Evaluating nonlinear effective stress site response analyses using records from the Canterbury earthquake sequence

A widely used one-dimensional nonlinear effective stress site response analysis program is used to model the response of potentially liquefiable soils during strong shaking. Ground motion records from six events of the 2010–2011 Canterbury earthquake sequence and the extensive site investigation data that have been obtained for the Christchurch area provide the basis for the analyses. The results of the analyses depend significantly on the input motions and soil profile characterization, so these important aspects are examined. Deconvolved Riccarton Gravel input motions were generated, because recorded rock or firm layer motions were not available. Nonlinear effective stress seismic site response analyses are shown to capture key aspects of the observed soil response through the comparison of acceleration response spectra of calculated surface motions to those of recorded surface motions; however, equivalent-linear and total stress nonlinear analyses capture these aspects as well. Biases in the computed motions compared to recorded motions were realized for some cases but they can be attributed primarily to the uncertainty in the development of the input motions used in the analyses.     

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%.     

Observed Evolution of Linear and Nonlinear Effects at the Dahan Downhole Array,Taiwan: Analysis of the September 21, 1999 M 7.3 Chi-Chi Earthquake Sequence

— In this paper, the site characteristics of the Dahan downhole array are studied by analyzing the September 21, 1999 M 7.3 Chi-Chi earthquake sequence including the main shock and some aftershocks. The four-level array (0 m, 50 m, 100 m and 200 m) is located to the north of Hualien City in eastern Taiwan. Polarization analysis is used to check the orientation errors of the seismometers at different levels of depth. If the surface instrument is chosen as reference, the angle between the major polarization axes of the surface and any downhole records is the orientation error that must be corrected for the downhole accelerographs. The orientation errors at depths of 50 m, 100 m and 200 m are 32°, 120° and –84°. After the corrections, the coherency between the surface and downhole records is substantially improved. Spectral ratio analysis shows that the predominant frequency of the Chi-Chi main shock shifts to a lower frequency. We also simulate ground motions at different depths by using the Haskell method with a linear velocity structure model. The record at surface is chosen as the input motion. Compared with the observed data, ground acceleration can be well reproduced for the aftershocks (weak-motion events) of the September 21, 1999 M 7.3 Chi-Chi earthquake. However, for the Chi-Chi main shock, the synthetic waveform cannot match well with the observation neither in amplitude nor in phase. This indicates that large ground shaking probably induced the nonlinear site effect at that time, and the model used cannot support it.Acknowledgement. The authors would like to express their thanks to Dr. L.F. Bonilla and one anonymous reviewer for their valuable suggestions. This research was supported by the National Science Council under grant number NSC 89-2921-M-194-007. The Institute of Earth Sciences, Academia Sinica supplied the strong-motion data. The support of these organizations is gratefully acknowledged.     

Nonlinearity in the response of soils in the 1995 Kobe earthquake in vertical components of records

Strong motion records provided by seismic vertical arrays allow estimation of stress–strain relations in soils at depths from the surface to the location of the deepest device. As an example, time-dependent nonlinear soil behavior was estimated in vertical components of records obtained in the epicentral area of the 1995 Kobe earthquake. Degradation of the rigidity of soils in the strong motion was observed. The constructed nonlinear models of the soil behavior were used for estimating the nonlinear parts in the ground response by the nonlinear system identification technique. Nonlinear parts in the ground response were found to be as high as 50% at 2 km from the fault and 10% at 6–15 km from the fault plane. Odd types of nonlinearity, such as cubic, the fifth, seventh, etc. order, were found to be typical for soils, whereas, nonlinearities of even types are usually weak, but increase in liquefied soils.     

Experimental analysis of seismic torsional ground motion recorded by the LSST‐Lotung array

The purpose of this study was to perform an experimental analysis of the amplitude of full‐scale spatial variability of seismic motions with regard to earthquake engineering. The LSST‐Lotung array in Taiwan provides a good set of records for this type of study. Of interest are the free‐field torsional seismic components induced by the spatial variability of seismic motions. In this study, three events have been considered: LSST‐06, LSST‐07 and LSST‐16. In time domain analysis, the experimental results obtained show that when the separation distance increases, the induced torsion decreases, and the normalized differential motion parameter increases. Also, the results show that the stronger the event, in terms of maximum PGA, the larger the induced torsional amplitude and the smaller the induced normalized differential motion parameter. Copyright © 2002 John Wiley & Sons, Ltd.     

Earthquake response analysis of the Hualien soil–structure interaction system based on updated soil properties using forced vibration test data

This paper presents results of the earthquake response analysis on a large‐scale seismic test (LSST) structure which was built at Hualien in Taiwan for an international cooperative research project. The analysis is carried out using a computer program which has been developed based on axisymmetric finite element method incorporating dynamic infinite elements for far‐field soil region and a substructured wave input technique. The non‐linear behaviour of the soil medium is taken into account using an iterative equivalent linearization procedure. Two sets of the soil and structural properties, namely the unified and the FVT‐correlated models, are utilized as the initial linear values. The unified model was provided by a group of experts in charge of the geotechnical experiments, and the correlated model was obtained through a system identification procedure using the forced vibration test (FVT) results by the present authors. Three components of ground accelerations are artificially generated through an averaging process of the Fourier amplitude spectra of the ground accelerations measured near the test structure, and they are used as the control input motions for the earthquake analysis. It has been found that the earthquake responses predicted using the generated control motions and with the FVT‐correlated model as the initial linear properties in the equivalent linearization procedure compare very well with the observed responses. Copyright © 2001 John Wiley & Sons, Ltd.     

Effects of spatially variable ground motions on the seismic response of a skewed, multi-span, RC highway bridge

This paper presents a study of the influence of spatially variable ground motions on the longitudinal seismic response of a short, three-span, 30-degree skewed, reinforced concrete highway bridge. Linear and nonlinear finite element models are created for the bridge and linear elastic and nonlinear inelastic time history analyses conducted. Three different types of illustrative excitations are considered: The first utilizes spatially variable ground motions incorporating the effects of variable soil conditions, loss of coherency and wave passage as input motions at the structures' supports. The time history with the smallest peak displacement and the one with the largest peak displacement from the spatially variable ones are then used as uniform input motions at all bridge supports. The comparative analysis of the bridge model shows that the uniform ground motion input with the largest peak displacement cannot provide conservative seismic demands for all structural components—in a number of cases it results in lower response than that predicted by spatially variable motions. The present results indicate that there is difficulty in establishing uniform input motions that would have the same effect on the response of bridge models as spatially variable ones. Consequently, spatially variable input motions need to be applied as excitations at the bridge supports.     

Estimation of Nonlinear Time-dependent Soil Behavior in Strong Ground Motion Based on Vertical Array Data

To improve our understanding of nonlinear elastic properties of soils, a method is proposed of estimation of stress-strain relations of soils in situ in strong ground motion based on vertical array data. Strong motion records provided by seismic vertical arrays allow estimation of nonlinear stress-strain relations in soil layers at different depths, from the surface down to the location of the deepest device. As an example, records obtained during the main shock of the 1995 Kobe earthquake at Port-Island, SGK, and TKS sites were used to estimate the stress-strain relations in the soil profiles. For different layers, different types of nonlinear stress-strain relations were selected, according to the profiling data. To account for temporal changes in the soil behavior, consecutive parts of records were examined, and for successive time intervals, the relations were found showing the best-fit approximation to the observed data. At Port Island and SGK sites, where the strongest accelerations were recorded, the obtained stress-strain relations showed systematic changes in the upper layers (0–14 m), such as, a progressive reduction of the slopes of the stress-strain curves due to liquefaction at Port Island and reduction and recovery of the slopes at SGK and TKS sites. At the three sites, the stress-strain relations remained stable in layers below 11–14 m. Thus, the proposed approach gives us a representation of the soil behavior in layers at different depths in strong ground motion; it allows calculation of the propagation of arbitrary seismic signals in the studied profiles and estimation of nonlinear components in the ground response by the nonlinear system identification technique. The method can also be applied to evaluate the ground response at sites where profiling data are available and an imposed motion can be estimated.     

Anisotropic seismic ground responses identified from the Hualien vertical array

This paper presents the results of ground response analyses using the free-field motions of six earthquakes recorded at the site of the Hualien Large Scale Seismic Test. From the phase spectra of transfer functions between the ground motions recorded at the surface and various depths, the predominant frequencies of soil layers are identified and used to estimate the shear wave velocities of soil layers. Results show that the soils at the Hualien LSST site are anisotropic, such that the earthquake responses exhibit different characteristics in two horizontal principal directions.     

1-g Experimental investigation of bi-layer soil response and kinematic pile bending

The effect of soil inhomogeneity and material nonlinearity on kinematic soil–pile interaction and ensuing bending under the passage of vertically propagating seismic shear waves in layered soil, is investigated by means of 1-g shaking table tests and nonlinear numerical simulations. To this end, a suite of scale model tests on a group of five piles embedded in two-layers of sand in a laminar container at the shaking table facility in BLADE Laboratory at University of Bristol, are reported. Results from white noise and sine dwell tests were obtained and interpreted by means of one-dimensional lumped parameter models, suitable for inhomogeneous soil, encompassing material nonlinearity. A frequency range from 0.1 Hz to 100 Hz and 5 Hz to 35 Hz for white noise and sine dwell tests, respectively, and an input acceleration range from 0.015 g to 0.1 g, were employed. The paper elucidates that soil nonlinearity and inhomogeneity strongly affect both site response and kinematic pile bending, so that accurate nonlinear analyses are often necessary to predict the dynamic response of pile foundations.     

基础非线性对桥墩地震反应的影响

在桩基础桥墩滞回特性的模型试验基础上,提出了用Clough模型模拟基础(地基)的恢复力特性。桥墩采用Takeda恢复力模型。用强震记录与人工合成地震动作为输入对铁路简支梁桥进行了非线性地震反应分析,讨论了不同地震动输入及不同地震强度时基础非线性对桥梁地震反应的影响。研究结果表明,考虑基础的非线性一般会使墩顶位移增大,而墩底的曲率明显减小,且随着地震动强度的增加,基础的非线性影响更加明显。     

考虑土体非线性及倾角影响的盆地地震响应研究

基于二维沉积盆地模型,采用D-P弹塑性模型模拟盆地的非线性特征。利用显式有限元与黏弹性边界结合的方法,通过改变盆地边缘倾角,在时域和频域内分析盆地地表的地震动响应,对比线性与非线性盆地地震反应的差异。结果表明:(1)土体非线性对整个盆地范围内地震动的影响都较显著。考虑非线性时地震动放大系数明显降低,降低幅度在30%~50%。同时,考虑非线性和倾角影响时最强烈放大区域的范围和位置变化,且很小倾角下的分布特征显著不同。(2)两分量的放大系数都有随边缘倾角的增大而增强的趋势,但均是盆地边缘区域受非线性的影响最为显著。此外,真实地震波输入下显著放大区域的范围及线性与非线性结果的差异程度相对更大。(3)考虑非线性时,对于不同频率地震波的放大系数差别明显,但都表现出从低频到高频谱比分布越来越复杂的现象,同时盆地倾角的影响程度随频率的增大更加明显。(4)考虑土体非线性并未改变地震波传播的总体特征,但各震相强度相对降低。     

面向地下结构的最优地震动峰值指标随埋深变化规律

选取了50条实际地震动,采用一维场地等效线性化方法分别对均匀半空间场地和成层半空间场地进行地震响应分析,同时选择效益性作为判别标准来探究最优地震动峰值指标(峰值加速度PGA,峰值速度PGV,峰值位移PGD)随埋深变化的规律.研究结果表明:对于选取的两类场地,最优地震动峰值指标均随埋深的改变而变化,埋深浅时PGA效益性最...     

Coupling of topographic and stratigraphic effects on seismic response of slopes through 2D linear and equivalent linear analyses

In this paper the seismic response of simple slope geometries under vertically propagating in-plane shear waves (SV waves) is assessed through two-dimensional finite element analyses to investigate the amplification of the ground motion induced by soil topography. Topographic horizontal and vertical amplification factors were evaluated through different sets of analyses focused on slopes in homogeneous half space and on slopes overlying either a rigid or a compliant bedrock. Soil was assumed to behave as a linear visco-elastic or as an equivalent-linear visco-elastic material. In the analyses the effects of slope inclination and of the characteristics of the input motion were also investigated.In order to calibrate the numerical model, the results obtained in linear visco-elastic analyses were compared with the results of parametric numerical analyses available in the literature, showing a good agreement. The results confirmed that a complex interaction exists between stratigraphic and topographic effects on the amplification of the ground motion and that the two effects cannot be evaluated independently and easily uncoupled. In the case of compliant bedrock the effect of the impedance ratio was also investigated.The results of the equivalent-linear analyses pointed out the remarkable dependence on soil non-linear behavior and, when compared to the results of linear visco-elastic analyses, showed that without accounting for soil non-linear behavior, topographic amplification factors may result underestimated.     

基于小田原试验场地数据的不同基岩输入模型对预测地震动特征的影响研究

随着强震台网的密布及观测记录的增加,为研究各类局部场地地震反应预测模型的合理性提供了有效的参考依据,也使利用强震记录及场地条件研究地震动特征成为可能。选取场地地质参数资料和地震记录数据齐全的日本小田原（Ashigara Valley）盲测试验场地,通过对比不同地震动输入方式及场地反应分析模型,研究地震动特征,分析现有模型的优劣。基于1990年8月5日M5.1强震事件的地表基岩记录和地下基岩地震记录,采用地下台强震记录直接输入、地表基岩台强震记录减半为基底地震动输入、地表基岩台强震记录反演为基底地震动输入作为3种基岩地震动输入。基于局部场地条件分别建立一维等效线性模型、二维黏弹性模型及二维时域等效线性化模型等工程中常用的场地数值分析模型,进行局部场地地震反应分析,预测该盲测场地的地表地震动特征,并与对应的实测强震记录结果进行对比,分析不同基岩地震动输入方式对预测地震动特征及地表土层反应谱特征的影响,重点分析地震动输入、土体非线性、场地横向不均匀性及几何与非线性特征共同作用等因素对地表地震动特征的影响,以期为地表地震动的合理预测提供参考。     

Identification of modal parameters of non‐classically damped linear structures under multi‐component earthquake loading

A method for parametric system identification of classically damped linear system in frequency domain is adopted and extended for non‐classically damped linear systems subjected up to six components of earthquake ground motions. This method is able to work in multi‐input/multi‐output (MIMO) case. The response of a two‐degree‐of‐freedom model with non‐classical damping, excited by one‐component earthquake ground motion, is simulated and used to verify the proposed system identification method in the single‐input/multi‐output case. Also, the records of a 10 storey real building during the Northridge earthquake is used to verify the proposed system identification method in the MIMO case. In this case, at first, a single‐input/multi‐output assumption is considered for the system and modal parameters are identified, then other components of earthquake ground motions are added, respectively, and the modal parameters are identified again. This procedure is repeated until all four components of earthquake ground motions which are measured at the base level of the building are included in the identification process. The results of identification of real building show that consideration of non‐classical damping and inclusion of the multi‐components effect of earthquake ground motions can improve the least‐squares match between the finite Fourier transforms of recorded and calculated acceleration responses. Copyright © 2006 John Wiley & Sons, Ltd.     

S-wave velocity structures of sediments estimated from array microtremor records and site responses in the near-fault region of the 1999 Chi-Chi,Taiwan earthquake

The 1999 Chi-Chi, Taiwan earthquake, M_W = 7.6, caused severe damage in the near-fault region of the earthquake. In order to evaluate site effects in the near-field strong motions we estimate S-wave velocity structures of sediments at four sites using array records of microtremors. We also recalculated S-wave velocity structures at other four sites previously reported. To show the validity of the estimated S-wave velocity structures we separate empirical site responses from aftershock records using the generalized inversion method and show the agreement between empirical and theoretical site responses. We also show an observed fact that suggests soil nonlinearity during the Chi-Chi earthquake by comparing horizontal-to-vertical spectral ratios (HVRs) for main shock records with HVRs for aftershock records. Then we calculate one-dimensional equivalent-linear site responses using the estimated S-wave velocity structures and the main shock records observed on the surface. It is found that site amplification due to thick (about 6 km) sediments is one of the important factors for explaining the long-period velocity pulses of about 5 to 10 sec observed at sites in the footwall during the Chi-Chi earthquake. It is also found that the theoretical site responses of shallow soft sediments at sites that sustained severe damage in the hanging wall shows significant amplification around 1 sec. As the amplitude of velocity pulses with period around 1 sec is most critical in causing damage to ordinary buildings of moderate heights, our results suggest that the 1-sec period velocity pulses, amplified by the site response of shallow sediments should contribute to the severe damage during the Chi-Chi earthquake.     

Probabilistic evaluation of soil–foundation–structure interaction effects on seismic structural response

Complex seismic behaviour of soil–foundation–structure (SFS) systems together with uncertainties in system parameters and variability in earthquake ground motions result in a significant debate over the effects of soil–foundation–structure interaction (SFSI) on structural response. The aim of this study is to evaluate the influence of foundation flexibility on the structural seismic response by considering the variability in the system and uncertainties in the ground motion characteristics through comprehensive numerical simulations. An established rheological soil‐shallow foundation–structure model with equivalent linear soil behaviour and nonlinear behaviour of the superstructure has been used. A large number of models incorporating wide range of soil, foundation and structural parameters were generated using a robust Monte‐Carlo simulation. In total, 4.08 million time‐history analyses were performed over the adopted models using an ensemble of 40 earthquake ground motions as seismic input. The results of the analyses are used to rigorously quantify the effects of foundation flexibility on the structural distortion and total displacement of the superstructure through comparisons between the responses of SFS models and corresponding fixed‐base (FB) models. The effects of predominant period of the FB system, linear vs nonlinear modelling of the superstructure, type of nonlinear model used and key system parameters are quantified in terms of different probability levels for SFSI effects to cause an increase in the structural response and the level of amplification of the response in such cases. The results clearly illustrate the risk of underestimating the structural response associated with simplified approaches in which SFSI and nonlinear effects are ignored. Copyright © 2010 John Wiley & Sons, Ltd.     

A new approach of selecting real input ground motions for seismic design: The most unfavourable real seismic design ground motions

This paper presents a new way of selecting real input ground motions for seismic design and analysis of structures based on a comprehensive method for estimating the damage potential of ground motions, which takes into consideration of various ground motion parameters and structural seismic damage criteria in terms of strength, deformation, hysteretic energy and dual damage of Park & Ang damage index. The proposed comprehensive method fully involves the effects of the intensity, frequency content and duration of ground motions and the dynamic characteristics of structures. Then, the concept of the most unfavourable real seismic design ground motion is introduced. Based on the concept, the most unfavourable real seismic design ground motions for rock, stiff soil, medium soil and soft soil site conditions are selected in terms of three typical period ranges of structures. The selected real strong motion records are suitable for seismic analysis of important structures whose failure or collapse will be avoided at a higher level of confidence during the strong earthquake, as they can cause the greatest damage to structures and thereby result in the highest damage potential from an extended real ground motion database for a given site. In addition, this paper also presents the real input design ground motions with medium damage potential, which can be used for the seismic analysis of structures located at the area with low and moderate seismicity. The most unfavourable real seismic design ground motions are verified by analysing the seismic response of structures. It is concluded that the most unfavourable real seismic design ground motion approach can select the real ground motions that can result in the highest damage potential for a given structure and site condition, and the real ground motions can be mainly used for structures whose failure or collapse will be avoided at a higher level of confidence during the strong earthquake. Copyright © 2007 John Wiley & Sons, Ltd.