a multi-axial experimental setup for seismic analysis of soil-structure systems is proposed and the corresponding VHS framework was developed using OpenFresco and OpenSees. To demonstrate the ability of the VHS method in accurately and efficiently capturing seismic behavior of underground structures, the proposed VHS method was applied to evaluate seismic response of the Daikai subway station, during which a good agreement was achieved when comparing the VHS results with those of the complete numerical simulation (CNS). Moreover, the advantages of the expanded multi-axial experimental setup in the proposed VHS method over the simplified single-DOF experimental setup are evaluated and discussed.

Introduction

In recent earthquakes, underground structures in seismically active areas were subjected to extensive damage. For example, the Daikai subway station collapsed in the 1995 Hyogoken-Nambu earthquake in Japan, which attracted significant attentions to the seismic analysis of underground structures. Currently, seismic response evaluations of underground structures are mainly relied on analytical or numerical methods (Wang et al., 2017, Zhao et al., 2019, Chen et al., 2020, Zakian, 2017, Miao et al., 2018, Zhao et al., 2019) and scaled model tests (Zhang et al., 2019a, Zhang et al., 2019b, Chen et al., 2020, Yu et al., 2018). Generally, assumptions and simplifications of numerical models are required in analytical formulations to reach a solution (Liang et al., 2020, Yu et al., 2019, Yu et al., 2020, Yang et al., 2020, St. John and Zahrah, 1987, Hashash et al., 2001), while design of structural system requires numerical methods (Pitilakis et al., 2014) to account for the structural details and non-linear behaviors. However, numerical methods in many cases fail to capture complex behavior or failure modes at structural system levels. Alternatively, shaking table and centrifuge tests are carried out to determine the dynamic response of underground structures and to validate or develop numerical approaches. Nevertheless, small-scale structural models are tested in these experiments due to the limited size and capacity of loading equipment, resulting in difficulties to accurately replicate seismic behaviors of underground structures. Virtual hybrid simulation (VHS) combines numerical approaches and experimental methods while taking the advantages of both, making it an efficient alternative to predict seismic responses of underground structures.

Hybrid simulation, also named as the substructure pseudo-dynamic (PSD) testing method, was originally proposed by Hakuno et al. in 1969 (Hakuno et al., 1969). In the process of a hybrid simulation, the most critical portion of a structural system with uncertain nonlinear behavior is experimentally tested in a laboratory, while the remainder of the structure whose behavior can be predicted numerically with confidence, is simultaneously analyzed using a finite element software application (Schellenberg et al., 2017). Being developed for decades, hybrid simulation technique has improved in several aspects, including expanding implementation scope, improving accuracy and stability of integration algorithms, developing robust control strategy to compensate undesired hydraulic equipment dynamics and devising flexible hybrid simulation software platforms for both local and distributed hybrid simulation (Shao and Griffith, 2013). Until now, hybrid simulation has mainly been adopted for seismic evaluation of superstructures. When being applied to evaluate seismic performance of underground structure, the soil-structure interaction (SSI) must be considered as it significantly affects the response of underground structures. Shao et al., 2010, Stefanaki et al., 2015 proposed a hybrid simulation method using both shaking table and dynamic actuators to investigate the SSI. However, real-time dynamic control and implementation of boundary conditions remain to be challenging (Nakata and Stehman, 2012). Sakai et al., 2005, Yang et al., 2019, Cai et al., 2020 explored to apply hybrid simulations to underground structures, where the column was selected as the physical substructure. A simplified substructure loading scheme based on an assumed inflection point on the column was adopted in their studies, and thus only the tangential response at the inflection point was simulated using the simple One-DOF loading setup. Note, however, that, such a simplified substructure loading scheme has shortcomings for the hybrid simulation of underground structures subjected to intense earthquake motions, due to the fact that large nonlinear responses arising from strong motions cannot be captured using the simplified loading scheme. The aim of the paper is therefore to address these issues.

In this paper, a novel generalized VHS method for underground structures is developed with the function extension from the One-DOF scheme to the Three-DOF scheme by incorporating a multi-axial ExpSetup into the VHS framework. Both the physical and numerical substructures are modelled by the finite element software OpenSees, and the continuous data exchange between the two substructures is carried out by the middleware OpenFresco. The VHS framework is then applied to the soil-structure system of the Daikai subway station. The intermediate column of the station, which was seriously damaged in the 1995 Kobe strong earthquake, is selected as the physical substructure, while the rest of the structure and surrounding soil are assumed as the numerical substructure. The validation of the proposed VHS framework is done by comparing its predictions with those of the complete numerical simulation (CNS). The advantage of the proposed scheme with a multi-axial loading setup over the simplified One-DOF loading setup in capturing tangential, axial and rotational responses of the column under strong seismic motions is further discussed.

Section snippets

VHS method

Virtual hybrid simulation (VHS) is carried out with both numerical and physical substructures being computationally simulated, which is commonly used as a preparatory simulation before the implementation of a real hybrid test to ensure that the computational model, the experimental setup, and the network communication are functioning properly. During a VHS, finite element programs used for modeling both substructures are coupled, and continuous data exchange between them is enabled by a

VHS of the Daikai station

The Daikai station, a reinforced concrete underground structure, collapsed in the 1995 Kobe strong earthquake. VHS of the subway station is carried out to validate the accuracy and robustness of the proposed VHS framework for underground structures, during which a 2D cross-sectional model is setup based on the plane strain assumption.

The geological profile and the cross-section of the station structure are shown in Fig. 3. The buried depth of the station is 4.8 m. The thicknesses of the top

Discussion

Although Fig. 8, Fig. 9, Fig. 10, Fig. 11 demonstrate the capability of the VHS to accurately reproduce the nonlinear response of the subway station, the Three-DOF loading scheme employed by the VHS requires at least three actuators, which may not be always available in laboratories. Moreover, the cross-coupling effect among the actuators will influence the loading accuracy during a real hybrid simulation experiment. On the other hand, the One-DOF scheme, adopted in previous hybrid simulation,

Conclusions

A VHS method employing the expanded multi-axial experimental setup for underground structures is proposed to acount for more realistic boundary conditions between the physical and numerical substructures. The proposed VHS method was applied to the seismic response simulation of the Daikai subway station and its capability to capture nonlinear responses of the underground structure was verified by providing comparisons of the VHS responses with those obtained from the CNS. Moreover, the proposed

CRediT authorship contribution statement

Haitao Yu: Conceptualization, Methodology, Writing - review & editing, Supervision, Project administration, Funding acquisition. Yanxi Li: Software, Data curation, Validation, Writing - original draft. Xiaoyun Shao: Supervision, Writing - review & editing. Xuesong Cai: Software, Visualization, Investigation.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The research has been supported by the National Key Research and Development Plan of China (2017YFC1500703 & 2018YFC0809602 & 2018YFC1504305), the National Natural Science Foundation of China (41922059 & 51678438), and the Shanghai Committee of Science and Technology (18DZ1205103 & 17DZ1203804). The authors also acknowledge the support from the Foundation of the Key Laboratory of Urban Underground Engineering of Ministry of Education, Beijing Jiaotong University (TUE2018-04), and the

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