Seismic Analysis of Elevated Water Storage Tanks Subjected to Six Correlated Ground Motion Components

Rotational components of ground motion including rocking and torsional components have rarely been accounted for in designing and analyzing water storage tanks. In this paper, the effects of these components on the dynamic response of water storage tanks are studied. The rotational components of ground motion acceleration have been obtained using an improved approach from the corresponding available translational components based on the transversely isotropic elastic wave propagation and classical elasticity theories. Based on this approach, it becomes possible to consider the frequency-dependent wave velocities and incident wave angle to generate the rotational components. For this purpose, the translational components of four earthquakes have been selected to generate their relative rotational components based on SV and SH wave incidence. The translational and computed rotational motions were then applied to the concrete elevated water storage tank with different water elevations considering fluid–structure interaction using the finite element method. The linear responses of these structures considering the full six components of the ground motion show that the rotational components of ground motion can affect the displacement and reaction force of the structure, depending on the frequency of structure and predominant frequencies of translational and rotational components of ground motion.

Characterizing rotational components of earthquake ground motion using a surface distribution method and response of sample structures

Data recorded from dense seismic arrays such as the Large Scale Seismic Testing array in Lotung, Taiwan, are used for multiple purposes, including development of attenuation and coherency functions, computing dynamic strains in soil, and estimating rotational components of ground motion. The required footprint of a seismic array deployed to compute rotational components of ground motion is a function of the method used for the computations and site specific characteristics, including the apparent seismic wave velocity and the frequency content of expected ground motions. A design procedure for a general two-dimensional seismic array is presented together with a site-specific example using the Surface Distribution Method to extract the rotational components of ground motion. A sensitivity study is performed to determine how the location of recording stations of translational motion in a dense array affects the computed rotational components of earthquake ground motion.

Ground motions at a point on the ground surface can be decomposed to six components, namely three translational components and three rotational components; translational components include two components in the horizontal plane, and one in the vertical direction. Rotation about horizontal axes leads to rising of rocking, while the rotational component about a vertical axis generates torsional effects even in symmetrical buildings. Due to evident and significant contribution of ground shakings to the overall response of structures, rocking and torsional components of these motions resulted by strong earthquakes are recently subjected to widespread researches by engineering and research communities. In this study, first rotational components of ground motion are determined using a method developed by Hong-Nan Li and et al (2004). This method is based on frequency dependence on the angle of incidence and the wave velocity. In consequence, aboveground steel storage tanks (ASSTs) with different water elevations have been analyzed with the effects of these six components of earthquake. Three translational components of six important earthquakes have been adopted to generate relevant rotational components based on SV and SH wave incidence by the Fast Fourier Transform (FFT) with the discrete frequencies of time histories of translational motion. Using finite element method, linear properties of tank material including steel for cylindrical tanks have been taken into with considering fluid-structure interaction. Numerical linear dynamic analysis of these structures considering six components of earthquake motions is presented; results are compared with cases in which three translational components are considered.

Under the assumption of an immovable point source for the earthquake energy release, a mathematical model is developed to compute the components of the free field surface rotation consistent with assigned translational components.Experimental evidence on these quantities is offered by the strong‐motion instrument arrays. However, lack of adequate identification of the different wave contributions prevents in general a direct measurement of rotational and torsional components, allowing only a qualitative assessment of just how large these components might be. The only exceptions are the records of SMART‐1, which offer the entire information to derive rotations.The available data of strong‐motion instrument arrays for this problem are summarized in Table I. They are in qualitative agreement with the suggestions of the mathematical model.Earthquake response spectra for the rotational components are developed for a few selected cases, in particular a rotational spectrum consistent with the prescription of USNRC Regulatory Guide 1.60.The correlations between the translational and rotational components of the ground motion are also shown.

ABSTRACTRotational components of earthquake ground motion have not been considered for seismic analysis, design and performance assessment because recordings of these components are unavailable. A number of procedures have been proposed to extract rotational components of ground motion from translational time series recorded at multiple, closely spaced recording stations. In this paper, a new procedure that is capable of capturing higher frequency content in rotational time‐series is presented. The frequencies at which numerical errors are introduced in the solution, which are a function of apparent wave velocity and array dimension, are identified. Results are presented for the proposed procedure, the widely accepted geodetic method, and a single‐station procedure developed by the authors, all using data recorded at the Lotung array in Taiwan. Copyright © 2012 John Wiley & Sons, Ltd.

Classical Russian S-5-S pendulum seismometer was modified for recording of the rotational components of ground motion. This seismometer was used for monitoring of mining induced seismic events in the Karviná region (Czech Republic). Together, three translational components of ground vibration velocity and one rotational component of ground vibration velocity around the vertical axis were recorded. Elaborated mining induced seismic events with epicentral distances up to 9 km were recorded in Doubrava locality, where the exploitation of black coal is still active. Numerical study of measured component attributes of mining induced seismic events is presented in this paper, namely squared Morlet wavelet coefficients and squared coherence spectrum between rotational and translational components. Squared Morlet wavelet coefficients enable to analyse time-and-frequency structure of elaborated signal, e.g. dynamics of the onset, evolution and disappearance of typical periods of the harmonic peaks, etc. Spectral measure of coherence was applied here for investigation of synchronization effects in 2-dimensional time series of translational and rotational components.

Investigating the effect of rotational components on the progressive collapse of steel structures

The motion of a point is specified completely through six components, three translational and three rotational. Three rotational components of ground motion are classified to two rocking components and one torsional component. The transitional components of ground motion are easily measurable by standard techniques, whereas the rotational components are not directly accessible. In this study, the rotational component of production technique was described, and the influences of soil type and the distance from the fault on the rotational component were investigated. The results showed that the effect of the rotational components is more significant in low periods. Also, the value of the normalized response spectra for soft soil is more than stiff soil, but for far-fault earthquake, it is less than near-fault earthquake.

Seismic analysis, design, and performance assessment of buildings, bridges, and safety-related nuclear structures is based on two or three translational components of earthquake ground motion. Although rotational components (rocking and torsional) may contribute significantly to translational and torsional response and damage, they are not considered in design and assessment because their intensity and frequency content are not measured by accelerograms deployed in the free field. A method for developing rotational time series by first deconstructing the three translational time series of a ground motion recorded at one station into body waves is presented in this paper. The body waves are then reassembled to generate rotational time series. Point and line source representations of the fault rupture are considered. Results of the single station procedure are presented using rotational acceleration spectra and compared with the multiple-station-based geodetic method. The spectra are similar at periods greater than 1 s. The spectral ordinates computed using the geodetic method are significantly smaller at shorter periods, which is attributed to the underlying assumption of a plane surface for the recorded data at any time instant in the method.

Rotational ground motions are not being measured by the accelerographs deployed in the free-field, but rather extracted from the recorded three-component translation data, usually at one single station (single station procedure, SSP). These SSPs differ from one another in terms of approximating the underlying wave propagation scenario in the field. Increasing order of complexity does not always guarantee better product and may lead to unrealistic results because of the assumptions of compatibility. This paper aims to develop a simplified procedure for estimating rotational motion that may compete with far more rigorous approaches. The proposed procedure makes use of the existence of appropriate translational components (ATCs) and time derivatives that lead to the rotational motion with due scaling through apparent wave velocity. First, a spectral window is proposed and a set of invariant characteristics are identified (with respect to the limited studies carried out in this paper). Next, an empirical rotational window is derived that enables computation of the apparent wave velocity. Three seismic events recorded in a dense array comprising 15 surface-stations are considered for assessing the proposed simplified method.

The numerical investigation on the seismic response of RC elevated liquid storage tanks installed with viscous dampers is presented. A discrete two-mass model for the liquid and multi-degree of freedom system for staging, installed with the dampers are developed for Reinforced Concrete (RC) elevated liquid storage tanks. The elevated tank is assessed for seismic response reduction when provided with Linear Viscous Damper (LVD) and Nonlinear Viscous Damper (NLVD), installed in the staging. The RC elevated liquid storage tanks are analyzed for two levels of liquid containment in the tank, 100% and 25% of the tank capacity. Three Configurations of placements of dampers viz. dampers at alternate levels (Configuration I and Configuration II) and dampers at all the panels of the staging of the tank (Configuration III) are considered. To study the effect of peak ground acceleration, eight real earthquake time histories with accelerations varying from 0.1 g to 0.93 g are considered. The nonlinearity in the viscous damper is modified by taking force proportional to various velocity exponents. It is found that the nonlinear viscous dampers with lower damping constant result in a comparable reduction in the response of RC elevated liquid storage tank, to that of linear viscous dampers with higher damping constant. A lower damping constant signifies compact the size of the damper. Doi: 10.28991/cej-2020-SP(EMCE)-09 Full Text: PDF

Effects of rotational component of ground motions on seismic responses of asymmetric base-isolated structures

Elevated water storage tanks are one of the most crucial structures to be considered under seismic action due to the complex behaviour of fluid–structure interaction. The modelling of this fluid–structure interaction can be carried out by rigorous application of Finite Elements Analysis (FEA) with Computational Fluid Dynamics (CFD). But in case of professional practice and design, these methods are very tedious and time-consuming for day-to-day application. Following the Housner model of elevated storage tanks, previous studies suggest that if the time period of the convective (Tc) and the impulsive (Ti) mode are well separated by factors above 2.5, then the complex fluid–structure interaction can be uncoupled to perform approximate analysis. Also, it eliminates the risk of coupled resonating condition of fluid and structure. The present Indian Standard (IS) seismic code for liquid storage tank follows this idealization for simplified analysis. But, the aspect ratio or height to diameter ratio (hs/Ds) of the tank staging and number of panels in it plays a significant role on the assumption where Tc/Ti can be smaller than 2.5. Hence, this present study reveals the range of hs/Ds for which the Tc/Ti value lies above 2.5 to conduct simplified analysis following the IS provisions and to avoid the coupled resonance. The tank is considered as elevated circular concrete water storage tank with flat roof.

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