Nonlinear Site Response Analysis Research Articles

Challenges associated with site response analyses for soft soils subjected to high-intensity input ground motions

Nonlinear site response analyses are generally preferred over equivalent linear analyses for soft soil sites subjected to high-intensity input ground motions. However, both nonlinear (NL) and equivalent linear (EQL) analyses often result in large shear strain estimates (3–10%) at soft sites, and these large strains may generate unusual characteristics in the predicted surface ground motions, such as irregular time histories and atypical spectral shapes. One source of unusual ground motion predictions may be attributed to unrealistically low shear strengths implied by commonly used modulus reduction curves. Therefore, modulus reduction and damping curves can be modified at shear strains greater than approximately 0.1% to provide a more realistic soil model for site response. However, even after these modifications, nonlinear and equivalent linear site response analyses still may generate unusual surface acceleration time histories and Fourier amplitude spectra at soft soil sites when subjected to high-intensity input ground motions. In this study, we use equivalent linear and nonlinear 1D site response analyses for the well-known Treasure Island site to demonstrate challenges associated with accurately modeling large shear strains, and subsequent surface response, at soft soil sites.

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

Ground Motion Site Amplification Factors for Sites Located within the Mississippi Embayment with Consideration of Deep Soil Deposits

In this study, site amplification factors for the deep soil deposits of the Mississippi embayment are computed using a nonlinear site response analysis program first to develop a model for nonlinear soil response for possible use by ground motion developers and second to address site amplification estimation. The effects of geology, sediment depth, and average shear wave velocity at the upper 30 m of soil ranging 180–800 m/s, as well as the effect of peak ground acceleration at the bedrock on nonlinear ground motion amplification for the upper embayment, are investigated. The site response computations cover various site conditions, sediment depth of 70–750 m, and peak acceleration of input rock motions of 0.01–0.90 g. The amplification (or de-amplification) at various frequencies implied by the sediment depth is greater than that implied just by site classification of the top 30 m of soil.

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%.

Equivalent linear and nonlinear site response analysis for design and risk assessment of safety-related nuclear structures

Site response analysis is a precursor to soil-structure interaction analysis, which is an essential component in the seismic analysis of safety-related nuclear structures. Output from site response analysis provides input to soil-structure interaction analysis. Current practice in calculating site response for safety-related nuclear applications mainly involves the equivalent linear method in the frequency-domain. Nonlinear time-domain methods are used by some for the assessment of buildings, bridges and petrochemical facilities. Several commercial programs have been developed for site response analysis but none of them have been formally validated for large strains and high frequencies, which are crucial for the performance assessment of safety-related nuclear structures. This study sheds light on the applicability of some industry-standard equivalent linear (SHAKE) and nonlinear (DEEPSOIL and LS-DYNA) programs across a broad range of frequencies, earthquake shaking intensities, and sites ranging from stiff sand to hard rock, all with a focus on application to safety-related nuclear structures. Results show that the equivalent linear method is unable to reproduce the high frequency acceleration response, resulting in almost constant spectral accelerations in the short period range. Analysis using LS-DYNA occasionally results in some unrealistic high frequency acceleration ‘noise’, which can be removed by smoothing the piece-wise linear backbone curve. Analysis using DEEPSOIL results in abrupt variations in the peak strains of consecutive soil layers. These variations are found to be a consequence of the underlying hysteresis rules. There are differences between the site response predictions from equivalent linear and nonlinear programs, especially for large strains and higher frequencies, which are important for nuclear applications. The acceleration predictions from nonlinear programs are reasonably close for most cases, but the peak strain predictions can be significantly different despite using identical backbone curves. Variability in the predictions of different site response analysis programs is significant for large strains and at higher frequencies, underlining the need for the validation of these programs. Biaxial horizontal site response analyses are also performed for the stiff soil site using LS-DYNA. Results from these analyses show that the inclusion of the orthogonal component of the ground motion in site response analysis can significantly influence the acceleration response.

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.

Ground motion amplification due to shallow cavities in nonlinear soils

Subsurface cavities or stiff inclusions represent mechanical discontinuities for seismic waves propagating in soils. They modify the propagation pattern of seismic waves and alter soil response in correspondence to the ground level or building foundations. In the literature, different analytical and numerical solutions have been proposed to account for the effect of underground cavities or inclusions on the motion generated by P, S or R waves. In these former studies, the subsoil was assimilated to a homogeneous, isotropic and linear elastic halfspace containing one or more cavities. In the present study, the effect of subsurface cavities on ground motion amplification has been analysed accounting for soil stiffness degradation and associated damping increase with increasing levels of shear strains, a fundamental aspect of soil behaviour under earthquakes. The analysed model was inspired to a real case represented by the village of Castelnuovo (Italy), which during the 2009 Abruzzo earthquake suffered huge damage. The main shock (6 April 2009) caused the collapse of 50 % of the whole built environment. The historical centre of Castelnuovo rises on a hill. In its subsoil, there are many cavities with roofs 2–3 m below the ground level. The longitudinal NW–SE section of the hill has been investigated by 2D nonlinear site response analyses. A preliminary site response analysis was performed without modelling cavities, to identify ground motion amplification due to mere stratigraphic and topographic factors. The numerical model was later refined inserting: (1) a single cavity below the hilltop, (2) multiple cavities placed below the ground surface of the hill and (3) multiple cavities filled with concrete (inclusions). The performed study highlights the important role exerted by underground cavities on the ground motion computed at the hill surface. This effect should be properly considered for both microzonation studies and the correct determination of the seismic actions on specific buildings.

Seismic microzonation of Chania, Crete (Greece) based on SASW measurements and non-linear site response analyses

Following a brief overview of past applications of, and more recent advances on seismic microzonation, the results of a seismic microzonation study for the city of Chania, Greece, are presented. The study was based on Vs vs. depth profiles obtained at 19 sites of the urban area by performing SASW measurements. The spatial distribution of Vs values was utilized in estimating Vs30 values, depth to bedrock and the fundamental ground period variation across the area of the city as well as for conducting 1-D finite element non-linear inelastic site response analyses. The input earthquake excitations employed in the response analyses were based on the results of an available seismic hazard study for the Chania Area. The results of analyses were utilized for establishing the spatial distribution of rock motion amplification, the expected ground motions and spectral values in the area of the city. Contour maps providing values of the expected ground motion in the urban area are given which may become a practical tool in assessing the seismic risk and expected damage in the Chania area. The maps can also be used in the design of new earthquake resistant structures or the seismic retrofitting of existing ones. Finally, the results were utilized to demonstrate the inadequacy of using Vs,30 values for classifying the soil conditions in the Chania area.

Seismic design spectra for different soil classes

This paper investigates the validity of the soil class dependent spectral shape factors used to calculate seismic design actions in the New Zealand seismic design standard NZS1170.5, which currently specifies seismic design spectra corresponding to five different soil classes. According to the current provisions stipulated in NZS1170.5, for all natural periods, the seismic demand for structures on soft soil is either equal to or greater than that for structures on hard soil. This is opposite to the basic structural dynamics theory which suggests that an increase in stiffness of a system results in an increase in the acceleration response. In this pretext, a numerical parametric study is undertaken using a nonlinear site response analysis tool in order to capture the effect of soil characteristics on structural seismic demand and to scrutinize the validity of the current site specific seismic design spectra. It is identified that the level of input ground motion intensity and shear stiffness of the soil deposit (represented by its shear wave velocity Vs) greatly affect the maximum acceleration and frequency content of the surface motion. The study found some shortfalls in the way the current code defines seismic design demand, in particular the hierarchy of soil stiffness at low structural periods. It was found that stiff soils generally tend to have a higher spectral acceleration response in comparison to soft soils although this trend is less prominent for high intensity bed rock motions. It was also found that for medium to hard soils the spectral acceleration response at short period is grossly underestimated by the current NZS1170.5 provisions. Based on the outcomes of the parametric numerical analyses, a revised strategy to determine structural seismic demand for different soil classes is proposed and its application is demonstrated through an example.

Sensitivity of site response analysis on the number of ground motion records and implications for PSHA

This paper investigates issues related to the number of ground-motion records required for the performance of site response analysis and the inclusion of the site-specific amplification function within probabilistic seismic hazard calculations (PSHA). It explores the minimum number of records required for a robust estimation of the median and standard deviation of the site amplification function, as well as the impact of the selected ground-motion suites on the results of PSHA. Site response analyses are performed using both equivalent linear and nonlinear methodologies. Although the median amplification was observed to be relatively easy to capture, the standard deviation was seen to fluctuate considerably, especially when suites of few records were used. It was observed that in the case of the nonlinear site response analysis 10 records provide relatively stable estimates of the hazard curves for the majority of periods, while in the case of the equivalent linear analysis 20 records or more are required to achieve a similar level of accuracy.

Development of an inverse analysis framework for extracting dynamic soil behavior and pore pressure response from downhole array measurements

SUMMARYObservations from earthquakes over the past several decades have highlighted the importance of local site conditions on propagated ground motions. Downhole arrays are deployed to measure motions at the ground surface and within the soil profile, and also to record the pore pressure response within the soft soil profiles during excitation. The degradation of soil stiffness as excess pore pressures are generated during earthquake events has also been observed. An inverse analysis framework is developed and demonstrated to directly extract soil material behavior including pore water pressure (PWP) generation from downhole array measurements that can then be readily used in 1D nonlinear site response analysis. The self‐learning simulations (SelfSim) inverse analysis framework, previously developed for total stress site response analysis, is extended to extract PWP generation behavior of the soil in addition to cyclic response during ground shaking. A Neural Network based constitutive model is introduced to represent PWP generation during cyclic loading. A new analysis scheme is introduced that can use data from co‐located piezometer and accelerometer sensors. The successful performance of the proposed framework is demonstrated using four synthetic vertical array recordings. Copyright © 2013 John Wiley & Sons, Ltd.

Effect of Parameters on Equivalent Number of Cycles Using ‎Nonlinear Seismic Site Response Analysis

The concept of equivalent number of uniform stress cycles, is essential for assessment of soil liquefaction potential. In this regard, various procedures are used to convert random acceleration time history to uniform cycles having amplitude of 0.65 of peak acceleration. Equivalent number of cycles (Neq) defines equivalent energy generated by harmonic loading as that imposed by irregular motion during an earthquake. Neq is assumed to be a function of earthquake magnitude. Over the past years, in accordance with development in methods of soil liquefaction evaluation, various methods have been proposed to determinate equivalent number of cycles. In particular, parameters like site to source distance (r), have been related directly to Neq. In this study, more than 80 earthquake records have been investigated and their Neqs are assessed using energy approach and nonlinear site response analysis. It is shown that equivalent number of cycles is related to earthquake magnitude (M), r and depth of originated signals. Unlike previous methods which result in scatter in output data, current approach has led to more uniform and consistent results for each earthquake.

Comparative study on the equivalent linear and the fully nonlinear site response analysis approaches

Seismic site effect has been a major issue in the field of earthquake engineering due to the large local amplification of the seismic motion. This paper presents the importance of an appropriate soil behavior model to simulate earthquake site response and gives an overview of the field of site response analysis. Some of the well-known site response analysis methods are discussed. The objective of this paper is to investigate the influences of nonlinearity on the site response analysis by means of a more precise numerical model. In this respect, site responses of four different types of one-layered soil deposit, based on various shear wave velocities with the assumption of linear and rigid base bedrock, were analyzed by using the equivalent linear and fully nonlinear approaches. Nonlinear analyses’ results were compared with those of the linear method, and both of the similarities and differences are discussed. It is concluded that in the case of nonlinearity of soil under strong ground motions, 1-D equivalent linear modeling overestimates the amplification patterns in terms of absolute amplification level, and cannot correctly account for resonant frequencies and hysteric soil behavior. Therefore, more practical and appropriate numerical techniques for ground response analysis should be surveyed.

Surface level ground motion estimation for 1869 Cachar earthquake (Mw7.5) at Imphal city

In this paper, the seismic susceptibility of Imphal city with respect to ten synthetically generated samples of the historic 1869 Cachar (Mw 7.5) earthquake that occurred in the Kopili fault is presented based on the finite-fault seismological model in conjunction with nonlinear site response analyses. For all the synthetic sample earthquake events, the mean and standard deviation of surface level spectral ground acceleration at peak ground acceleration (PGA) and natural periods of 0.3 and 1 s have been reported in the form of contour maps. These contour maps can serve as guidelines for engineers and planners to identify vulnerable areas for possible seismic disaster mitigation of Imphal city.

A comparative case study on time domain nonlinear site response analysis subjected to earthquake excitation with elastic and rigid half space (site of Damghan earth dam-Semnan province-Iran)

The aim of this study was evaluate the site response with consideration rigid and elastic half space as the bedrock and quantify the site effect on the surface over a number of geotechnical areas. The authors have an intention to establish a comparative study on time domain analysis with consideration of bedrock type as the location of input motion and its effect on top layers over it. For this aim the site of Damghan earth dam in Seman province of Iran was selected. At the first by field investigation, the required data were collected and by primary processing the acceptable data were selected. Then in nonlinear analysis, for elastic and rigid half space bedrock, Standard Hyperbolic Model was selected and performed and the results of them were compared to each other which clearly showed the effect of bedrock on soil behavior under the earthquake excitation is one of the main factors on computation of response spectra in ground response prediction. A critical element in this work was to develop and use a computer code that could be installing quickly and act as a logic relation link between used softwares. This produced computer code which namely as “Abbas Converter” can change and support various recorded format to applicable form for used softwares can make easy and render this analysis with generation and producing the required data for used softwares and take over the encountered problem. Key word: Nonlinear time domain analysis, “Abbas converter”, elastic and rigid half space bedrock.

Damping formulation for nonlinear 1D site response analyses

Measurements and observations of ground shaking during large earthquakes have demonstrated the predominant role of site effects in the response of infrastructure during a seismic event. Despite significant efforts to model the hysteretic response and nonlinearity of soils due to medium and large ground motions, the most widely accepted nonlinear site response methods are not able to represent simultaneously the changes of stiffness and energy dissipation (damping) observed in both laboratory tests and during earthquake events. This paper presents two new soil damping formulations implemented in nonlinear one-dimensional site response analysis for small and large strains. The first formulation introduces an approach to construct a frequency-independent viscous damping matrix which reduces the over-damping at high frequencies, and therefore, the filtering at those frequencies. The second formulation introduces a reduction factor that modifies the extended Masing loading/unloading strain–stress relationship to match measured modulus reduction and damping curves simultaneously over a wide range of shear strains. A set of examples are introduced to illustrate the effect of using the two proposed formulations, separately and simultaneously, in nonlinear site response analyses.

Quantifying Nonlinearity Susceptibility via Site-Response Modeling Uncertainty at Three Sites in the Los Angeles Basin

The effects of near-surface soil stratigraphy on the amplitude and frequency content of ground motion are accounted for in most modern U.S. seismic design codes for building structures as a function of the soil conditions prevailing in the area of interest. Nonetheless, currently employed site-classification criteria do not adequately describe the nonlinearity susceptibility of soil formations, which prohibits the development of standardized procedures for the computationally efficient integration of nonlinear ground response analyses in broadband ground-motion simulations. In turn, the lack of a unified methodology for nonlinear site-response analyses affects both the prediction accuracy of site-specific ground-motion intensity measures and the evaluation of site-amplification factors when broadband simulations are used for the development of hybrid attenuation relations. In this article, we introduce a set of criteria for quantification of the nonlinearity susceptibility of soil profiles based on the site conditions and incident ground-motion characteristics, and we implement them to identify the least complex ground response prediction methodology required for the simulation of nonlinear site effects at three sites in the Los Angeles basin. The criteria are developed on the basis of a comprehensive nonlinear site-response modeling uncertainty analysis, which includes both detailed soil profile descriptions and statistical adequacy of ground-motion time histories. Approximate and incremental nonlinear models are implemented, and the limited site-response observations are initially compared to the ensemble site-response estimates. A suite of synthetic ground motions for rupture scenarios of weak, medium, and large magnitude events (M 3.5–7.5) is next generated, parametric studies are conducted for each fixed magnitude scenario by varying the source-to-site distance, and the variability introduced in ground-motion predictions is quantified for each nonlinear site-response methodology. A frequency index is developed to describe the frequency content of incident ground motion relative to the resonant frequencies of the soil profile, and this index is used in conjunction with the rock-outcrop acceleration peak amplitude (PGA_(RO)) to identify the site conditions and ground-motion characteristics where incremental nonlinear analyses should be employed in lieu of approximate methodologies. We show that the proposed intensity-frequency representation of ground motion may be implemented to describe the nonlinearity susceptibility of soil formations in broadband simulations by accounting both for the magnitude-distance-orientation characteristics of seismic motion and the profile stiffness characteristics. The synthetic ground-motion predictions are next used for the development of site-amplification factors for the alternative site-response methodologies, and the results are compared to published site factors of attenuation relations. For the site conditions investigated, currently established amplification factors compare well with synthetic simulations for class C and D site conditions, while long-period amplification factors are overestimated by a factor of 1.5 at the class E site, where site-specific nonlinear analyses should be employed for levels of PGA_(RO)>0.2g.

Ground motion estimation at Guwahati city for an Mw 8.1 earthquake in the Shillong plateau

In this paper, the ground motion at Guwahati city for an 8.1 magnitude earthquake on Oldham fault in the Shillong plateau has been estimated by stochastic finite-fault simulation method. The corresponding acceleration time histories on rock level at several sites in the epicentral region have been computed. These results are validated by comparing them with the estimates obtained from Medvedev–Sponheuer–Karnik (MSK) intensity observations of 1897 Shillong earthquake. Using the local soil parameters, the simulated rock level acceleration time history at Guwahati city is further amplified up to the ground surface by nonlinear site response analysis. The results obtained are presented in the form of peak ground acceleration (PGA) contour map. The maximum amplification for PGA over Guwahati city is as high as 2.5. Based on the simulated PGA, the liquefaction susceptibility at several locations in the city has been estimated. The results are presented in the form of contours of factor of safety against liquefaction at different depths below the ground surface. It is observed that over a large part of the Guwahati city, the factor of safety against liquefaction is less than one, indicating that the city is highly vulnerable to liquefaction in the event of this earthquake. The contour maps obtained can be used in identifying vulnerable areas and disaster mitigation.

Seismic Site Response for Near-Fault Forward Directivity Ground Motions

Forward directivity effects in the near-fault region produce pulse-type motions that differ significantly from ordinary ground motions that occur at greater distances from the causative fault. Current code site factors are based on empirical observations and analyses involving less intense nonpulse ordinary ground motions. Nonlinear site response analyses with bidirectional shaking are performed using representative site profiles to quantify seismic site response effects for intense near-fault motions resulting from forward directivity. Input rock motions are represented with simplified velocity pulses that characterize the amplitude and period of forward directivity motions. Results indicate that site response affects both the amplitude and period of forward directivity pulses, and hence, local site conditions should be considered when evaluating seismic designs in the near-fault region. Stiff soil sites tend to amplify the peak ground velocity and increase the period of pulse-type motions, particularly, when the period of the rock motion coincides with the degraded period of the site. Amplification is limited at soft soil sites by the dynamic strength of the weak soil, so attenuation occurs for intense input motions. This nonlinearity is not reflected in the site factors in current building codes. Guidance is provided for estimating the amplitude and pulse period for velocity pulses at soil sites.

A comparative study on linear and nonlinear site response analysis

Site response analysis is usually the first step of any seismic soil-structure study. Geotechnical earthquake engineers and engineering geologist have been trying to find both practical and most appropriate solution techniques for ground response analysis under earthquake loadings. The paper attempts to give a critical overview of the field of site response analysis. In this paper, the influences of nonlinearity on the site response analysis summarized and were evaluated with a numerical example. Site response of a two layered soil deposit with the assumption of linear and rigid base bedrock (or viscoelastic half-space) was analyzed by using linear and nonlinear approaches. The amplification spectrum of the soil column is computed between the top and the bottom of this soil deposit. Nonlinear analysis was compared with the linear method of analysis. Steps involved in ground response analyses to develop site-specific response spectra at a soil site are briefly summarized. Some of the well-known site response analysis methods are summarized and similarities and differences between linear and nonlinear methods are compared by a numerical example.