Considering dynamic soil structure interaction (SSI) effects on seismic isolation retrofit efficiency and the importance of natural frequency ratio

This paper utilizes and expands on existing coupled BEM–FEM (finite element method) methods for the investigation of the effects of soil structure interaction (SSI) on both an un-retrofitted and seismically isolated typical bridge structure. A simple numerical model of the bridge and surrounding soil is formulated and excited by an earthquake excitation. Utilizing Newmark's β FEM solution method along with the closed form B-spline BIRF method, the structural damped period, composite damping ratio, pier relative displacement, and base shear demand are monitored. From these results, the effects of SSI on this structure are identified. Additionally, the importance of the relative rigidity between the soil-foundation system and the bridge structure is also investigated. The results of the studies indicate that the response of the complete structure system considered is affected by the inclusion of SSI effects. Furthermore, the efficiency of the isolation measures designed using fixed base conditions is decreased by considering SSI over a certain relative rigidity range that is quantified using the structure to soil-foundation natural frequency ratio.     

高层建筑结构-地基动力相互作用效果的振动台试验对比研究

本文通过对高层建筑结构－地基动力相互作用体系和刚性地基上高层建筑结构的振动台模型试验成果的对比分析，研究了相互作用对结构动力特性和地震反应的影响。结果－地基动力相互作用使结构频率减小，阻尼增大；相互作用体系的振型曲线与刚性地基上结构的振型曲线不同，基础处存在平动和转动；在地震动作用下考虑相互作用的结构加速度、层间剪力、弯矩以及应变通常比刚性地基上的情况小，而位移则比刚性地基上的情况大。     

Seismic design of yielding structures on flexible foundations

This paper introduces a simple method to consider the effects of inertial soil–structure interaction (SSI) on the seismic demands of a yielding single‐degree‐of‐freedom structure. This involves idealizing the yielding soil–structure system as an effective substitute oscillator having a modified period, damping ratio, and ductility. A parametric study is conducted to obtain the ratio between the displacement ductility demand of a flexible‐base system and that of the corresponding fixed‐base system. It is shown that while additional foundation damping can reduce the overall response, the effects of SSI may also increase the ductility demand of some structures, mostly being ductile and having large structural aspect ratio, up to 15%. Finally, a design procedure is provided for incorporation of the SSI effects on structural response. Copyright © 2015 John Wiley & Sons, Ltd.     

Evaluation of FEMA-440 for including soil-structure interaction

Replacing the entire soil-structure system with a fixed base oscillator to consider the effect of soil-structure interaction (SSI) is a common analysis method in seismic design. This technique has been included in design procedures such as NEHRP, ASCE, etc. by defining an equivalent fundamental period and damping ratio that can modify the response of the structure. However, recent studies indicate that the effects of SSI should be reconsidered when a structure undergoes a nonlinear displacement demand. In recent documents on Nonlinear Static Procedures (NSPs), FEMA-440 (2005), a modified damping ratio of the replacement oscillator was proposed by introducing the ductility of the soil-structure system obtained from pushover analysis. In this paper, the damping defined in FEMA-440 to include the soil-structure interaction effect is evaluated, and the accuracy of the Coefficient Method given in FEMA-440 and the Equivalent Linearization Method is studied. Although the improvements for Nonlinear Static Procedures (NSPs) in FEMA-440 are achieved for a fixed base SDOF structure, the soil effects are not perfectly obtained. Furthermore, the damping definition of a soil-structure system is extended to structures to consider bilinear behavior.     

A comparative study of seismic provisions between International Building Code 2003 and Uniform Building Code 1997

This study focuses on the comparison of the Uniform Building Code （UBC） 1997 and International Building Code （IBC） 2003 in relation to the seismic design and analysis of special steel moment resisting frame buildings （SMRF）. This paper formulates a numerical study of a steel SMRF building, studied in four different situations, namely： as an office building in San Francisco; as an office building in Sacramento; as an essential facility in San Francisco, and as an essential facility in Sacramento. The analytical results of the model buildings are then compared and analyzed taking note of any significant differences. This case study explores variations in the results obtained using the two codes, particularly the design base shear and drift ratios as they relate to different locations and occupancy use. This study also proves that IBC 2003 is more stringent for the redundancy factor under design category E for the SMRF building, and drift limits for essential facilities.     

Seismic fragilities of non-ductile reinforced concrete frames with consideration of soil structure interaction

Seismic fragilities of buildings are often developed without consideration of soil-structure interaction (SSI), where base of the building is assumed to be fixed. This study highlights effect of SSI and uncertainty in soil properties such as friction angle, cohesion, density, shear modulus and Poisson's ratio and foundation parameters on seismic fragilities of non-ductile reinforced concrete frames resting in dense silty sand. Three-, five-, and nine-storey three-bay moment resisting reinforced concrete frames resting on isolated shallow foundation are studied and the numerical models for SSI are developed in OpenSees. Three sets of 10 ground motions, with mean spectrum of 100, 500, and 1000 yr return period hazard level (matching EC-8 design spectrum), are used for the nonlinear time history analyses. An optimized Latin Hyper Cube sampling technique is used to draw the sample of soil properties and foundation parameters. The fragilities are developed for the fixed base model and SSI models. However, the fragilities that incorporate the soil parameter and foundation uncertainties are only slightly different from those based solely on the uncertainty in seismic demand from earthquake ground motion, suggesting that fragilities that are developed under the assumption that all soil and foundation parameters at their median (or mean) values are sufficient for the purpose of earthquake damage or loose estimation of structures resting on dense silty sand. But the consideration of the SSI effect has the significant influence on the fragilities compare to the fixed base model. The structural parameter uncertainty and foundation modeling uncertainty are not considered in the study.     

Seismic performance of three-dimensional frame structures with underground stories

This paper investigates the seismic performance of moment-resisting frame steel buildings with multiple underground stories resting on shallow foundations. A parametric study that involved evaluating the nonlinear seismic response of five, ten and fifteen story moment-resisting frame steel buildings resting on flexible ground surface, and buildings having one, three and five underground stories was performed. The buildings were assumed to be founded on shallow foundations. Two site conditions were considered: soil class C and soil class E, corresponding to firm and soft soil deposits, respectively. Vancouver seismic hazard has been considered for this study. Synthetic earthquake records compatible with Vancouver uniform hazard spectrum (UHS), as specified by the National Building Code of Canada (NBCC) 2005, have been used as input motion. It was found that soil–structure interaction (SSI) can greatly affect the seismic performance of buildings in terms of the seismic storey shear and moment demand, and the deformations of their structural components. Although most building codes postulate that SSI effects generally decrease the force demand on buildings, but increase the deformation demand, it was found that, for some of the cases considered, SSI effects increased both the force and deformation demand on the buildings. The SSI effects generally depend on the stiffness of the foundation and the number of underground stories. SSI effects are significant for soft soil conditions and negligible for stiff soil conditions. It was also found that SSI effects are significant for buildings resting on flexible ground surface with no underground stories, and gradually decrease with the increase of the number of underground stories.     

Probabilistic estimation of inelastic displacement demands in soil–structure interaction systems on cohesive soils

Inelastic displacement ratios (IDRs) of nonlinear soil–structure interaction (SSI) systems located at sites with cohesive soils are investigated in this study. To capture the effects of inelastic cyclic behavior of the supporting soil, the Beam on Nonlinear Winkler Foundation (BNWF) model is used. The superstructure is modeled using an inelastic single-degree-of-freedom (SDOF) system model. Nonlinear SSI systems representing various combinations of unconfined compressive strengths and shear wave velocities are considered in the analysis. A set of strong ground motions recorded at sites with soft to stiff soils is used for considering the record-to-record variability of IDRs. It is observed that IDRs for nonlinear SSI systems are sensitive to the strength and the stiffness properties of both the soil and the structure. For the case of SSI systems on the top of cohesive soils, the compressive strength of the soil has a significant impact on the IDRs, which cannot be captured by considering only the shear wave velocity of the soil. Based on the results of nonlinear time-history analysis, a new equation is proposed for estimating the mean and the dispersion of IDRs of SSI systems depending on the characteristic properties of the supporting soil, dimensions of the foundation, and properties of the superstructure. A probabilistic framework is presented for the performance-based seismic design of SSI systems located at sites with cohesive soils.     

Inelastic seismic behavior of soil–pile raft–structure system under bi-directional ground motion

Performance based design of structure requires a reasonably accurate prediction of displacement or ductility demand. Generally, displacement demand of structure is estimated assuming fixity at base and considering base motion in one direction. In reality, ground motions occur in two orthogonal directions simultaneously resulting in bidirectional interaction in inelastic range, and soil–structure interaction (SSI) may change structural response too. Present study is an attempt to develop insight on the influence of bi-directional interaction and soil–pile raft–structure interaction for predicting the inelastic response of soil–pile raft–structure system in a more reasonably accurate manner. A recently developed hysteresis model capable to simulate biaxial interaction between deformations in two principal directions of any structural member under two orthogonal components of ground motion has been used. This study primarily shows that a considerable change may occur in inelastic demand of structures due to the combined effect of such phenomena.     

Seismic response of steel frame structures with hybrid passive control systems

The concept of the hybrid passive control system is studied analytically by investigating the seismic response of steel frame structures. Hybrid control systems consist of two different passive elements combined into a single device or system. The hybrid systems investigated in this research consist of a rate‐dependent damping device paired with a rate‐independent energy dissipation element. The innovative configurations exploit individual element strengths and offset their weaknesses through multiphased behavior. A nine‐story, five‐bay steel moment‐frame was used for the analysis. Six different seismic resisting systems were analyzed and compared. The conventional systems included a special moment‐resisting frame (SMRF) and a dual SMRF–buckling‐restrained brace (BRB) system. The final four configurations are hybrid passive systems. The different hybrid configurations utilize a BRB and either a high‐damping rubber damper or viscous fluid damper. The analyses were run in the form of an incremental dynamic analysis. Several damage measures were calculated, including maximum roof drift, base shear, and total roof acceleration. The results demonstrate the capability of hybrid passive control systems to improve structural response compared with conventional lateral systems and to be effective for performance‐based seismic design. Each hybrid configuration improved some aspect of structural response with some providing benefits for multiple damage measures. The multiphased nature provides improved response for frequent and severe seismic events. Copyright © 2011 John Wiley & Sons, Ltd.     

基于能力谱法的SSI体系抗震pushover分析方法

本文首先经过2次等效将土与结构相互作用的多自由度体系等效为单自由度体系,并给出了修正反应谱和等价能力谱的确定方法,进而提出了基于能力谱法考虑土与结构动力相互作用(SSI)效应的结构体系pushover分析方法(SSIPA);然后对3种不同高度考虑SSI效应的结构体系在5条地震动作用下采用本文提出的方法进行了算例分析,将结果与非线性时程分析的结果进行了比较,研究了本方法的适用性和准确性;最后,与建筑抗震设计规范的设计反应谱相结合,对9层考虑SSI效应的钢结构用本文提出的方法进行了弹塑性地震反应分析,根据我国抗震设计规范的规定进行抗震性能的评估验证了本方法的可行性。     

Pushover analysis procedure for systems considering SSI effects based on capacity spectrum method

This paper presents a new procedure to transform an SSI system into an equivalent SDOF system using twice equivalence. A pushover analysis procedure based on the capacity spectrum method for buildings with SSI effects （PASSI） is then established based on the equivalent SDOF system, and the modified response spectrum and equivalent capacity spectrum are obtained. Furthermore, the approximate formulas to obtain the dynamic stiffness of foundations are suggested. Three steel buildings with different story heights （3, 9 and 20） including SSI effects are analyzed under two far-field and two near-field historical records and an artificial seismic time history using the two PASSI procedures and the nonlinear response history analysis （NLhRHA） method. The results are compared and discussed. Finally, combined with seismic design response spectrum, the nonlinear seismic response of a 9-story building with SSI effects is analyzed using the PASSI procedures, and its seismic performance is evaluated according to the Chinese ＇Code for Seismic Design of Buildings. The feasibility of the proposed procedure is verified.     

Effect of soil parameter uncertainty on seismic demand of low-rise steel buildings on dense silty sand

Focusing on low-rise steel buildings supported by shallow isolated foundations on dense silty sand, this study demonstrates the effect of uncertainty in soil parameters on seismic response of structures. Considering a set of 20 ground motions representing 10% in 50 years hazard level and concentrating on peak base moment, base shear and interstory drift as the demand variables of interest, it is found that uncertainty in soil parameters may result in significant response variability of the structures, especially when vertical factor of safety is low and the structure is relatively stiff. Uncertainty in friction angle results in significant variability of the peak base moment and base shear, while peak interstory drift ratio is found to be virtually unaffected by uncertainty in soil parameters. It is also found that a linear soil–structure-interaction (SSI) model will not be able to predict such response variability under these set of ground motions.     

Multiobjective optimization for performance‐based seismic design of steel moment frame structures

The performance‐based seismic design of steel special moment‐resisting frame (SMRF) structures is formulated as a multiobjective optimization problem, in which conflicting design criteria that respectively reflect the present capital investment and the future seismic risk are treated simultaneously as separate objectives other than stringent constraints. Specifically, the initial construction expenses are accounted for by the steel material weight as well as by the number of different standard steel section types, the latter roughly quantifying the degree of design complexity related additional construction cost; the seismic risk is considered in terms of maximum interstory drift demands at two hazard levels with exceedance probabilities being 50% and 2% in 50 years, respectively. The present formulation allows structural engineers to find an optimized design solution by explicitly striving for a desirable compromise between the initial investment and seismic performance. Member sizing for code‐compliant design of a planar five‐story four‐bay SMRF is presented as an application example using the proposed procedure that is automated by a multiobjective genetic algorithm. Copyright © 2004 John Wiley & Sons, Ltd.     

Efficient seismic analysis for nonlinear soil-structure interaction with a thick soil layer

The direct finite element method is a type commonly used for nonlinear seismic soil-structure interaction(SSI) analysis. This method introduces a truncated boundary referred to as an artificial boundary meant to divide the soilstructure system into finite and infinite domains. An artificial boundary condition is used on a truncated boundary to achieve seismic input and simulate the wave radiation effect of infinite domain. When the soil layer is particularly thick, especially for a three-dimensional problem, the computational efficiency of seismic SSI analysis is very low due to the large size of the finite element model, which contains an whole thick soil layer. In this paper, an accurate and efficient scheme is developed to solve the nonlinear seismic SSI problem regarding thick soil layers. The process consists of nonlinear site response and SSI analysis. The nonlinear site response analysis is still performed for the whole thick soil layer. The artificial boundary at the bottom of the SSI analysis model is subsequently relocated upward from the bottom of the soil layer(bedrock surface) to the location nearest to the structure as possible. Finally, three types of typical sites and underground structures are adopted with seismic SSI analysis to evaluate the accuracy and efficiency of the proposed efficient analysis scheme.     

Seismic response and damage analysis of buildings supported on flexible soils

The investigation reported in this paper studies the effects of soil–structure interaction (SSI) on the seismic response and damage of building–foundation systems. A simple structural model is used for conducting a parametric study using a typical record obtained in the soft soil area of Mexico City during the 1985 earthquake. Peak response parameters chosen for this study were the roof displacement relative to the base and the hysteretic energy dissipated by the simple structural model. A damage parameter is also evaluated for investigating the SSI effects on the seismic damage of buildings. The results indicate that in most cases of inelastic response, SSI effects can be evaluated considering the rigid‐base case and the SSI period. Copyright © 2000 John Wiley & Sons, Ltd.     

Probabilistic analysis of soil‐structure interaction effects on the seismic performance of structures

This paper revisits the phenomenon of dynamic soil‐structure interaction (SSI) with a probabilistic approach. For this purpose, a twofold objective is pursued. First, the effect of SSI on inelastic response of the structure is studied considering the prevailing uncertainties. Second, the consequence of practicing SSI provisions of the current seismic design codes on the structural performance is investigated in a probabilistic framework. The soil‐structure system is modeled by the sub‐structure method. The uncertainty in the properties of the soil and the structure is described by random variables that are input to this model. Monte Carlo sampling analysis is employed to compute the probability distribution of the ductility demand of the structure, which is selected as the metrics for the structural performance. In each sample, a randomly generated soil‐structure system is subjected to a randomly selected and scaled ground motion. To comprehensively model the uncertainty in the ground motion, a suite of 3269 records is employed. An extensive parametric study is conducted to cover a wide range of soil‐structure systems. The results reveal the probability that SSI increases the ductility demand of structures designed based on the conventional fixed‐based assumption but built on flexible soil in reality. The results also show it is highly probable that practicing SSI provisions of modern seismic codes increase the ductility demand of the structure. Copyright © 2016 John Wiley & Sons, Ltd.     

Estimation of hysteretic energy demand using concepts of modal pushover analysis

Hysteretic energy dissipation in a structure during an earthquake is the key factor, besides maximum displacement, related to the amount of damage in it. This energy demand can be accurately computed only through a nonlinear time‐history analysis of the structure subjected to a specific earthquake ground acceleration. However, for multi‐story structures, which are usually modeled as multi‐degree of freedom (MDOF) systems, this analysis becomes computation intensive and time consuming and is not suitable for adopting in seismic design guidelines. An alternative method of estimating hysteretic energy demand on MDOF systems is presented here. The proposed method uses multiple ‘generalized’ or ‘equivalent’ single degree of freedom (ESDOF) systems to estimate hysteretic energy demand on an MDOF system within the context of a ‘modal pushover analysis’. This is a modified version of a previous procedure using a single ESDOF system. Efficiency of the proposed procedure is tested by comparing energy demands based on this method with results from nonlinear dynamic analyses of MDOF systems, as well as estimates based on the previous method, for several ground motion scenarios. Three steel moment frame structures, of 3‐, 9‐, and 20‐story configurations, are selected for this comparison. Bias statistics that show the effectiveness of the proposed method are presented. In addition to being less demanding on the computation time and complexity, the proposed method is also suitable for adopting in design guidelines, as it can use response spectra for hysteretic energy demand estimation. Copyright © 2008 John Wiley & Sons, Ltd.     

三维土-结构动力相互作用体系分析的两步时域显式波动有限元过程

为减少直接分析三维大尺度复杂土-结构动力相互作用问题的计算量,提高计算效率,本文直接从波动方程出发,提出了较常规子结构法更简单的两步简化计算过程,即第一步简化上部复杂结构体系为集中质量杆系模型,并求基础处等效输入,第二步通过等效输入求上部结构各位置的动力反应.其中第一步计算主要采用集中质量显式有限单元法结合局部透射人工...     

On the evaluation of seismic response of structures by nonlinear static methods

In the most recent seismic codes, the assessment of the seismic response of structures may be carried out by comparing the displacement capacity, provided by nonlinear static analysis, with the displacement demand. In many cases the code approach is based on the N2 method proposed by Fajfar, which evaluates the displacement demand by defining, as an intermediate step, a single degree‐of‐freedom (SDOF) system equivalent to the examined structure. Other codes suggest simpler approaches, which do not require equivalent SDOF systems, but they give slightly different estimation of the seismic displacement demand. The paper points out the differences between the methods and suggests an operative approach that provides the same accuracy as the N2 method without requiring the evaluation of an equivalent SDOF system. A wide parametric investigation allows an accurate comparison of the different methods and demonstrates the effectiveness of the proposed operative approach. Copyright © 2009 John Wiley & Sons, Ltd.