Comparison of the Spectral Representation Method to Simulate Spatially Variable Ground Motions

The spectral representation method (SRM) is widely used when simulating spatially variable ground motions. It has mainly two formulas, i.e., the random amplitudes and the random phases formulas. There exist three methods for decomposing the cross spectral density matrix: Cholesky decomposition, eigen decomposition, and root decomposition. Therefore, there are six forms with respect to the different combinations of the simulation formulas and the decomposition methods. To provide researchers and engineers with the guidance on choosing simulation method, the six forms are systematically investigated from five aspects: the power intensity, response spectra, and stochastic error of auto/cross spectral density, Fourier spectra, and difference indexes for Fourier amplitudes and phases. Finally, we give the following advice: the characteristics of the ground motions simulated by the random amplitudes formula are independent of the decomposition method, while the characteristics of the ground motions simulated by random phases formula are dependent of the decomposition method. Furthermore, the root decomposition is strongly recommended when utilizing the random phases formula.     

Site Effects at Long Periods from Digital Strong Motion Records of the KiK-net,Japan

The high-quality digital records of the Japanese KiK-net were examined, with the aim of studying the influence of local site conditions on the displacement spectral ordinates at long periods. The attention was limited to those records for which the velocity profiles up to 100–200 m depth were known, and corresponding surface and borehole accelerograms were available. Based on the available records and with the support of 1D numerical simulations, different aspects that may have an influence on the amplification of long period spectral ordinates were studied, including the bedrock velocity profile, the site classification using V_s,30, and the earthquake magnitude.

Small amplification factors at long periods were found, ranging from 1 to 1.3, with median value from 1.05 to 1.1, for Eurocode 8 site classes B and C, respectively. Only for two records on soft soils (at the boundary between Eurocode 8 classes C and D), from small magnitude earthquakes, large amplification factors were obtained, up to about 4. A good correlation was found of the amplification levels with the response spectral ratio D(T₀)/D(10), where D(T₀) and D(10) are displacement spectral ordinates of the input signal at bedrock, at the fundamental period T₀ of the soil profile and at T = 10 s, respectively.     

Probabilistic Seismic Design of Pile Foundations in Non Liquefiable Soil by Response Spectrum Approach

The behavior of pile foundations in non liquefiable soil under seismic loading is considerably influenced by the variability in the soil and seismic design parameters. Hence, probabilistic models for the assessment of seismic pile design are necessary. Deformation of pile foundation in non liquefiable soil is dominated by inertial force from superstructure. The present study considers a pseudo-static approach based on code specified design response spectra. The response of the pile is determined by equivalent cantilever approach. The soil medium is modeled as a one-dimensional random field along the depth. The variability associated with undrained shear strength, design response spectrum ordinate, and superstructure mass is taken into consideration. Monte Carlo simulation technique is adopted to determine the probability of failure and reliability indices based on pile failure modes, namely exceedance of lateral displacement limit and moment capacity. A reliability-based design approach for the free head pile under seismic force is suggested that enables a rational choice of pile design parameters.     

Empirical Fragility Curves for Non-Residential Buildings from the 2010–2011 Canterbury Earthquake Sequence

This study develops a motion-damage database (the Canterbury Earthquake Building Assessment, CEBA database) using surveyed information obtained from the Canterbury earthquake sequence. The database is then applied to derive fragility curves for non-residential buildings in New Zealand. The results indicate that unreinforced masonry buildings are the most vulnerable to damage, while the concrete shear wall buildings were found to be the most resilient. Discrepancies were found when comparing equivalent structures in New Zealand and the United States. Inherent difference of building characteristics between the two countries, significant ground failure, and accumulated damage from multiple events might explain the difference.     

Unconditional Reliability-Based Design of Tuned Liquid Column Dampers Under Stochastic Earthquake Load Considering System Parameters Uncertainties

The reliability-based design of tuned mass damper considering system parameters uncertainties is noteworthy. However, the same is not the case for liquid dampers. The present study deals with the reliability-based design of tuned liquid column dampers under random earthquake considering system parameters uncertainties. Using the conditional second-order information of response quantities, the total probability concept is applied to evaluate the unconditional failure probability which is subsequently used as the objective function to obtain the damping parameters. A numerical study elucidates the effect of system parameters uncertainties on the damper parameters optimization and safety of the structure.     

A Multi-Mode Method for Estimation of Floor Response Spectra

A new simplified procedure for estimation of floor response spectra (FRS) is proposed. This methodology enriches the most common procedures using nonlinear response-history analysis to predict FRS by including a direct multi-mode technique to estimate FRS. A novel feature of the procedure is that the coupling effect is considered to establish equivalent modal systems and the FRS are developed by incorporating capacity spectrum method in conjunction with ductility-based FRS for each modal system. Both the proposed method and the traditional method are applied to three steel moment frame structures, and a reasonable accuracy is demonstrated.