Nonlinear Site Amplification Research Articles

Development of Nonlinear Site Amplification Model Based on Average Shear-wave Velocity of Soil Layer and Bedrock Depth

Development of Nonlinear Site Amplification Model Based on Average Shear-wave Velocity of Soil Layer and Bedrock Depth

Combining observed linear basin amplification factors with 1D nonlinear site-response analyses to predict site response for strong ground motions: Application to Wellington, New Zealand

This study develops a method for estimating site amplification that combines instrumentally observed site-specific amplification factors with adjustment factors from nonlinear site-response analyses. This approach provides estimates of site response for large-strain motions based on observations and sophisticated nonlinear modeling. A database of weak-to-moderate intensity ground motions recorded in three basins of Wellington, New Zealand is used to study the observed site amplification. A subset of nine strong-motion stations was selected to perform nonlinear site-response analyses with scaled strong ground motions to assess the influence of nonlinearity on site amplification factors and demonstrate the approach. Different shear-wave velocity ( VS) profiles, constitutive models, and modeling approaches (e.g. one-dimensional (1D) site-response analyses vs empirical [Formula: see text]-based approaches) are used to quantify the sensitivity and modeling uncertainty in the nonlinear site-response analyses. It was found that for soft sites subjected to strong ground motions, there may be a decrease in spectral acceleration amplification factors for periods up to approximately 2 s, relative to the expected linear site response. For longer periods, there is little to no amplification from the effects of soil nonlinearity. However, at stiffer sites, which generally experience less basin amplification in observations, there may be moderate amplification at longer periods when nonlinearity is considered due to softening of the soil profile. Empirical ground-motion models were found to under-represent the observed amplification between basin sites and the nearby reference site, especially at intermediate to long periods, corresponding to resonant frequencies of these basin sites. In addition, the empirical nonlinear site amplification models ([Formula: see text]-based) were found to deviate from nonlinear analyses at large strains, where such models are poorly constrained due to such a limited number of observations.

Observed nonlinear site amplification of vertical ground motion in Taiwan

The objective of this study is to evaluate the possible reason for the observed nonlinear site amplification (NSA) of vertical ground motions in Taiwan. First, we observe that NSA generally occurs simultaneously in both the horizontal and vertical components of a ground-motion record and that the NSA levels are similar between these components. We also observe that most vertical peak ground acceleration (PGA) and vertical peak oscillator spectral acceleration (SA) responses for different periods occur during the shear wave (S-wave) window after S-wave arrival. The differences in the source, path, and site effects on PGA and SA responses occurring during the pressure wave (P-wave) and S-wave windows are evaluated individually through a regression analysis. We determine that NSA is observed only when PGA and SA responses occur during the S-wave window. This evidence demonstrates that the observed NSA of vertical ground motions in Taiwan may result from the hysteresis of the soil layer subjected to S-waves. This study provides physical evidence for the observed NSA of vertical ground motions in Taiwan.

Velocity structure above seismological bedrock estimated from earthquake recordings: an application of diffuse wave-field concept to strong motions in Iran

We present velocity structure inversion for three stations of Iranian Strong Motion Network (ISMN), and one KiK-net station that is used as a benchmark, for the application of diffuse wave-field concept in tectonic and geological setting of the west of Iran. This study compares the results of two existing computer codes for the velocity structure inversion at these sites. The computer codes use different search space parameterization, and error-minimization algorithms. Firstly, the available information on subsurface structure and surface geology from the strong motion stations is introduced. Then, ground motions of MW larger than 4, with PGA of all components less than 50 cm/s2 are used to calculate horizontal-to-vertical spectral ratios of earthquakes (eHVSR) at each station. The observed eHVSR curves are inverted for the velocity structure of the stations, and the results are compared with each other and the information of previous studies. Finally, the eHVSR curves of the mainshock records of the recent MW 7.3 earthquake at two ISMN sites are investigated. The velocity inversion is repeated by considering the shear modulus degradation of several shallow layers. Empirical nonlinear site amplification functions are calculated based on the modified VS structure and the VS structure of the linear ground response for two ISMN stations.Graphical

A Nonlinear Site Amplification Model for the Horizontal Component Developed for Ground-Motion Prediction Equations in Japan Using Site Period as the Site-Response Parameter

ABSTRACT This article presents a nonlinear site amplification model for ground-motion prediction equations (GMPEs), using site period as site-effect proxy based on the measured shear-wave velocity profiles of selected KiK-net and K-NET sites in Japan. This model was derived using 1D equivalent-linear site-response analysis for a total of 516 measured soil-site shear-wave velocity profiles subjected to a total of 912 components of rock-site records. The modulus reduction and damping curves for each soil layer were assigned based on the soil-type description for a particular layer. The site period and site impedance ratio affect both the linear and nonlinear parts of this study, and were used as the site parameters in the 1D amplification model. A large impedance ratio enhances the amplification ratios when the site responds elastically and enhances the nonlinear response when the site develops a significant nonlinear response. The effects of moment magnitude and source distance on the linear part of the 1D amplification model were also incorporated in the model. To implement the 1D amplification model into GMPEs, a model adjustment is required to match the GMPE amplification ratio at weak motion and to retain the nonlinear amplification ratio at the strong motion of the 1D model. The two-step adjustment method by Zhao, Hu, et al. (2015) was adopted in this study with significant modifications. It is not possible to obtain a credible second-step adjustment parameter using the GMPEs dataset only. We proposed three methods for calculating the scale factors. Method 1 is a constant angle in a 30°–60° range for all spectral periods; method 2 was based on the GMPE dataset and 1-D model parameters; and method 3 was based on the strong-motion records used for the 1D site modeling. A simple second-step adjustment factor leads to smoothing amplification ratios and soil-site spectrum.

A simulation-based nonlinear site amplification model for ground-motion prediction equations in Japan

A simulation-based nonlinear site amplification model for ground-motion prediction equations in Japan

Shallow soil effects for contrasting PGAs at nearby strong-motion stations during the 2017, Mj 5.2, southern Akita Prefecture earthquake

On September 8, 2017, an earthquake of Mj 5.2 occurred with the epicenter in southern Akita Prefecture, Japan, at 22:23 local time. According to the Japan Meteorological Agency (JMA), the focal depth was 9 km. Many strong-motion stations of K-NET and KiK-net recorded ground motions from the earthquake. The maximum horizontal vector peak ground acceleration (PGA) of approximately 136 cm/s2 was recorded at one of the KiK-net stations at an epicentral distance of about 8 km. However, despite being 37 km and 53 km far from the epicenter, two stations recorded PGAs of approximately 126 and 113 cm/s2, respectively, similar to that near the epicenter. Even though these PGAs are not rare, we found that the PGAs at the two sites strongly deviated from the median values suggested by a ground motion prediction equation (GMPE), while the nearby sites generally followed the GMPE. Available velocity models showed that shallow shear wave velocities, especially in the top 5 m, were lower (i.e., the soils were softer) at the two sites compared to those at their nearest neighboring sites. We compared the ratios of the PGAs and peak ground velocities (PGVs) at the two sites with respect to their neighboring sites for many earthquakes covering a wide range of magnitudes and azimuths. We found that the PGAs and PGVs at the two sites were systematically larger than those at the adjacent sites. Linear theoretical site amplifications using the available soil models gave peak frequencies around 6-8 Hz at the larger PGA sites. Bandpass-filtered records showed significantly larger PGAs around these frequencies at the larger PGA sites. The above results showed that local site condition is one of the major contributing factors to induce large PGAs. Furthermore, softer sites experience more substantial nonlinear site amplification than the stiffer sites when input motions exceed some threshold PGAs. This latter effect means that the softer sites can produce a variety of ground motion spectra. Nevertheless, the degree of damage to built structures depends on several factors, including the design and quality of construction. We expect that this study contributes to developing improved microzonation maps for earthquake disaster mitigation.

Testing Nonlinear Amplification Factors of Ground-Motion Models

ABSTRACT We explore nonlinear site effects in the new Japanese ground-motion dataset compiled by Bahrampouri et al. (2020). Following the approach of Seyhan and Stewart (2014), we evaluate the decrease of soil amplification according to the increasing and corresponding ground motion on surface rock (VS30=760 m/s). To better predict the rock ground motion associated with each record, we take into account the between-event variability of the ground motion, and to better evaluate the impact of nonlinearity, we correct observed ground motion on soil by the site-specific linear amplification. Instead of grouping the stations by site-response proxy, we focus on individual stations with several strong-motion records. We develop a framework to test recently published nonlinear site amplification models against a linear site amplification model and compare the results with recent building codes that include nonlinearity. The results show that the site response varies greatly from site to site, indicating that conventional site proxies, such as VS30, are not sufficient to characterize nonlinear site response. Out of all of the Kiban–Kyoshin network stations, 20 stations are selected as having recorded sufficient data to be used in the test. Out of these 20 stations, five stations show signs of nonlinearity, that is, the nonlinear models performed better than the linear-amplification model for all periods T. For most sites, however, the linear site amplification models get the best score. This suggest that, for the range of predicted rock motion considered in this study (peak ground acceleration <0.2g), nonlinearity may not have a sufficiently large impact on soil ground motion to justify the use of nonlinear site terms in ground-motion functional forms and seismic building codes for such moderate-level shaking.

An empirical relationship between resonance frequency, bedrock depth and VS30 for Croatia based on HVSR forward modelling

Seismic bedrock depth represents one of the crucial steps in site response analysis as the input seismic ground motion is propagated from the bedrock level through soil profile column to estimate surface ground motion. In the last two decades, several studies estimated bedrock depth using microtremor horizontal-to-vertical-spectral ratio fundamental (resonance) frequency and known (mostly boreholes) bedrock depth in different regions through power-law regression. In this study, seismic bedrock (H800—depth of the bedrock formation identified by shear wave velocity VS ≥ 800 m/s) is estimated using H/V forward modelling routine in which shear wave velocity profile from geophysical measurements was used as an initial soil model. Based on geological, geophysical and microtremor data, empirical relationships between average shear wave velocity in top 30 m, resonance frequency and bedrock depth are derived. Given evaluation of sedimentary thicknesses showed to be within the range of published studies for similar geological and site characteristics if the errors between different methods, approaches and site parameters are considered. The main limitation to validate proposed relationships is the lack of realistic deep borehole data like in similar studies. Further work is required that should include deep data from borehole drilling, seismic refraction and reflection or vertical electrical sounding. The intention is that presented regressions between resonance frequency, bedrock depth and VS30 would be implemented into nonlinear site amplification model and further development towards Ground Motion Prediction Equations for Croatia.

Ground motion prediction equation for crustal earthquakes in Taiwan

We develop a ground motion prediction equation (GMPE) for estimating horizontal ground motion amplitudes caused by crustal earthquakes, based on an integrated data set that includes strong motion recordings mainly from Taiwan earthquakes and only from large magnitude earthquakes in the NGA-West2 database. This GMPE is developed for probabilistic seismic hazard analysis study, which is introduced as a part of Taiwan Senior Seismic Hazard Analysis Committee Level 3 projects. The functional form developed by Chiou and Youngs was carefully studied to determine the key modeling parameters needed to regress against ground motion in the target region. Using this functional form, the GMPE achieves considerable improvement over previously developed Taiwan GMPEs. In particular, the use of a high-order function in magnitude scaling enables representation of the saturation effects of large earthquakes. Moreover, consideration of focal mechanisms, depth effects, and dip effects are used to correct the magnitude scaling; consideration of nonlinear site amplification is conditioned on VS30 and reference ground motion on rock; and consideration of basin depth effect is a function of Z1.0 in correlation with VS30. In addition, ground motion data used in this study are not only expanded by more than three times as many earthquakes and records compared with a previous Taiwan model but also provide the metadata of these records that were not available or were previously incomplete. In this study, we compare the proposed model with the NGA-West2 models and discuss the regional difference in ground motion in terms of spectral shape, magnitude scaling, distance scaling, depth scaling, style of faulting, and site effects. We provide median and single standard deviations of peak ground acceleration and 5% damped pseudospectral acceleration response ordinates of the orientation-independent average horizontal component of ground motion (RotD50) for the spectral period of 0.01–10 s.

Two-stage nonlinear site amplification modeling for Japan with VS30 and fundamental frequency dependency

We describe a two-stage nonlinear site amplification model that considers both the sediment depth and the fundamental frequency of the soil. Adopting a non-reference site approach, empirical site amplification ratios for 1591 Kyoshin and Kiban Kyoshin network sites are developed. This process involves analyzing 92,025 surface ground motion recordings from 305 earthquakes between 1997 and 2012. The model is developed in two stages: first, we regress the total empirical site effects in terms of VS30; second, we fit a functional form to the residuals from the first stage using the fundamental period of the site. We validate the model through residual analyses and statistical methods. This study shows that the peak soil period increases with the equivalent shear strain ( Iγ), while the peak amplitude decreases with Iγ. The first-stage site term reduces the error at mid-to-long period ranges (>0.1 s) by 0.11 from the error of the initial site term without any constraints. The second-stage site term reduces the error further as 0.06. Finally, we discuss the model limitations and the applicability range of the predictor variables.

Nonlinear site amplification model for ergodic seismic hazard analysis in Central and Eastern North America

This article presents recommendations for nonlinear site amplification models in Central and Eastern North America (CENA), which are developed from one-dimensional site response analyses results and accompanies linear site amplification model in a companion article. Two median nonlinear amplification models using identical functional forms are produced as a function of VS30 and peak ground acceleration for reference conditions ( PGAr) of VS = 3000 m/s and VS30 = 760 m/s. An epistemic uncertainty model on median nonlinear amplification is proposed as a piecewise functional form to generate reasonable variations of nonlinear amplification across the period and VS30 ranges of interest. Limitations of the models are based on both the methodology of the model derivation and assumptions of nonlinear amplification model forms.

Summary of the BA18 Ground‐Motion Model for Fourier Amplitude Spectra for Crustal Earthquakes in California

AbstractWe present a summary of the Bayless and Abrahamson (2018b) empirical ground‐motion model (GMM) for shallow crustal earthquakes in California based on the Next Generation Attenuation‐West2 database (Ancheta et al., 2014). This model is denoted as BA18. Rather than the traditional response spectrum GMM, BA18 is developed for the smoothed effective amplitude spectrum (EAS), as defined by the Pacific Earthquake Engineering Research Center (Goulet et al., 2018). The EAS is the orientation‐independent horizontal‐component Fourier amplitude spectrum of ground acceleration. The model is developed using a database dominated by California earthquakes but takes advantage of crustal earthquake data worldwide to constrain the magnitude scaling and geometric spreading. The near‐fault saturation is guided by finite‐fault numerical simulations, and nonlinear site amplification is incorporated using a modified version of Hashash et al. (2018). The model is applicable for rupture distances of 0–300 km, M 3.0–8.0, and over the frequency range 0.1–100 Hz. The model is considered applicable for VS30 in the range 180–1500 m/s, although it is not well constrained for VS30 values >1000 m/s. Models for the median and the aleatory variability of the EAS are developed. Regional models for Japan and Taiwan will be developed in a future update of the model. A MATLAB program that implements the EAS GMM is provided in the Ⓔ supplemental content to this article.

Peak ground motions and characteristics of nonlinear site response during the 2018 Mw 6.6 Hokkaido eastern Iburi earthquake

The observed peak ground accelerations and peak ground velocities (PGVs) of the 2018 Mw 6.6 Hokkaido eastern Iburi earthquake generally followed the median values from ground motion prediction equations with reasonable errors at fault distances ≥ 50 km. However, at smaller distances, the equations significantly underestimated the peak ground motions, and it was eminent for PGVs. A comparison of surface-to-borehole spectral ratios of S-waves during the mainshock and other events revealed that the sites at smaller distances experienced various degrees of nonlinear site response. The two most widely known characteristics of nonlinear site response are the weakening of higher-frequency components and shifting of predominant frequencies to lower ones in comparison with the linear site response. At one of the sites that recorded the largest intensity of 7 in JMA scale of 0–7, the latter nonlinear effect was so dominant that the ground motions around the new predominant frequency got intensified by one order of magnitude in comparison with that during the weak-motions. Two sites, which were closely located, recorded vertical peak ground accelerations exceeding 1 g for the up-going motions. The recordings showed asymmetric waveforms and amplitudes characteristics of the nonlinear site response in extreme vertical ground motions recorded during a few earthquakes in the past. Few sites having lower vertical peak ground accelerations were also suspected of being experienced nonlinear site response on vertical motions. These findings suggest taking a cautious approach to enumerate the reduction in amplification at higher frequencies using the single-station horizontal-to-vertical (H-to-V) spectral ratio technique. However, we found that the H-to-V technique was still useful to detect nonlinearity. Finally, an ad hoc equation was derived to correct the nonlinear site amplification in predicting horizontal PGVs with respect to one of the most widely used attenuation models in Japan. The results indicated that the effect was much stronger for a larger input motion than that for a proportional change in the Vs30 values.

Integration of Site Effects into Probabilistic Seismic Hazard Assessment (PSHA): A Comparison between Two Fully Probabilistic Methods on the Euroseistest Site

The integration of site effects into Probabilistic Seismic Hazard Assessment (PSHA) is still an open issue within the seismic hazard community. Several approaches have been proposed varying from deterministic to fully probabilistic, through hybrid (probabilistic-deterministic) approaches. The present study compares the hazard curves that have been obtained for a thick, soft non-linear site with two different fully probabilistic, site-specific seismic hazard methods: (1) The analytical approximation of the full convolution method (AM) proposed by Bazzurro and Cornell 2004a,b and (2) what we call the Full Probabilistic Stochastic Method (SM). The AM computes the site-specific hazard curve on soil, HC(Sas(f)), by convolving for each oscillator frequency the bedrock hazard curve, HC(Sar(f)), with a simplified representation of the probability distribution of the amplification function, AF(f), at the considered site The SM hazard curve is built from stochastic time histories on soil or rock corresponding to a representative, long enough synthetic catalog of seismic events. This comparison is performed for the example case of the Euroseistest site near Thessaloniki (Greece). For this purpose, we generate a long synthetic earthquake catalog, we calculate synthetic time histories on rock with the stochastic point source approach, and then scale them using an adhoc frequency-dependent correction factor to fit the specific rock target hazard. We then propagate the rock stochastic time histories, from depth to surface using two different one-dimensional (1D) numerical site response analyses, while using an equivalent-linear (EL) and a non-linear (NL) code to account for code-to-code variability. Lastly, we compute the probability distribution of the non-linear site amplification function, AF(f), for both site response analyses, and derive the site-specific hazard curve with both AM and SM methods, to account for method-to-method variability. The code-to-code variability (EL and NL) is found to be significant, providing a much larger contribution to the uncertainty in hazard estimates, than the method-to-method variability: AM and SM results are found comparable whenever simultaneously applicable. However, the AM method is also shown to exhibit severe limitations in the case of strong non-linearity, leading to ground motion “saturation”, so that finally the SM method is to be preferred, despite its much higher computational price. Finally, we encourage the use of ground-motion simulations to integrate site effects into PSHA, since models with different levels of complexity can be included (e.g., point source, extended source, 1D, two-dimensional (2D), and three-dimensional (3D) site response analysis, kappa effect, hard rock …), and the corresponding variability of the site response can be quantified.

Erratum to: Implications of non-synchronous excitation induced by nonlinear site amplification and of soil-structure interaction on the seismic response of multi-span bridges founded on piles

This work investigates the effects of soil-structure interaction and spatial variability of seismic motion due to nonlinear site amplification on the seismic behaviour of long multi-span bridges founded on piles. An analysis framework able to include the spatial variation of ground motion induced by specific geological and geomorphological scenarios in the seismic soil-structure interaction analysis of long bridges is adopted, exploiting advantages of the substructure approach. The methodology is applied to a case study constituted by a pile-supported multi-span bridge founded in a soft clay deposit overlaying a stiff bedrock with three different configurations: horizontal, inclined and wedge-shaped. The reference input motion at the outcropping bedrock is represented by a set of real accelerograms and different seismic response models are used to compute site amplification effects, discussing the contribution to the free-field ground motion of both the two-dimensional configuration of the deposit and the nonlinear soil behaviour. The ground motions obtained from the different models are then used for computing the foundation input motion accounting for the pile–soil kinematic interaction; thereafter, inertial interaction analyses are performed on structural models with either fixed or compliant base, considering the non-synchronous seismic actions at the piers foundation. The results, compared in terms of piers head displacements, ductility demand and deck transverse bending moments, finally show the relative importance of bedrock morphology, soil nonlinearity and soil-structure interaction on the structural response.

Implications of non-synchronous excitation induced by nonlinear site amplification and of soil-structure interaction on the seismic response of multi-span bridges founded on piles

Implications of non-synchronous excitation induced by nonlinear site amplification and of soil-structure interaction on the seismic response of multi-span bridges founded on piles

Ground‐Motion Prediction Equations for Subduction Slab Earthquakes in Japan Using Site Class and Simple Geometric Attenuation Functions

The frequency content of strong ground motions from subduction slab earthquakes differs significantly from that of ground motions produced by other categories (tectonic locations: shallow crustal, upper mantle, and subduction interface) of earthquakes in subduction zones. In the last two decades, a large number of records from subduction slab events have been obtained in Japan. We present a ground‐motion prediction equation (GMPE) for this category of earthquakes. We used a large dataset from reliably identified slab events up to the end of 2012. The GMPEs were based on a set of simple geometric attenuation functions, site classes were used as site terms, and nonlinear site amplification ratios were adopted. A bilinear magnitude‐scaling function was adopted for large earthquakes with moment magnitude M w≥7.1, with the scaling rates for large events being much smaller than for the smaller events. A magnitude‐squared term was used for events with M w<7.1 as well as the bilinear magnitude‐scaling function. We also modeled the effect of volcanic zones using an anelastic attenuation coefficient applied to a horizontal portion of the seismic‐wave travel distance within possible volcanic zones. We found that excluding the records from sites with inferred site classes improved the model goodness of fit. The within‐event residuals were approximately separated into within‐site and between‐site residuals, and the corresponding standard deviations were calculated using a random effects model. The separation of within‐event residuals into within‐site and between‐site components allows for the possibility of adopting different standard deviations for different site classes in a probabilistic seismic‐hazard analysis if desired. Online Material: Figures showing the distribution of between‐event residuals with respect to magnitude and fault‐top depth and the distribution of within‐event residuals with respect to magnitude and source distance.

Ground‐Motion Prediction Equations for Subduction Interface Earthquakes in Japan Using Site Class and Simple Geometric Attenuation Functions

The frequency content of strong ground motions from subduction slab earthquakes differs significantly from that of ground motions produced by other categories (tectonic locations: shallow crustal, upper mantle, and subduction interface) of earthquakes in subduction zones. In the last two decades, a large number of records from subduction slab events have been obtained in Japan. We present a ground‐motion prediction equation (GMPE) for this category of earthquakes. We used a large dataset from reliably identified slab events up to the end of 2012. The GMPEs were based on a set of simple geometric attenuation functions, site classes were used as site terms, and nonlinear site amplification ratios were adopted. A bilinear magnitude‐scaling function was adopted for large earthquakes with moment magnitude M w≥7.1, with the scaling rates for large events being much smaller than for the smaller events. A magnitude‐squared term was used for events with M w<7.1 as well as the bilinear magnitude‐scaling function. We also modeled the effect of volcanic zones using an anelastic attenuation coefficient applied to a horizontal portion of the seismic‐wave travel distance within possible volcanic zones. We found that excluding the records from sites with inferred site classes improved the model goodness of fit. The within‐event residuals were approximately separated into within‐site and between‐site residuals, and the corresponding standard deviations were calculated using a random effects model. The separation of within‐event residuals into within‐site and between‐site components allows for the possibility of adopting different standard deviations for different site classes in a probabilistic seismic‐hazard analysis if desired. Online Material: Figures showing the distribution of between‐event residuals with respect to magnitude and fault‐top depth and the distribution of within‐event residuals with respect to magnitude and source distance.

BC Hydro Ground Motion Prediction Equations for Subduction Earthquakes

An updated ground motion prediction equation (GMPE) for the horizontal component response spectral values from subduction zone earthquakes is developed using a global data set that includes 2,590 recordings from 63 slab earthquakes (5.0 ≤ M ≤7.9) and 953 recordings from 43 interface earthquakes (6.0 ≤ M ≤8.4) at distances up to 300 km. The empirical data constrain the moment magnitude scaling up to M8.0. For M &gt; 8.0, a break in magnitude scaling is included in the model based on the magnitude scaling found in numerical simulations for interface earthquakes in Cascadia. The focal depth scaling of the short-period spectral values are strong for slab earthquakes, but it is not seen for interface events. The distance scaling is different for sites located in the forearc and backarc regions, with much steeper attenuation for backarc sites. The site is classified by V S30 with constrained nonlinear site amplification effects.