Seismic fragility analysis of the wall of storage tanks

Unanchored steel storage tanks, commonly used in industrial facilities, can suffer damage during major earthquakes due to various failures, including elasto-plastic buckling in the shape of an elephant's foot, which is the focus of the research presented in this dissertation. The primary result of the research is the methodology to assess the seismic fragility of elephant-foot buckling (EFB) of the tank wall. The methodology includes seismic site response analysis (SRA) using equivalent-linear dynamic analysis of a 1D model and seismic performance assessment of the tank wall using a FEM 3D non-linear model of the tank and pushover analysis. The seismic load for the SRA is defined by ground motion recordings for the reference rock. The analysis results in the acceleration spectra at the tank's foundation level, representing the seismic load on the tank, considering only the spectral acceleration at the tank's impulsive period for determining hydrodynamic pressures. The SRA is performed for a set of soil profiles and a set of accelerograms, so the seismic demands on the tank wall are determined by a cloud of points defined by ground motion intensities for the considered accelerograms (maximum peak acceleration at the reference rock and spectral acceleration at the reference rock or at the tank foundation level at the impulsive period) and the corresponding engineering demand parameters on the tank wall, defined by the maximum axial compressive stress. Based on cloud analysis, the seismic demand model is built and compared to the EFB limit state to determine the value of the intensity measure at the bedrock level causing the EFB (IMEFB) and the corresponding fragility function for a given tank-soil configuration. The introduced methodology is relatively easily applicable if the cloud-based site response analysis is automated. However, it does not fully consider the effects of soil-structure interaction and the dynamic impact between the base plate and foundation during an earthquake, which can significantly influence the initiation of elephant-foot buckling in unanchored storage tanks, as demonstrated by the conducted dynamic analyses. The proposed methodology was applied to a parametric study for the seismic fragility assessment of 18 tank-soil configurations. The findings reveal that the axial compressive stress due to seismic action in the wall of broader tanks is relatively low, and the bulging at the bottom of the wall is mainly due to high hydrodynamic pressure and the resulting hoop stress. In contrast, the wall of slender tanks buckles primarily due to high axial stresses, leading to EFB. Based on the EFB fragility functions, a parametric seismic fragility model of EFB in the tank wall was developed. The model can be used to rapidly assess the seismic vulnerability to EFB for a larger number of tanks, either using the spectral acceleration at the tank’s impulsive period or the peak ground acceleration for the seismic intensity measure, both considered at the reference rock level. The input parameters of the introduced parametric seismic fragility model are the harmonic average shear-wave velocity in the top 30 m of soil, Vs,30, the slenderness ratio of the tank, H/R, the ratio between radius and wall thickness of the tank, R/t, and the standard deviation of log values for the IMEFB. The model reliably predicts the median intensity measure causing the onset of EFB in the investigated tank-soil configurations, but further research is needed to understand the proposed model's validity better.