Aseismic Code Research Articles

Survival probability surfaces of hysteretic fractional order structures exposed to non-stationary code-compliant stochastic seismic excitation

A novel first-passage probability stochastic incremental dynamics analysis (SIDA) methodology tailored for hysteretic fractional order structural systems under a fully non-stationary seismic excitation vector consistently designated with contemporary aseismic codes provisions (e.g., Eurocode 8) is developed. Specifically, the vector of the imposed seismic excitations is characterised by evolutionary power spectra that stochastically align with aseismic codes elastic response acceleration spectra, defined for specified modal damping ratios and scaled ground accelerations. Leveraging the concepts of stochastic averaging and statistical linearization, the approximative non-stationary response displacement joint probability density function (PDF) is derived, retaining the particularly coveted attribute of computational efficacy. Subsequently, the coupling with the survival probability model allows for the efficient determination of the response first-passage time probability density surfaces and the survival probability surfaces across various limit-state rules and scalable intensity measures. The first-passage time probability serves as a robust engineering demand parameter, effectively monitoring structural behaviour by considering both intensity and timing information, while inherently aligned with pertinent limit-state requirements. Notably, the associated low computational cost and the ability to handle a wide range of complex nonlinear/hysteretic structural behaviours, coupled with its compliance with modern aseismic codes, underscore its potential for applications in the fields of structural and earthquake engineering. A nonlinear system endowed with fractional derivative elements is used to exemplify the method’s reliability. The accuracy of the proposed method is validated in a Monte Carlo-based context, conducting nonlinear response time–history analyses with an extensive ensemble of accelerograms compatible with Eurocode 8 response acceleration spectra.

First-excursion stochastic incremental dynamics methodology for hysteretic structural systems subject to seismic excitation

A novel efficient stochastic incremental dynamics methodology considering first-excursion probability for nonlinear structural systems subject to stochastic seismic excitations in alignment with contemporary aseismic codes provisions is developed. To this aim, an approximate nonlinear stochastic dynamics technique for conducting first-passage probability density function (PDF) based stochastic incremental dynamic analysis is developed. Firstly, an efficient stochastic iterative linearization methodology is devised achieving convergence of the equivalent system damping ratios with the damping premises of the excitation response spectrum leading to a coherent determination of a robust scalable intensity measure (IM) which bears direct relation to its damaging potential. Subsequently, utilizing the stochastically derived time-varying forced vibrational system properties in conjunction with a combination of deterministic and stochastic averaging treatment the first-excursion PDF is efficiently determined for each and every of the considered limit-state rules (LSs). Lastly, an incremental mechanization analogous to the one used in normal incremental dynamic analysis (IDA) is proposed to ensure the necessary compatibility for applications in the fields of structural and earthquake engineering. The back-and-forth twisting pattern of IDA curves which is related with the multiple points satisfaction of the very same limit-state rule encourages the study of the problem from a first-passage perspective considering timing in addition to the intensity of the excitation variable. The selected engineering demand parameter (EDP) of the first-excursion time constitutes an excellent response related variable with twofold meaning; it performs structural behavior monitoring considering intensity and timing information whereas it is inherently coupled with limit-state requirements. The developed stochastic dynamics technique provides with reliable higher order statistics (i.e., PDF) of the chosen EDP. A structural system comprising the bilinear hysteretic model serves as a numerical example for demonstrating the reliability of the proposed first-excursion PDF-based stochastic incremental dynamics methodology. Nonlinear response time-history analysis involving a large ensemble of Eurocode 8 spectrum compatible accelerograms is conducted to assess the accuracy of the proposed methodology in a Monte Carlo-based context.

Modal decomposition method for response spectrum based analysis of nonlinear and non-classically damped systems

Abstract A novel inelastic modal decomposition method for random vibration analysis in alignment with contemporary aseismic code provisions (e.g., Eurocode 8) considering non-classically damped and nonlinear multi degree-of-freedom (MDOF) systems is developed. Relying on statistical linearization and state-variable formulation the complex eigenvalue problem considering inelastic MDOF structural systems subject to a vector of stochastic seismic processes is addressed. The involved seismic processes are characterized by power spectra compatible in a stochastic sense with an assigned elastic response uniform hazard spectrum (UHS) of specified modal damping ratio. Equivalent modal properties (EMPs) of the linearized MDOF system, namely equivalent pseudo-undamped natural frequencies and equivalent modal damping ratios are provided. To this aim, each mode of vibration is assigned with a different stationary random process compatible with the excitation response spectrum adjusted to the corresponding equivalent modal damping ratio property. Next, an efficient iterative scheme is devised achieving convergence of the equivalent modal damping ratios and the damping premises of the excitation response spectrum corresponding to each mode of the system. Subsequently, the stochastically derived forced vibrational modal properties of the structure are utilized together with the appropriate mean response elastic UHS for determining peak nonlinear responses in modal coordinates. The modal participation factors are determined for the complex-valued mode shapes and generalized square-root-of-sums-squared (SRSS) is employed as the modal combination rule for determining the peak total responses of the system in physical space. The pertinency and applicability of the proposed framework is numerically illustrated using a three-storey bilinear hysteretic frame structure exposed to the Eurocode 8 elastic response spectrum. Nonlinear response time-history analysis (RHA) involving a large ensemble of stationary Eurocode 8 spectrum compatible accelerograms is conducted to assess the accuracy of the proposed methodology in a Monte Carlo-based context.

An approach for synthesizing tri-component ground motions compatible with hazard-consistent target spectrum - Italian aseismic code application

A versatile approach for synthesizing non-stationary multicomponent ground motions compatible with a given target response spectrum is presented. In conjunction with performance-based structural design, the proposed approach combines a scenario-based procedure to select the target spectra of the three components of the motion, and a stochastic scheme, with an iterative wavelet-based method to generate the artificial time histories. In this context, the selection of an appropriate target spectrum is mandatory to synthesizing accelerograms with proper frequency content, input-energy, effective duration, and inelastic demand. In the scenario-based assessments, the target spectrum is derived directly from an earthquake scenario defined by seismic hazard disaggregation and strong ground-motion attenuation relationships. Firstly, the design spectrum specified by aseismic code provisions is replaced by a set of conditional mean spectra (CMS) for each of the ground motion components. Subsequently, an inverse stochastic dynamics problem, defined by a set of parametric evolutionary power spectra (EPS), is formulated and solved in a point-wise format for each CMS and for the three components of the motion. To improve the matching between the response spectrum of the simulated records and the CMS, an iterative procedure involving the family of harmonic wavelets is then employed. Post-processing for a proper baseline correction of the records is performed to synthesize ground-motions yielding realistic velocity and displacement traces. To illustrate the effectiveness of the approach, extensive numerical results pertaining to the Italian aseismic code provisions are included in this paper. In this regard, Monte Carlo simulations are undertaken to relate the CMSs to the evolutionary power spectrum. In particular, non-constant peak factor expressions via regression analysis are derived for various ground-motion durations. Finally, the nonlinear responses of elasto-plastic SDOF oscillators with different values of the yield strength reduction factor are considered. The oscillators subjected to artificially generated records and a set of natural unscaled and spectrum-compatible accelerograms, are examined in terms of ductility demand and equivalent number of yield cycles.

Seismic Response of a Prestressed Concrete Wind Turbine Tower

This paper compares the seismic load of a 5-MW wind turbine supported by a 100-m-high prestressed concrete tower calculated via time history analysis and response spectrum analysis using elastic acceleration spectrum provided by the China Aseismic Code for Buildings. With 5 % damping ratio, the fixed-base multi-degree of freedom model and finite element model considering soil structure interaction are used for response spectrum analysis and time history analysis, respectively. The results indicated that the seismic load calculated by response spectrum analysis is significantly larger than those obtained using the time history analysis method. It implies that the seismic load determined from common building code procedures along with other loads for wind turbine foundation design is too conservative. Within this paper, the effects of damping ratio, horizontal acceleration amplitude, spring stiffness, and damping coefficient of foundation on the seismic load of the prestressed concrete wind turbine tower are discussed. It is shown that the seismic load with mode damping ratio for the prestressed concrete wind turbine tower is not significant when compared with traditional tubular steel tower designs. The maximum moment demand at the base of the tower may be controlled by earthquake loading as the seismic fortification intensity lever is more than seven. The foundation spring stiffness has an immense impact on the base bending moment and the natural frequency. Finally, seismic load should be considered more in detail when designing wind turbines that are supported by concrete towers, particularly for turbines over 100 m height and located in seismically active zones.

A Critical Evaluation Of Near-field Seismic Records In Greece

The study of seismic records characterized as “near-field” ground motions is increasingly drawing more attention. It has been recognized that accelerograms obtained in recent years close to the source of strong earthquakes reveal exceptional features that challenge widely held concepts about the nature of strong ground motion. This study presents systematic processing and evaluation of over 860 records of strong ground motions in Greece in order to identify “near-field” features with the aid of damage potential parameters. The findings serve as a basis to evaluate the adequacy of the current aseismic code to specify seismic demand. In addition “well known” damage potential parameters are

Response of a wind turbine subjected to near-fault excitation and comparison with the Greek Aseismic Code provisions

The paper focuses on the study of the dynamic response of a wind turbine installed close to seismic fault in an earthquake prone region of Greece. The investigation of the seismic behavior of the turbine is performed with response spectrum analysis using the elastic acceleration spectrum provided by the Greek National Aseismic Code for the project area, increased by 25% due to proximity to seismic fault, as recommended by the Code. Also, dynamic analysis is performed using the spectrum obtained from the assessment of seismic hazard at the site of the project (Local), for two typical cases of earthquakes of magnitudes Ms=5.8 and Ms=7.3 with epicentral distances of 1km and 11km from the test position, respectively. Finally, a time-history analysis is carried out using an artificial accelerogram obtained from the local spectrum envelope, for the site of the project, considering 1% damping ratio. The direct comparison of the response spectrum analysis results with the corresponding ones obtained from the dynamic and time-history analyses indicates that the implementation of the elastic acceleration spectrum is insufficient, although increased, and therefore it could be deduced that the current recommendation of the Greek National Aseismic Code to consider an increment of 25% on the elastic acceleration spectrum in regions close to seismic faults, requires review and further improvement.

Derivation of response spectrum compatible non-stationary stochastic processes relying on Monte Carlo-based peak factor estimation

In this paper a novel approach is proposed to address the problem of deriving non-stationary stochastic processes which are compatible in the mean sense with a given (target) response (uniform hazard) spectrum (UHS) as commonly desired in the aseismic structural design regulated by contemporary codes of practice. The appealing feature of the approach is that it is non-iterative and “one-step”. This is accomplished by solving a standard over-determined minimization problem in conjunction with appropriate median peak factors. These factors are determined by a plethora of reported new Monte Carlo studies which on their own possess considerable stochastic dynamics merit. In the proposed approach, generation and treatment of samples of the processes individually on a deterministic basis is not required as is the case with the various “two-step” approaches found in the literature addressing the herein considered task. The applicability and usefulness of the approach is demonstrated by furnishing extensive numerical data associated with the elastic design UHS of the current European (EC8) and the Chinese (GB 50011) aseismic code provisions. Purposely, simple and thus attractive from a practical viewpoint, uniformly modulated processes assuming either the Kanai-Tajimi (K-T) or the Clough-Penzien (C-P) spectral form are employed. The Monte Carlo studies yield damping and duration dependent median peak factor spectra, given in a polynomial form, associated with the first passage problem for UHS compatible K-T and C-P uniformly modulated stochastic processes. Hopefully, the herein derived stochastic processes and median peak factor spectra can be used to facilitate the aseismic design of structures regulated by contemporary code provisions in a Monte Carlo simulation-based or stochastic dynamics-based context of analysis.

Effective linear damping and stiffness coefficients of nonlinear systems for design spectrum based analysis

A stochastic approach for obtaining reliable estimates of the peak response of nonlinear systems to excitations specified via a design seismic spectrum is proposed. This is achieved in an efficient manner without resorting to numerical integration of the governing nonlinear equations of motion. First, a numerical scheme is utilized to derive a power spectrum which is compatible in a stochastic sense with a given design spectrum. This power spectrum is then treated as the excitation spectrum to determine effective damping and stiffness coefficients corresponding to an equivalent linear system (ELS) via a statistical linearization scheme. Further, the obtained coefficients are used in conjunction with the (linear) design spectrum to estimate the peak response of the original nonlinear systems. The cases of systems with piecewise linear stiffness nonlinearity, along with bilinear hysteretic systems are considered. The seismic severity is specified by the elastic design spectrum prescribed by the European aseismic code provisions (EC8). Monte Carlo simulations pertaining to an ensemble of nonstationary EC8 design spectrum compatible accelerograms are conducted to confirm that the average peak response of the nonlinear systems compare reasonably well with that of the ELS, within the known level of accuracy furnished by the statistical linearization method. In this manner, the proposed approach yields ELS which can replace the original nonlinear systems in carrying out computationally efficient analyses in the initial stages of the aseismic design of structures under severe seismic excitations specified in terms of a design spectrum.

Synthesis of accelerograms compatible with the Chinese GB 50011-2001 design spectrum via harmonic wavelets: artificial and historic records

A versatile approach is employed to generate artificial accelerograms which satisfy the compatibility criteria prescribed by the Chinese aseismic code provisions GB 50011-2001. In particular, a frequency dependent peak factor derived by means of appropriate Monte Carlo analyses is introduced to relate the GB 50011-2001 design spectrum to a parametrically defined evolutionary power spectrum (EPS). Special attention is given to the definition of the frequency content of the EPS in order to accommodate the mathematical form of the aforementioned design spectrum. Further, a one-to-one relationship is established between the parameter controlling the time-varying intensity of the EPS and the effective strong ground motion duration. Subsequently, an efficient auto-regressive moving-average (ARMA) filtering technique is utilized to generate ensembles of non-stationary artificial accelerograms whose average response spectrum is in a close agreement with the considered design spectrum. Furthermore, a harmonic wavelet based iterative scheme is adopted to modify these artificial signals so that a close matching of the signals’ response spectra with the GB 50011-2001 design spectrum is achieved on an individual basis. This is also done for field recorded accelerograms pertaining to the May, 2008 Wenchuan seismic event. In the process, zero-phase high-pass filtering is performed to accomplish proper baseline correction of the acquired spectrum compatible artificial and field accelerograms. Numerical results are given in a tabulated format to expedite their use in practice.

Correlation between seismic acceleration parameters and overall structural damage indices of buildings

This article describes the interdependency between several seismic acceleration parameters and the behavior of the reinforced concrete frame structures in the form of correlation coefficients. The structural behavior is expressed in form of overall structural damage indices. After the numerical evaluation of several seismic parameters, a nonlinear dynamic analysis is carried out to provide the total damage status of a structure. The aim is to select those, which have drastic influence on structural damage. Furthermore, the design philosophy of aseismic codes can be verified. The attention is focussed on the earthquake acceleration time histories of the worldwide well-known sites with a strong seismic activity.

Seismic Testing of Eccentrically Braced Dual Steel Systems

Two six-story eccentrically braced dual steel systems (EBDSs) were tested as part of the U.S.-Japan Cooperative Earthquake Research Program. The first, a full-scale structure ( prototype) was pseudo-dynamically tested in the Large Size Structures Laboratory of the Building Research Institute in Tsukuba, Japan. The second, a similitude scaled replica of the first, was tested on the earthquake simulator at the University of California at Berkeley. The prototype was designed for the minimum earthquake forces specified by the 1981 Japanese Aseismic Code and satisfied the current earthquake-resistant design regulations in the U.S.A. (1985 UBC, 1984 ATC 3-06 and 1986 SEAOC). The performance of the EBDS (both prototype and model) was outstanding in terms of its elastic strength and stiffnesses during minor earthquake shaking and its ability to absorb and dissipate energy, without strength and stiffness degradation, during severe earthquake shaking. Substantial overstrengths of both EBDSs with respect to their nominal yielding strengths were observed during severe earthquake shaking. However, the response modification factors currently adopted by the ATC and SEAOC significantly overestimated the experimental values in both instances.

Statistical analysis of the inelastic response of shear structures subjected to earthquakes

AbstractInelastic deformations of structures subjected to strong earthquakes are commonly accepted by Aseismic Codes; some discrepancies exist in the different procedures proposed to design a structure for which the ductility demand is to be limited within acceptable values. To have a better insight into the seismic behaviour of multi‐degree‐of‐freedom structures beyond the elastic range, the dynamic elasto‐plastic response of a ten‐storey shear system under two sets of artificial and recorded accelerograms is studied considering different stiffness‐strength distributions and constitutive laws. Statistics of the results are presented, demonstrating the dependence of the overall and storey ductility values and of their ratio on the characteristics of the structure and excitation.