Y. H. Chai

Inelastic Seismic Response of Extended Pile-Shaft-Supported Bridge Structures

Nonlinear static and dynamic analyses were used to evaluate the inelastic seismic response of bridge and viaduct structures supported on extended cast-in-drilled-hole (CIDH) pile shafts. The nonlinear dynamic analyses used a beam-on-nonlinear-Winkler foundation (BNWF) framework to model the soil-pile interaction, nonlinear fiber beam-column elements to model the reinforced concrete sections, and one-dimensional site response analyses for the free-field soil profile response. The study included consideration of ground motion characteristics, site response, lateral soil resistance, structural parameters, geometric nonlinearity (P-Δ effects), and performance measures. Results described herein focus on how the ground motion characteristics and variations in structural configurations affect the performance measures important for evaluating the inelastic seismic response of these structures. Presented results focus on a representative dense soil profile and thus are not widely applicable to dramatically different soil sites.

Understanding Poor Seismic Performance of Concrete Walls and Design Implications

The 2010–2011 Canterbury earthquakes in New Zealand revealed (1) improved structural response resulting from historical design advancements, (2) poor structural performance due to previously identified shortcomings that had been insufficiently addressed in design practice, and (3) new deficiencies that were not previously recognized because of premature failure resulting from other design flaws. This paper summarizes damage to concrete walls observed in the February 2011 Christchurch earthquake, proposes links between the observed response and specific design concerns, and offers suggestions for improving seismic design of walls in the following areas: amount of longitudinal reinforcement in wall end regions, suitable wall thickness to minimize the potential for out-of-plane buckling, and minimum vertical reinforcement requirements.

A PROCEDURE FOR ESTIMATING INPUT ENERGY SPECTRA FOR SEISMIC DESIGN

In this paper, the damage potential of an earthquake ground motion is evaluated in terms of the total power of the acceleration of the ground motion. By assuming an appropriate spectral shape for the input energy spectrum, and using the well-known Parseval theorem for evaluating the total power of a random signal, the peak amplification factor for the equivalent input energy velocity spectrum can be determined. It is shown that the peak amplification factor for the input energy spectrum depends on the peak-ground-acceleration to peak-ground-velocity ratio and duration of the strong motion phase of the ground motion. Values for the equivalent input energy velocity amplification factor vary from about 2 to 10 for most of the recorded ground motions used in this study. Although a considerable scatter of data is observed in this study, the peak amplification factor predicted by the Fourier amplitude spectrum of the ground acceleration provides a fairly good estimate of the mean value of the peak input energy compared to that determined from inelastic dynamic time history analyses, particularly for systems with high damping and low lateral strength. The peak amplification factor derived in this paper provides a more consistent approach for estimation of seismic demand when compared to an earlier empirical expression used for the formulation of duration-dependent inelastic seismic design spectra, even though only a slight difference in the required lateral strength results from the use of the new formula.

AN APPLICATION OF DIFFERENTIAL TRANSFORMATION TO STABILITY ANALYSIS OF HEAVY COLUMNS

This paper uses a recently developed technique, known as the differential transformation, to determine the critical buckling load of axially compressed heavy columns of various support conditions. In solving the problem, it is shown that the differential transformation technique converts the governing differential equation into an algebraic recursive equation, which must be solved together with the differential transformation of the boundary conditions. Although a fairly large number of terms are required for convergence of the solution, the differential transformation method is nonetheless efficient and fairly easy to implement. The method is also shown to be very accurate when compared with a known analytical solution. The stability of heavy columns is further examined using approximate formulae currently available in the literature. In this case, the differential transformation method offers a reference for assessing the accuracy of the approximate buckling formulae.

An analysis of the seismic characteristics of steel-jacketed circular bridge columns

The current approach for seismic retrofit of deficient bridge columns in California involves extensive use of steel jacketing. In this paper, the influence of steel jacketing on the lateral response of circular bridge columns is studied; particularly, the enhancement of the ultimate compressive strain of concrete, the increase in curvature ductility capacity and the increase in lateral stiffness are investigated. The current steel jacket thickness used in California is shown to enhance the ultimate compressive strain of concrete by 4-9 times the spalling strain of unconfined concrete. For larger steel jacket thickness, the ultimate limit state of steel-jacketed columns may be governed by the low-cycle fatigue fracture of the longitudinal reinforcement instead of the ultimate compressive strain of concrete. Steel jacketing is also expected to increase significantly the lateral stiffness of columns if full-height steel jackets are used. The increase in lateral stiffness of flexural columns (3 ≤ L/D ≤ 9) is estimated to be 35-60 per cent using current jacket thickness. Inelastic dynamic analyses of steel-jacketed columns using ground motions recorded during the 1989 Loma Prieta earthquake indicated that the current steel jacket thickness provides adequate protection against the damage potential of the ground motions with comparable spectral acceleration as that specified in current design spectra, and the damage sustained by the steel-jacketed column is likely to be repairable.

Reexamination of the Vibrational Period of Coupled Shear Walls by Differential Transformation

In multistory buildings, coupled shear walls are frequently used as the main lateral load resisting system, the seismic design of which requires some knowledge of their periods of vibration. Although the vibrational characteristics of coupled shear walls have been extensively studied since the 1970’s, most of the studies were based on approximations resulting in varying degree of accuracies and complexities. Methods proposed by these studies ranged from the Rayleigh’s quotient to the Dunkerley’s formula, to the Galerkin’s method of weighted residuals, and to the solution of the Sturm-Louiville type differential equation. A review of the literature, including a recent publication, shows conflicting results regarding the accuracy and implementation of these methods. With this as motivation, this paper re-examines the vibrational characteristics of coupled shear walls and compares their periods of vibration with previous methods when available. The governing equation, established on the basis of replacing th...

Correlation between Strain‐Based Low‐Cycle Fatigue and Energy‐Based Linear Damage Models

Although the potential for cumulative damage of structures during long duration earthquakes is generally recognized, most design codes do not explicitly takes into account the damage potential of such events. In this paper, a strain-based low-cycle fatigue model commonly used for the prediction of fatigue life in metals is adapted for cumulative damage assessment of structures under seismic conditions. By defining the number of load cycles in terms of the total plastic strain energy dissipated by the structure, the model is presented in a form capable of predicting the plastic strain energy capacity of the structure at the ultimate limit state. The plastic strain energy is expected to decrease rapidly with increased displacement in the small displacement range and to decrease gradually in a near linear manner with increased displacement in the large displacement range. The model is shown to calibrate reasonably well with small-scale aluminum cantilever specimens tested under large-amplitude reversed cyclic loading. At the ultimate limit state, the modified Park and Ang damage model may be considered as a linear approximation to the low-cycle fatigue model in the large displacement range.

Estimating inelastic displacements for design: Extended pile-shaft-supported bridge structures

Accurate estimation of inelastic displacements is important for the evaluation of the seismic performance of structures with desired ductile response. In this paper, nonlinear dynamic analyses results from a companion numerical study investigating the response of ductile-designed bridge structures, were compared with a commonly applied inelastic displacement estimation approach and an alternative approach. The extended pile-shaft-supported bridge structures considered are susceptible to amplified response under long-period velocity pulses, and hence an evaluation of design methods for estimating inelastic displacement demands is warranted. In this case, force-reduction–displacement-ductility–period (R−μΔ−T) relations and a mean spectral displacement approach are investigated. The alternative approach estimates inelastic displacement demand using the mean elastic spectral displacement between two spectral periods that are important for the structures response. Results support the conceptual merits of using the mean spectral displacement method, indicating that the approach is capable of reducing the uncertainty in predicting inelastic displacement demands for the types of structures considered when subjected to near-fault ground motions.

Characterization of story-level seismic damage using an energy-based damage model

An energy-based damage model currently used for seismic analysis of structures is modified to ensure a positive value in the damage index at all levels of inelastic response. At the ultimate limit state, the modified model gives the same plastic strain energy capacity as the previous damage model. Testing of small-scale cantilever specimens showed different strength deterioration parameters for coldrolled and hot-rolled steel and composite systems of double cantilevers. The strength deterioration parameter for the composite system is smaller than that of the individual cantilevers. Various weighted-average rules for combining local member damage indices into story-level damage indices are compared with measured story-level damage indices. Based on testing of small-scale steel cantilevers, the current combination rules predict the story-level damage reasonably well near the ultimate limit state but tend to underestimate the story-level damage in the less severely damaged states. A combination rule based on best fitting of the experimental data obtained in this study is presented.

Influence of Nonviscous Damping on Seismic Inelastic Displacements

Viscous damping, which assumes a resisting force proportional to the instantaneous velocity, results in energy dissipation that increases linearly with frequency. Such energy dissipation, however, is not strongly supported by experiments. The energy dissipative characteristics of damping can be improved by nonviscous hereditary model, where the damping force is treated as dependent on the response history. A weighting function with built-in exponential decay can be used to represent the fading memory of damping where the recent history is given a greater influence over its distant past. This paper investigates the seismic response of structures using exponentially decaying nonviscous damping and compares the response with that of classical viscous damping. Preliminary results show an increase in inelastic displacements in the exponential damping model for both normal and near-fault ground motions. As part of the study, system characteristics of the exponential damping model are investigated.