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.     

黄土高原混凝土建筑物的地震随机反应分析

本文利用随机振动理论和动力分析有限元法,计算了在9度地震作用下黄土高原混凝土建筑物在随机地震下响应的统计特性,分析了黄土层对混凝土建筑物地震反应的影响。     

3D soil structure of the Mygdonian basin for site response analysis

The 3D structure of the Mygdonian sedimentary basin (N. Greece) is investigated. The aim of this study is to propose a 3D model of this sedimentary structure that can later be used to model the seismic records currently being obtained by the permanent accelerograph network operating in the area. This model builds on previous efforts and incorporates new data. The geometry and dynamic properties of the soil layers were inverted using data from microtremor array measurements, seismic refraction profiles, boreholes, and geotechnical investigations. Phase-velocity dispersion curves of Rayleigh waves were determined at 27 sites in the basin using the spatial autocorrelation method (SPAC) introduced by Aki [1]. S-wave velocity profiles were inverted from these dispersion curves and the whole valley structure was interpolated using our new results and all previously available data. The proposed 3D model describes the geometry and shear-wave velocities of the Mygdonian and pre-Mygdonian sedimentary systems, and the top bedrock surface. Our results indicate that this 3D model correctly reflects the geometry and dynamic properties of the sedimentary layers. The case of Euroseistest, where the subsoil structure is the result of bringing together many disparate data, could be used as an example for similar alluvial basins throughout the world, where usually only scarce data is available.     

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%.     

Stochastic characteristics of seismic excitations at a non-uniform (rock and soil) site

This study analyzes data recorded at the dense array in the Parkway Valley, Wainuiomata, New Zealand, a small alluvial valley surrounded by graywacke outcrops. The array consisted of stations on both the sediment basin and the surrounding soft rock, with station separation distances pertinent for earthquake engineering applications. The array's configuration renders itself uniquely for the study of the spatial variation of seismic ground motions at sites with irregular topography for bridge response evaluations: the locations of the soft-rock stations surrounding the valley may be viewed as the locations of the bridge's abutments, and the locations of the stations in the basin as those of the bridge's intermediate piers. A further-away station, north-east of the valley, provided information on firm-rock data.     

Stochastic seismic response analysis of hysteretic multi-degree-of-freedom structures

Analytical study of random vibration of non-linear mutli-degree-of-freedom (MDF) systems is generally difficult. This is particularly true for MDF inelastic systems due to the highly non-linear and hereditary behaviour of the restoring force. On the other hand, to obtain the response statistics using a step-by-step Monte Carlo simulation requires a large sample, and it could be very costly. The purpose of this paper is to present a practical analytical-empirical method for an MDF yielding system. The method is based on a substitute structure (SS) concept in which the SS parameters are determined from empirical results of single-degree-of-freedom systems, i.e. each element in the system is replaced by a linear counterpart with ductility-dependent stiffness and damping. Based on a linear random vibration response analysis, the statistics of the maximum response (ductility) of each element are obtained by iteration. Numerical examples are given for multi-storey buildings with deteriorating (reinforced concrete frame) or non-deteriorating (steel frame) restoring forces. Comparisons with empirical results are satisfactory qualitatively. The main advantage of this method is that it requires relatively insignificant computation time, e.g. 1 s of execution time on the IBM 360–75 system for an eight-storey steel frame.     

Stochastic analysis of ground response using non-recursive algorithm

During an earthquake, the amplitudes of seismic wave may amplify significantly as it propagates through the soil layers near the ground surface. Analysis of site amplification potential is strongly influenced by the uncertainty associated to the definition of soil thickness and its properties. In this paper, the non-recursive algorithm is used in linear and nonlinear Hybrid Frequency Time Domain (HFTD) approaches for stochastic analysis of site amplification. The non-recursive algorithm causes time reduction of analysis that is the essential base of stochastic analysis. The selected soil stochastic parameters are shear wave velocity, density, damping and thickness. The results of sensitivity analysis also show that the damping ratio is the most effective parameter in PGA at ground surface. The stochastic peak ground acceleration, response spectrum and amplification factor at the ground surface are determined by the two approaches for four sites with different average shear wave velocities. Comparison of the results shows that the nonlinear HFTD approach predicts closer response to real recorded data with respect to linear HFTD.     

From surface wave inversion to seismic site response prediction: Beyond the 1D approach

Surface wave methods consist of the extraction and inversion of the Rayleigh wave phase-velocity dispersion curve to recover the (usually 1D) shear-wave velocity profile. In the literature, uncertainty due to data error has not received much attention, but the discussion about uncertainty due to model error is even poorer. Even with an unrealistic noise-free dataset and an exact forward model, an inappropriate parameterization can generate solutions very far from the actual soil structure. In general, the model used for the dispersion curve interpretation is 1D. Hence, when the velocity distribution is laterally heterogeneous, model errors can have significant consequences on the reliability of the resulting shear-wave velocity distribution. From a poor velocity reconstruction, an unsatisfactory, and often dangerous site response analysis follows. In fact, shear wave measurements play a relevant role in seismic ground motion amplification estimation. In this paper, we discuss the possibility of processing the seismograms using a multi-offset phase analysis (MOPA), in order to derive soil elastic parameters for weak motion predictions. This technique allows the detection and location of the lateral discontinuities, and a better model parameterization. In fact, once the discontinuities are identified, we can split the profile into several, truly 1D, parts. The use of the standard 1D dispersion curve extraction and inversion for each side of the heterogeneity generates velocity profiles that we can put side by side to get correct 2D reconstructions of the shear-wave distributions. From 2D velocity reconstruction, we can calculate the site response that may be significantly different from the site response generated from a traditional 1D analysis of the same seismograms. In this work, we discuss the site responses of two synthetic examples with lateral heterogeneities. We show how misleading a 1D analysis may be if applied to a truly 2D velocity distribution, particularly in terms of site response prediction.     

A hypoplastic model for site response analysis

Site response analyses must take into account the nonlinear behavior of soils. This is typically achieved using an equivalent linear approach or using numerical analyses with an appropriate constitutive model. In this work a family of hypoplastic models is proposed for use in site response analyses. These nonlinear models use a rate-type tensorial equation and are capable of reproducing plastic deformation of soils for cyclic loading under both drained and undrained conditions. A methodology for the calibration of hypoplastic parameter for dynamic loading is proposed. The hypoplastic constitutive models are implemented in a finite element code and the site response of the Lotung downhole array site is used to validate the use of hypoplastic models for site response analysis. The hypoplastic models reproduce accurately site response at the Lotung site. The advantages and disadvantages of the hypoplastic models compared to other models are discussed.     

Atrazine retention and degradation in the vadose zone at a till plain site in central Indiana

The vadose zone was examined as an environmental compartment where significant quantities of atrazine and its degradation compounds may be stored and transformed. The vadose zone was targeted because regional studies in the White River Basin indicated a large discrepancy between the mass of atrazine applied to fields and the amount of the pesticide and its degradation compounds that are measured in ground and surface water. A study site was established in a rotationally cropped field in the till plain of central Indiana. Data were gathered during the 1994 growing season to characterize the site hydrogeology and the distribution of atrazine, desethylatrazine, deisopropylatrazine, didealkylatrazine and hydroxyatrazine in runoff, pore water, and ground water. The data indicated that atrazine and its degradation compounds were transported from land surface to a depth of 1.5 m within 60 days of application, but were undetected in the saturated zone at nearby monitoring wells. A numerical model was developed, based on the field data, to provide information about processes that could retain and degrade atrazine in the vadose zone. Simulations indicated that evapotranspiration is responsible for surface directed soil-moisture flow during much of the growing season. This process causes retention and degradation of atrazine in the vadose zone. Increased residence time in the vadose zone leads to nearly complete transformation of atrazine and its degradation products to unquantified degradation compounds. As a result of macropore flow, small quantities of atrazine and its degradation compounds may reach the saturated zone.     

Consistency of dynamic site response at Port Island

System identification (SI) methods are used to determine empirical Green's functions (EGF) for soil intervals at the Port Island Site in Kobe, Japan and in shake table model tests performed by the Port and Harbor Research Institute (PHRI) to emulate the site during the 17 January 1995 Hyogo‐ken Nanbu earthquake. The model form for the EGFs is a parametric auto‐regressive moving average (ARMA) model mapping the ground motions recorded at the base of a soil interval to the top of that interval, hence capturing the effect of the soil on the through‐passing wave. The consistency of site response at Port Island before, during, and after the mainshock is examined by application of small motion foreshock EGFs to incoming ground motions over these time intervals. The prediction errors (or misfits) for the foreshocks, the mainshock, and the aftershocks, are assessed to determine the extent of altered soil response as a result of liquefaction of the ground during the mainshock. In addition, the consistency of soil response between field and model test is verified by application of EGFs calculated from the shake table test to the 17 January input data. The prediction error is then used to assess the consistency of behaviour between the two cases. By using EGFs developed for small‐amplitude foreshock ground motions, ground motions were predicted for all intervals of the vertical array except those that liquefied with small error. Analysis of the post‐liquefied ground conditions implies that the site response gradually returns to a pre‐earthquake state. Site behaviour is found to be consistent between foreshocks and the mainshock for the native ground (below 16 m in the field) with a normalized mean square error (NMSE) of 0.080 and a peak ground acceleration (PGA) of 0.5g. When the soil actually liquefies (change of state), recursive models are needed to track the variable soil behaviour for the remainder of the shaking. The recursive models are shown to demonstrate consistency between the shake table tests and the field with a NMSE of 0.102 for the 16 m to surface interval that liquefied. The aftershock ground response was not modelled well with the foreshock EGF immediately after the mainshock (NMSE ranging from 0.37 to 0.92). One month after the mainshock, the prediction error from the foreshock modeled was back to the foreshock error level. Copyright © 2001 John Wiley Sons, Ltd.     

水平成层场地地震反应非线性分析

本文首先推导了李小军积分格式(中心差分与Newmark平均加速度法相结合)的增量形式,并据此离散动力平衡方程,同时,采用Pyke提出的土动力本构模型以及多次透射人工边界条件,提出了一种水平成层场地地震反应非线性分析的显式有限元方法,并据此编制了计算机程序。数值实验表明,这种方法能较好地模拟土层在强地震作用下的非线性特性。     

Parametric analysis of the seismic response of a 2D sedimentary valley: implications for code implementations of complex site effects

A detailed 2D model has been constructed and validated for Euroseistest valley, in northern Greece. We take advantage of this model to investigate what parameters, in addition to surface soil conditions (obviously the most important parameter), can be used to correctly characterize site response in a 2D structure. Through a parametric analysis using 2D numerical simulations for SH waves, we explore the differences between the computed ground motion for different simplifications of the valley's structure. We consider variations in the velocity structure within the sediments, and variations of the shape between sediments and bedrock. We also compare the results from different 1D models reflecting current approaches to the determination of site response. Our results show clearly that, in the case of Euroseistest, site response owes fundamentally to its closed basin shape because it is largely controlled by locally generated surface waves. Thus, in terms of predicting site response, a rough idea of its shape ratio and of the average mechanical properties of the sediments are better than a very detailed 1D profile at the central site. Although the details of ground motion may vary significantly between the models, the relative amount of surface waves generated in the 2D models seems to be relatively constant. Moreover, if we quantify the additional amplification caused by the lateral heterogeneity in terms of the ‘aggravation factor’ introduced by Chávez-García & Faccioli [7], a roughly constant factor between 2 and 3 seems to appropriately take into account the effects of lateral heterogeneity. Of course, a correct estimate of the overall impedance contrast is necessary to correctly predict the maximum amplification, a caveat that also applies to 1D models. In this sense, Euroseistest rings an alarm bell. In this valley the more significant impedance contrast lies at about 200 m depth, and it is missed both by consideration of the average shear wave velocity of the first 30 m (the V_s30 criterion) or using the detailed velocity profile down to a depth where a shear wave velocity larger than 750 m/s is found. Our conclusions indicate that, in order to improve current schemes to take into account site effects in building codes, the more to be gained comes from consideration of lateral heterogeneity, at least in the case of shallow alluvial valleys, where locally generated surface waves are likely to be important.     

Stochastic multimedia risk assessment for a site with contaminated groundwater

 There exist many sites with contaminated groundwater because of inappropriate handling or disposal of hazardous materials or wastes. Health risk assessment is an important tool to evaluate the potential environmental and health impacts of these contaminated sites. It is also becoming an important basis for determining whether risk reduction is needed and what actions should be initiated. However, in research related to groundwater risk assessment and management, consideration of multimedia risk assessment and the separation of the uncertainty due to lack of knowledge and the variability due to natural heterogeneity are rare. This study presents a multimedia risk assessment framework with the integration of multimedia transfer and multi-pathway exposure of groundwater contaminants, and investigates whether multimedia risk assessment and the separation of uncertainty and variability can provide a better basis for risk management decisions. The results of the case study show that a decision based on multimedia risk assessment may differ from one based on risk resulting from groundwater only. In particular, the transfer from groundwater to air imposes a health threat to some degree. By using a methodology that combines Monte Carlo simulation, a rank correlation coefficient, and an explicit decision criterion to identify information important to the decision, the results obtained when uncertainty and variability are separate differ from the ones without such separation. In particular, when higher percentiles of uncertainty and variability distributions are considered, the method separating uncertainty and variability identifies TCE concentration as the single most important input parameter, while the method that does not distinguish the two identifies four input parameters as the important information that would influence a decision on risk reduction.     

On intermediate-term earthquake prediction in central Italy

The Time of Increased Probability (TIP) for the occurrence of a strong earthquake is determined in Central Italy. This is done with an algorithm that has been successfully applied in other regions of the world (algorithm CN, from the initials of California and Nevada, where the first diagnoses of TIPs were made). The use of normalized functions allows direct application of the orginal algorithm to the new region being studied, without anyad hoc adjustment of the parameters.Retrospective analysis carried on until 1986 shows that TIPs occupy 26 percent of the total time considered and precede four out of five strong earthquakes. Forward monitoring indicates the possible existence of a TIP started in May 1988.Several tests indicate that the results obtained are quite stable, even when using catalogues from different agencies. Apart from obvious practical interest, this research is essential for the worldwide investigation of self-similarity in the origin of strong earthquakes.     

Modeling shear rigidity of stratified bedrock in site response analysis

Where a distinct soil-rock interface exists, the bedrock medium is commonly treated as elastic half-space and the bedrock surface as the lower boundary of the soil-column model for site response analyses (or the lower boundary of the finite element model for soil-structure interaction analyses). While shear wave velocity in bedrock varies with depth, there has been no consensus amongst scientists and practitioners over the value of “effective depth” into bedrock at which the “half-space” shear wave velocity value should be taken for modeling purposes. This paper reports an interesting and important observation that the effective depth into bedrock is sensitive to the shear wave velocity profile of the overlying soil sediments. A simple and heuristic method, namely Resonant Period Equivalence (RPE) Method, is proposed herein for representing a stratified elastic bedrock of inhomogeneous properties by an equivalent homogeneous elastic half-space medium, which is characterized by a single equivalent shear wave velocity (V_R) value. The proposed calculation method has been verified by extensive comparative analyses involving the use of programs SHAKE and NERA and employing the complete shear wave velocity models of both the soil sediments and the underlying stratified bedrock.     

Large amplification of ground motion at rock sites within a fault zone in Nocera Umbra (central Italy)

During the two mainshocks of September 26, 1997 inthe Umbria-Marche border a strong-motion accelerographrecorded peak ground accelerations as large as 0.6 g,approximately, in the town of Nocera Umbra, atdistances of 10 to 15 km from the epicentres. Thisvalue is significantly larger than expected on thebasis of the usual regressions with magnitude anddistance. A broad-band amplification up to a factor of10 was consistently estimated in previous papers,using both weak and strong motion data recorded at theaccelerograph site during local moderate earthquakes.To study the cause of this amplification we deployedsix seismologic stations across the tectonic contactbetween the Ceno-Mesozoic limestone and the Mesozoicmarly sandstone where the accelerograph is installed.Seismograms of 21 shallow aftershocks in the magnituderange from 2.2 to 4.0 and a subcrustal M_w = 5.3event are analysed. Regardless of epicentre location,waveforms show a large complexity in an approximately200 m wide band adjacent to the tectonic contact. Thisis interpreted as the effect of trapped waves in thehighly fractured, lower velocity materials within thefault zone.     

Evidence that bio-metallic mineral precipitation enhances the complex conductivity response at a hydrocarbon contaminated site

The complex conductivity signatures of a hydrocarbon contaminated site, undergoing biodegradation, near Bemidji, Minnesota were investigated. This site is characterized by a biogeochemical process where iron reduction is coupled with the oxidation of hydrocarbon contaminants. The biogeochemical transformations have resulted in precipitation of different bio-metallic iron mineral precipitates such as magnetite, ferroan calcite, and siderite. Our main objective was to elucidate the major factors controlling the complex conductivity response at the site. We acquired laboratory complex conductivity measurements along four cores retrieved from the site in the frequency range between 0.001 and 1000 Hz. Our results show the following: (1) in general higher imaginary conductivity was observed for samples from contaminated locations compared to samples from the uncontaminated location, (2) the imaginary conductivity for samples contaminated with residual and free phase hydrocarbon (smear zone) was higher compared to samples with dissolved phase hydrocarbon, (3) vadose zone samples located above locations with free phase hydrocarbon show higher imaginary conductivity magnitude compared to vadose zone samples from the dissolved phase and uncontaminated locations, (4) the real conductivity was generally elevated for samples from the contaminated locations, but not as diagnostic to the presence of contamination as the imaginary conductivity; (5) for most of the contaminated samples the imaginary conductivity data show a well-defined peak between 0.001 and 0.01 Hz, and (6) sample locations exhibiting higher imaginary conductivity are concomitant with locations having higher magnetic susceptibility. Controlled experiments indicate that variations in electrolytic conductivity and water content across the site are unlikely to fully account for the higher imaginary conductivity observed within the smear zone of contaminated locations. Instead, using magnetite as an example of the bio-metallic minerals in the contaminated location at the site, we observe a clear increase in the imaginary conductivity response with increasing magnetite content. The presence of bio-metallic mineral phases (e.g., magnetite) within the contaminated location associated with hydrocarbon biodegradation may explain the high imaginary conductivity response. Thus, we postulate that the precipitation of bio-metallic minerals at hydrocarbon contaminated sites impacts their complex conductivity signatures and should be considered in the interpretation of complex conductivity data from oil contaminated sites undergoing intrinsic bioremediation.     

Site response using coda-wave techniques: Applications to short period data from central and southern Italy

The method of coda waves was applied to two different sets of data for the evaluation of the relative site response.The first set of data consists of low magnitude earthquakes with closely spaced locations, recorded at a small aperture array of velocimeters located in the Abruzzo region, central Italy. The second set of data is composed of events with epicentral distance ranging from 20 to 300 km, recorded at a seismological network with an aperture of about 100 km located in the Puglia region, southern Italy.Results show that the coda wave method furnishes stable estimates of the site effect. An amplification, relative to an arbitrary site, of a factor of about 2 occurs in the 1.7–6 Hz frequency band for two stations of the Abruzzo network, while an amplification factor of about 0.5 occurs in the whole frequency band (1–24 Hz) for one of the stations of the Puglia network. This station is located in an area which is correlated with a low macroseismic intensity anomaly.