• Journal of the Korean Geotechnical Society
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• v.26 no.3
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• pp.47-57
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• 2010

Yield seismic coefficient plays an important role in the estimation of permanent displacement of a soil slope subjected to earthquake using Newmark's sliding block theory. However, yield seismic coefficients currently used in practices are not mechanically rigorous since most of them are estimated using limit equilibrium methods considering equilibrium condition only. Therefore, estimation of permanent displacement of a soil slope based on existing yield seismic coefficient may cause problems. Limit analysis estimating the range of mechanically rigorous solution is thought to be effective in evaluating the validity of existing yield seismic coefficient. In this study, a simple stability chart for yield seismic coefficient useful in practices is proposed by considering various slope conditions including stability number, slope inclination, strength parameters, etc.

• Earthquakes and Structures
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• v.13 no.1
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• pp.59-66
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• 2017

Modern seismic codes rely on performance-based seismic design methodology which requires that the structures withstand inelastic deformation. Many studies have focused on the inelastic deformation ratio evaluation (ratio between the inelastic and elastic maximum lateral displacement demands) for various inelastic spectra. This paper investigates the inelastic response spectra through the ductility demand ${\mu}$, the yield strength reduction factor $R_y$, and the inelastic deformation ratio. They depend on the vibration period T, the post-to-preyield stiffness ratio ${\alpha}$, the peak ground acceleration (PGA), and the normalized yield strength coefficient ${\eta}$ (ratio of yield strength coefficient divided by the PGA). A new inelastic deformation ratio $C_{\eta}$ is defined; it is related to the capacity curve (pushover curve) through the coefficient (${\eta}$) and the ratio (${\alpha}$) that are used as control parameters. A set of 140 real ground motions is selected. The structures are bilinear inelastic single degree of freedom systems (SDOF). The sensitivity of the resulting inelastic deformation ratio mean values is discussed for different levels of normalized yield strength coefficient. The influence of vibration period T, post-to-preyield stiffness ratio ${\alpha}$, normalized yield strength coefficient ${\eta}$, earthquake magnitude, ruptures distance (i.e., to fault rupture) and site conditions is also investigated. A regression analysis leads to simplified expressions of this inelastic deformation ratio. These simplified equations estimate the inelastic deformation ratio for structures, which is a key parameter for design or evaluation. The results show that, for a given level of normalized yield strength coefficient, these inelastic displacement ratios become non sensitive to none of the rupture distance, the earthquake magnitude or the site class. Furthermore, they show that the post-to-preyield stiffness has a negligible effect on the inelastic deformation ratio if the normalized yield strength coefficient is greater than unity.

• Journal of the Earthquake Engineering Society of Korea
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• v.20 no.2
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• pp.125-134
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• 2016

In order to improve seismic safety of nuclear power plant (NPP) structures in high seismicity area, seismic isolation system can be adapted. In this study, friction pendulum system (FPS) is used as the seismic isolation system. According to Coulomb's friction theory, friction coefficient is constant regardless of bearing pressure and sliding velocity. However, friction coefficient under actual situation can be changed according to bearing pressure, sliding velocity and temperature. Seismic responses of friction pendulum system with constant friction and various velocity-dependent friction are compared. The velocity-dependent friction coefficients of FPS are varied between low-and fast-velocity friction coefficients according to sliding velocity. From the results of seismic analysis of FPS with various cases of friction coefficient, it can be observed that the yield force of FPS becomes larger as the fast-velocity friction coefficient becomes larger. Also, the displacement response of FPS becomes smaller as the fast-velocity coefficient becomes larger.

• Structural Engineering and Mechanics
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• v.52 no.6
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• pp.1225-1256
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• 2014

Calculating the seismic displacement of retaining walls has an important role in the optimum design of these structures. Also, studying the effect of surcharge is important for the calculation of active pressure as well as permanent displacements of the wall. In this regard, some researchers have investigated active pressure; but, unfortunately, there are few investigations on the seismic displacement of retaining walls with surcharge. In this research, using limit analysis and upper bound theorem, permanent seismic displacement of retaining walls with surcharge was analyzed for sliding and overturning failure mechanisms. Thus, a new formulation was presented for calculating yield acceleration, critical angle of failure wedge, and permanent displacement of retaining walls with surcharge. Also, effects of surcharge, its location and other factors such as height of the wall and internal friction angle of soil on the amount of seismic displacements were investigated. Finally, designing charts were presented for calculating yield acceleration coefficient and angle of failure wedge.

• Earthquakes and Structures
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• v.12 no.4
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• pp.397-407
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• 2017

To estimate the structural seismic demand, some methods are based on an equivalent linear system such as the Capacity Spectrum Method, the N2 method and the Equivalent Linearization method. Another category, widely investigated, is based on displacement correction such as the Displacement Coefficient Method and the Coefficient Method. Its basic concept consists in converting the elastic linear displacement of an equivalent Single Degree of Freedom system (SDOF) into a corresponding inelastic displacement. It relies on adequate modifying or reduction coefficient such as the inelastic deformation ratio which is usually developed for systems with known ductility factors ($C_{\mu}$) and ($C_R$) for known yield-strength reduction factor. The present paper proposes a rational approach which estimates this inelastic deformation ratio for SDOF bilinear systems by rigorous nonlinear analysis. It proposes a new inelastic deformation ratio which unifies and combines both $C_{\mu}$ and $C_R$ effects. It is defined by the ratio between the inelastic and elastic maximum lateral displacement demands. Three options are investigated in order to express the inelastic response spectra in terms of: ductility demand, yield strength reduction factor, and inelastic deformation ratio which depends on the period, the post-to-preyield stiffness ratio, the yield strength and the peak ground acceleration. This new inelastic deformation ratio ($C_{\eta}$) is describes the response spectra and is related to the capacity curve (pushover curve): normalized yield strength coefficient (${\eta}$), post-to-preyield stiffness ratio (${\alpha}$), natural period (T), peak ductility factor (${\mu}$), and the yield strength reduction factor ($R_y$). For illustrative purposes, instantaneous ductility demand and yield strength reduction factor for a SDOF system subject to various recorded motions (El-Centro 1940 (N/S), Boumerdes: Algeria 2003). The method accuracy is investigated and compared to classical formulations, for various hysteretic models and values of the normalized yield strength coefficient (${\eta}$), post-to-preyield stiffness ratio (${\alpha}$), and natural period (T). Though the ductility demand and yield strength reduction factor differ greatly for some given T and ${\eta}$ ranges, they remain take close when ${\eta}>1$, whereas they are equal to 1 for periods $T{\geq}1s$.

• Computational Structural Engineering
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• v.9 no.4
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• pp.229-237
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• 1996

In some current procedures, ground motions from different sources have been scaled by their peak ground accelerations and combined to obtain smoothed response spectra for specific regions. As consideration of the inelastic deformation capacity of structure, inelastic deformations are permitted under seismic ground excitation in all codes. In the ATC(Applied Technology Council) and UBC(Uniform Building Code), the inelastic design spectrum is obtained by reducing the elastic design spectrum by a factor that is independent of structural period. In this study, the average of nonlinear response spectra calculated from a sample of 20 records for each event are constructed to obtain the smoothed response spectra. These response spectra are used to examine the effects of structural strength factors such as the yield strength ratio and damping value. Through the regression analysis of nonlinear response of system for a given damping value and yield strength ratio, the required yield strength for seismic design can be estimated for a certain earthquake event. And a response modification coefficient depending on the natural period for current seismic design specifications are proposed.

• Earthquakes and Structures
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• v.4 no.4
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• pp.365-381
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• 2013

In this paper, a numerical simulation study was conducted on the seismic behavior and ductility demand of single-degree-of-freedom (SDOF) systems with partially self-centering hysteresis. Unlike fully self-centering systems, partially self-centering systems display noticeable residual displacement after unloading is completed. Such partially self-centering behavior has been observed in a number of recently researched self-centering structural systems with energy dissipation devices. It is thus of interest to examine the seismic performance such as ductility demand of partially self-centering systems. In this study, a modified flag-shaped hysteresis model with residual displacement is proposed to represent the hysteretic behavior of partially self-centering structural systems. A parametric study considering the effect of variations in post-yield stiffness ratio, energy dissipation coefficient, and residual displacement ratio on the displacement ductility demand of partially self-centering systems was conducted using a suite of 192 scaled ground motions. The results of this parametric study reveal that increasing the post-yield stiffness, energy dissipation coefficient or residual displacement ratio of the partially self-centering systems generally leads to reduced ductility demand, especially for systems with lower yield strength.

• Structural Engineering and Mechanics
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• v.42 no.5
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• pp.631-644
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• 2012

Current seismic codes require from the seismically designed structures to be capable to withstand inelastic deformation. Many studies dealt with the development of different inelastic spectra with the aim to simplify the evaluation of inelastic deformation and performance of structures. Recently, the concept of inelastic spectra has been adopted in the global scheme of the performance-based seismic design through capacity-spectrum methods. In this paper, the median of the ductility demand ratio for 80 ground motions are presented for different levels of normalized yield strength, defined as the yield strength coefficient divided by the peak ground acceleration (PGA). The influence of the post-to-preyield stiffness ratio on the ductility demand is investigated. For fixed levels of normalized yield strength, the median ductility versus period plots demonstrated that they are independent of the earthquake magnitude and epicentral distance. Determined by regression analysis of the data, two design equations have been developed; one for the ductility demand as function of period, post-to-preyield stiffness ratio, and normalized yield strength, and the other for the inelastic deformation as function of period and peak ground acceleration valid for periods longer than 0.6 seconds. The equations are useful in estimating the ductility and inelastic deformation demands for structures in the preliminary design. It was found that the post-to-preyield stiffness has a negligible effect on the ductility factor if the yield strength coefficient is greater than the PGA of the design ground motion normalized by gravity.

• Journal of the Korean Geotechnical Society
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• v.28 no.12
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• pp.123-131
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• 2012

Recent earthquake records indicate that the vertical component of earthquake loading, generally neglected in seismic slope stability analysis, has a significant influence on the stability. This is particularly true for the earthquakes originating inside the continent, not from its boundaries. Therefore the design of geotechnical structures without consideration of vertical component of earthquake loading may result in unsafe design. In this study, with a consideration of the effect of vertical seismic loading, the horizontal yield seismic coefficients under various slope conditions are estimated, using the lower bound limit analysis. In addition, the equation for the determination of the critical direction (either upward or downward) of vertical seismic loading is proposed.

• Geomechanics and Engineering
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• v.5 no.2
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• pp.143-164
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• 2013

Calculation of seismic displacements in reinforced slopes plays a crucial role in appropriate design of these structures however current analytical methods result indifferent values for permanent displacements of the slope. In this paper, based on limit equilibrium and using the horizontal slices method, a new formulation has been proposed for estimating the seismic displacements of a reinforced slope under earthquake records. In this method, failure wedge is divided into a number of horizontal slices. Assuming linear variations for tensile forces of reinforcements along the height of the slope, the coefficient of yield acceleration has been estimated. The simplicity of calculations and taking into account the frequency content of input triggers are among the advantages of the present formulation. Comparison of the results shows that the yield acceleration calculated by the suggested method is very close to the values resulted from other techniques. On the other hand, while there is a significant difference between permanent displacements, the values obtained from the suggested method place somehow between those calculated by the other techniques.