Response spectral amplification ratios from 1- and 2-dimensional nonlinear soil site models

In order to determine the effect of geometry on the ground response of 2-dimensional (2-D) basins filled with soils that can develop nonlinear response, we use three basin models with width/depth ratios 3, 6 and 10. The three basins are subjected to a suite of rock site records with various magnitudes and source distances. We compute response spectral amplification ratios at four locations on the surface of the 2-D basins, and determine the average variation of the amplification ratios with respect to excitation spectra, for peak ground acceleration (PGA) and 3 spectral periods of 0.2, 0.5, 1 s. Similarly, we compute the average response spectral amplification ratios for two 1-dimensional (1-D) nonlinear models, one having the soil profile at the basin centre and the other having a soil profile at half the depth of the basin. From the relationship between the average amplification ratios and excitation spectra, we determine the cross-over point in terms of excitation spectral values that separate the amplification range from the deamplification range. Our results show that the cross-over point varies significantly from one location to another on the ground surface and from one basin to another, in a range of 0.3–1.1g for PGA. The effects of basin geometry are very strong at weak and moderate excitation, but decrease with increasing excitation spectra in a significant portion around the basin centre. Our results provide some justification for using 1-D models for 2-D basins with a width/depth ratio ?6 if the soil site is subjected to strong ground shaking.     

Site Effects and Design Provisions: The Case of Euroseistest

—?Modern seismic codes usually include provisions for site effects by considering different coefficients chosen on the basis of soil properties at the surface and an estimate of the depth of bedrock. However, complex local geology may generate site amplification on soft soils significantly larger than what would be expected if we assume that the subsoil consists of plane soil layers overlaying a homogeneous half-space. This paper takes advantage of the large number of previous studies of site effects done at Euroseistest (northern Greece). Those studies have supplied a very detailed knowledge of the geometry and properties of the materials filling this shallow valley. In this paper we discuss the differences between site effects evaluated at the surface using simple 1-D computations and those evaluated using a very detailed 2-D model of the subsoil structure. The 2-D model produces an additional amplification in response spectra that cannot be accounted for without reference to the lateral heterogeneity of the valley structure. Our numerical results are extensively compared with observations, which show that the additional amplification computed from the 2-D model is real and affects by a significant factor response spectra, and thus suggests that some kind of aggravation factor due to the complexity of local geology is worthy of consideration in microzonation studies and seismic codes.     

1-D Theoretical Modeling for Site Effect Estimations in Thessaloniki: Comparison with Observations

—?We apply an algorithm based on the modal summation method to theoretically estimate the site effect at selected locations underlain by different geological formations within the city of Thessaloniki (Greece). Complete strong motion synthetics are constructed for all components of motion at each site, for a maximum frequency of 10?Hz. The anelastic, local 1-D velocity models are based on cross-hole data. Four point sources with different azimuths and distances from the city are used to compute the input signals. The theoretical amplification is estimated through spectral ratios of accelerograms obtained by the local 1-D over those obtained by the regional 1-D velocity model. The results from the numerical modeling are compared with those derived from experimental techniques, such as of Standard Spectral Ratio and Horizontal-to-Vertical Spectral Ratio, which had been applied to acceleration data recorded at the same sites. The comparison demonstrates that the theoretical amplifications based on known and simple subsurface geology can be used as a first-order estimate, while for cases of more complex geometries the use of at least 2-D modeling in site effects estimation is mandatory.     

Stochastic models for simulation of strong ground motion in Iceland

Two types of modelling approaches for simulating ground motion in Iceland are studied and compared. The first type of models, named discrete‐time series models (ARMA), are based solely on measured acceleration in earthquakes occurring in Iceland. The second type of models are based on a theoretical seismic source model called the extended Brune model. Based on measured acceleration in Iceland during the period 1986–1996, the parameters for the extended Brune models have been estimated. The seismic source models are presented here as ARMA models, which simplifies the simulation process. A single‐layer soil amplification model is used in conjunction with the extended Brune model to estimate local site amplification. Emphasis is put on the ground motion models representing the variability in the measured earthquakes, with respect to energy, duration and frequency content. Demonstration is made using these models for constructing linear and non‐linear probabilistic response spectra using a discretised version of the Bouc–Wen model for the hysteresis of the second‐order system. Copyright © 2001 John Wiley & Sons, Ltd.     

Amplification of strong ground motion in the city of Zagreb, Croatia, estimated by computation of synthetic seismograms

A hybrid technique consisting of modal summation and subsequent finite differences modelling is applied for the computation of synthetic accelerograms along a profile crossing the city of Zagreb, the capital of Croatia. Assuming the source geometry is known, the amplification properties of the underlying soil may be determined by comparison of synthetics and their response spectra computed for a bedrock model with the ones obtained under the assumption of a realistic laterally varying local model. The peak ground acceleration is larger by a factor of up to 3.5 than the value obtained for the bedrock model. The amplification of the response spectra is most prominent for frequencies below 2 Hz, and increases sharply to the SW from the mapped fault running through the centre of the city.     

Modeling of spatially correlated,site-reflected,and nonstationary ground motions compatible with response spectrum

Seismic risk analysis and mitigation of spatially extended structures require the synthesis of spatially varying ground motions in the response history analysis of these structures. These synthetic motions are usually desired to be spatially correlated, site reflected, nonstationary, and compatible with target design response spectra. In this paper, a method is presented for simulating spatially varying ground motions considering the nonstationarity, local site effects, and compatibility of response spectra. The scheme for generating spatially varying and response spectra compatible ground motions is first established for spatial locations on the ground surface with varying site conditions. The design response spectrum is introduced as the “power” spectrum at the base rock. The site amplification approach is then derived based on the deterministic wave propagation theory, by assuming that the base rock motions consist of out-of-plane SH wave or in-plane combined P and SV waves propagating into the site with assumed incident angles, from which tri-directional spatial ground motions can be generated. The phase difference spectrum is employed to model ground motions exhibiting nonstationarity in both frequency and time domains with different site conditions. The proposed scheme is demonstrated with numerical examples.     

Local seismic site amplification: effects of obliquely incident antiplane motions

Seismic site amplification studies are generally used to assess the effects of local geology and soil conditions on ground motion characteristics. Although extensive reviews on site amplification phenomena associated with stratigraphic effects can be found in the specialized literature, it should be pointed out that most of the practical applications have been limited to the study of vertically propagating shear horizontal (SH) waves, i.e., to the 1-D soil amplification problem. Furthermore, little attention, if any, has been devoted to the study of the effects of non-vertically incident SH waves on surface accelerograms and on the earthquake response of structures. In the present work, the study is extended to an investigation of 2-D site amplification of non-vertically propagating seismic shear waves in multilayered viscoelastic soil deposits. Sensitivity analyses of the effects of non-vertical incidence on site amplification functions are performed based on site geotechnical data collected from post-seismic investigations of the 1980 El-Asnam earthquake. Analytical results are discussed in terms of seismic site transfer functions, spectral ratios, surface acceleration time histories, and structural response spectra for different values of wave incidence angle. Both bedrock and rock outcropping cases are examined.     

Characterization of earthquake shaking severity in the town of Lorca during the May 11, 2011 event

Exceptional ground motions have been observed in the near-source region in relatively small and moderate earthquakes such as the Lorca earthquake of 2011. In the Mw 5.2 mainshock, horizontal peak ground acceleration reached 0.37 g at the LOR accelerograph station in the north-central part of the town. Maximum ground acceleration and velocity in this station was strongly polarised in the fault’s strike-normal axis, a feature interpreted as a near-field effect of rupture directivity. This quake hit the Lorca area causing serious structural damage, unevenly distributed in the urban area as result of a heterogeneous spread of building vulnerability and seismic shaking severity. This study investigates the characteristics of the earthquake shaking at the LOR station (on rock) and other 11 zones of Lorca with different site conditions. We have computed the 1-D transfer functions of the shallow structure at these 11 points with available local Vs models obtained with SPAC technique. These transfer functions were used to convolve the LOR accelerogram and simulate the ground motion which occurred at each site. A set of key engineering ground-motion parameters obtained here, indicate different shake levels at each site and all these values are clearly above the LOR station ones. These parameter values are in the range of typical expected values for European earthquakes with local intensity VIII. Their large values, especially those of acceleration response spectra and energy input spectra, more clearly for periods between 0.4 and 0.6 s, point out that the seismic demand has been quite high and help to explain the heavy damage spread on the town’s buildings.     

1-D and 2-D analyses of weak motion data in Fraser Delta from 1966 Duvall earthquake

The 1996 Duvall earthquake in Washington State triggered ground motion stations in the Fraser Delta, British Columbia, located on varying depths of Holocene and Pleistocene soils to a maximum depth of 800 m and one station on bedrock. Recorded ground motions were used to examine the applicability of 1-D and 2-D site response analyses for amplification studies in the Delta. 1-D response analysis gave a good indication of the period of peak response. Response spectra computed by 1-D analysis did not compare well with recorded spectra except at very deep sites. The use of 2-D analyses to include buried topography generally improved the predictions of site response spectra at the shallow sites. However, for the shallow earth sites, the recorded motions showed a strong spectral response at short periods in the range of 0.1–0.25 s. Neither 1-D nor 2-D analysis predicted this response.     

2-D Modeling of Site Effects Along the EURO-SEISTEST Array (Volvi Graben, Greece)

v--vAn estimation of local site effects in the Volvi basin as derived from observation and modeling is presented in this paper. The Volvi basin is located in the Mygdonian graben in northern Greece near the city of Thessaloniki. This test site has been studied and instrumented in the framework of the "EURO-SEISTEST" and "EURO-SEISMOD" projects funded by the European Union, aimed at improving knowledge of the influence of the local geology on the seismic response of a target area. In this context we calculate synthetic seismograms along a 2-D profile intersecting the graben, instrumented and accurately investigated with a geophysical survey and geotechnical tests. The seismic wavefield from the source to the target area has been computed with the modal summation method, while inside two of the investigated models representing the 2-D section, the wavefield has been numerically propagated with the finite-difference method. We compare the results of the two simulations, both in the time and frequency domain. We also compare the results with experimental data related to an event recorded by the Reftek network installed in the target area. This permits a better understanding of how the structural features of the 2-D models affect the seismic wavefield, especially in the frequency range between 2 Hz and 4 Hz, where one can observe differences between the simulations and the observations. This means that the general features of the models are able to reproduce observed amplification effects, apart from some discrepancies due to still unresolved structural features of the site.     

Site-specific Microzonation Study in Delhi Metropolitan City by 2-D Modelling of SH and P-SV Waves

— Delhi – the capital of India lies on a severe earthquake hazard threat not only from local earthquakes but also from Himalayan events just 200–250 km apart. The seismic ground motion in a part of Delhi City is computed with a hybrid technique based on the modal summation and the finite-difference scheme for site-specific strong ground motion modelling. Complete realistic SH and #E5/E5#-SV wave seismograms are computed along two geological cross sections, (1) north-south, from Inter State Bus Terminal (ISBT) to Sewanagar and (2) east-west, from Tilak Bridge to Punjabi Bagh. Two real earthquake sources of July 15, 1720 (MMI=IX, M=7.4) and August 27, 1960 (M=6.0) have been used in modelling. The response spectra ratio (RSR), i.e. the response spectra computed from the signals synthesized along the laterally varying section and normalized by the response spectra computed from the corresponding signals, synthesized for the bedrock reference regional model, have been determined. As expected, the sedimentary cover causes an increase of the signal amplitude, particularly in the radial and transverse components. To further check the site-effects, we reversed the source location to the other side of the cross section and recomputed the site amplifications. There are only a few sites where a large amplification is invariant with respect to the two source locations considered. The RSR ranges between 5 to 10 in the frequency range from 2.8 to 3.7 Hz for the radial and transverse components of motion along the NS cross section. Along the EW cross section RSR varies between 3.5 to 7.5 in the frequency range from 3.5 to 4.1 Hz. The amplification of the vertical component is considerable at high frequency (>4 Hz.) whereas it is negligible in lower frequency range.     

Side-effect of using response spectral amplification ratios for soft soil sites—Earthquake source-type dependent amplification ratios

Our previous studies show that site effects (amplification of rock motions), source and path effects are coupled when response spectra are used to characterize the amplification ratios for a soil site modelled as nonlinear or elastic. The coupling is referred to as a “side effect” of using response spectral amplification ratios. In the present study we use a suite of rock site records, well distributed with respect to magnitude and source distance, from crustal, subduction interface and slab earthquakes to evaluate the response spectral amplification ratio for soft soil sites. We compare these side-effects for ground motions generated by three types of earthquakes, and we find that, at periods much shorter or much longer than the natural period of a soil site modelled as elastic, the average amplification ratios with respect to rock site ground motions from three types of earthquakes are moderately different and are very similar for other spectral periods. These differences are not statistically significant because of the moderately large scatter of the amplification ratios. However, the extent of magnitude- and source-distance-dependence of amplification ratios differs significantly. After the effects of magnitude and source distance on the amplification ratios are accounted for, the differences in amplification ratios between crustal and subduction earthquake records are very large in some particular combinations of source distance and magnitude range. These findings may have potential impact in establishing design spectra for soft soil sites using strong motion attenuation models or numerical modelling.     

Linear Amplification of Horizontal Strong Ground Motion in Zagreb (Croatia) for a Realistic Range of Scaled Point Sources

— The linear amplification of the larger horizontal component of strong ground motion along a selected profile in the city of Zagreb is estimated by examining the synthetic waveforms corresponding to a suite of 16 realistically chosen scaled point sources. The accelerograms, computed for the average bedrock model by modal summation, are propagated through local laterally heterogeneous anelastic models by the finite-difference algorithm. The ratio of peak ground acceleration (PGA) and of the response spectra (RS), obtained by using local and bedrock models, define the PGA and RS amplification AMP(PGA) and AMP(RS), respectively. Even variations of the order of commonly observed uncertainties of only dip and rake angles of the causative fault show that both AMP(PGA) and AMP(RS) vary at some sites by more than a factor of two. It follows that, especially for strongly laterally heterogeneous structures, local effects must be determined for each of the relevant sources considering all associated uncertainties as completely as possible. Such a conclusion certainly holds for the case of the microzonation of Zagreb, where the local geology is quite complex, and the seismicity is not confined to a single seismic source zone.     

Validation of 3-D basin structure models for long-period ground motion simulation in the Osaka basin, western Japan

We studied the applicability of two types of existing three-dimensional (3-D) basin velocity structure models of the Osaka basin, western Japan for long-period ground motion simulations. We synthesized long-period (3–20 s) ground motions in the Osaka basin during a M6.5 earthquake that occurred near the hypothetical Tonankai earthquake source area, approximately 200 km from Osaka. The simulations were performed using a 3-D finite-difference method with nonuniform staggered grids using the two basin velocity structure models. To study the ground motion characteristics inside the basin, we evaluated the wave field inside the basin using the transfer functions derived from the synthetics at the basin and a reference rock site outside the basin. The synthetic waveforms at the basin site were obtained by a convolution of the calculated transfer function and the observed waveform at the reference rock site. First, we estimated the appropriate Q values for the sediment layers. Assuming that the Q value depends on the S wave velocity V _S and period T, it was set to Q = (1/3V _S)(T ₀/T) where V _S is in m/s and the reference period T ₀ is 3.0 s. Second, we compared the synthetics and the observations using waveforms and pseudovelocity response spectra, together with a comparison of the velocity structures of the two basin models. We also introduced a goodness-of-fit factor to the pseudovelocity response spectra as an objective index. The synthetics of both the models reproduced the observations reasonably well at most of the stations in the central part the basin. At some stations, however, especially where the bedrock depth varies sharply, there were noticeable discrepancies in the simulation results of the models, and the synthetics did not accurately reproduce the observation. Our results indicate that the superiority of one model over the other cannot be determined and that an improvement in the basin velocity structure models based on simulation studies is required, especially along the basin edges. We also conclude that our transfer function method can be used to examine the applicability of the basin velocity structure models for long-period ground motion simulations.     

The seismic microzonation of the city of Catania (Italy) for the maximum expected scenario earthquake of January 11, 1693

Safety against earthquake hazards presents two aspects: structural safety against potentially destructive dynamic forces and site safety related to geotechnical phenomena, such as amplification, landsliding and soil liquefaction. The correct evaluation of seismic hazard is, therefore, highly affected by risk factors due to geological nature and geotechnical properties of soils. In response to these new developments, several attempts have been made to identify and appraise geotechnical hazards and to represent them in the form of zoning maps, in which locations or zones with different levels of hazard potential are identified. The geotechnical zonation of the subsoil of the city of Catania (Italy) suggests a high vulnerability of the physical environment added to site amplification of the ground motion phenomena. The ground response analysis at the surface, in terms of time history and response spectra, has been obtained by some 1D equivalent linear models and by a 2D linear model, using a design scenario earthquake as input at the conventional bedrock. In particular, the study has regarded the evaluation of site effects in correspondence of the database of about 1200 boreholes and water-wells available in the data-bank of the Catania area. According to the response spectra obtained through the application of the 1D and 2D models, the city of Catania has been divided into some zones with different peak ground acceleration at the surface, to which corresponds a different value of the Seismic Geotechnical Hazard. A seismic microzoning map of the urban area of the city of Catania has been obtained. The map represents an important tool for the seismic improvement of the buildings, indispensable for the mitigation of the seismic risk.     

An investigation of the significance of local site effects in Plovdiv, Bulgaria

Plovdiv is the second largest city in the Republic of Bulgaria. A large part of the city is located on Holocene alluvial sediments and the oldest neighborhoods are situated on syenitic rock outcrops. We believe that local site effects may be an important contributor to the destruction caused by earthquakes. The primary objective of this study was to estimate quantitatively the local site effects in the central area of Plovdiv in terms of fundamental site frequency and amplification factor. Another important objective was to see how these correlate with the geological structures underlying the city. Measurements of the seismic noise at more than two hundred regularly placed points were made in the central area of the city. The H/V spectra were then calculated and analyzed to determine the spatial distribution of the fundamental site frequency and the amplification factor. The results exhibit very good correlation with the local geology. They were also compared with an intensity map from the strong 1928 Plovdiv earthquake. The comparison clearly demonstrates that the local site effects were the main factor in the destruction of buildings—the zones where the most damage was observed are also the zones where we have low fundamental site frequencies and high amplifications. Similarly the areas with high fundamental site frequencies and low amplification factors cover the neighborhoods where less damage has been observed. This study may form a basis for a more comprehensive and systematic microzonation study in Plovdiv.     

Topographic effects on the Monte Po Hill in Catania (Italy)

The study regards an evaluation of site effects on and near the Monte Po hill, located in the north-eastern part of the city of Catania (Italy), an area at high seismic risk. At the beginning of 2007 a seismic station was located in a school building, situated at the slope toe, but no seismic events have been recorded as yet. Therefore, synthetic seismograms have been used to evaluate the ground response analysis at the surface. Because the average slope is moderate (less than 15°), 1-D computer codes have been used to model the equivalent-linear earthquake site response analyses of layered hill deposits, as generally performed by professionals. However, the slope response has also been analysed in greater detail, using a 2-D computer code and the soil characterisation has been evaluated accurately by means of borings, Down-Hole tests, SDMT tests and laboratory tests. Comparing 1-D with 2-D results the stratigraphic site amplification and the Topographic Aggravation Factor (TAF) have also been computed. The aim of the study is that it will form a basis for the design of works to remediate the damage caused by a landslide reactivated by the earthquake in Eastern Sicily on December 13, 1990 (M_L=5.4).     

Seismic microzonation of Dehradun City using geophysical and geotechnical characteristics in the upper 30 m of soil column

The understanding of geotechnical characteristics of near-surface material is of fundamental interest in seismic microzonation. Shear wave velocity (Vs), one of the most important soil properties for soil response modeling, has been evaluated through seismic profiling using the multichannel analysis of surface waves in the city of Dehradun situated along the foothills of northwest Himalaya. Fifty sites in the city have been investigated with survey lines between 72 and 96 m in length. Multiple 1-D and interpolated 2-D profiles have been generated up to a depth of 30–40 m. The Vs were used in the SHAKE2000 software in combination with seismic input motion of the recent Chamoli earthquake to obtain site response and amplification spectra. The estimated Vs are higher in the northern part of the study area (i.e., 200–700 m/s from the surface to a depth of about 30 m) as compared to the south and southwestern parts of the city (i.e., 180–400 m/s for the same depth range). The response spectra suggest that spectral acceleration values for two-story structures are three to eight times higher than peak ground acceleration at bedrock. The analysis also suggests peak amplification at 3–4, 2–2.5, and 1–1.5 Hz in the northern, central, and south-southwestern parts of the city, respectively. The spatial distributions of Vs and spectral accelerations provide valuable information for the seismic microzonation in different parts of the urban area of Dehradun.     

Deterministic Earthquake Scenarios for the City of Sofia

— The city of Sofia is exposed to a high seismic risk. Macroseismic intensities in the range of VIII – X (MSK) can be expected in the city. The earthquakes that can influence the hazard in Sofia originate either beneath the city or are caused by seismic sources located within a radius of 40 km. The city of Sofia is also prone to the remote Vrancea seismic zone in Romania, and particularly vulnerable are the long-period elements of the built environment. The high seismic risk and the lack of instrumental recordings of the regional seismicity make the use of appropriate credible earthquake scenarios and ground-motion modelling approaches for defining the seismic input for the city of Sofia necessary. Complete synthetic seismic signals, due to several earthquake scenarios, were computed along chosen geological profiles crossing the city, applying a hybrid technique, which combines the modal summation technique and finite differences. The modelling takes into account simultaneously the geotechnical properties of the site, the position and geometry of the seismic source and the mechanical properties of the propagation medium. Acceleration, velocity and displacement time histories and related quantities of earthquake engineering interest (e.g., response spectra, ground-motion amplification along the profiles) have been supplied. The approach applied in this study allows us to obtain the definition of the seismic input at low cost, exploiting large quantities of existing data (e.g. geotechnical, geological, seismological). It may be efficiently used to estimate the ground motion for the purposes of microzonation, urban planning, retrofitting or insurance of the built environment, etc.     

表层沉积物特性对地震地面运动的影响研究

建立包含震源、沉积盆地和表层低速沉积层的二维模型,采用交错网格有限差分/伪谱混合方法求解地震波传播,讨论沉积层厚度和速度对地震地面运动的作用。结果表明:沉积层内产生的地震波的多重反射以及转换会引起地面运动持续时间的延长,它们的相干叠加会造成地面运动峰值的放大;随着沉积层速度的增加,多重反射与转换波的能量减小,地面运动持续时间减小,但是不同速度或者不同厚度的低速层模型均显示出一致的地面运动峰值放大特征。结果说明,在包含震源、沉积盆地和沉积层的模型中,沉积层对地面运动的作用机理更复杂。在实际应用中有必要同时考虑这些因素的综合作用。