Shahram Pezeshk

Selection and Scaling of Ground Motion Time Histories for Structural Design Using Genetic Algorithms

This paper presents a new approach to selection of a set of recorded earthquake ground motions that in combination match a given site-specific design spectrum with minimum alteration. The scaling factors applied to selected ground motions are scalar values within the range specified by the user. As a result, the phase and shape of the response spectra of earthquake ground motions are not tampered with. Contrary to the prevailing scaling methods where a preset number of earthquake records (usually between a single component to seven pairs) are selected first and scaled to match the design spectrum next, the proposed method is capable of searching a set consisting of thousands of earthquake records and recommending a desired subset of records that match the target design spectrum. This task is achieved by using a genetic algorithm (GA), which treats the union of 7 records and corresponding scaling factors as a single “individual.” The first generation of individuals may include a population of, for example, 200 records. Then, through processes that mimic mating, natural selection, and mutation, new generations of individuals are produced and the process continues until an optimum individual (seven pairs and scaling factors) is obtained. The procedure is fast and reliable and results in records that match the target spectrum with minimal tampering and the least mean square of deviation from the target spectrum.

Hybrid Empirical Ground-Motion Prediction Equations for Eastern North America Using NGA Models and Updated Seismological Parameters

In the field of earthquake engineering, ground-motion prediction models are frequently used to estimate the peak ground acceleration (PGA) and the pseudos- pectral acceleration (PSA). In regions of the world where ground-motion recordings are plentiful, such as western North America (WNA), the ground-motion prediction equations are obtained using empirical methods. In other regions, such as eastern North America (ENA), with insufficient ground-motion data, alternative methods must be used to develop ground-motion prediction equations (GMPEs). The hybrid empiri- cal method is one such method used to develop ground-motion prediction equations in areas with sparse ground motions. This method employs the stochastic simulation method to adjust empirical GMPEs developed for a region with abundant strong- motion recordings in order to estimate strong-motion parameters in a region with a sparse database. The adjustments take into account differences in the earthquake source, wave propagation, and site-response characteristics between the two regions. In this study, a hybrid empirical method is used to develop a new GMPE for ENA, using five new ground-motion prediction models developed by the Pacific Earthquake Engineering Research Center (PEER) for WNA. A new ENA GMPE is derived for a magnitude range of 5 to 8 and closest distances to the fault rupture up to 1000 km. Ground-motion prediction equations are developed for the response spectra (pseudoacceleration, 5% damped) and the PGA for hard-rock sites in ENA. The resulting ground-motion prediction model developed in this study is compared with two ENA ground-motion models used in the 2008 national seismic hazard maps as well as with available observed data for ENA.

Empirical-Stochastic Ground-Motion Prediction for Eastern North America

An alternative approach based on a hybrid-empirical model is utilized to predict the ground-motion relationship for eastern North America (ENA). In this approach, a stochastic model is first used to derive modification factors from the ground motions in western North America (WNA) to the ground motions in ENA. The ground-motion parameters are then estimated to develop an empirical attenuation relationship for ENA using empirical ground-motion relationships from WNA .W e develop an empirical-stochastic source model for both regions to obtain ground mo- tions at different magnitude-distance range of interest. At short distances (R 30 km) and large magnitudes (Mw 6.4), an equivalent point-source model is carried out to consider the effect of finite-fault modeling on the ground-motion parameters. Source focal depth and Brune stress drop are assumed to be magnitude dependent. We choose three well-defined empirical attenuation relationships for WNA to com- pare the empirical ground-motion processes between the two regions. A composite functional attenuation form is defined, and, in turn, a nonlinear regression analysis is performed by using a genetic algorithm (GA) for a wide range of magnitudes and distances to develop an empirical attenuation relationship from the stochastic ground- motion estimates in ENA. The empirical-stochastic attenuation relationship for hor- izontal peak ground acceleration and spectral acceleration are applicable to earth- quakes of Mw 5.0-8.2 at distances of up to 1000 km. The resulting attenuation model developed in this study is compared with those used in the 2002 national seismic hazard maps, derived in the 2003 Electric Power Research Institute studies and re- corded in ENA. The comparison of the results to the other attenuation functions and the available ENA data show a reasonable agreement for the ENA ground motions.

A New Inversion Procedure for Spectral Analysis of Surface Waves Using a Genetic Algorithm

A new inversion procedure for spectral analysis of surface waves (SASW) using a genetic algorithm (GA) is presented. The inversion process proposed in this study starts by running a forward solution for the Rayleigh dispersion equation, with sets of random inputs, to find the theoretical phase velocities. Then, it continues by finding new and better sets of inputs through processes that mimic natural mating, selection, and mutation in each generation. The goal of the GA is to find the best match between the theoretical and the experimental dispersion curves. Therefore, with each new generation there is a better agreement between the calculated output theoretical dispersion curve and the input experimental dispersion curve. To start the procedure, two options are available, either requesting the GA-based optimization process to obtain shear-wave velocities and thicknesses for each layer, or providing the thicknesses and requesting the optimization process to obtain the best set of shear- wave velocities. The GA part of the procedure is fast, stable, and accurate, with several advantages compared to the traditional methods. The strength and accuracy of the proposed procedure are presented through two example problems. We show that (1) the inversion process using a GA results in a good agreement between the theoretical and experimental dispersion curves, and (2) the shear-wave velocity pro- files obtained from the approach presented in this study and a downhole seismic survey show a good level of agreement.

Unexpected Values of Qs in the Unconsolidated Sediments of the Mississippi Embayment

We studied the attenuation of shear waves at three sites in the Mississippi embayment using data recorded in boreholes drilled to depths of up to 60 m. The source was a highly repeatable compressed-air-driven hammer. To estimate attenuation we used a spectral ratio technique for fixed depth and variable frequency. The best-fit line for each depth z gives a measure of the cumulative attenuation, indicated by α( z ). Then we fit a straight line to α( z ) for a range of values of z . The slope of this line gives an estimate of the average attenuation per distance and was used to determine an average Q s. For one of the sites (Newport, northeastern Arkansas), Q s ranges between 34 (1.5 m ≤ z ≤ 44.2 m) and 44 (1.5 m ≤ z ≤ 51.8 m). These values are significantly higher than the more typical value of about 10 determined for unconsolidated sediments by other authors. In addition, these high values correspond to sediments with low average shear-wave velocity (about 300 m/sec). In contrast, average Q s and velocity for sediments in Shelby Forest (near Memphis, Tennessee) are 22 and 348 m/sec (22.6 m ≤ z ≤ 60.1 m), respectively. Therefore, these results go against the conventional wisdom that low velocity implies low Q . For the third site (Marked Tree, northeastern Arkansas), average Q s and velocity are 18 and 251 m/sec (9.8 m ≤ z ≤ 33.6 m), respectively. This site is about 75 km from Newport, and the differences in attenuation appear related to differences in lithology. Manuscript received 5 April 2001.

Risk-Based Seismic Design for Optimal Structural and Nonstructural System Performance

An automated performance-based design methodology to optimize structural and nonstructural system performance is outlined and it is shown that it can be used to enhance understanding of structural steel system design for minimum life-cycle costs. Performance is assessed using loss probability with direct economic loss expressed as a percentage of the building replacement cost. Time-based performance assessment is used to compute the expected annual loss of a given steel framing system assuming exposure to three seismic hazard levels. Damage to the structural system, nonstructural displacement-sensitive components, and nonstructural acceleration-sensitive components is characterized using fragility functions. A steel building with three-story, four-bay topology taken from the literature is used to demonstrate application of the algorithm with subsequent comparison of designs obtained using the proposed methodology and others found in the literature.

A Study of Horizontal-to-Vertical Component Spectral Ratio in the New Madrid Seismic Zone

The horizontal-to-vertical component (H/V) spectral ratio of the small and moderate earthquake ground motions for the shear-wave window was used as an estimation of the site response in the New Madrid seismic zone (NMSZ). The database used in this study consisted of 500 broadband seismograms from 63 events of magnitude Mw 2.5 to 5.2, recorded on 11 stations operated by the University of Memphis Center for Earthquake Research and Information (CERI) at the University of Memphis. All the broadband stations were located within the Mississippi embayment. Soil deposits overlying the rock basement of the embayment strongly affected the amplitudes of the ground motions. The horizontal-to-vertical component ratios were evaluated for the frequency range of 0.2 to 20 Hz. The observed average H/V ratios suggested site amplification between 2 and 4 in the low-frequency range (f ≤ 5 Hz) for stations located on the lower shear-wave velocity deposits (lowlands). The higher shear-wave velocity deposits (uplands) indicated low-frequency amplification be- tween 1.5 and 3 Hz. The observed average H/V ratios were also compared with the soil amplifications in the upper Mississippi embayment developed by Romero and Rix (2005) from the 1D (equivalent linear) method for generic regional profiles. The H/V ratios were also compared with the theoretical quarter-wavelength approx- imation. These comparisons suggested that the H/V ratios could be a first estimate of the site amplifications. Finally, the variability of the H/V ratios with distance was examined and no discernible trends were found; therefore, the path effect model developed by Zandieh and Pezeshk (2010) for thevertical ground motions in NMSZ using the database of this study was also applicable for the horizontal ground motions.

An empirical method to estimate shear wave velocity of soils in the New Madrid seismic zone

Abstract In this study, a set of charts are developed to estimate shear wave velocity of soils in the New Madrid seismic zone (NMSZ), using the standard penetration test (SPT) N values and soil depths. Laboratory dynamic test results of soil samples collected from the NMSZ showed that the shear wave velocity of soils is related to the void ratio and the effective confining pressure applied to the soils. The void ratio of soils can be estimated from the SPT N values and the effective confining pressure depends on the depth of soils. Therefore, the shear wave velocity of soils can be estimated from the SPT N value and the soil depth. To make the methodology practical, two corrections should be made. One is that field SPT N values of soils must be adjusted to an unified SPT N′ value to account the effects of overburden pressure and equipment. The second is that the effect of water table to effective overburden pressure of soils must be considered. To verify the methodology, shear wave velocities of five sites in the NMSZ are estimated and compared with those obtained from field measurements. The comparison shows that our approach and the field tests are consistent with an error of less than of 15%. Thus, the method developed in this study is useful for dynamic study and practical designs in the NMSZ region.

Investigation of Geometrical Spreading and Quality Factor Functions in the New Madrid Seismic Zone

The accuracy and applicability of geometrical spreading and quality factor functions are investigated for the New Madrid seismic zone (NMSZ) using recorded small and moderate earthquakes. These functions represent the path effect in frequency domain. The database used in this study consists of 500 broadband seismograms from 63 eventsofmagnitudeMw 2.5to5.2,recordedbytheCenterforEarthquakeResearchand Information (CERI) at the University of Memphis. The hypocentral distances range from 10 to 400 km. All the broadband stations are located within the Mississippi embayment with different site conditions. The vertical components of the records areprocessedandusedtodefinethepatheffectterminfrequencyrangeof0.2to30Hz. A hinged-trilinear geometrical spreading and frequency-dependent quality factor functions are used to describe the path term. The regression analysis using a genetic algorithm(GA)indicatesthatatdistanceslessthan70kmthespectralamplitudesdecay as R � 1 ; between 70 and 140 km spectral amplitudes increase with distance and the geometric spreading is defined as R � 0:25 ; beyond 140 km, the attenuation is described by R � 0:5 . The quality factor function is expressed as Q � 614f 0:32 for frequencies greater than 1 Hz after the regression analysis. For the broader range offrequency used in this study (0.2 to 30 Hz), the Q function is described by a third-degree polynomial described as logQf �� 2:898 � 0:464logf � 1:238� logf� 2 � 0:540� logf� 3 . The results of this study are compared with those of Atkinson (2004) and Samiezade-Yazd etal.(1997).Thepathtermobtainedinthisstudycanbeusedinthestochasticmethodto predict ground motions in the NMSZ and eastern North America (ENA).

Improved Velocity and Displacement Time Histories in Frequency Domain Spectral-Matching Procedures

Existing spectral-matching techniques in the frequency domain distort the displacement time history of the ground motions. In the time domain spectral- matching procedures, scale functions (wavelets) are additive and, with an appropriate scale functional form, extra displacement will not be imposed to the record. However, matching in the frequency domain with a multiplicative scale function applied to the Fourier spectrum requires a special attention in the matching process to have control on the displacement time history. This study shows that thevelocity value at the end of the record is not affected by the Fourier amplitude spectrum scaling, but the displace- ment may linearly increase (or decrease) boundlessly. Two numerical solutions are proposed to solve the displacement drift problem in the frequency domain. Following the proposed frequency domain baseline correction procedure, one does not need to perform baseline correction in the time domain after completing the spectral matching. As a result, acceleration, velocity, and displacement time histories will remain fully compatible, and the boundary conditions of the velocity and displacement time histories will be preserved. The proposed procedure is not limited to spectral-matching methods and can be used with any general filtering process to retain the final dis- placement of the record. The possibility of applying a zero-padding technique to the spectral-matching filter is also discussed. It is shown that applying an appropriate window along with the zero-padding technique can lead to a reasonable displacement time history. The proposed procedures can be easily added to the existing or new frequency domain spectral-matching algorithms without significantly disrupting the spectral-matching process.