Evaluation of various seismic response analysis methods for underground structures in saturated sand
Introduction
Damage to underground structures has been frequently observed in several major earthquakes, especially in liquefiable saturated sand (Hamada et al. 1996). These observations include the famous failure case of the Dakai station (Iida et al., 1996, Samata et al., 1997, Uenishi and Sakurai, 2000), and the damage of rectangular cross-section structures such as subway stations (Erdik, 2001, Yamaguchi et al., 2012, Tokimatsu et al., 2012, Chian and Tokimatsu, 2012) and circular cross-section structures such as tunnels and pipelines (Schmidt et al., 1998, Wang et al., 2001, Yasuda and Kiku, 2006, Elnashai et al., 2010, Kaiser et al., 2011). Therefore, it is crucial for the seismic design and assessment of underground structures to accurately analyze their seismic response in liquefiable ground.
Simplified pseudo-static analysis methods with different assumptions are the most commonly adopted methods in the seismic design of underground structures considering their simplicity (Tsinidis et al. 2020). Typical simplified pseudo-static analysis methods recommended by existing design codes and guidelines can be classified into four main categories, as suggested by Pitilakis and Tsinidis (2014): 1) displacement-based pseudo-static methods, adopted by design procedures of Japan (Kawashima 1994), France (AFPS/AFTES 2001), ISO (ISO 23469 2005), USA (FHWA 2009), and China (MOHURD, 2010, MOHURD, 2018); 2) force-based pseudo-static methods, adopted by Greece (EAK2000 2003), EU (CEN 2004), and ISO (ISO 23469 2005); 3) F(flexibility ratio)-R(racking ratio) methods, adopted by France (AFPS/AFTES 2001) and USA (FHWA 2009); and 4) detailed equivalent static methods, adopted by ISO (ISO 23469 2005), USA (FHWA 2009), and China (MOHURD, 2010). These pseudo-static methods have been applied to the seismic analysis of underground structures in different ground conditions with different degrees of success. However, their effectiveness in analyzing underground structure response in strongly nonlinear liquefiable ground, with drastic temporal and spatial changes in soil effective stress and excess pore pressure, have yet to be systematically evaluated (ISO 23469 2005).
Although in-situ and model test measurements are an ideal data source for the validation of these analysis methods, the data from these valuable sources are often limited. Usually in model tests, only free field and surface displacement, acceleration and excess pore water pressure within the soil, acceleration and strain on the structure, at limited number of locations can be obtained (Koseki et al., 1997, Ling et al., 2003, Chen et al., 2013, Chen et al., 2020, Taylor and Madabhushi, 2020). Due to these limitations, validation of simplified pseudo-static methods in seismic design against well calibrated high-fidelity dynamic analysis can be a feasible and attractive alternative. With the appropriate numerical computation setup, especially in terms of constitutive model for saturated sand, such dynamic analysis can accurately reproduce the seismic response of underground structures in liquefiable ground. Investigation of the seismic response of underground structures in liquefiable ground have been conducted using dynamic analysis methods for underground structures such as subway stations (Liu and Song, 2005, Zhuang et al., 2015, Hu et al., 2018, Chen et al., 2018, Wang et al., 2019) and tunnels (Azadi and Hosseini, 2010, Madabhushi and Madabhushi, 2015, Bao et al., 2017, Banerjee and Chakraborty, 2018, Nariman et al., 2019, Zheng et al., 2020), using elasto-plastic constitutive models. Over the past two decades, several advanced constitutive models have been developed specifically to reflect the behavior of saturated sand under cyclic loading (Elgamal et al., 2002, Iai and Ozutsumi, 2005, Zhang and Wang, 2012, Boulanger and Ziotopoulou, 2013, Wang et al., 2014, Tasiopoulou and Gerolymos, 2016, Ye et al., 2018, Barrero et al., 2019, Fuentes et al., 2019, Liu et al., 2019). Within these efforts, Wang et al. (2014) proposed a plasticity constitutive model for large post-liquefaction deformation of sand, which is able to provide unified description of sand from pre-liquefaction effective stress reduction to post-liquefaction shear deformation generation under cyclic loading. Here, liquefaction specifically refers to the state of zero effective stress or excess pore pressure ratio (ratio between excess pore pressure and initial vertical effective stress) of 1. The model has been successfully applied in the research of seismic response of saturated sand (He et al. 2020), underground structures (Chen et al. 2018) and other geotechnical structures (Wang et al., 2017, Liu et al., 2020).
This study aims to evaluate the effectiveness of the four classical simplified pseudo-static seismic response analysis methods for underground structures in liquefiable ground. High-fidelity dynamic analysis that has been proven effective in analyzing soil-structure interaction in liquefiable ground is used to provide a basis for the evaluation. Dynamic analysis and simplified pseudo-static analysis, using a displacement-based method, a force-based method, a F(flexibility ratio)-R(racking ratio) method, and a detailed equivalent static method, are first conducted for underground structures with rectangular and circular cross-section in non-liquefiable ground, to serve as benchmark for comparison, showing that most simplified pseudo-static methods can provide reasonable analysis results under such conditions. The seismic response of underground structures, including rectangular and circular cross-section structures, in liquefiable ground are then investigated in detail using dynamic analysis and simplified pseudo-static analysis methods, exhibiting significant deviation of simplified pseudo-static analysis results from dynamic analysis results. This deviation of analysis results in liquefiable ground is explained based on the investigation of spatial and temporal soil-structure interaction patterns.
Section 2 presents the conditions and specifications of seismic response analysis. Typical results from dynamic and simplified pseudo-static analysis are discussed and compared for rectangular and circular cross-section underground structures in non-liquefiable and liquefiable ground in Section 3. In Section 4, soil-structure interaction in liquefiable ground are analyzed for various underground structure shapes to explain the cause of the deviation of simplified pseudo-static analysis results from dynamic analysis results in liquefiable ground.
Section snippets
Evaluation conditions
Underground structures in two different types of soil profiles are evaluated in this study, as shown in Fig. 1(a) and (b). The first type of soil profile consists of a uniform 50 m deep non-liquefiable linear elastic soil layer, and the second type consists of a 25 m liquefiable soil layer overlying a 25 m non-liquefiable linear elastic soil layer. The non-liquefiable soil is regarded as a simple linear elastic material with Young's modulus E = 50 MPa and Poisson’s ratio ν = 0.4. The
Soil and structure response based on dynamic analysis
Typical seismic response of the soil and underground structures in both non-liquefiable and liquefiable ground is first presented here for an overall view.
The typical difference between the liquefiable ground and non-liquefiable ground is that the liquefiable soil will accumulate excess pore pressure during the earthquake. As shown in Fig. 6, all the 7 input ground motions cause some extent of liquefaction of the ground. The liquefaction depth in the far-field is deeper than the top of
Inadequacy of pseudo-static methods in considering the effects of dynamic soil-structure interaction in liquefiable ground
The cause for the unsatisfactory performance of the pseudo-static methods in analyzing the seismic response of underground structures in liquefiable ground lies within their inherent inadequacy in considering the complex nature of soil-structure interaction (SSI) in liquefiable soil. The SSI features that contribute to the deviation of the simplified pseudo-static analysis methods are discussed in this section. Some of these features can be incorporated into the pseudo-static methods through
Conclusions
Evaluation of the effectiveness of various seismic response analysis methods for underground structures in saturated sand is conducted systematically in this study. Dynamic analysis on the seismic response of typical rectangular and circular cross-section underground structures in non-liquefiable and liquefiable ground under 7 input ground motions are reported to provide a basis for the evaluation. Four categories of simplified pseudo-static methods commonly used in current design codes and
CRediT authorship contribution statement
Tong Zhu: . Rui Wang: Conceptualization, Writing - review & editing. Jian-Min Zhang: Supervision.
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 authors would like to thank the National Natural Science Foundation of China (No. 52022046 and No. 52038005) and Tsinghua University Initiative Scientific Research Program (2019Z08QCX01) for funding this study. We would also like to thank the three anonymous reviewers for their comments and suggestions that have improved the quality of the paper.
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