Generation of Tri-Directional Spectra-Compatible Time Histories Coupling the Influence Matrix Method and Gram–Schmidt Orthogonalization

This study presents a new approach for obtaining a set of tri-directional time histories compatible with target design spectra by modifying real recorded earthquake ground motions. The influence matrix method (IMM) based on eigenfunction expansion is improved for typical design response spectra with different shapes and employed in order to achieve accurate matching with the target design spectra. By applying the Gram–Schmidt orthogonalization in each iteration of the IMM procedure, the correlation coefficient between any two components can be guaranteed to be strictly zero. Hence, the generated three components in the orthogonal directions are statistically independent. The generated time histories satisfy the requirements of current codes and standards. Two examples are presented to illustrate the procedure and the superiority of the proposed method, with the maximum relative error between the generated time histories and target design spectra being less than 0.2% in [0.6, 100] Hz, and the code requirements being satisfied strictly.

Reliability-based strength modification factor for seismic design spectra considering structural degradation

For earthquake-resistant design, structural degradation is considered using traditional strength modification factors, which are obtained via the ratio of the nonlinear seismic response of degrading and non-degrading structural single-degree-of-freedom (SDOF) systems. In this paper, with the aim to avoid the nonlinear seismic response to compute strength modification factors, a methodology based on probabilistic seismic hazard analyses (PSHAs), is proposed in order to obtain strength modification factors of design spectra which consider structural degradation through the spectral-shape intensity measure INp. PSHAs using INp to account for structural degradation and Sa(T1), which represents the spectral acceleration associated with the fundamental period and does not consider such degradation, are performed. The ratio of the uniform hazard spectra in terms of INp and Sa(T1), which represent the response of degrading and non-degrading systems, provides new strength modification factors without the need to develop nonlinear time history analysis. A mathematical expression is fitted to the ratios that correspond to systems located in different soil types. The expression is validated by comparing the results with those derived from nonlinear time history analyses of structural systems.

Maximum Credible Earthquake Ground Motions with Focus on Site Amplification due to Deep Subsurface

Since an Earthquake Ground Motion (EGM) is amplified from the propagation through the ground, different models are required for each ground type in the seismic design of structures. While the shallow subsurface indicators are used for the classification of ground types, a deep subsurface has a significant impact on the amplification of the EGMs. This study discusses the maximum credible EGMs for seismic design reflecting seismic amplification due to deep subsurface. The design spectra, reflecting the site amplification factor of the target location, are presented by the calculation of the EGMs with the same source and path characteristics and different site amplification factors as recent major Japanese earthquake records have shown, from the perspective of establishing the maximum credible EGMs that may occur in the future at a target site. The present design spectra, which are based on the natural period of a shallow subsurface, are compared with those based on the site amplification factors, considering the effect of deep subsurfaces. Although there are almost no differences in the design spectra with the present design methods according to the surface ground type, the proposed method provides significantly different design spectra for each site amplification factor.

Direct generation of floor design spectra (FDS) from uniform hazard spectra (UHS) — Part I: formulation of the method

In most current building codes, seismic design of non-structural components (NSCs) is addressed through empirical equations that do not capture NSC response amplification due to tuning effects with higher and torsional modes of buildings and that neglect NSC damping. This work addresses these shortcomings and proposes a practical approach to generate acceleration NSC floor design spectra (FDS) in buildings directly from their corresponding uniform hazard spectra (UHS). The study is based on the linear seismic analysis of 27 reinforced concrete buildings located in Montréal, Canada, for which ambient vibration measurements (AVM) are used to determine their in situ three-dimensional dynamic characteristics. Pseudo acceleration floor response spectra (PA-FRS) are derived at every building floor for four different NSCs damping ratios. The calculated roof FRS are compared with the 5% damped UHS and a formulation is proposed to generate roof FDS for NSCs with 5% damping directly from the UHS.

Direct generation of floor design spectra (FDS) from uniform hazard spectra (UHS) — Part II: extension and application of the method

This paper extends the methodology presented in the companion paper to study the effects of non-structural components’ (NSCs) damping ratio and their location in the building on the pseudo-acceleration floor response spectra (PA-FRS) of reinforced concrete buildings, and propose equations to derive floor acceleration design spectra (FDS) directly from the uniform hazard design spectra (UHS) for Montréal, Canada. The buildings used in the study are 27 existing reinforced concrete structures with braced frames and shear walls as their lateral load resisting systems: 12 are low-rise (up to 3 stories above ground), 10 are medium-rise (4 to 7 stories), and 5 are high-rise (10 to 18 stories). Based on statistical and regression analysis of floor acceleration spectra generated from linear dynamic analysis of coupled building–NSC systems, two sets of modification factors are proposed to account for floor elevation and NSC damping, applicable to the experimentally-derived FDS for roof level and 5% NSC damping. Modification factor equations could be derived only for the low-rise and medium-rise building categories, as insufficient correlation in trends could be obtained for high-rises given their low number. The approach is illustrated in detail for two typical buildings of the database, one low-rise (Building #4) and one medium-rise (Building #18), where the proposed FDS/UHS results show agreement with those obtained from detailed dynamic analysis. The work is presented in the context of a more general methodology to show its potential general applicability to other building types and locations.