Evaluation of combination rules for peak response calculation in three‐component seismic analysis

The responses, r_e, given by several multicomponent combination rules used in seismic codes for determining peak responses to three ground motion components are evaluated for elastic systems and compared with the critical response r_cr; this is defined as the largest response for all possible incident angles of the seismic components and obtained by means of the CQC3‐rule when a principal seismic component is vertical, or the GCQC3‐rule when it departs from the vertical direction. The combination rules examined are the SRSS‐, 30%‐, 40%‐ and IBC‐rules, considering different alternatives for the design horizontal spectrum. Assuming that a principal seismic component is along the vertical direction, the upper and lower bounds of the ratio r_e/r_cr for each combination rule are determined as a function of the spectral intensity ratio of the horizontal seismic components and of the responses to one seismic component acting alternately along each structural axis. Underestimations and overestimations of the critical response are identified for each combination rule and each design spectrum. When a component departs from the vertical direction, the envelopes of the bounds of the ratio r_e/r_cr for each combination rule are calculated, considering all possible values of the spectral intensity ratios. It is shown that the inclination of a principal component with respect to the vertical axis can significantly reduce the values of r_e/r_cr with respect to the case when the component is vertical. Copyright © 2003 John Wiley & Sons, Ltd.     

Evaluation of combination rules for maximum response calculation in multicomponent seismic analysis

The existing rules for combining peak response to individual components of ground motion are evaluated. The response values r_e to two horizontal components of ground motion estimated by four multicomponent combination rules—SRSS‐, 30%‐, 40%‐ and simplified‐SRSS‐rules—are compared with the critical response, r_cr, obtained by the CQC3‐rule, which takes into account the direction of the principal ground components with respect to the structural axes and provides the largest response over all possible seismic incident angles. The following results are obtained in the first part of the paper and are valid for any elastic structure and any earthquake design response spectrum: For realistic values of the ratio γ of the design spectra for the two principal components of ground motion the SRSS‐rule estimate lies between 0.79r_cr and 1.00r_cr, the Simplified‐SRSS‐rule estimate lies between 1.00r_cr and 1.26r_cr, the 40%‐rule estimate lies between 0.99r_cr and 1.25r_cr, and the 30%‐rule estimate lies between 0.92r_cr and 1.16r_cr. None of the multicomponent combination rules account for the increase in response of systems if the vibration periods of the two modes that contribute most to the response to the x‐ and y‐components of ground motion are close to each other. Evaluated in the second part of the paper is the accuracy of the multicomponent combination rules in estimating the response of a range of one‐storey systems with (a) symmetrical plan and (b) unsymmetrical plan, and of two multistorey buildings. The SRSS‐rule underestimates the response by up to 16% and the other three rules overestimate it by up to 18%. Although these errors appear to be smaller than the many approximations inherent in structural design, they can be eliminated with very little additional computation by using an explicit formula for the critical response based on the CQC3 rule. Copyright © 2001 John Wiley & Sons, Ltd.     

Critical response of structures to multicomponent earthquake excitation

This paper aims to develop an improved understanding of the critical response of structures to multicomponent seismic motion characterized by three uncorrelated components that are defined along its principal axes: two horizontal and the vertical component. An explicit formula, convenient for code applications, has been derived to calculate the critical value of structural response to the two principal horizontal components acting along any incident angle with respect to the structural axes, and the vertical component of ground motion. The critical response is defined as the largest value of response for all possible incident angles. The ratio r_cr/r_srss between the critical value of response and the SRSS response—corresponding to the principal components of ground acceleration applied along the structure axes—is shown to depend on three dimensionless parameters: the spectrum intensity ratio γ between the two principal components of horizontal ground motion characterized by design spectra A(T_n) and γA(T_n); the correlation coefficient α of responses r_x and r_y due to design spectrum A(T_n) applied in the x‐ and y‐directions, respectively; and β = r_y/r_x. It is demonstrated that the ratio r_cr/r_srss is bounded by 1 and . Thus the largest value of the ratio is , 1.26, 1.13 and 1.08 for γ = 0, 0.5, 0.75 and 0.85, respectively. This implies that the critical response never exceeds times the result of the SRSS analysis, and this ratio is about 1.13 for typical values of γ, say 0.75. The correlation coefficient α depends on the structural properties but is always bounded between −1 and 1. For a fixed value of γ, the ratio r_cr/r_srss is largest if β = 1 and α = ±1. The parametric variations presented for one‐storey buildings indicate that this condition can be satisfied by axial forces in columns of symmetric‐plan buildings or can be approximated by lateral displacements in resisting elements of unsymmetrical‐plan buildings. Copyright © 2000 John Wiley & Sons, Ltd.     

Seismic response estimation method for earthquake‐damaged RC buildings

This study proposes a procedure for identifying spectral response curves for earthquake‐damaged areas in developing countries without seismic records. An earthquake‐damaged reinforced concrete building located in Padang, Indonesia was selected to illustrate the identification of the maximum seismic response during the 2009 West Sumatra earthquake. This paper summarizes the damage incurred by the building; the majority of the damage was observed in the third story in the span direction. The damage was quantitatively evaluated using the damage index R according to the Japanese guidelines for post‐earthquake damage evaluation. The damage index was also applied to the proposed spectral response identification method. The seismic performance of the building was evaluated by a nonlinear static analysis. The analytical results reproduced a drift concentration in the third story. The R‐index decreased with an increase in the story drift, which provided an estimation of the maximum response of the building during the earthquake. The estimation was verified via an earthquake response analysis of the building using ground acceleration data, which were simulated based on acceleration records of engineering bedrock that considered site amplification. The maximum response estimated by the R‐index was consistent with the maximum response obtained from the earthquake response analysis. Therefore, the proposed method enables the construction of spectral response curves by integrating the identification results for the maximum responses in a number of earthquake‐damaged buildings despite a lack of seismic records. Copyright © 2016 The Authors. Earthquake Engineering & Structural Dynamics published by John Wiley & Sons Ltd.     

Structural performance assessment under near‐source pulse‐like ground motions using advanced ground motion intensity measures

This paper demonstrates the effectiveness of utilizing advanced ground motion intensity measures (IMs) to evaluate the seismic performance of a structure subject to near‐source ground motions. Ordinary records are, in addition, utilized to demonstrate the robustness of the advanced IM with respect to record selection and scaling. To perform nonlinear dynamic analyses (NDAs), ground motions need to be selected; as a result, choosing records that are not representative of the site hazard can alter the seismic performance of structures. The median collapse capacity (in terms of IM), for example, can be systematically dictated by including a few aggressive or benign pulse‐like records into the record set used for analyses. In this paper, the elastic‐based IM such as the pseudo‐spectral acceleration (S_a) or a vector of S_a and epsilon has been demonstrated to be deficient to assess the structural responses subject to pulse‐like motions. Using advanced IMs can be, however, more accurate in terms of probabilistic response prediction. Scaling earthquake records using advanced IMs (e.g. inelastic spectral displacement, S_di, and IM _1I&2E; the latter is for the significant higher‐mode contribution structures) subject to ordinary and/or pulse‐like records is efficient, sufficient, and robust relative to record selection and scaling. As a result, detailed record selection is not necessary, and records with virtually any magnitude, distance, epsilon and pulse period can be selected for NDAs. Copyright © 2008 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.     

Development and validation of p‐y modeling approach for seismic response predictions of highway bridges

This study aims to realistically simulate the seismic responses of typical highway bridges in California with considerations of soil–structure interaction effects. The p‐y modeling approaches are developed and validated for embankments and pile foundations of bridges. The p‐y approach models the lateral and vertical foundation flexibility with distributed p‐y springs and associated t‐z and q‐z springs. Building upon the existing p‐y models for pile foundations, the study develops the nonlinear p‐y springs for embankments based on nonlinear 2D and 3D continuum finite element analysis under passive loading condition along both longitudinal and transverse directions. Closed‐form expressions are developed for two key parameters, the ultimate resistant force p_ult and the displacement y₅₀, where 0.5p_ult is reached, of embankment p‐y models as functions of abutment geometry (wall width and height, embankment fill height, etc.) and soil material properties (wall‐soil friction angle, soil friction angle, and cohesion). In order to account for the kinematic and site responses, depth‐varying ground motions are derived and applied at the free‐end of p‐y springs, which reflects the amplified embankment crest motion. The modeling approach is applied to simulate the seismic responses of the Painter Street Bridge and validated through comparisons with the recorded responses during the 1992 Petrolia earthquake. It is demonstrated that the flexibility and motion amplification at end abutments are the most crucial modeling aspects. The developed p‐y models and the modeling approach can effectively predict the seismic responses of highway bridges. Copyright © 2016 John Wiley & Sons, Ltd.     

A ground motion selection procedure for enforcing hazard consistency and estimating seismic demand hazard curves

This paper develops a procedure to select unscaled ground motions for estimating seismic demand hazard curves (SDHCs) in performance‐based earthquake engineering. Currently, SDHCs are estimated from a probabilistic seismic demand analysis, where several ensembles of ground motions are selected and scaled to a user‐specified scalar conditioning intensity measure (IM). In contrast, the procedure developed herein provides a way to select a single ensemble of unscaled ground motions for estimating the SDHC. In the context of unscaled motions, the proposed procedure requires three inputs: (i) database of unscaled ground motions, (ii) I M , the vector of IMs for selecting ground motions, and (iii) sample size, n; in the context of scaled motions, two additional inputs are needed: (i) a maximum acceptable scale factor, SF_max, and (ii) a target fraction of scaled ground motions, γ. Using a recently developed approach for evaluating ground motion selection and modification procedures, the proposed procedure is evaluated for a variety of inputs and is demonstrated to provide accurate estimates of the SDHC when the vector of IMs chosen to select ground motions is sufficient for the response quantity of interest. Copyright © 2015 John Wiley & Sons, Ltd.     

Principal axes of M-DOF structures Part II: Dynamic loading

This paper is the second in a two-part series that discusses the principal axes of M-DOF structures subjected to static and dynamic loads. The primary purpose of this series is to understand the magnitude of the dynamic response of structures to enable better design of structures and response modification devices/systems. Under idealized design conditions, the structural responses are obtained by using single direction input ground motions in the direction of the intended response modification devices/systems, and by assuming that the responses of the structure is decoupleable in three mutually perpendicular directions. This standard practice has been applied to both new and retrofitted structures using various seismic protective systems. Very limited information is available on the effects of neglecting the impact of directional couplings (cross effects of which torsion is a component) of the dynamic response of structures. In order to quantify such effects, it is necessary to examine the principal axes of structures under both static and dynamic loading. In this two-part series, the first paper is concerned with static loading, which provides definitions and fundamental formulations, with the conclusion that cross effects of a statically loaded M-DOF structure resulting from the lack of principal axes are of insignificant magnitude. However, under dynamic or earthquake loading, a relatively small amount of energy transferred across perpendicular directions is accumulated, which may result in significant enlargement of the structural response. This paper deals with a formulation to define the principal axes of M-DOF structures under dynamic loading and develops quantitative measures to identify cross effects resulting from the non-existence of principal axes.     

Numerical study of a full‐scale six‐story reinforced concrete wall‐frame structure tested at E‐Defense

A full‐scale shake table test on a six‐story reinforced concrete wall frame structure was carried out at E‐Defense, the world's largest three‐dimensional earthquake simulation facility, in January 2006. Story collapse induced from shear failure of shear critical members (e.g., short columns and shear walls) was successfully produced in the test. Insights gained into the seismic behavior of a full‐scale specimen subjected to severe earthquake loads are presented in this paper. To reproduce the collapse process of the specimen and evaluate the ability of analytical tools to predict post‐peak behavior, numerical simulation was also conducted, modeling the seismic behavior of each member with different kinds of models, which differ primarily in their ability to simulate strength decay. Simulated results showed good agreement with the strength‐degrading features observed in post‐peak regions where shear failure of members and concentrated deformation occurred in the first story. The simulated results tended to underestimate observed values such as maximum base shear and maximum displacement. The effects of member model characteristics, torsional response, and earthquake load dimensions (i.e., three‐dimensional effects) on the collapse process of the specimen were also investigated through comprehensive dynamic analyses, which highlighted the following seismic characteristics of the full‐scale specimen: (i) a model that is incapable of simulating a specimen's strength deterioration is inadequate to simulate the post‐peak behavior of the specimen; (ii) the torsional response generated from uniaxial eccentricity in the longitudinal direction was more significant in the elastic range than in the inelastic range; and (iii) three‐dimensional earthquake loads (X–Y–Z axes) generated larger maximum displacement than any other loading cases such as two‐dimensional (X–Y or Y–Z axes) or one‐dimensional (Y axis only) excitation. Copyright © 2011 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.     

基础刚度对砖石古塔地震响应影响研究

以西安万寿寺塔纠偏工程为研究背景,分别建立增加圈梁、圈梁-地梁组合以及圈梁-地梁-托盘组合模型下的塔体与基础协同工作模型。采用时程分析法,对不同基础刚度条件下塔体的地震响应进行分析及评估,结果表明:(1)增大基础刚度的同时结构的地震位移响应将会被放大,但应力时程曲线的波动范围随之缩小、幅值减小;(2)增设圈梁时由于塔底三向受力,塔底应力将被放大;(3)进行基础完全托换能够大幅改善塔底在地震作用下的受力状态。在塔体加固维修时应综合考虑地震作用下塔体的位移放大效应与塔体应力分布的影响,选取合适的基础刚度。     

Response spectrum analysis for floor acceleration

The peak floor acceleration (PFA) is a critical parameter influencing the performance of non‐structural elements in buildings. This paper develops a response spectrum analysis method based on the complete quadratic combination (CQC) rule to estimate the PFA. The method accounts for the rigid contribution of truncated higher modes and the cross‐correlations between all pairs of modes. The approximation is introduced in the time domain and then formulated in the frequency domain by CQC. Application of the method to a continuous cantilever beam idealizing a building with shear walls is presented and compared with alternative formulations. The proposed method is able to provide a consistent estimation of the PFA along the entire structure, not only where the PFA is principally influenced by the first few flexible modes but also where the PFA is mainly related to the rigid response of the structure, for example, near its base. Copyright © 2015 John Wiley & Sons, Ltd.     

1970年以来鲜水河断裂带地震活动特征与2014年康定M_S6.3地震

本文基于1970年以来的地震目录及四川地区4.0级以上地震的震源机制解资料,分析鲜水河断裂带分段(炉霍段、道符段、康定段、石棉段)的地震活动特征及研究区现代构造应力场,结合深部速度结构,探讨鲜水河断裂带上地震活动频度与龙门山断裂带地震活动的关系及康定地段6.3级地震的孕震环境。结果发现:(1)鲜水河断裂带北段和南段地震活动性存在差异,炉霍段和道孚段的地震活动频度1981年前要高于2000年后,康定段和石棉段的地震活动频度2000年以后高于1981年前;(2)分析地壳P波速度结构发现康定震区西侧川滇块体表现出低速异常,东侧表现出高速异常;(3)对构造应力场的分析结果表明龙门山断裂带主要以NW-SE向挤压为主,鲜水河断裂带构造应力场以NWW-SEE向为主。综合鲜水河断裂带应力场特征、深部速度结构、断层间的相互作用等信息推断,康定M6.3地震的发生与该地区应力积累及深部孕震环境相关,同时由于龙门山断裂带地震活动性影响,导致鲜水河断裂带康定段的能量释放。     

Determination of the seismic performance factors for post‐tensioned rocking timber wall systems

Post‐tensioned technologies for concrete seismic resistant buildings were first developed in the 1990s during the PREcast Seismic Structural Systems program. Among different solutions, the hybrid system proved to be the most resilient solution providing a combination of re‐centering and energy dissipative contributions respectively by using post‐tensioned tendons and mild steel reinforcement. The system, while providing significant strength and energy dissipation, reduces structural element damage and limits post‐earthquake residual displacements. More recently, the technology was extended to laminated veneer lumber (LVL) structural members, and extensive experimental and numerical work was carried out and allowed the development of reliable analytical and numerical models as well as design guidelines. On the basis of the experimental and numerical outcomes, this paper presents the evaluation of the seismic performance factors for post‐tensioned rocking LVL walls using the FEMA P‐695 procedure. Several archetype buildings were designed considering different parameters such as the building and story height, the type of seismic resistant system, the magnitude of gravity loads and the seismic design category. Lumped plasticity models were developed for each index archetype to simulate the behavioral aspects and collapse mechanisms. Non‐linear quasi‐static analyses were carried out to evaluate the system over‐strength factor; moreover, non‐linear time history analyses were performed using the incremental dynamic analysis concept to assess the collapse of each building. From the results of quasi‐static and dynamic analyses the response modification factor, R, system over‐strength factor, Ω₀, and deflection amplification factor, C_d, values of, respectively, 7, 3.5 and 7.5 are recommended. Copyright © 2016 John Wiley & Sons, Ltd.     

Principal axes of M-DOF structures part I: Static loading

This paper is the first in a two-part series that discusses the principal axes of M-DOF structures subjected to static and dynamic loads. The primary purpose of this series is to understand the magnitude of the dynamic response of structures to enable better design of structures and control modification devices/systems. Under idealized design conditions, the structural responses are obtained by using single direction input ground motions in the direction of the intended control devices/systems, and by assuming that the responses of the structure is decoupleable in three mutually perpendicular directions. This standard practice has been applied to both new and retrofitted structures using various seismic protective systems. Very limited information is available on the effects of neglecting the impact of directional couplings (cross effects - of which torsion is a component) of the dynamic response of structures. In order to quantify such effects, it is necessary to examine the principal axes of structures under both static and dynamic loading. This first paper deals with quantitative definitions of principal axes and “cross effects” of three-dimensional structures under static load by using linear algebra. It shows theoretically that, for three-dimensional structures, such principal axes rarely exist. Under static loading conditions, the cross effect is typically small and negligible from the viewpoint of engineering applications. However, it provides the theoretical base for subsequent quantification of the response couplings under dynamic loads, which is reported in part II of this series.     

山东长岛地区地震波非弹性衰减Q值、场地响应及震源参数研究

利用山东台网记录的长岛震群2017年2月14日—9月1日期间的波形与震相资料研究长岛地区非弹性衰减系数,得到该地区介质平均Q值与频率f的关系式为Q(f)=363.9f1.374 1。采用Moya等[1]提出的利用遗传算法联合反演得到长岛周边台站的场地响应,根据Brune模型震源参数计算公式求解长岛震群序列地震震源参数。结果显示,各个震源参数之间均存在一定的相关关系,地震矩随ML震级的增大而增加,地震矩与破裂半径R之间存在半对数关系,拐角频率fc随地震矩的增大而减少;长岛地震序列的应力降数值普遍偏小,最大不超过0.9MPa,这意味着长岛震源区整体构造应力较低,也可能指示长岛震群为低摩擦应力的断层作用;震源参数随时间的变化方面,整体而言,长岛震群地震应力降变化起伏很大,在M4.1地震发生前,拐角频率与应力降均发生快速下降后随即翻转上升的现象,证明在M4.1地震发生前震源区整体应力的挤压逐渐增强。     

Structural seismic response analysis based on multiscale approach of computing fault–structure system

Structural safety for earthquake waves emitted from a nearby fault is a major concern. For a large complex structure, it might be desired to estimate its seismic response by analyzing a fault–structure system: a full three‐dimensional model in which a source fault and a target structure are modeled so that fault processes, wave propagation and amplification processes, and resulting dynamic responses of the structure can be computed numerically. To analyze this fault–structure system, this paper proposes an efficient approach based on multiscale analysis, i.e. waves emitted from the source fault are computed in the entire system in the geological length‐scale; then they are refined in a small part of the system that includes the structure, and the seismic response of the structure is accurately computed in the engineering length‐scale. Using a long highway tunnel as an example, this paper examines the validity of the proposed approach. The usefulness and applicability of the proposed approach to estimate the structural seismic responses are discussed. Copyright © 2008 John Wiley & Sons, Ltd.     

Seismic response analysis of multidrum classical columns

This paper presents a numerical investigation on the seismic response of multidrum classical columns. The motivation for this study originates from the need to understand: (a) the level of ground shaking that classical multidrum columns can survive, and (b) the possible advantages or disadvantages of retrofitting multidrum columns with metallic shear links that replace the wooden poles that were installed in ancient times. The numerical study presented in this paper is conducted with the commercially available software Working Model 2D?, which can capture with fidelity the sliding, rocking, and slide‐rocking response of rigid‐body assemblies. This paper validates the software Working Model by comparing selected computed responses with scarce analytical solutions and the results from in‐house numerical codes initially developed at the University of California, Berkeley, to study the seismic response of electrical transformers and heavy laboratory equipment. The study reveals that relative sliding between drums happens even when the g‐value of the ground acceleration is less than the coefficient of friction, µ, of the sliding interfaces and concludes that: (a) typical multidrum classical columns can survive the ground shaking from strong ground motions recorded near the causative faults of earthquakes with magnitudes M_w=6.0–7.4; (b) in most cases multidrum classical columns free to dislocate at the drum interfaces exhibit more controlled seismic response than the monolithic columns with same size and slenderness; (c) the shear strength of the wooden poles has a marginal effect on the sliding response of the drums; and (d) stiff metallic shear links in‐between column drums may have an undesirable role on the seismic stability of classical columns and should be avoided. Copyright © 2005 John Wiley & Sons, Ltd.     

Winkler model for dynamic response of composite caisson–piles foundations: Seismic response

A simplified method with a dynamic Winkler model to study the seismic response of composite caisson–piles foundations (CCPF¹) is developed. Firstly, with the dynamic Winkler model, the kinematic response of the CCPF subjected to vertically propagating seismic S-wave is analyzed by coupling the responses of caisson part and pile part. Secondly, a simplified model for the foundation–structure system is created with the structure simplified as a lumped mass connected to the foundation with an elastic column, and through the Fast Fourier Transformation (FFT) this model is enabled to solve transient seismic problems. Thirdly, the proposed method for the seismic response of CCPF-structure systems is verified by comparison against 3D dynamic finite element simulation, in which the Domain Reduction Method (DRM²) is utilized. Lastly, the mechanism and significance of adding piles in improving the earthquake resistance of the foundation and structure is analyzed through an example with different soil conditions. Discovered in this study is that adding piles under the caisson is an efficient way to increase seismic resistant capability of the soil–foundation–structure system, and the main mechanism of that is the elimination of the pseudo-resonance.