Equivalent Linear Site Response Research Articles

City-scale buildings damage estimation based on broadband physics-based ground motion simulation of 2021 Ms 6.4 Yangbi, China, earthquake

This article proposed a computational workflow for city-scale building damage estimation based on broadband physics-based ground motion simulation. The dynamic stiffness matrix method in frequency-wavenumber domain is employed for broadband physics-based ground motion simulation of finite fault along with site response correction using equivalent-linear site response analysis approach. With simulated ground motion, seismic response of buildings, using multi-degree of freedom model, is simulated using nonlinear time history analysis, and building damage is evaluated based on a trilinear backbone curve of story’s nonlinear force-drift model. Main advantage of the framework lies in the employed dynamic stiffness matrix method for ground motion simulation, which can efficiently generate broadband ground motions in perfect parallel and naturally capture the physics of finite fault source, propagation path, and spatial variability characteristics of ground motion. To demonstrate the salient features of proposed workflow, the 2021 Ms 6.4 Yangbi earthquake is simulated with frequency resolution up to 20 Hz, and seismic damage of buildings in Yangbi county are estimated. Results show that most traditional wood-adobe structures suffer moderate to severe damage, and engineered seismic buildings (mostly RC frame) in Yangbi county suffer minor damage, which agrees with field investigation results.

Response Spectrum Design Based on Site Class and Site-Specific Analysis in the Transition Zone

The building structure design needs to pay attention to the seismic code and all its consequences. Building A which will be built in Sleman, Special Region of Yogyakarta is 12.20 km from the Opak Fault causing the Bantul Earthquake of Mw 6.3 in 2006, needs seismic analysis properly using SNI 1726:2019. Based on the site near fault criteria on seismic code, Building A does not belong to the site near fault category, so it used the Probabilistic Seismic Hazard Analysis method. However, considering its distance and magnitude, the value is in the range of the requirements limit. Hence, it is still relevant when compared to the Deterministic Seismic Hazard Analysis method for designing the response spectrum. Based on the site classification in the seismic code, a site that is vulnerable to liquefaction belongs to the site class F and therefore requires site-specific analysis. The site-specific surface response spectrum is taken from the equivalent-linear and non-linear site response analysis using Deepsoil v7.0 software. The response spectrum is also calculated based on site class according to the shear wave velocity (v s) and N-SPT criteria. The site-specific spectral acceleration results are compared to 80% of the site class E spectral acceleration, as required. The site belongs to site class D using v s criteria and belongs to site class E using the N-SPT criteria. Only the equivalent-linear site response spectrum in the modified maximum horizontal direction spectrum is eligible when compared to requirements. Most of the non-linear site response spectrum results or the geometric mean response spectrum of the equivalent-linear site response results can satisfy the requirements compared to 80% of the site class D spectral acceleration because the site response analysis uses the v s parameter. The non-linear site response spectral acceleration is smaller than the equivalent-linear site response spectral acceleration.

Evaluation of Uncertainties in Site Response Analysis of Deep Soil Profiles in South Carolina Coastal Plain

ABSTRACTThe South Carolina Coastal Plain consists of deep soil sediments over basement bedrock. The depth of basement bedrock varies from being present at the surface to a depth of more than 1200 m at the southern tip of the state. A large variation exists in the thickness of the sediment, which impacts the seismic site response analyses of the Coastal Plain, particularly in areas where the availability of deep shear-wave velocity profiles is limited. This study evaluates the impact of variations in the shear-wave velocity profiles for two sites in the South Carolina Coastal Plain. The shear-wave velocity profiles were measured using different geophysical methods, including a combined multichannel analysis of surface waves and microtremor array measurement (MASW-MAM) method and P–S suspension logging. The equivalent-linear site response analyses were conducted by applying a synthetic earthquake motion at the depth of the B–C boundary (a depth of competent rock in which the shear-wave velocity is 760 m/s). The results are presented in terms of the amplification factor and its standard deviation. Results show that the average shear-wave velocity at the first 30 m (VS30), the shear-wave velocity contrast at the interface of the base layer and the B–C boundary, and the depth to the B–C boundary have a significant impact on the amplification factor and its variability, particularly for the amplification factor at periods higher than 0.1 s. The MASW-MAM method provided significantly lower VS30 values than the P–S suspension logging method at one of the two sites. Consequently, an additional peak in the amplification factor was observed for the site that had a low VS30, and the corresponding period was close to the resonant period of the loose, surface deposit.

Adjustment of site factors for basin effects from site response analysis and deep downhole array measurements in Taipei

Local site effects can amplify seismic shaking and damage caused by earthquakes. Site factors (SF) are used in seismic design to account for these effects to modify ground motions from a reference rock site. Average shear wave velocity in the top 30 m of soil (V s,30 ) is typically used to predict SF. However, recent studies have shown that using V s,30 alone may be insufficient in quantifying SF under the presence of deep soil deposits and proposed SFs that account for the bedrock depth (e.g. Z 1.0 , depth with V s of 1 km/s). This study evaluates these depth-dependent SFs using 1D nonlinear and equivalent-linear site response analyses. The predicted SFs are also compared with observations of downhole arrays installed within Taipei Basin. Based on numerical and observational results, depth correction factors are recommended in conjunction with SFs of seismic design code to reflect the effect of different sediment thicknesses in the design process. • We characterize the amplification behavior associated with bedrock depth and V s,30 . • Review recently proposed site factors (SF) that account for the bedrock depth • Assess SFs versus bedrock depth (Z 1.0 ) via 1D site response analyses • Empirical assessment of SFs using seven downhole arrays in Taipei Basin • Basin-depth correction factors in conjunction with code-based SFs for seismic design

The effect of soil nonlinearity on high-frequency spectral decay and implications for site response analysis

This study uses recorded ground motions at soil sites over a range of shaking intensities to investigate the effects of soil nonlinearity on the high-frequency spectral decay, as quantified by the parameter [Formula: see text]. Equivalent-linear site response analyses indicate that [Formula: see text] should increase significantly with increasing shear strain and ground motion intensity due to increases in soil damping. However, using more than 2500 motions from 32 sites, this study shows that [Formula: see text] does not vary systematically with the induced shear strain but instead remains at its small-strain value. This observation indicates that high-frequency components of motion are consistent with small-strain damping, rather than the strain-compatible damping used in site response analysis. It is demonstrated that equivalent-linear site response analyses for large strains can be modified to generate surface motions with more realistic high-frequency content by scaling the predicted surface motion to fit the small-strain [Formula: see text] or by employing frequency-dependent soil properties that account for the frequency dependence of the induced strains.

Seismic hazard analysis and local site effect of the 2017 Mw 7.3 Sarpol-e Zahab, Iran, earthquake

A strong earthquake occurred on November 12, 2017, in Sarpol-e Zahab city, western Iran, with the moment magnitude ( $$M_{{\text{w}}}$$ ) of 7.3 and a focal depth of 18 km. The maximum horizontal peak ground acceleration of 0.69 g was recorded at the Sarpol-e Zahab station. Significant damages were observed in frame and masonry buildings, while the damage distribution was non-uniform throughout this small city. The preliminary site reconnaissance revealed that numerous engineering structures collapsed or considerably damaged in some regions, contrary with those non-structural masonry buildings in other regions which remained intact during earthquake. This paper represents a preliminary reconnaissance report prepared through the site visit done by the authors, a few days following the earthquake occurrence. Then, the data recorded by the strong ground motion stations in the affected city and the surrounding regions together with the geotechnical data gathered from the available boreholes in Sarpol-e Zahab are incorporated for probabilistic seismic hazard and local site effect analyses. The observed response spectra at two stations and distance-dependency of ground acceleration are compared with those predicted by some attenuation models. The results of probabilistic seismic hazard analysis in the return periods of 475 and 2475 years are compared with the observed ground response and the design spectra recommended by the Iranian seismic code (for site classes Types I and II). Several geotechnical boreholes from the previous works in the affected area were analyzed through the equivalent-linear site response approach in order to obtain the seismic response at the soil surface. The results are then compared with the code design spectra for the site classes of Types III and IV. It is demonstrated that the calculated response spectra are generally larger than those recommended by the Iranian seismic code, especially for the 4–7 stories buildings.

Assessment of the Seismic Site Amplification in the City of Ivanec (NW Part of Croatia) Using the Microtremor HVSR Method and Equivalent-linear Site Response Analysis

The city of Ivanec is located between valley of the Bednja River and Mt. Ivanščica and this area can be prone to significant seismic site amplification due to local site characteristics. This study presents the first assessment of seismic site amplification for the city of Ivanec by the microtremor horizontal-to-vertical-spectral-ratio (HVSR) method and the equivalent-linear (EQL) site response analysis. Based on microtremor measurements and HVSR analysis, fundamental soil frequency and HVSR peak amplitude maps indicate potentially seismic danger zones. The 1-D EQL site response analysis was performed using multiple suites of earthquake ground motions scaled to the 95- and 475-year return periods of peak ground accelerations. Site amplification maps at the predominant peak frequency and ground surface indicate two microzones, one with high amplification in the central part of the city due to soft soil characteristics, and the other with small amplification in the transitional zone from alluvial basin towards the foothills of Mt. Ivanščica. HVSR peak amplitudes and site response peak amplifications showed similar spatial distributions with similar predominant peak frequencies but with different amplitude levels. Site amplification maps provided significant information about potential resonance effects for structures of certain heights that can be correlated with the local ground shaking characteristics.

Can a buried gas pipeline experience local buckling during earthquake ground shaking?

The damage potential of spatially variable seismic ground motion on buried pipelines has long been confirmed by field evidence, but it is still debatable whether transient seismic loads can be truly detrimental to the pipeline integrity. In the absence of systematic scrutiny of the effects of local site conditions on the seismic behaviour of such structures, this study presents a staged approach to numerically investigate the elastic-plastic buckling response of buried steel natural gas pipelines subject to transient differential ground motions arising from strong lateral site inhomogeneities. The first stage involves the study of 2D linear viscoelastic and equivalent-linear site response for the case of two sites and the resulting seismic demand in terms of longitudinal strains for input motions of various intensities and frequency content. The influence of key problem parameters is examined, and the most unfavourable relative ground deformation cases are identified. In the second stage of analysis, the critical in-plane ground displacement field is imposed monotonically on a near-field trench-like 3D continuum soil model encasing a long cylindrical shell model of the pipeline. Next, the performance of the buried pipeline is assessed under axial compression. The impedance contrast between the laterally inhomogeneous soil profiles is shown to govern the amplitude of induced elastic strains, which are maximized for low-frequency excitations. It is also demonstrated that peak axial strains along the pipeline considering equivalent-linear soil behaviour under strong earthquake motion can be as much as two orders of magnitude larger than their linear counterparts, as a result of the severe, spatially variable moduli degradation. It is finally shown that the seismic vibrations of certain inhomogeneous sites can produce appreciable axial stress concentration in the critically affected pipeline segment near the material discontinuity, enough to trigger coupled buckling modes in the plastic range. This behaviour is found to be controlled by pronounced axial force-bending moment interaction and is not accounted for in code-prescribed limit states.

Linear and nonlinear site response analyses to determine dynamic soil properties of Kirikkale

In order to make reliable earthquake-resistant design of civil engineering structures, one of the most important considerations in a region with high seismicity is to pay attention to the local soil condition of regions. It is aimed in the current study at specifying dynamic soil characteristics of Kirikkale city center conducting the 1-D equivalent linear and non-linear site response analyses. Due to high vulnerability and seismicity of the city center of Kirikkale surrounded by active many faults, such as the North Anatolian Fault (NAF), the city of Kirikkale is classified as highly earthquake-prone city. The first effort to determine critical site response parameter is to perform the seismic hazard analyses of the region through the earthquake record catalogues. The moment magnitude of the city center is obtained as Mw=7.0 according to the recorded probability of exceedance of 10% in the last 50 years. Using the data from site tests, the 1-D equivalent linear (EL) and nonlinear site response analyses (NL) are performed with respect to the shear modulus reduction and damping ratio models proposed in literature. The important engineering parameters of the amplification ratio, predominant site period, peak ground acceleration (PGA) and spectral acceleration values are predicted. Except for the periods between the period of T=0.2-1.0 s, the results from the NL are obtained to be similar to the EL results. Lower spectral acceleration values are estimated in the locations of the city where the higher amplification ratio is attained or vice-versa. Construction of high-rise buildings with modal periods higher than T=1.0 s are obtained to be suitable for the city of Kirikkale. The buildings at the city center are recommended to be assessed with street survey rapid structural evaluation methods so as to mitigate seismic damages. The obtained contour maps in this study are estimated to be effective for visually characterizing the city in terms of the considered parameters.

A numerical comparison of random vibration theory and time histories based methods for equivalent-linear site response analyses

Dynamic site response is usually implemented using an equivalent-linear approach through analyses based on time-histories or random vibration theory (RVT). In the RVT approach the input motion is characterized in the frequency domain by means of Fourier Amplitude Spectra (FAS) or power spectral densities so that the need for selecting/developing multiple suitable time-histories is avoided. Nevertheless, past studies have found that RVT may produce results that differ significantly from empirically determined site amplification functions and from the time history approach. This work is aimed to further understand the potential differences in the results from RVT and time-histories based approaches by performing a comprehensive numerical evaluation that takes into account the effect of the input intensity level, input spectral shape, site conditions, and the methodology used to produce the input FAS. The results obtained corroborate that RVT over-predictions occur mainly at the site fundamental frequencies and are larger for relatively soft soil deposits with significant impedance contrast at the soil/rock interface. However, in the soft site evaluated the magnitude of the over-prediction was rather insensitive to the increase in the inelastic demand, conversely, the over-prediction in the stiffer site increased as the site softened due to the rising inelastic demand.

Equivalent-linear site response analysis on the site of the historical Trakošćan Castle, Croatia, using HVSR method

This paper presents a major extension of seismic vulnerability research project on the site of Trakoscan Castle based on the initial horizontal-to-vertical-spectral-ratio (HVSR) results from Stanko et al. (2016). The estimated HVSR site frequencies and HV amplification at Trakoscan Castle can only be used as an indication of the initial soil site frequency and amplification, so-called natural soil model, corresponding to the subsoil profile without the influence of an earthquake. The equivalent-linear (EQL) site response analysis has been carried out for different earthquake scenarios for a maximum input rock peak ground acceleration (PGAROCK) that corresponds to return periods of 95 (0.08 g), 475 (0.18 g) and 1000 years (0.31 g). The aim of the research is to evaluate structural seismic design responses and to determine type and degree of damage caused by local site effect, which is the result of an alluvial basin and topographic influences. The main objective of this research is the formation of local microseismic zones based on an EQL analysis: surface spectral acceleration and amplification maps at the predominant frequency. Based on the HVSR frequency response of the core structure of Trakoscan Castle and the Tower itself (fundamental and higher frequency modes), maps of surface spectral acceleration and soil amplification at different frequencies (3, 5 and 10 Hz) are developed for different input PGAROCK levels (0.08, 0.18 and 0.31 g) to evaluate seismic response of the Castle. Observed amplifications are correlated with ground motion polarization and directionality of the ground motion from the alluvial basin to the hilltop. Shortening of predominant frequencies (lengthening of the period), particularly in the alluvial basin, has been observed with higher input PGAROCK in the EQL analysis. This effect is not manifested in the Trakoscan hill, and predominant frequencies match HVSR frequencies. The use of certain geophysical survey methods at historical sites is a big problem, because terrain features (e.g. steep hills, mountains, ridges, slopes, cliffs) create lack of space and make it impossible to carry out geophysical investigation. Microtremor measurements at historical sites can overcome this limitation and provide local seismic response and vulnerability behaviour of historical monuments without destroying their authenticity. Also, computational modelling can greatly improve the results. The EQL site response analysis on the site of Trakoscan Castle has confirmed and improved the results of seismic response and vulnerability based on HVSR method.

New Stress Reduction Coefficient Relationship for Liquefaction Triggering Analyses

AbstractSince its inception in the early 1970s, the stress-based simplified procedure has become the standard of practice worldwide for evaluating liquefaction triggering potential. Central to this procedure is the stress reduction coefficient, rd, which allows the estimation of the seismically induced stresses at depth in a soil profile without the need to perform a numerical site response analysis. Proposed herein is a new rd relationship that was developed from equivalent-linear site response analyses performed on soil profiles representative of those in the liquefaction case history databases. The input motions used in the analyses are representative of those from shallow crustal earthquakes. Two variants of the rd relationship are presented that allow it to be used when the profile’s shear-wave velocities are either known or unknown, with the former yielding values having less uncertainty. Additionally, calibration coefficients are provided for both active and stable continental tectonic regimes. In ...

Effect of bedrock stiffness and thickness of weathered rock on response spectrum in Korea

The Standard Penetration Test (SPT) is increasingly used to generate shear wave velocity (VS) profile of a site for seismic hazard assessment. However, it is difficult to perform site investigation using the SPT for weathered rock and bedrock even at shallow depths in most cases. Consequently, the stiffness of bedrock (VSb) is assumed to be 760 m/s, and only partial thickness of weathered rock is used for site response assessment in Korea. The increase in VSb and thickness of weathered rock (Hw) may affect the overall seismic response of a site, even though the site response is mostly governed by the upper soil layers. In this study, the effect of VSb and Hw on response spectrum in Korea was investigated by performing equivalent-linear site response analyses on three representative sites each of SC and SD soil categories as defined in the Korean seismic code based on the average shear wave velocity of top 30 m of a site (VS30). The SC and SD categories are defined similar to that in the International Building Code (IBC). Further, the effect of increase in VSb and Hw on the selection of design response spectrum based on seismic codes was also investigated. An increase in VSb resulted in an increase in spectral amplification, while the effect of increase in Hw was not substantial for the representative sites considered in this study. This means that the VS of bedrock needs to be assessed properly. On the other hand, it is possible to get a reliable seismic response even if the Hw cannot be determined accurately. The incorporation of VSb in VS30 for shallow bedrock sites (bedrock depth < 30 m) fails to consider the effect of increase in seismic amplification at large VSb. Hence, it is preferable to consider the effect of VSb separately on the design response spectrum. In addition, the effect on soil non-linearity due to variation in the VSb and Hw was found to be insignificant.

Soil amplification with a strong impedance contrast: Boston, Massachusetts

In this study, we evaluate the effect of strong sediment/bedrock impedance contrasts on soil amplification in Boston, Massachusetts, for typical sites along the Charles and Mystic Rivers. These sites can be characterized by artificial fill overlying marine sediments overlying glacial till and bedrock, where the depth to bedrock ranges from 20 to 80m. The marine sediments generally consist of organic silts, sand, and Boston Blue Clay. We chose these sites because they represent typical foundation conditions in the City of Boston, and the soil conditions are similar to other high impedance contrast environments. The sediment/bedrock interface in this region results in an impedance ratio on the order of ten, which in turn results in a significant amplification of the ground motion. Using stratigraphic information derived from numerous boreholes across the region paired with geologic and geomorphologic constraints, we develop a depth-to-bedrock model for the greater Boston region. Using shear-wave velocity profiles from 30 locations, we develop average velocity profiles for sites mapped as artificial fill, glaciofluvial deposits, and bedrock. By pairing the depth-to-bedrock model with the surficial geology and the average shear-wave velocity profiles, we can predict soil amplification in Boston. We compare linear and equivalent-linear site response predictions for a soil layer of varying thickness over bedrock, and assess the effects of varying the bedrock shear-wave velocity (VSb) and quality factor (Q). In a moderate seismicity region like Boston, many earthquakes will result in ground motions that can be modeled with linear site response methods. We also assess the effect of bedrock depth on soil amplification for a generic soil profile in artificial fill, using both linear and equivalent-linear site response models. Finally, we assess the accuracy of the model results by comparing the predicted (linear site response) and observed site response at the Northeastern University (NEU) vertical seismometer array during the 2011M 5.8 Mineral, Virginia, earthquake. Site response at the NEU vertical array results in amplification on the order of 10 times at a period between 0.7–0.8s. The results from this study provide evidence that the mean short-period and mean intermediate-period amplification used in design codes (i.e., from the Fa and Fv site coefficients) may underpredict soil amplification in strong impedance contrast environments such as Boston.

Comparison of Equivalent Linear and Nonlinear Site Response Analysis Results and Model to Estimate Maximum Shear Strain

Comparison of Equivalent Linear and Nonlinear Site Response Analysis Results and Model to Estimate Maximum Shear Strain

Comparison of 1D linear, equivalent-linear, and nonlinear site response models at six KiK-net validation sites

Vertical seismometer arrays represent a unique interaction between observed and predicted ground motions, and they are especially helpful for validating and comparing site response models. In this study, we perform comprehensive linear, equivalent-linear, and nonlinear site response analyses of 191 ground motions recorded at six validation sites in the Kiban–Kyoshin network (KiK-net) of vertical seismometer arrays in Japan. These sites, which span a range of geologic conditions, are selected because they meet the basic assumptions of one-dimensional (1D) wave propagation, and are therefore ideal for validating and calibrating 1D nonlinear soil models. We employ the equivalent-linear site response program SHAKE, the nonlinear site response program DEEPSOIL, and a nonlinear site response overlay model within the general finite element program Abaqus/Explicit. Using the results from this broad range of ground motions, we quantify the uncertainties of the alternative site response models, measure the strain levels at which the models break down, and provide general recommendations for performing site response analyses. Specifically, we find that at peak shear strains from 0.01% to 0.1%, linear site response models fail to accurately predict short-period ground motions; equivalent-linear and nonlinear models offer a significant improvement at strains beyond this level, with nonlinear models exhibiting a slight improvement over equivalent-linear models at strains greater than approximately 0.05%.

A practical method for utilization of commercial cyclic testing apparatuses for computation of site response in central Adapazari

We suggest a practical method for estimating strain–modulus–damping relationships for utilization in equivalent-linear site response analyses, so that the necessity for more sophisticated sampling and testing procedures can be justified. The method employs the commercial cyclic testing apparatuses, which have limitations in low-strain ranges, and the in-situ seismic tests. The shear modulus at about 1% cyclic shear strain amplitude and the shear-wave velocity measured in-situ is used for building a hyperbolic relationship between shear stress and shear strain. An extension of Masing׳s rule and the constraint on hysteretic damping at 1% cyclic shear strain amplitude leads to a strain–damping relationship. By putting a particular emphasis on the soils of Adapazarı, a city famous for the concentrated damage on alluvium basin during the 1999 Kocaeli (Mw7.4) earthquake, we demonstrated the usefulness of the method, and concluded that the shear-modulus reduction and damping characteristics of Adapazarı soils can yield to site amplification factors greater than those predicted by strain–modulus–damping relationships presented in literature, and can more efficiently explain the concentration of damage on the alluvium basin. Through the comparisons of spectral amplification factors computed by equivalent-linear site response analyses, we justified the necessity to run a more sophisticated testing program on determination of cyclic stress–strain behavior of Adapazarı soils, and consequently to consider transient nonlinear site-response analyses in order to reduce the possible bias in calculation of spectral amplification factors.

Performance of a transparent Flexible Shear Beam container for geotechnical centrifuge modeling of dynamic problems

A transparent Flexible Shear Beam (FSB) container was designed and constructed to simulate the dynamic response of a stratum of soil under horizontal, one-dimensional (1-D) earthquake shaking in a geotechnical centrifuge. A stack of four rectangular, acrylic frames separated by layers of flexible, high-strength rubber was used to form the transparent container. The fundamental natural frequency of the container was estimated to be similar to a layer of sand in its softened or liquefied state. The suitability of the container in simulating 1-D site response with minimal boundary effects was evaluated by monitoring the uniformity of the induced accelerations and settlements across the soil specimen. Further, the measured lateral displacements were compared with equivalent-linear site response analyses. The new FSB container was found to provide satisfactory boundary conditions for studying complex Soil–Structure-Interaction problems, while simultaneously enabling researchers to visualize deformations of the soil and buried structures during shaking.

Influence of Input Motion and Site Property Variabilities on Seismic Site Response Analysis

Seismic site response analysis evaluates the influence of local soil conditions on earthquake ground shaking. There are multiple sources of potential uncertainty in this analysis; the most significant pertaining to the specification of the input motions and to the characterization of the soil properties. The influence of the selection of input ground motions on equivalent-linear site response analysis is evaluated through analyses performed with multiple suites of input motions selected to fit the same target acceleration response spectrum. The results indicate that a stable median surface response spectrum (i.e., within ±20% of any other suite) can be obtained with as few as five motions, if the motions fit the input target spectrum well. The stability of the median is improved to ±5 to 10% when 10 or 20 input motions are used. If the standard deviation of the surface response spectra is required, at least 10 motions (and preferably 20) are required to adequately model the standard deviation. The influence of soil characterization uncertainty is assessed through Monte Carlo simulations, where variations in the shear-wave velocity profile and nonlinear soil properties are considered. Modeling shear-wave velocity variability generally reduces the predicted median surface motions and amplification factors, most significantly at periods less than the site period. Modeling the variability in nonlinear properties has a similar, although slightly smaller, effect. Finally, including the variability in soil properties significantly increases the standard deviation of the amplification factors but has a lesser effect on the standard deviation of the surface motions.

Site Effects for the Sacramento-San Joaquin Delta

Seismic site response and site effects models are presented for levees in the Sacramento-San Joaquin Delta where the subsurface soils include thick deposits of highly organic soils. Sources of uncertainty that contribute to the variation of seismic wave amplification are investigated, including variations in the input ground motions, soil profiles, and dynamic soil properties through Monte Carlo simulations of equivalent-linear site response analyses. Regression models for seismic wave amplification for levees in the Delta are presented that range from a function of peak outcrop acceleration alone to a vector of response spectra ordinates and soil profile parameters. The site effects models were incorporated into a probabilistic seismic hazard analysis for a representative location, and the relative impacts of the various models on the computed hazard are evaluated.