Semi‐empirical model for site effects on acceleration time histories at soft‐soil sites. Part 1: formulation and development

A criterion is developed for the simulation of realistic artificial ground motion histories at soft‐soil sites, corresponding to a detailed ground motion record at a reference firm‐ground site. A complex transfer function is defined as the Fourier transform of the ground acceleration time history at the soft‐soil site divided by the Fourier transform of the acceleration record at the firm‐ground site. Working with both the real and the imaginary components of the transfer function, and not only with its modulus, serves to keep the statistical information about the wave phases (and, therefore, about the time variation of amplitudes and frequencies) in the algorithm used to generate the artificial records. Samples of these transfer functions, associated with a given pair of soft‐soil and firm‐ground sites, are empirically determined from the corresponding pairs of simultaneous records. Each function included in a sample is represented as the superposition of the transfer functions of the responses of a number of oscillators. This formulation is intended to account for the contributions of trains of waves following different patterns in the vicinity of both sites. The properties of the oscillators play the role of parameters of the transfer functions. They vary from one seismic event to another. Part of the variation is systematic, and can be explained in terms of the influence of ground motion intensity on the effective values of stiffness and damping of the artificial oscillators. Another part has random nature; it reflects the random characteristics of the wave propagation patterns associated with the different events. The semi‐empirical model proposed recognizes both types of variation. The influence of intensity is estimated by means of a conventional one‐dimensional shear wave propagation model. This model is used to derive an intensity‐dependent modification of the values of the empirically determined model parameters in those cases when the firm‐ground earthquake intensity used to determine these parameters differs from that corresponding to the seismic event for which the simulated records are to be obtained. Copyright © 2004 John Wiley & Sons, Ltd.     

Estimating non‐linear site response by single period approximation

Site effects characterize the filtering mechanisms within the soil sedimentary layers overlying bedrock. In regions of high seismicity such as California where strong motion records are relatively abundant, site coefficients can be developed by regression of recorded ground shaking parameters. In regions of low‐to‐moderate seismicity or of high seismicity but with a paucity of recorded strong motion data, such empirical models cannot be obtained in the same way. This study describes the theoretical development of a simple, rational manual procedure to calculate site coefficients, based on a single period approximation (SPA), and to construct displacement response spectra (RSD) for soil sites. The proposed simplified model, which takes into account the non‐linear behaviour of soil that is dependent on the level of shaking, impedance contrast at the soil–bedrock interface and the plasticity of soil material, has been verified by comparison with results obtained from non‐linear shear wave analyses and data recorded during the 1994 Northridge earthquake. The proposed model is believed to be a convenient tool for calculating non‐linear site responses and constructing site‐specific response spectra, which has the potential of being incorporated into code provisions. Copyright © 2006 John Wiley & Sons, Ltd.     

Simple models for estimating period‐shift and damping in soil

This study describes the development of a simple, heuristic manual calculation procedure for estimating the site period‐shift factor and soil damping ratio, with appropriate considerations for the level of shaking, impedance contrast between soil and bedrock interface and the plasticity of the soil layers. Essentially, the analogy of a building shear‐frame has been used to represent the seismic response behaviour of a soil column. The proposed procedure has been verified by comparing the predictions with results obtained directly from non‐linear shear wave analyses of soil column models. Copyright © 2006 John Wiley & Sons, Ltd.     

Multi‐variable relations for soil effects on seismic ground motion

Soil effects on peak ground acceleration, velocity and elastic response spectra (5% damping) are expressed by simple approximate relations in terms of five key parameters: (a) the fundamental vibration period of the non‐linear soil, T_S, (b) the period of a bedrock site of equal thickness, T_b, (c) the predominant excitation period, Te, (d) the peak seismic acceleration at outcropping bedrock, a, and (e) the number of significant excitation cycles, n. Furthermore, another relation is proposed for the estimation of T_S in terms of the soil thickness H, the average shear wave velocity of the soil V?_S,o and a. The aforementioned parameters were first identified through a simplified analytical simulation of the site excitation. The multivariable approximate relations were then formulated via a statistical analysis of relevant data from more than 700 one‐dimensional equivalent‐linear seismic ground response analyses, for actual seismic excitations and natural soil conditions. Use of these relations to back‐calculate the numerical results in the database gives an estimate of their error margin, which is found to be relatively small and unbiased. The proposed relations are also independently verified through a detailed comparison with strong motion recordings from seven well‐documented case studies: (a) two sites in the San Fernando valley during the Northridge earthquake, and (b) five different seismic events recorded at the SMART‐1 accelerometer array in Taiwan. It is deduced that the accuracy of the relations is comparable to that of the equivalent‐linear method. Hence, they can be readily used as a quick alternative for routine applications, as well as for spreadsheet computations (e.g. GIS‐aided seismic microzonation studies) where numerical methods are cumbersome to implement. Copyright © 2003 John Wiley & Sons, Ltd.     

Intensity measures for probabilistic assessment of non‐structural components acceleration demand

A fundamental issue in the framework of seismic probabilistic risk analysis is the choice of ground motion intensity measures (IMs). Based on the floor response spectrum method, the present contribution focuses on the ability of IMs to predict non‐structural components (NSCs) horizontal acceleration demand. A large panel of IMs is examined and a new IM, namely equipment relative average spectral acceleration (E‐ASA_R), is proposed for the purpose of NSCs acceleration demand prediction. The IMs efficiency and sufficiency comparisons are based on (i) the use of a large dataset of recorded earthquake ground motions; (ii) numerical analyses performed on three‐dimensional numerical models, representing actual structural wall and frame buildings; and (iii) systematic statistical analysis of the results. From the comparative study, the herein introduced E‐ASA_R shows high efficiency with respect to the estimation of maximum floor response spectra ordinates. Such efficiency is particularly remarkable in the case of structural wall buildings. Besides, the sufficiency and the simple formulation allowing the use of existing ground motion prediction models make the E‐ASA_R a promising IMs for seismic probabilistic risk assessment. Copyright © 2015 John Wiley & Sons, Ltd.     

On the use of multi‐algorithm,genetically adaptive multi‐objective method for multi‐site calibration of the SWAT model

With the availability of spatially distributed data, distributed hydrologic models are increasingly used for simulation of spatially varied hydrologic processes to understand and manage natural and human activities that affect watershed systems. Multi‐objective optimization methods have been applied to calibrate distributed hydrologic models using observed data from multiple sites. As the time consumed by running these complex models is increasing substantially, selecting efficient and effective multi‐objective optimization algorithms is becoming a nontrivial issue. In this study, we evaluated a multi‐algorithm, genetically adaptive multi‐objective method (AMALGAM) for multi‐site calibration of a distributed hydrologic model—Soil and Water Assessment Tool (SWAT), and compared its performance with two widely used evolutionary multi‐objective optimization (EMO) algorithms (i.e. Strength Pareto Evolutionary Algorithm 2 (SPEA2) and Non‐dominated Sorted Genetic Algorithm II (NSGA‐II)). In order to provide insights into each method's overall performance, these three methods were tested in four watersheds with various characteristics. The test results indicate that the AMALGAM can consistently provide competitive or superior results compared with the other two methods. The multi‐method search framework of AMALGAM, which can flexibly and adaptively utilize multiple optimization algorithms, makes it a promising tool for multi‐site calibration of the distributed SWAT. For practical use of AMALGAM, it is suggested to implement this method in multiple trials with relatively small number of model runs rather than run it once with long iterations. In addition, incorporating different multi‐objective optimization algorithms and multi‐mode search operators into AMALGAM deserves further research. Copyright © 2009 John Wiley & Sons, Ltd.     

Modeling of a large‐scale magneto‐rheological damper for seismic hazard mitigation. Part II: Semi‐active mode

A magneto‐rheological (MR) damper is a semi‐active device where the damper force capacity is controlled by varying the input current into the damper. In this paper, the dynamics of MR dampers associated with variable current input is studied. Electromagnetic theory is used to model the dynamics of an MR damper including the eddy current effect and the nonlinear hysteretic behavior of damper material magnetization. A nonlinear differential equation that relates the input current to the damper with a constant equivalent current is proposed. The nonlinear differential equation is combined with the Maxwell Nonlinear Slider (MNS) model to create the variable current MNS model to predict the damper force under variable input current and random damper displacement loading. The model is evaluated by comparing the predicted response of a large‐scale MR damper to the measured damper response from experiments. The experiments include a real‐time hybrid simulation of a 3‐story building structure with a large‐scale MR damper subjected to the design earthquake. The exceptional agreement observed between the predicted and experimental results illustrate the robustness and the accuracy of the variable current MNS model. Copyright © 2012 John Wiley & Sons, Ltd.     

Sliding fragility of block‐type non‐structural components. Part 2: Restrained components

This paper focuses on seismic vulnerability assessment of restrained block‐type non‐structural components under sliding response on the basis of seismic inputs specified by current seismic codes. The general representation of restrained equipment considered in this study consists of a rigid block restrained by four post‐tensioned, symmetrically arranged cables. Two sliding‐related failure modes are considered: restraint breakage and excessive absolute acceleration. Fragility analysis is proposed as an appropriate tool to evaluate these failure modes. Sample fragility curves developed through Monte‐Carlo simulations show that the restraint breakage limit state is sensitive to the parameters of the equation of motion. For instance, fragility estimates obtained without taking into account vertical base accelerations can be significantly unconservative for relatively large values of the coefficient of friction. In contrast, the excessive absolute acceleration limit state exhibits little sensitivity to the parameters of the equation of motion. Peak absolute acceleration response is almost always equal to or greater than the horizontal peak base acceleration. Representative results suggest that reasonable response estimates for blocks located at stories other than the ground in multistorey buildings can in general be obtained by simply scaling the ground acceleration to the peak acceleration at the corresponding storey. Copyright © 2002 John Wiley & Sons, Ltd.     

Hybrid platform for vibration control of high‐tech equipment in buildings subject to ground motion. Part 2: analysis

The experimental results of using a hybrid platform to mitigate vibration of a batch of high‐tech equipment installed in a building subject to nearby traffic‐induced ground motion have been presented and discussed in the companion paper. Based on the identified dynamic properties of both the building and the platform, this paper first establishes an analytical model for hybrid control of the building‐platform system subject to ground motion in terms of the absolute co‐ordinate to facilitate the absolute velocity feedback control strategy used in the experiment. The traffic‐induced ground motion used in the experiment is then employed as input to the analytical model to compute the dynamic response of the building‐platform system. The computed results are compared with the measured results, and the comparison is found to be satisfactory. Based on the verified analytical model, coupling effects between the building and platform are then investigated. A parametric study is finally conducted to further assess the performance of both passive and hybrid platforms at microvibration level. The analytical study shows that the dynamic interaction between the building and platform should be taken into consideration. The hybrid control is effective in reducing both velocity response and drift of the platform/high‐tech equipment at microvibration level with reasonable control force. Copyright © 2003 John Wiley & Sons, Ltd.     

Soil‐structure system frequency and damping: Estimation from eigenvalues and results for a 2D model in layered half‐space

This paper presents a formulation for estimation of the frequency and damping of a soil‐structure interaction system based on the classical modal analysis and solving the system eigenvalue problem. Without loss of generality, the structure is represented by a single degree of freedom oscillator, while the soil effects are included through impedance functions for in‐plane motion of a 2D rigid foundation. For the results presented in this paper, the impedance functions were computed by the indirect boundary element method for a rectangular foundation embedded in a soil layer over elastic bedrock. The study shows that the classical modal‐analysis approach works well, with the exception of squat, stiff structures, even though the impedance functions are frequency‐dependent and the soil‐structure interaction system does not possess normal modes. The study also shows that system frequency and damping are independent of the wave passage effects, contrary to findings of some previous studies, and that the site conditions, represented by the soil‐layer thickness and stiffness contrast between bedrock and soil layer, have significant influences on both system frequency and system damping. Finally, the paper examines the accuracy of some of the simple methods for estimation of these two system parameters and comments on some conflicting conclusions of previous studies about the effects of foundation embedment.     

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.     

Conditional spectrum‐based ground motion selection. Part II: Intensity‐based assessments and evaluation of alternative target spectra

In a companion paper, an overview and problem definition was presented for ground motion selection on the basis of the conditional spectrum (CS), to perform risk‐based assessments (which estimate the annual rate of exceeding a specified structural response amplitude) for a 20‐story reinforced concrete frame structure. Here, the methodology is repeated for intensity‐based assessments (which estimate structural response for ground motions with a specified intensity level) to determine the effect of conditioning period. Additionally, intensity‐based and risk‐based assessments are evaluated for two other possible target spectra, specifically the uniform hazard spectrum (UHS) and the conditional mean spectrum (CMS, without variability).It is demonstrated for the structure considered that the choice of conditioning period in the CS can substantially impact structural response estimates in an intensity‐based assessment. When used for intensity‐based assessments, the UHS typically results in equal or higher median estimates of structural response than the CS; the CMS results in similar median estimates of structural response compared with the CS but exhibits lower dispersion because of the omission of variability. The choice of target spectrum is then evaluated for risk‐based assessments, showing that the UHS results in overestimation of structural response hazard, whereas the CMS results in underestimation. Additional analyses are completed for other structures to confirm the generality of the conclusions here. These findings have potentially important implications both for the intensity‐based seismic assessments using the CS in future building codes and the risk‐based seismic assessments typically used in performance‐based earthquake engineering applications. Copyright © 2013 John Wiley & Sons, Ltd.     

Ground motion scaling methods for linear‐elastic structures: an integrated experimental and analytical investigation

The task of selecting and scaling an appropriate set of ground motion records is one of the most important challenges facing practitioners in conducting dynamic response history analyses for seismic design and risk assessment. This paper describes an integrated experimental and analytical evaluation of selected ground motion scaling methods for linear‐elastic building frame structures. The experimental study is based on the shake table testing of small‐scale frame models with four different fundamental periods under ground motion sets that have been scaled using different methods. The test results are then analytically extended to a wider range of structural properties to assess the effectiveness of the scaling methods in reducing the dispersion and increasing the accuracy in the seismic displacement demands of linear‐elastic structures, also considering biased selection of ground motion subsets. For scaling methods that are based on a design estimate of the fundamental period of the structure, effects of possible errors in the estimated period are investigated. The results show that a significant reduction in the effectiveness of these scaling methods can occur if the fundamental period is not estimated with reasonable certainty. Copyright © 2012 John Wiley & Sons, Ltd.     

Hybrid platform for vibration control of high‐tech equipment in buildings subject to ground motion. Part 1: experiment

This paper presents an experimental study, while a companion paper addresses an analytical study, to explore the possibility of using a hybrid platform to mitigate vibration of a batch of high‐tech equipment installed in a building subject to nearby traffic‐induced ground motion. A three‐storey building model and a hybrid platform model are designed and manufactured. The hybrid platform is mounted on the building floor through passive mounts composed of leaf springs and oil dampers and controlled actively by an electromagnetic actuator with velocity feedback control strategy. The passive mounts are designed in such a way that the stiffness and damping ratio of the platform can be changed. A series of shaking table tests are then performed on the building model without the platform, with the passive platform of different parameters, and with the hybrid platform. The experimental results demonstrate that the hybrid platform is very effective in reducing the velocity response of a batch of high‐tech equipment in the building subject to nearby traffic‐induced ground motion if dynamic properties of the platform and control feedback gain are selected appropriately. Copyright © 2003 John Wiley & Sons, Ltd.     

A macro‐element model for non‐linear soil–shallow foundation–structure interaction under seismic loads: theoretical development and experimental validation on large scale tests

In this paper, different formulations of a macro‐element model for non‐linear dynamic soil‐structure interaction analyses of structures lying on shallow foundations are first reviewed, and secondly, a novel formulation is introduced, which combines some of the characteristics of previous approaches with several additional features. This macro‐element allows one to model soil‐footing geometric (uplift) and material (soil plasticity) non‐linearities that are coupled through a stiffness degradation model. Footing uplift is introduced by a simple non‐linear elastic model based on the concept of effective foundation width, whereas soil plasticity is treated by means of a bounding surface approach in which a vertical load mapping rule is implemented. This mapping is particularly suited for the seismic loading case for which the proposed model has been conceived. The new macro‐element is subsequently validated using cyclic and dynamic large‐scale laboratory tests of shallow foundations on dense sand, namely: the TRISEE cyclic tests, the Public Works Research Institute and CAMUS IV shaking table tests. Based on this comprehensive validation process against a set of independent experimental results, a unique set of macro‐element parameters for shallow foundations on dense sand is proposed, which can be used to perform predictive analyses by means of the present model. Copyright © 2011 John Wiley & Sons, Ltd.     

Conditional spectrum‐based ground motion selection. Part I: Hazard consistency for risk‐based assessments

The conditional spectrum (CS, with mean and variability) is a target response spectrum that links nonlinear dynamic analysis back to probabilistic seismic hazard analysis for ground motion selection. The CS is computed on the basis of a specified conditioning period, whereas structures under consideration may be sensitive to response spectral amplitudes at multiple periods of excitation. Questions remain regarding the appropriate choice of conditioning period when utilizing the CS as the target spectrum. This paper focuses on risk‐based assessments, which estimate the annual rate of exceeding a specified structural response amplitude. Seismic hazard analysis, ground motion selection, and nonlinear dynamic analysis are performed, using the conditional spectra with varying conditioning periods, to assess the performance of a 20‐story reinforced concrete frame structure. It is shown here that risk‐based assessments are relatively insensitive to the choice of conditioning period when the ground motions are carefully selected to ensure hazard consistency. This observed insensitivity to the conditioning period comes from the fact that, when CS‐based ground motion selection is used, the distributions of response spectra of the selected ground motions are consistent with the site ground motion hazard curves at all relevant periods; this consistency with the site hazard curves is independent of the conditioning period. The importance of an exact CS (which incorporates multiple causal earthquakes and ground motion prediction models) to achieve the appropriate spectral variability at periods away from the conditioning period is also highlighted. The findings of this paper are expected theoretically but have not been empirically demonstrated previously. Copyright © 2013 John Wiley & Sons, Ltd.     

Analysis of the weightiness of site effects on reinforced concrete (RC) building seismic behaviour: The Adra town example (SE Spain)

The damage distribution in Adra town (south‐eastern Spain) during the 1993 and 1994 Adra earthquakes (5.0 magnitude), that reached a maximum intensity degree of VII (European Macroseismic Scale (EMS scale)), was concentrated mainly in the south‐east zone of the town and the most relevant damage occurred in reinforced concrete (RC) buildings with four or five storeys. In order to evaluate the influence of ground condition on RC building behaviour, geological, geomorphological and geophysical surveys were carried out, and a detailed map of ground surface structure was obtained. Short‐period microtremor observations were performed in 160 sites on a 100m × 100m dimension grid and Nakamura's method was applied in order to determine a distribution map of soil predominant periods. Shorter predominant periods (0.1–0.3 s) were found in mountainous and neighbouring zones and larger periods (greater than 0.5 s) in thicker Holocene alluvial fans. A relationship T = (0.049 ± 0.001)N, where T is the natural period of swaying motion and N is the number of storeys, has been empirically obtained by using microtremor measurements at the top of 38 RC buildings (ranging from 2 to 9 storeys). 1‐D simulation of strong motion on different soil conditions and for several typical RC buildings were computed, using the acceleration record in Adra town of the 1993 earthquake. It is noteworthy that all the aforementioned results show the influence of site effects in the degree and distribution of observed building damage. Copyright © 2007 John Wiley & Sons, Ltd.     

Inelastic dynamic analysis of RC bridges accounting for spatial variability of ground motion,site effects and soil–structure interaction phenomena. Part 2: Parametric study

The methodology for dealing with spatial variability of ground motion, site effects and soil–structure interaction phenomena in the context of inelastic dynamic analysis of bridge structures, and the associated analytical tools established and validated in a companion paper are used herein for a detailed parametric analysis, aiming to evaluate the importance of the above effects in seismic design. For a total of 20 bridge structures differing in terms of structural type (fundamental period, symmetry, regularity, abutment conditions, pier‐to‐deck connections), dimensions (span and overall length), and ground motion characteristics (earthquake frequency content and direction of excitation), the dynamic response corresponding to nine levels of increasing analysis complexity was calculated and compared with the ‘standard’ case of a fixed base, uniformly excited, elastic structure for which site effects were totally ignored. It is concluded that the dynamic response of RC bridges is indeed strongly affected by the coupling of the above phenomena that may adversely affect displacements and/or action effects under certain circumstances. Evidence is also presented that some bridge types are relatively more sensitive to the above phenomena, hence a more refined analysis approach should be considered in their case. Copyright @ 2003 John Wiley & Sons, Ltd.     

A numerical coupling scheme for nonlinear time history analysis of buildings on a regional scale considering site‐city interaction effects

Seismic damage simulation of buildings on a regional scale is important for loss estimation and disaster mitigation of cities. However, the interaction among densely distributed buildings in a city and the site, ie, the “site‐city interaction (SCI) effects,” is often neglected in most regional simulations. Yet, many studies have found that the SCI effects are very important in regional simulations containing a large number of tall buildings and underground structures. Therefore, this work proposed a numerical coupling scheme for nonlinear time history analysis of buildings on a regional scale considering the SCI effects. In this study, multiple‐degree‐of‐freedom models are used to represent different buildings above the ground, while an open source spectral element program, SPEED, is used for simulating wave propagation in underlying soil layers. The proposed numerical scheme is firstly validated through a shaking table test. Then, a detailed discussion on the SCI effects in a 3D basin is performed. Finally, a nonlinear time history analysis of buildings on a regional scale is performed using the Tsinghua University campus in Beijing as a case study. The Tsinghua University campus case results show that the SCI effects will reduce the seismic responses of most buildings. However, some buildings will suffer much more severe damage when the SCI effects are considered, which may depend on the input motions, site characteristics, and building configurations.