Evaluation of various seismic response analysis methods for underground structures in saturated sand

Highlights

• Systematic evaluation of underground structure seismic response analysis methods.

• Simplified seismic response analysis methods perform poorly in liquefiable ground.

• Soil-structure interaction spatial variability non-negligible in liquefiable soil.

• Modified simplified method proposed for circular structures in liquefiable ground.

Abstract

Underground structures in liquefiable saturated sand are prone to earthquake damage. Various simplified pseudo-static seismic response analysis methods for underground structures have been recommended by current design codes and guidelines, but lack adequate systematic validation in liquefiable ground. In this study, the effectiveness of four categories of simplified pseudo-static methods in saturated sand are evaluated. These methods include a displacement-based method, a force-based method, a F(flexibility ratio)-R(racking ratio) method, and a detailed equivalent static method. High-fidelity dynamic analysis of circular and rectangular cross-section underground structures in non-liquefiable and liquefiable ground under different input ground motions are conducted, using a validated plasticity constitutive model for large post-liquefaction deformation of sand, to serve as a basis for the evaluation. Although the pseudo-static methods can generally provide adequate analysis results for underground structures in non-liquefiable ground, especially the displacement-based method, their performance in saturated sand are generally poor. The deviation of pseudo-static analysis results from reality stems from their inadequacies in considering the effects of dynamic soil-structure interaction in liquefiable ground. Temporal and spatial variability of soil-structure interaction in saturated sand, caused by the accumulation of excess pore pressure and subsequent decrease in soil effective stress and constraint on underground structures, are not considered in pseudo-static analysis methods. Modifications to the pseudo-static analysis methods and high-fidelity dynamic analysis methods are suggested to be adopted for the evaluation of the seismic response of underground structures in liquefiable ground.

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.