Peak Ground Acceleration Ratio Research Articles

Evaluation of wavelet decomposition level to enhance numerical analysis of seismic responses

In this study, the discrete wavelet transform (DWT) is used to enhance the efficiency of numerical analysis by decomposing earthquake excitation signals into low- and high-frequency components. The low-frequency components, considered as the main damaging factor in earthquake waves, stored in approximation coefficients have been used to perform time response analysis. In the selection of the ground motions, the special attention is given to the ratio of peak ground acceleration (PGA) to peak ground velocity (PGV). An ensemble of nine earthquake records have been selected and used. For each earthquake, displacement response spectra have been generated for both the original signal and its approximations at different DWT levels. To determine the most accurate decomposition level, the normalized root-mean-squared error (NRMSE) of wavelet energy has been computed in spectral displacement responses. The outcomes reveal a dependency of the decomposition level on the specific characteristics of each earthquake. Subsequently, structural analyses are conducted on base-isolated structures with varying story numbers, to examine the accuracy of decomposed signals. Employing both the original signal and its approximations to the structures, base mat displacements and roof accelerations are computed. The findings of the seismic analyses demonstrate the effectiveness of the proposed decomposition levels.

Characterization of Seismic Dynamic Response of Uranium Tailings Dams Based on Discrete Element Method

Tailings dams play a critical role in ensuring the safety of mining operations. However, earthquakes can cause breaches in these dams, resulting in significant casualties and property damage. This study investigates the dynamic response characteristics of uranium tailings dams subjected to seismic loading, employing the discrete element method. It specifically analyzes how seismic wave amplitude, frequency, and the friction angle of tailings sand affect the dams’ dynamic response. The results reveal that the peak ground acceleration ratio (PGAR) exhibits an increasing–decreasing–increasing pattern with elevation. When the friction angle of the tailings sand exceeds 35°, the overall stability of the dam improves. Conversely, a friction angle below 25° significantly increases the risk of dam failure. Additionally, the dam shows a reduced dynamic response to seismic waves with frequencies exceeding 15 Hz. At lower frequencies, deformation and damage are primarily concentrated on the slope face, while at higher frequencies, damage is predominantly located at the bottom of the model. These findings provide a theoretical foundation and reference for the safe operation of tailings dams, highlighting their practical significance.

Effect of material characteristics of lead rubber isolators on seismic performance of box girder bridge

Near-field (NF) earthquakes have distinct ground motions, forward directivity pulses, and fling-step motions, causing structural responses to differ from far-field (FF) earthquakes. Seismic isolation is regarded as a developed and successful technology that may be applied to enhance a structure’s functionality and safeguard it against catastrophic earthquake effects. The variation in mechanical properties of seismic isolation also significantly influences bridge seismic response. The study investigates the influence of lead rubber (LRB) isolators and the characteristics of ground motions on seismically isolated bridges, aiming to determine optimal parameters for minimal earthquake response. Key parameters include ground motion characteristics, characteristic strength (Q), and isolator flexibility. The study modeled the force-deformation behavior of isolators using bilinear behavior, reflecting the Bouc-Wen hysteric model. CSI Bridge was used to model seismically isolated steel box girder bridges, with eight natural accelerograms assessing a 2% probability of exceedance in 50 years. The peak responses of pier displacement (MPD), isolator hysteric energy (HED), base shear, and deck acceleration are chosen as the response parameters for the comparison. To evaluate the response parameters, the earthquake data are scaled to the three studied peak ground acceleration (PGA) levels of design level (0.2 g), extreme level (0.4 g), and rare-extreme level (0.8 g). The findings offer insight on the relevance of isolator stiffness and its influences on the seismic performance of isolated bridges. The study identifies minimum values for pier displacement, hysteric energy, deck acceleration, and base shear at specific Q/weight sustained by isolator (W) and time period (T) values. Recommendations are made for the preliminary seismic isolation design of bridges with LRB isolators, highlighting the importance of PGV to PGA ratio in earthquake damage assessment.

Effects of seismic characteristics and baffle damping on liquid sloshing

The present work concentrates on liquid sloshing in tanks under real seismic excitations with various frequency contents [the ratio of peak ground acceleration (PGA) to peak ground velocity (PGV)] by a finite-difference turbulent model. The turbulence is modeled by the large eddy simulation, and the fluid–structure interaction is resolved by the Virtual Boundary Force method. Thirteen seismic records, covering the low, intermediate and high frequency contents, are adopted to excite nonlinear sloshing waves. Both sloshing wave and hydrodynamic pressure are recorded, and their correlations with the filling level, PGA, PGV and frequency content have been identified. The findings suggest that (1) the sloshing responses are in general positively correlated with the filling level; (2) the sloshing height strongly relates to PGV and frequency content, and the seismic excitation of low frequency and meantime with a larger PGV can trigger more violent sloshing waves than others; and (3) the dynamic pressure along the tank sidewall decreases from the bottom up, which is dominated by PGA at the lower part but the stronger correlation is established with PGV and frequency content at the upper part. Finally, to damp severe sloshing waves, the horizontal, vertical and coupled horizontal and vertical baffles are introduced, and their inhibiting effects are discussed. The present work may guide the design of partially filled storage tanks under seismic excitations.

Study on the Influence of Earthquakes with Different Frequency Content on the Peak Liquid Sloshing Wave Height of Liquid Storage Tank

Liquid storage tank is an irreplaceable and extremely important vessel structure used to store liquid medium. In earthquake disaster, the liquid storage tank will not only be seriously damaged directly, but also cause serious secondary disasters, such as fire, explosion, poisoning, nuclear radiation, etc. The peak liquid sloshing wave height is an important reference index to judge whether the seismic design of the liquid storage tank is reasonable or not. The ratio of peak ground acceleration to peak ground velocity of the earthquake records (shown by A/V ratio) can well represent the characteristics of frequency content of earthquake records. In this paper, the finite element numerical simulation method is used to analyze the seismic response of six rectangular concrete tanks with different liquid heights, and their respective peak liquid sloshing wave heights are calculated. Nine seismic records with different A/V ratios are used, which are low frequency category, medium frequency category and high frequency category and there are three records in each category. At the same time, the equation in Eurocode 8 is used to calculate the peak liquid sloshing wave height of each tank for comparative study. The study results show that the peak liquid sloshing wave height calculated by the Eurocode 8 is greater than that calculated by the finite element method under low frequency and medium frequency earthquake records, indicating that Eurocode 8 is conducive to the preliminary design of the seismic performance of the liquid storage tank. However, in the case of high frequency earthquake records, the calculation result of the finite element method is larger than that of the equation in Eurocode 8. The peak liquid sloshing wave height of the liquid storage tank is more sensitive to the earthquakes with high frequency content, and the Eurocode 8 underestimates the impact of high frequency seismic response on the liquid storage tank.

Comparison of meta-heuristic approaches for the optimization of non-linear base-isolation systems considering the influence of superstructure flexibility

The main aim of this study is to investigate the meta-heuristic approaches called Harmony Search (HS), Grey Wolf Optimizer (GWO), Teaching-Learning Based Optimization (TLBO), and Jaya Algorithm (JA) in the optimization process of non-linear base isolation systems under near-fault earthquakes considering the effect of the superstructure flexibility. The optimization processes were performed by achieving the objective function set as minimizing the peak top floor acceleration to peak ground acceleration ratio with and without base displacement limits. The context of the optimization process, the analytical model of the superstructure, and the number of isolators are considered as the design constants. The mechanical parameters of the non-linear isolation systems, such as the isolation system period, the total characteristic strength ratio, and the yield displacement, are determined as the independent design variables. According to the results obtained in this study, GWO, JA, and TLBO algorithms can be more suitable for solving such design problems among the considered algorithms. Although the objective function values are amplified with the increase in the superstructure flexibility, these values remain around 1.0, even for the most stringent base displacement limit. It can be expressed as a successful seismic performance, especially considering such strong near-fault ground motions, which are the most challenging types for seismically isolated buildings.

Damage assessment of circular bridge pier incorporating high-strength steel reinforcement under near-fault ground motions

Bridge piers are typically the most vulnerable to damage during an earthquake, and the entire seismic performances of the bridge is determined to some extent by the hysteretic energy of its piers. It was discovered that partially embedding high-strength reinforcements in bridge piers is a reliable and efficient method to increase the ductility performance. The term “high-strength reinforcement” refers to reinforcement with a yield strength of (500 MPa) or above. The use of certain high-performance materials can help to enhance bridge pier seismic performance. Because of their strong and impulsive impact on structures, near-fault ground vibrations deserve special attention. These features are distinct from far-field ground vibrations, which are the basis of practically all seismic design requirements. The goal of this study is to evaluate the effects of near-fault ground vibrations on reinforced concrete bridge piers, as well as to develop a framework for evaluating bridge columns near active faults. The impact of Forward-directivity pulses effect on the behavior of a continuous steel box girder bridge pier is investigated in this work using fragility analysis. Damage measures such as pier displacement ductility and rotational ductility of pier are used to generate fragility curves and Probabilistic seismic demand model for bridge pier using high strength reinforcement bars under the ensemble of near-field forward- directivity earthquakes. The damage model presented may be assumed to be a well-versed model which may address the variability in earthquake ground motion while performing the bridges pier seismic vulnerability evaluation. Two sets of near-field forward-directivity records with peak ground velocity to peak ground acceleration ratio (high PGV: PGA > 150 cm/s/g and low PGV: PGA < 150 cm/s/g) are employed to carry out incremental dynamic analysis. The findings show that even at low PGA levels, near-field directivity pulses result in a substantial chance of pier damage exceedance.

Influence of thick soft superficial layers of seabed on ground motion and its treatment suggestions for site response analysis

AbstractThe thick soft superficial layers of the seabed greatly influence ground motion generally. It is worth studying how to find out the influence of these soft layers on ground motion parameters and determine reasonable seismic fortification parameters for ocean engineering. Numerical experiments of site response analysis are designed using two offshore engineering sites in this study. First, the borehole profiles are selected and stripped layer by layer to generate new profiles. Second, 108 acceleration time histories are synthesized which basically represent the diversity of input motions’ amplitude and frequency. Third, a method that can automatically calculate characteristic periods and normalize response spectra is created to improve calculation efficiency. Fourth, peak accelerations, response spectra, and characteristic periods at different depths of the profiles with different stripping depths are calculated. The results show that the thick soft superficial layers can significantly decrease peak ground accelerations and increase characteristic periods, resulting in serious “low-fat” response spectra. The situation can be greatly improved by stripping off the soft superficial layers. After stripping off the thick soft superficial silt layers, if stripping is continued further, the variation in the superficial amplification ratios of peak accelerations and superficial characteristic periods will no longer be drastic, and the superficial amplification ratios and characteristic periods both tend to be mostly the same. The relative deviation of the amplification ratio of peak ground acceleration between a profile stripped and that without stripping can be 143%, and it can be 83% for characteristic period. It is advisable to strip off thick soft superficial layers to perform site response analysis, and the shear force at the bottom of the silt should be considered in engineering based on local seismic activity level, and the silt’s and the structure’s physical parameters.

A new ground motion intensity measure for short period reinforced concrete structures subjected to near-fault pulse-like ground motions

This study is aimed at developing a new ground motion (GM) intensity measure (IM) based on: (i) the shape of the response spectrum and (ii) spectral acceleration at the fundamental elastic period of the structure, Sa(T1). The proposed GM-IM is developed mainly for short period reinforced concrete (RC) structures subjected to near-fault (NF) pulse-like GM records. The main parameter used in the development of the proposed IM is the ratio of peak ground acceleration (PGA) to peak ground velocity (PGV) of a ground motion record. The proposed IM displayed an improved performance among the other evaluated IMs.

Parametric study for long-span roof truss subjected to vertical ground motion

Generally in the seismic resistant design of structures, effects of horizontal ground motions are mainly considered and effects of vertical ground motions (VGMs) are ignored. However, considering the field evidences of damage of structures due to vertical component of ground motion for near-fault earthquakes, the importance of inclusion of effect of vertical component of earthquake in seismic design has been recognized. Therefore in this paper, a parametric study has been carried out on 25 m long-span industrial steel roof truss with the help of 12 near-fault ground motions without pulse. The parameters related to roof truss as well as an earthquake data are studied to get the response of long-span roof truss under vertical ground motion (VGM) with nonlinear time history analysis using SAP2000V19.2.1 software. From the parametric study, it has been realized that for a chosen long-span industrial roof truss, the parameters such as vertical to horizontal peak ground acceleration ratio, axial force, vertical displacement and base bending moment are identified as critical. From the time history analysis results, it is also found that response of truss under vertical ground motion is critical for ground motions having V/H ratio more than 1 and therefore the long-span structure in near-fault zone should be considered separately in design rather than taken as 2/3 of horizontal acceleration as per given in IS1893:2016 (Part-1).

Seismic fragility evaluation of semi-rigid frames subjected to near-field earthquakes

The studies on the seismic fragility evaluation of semi-rigid (SR) steel moment frames are meager in the existing literature. The purpose of the present numerical study is to investigate the seismic fragility of SR frames subjected to near-field earthquakes. Specific characteristics of the fragility curves for near-field earthquakes are highlighted by comparing them with those for far-field earthquakes. A ten-story SR frame is analyzed subjected to four sets of earthquakes considering the moderate degree of semi-rigidity. The four sets of earthquakes, namely, far-field, near-field with high directivity, low directivity, and fling-step consist of ensembles of ten real ground motion records in each ensemble. The fragility plots are developed by considering a number of damage measures, namely, the maximum inter-story drift ratio, maximum base shear, maximum roof drift angle, maximum top-story acceleration with the peak ground acceleration (PGA) as an intensity measure. Threshold values for different damage states are decided based on the engineering judgment. For the near-field earthquake with directivity effect, the frequency repercussions on the fragility curves are investigated by varying the peak ground velocity (PGV) to PGA ratio with high ( > 160 cm/s-g), and low (< 160 cm/s-g) ratios. The major findings of the numerical study show that a high directivity ratio of the near-field earthquake has a significant effect on the probability of exceedance as compared to the far-field earthquake.

A prediction model for vertical-to-horizontal spectral ratios of ground motions on the seafloor for moderate magnitude events for the Sagami Bay region in Japan

A prediction model for offshore vertical-to-horizontal (V/H) spectral ratios of peak ground acceleration (PGA) and 5%-damped elastic response spectra for periods ranging from 0.01 to 10 s for an offshore area off Sagami Bay was developed. To compare differences between offshore and onshore ground motions in the V/H spectral ratios, an onshore V/H prediction model was derived for onshore stations adjacent to the studied offshore sites. The offshore dataset includes 738 three-component records, and the onshore dataset includes 2219 records; both datasets are derived from the same set of 233 earthquakes selected for this study. The moment magnitude, hypocentral distance, focal depth, tectonic source type, and individual site correction term are used as independent variables in the V/H models. A comparison drawn between the offshore and onshore models shows that the V/H spectral ratios of offshore ground motions are obviously smaller than those of the onshore motions over short periods (< 1.0 s) but are comparable for periods of longer than 1.0 s. Water layer reduces vertical ground motions, especially over short periods, and as the periods increase, the effect of water layer decreases. The effect of the moment magnitude on offshore V/H ratios is stronger than that of onshore ratios, especially for long periods; the effect of hypocentral distance and focal depth is considerable for long periods for offshore V/H ratios, and the V/H ratios between offshore sites are very different due to complex local site geologies beneath the offshore stations.

The Effect of Topographic Irregularities on Seismic Response of the Concrete Rectangular Liquid Storage Tanks Incorporating Soil–Structure–Liquid Interaction

Theoretical and experimental studies on topographic irregularities show an extra amplification in these sites due to seismic waves. This significant fact compelled the researchers not only to evaluate the wave motion pattern, but also to consider its effect on structures built on the slopes. The main purpose of this study was to investigate the effect of topographic irregularities on seismic behavior of rectangular liquid storage tanks. To achieve this, several parametric studies have been done using the finite element method in the two-dimensional space. In order to evaluate the effect of topographic irregularities, flat and inclined soil surfaces with three different soil types are taken into account. Broad and slender tank configurations are studied under the effect of six different seismic motions with various ratios of peak ground acceleration to peak ground velocity. Also, in order to evaluate the effect of the presence of liquid on the tank response, the full tank and empty tank are studied. Using these different parameters, some comparisons are made on the base shear forces, tank wall displacement and sloshing responses. The results showed that amplification due to topographic irregularities has a significant effect on tank response. Furthermore, it is concluded that the earthquake frequency content considerably affects the dynamic behavior of the liquid tanks.

Probabilistic Behavior Assessment of Base-Isolated Buildings and Base Isolation Systems Subjected to Various Earthquakes with Different Components

One of the greatest challenges of researchers is to understand the behavior of base isolation systems and base-isolated buildings under the conditions of different ground motions. The specific objective of this study is to evaluate the seismic response of multi-story base-isolated buildings with lead core rubber bearings (LCRBs) and buildings that are not isolated when subjected to different types of ground motions with different components. Under these conditions, the equations of motion of buildings with isolation systems are obtained, and LCRB force–deformation behavior is modeled as bilinear in MATLAB. Then, the behaviors of the base isolation system and base-isolated buildings are evaluated for 45 different earthquake scenarios, which are categorized into three different groups with regard to the ratio of peak ground acceleration to peak ground velocity (PGA/PGV). The dissipation of energy by a base isolation system, which is induced by the earthquake, varies for three different ranges of the PGA/PGV ratio. Despite the fact that by increasing the number of stories, the effectiveness of the isolator system decreases, this paper shows the most important finding to be that the damage limitation requirement is kept below 1% according to Eurocode 8, which is the requirement for buildings at the upper limit on the inter-story drift ratio under seismic loading, and the inter-story drifts significantly decreases for the base-isolated buildings and even for high-rise buildings.

Coupled Horizontal and Vertical Component Analysis of Strong Ground Motions for Soil–Pile–Superstructure Systems: Application to a Bridge Pier with Soil–Structure Interaction

ABSTRACT This study investigates the influence of vertical components (VCs) of seismic excitations on the response of short and tall (slender) superstructures, and compares them with the system response under only horizontal components (HCs). The first part of the study examines the capability of the bounding multi-surface plasticity model to identify dynamic soil properties and soil–pile–superstructure system response to the HCs of a strong ground motion using existing results from dynamic centrifuge tests. The influence of VCs on short and tall superstructures is then investigated, and compared with system response under only HCs. A procedure is proposed to select strong vertical ground motion to complete a nonlinear time-history analysis with a three-dimensional finite element model. Step-by-step modelling techniques are described with a direct-method framework to simulate complex soil–pile–superstructure systems. This study emphasises the role of VCs in the general response of the system in regard to selected damage parameters for pile foundations. The results indicate that VCs may have increasing effects on axial loads and maximum pile-cap displacements for short superstructures. In addition, contrary to the vertical vibration period of the superstructure, the variation of the superstructure’s horizontal vibration period with the peak ground acceleration ratio (V/H) may be significant.

A prediction model for vertical-to-horizontal ratios of PGA, PGV, and 5%-damped response spectra (0.01–10 s) for Iran

New models are developed for the prediction of vertical-to-horizontal (V/H) spectral ratios of peak ground acceleration (PGA), peak ground velocity (PGV), and 5%-damped elastic response spectra for periods ranging from 0.01 to 10 s. The models use moment magnitude, source-to-site distance, style-of-faulting (SoF), and site classification terms as independent variables. The study is based on a well-compiled Iranian ground-motion databank, consisting of 1350 (*3) three-component accelerograms generated by 370 earthquakes. Only records with known measured time-averaged shear-wave velocity in the uppermost 30 m (VS30) are used for regression analyses. The presented models are valid for moment magnitude ranging from 4.5 to 7.4, distance up to 200 km, and for earthquakes with reverse and strike–slip fault mechanisms. Four alternative mathematical forms are evaluated in terms of magnitude and distance in order to find the optimal functional form for reliable prediction of V/H ratios. Out of four proposed forms, two were chosen for further investigation. The point source (hypocentral and epicentral) as well as extended source (rupture and Joyner-Boore) distance metrics are employed to derive four models. The overall validity of the proposed models is examined by detailed residual analyses as well as comparison with some of the local and regional predictive V/H models. Our proposed models showed significant reduction in the total standard deviation across all periods. The proposed V/H models facilitate assessment of vertical components of response spectrum where horizontal component of response spectrum is known, using V/H spectral ratios as scaling factors.

Seismic Fragility Analysis of Steel Liquid Storage Tanks Using Earthquake Ground Motions Recorded in Korea

Liquid‐containing storage tanks are important structures in industrial complexes. Because earthquake damages to liquid storage tanks can cause structural collapse, fires, and hazardous material leaks, there have been continuous efforts to mitigate earthquake damages using seismic fragility analysis. In this regard, this study focuses on the seismic responses and fragility of liquid storage tanks. First, the characteristics of earthquake ground motions are a critical factor influencing the seismic fragility of structures; thus, this study employs real earthquake records observed in the target area, southeastern Korea, with the earthquake characteristics estimated based on the ratio of peak ground acceleration to peak ground velocity. When a liquid storage tank oscillates during an earthquake, additional forces can impact the tank wall owing to hydrodynamic pressures. Therefore, this study presents a sophisticated finite element (FE) model that reflects the hydrodynamic effect of an oscillating liquid. Another advantage of such an FE model is that detailed structural responses of the entire wall shells can be estimated; this is not possible in simplified lumped mass or surrogate models. Lastly, probabilistic seismic demand models are derived for three critical limit states: elastic buckling, elephant’s foot buckling, and steel yielding. Using the real earthquake ground motion records, constructed FE model, and limit states, a seismic fragility analysis is performed for a typical anchored steel liquid storage tank in Korea. In addition, for comparison purposes, a ring‐stiffened model is investigated to derive a seismic fragility curve. The results of the seismic fragility assessment show that elastic buckling is the most vulnerable damage state. In contrast, elephant’s foot buckling and steel yielding indicate relatively severe damage levels. Furthermore, it is observed that ring stiffeners decrease the elastic buckling damage, although there is no practical effect on elephant’s foot buckling and steel yielding in all ground motion intensities.

Experimental study of the effect of vertical acceleration component on the slope stability

The paper deals with the stability of earth dams subjected to seismic and paraseismic excitations occurring in the close distance to the dam. The Newmark’s stability approach, classified as a simplified dynamic method, has been extended for two directional dynamic loading case and the evolution of the friction coefficient. The paper is focused on the experimental verification of the proposed method for harmonic and cyclic excitations generated by a simple oscillating device as well as by one-directional shaking table. Main assumptions of the proposed method have been proved and the effect of the vertical acceleration on the stability of the dam has been demonstrated. In the experiments conducted under cyclic loading, the impact of the vertical acceleration on the permanent displacement of the block was equal to 57 %. However, in general, the exact magnitude of this impact depends on many factors, such as the vertical to horizontal peak ground acceleration ratio or frequency range of the vertical component of the earthquake.

Direct use of peak ground motion parameters for the estimation of inelastic displacement ratio of SDOF systems subjected to repeated far fault ground motions

This study is aimed at developing statistical equations to estimate the inelastic displacement ratio of singledegree- of-freedom systems subjected to far fault repeated earthquakes. In the study, peak ground motion parameters are used to define the scatter of the original data. The ratio of peak ground acceleration to peak ground velocity, and peak ground velocity of the ground motion records and structural parameters such as period of vibration and lateral strength ratio are used in the proposed equations. For the development of the equations, nonlinear time history analyses of single-degree-offreedom systems are conducted. Then, the results are used in a multivariate regression procedure. The equations are verified by comparing the estimated results with the calculated results. The average error and coefficient of variation of the proposed equations are presented. The analyses results revealed that the direct use of peak ground motion parameters for the estimation of inelastic displacement ratio significantly reduced the scatter in the original data and yielded accurate results. From the comparative results it is also observed that results obtained using equations specific to peak ground velocity or peak ground acceleration to peak ground velocity ratio are similar.

Seismic vulnerability of air traffic control towers

Airports are one of the critical infrastructures that play an essential role in managing natural disasters through receiving or sending aid and supplies. Air traffic control (ATC) towers are an inseparable part of each airport as the performance of airports depends on the functionality of their ATC towers. Many ATC towers have been designed and constructed based on older versions of modern seismic codes in which seismic design has followed a force-based design approach. This study addresses the seismic vulnerability of three in-service ATC towers which have been designed and constructed according to a force-based design concept. The height of the towers ranges from 24 to 52 m. Fragility curves have been used for the seismic vulnerability study of these towers. For the derivation of seismic fragility curves, 45 earthquake records were selected and classified into low, medium and high classes based on their ratio of peak ground acceleration (PGA) to peak ground velocity (PGV). It was observed that records with a low PGA/PGV ratio imposed the highest level of damage to the towers. However, when towers were subjected to the records with a high PGA/PGV ratio, the damage intensity was not significant. Results indicated that the intensity of seismic-induced damage to the tallest tower was significantly more than that of the shortest tower. It was concluded that only the shortest tower could satisfy the expected seismic performance objectives.