Variability Of Ground Motion Research Articles

A Spatially Varying Ground Motion Model with an Evolving Energy Spectrum

Besides phase variability, amplitude variability is one of the two manifestations of the spatially varying ground motion (SVGM) in the frequency domain. Neglecting the amplitude variability of the earthquake spectra can result in an underestimation of the structural responses. Few existing amplitude variability models can be used for estimating spectra at a distance from a reference location. In this paper, a new amplitude variability model describing the evolution of the energy spectra is developed based on records of five earthquake events acquired from the SMART 1 array. The similarity between the spectra of two locations is used as a metric for measuring the spectrum changes. The energy spectra at a distance from a reference location are found to be composed of two parts, including the averaged spectra and the random variation part. In the new model, the former is estimated by the moving average of the reference spectrum, while the envelope of the latter is approximated by the wavelet approximation of the reference spectrum’s Fourier amplitude spectrum. The parameters of five models for each event and a general model for all five events are identified. Monte Carlo simulations are used for testing the models. The results validate the new model in terms of capturing the similarity changes of actual earthquakes.

Near-source ground motion estimation for assessing the seismic hazard of critical facilities in central Italy

We apply the Probabilistic Seismic Hazard Analysis (PSHA) and compute Physics-Based Simulations (PBS) of ground motion for three dams in the Campotosto area (Central Italy). The dams, which confine an artificial water reservoir feeding hydroelectric power plants, are located in an active seismic zone between the areas that experienced the 2009 L’Aquila and 2016–2017 Central Italy seismic sequences. The probabilistic disaggregation estimated for a return period of 2475 years, corresponding to the collapse limit state for critical facilities, indicates that the most dangerous fault is associated with a maximum magnitude of 6.75 ± 0.25 within a distance of 10 km. This fault is used in PBS to emulate the Maximum Credible Earthquake scenario. To capture the ground motion variability, we input a pseudo-dynamic source model to encompass spatial and temporal variations in the slip, rise time and rupture propagation, heavily affecting the near-source ground motion. Indeed, the ground motion above the rupture volume is mainly influenced by the epistemic uncertainties of rupture nucleation and slip distribution. The computed broadband seismograms are consistent with the near-source shaking recorded during the 2016 MW 6.6 Norcia earthquake and constrain the upper bound of the simulated ground motion at specific sites. Our modelling reinforces the importance of considering vertical ground motion near the source in seismic design. It could reach shaking values comparable to or larger than those of the horizontal components. This approach can be applied in other areas with high seismic hazard to evaluate the seismic safety of existing critical facilities.

Seismic behaviors of PCIC piers-supported bridge structures to spatially varying ground motions

Damages to bridge piers were repeatedly observed in many previous strong earthquakes, resulting in disruptions to traffic and impairing the functionality of road network. Extensive studies have been carried out to improve the seismic resistance of bridge piers so as to enhance the seismic performances of bridge structures. In a recent study, an innovative pendulum-type column-in-column (PCIC) system was proposed to reduce seismic induced vibrations of bridge piers. This study extends the previous study on investigating the seismic performances of PCIC piers-supported bridge structures subjected to spatially varying ground motions (SVGMs). Three-dimensional (3D) finite element (FE) models of a typical 5-span continuous bridge supported by the conventional piers and PCIC piers are developed in the ABAQUS software in the present study, and numerical simulations are performed to evaluate the dynamic responses of bridges with conventional and PCIC piers. It is demonstrated that the PCIC piers can effectively mitigate the seismic responses of bridge structures. The SVGMs tend to amplify seismic responses of bridges, therefore need be considered when evaluating the seismic responses of multi-span bridges. The results demonstrate the great potentials of the applications of PCIC piers for seismic-resistant design of bridge structures.

Stochastic Semi-Physical Model for Nonstationary Spatially Variable Ground Motions in an Engineering Site

Spatially variable ground motions are crucial for the seismic analysis and design of extended and multi-support structures. In this study, a new random nonstationary spatially variable ground motion model based on the propagation process of seismic waves is proposed. In particular, the amplitude and phase transfer functions of seismic waves at the local site are studied herein. The probability density function of the corresponding parameters is given. Two simple examples are used to show the generation of random ground motions. Compared with traditional methods, our proposed model not only has a clear physical background but also shows good practicability. The model should be for those researchers who want to use nonstationary spatially variable ground motions to study the seismic response of lifeline systems or building portfolios.

Probability-based residual displacement estimation of unbonded laminated rubber bearing supported highway bridges retrofitted with Transverse Steel Damper

Predicting the post-earthquake residual displacement of isolated bridges is crucial in deciding their operational and recovery strategies after a seismic event. This study proposes a probability-based approach to estimate the residual displacement of a trilinear hysteretic system representing the unbonded laminated rubber bearing (ULRB) supported highway bridge retrofitted with transverse steel dampers (TSDs), considering the uncertainty of structural parameters and the variability of ground motions. To this end, this study systematically derives the quasi-static residual displacement of a trilinear hysteretic system, and presents the statistical distribution model for the related structural parameters, especially for the pier height and the TSD model parameters. After that, the dynamic residual displacement property of the ULRB supported highway bridge retrofitted with TSDs is investigated considering the uncertainty of various parameters, including model parameters of TSD and ULRB, the mass of superstructure, the height of piers, as well as the ground motions with and without pulse. The maximum possible residual displacement of the trilinear hysteretic system is then related to its quasi-static residual displacement and peak displacement demand. Finally, an innovative probability-based approach is developed in this study to estimate the conditional probability of the dynamic residual displacement of the trilinear system exceeding a threshold at the given ground motion intensity, and this innovative approach is further validated by comparing it with the incremental dynamic analysis (IDA) method. Results show that the dynamic residual displacement of the TSD retrofitted ULRB supported highway bridge system is random, and the ratio between the dynamic residual displacement and the maximum possible residual displacement approximately satisfies a uniform distribution bounded by zero and one. The probability-based approach can obtain a close result with the IDA method and significantly reduce computational efforts. This research represents a first step toward developing a rapid post-earthquake assessment approach for seismically isolated bridges and the seismic design of these bridges considering the residual displacement.

Selection of Ground Motion Intensity Measures in Fragility Analysis of a Mega-Scale Steel Frame Structure at Separate Limit States: A Case Study

Selecting an appropriate ground motion intensity measure (IM) to estimate the aleatory uncertainty produced by ground motion variability is the first and crucial step in fragility analysis. The choice of IM is influenced not only by the structural system type itself but also by the limit state of the structural damage. In this study, an investigation of the selection of IM in fragility analysis with respect to different limit states is developed for a 48-story mega-scale steel frame structure with buckling restrained braces. A comparative study of the efficiency of 27 IMs is conducted at four structural damage limit states, i.e., negligible, light, moderate, and severe, through the lognormal standard deviation estimated in fragility equations. In addition, for the purpose of considering the influence of different earthquake characteristics, two completely different sets of ground motions are selected, namely near-field pulse-like and far-field earthquakes. The research shows that the ground motion characteristics and structural damage limit states have nonnegligible effects on the flexibility of intensity measures. For combination-type IMs, the number of combined terms and the combined power index have a significant impact on their performance; thus, an optimized dual-parameter combination-type intensity measure is recommended.

Liquefaction analysis of Izumio sands under variation of ground motions during strong earthquake in Osaka, Japan

This paper presents a study of liquefaction analysis at sand layers of the Izumio site, under ground motion variation during a strong earthquake in Osaka, Japan. Site investigation using standard penetration test and shear wave velocity measurement is conducted. Finite element liquefaction site response analysis integrated with a strain space multiple mechanism model is conducted. Ground motions variation is considered based on the seismic record at surrounding seismic stations. Attenuation analysis is conducted to determine the scaling factor for ground motions. Several results, such as acceleration profiles and cyclic behaviours are presented. The empirical analysis is also conducted to verify the results of the numerical analysis. The results explained that cyclic behaviours of sandy layers in the Izumio site show the liquefaction tendency. The results also showed that sandy layers are indicated as critical layers during the strong earthquake due to the excess pore water pressure reaching the liquefaction threshold. The results of the empirical analysis also present liquefaction indication at sand layers under the variation of ground motion, since the factor of safety against liquefaction is less than 1. The results are generally well-agree with liquefaction evidence and prediction presented in the previous study. The results could bring practical importance in understanding liquefaction potential in the study area.

Loss estimation of curved bridges considering the incidence angle and spatial variability of earthquake ground motion

The consideration for the angle of seismic incidence (ASI) is critical for the seismic design of curved bridges. Previous studies indicate that the effect of ASI weakens as the damage develops throughout the structure. Since curved bridges often extend over long distances and cross varied geological conditions, the spatial variability of earthquake ground motions (SVEGMs) may significantly affect their responses. However, the concurrent effects of ASI and SVEGM on the system performance of curved bridges have yet to be explored, and there are currently few reliable methodologies for conducting relevant research. To this end, this study takes the monetary repair costs as the metric for representing the entire performance of the bridge, and the impact of ASI on the total loss of long multi-span curved bridges considering the spatially variable nature of earthquake ground motions is investigated in a probabilistic manner. A multi-directional loss assessment approach is derived based on the extension of an existing loss methodology, and an already constructed, 638-m-long, twelve-span prestressed concrete curved bridge is selected as the test-bed. Twenty non-stationary and spectrum-compatible spatially variable earthquake ground motion (SVEGM) pairs are generated based on the Eurocode 8 (EC8) design spectrum and soil conditions of the bridge site for each ASI. Three seismic input motion scenarios are assumed according to the characteristics of SVEGMs, and variabilities of bridge loss with respect to the ASI under the scenario earthquakes are investigated for each excitation case. On these bases, the original ground motion records are amplified by 2 and 4 times, respectively, and 4320 (3 earthquake intensity levels × 3 excitation scenarios × 24 ASIs × 20 ground motion pairs) nonlinear response-history analyses (NRHAs) are implemented to identify the influence induced by the ground motion intensity on the loss variability. Results indicate that the impacts of ASI and SVEGMs weaken as the ground shaking intensity increases and the damage accumulates in the structure.

Variability of physics-based simulated ground motions in Thessaloniki urban area and its implications for seismic risk assessment

An accurate characterization of earthquake ground motion and its variability is crucial for seismic hazard and risk analysis of spatially distributed portfolios in urban areas. In this work, a 3D physics-based numerical approach, based on the high-performance spectral element code SPEED (http://speed.mox.polimi.it/), is adopted to generate ground shaking scenarios for strong earthquakes (moment magnitude MW=6.5–7) in the Thessaloniki area (Northern Greece). These simulations account for kinematic finite-fault rupture scenarios and a 3D seismic velocity including the two main geological structures present in the area (Thessaloniki and Mygdonia basins). The numerical model is successfully validated by comparing simulated motions, on the one hand, with the recordings of a real small-magnitude (MW4.4) earthquake and, on the other, with empirical Ground Motion Models for the historical MW6.5 1978 earthquake. The sensitivity of results to the velocity model, anelastic attenuation, and non-linear soil effects is evaluated. The variability of the ground motion intensity measures in Thessaloniki as a function of the finite-fault rupture realizations (causative fault, magnitude, hypocenter location) is explored to gain insight into its potential impact on seismic risk assessment in urban areas.

Assessment of the seismic behavior of short-to-medium overall length girder bridges under asynchronous ground motions

Proper seismic analysis and design of bridges are critical, especially in locations prone to high seismic activities where critical infrastructure is at a high risk of seismic damage leading to direct and indirect losses. The seismic performance of bridges has been widely investigated in the literature, but the effect of asynchronous ground motions for short-to-medium overall length girder bridges is a phenomenon that has not been adequately addressed by bridge codes and thus it warrants further research. For such bridges, the often-employed envelope response spectrum is not generally applicable for asynchronous ground motions as this is a multiple-support excitation problem where potential local demand concentrations are critical. This study investigates the effects of asynchronous ground motion on the seismic response of short-to-medium overall length girder bridges with reinforced concrete columns considering crustal, subcrustal and subduction earthquakes. The main source of spatial variability of ground motions considered was the variation in the local soil conditions at the foundation of 3-span (short) and 7-span (medium) overall length prototype girder bridges. Soil classes A (rocky soil) and E (softer soil) were considered to establish different combinations of soil distribution in the foundation and then compared to baseline models where site class C was applied to all the supports of the structure to study the effects of asynchronous ground motions. It was found that the variation of site class in the foundations for such structures could produce detrimental effects on the dynamic response of the structure. The presence of softer soil in most of the structure's foundations elongated the vibration period of the structure and resulted in higher displacement demands. Results also showed that critical demands are concentrated at locations where the soil conditions change, indicating increased sensitivity to seismic effects at certain locations, which would not be captured by the typical code-prescribed procedure in the presence of asynchronous ground motion effects.

Rapid Seismic Evaluation of Continuous Girder Bridges with Localized Plastic Hinges.

In seismic assessment of continuous girder bridges, plastic hinges form in bridge piers to dissipate seismic energy through nonlinear restoring forces. Considering temporal and spatial variations of ground motions, seismic evaluation of the bridges involves nonlinear stochastic vibration and expensive computation. This paper presents an approach to significantly increase the efficiency of seismic evaluation for continuous girder bridges with plastic hinges. The proposed approach converts nonlinear motion equations into quasi-linear state equations, solves the equations using an explicit time-domain dimension-reduced iterative method, and incorporates a stochastic sampling method to statistically analyze the seismic response of bridges under earthquake excitation. Taking a 3 × 30 m continuous girder bridge as an example, fiber beam-column elements are used to simulate the elastic–plastic components of the continuous girder bridge, and the elastic–plastic time history analysis of the continuous girder bridge under non-uniform seismic excitation is carried out. Results show that the computation time is only 5% of the time of the nonlinear time history approach while retaining the accuracy. This study advances the capability of rapid seismic assessment and design for bridges with localized nonlinear behaviors such as plastic hinges.

Conditional simulation of non-stationary spatially variable ground motions for long-span bridges across non-uniform site conditions

Non-stationary spatially variable ground motions (SVGMs) are commonly modelled as multivariate oscillatory processes based on evolutionary power spectral density (EPSD) functions. The existing conditional simulation algorithms require the known EPSD functions. The EPSD functions are usually assumed to be identical for all locations, which is unreasonable for long-span bridges because variable soil conditions are practically observed at different bridge piers. This paper proposes a conditional simulation algorithm for non-stationary SVGMs in consideration of non-uniform site conditions. The spatial interpolation tool, termed inverse-distance-weighted (IDW) interpolation, is introduced to estimate the EPSD functions at sites without ground motion measurement. Subsequently, the covariance matrix of the random Fourier coefficients of the multivariate oscillatory processes can be calculated. The Kriging estimation is adopted to obtain the unknown random Fourier coefficients, from which the time histories of the non-stationary SVGMs can be conditionally simulated. The proposed conditional simulation algorithm is first validated through a numerical example, in which the EPSD functions of non-uniform sites are represented by a non-stationary Kanai-Tajimi spectrum with different soil parameters. Then, the algorithm is applied to the Jiuzhou Channel Bridge, a navigation channel bridge of the Hong Kong-Zhuhai-Macau Bridge (HZMB), with complex soil and water conditions. Based on the limited in-situ seismic measurement data, the site characteristics in the bridge area are analysed, and the ground motion time histories at all piers can be generated.

Response of Aswan cable-stayed bridge to spatial non-synchronous seismic excitations

Cable-stayed bridges are important infrastructure facilities serving the world today. Therefore, their safety against earthquake ground motions is crucial. However, due to their long spans, the affecting seismic excitations might be spatially non-synchronous. This paper presents a study of the effect of non-synchronous seismic excitations on Aswan cable-stayed bridge located at southern Egypt. Nonlinear time history analysis was conducted on a three-dimensional finite element model of the bridge. The spatial variability was represented in terms of the wave passage effect which was simulated via different delay times between the arrivals of the ground motion to bridge supports. Results indicated that spatial variability of earthquake ground motion has, in general, a favorable effect on most bridge response parameters. This is attributed to the flexibility of the overall bridge provided by the flexibility of the bridge structural system and/or by existence of seismic isolation.

Selection of Ground Motion Intensity Measures and Evaluation of the Ground Motion-Related Uncertainties in the Probabilistic Seismic Demand Analysis of Highway Bridges

Probabilistic seismic demand analysis (PSDA) is known as one of the critical intermediate steps in the performance-based earthquake engineering (PBEE) design framework. Accuracy of the PSDA is influenced by various sources of uncertainties and mostly by that stemming from the ground motion-related variabilities. By taking a representative reinforced concrete (RC) continuous girder bridge as the case study, twenty-eight commonly used seismic intensity measures (IMs) were investigated in terms of the effectiveness, efficiency, practicality, proficiency, and sufficiency assessments. Probabilistic seismic demand models (PSDMs) of several critical bridge engineering demand parameters (EDPs) were developed under both the near-field and far-field ground motions through the nonlinear time history analyses (NTHAs). In addition, effects of ground motion-related uncertainties, such as the bin-to-bin (BTB) and record-to-record (RTR) variabilities, on the PSDA of highway bridges were also investigated. It is concluded that (1) IM efficiency contributes significantly to reflecting the RTR variability of ground motions and an efficient IM may reduce the influence of RTR variability in the estimation of structural demands; (2) IM sufficiency reflects the statistical independence of IM and ground motion parameters, and a sufficient IM is helpful in rendering the prediction of structural demands; and (3) uncertainties stemming from both the BTB and RTR variabilities of the seismic records have significant influences on the PSDA and the developed PSDMs of highway bridges.

A Nonergodic Ground Motion Model for Chile

ABSTRACTIn this study, we develop a new nonergodic ground motion model (GMM) for Chile, which better captures the trade-off between the aleatory variability and epistemic uncertainty on ground motion estimates compared with existing GMMs. The GMM is developed for peak ground acceleration and pseudospectral acceleration at a period of 1 s. Most existing GMMs for subduction earthquake zones were developed based on an ergodic assumption, and this is not the exception for the subduction zone in Chile. Under the ergodic assumption, the ground motion variability at a given single site–source combination is considered the same as the variability observed in a global database. However, recent efforts have highlighted significant location-specific systematic and repeatable effects for ground motions recorded within a particular region. These systematic effects promote the relaxation of the ergodic assumption and the transition to the development of nonergodic GMMs. The nonergodic GMM developed in this study uses an ergodic GMM as a backbone, the systematic source and site effects are modeled using Gaussian processes, and the path effects are modeled using the cell-specific attenuation approach enhanced with a computer graphics-based algorithm. The coefficients of the nonergodic GMM are estimated using Bayesian inference via Markov chain Monte Carlo (MCMC) methods, in which we use an integrated nested Laplace approximation approach to address the computational burden involved in MCMC. The developed nonergodic GMM reveals spatially varying and correlated location-specific source, path, and site effects in Chile, which cannot be captured by existing Chilean ergodic GMMs. Moreover, the developed nonergodic GMM shows a reduced aleatory variability compared to existing ergodic GMMs that are commonly used in Chile. In addition, the developed nonergodic GMM shows small epistemic uncertainty for regions with large ground motion data and large epistemic uncertainty for regions with few ground motion data. Finally, we provide guidelines on how to use the developed nonergodic GMM in the context of probabilistic seismic hazard analysis, which is important for performance-based earthquake engineering assessments in Chile.

Spectral representation-based efficient simulation method for fully non-stationary spatially varying ground motions

As one of the most commonly-used simulation methods, the spectral representation method (SRM) has been utilized to generate fully non-stationary spatially varying ground motions. However, this method usually fails to simulate these ground motions at a large number of interesting locations because of the heavy computational cost of the decomposition of spectral matrices and the superposition of harmonic functions, especially for simulations with time-frequency coupled modulation functions. To address this issue, this study develops an efficient SRM-based method based on a simple interpolation strategy and a quadratic regularization projected Barzilai–Borwein assisted non-negative matrix factorization (QRPBB-NMF). Concretely, the distribution of interpolation nodes is predetermined via spectral feature analysis and only the spectral matrix decomposition at these nodes is required. Then, QRPBB-NMF is introduced to decouple the decomposed spectra into the sum of the products of various time and frequency expressions. Finally, a simple spline interpolation is carried out for these expressions, thereby approximately achieving the SRM-required matrix decomposition in a decoupled manner. The developed method can decrease the operand of the matrix decomposition and invoke the Fast Fourier Transform to speed up the harmonic superposition. A case study in which the fully non-stationary spatially varying ground motions of a tunnel are simulated proves the effectiveness of the developed method in terms of accuracy and efficiency.

A substructure model for water-solid interaction under obliquely incident earthquake in canyon site

Structures crossing irregular topography features such as canyons and mountains may suffer from spatially varying ground motions due to topographic effect. In this paper, a two-dimensional substructure model of water-solid interaction in canyon site is proposed to study the effect of canyon topography on the seismic responses of water-canyon system, in which the wave radiation effect of infinite solid domains is simulated by the combined zigzag-paraxial boundary and the solid-water interaction is considered by interface conditions. Moreover, to verify the proposed substructure model, it is used to calculate the seismic responses of a V-shaped water-canyon system and a semi-circular water-canyon system under obliquely incident P-SV waves in homogeneous half space. Afterwards, we conduct the seismic analysis of water-canyon system. The results indicate that the amplification and reduction of ground motion is affected by geometric shape of canyons and water depth, and the maximum amplification of V-shaped water-canyon system can beyond an order of 200%, and the maximum amplification of semi-circular water-canyon system is less than 200%.

Simulation of Nonseparable Nonstationary Spatially Varying Ground Motions with an Enhanced Interpolation Approximation Approach

An enhanced interpolation approach is developed for simulating nonseparable nonstationary ground motions on the basis of the spectral representation method, which mainly contains two steps of interpolations and an optimization. Firstly, the interpolation technique is utilized to reduce the Cholesky decomposition time of the lagged coherence matrix. The square root of the evolutionary power spectral density is then decoupled into several time and frequency discrete functions using the proper orthogonal decomposition (POD) interpolation technique, which results in the availability of the fast Fourier transform (FFT) technique in the simulation. Compared with existing decoupling schemes, the POD interpolation achieves a significant efficiency improvement with a slight accuracy reduction. Finally, the simulation formula is further optimized to reduce the number of FFT operations. The accuracy and efficiency of this method are verified with the numerical examples of nonstationary ground motions simulation. Results show that the error introduced by two-step interpolations is fairly small and the simulation agrees with the targets very well. Furthermore, the efficiency generating sample function is significantly enhanced.

Seismic Response Analysis of Bongo Bridge Subjected to Multiple Support Excitation due to Spatial Variation of Ground Motion

The spatial variation of ground motion (SVGM) may cause detrimental effects on extended structures such as bridges. The SVGM is mainly caused by three phenomena: the incoherence effect, wave passage effect, and the local site effect, which leads the structure to undergo multiple support excitation. In most cases, in the Philippines, the conventional response spectrum analysis per DPWH Bridge Seismic Design Specifications (BSDS) 2013 is used to perform seismic analysis of bridges. However, the method assumes that the ground motion is spatially uniform, thus ignoring the potential effect of SVGM. The study focuses on the seismic response analysis of a conventional existing highway bridge in the Philippines subjected to multiple support excitation accounting for the effect of SVGM. The researcher used the Bongo Bridge located in Ilocos Norte, originally designed using the conventional response spectrum. A method for generating a modified response spectrum that accounts for the effect of SVGM based on the fundamental principle of random vibration theory was also presented to provide guidelines for bridge engineers in the Philippines. Three cases were performed where each seismic response of the existing bridge was obtained and evaluated to determine if the application of multiple support excitation due to SVGM will cause a significant effect on the existing bridge. Based on the results, the effect of multiple support excitation to Bongo Bridge amplified the seismic response of some pier columns and de-amplified some. The study also shows that the effect of multiple support excitation decreased the displacement demand significantly on the Bongo Bridge. Since the study is limited to Bongo Bridge and the seismic response can be affected by many factors, the result may vary to other bridges. Therefore, it is still recommended to perform a parametric analysis accounting for multiple support excitation especially if the structure is situated on a varying ground type or bridges with multiple and longer spans, to determine if this phenomenon will cause a significant effect on the bridge.

Optimum seismic design of curved cable-stayed bridges

One of the current advances in cable-stayed bridges design is the ability to create curved geometries to fulfill architectural requirements or site constraints. There are currently 68 curved cable-stayed bridges under operation, 56 of which have been completed in the current millennium. Most of them are footbridges, but the number of road and railway applications is increasing. However, there is not much information concerning the design of these structures. This paper concerns a 350 m long curved cable-stayed road bridge with a special emphasis on the seismic optimum design. The tower-deck connection is a key aspect for the seismic response. The longitudinal movement between tower and deck is released, the transverse and vertical support stiffness and damping are considered as design variables. For this structural-control optimization, linear viscous dampers are sought. The spatial variability of the seismic ground motion and construction erection stages for curved CSB are considered. An entropy-based algorithm is used to find the optimum solutions for two designs, S1 where the seismic loading is scaled to 30% and S2 with full seismic intensity. The results show that optimum design S2 costs 21.5% more than S1 optimum and 43% more than a similar straight bridge.