Hazard consistent record selection procedures accounting for horizontal and vertical components of the ground motion: Application to liquid storage tanks

Abstract

A methodology is proposed to enable state-of-the-art record selection using ground motion components in all three principal loading directions. Relying on the well-established Conditional Spectrum approach, its fundamental concepts are extended to ensure hazard consistency when the vertical ground motion component is considered along with the horizontal ones. To this end, different record selection techniques are employed, spanning sets of ground motion records with and without vertical motions, as well as with and without vertical ground motion hazard consistency. To demonstrate the effect that each record set can potentially have on a structure, an unanchored liquid storage tank is adopted as a case study, because of the vertical uplift motion it can exhibit, even under the application of horizontal loading only. A reduced-order structural model is employed to generate the numerical output via multi-stripe analysis, thus enabling the evaluation of the pertinent record selection approaches. Focusing on uplift and compressive meridional stress, response ratios and response hazard curves are extracted. It is shown that although the vertical ground motion component only mildly affects uplift, its effect on compressive meridional stress, on average, amplifies the response by a factor of 1.8 for moderate intensities and 2.8 for higher ones.

Damping‐dependent correlations between horizontal‐horizontal, horizontal‐vertical, and vertical‐vertical pairs of spectral accelerations

“…A scenario example was used to illustrate the application of the correlation models in the conditional spectrum implementation. The presented dampingdependent correlation models can be used in ground motion selection and vector-valued probabilistic seismic demand calculation for risk assessment of structure systems, especially when the multicomponent earthquake shaking and non-5% damping ratios are of interest (e.g., 1,12,16).…”

“…Although not illustrated herein, the generalized conditional intensity measure distributions 32 of PGA and PGV can also be constructed with the aid of the proposed correlation models. Besides, a conditioning vector of multicomponent SAs 12 can be considered for better representing ground motion features. Further investigation of the effects of damping‐dependent correlations on ground motion selection and associated structural response/loss analyses will be a subject of future study.…”

“…Although SAs of horizontal ground-motion components are mainly utilized in practice, documented field observations have also revealed the effects of vertical motions on structure response and damage. 8,9 Properly representing the vertical motion in addition to the horizontal shaking plays an important role in seismic risk assessments of buildings, 10 dams, 11 liquid storage tanks, 12 bridge systems, 5,13 and underground-aboveground structure systems, 14 etc. To this end, a series of methods have been developed to select horizontal and vertical ground-motion components that represent the seismic hazard for multicomponent SAs at a site (e.g., refs.…”

“…To this end, a series of methods have been developed to select horizontal and vertical ground‐motion components that represent the seismic hazard for multicomponent SAs at a site (e.g., refs. 12, 15–18). Given that structures such as the base‐isolated buildings and bridges with ξ ≠ 5% can be sensitive to vertical earthquake shaking, 19,20 it is of importance to understand and quantify damping‐dependent SA( T , ξ ) for both horizontal and vertical motions.…”

A risk‐targeted seismic performance assessment of elephant‐foot buckling in walls of unanchored steel storage tanks

“…The load pattern imposed in pushover analysis is based on the hydrodynamic pressure models defined in Equations () and () 32 . The load pattern for pushover analysis is based on the patterns of the hydrodynamic pressure due to horizontal seismic action p ir,h and vertical seismic action p ir,v , 7,8,54–58 which are applied on the tank accounting for the SRSS rule, 32 $$\sqrt {{p_{ir,h}}^{\rm{2}}{\rm{ + \ }}{p_{ir,v}}^{\rm{2}}} $$. The p ir,h and p ir,v are defined as follows 32 : $$$$\begin{equation}{p_{ir,h}} = {C_{ir,h}} \left( {\zeta ,\gamma } \right) {\Gamma _{ir,h}}\ {\rho _L}\ R{\rm{cos}}\left( \theta \right)\ {S_e},\end{equation}$$$$ $$$$\begin{equation}{p_{ir,v}} = \ {\rho _L}\left[ {H\left( {1 - \zeta } \right)} \right]{S_{e,v}},\end{equation}$$$$where $$\ {\rho _L}$$ is the liquid density, H is the filling height, $$\zeta \ {\rm{ = \ }}z{\rm{/}}H$$ is the dimensionless height and z is the elevation measured from the bottom to the top of the tank.$$\ {C_{ir,h}}( {\zeta ,\gamma } )$$ is the dimensionless impulsive rigid pressure function, dependent on the slenderness rati...…”