Inelastic Displacement Response of RC Systems with Cyclic Deterioration—An Energy Approach

Inelastic displacements of reinforced concrete systems are investigated by employing an energy-based approach. A hysteresis model is developed that accounts for stiffness degradation, strength deterioration and pinching. The model is calibrated by using experimental data from literature. Inelastic displacement ratios are calculated under a specific set of ground motion records with long effective durations. The results reveal the importance of deteriorating behavior under long duration excitations, especially for short and medium period structures. The last part of the study is devoted to the introduction of a simple empirical relationship for estimating the inelastic displacement demands of degrading RC structural systems.     

Estimation of the Displacement of Viscously Damped Pinching Hysteretic Structures Subjected to Near-fault Ground Motions

To fulfill a displacement-based design or response prediction for nonlinear structures, the concept of equivalent linearization is usually applied, and the key issue is to derive the equivalent parameters considering the characteristics of hysteretic model, ductility level, and input ground motions. Pinching hysteretic structures subjected to dynamic loading exhibit hysteresis with degraded stiffness and strength and thus reduced energy dissipation. In case of excitation of near-fault earthquake ground motions, the energy dissipation is further limited due to the short duration of vibration. In order to improve the energy dissipation capability, viscous-type dampers have been advantageously incorporated into these types of structures. Against the viscously damped pinching hysteretic structure under the excitation of near-fault ground motions, this study aims to develop a seismic response estimation method using an equivalent linearization technique. The energy dissipation of various hysteretic cycles, including stationary hysteretic cycle, amplitude expansion cycle, and amplitude reduction cycle, is investigated, and empirical formulas for the equivalent damping ratio is proposed. A damping modification factor that accounts for the near-fault effect is introduced and expanded to ensure its applicability to structures with damping ratios less than 5%. An approach for estimating the maximum displacement of a viscously damped pinching hysteretic structure, in which the pinching hysteretic effect of a structure and the near-fault effect of ground motions are considered, is developed. A time history analysis of an extensive range of structural parameters is performed. The results confirm that the proposed approach can be applied to estimate the maximum displacement of a viscously damped pinching hysteretic structure that is subjected to near-fault ground motions.     

Hysteretic Model for Flexure-shear Critical Reinforced Concrete Columns

A model for predicting the cyclic lateral load-deformation response of flexure-shear critical reinforced concrete (RC) columns subjected to combined axial load and cyclic shear is proposed. Strength deterioration in the primary curve due to the effect of shear after yielding is considered by a modification coefficient. Rules for unloading and reloading branches of the hysteretic curve are obtained from regression analysis of test results. Unloading stiffness is fitted as a function of displacement ductility and secant stiffness of the point with maximum displacement in the primary curve. Pinching is simulated by changing the slope of reloading branch. Path-based cyclic strength deterioration is incorporated in the proposed model. In the expression of cyclic strength deterioration, the effects of aspect ratio and axial-load ratio are considered. Comparison between the predicted cyclic response and experimental results indicates that the proposed model can predict the observed hysteretic response of flexure-shear critical RC columns well.     

ANALYTICAL MODELS FOR BRICK MASONRY INFILLED R/C FRAMES UNDER LATERAL LOADING

Proposed in this paper are two analytical models for predicting the inelastic response of unreinforced brick masonry infills in reinforced concrete frames subjected to mono-tonic and reversed cyclic loading. The first model is based on the traditional diagonal strut concept, while the second one is a simple isoparametric element with shear deformation only. All the essential characteristics of the hysteretic behaviour of the panel, including strength and stiffness degradation, pinching and slippage, are explicitly taken into account. The models are implemented in a general-purpose program for the inelastic time-history analysis of structures, and are used for studying the seismic behaviour of typical multistorey frames with various arrangements of infill panels, including structures with an open ground storey. The results of the analysis are in agreement with both experimentally observed behaviour and with experience regarding seismically damaged buildings.     

Experimental Investigation of Circular Reinforced Concrete Columns under Different Loading Histories

Three reinforced concrete (RC) circular column specimens without an effective concrete cover were tested under constant axial compressive as well as cyclic lateral loading. The seismic behavior of the specimens under different loading paths was examined with the objective of understanding the influence of displacement history sequence on the seismic behavior of the columns in near-fault earthquakes. The influence of displacement history sequence upon the hysteretic characteristics, stiffness degradation, lateral capacity, as well as energy dissipation analysis was conducted. The hoop strains of lateral reinforcement at varied column heights under cyclic loading were attained by means of 8–16 strain gauges attached along the hoops. Additionally, the characteristics of strain distribution were investigated in the transverse reinforcement. The results of strain distribution were evaluated with Mander’s confinement stress model and the distribution around the cross section. The length of the plastic hinge at the end of the specimen was evaluated by measurement as well as the inverse analysis. Finally, the deformation of the specimen, which includes the components of shear deformation, bending deformation and bonding-slip deformation, was evaluated and successfully separated.     

Characterization of Ductility and Inelastic Displacement Demand in Base-Isolated Structures Considering Cyclic Degradation

New designed or retrofitted structures with the use of isolation system may exhibit nonlinear deformations during strong ground motions. Inelastic displacement ratio of base-isolated structures is studied in this paper by employing two degree of freedom model taking into account inelastic behavior of isolators and superstructure. Parametric study is conducted to evaluate influence of isolator and superstructure properties on inelastic displacement ratio according to two sets of near-fault and far-fault ground motions. Accuracy of proposed equations in the literature to evaluate inelastic displacement ratio are studied, as well. Furthermore, cyclic degradation effects are investigated by considering stiffness and strength degradation and pinching in hysteresis model of superstructure. Eventually, inelastic responses of isolated structures with two types of isolators (lead rubber bearing and friction pendulum bearing) are compared.     

Quasi-Static Testing of RC Infilled Frames and Confined Stone-Concrete Bearing Walls

This article presents an experimental investigation of the seismic performance of gravity load-designed RC infilled frames and confined bearing walls of limestone masonry backed with plain concrete. Five infilled frames and two bearing walls were constructed at one-third scale and tested using reversed cyclic lateral loading and constant axial loads. Effects of openings, axial loading, and infill interface conditions were examined using quasi-static experimentation. The two structural systems exhibited similar lateral resistance and energy dissipation capacities with higher global displacement ductility for the infilled frames. Hysteretic behavior of the infilled frame models exhibited pinching of the hysteretic loops accompanied by extensive degradation of stiffness whereas loops of the bearing walls were free of pinching. Test results confirmed the beneficial effect of axial loading on lateral resistance, energy dissipation, and ductility of the bearing walls. Higher axial loading resulted in a substantial decrease in ductility with no significant effect on lateral resistance of the infilled frames. Openings within the infill panel reduced significantly the lateral resistance of infilled frames. Using dowels at the infill panel interfaces with the base block and bounding columns enhanced the maximum load-carrying capacity of infilled frames without impairing their ductility.     

COUPLED P-Y T-Z ANALYSIS OF SINGLE PILES IN COHESIONLESS SOIL UNDER VERTICAL AND/OR HORIZONTAL GROUND MOTION

Various approaches are currently used for the analysis of piles under vertical and lateral loading. Among these, the beam-on-a-nonlinear Winkler foundation (BNWF) approach using published P-y, T-z and Q-z curves is widely used in practice. In this approach, the P-y and T-z responses are generally uncoupled from each other. The objective of this paper is to investigate the influence that the coupling of the P-y and T-z responses has.on the cyclic and dynamic response of piles in cohesionless soil. A cyclic model is first developed and a parametric study is conducted to investigate the effect the initial confining pressure, angle of wall friction and effective vertical stiffness have on the lateral cyclic hysteretic response. A dynamic model is then developed, and used to study the response of a single pile in cohesionless soil under horizontal and/or vertical ground motion. Results from the parametric study showed that the three parameters did not have a significant influence on the lateral cyclic hysteretic response. Under horizontal and/or vertical ground motion, the horizontal ground motion was observed to dominate the inertial interaction response, and significantly affected both the horizontal and vertical displacement response, mainly due to second-order P-Δ and gapping effects.     

Probabilistic Characteristics of Seismic Ductility Demand of SDOF Systems with Bouc-Wen Hysteretic Behavior

This study investigates probabilistic characteristics of the peak ductility demand of inelastic single-degree-of-freedom systems. The hysteretic behavior of structural systems is represented by the Bouc-Wen model, which takes various hysteretic curves with degradation and pinching behavior into account, and a prediction equation of the peak ductility demand is developed. The application of the developed equation in reliability analysis of structures subject to earthquake loading is illustrated. The results indicate that the effects due to degradation and pinching behavior on the peak ductility demand as well as the reliability of structures can be significant, especially for stiff structures.     

Analytical Collapse Study of Lightly Confined Reinforced Concrete Frames Subjected to Northridge Earthquake Ground Motions

Review of older non seismically detailed reinforced concrete building collapses shows that most collapses are triggered by failures in columns, beam-column joints, and slab-column connections. Using data from laboratory studies, failure models have previously been developed to estimate loading conditions that correspond to failure of column components. These failure models have been incorporated in nonlinear dynamic analysis software, enabling complete dynamic simulations of building response including component failure and the progression of collapse. A reinforced concrete frame analytical model incorporating column shear and axial failure elements was subjected to a suite of near-fault ground motions recorded during the 1994 Northridge earthquake. The results of this study show sensitivity of the frame response to ground motions recorded from the same earthquake, at sites of close proximity, and with similar soil conditions. This suggests that the variability of ground motion from site to site (so-called intra-event variability) plays an important role in determining which buildings will collapse in a given earthquake.     

Inelastic Displacement Ratios for Seismic Assessment of Structures Subjected to Forward-Directivity Near-Fault Ground Motions

This article presents results of a statistical study focused on evaluating inelastic displacement ratios (i.e., ratio of maximum inelastic displacement with respect to maximum elastic displacement demand) of degrading and non degrading single-degree-of-freedom (SDOF) systems subjected to forward-directivity near-fault ground motions. C_R spectra are computed for normalized periods of vibration with respect to the predominant period of the ground motion to provide a better ground motion characterization. This period normalization allows reducing the record-to-record variability in the estimation of C_R. An equation to obtain estimates of C_R for the seismic assessment of structures exposed to forward-directivity near-fault ground motions is proposed.     

Beam-Column Joint Model for Nonlinear Analysis of Non-Seismically Detailed Reinforced Concrete Frame

An efficient and simplified plane beam-column joint model that can describe the strength deterioration, stiffness degradation, and pinching effect was developed for the nonlinear analysis of non-seismically detailed reinforced concrete frames. The proposed beam-column joint model is a super-element consisting of eight spring components and one panel zone component, representing the bond-slip mechanism of the longitudinal reinforcement and the shear deformation mechanism of the joint concrete core region, respectively. In order to represent the dynamic response at the system level, the elastic constitutive law is applied to the eight connector springs, while the Bouc-Wen-Baber-Noori (BWBN) model is adopted to describe the hysteretic behavior of the panel zone component. For the implementation of the finite element analysis, the algorithmically consistent tangent of the BWBN model is derived as a uni-axial constitutive model, while the initial stiffness of the panel zone component is determined by the concrete compression strut assumption. The accuracy and efficiency of the proposed beam-column joint model were calibrated at both the component and structural levels by comparing the simulated results with the experimental data for non-seismically detailed joint sub-assemblages and a reinforced concrete plane frame.     

Performance of Degrading Reinforced Concrete Frame Systems Under the Tohoku and Christchurch Earthquake Sequences

Field investigations after the recent Tohoku and Christchurch earthquakes reported failure of structural systems due to multiple earthquakes. In most failure cases the reported damage was mainly due to dramatic loss of stiffness and strength of structural elements as a result of material deterioration due to repeated earthquake loading. This study aims to investigate the degrading behavior of reinforced concrete frame systems subjected to Tohoku and Christchurch earthquake sequences. Numerical models of RC frames that incorporate damage features are established and inelastic response history analyses are conducted. The results presented in this study indicate that multiple earthquake effects are significant.     

Seismic Behavior of L-Shaped RC Squat Walls under Various Lateral Loading Directions

Considerable progress has been made on the research of non-rectangular reinforced concrete (RC) squat walls over the past decades. However, the experimental data of L-shaped RC squat walls remain limited, especially for their seismic behaviors under non-principal bending actions. This paper presents an experimental and numerical investigation on L-shaped RC squat structural walls with an emphasis on how varying the directions of lateral cyclic loading influences the seismic responses of these walls. Four L-shaped specimens are tested under lateral cyclic displacements and low levels of axial compression The variables are axial loads and lateral loading directions. The performance of specimens is discussed in terms of cracking patterns, failure mechanisms, hysteretic responses, deformation components and strain profiles. Furthermore, three-dimensional finite element models are developed to supplement the experimental results. The direction of lateral loading is found to have a significant effect on the peak shear strength of L-shaped RC squat walls.     

ESTIMATION OF NEAR-SOURCE GROUND MOTION AND SEISMIC BEHAVIOUR OF RC FRAMED STRUCTURES DAMAGED BY THE 1999 ATHENS EARTHQUAKE

On September 7, 1999 an earthquake with magnitude M _W =5.9 occurred close to the city of Athens in Greece. More than 80 buildings collapsed, about 150 deaths and hundreds of injuries were reported. Soon after the event a damage investigation was carried out by two of the authors in the most heavily struck areas. The most serious damages were observed in the northern suburbs of Athens, where reinforced concrete frames and masonry buildings represent the prevalent construction systems. The hysteretic energy demands imposed on RC buildings should have been rather severe considering the structural systems characteristics and the inadequate construction details. However, over-strengths, redundancy and especially the presence of infill walls, provided a significant increase of the seismic capacity and contributed to the survival of many buildings.

The objective of the present work is to reproduce and analyse the response of typical RC frames subjected to the 1999 Athens earthquake in areas where the observed damage was particularly severe but no recordings of the ground motion were available. After a general overview of the seismotectonic environment, seismological data, observed macro-seismic intensities, structural typologies and observed building behaviour, an attempt is made to identify representative excitations in the meizoseismal area. Specifically, the required accelerograms are obtained by modifying available records so as to reproduce a given global energy content and to be consistent with the observed damage. To study the seismic response of RC models, the obtained accelerograms are used to perform nonlinear dynamic analyses.     

PROCEDURE AND SPECTRA FOR ANALYSIS OF RC STRUCTURES SUBJECTED TO STRONG VERTICAL EARTHQUAKE LOADS

Abstract

In view of the compendium of field evidence and supporting analysis work indicating the possible damaging effects of vertical earthquake ground motion, this paper addresses the problem of code-type vertical force calculation. In light of recent engineering seismology studies of the relationship between vertical and horizontal peak ground acceleration, the inadequacy of the 2/3-rule depicted by codes is highlighted. A simple piece-wise linear relationship is proposed and shown to represent existing strong-motion measurements adequately. Bilinear and inelastic spectra are derived and studied. It is demonstrated that net tensile forces and displacements may ensue, thus eroding the shear resistance of RC columns. A simple procedure is outlined whereby modal analysis may be employed to estimate conservatively vertical earthquake forces on buildings. Finally, areas of further exploration and refinement are identified.     

YIELDING OSCILLATOR UNDER TRIANGULAR GROUND ACCELERATION PULSE

An analytical solution is presented for the response of a bilinear inelastic simple oscillator to a symmetric triangular ground acceleration pulse. This type of motion is typical of near-fault recordings generated by source-directivity effects that may generate severe damage. Explicit closed-form expressions are derived for: (i) the inelastic response of the oscillator during the rising and decaying phases of the excitation as well as the ensuing free oscillations; (ii) the time of structural yielding; (iii) the time of peak response; (iv) the associated ductility demand. It is shown that when the duration of the pulse is long relative to the elastic period of the structure and its amplitude is of the same order as the yielding seismic coefficient, serious damage may occur if significant ductility cannot be supplied. The effect of post-yielding structural stiffness on ductility demand is also examined. Contrary to presently-used numerical algorithms, the proposed analytical solution allows many key response parameters to be evaluated in closed-form expressions and insight to be gained on the'response of inelastic structures to such motions. The model is evaluated against numerical results from actual near-field recorded motions. Illustrative examples are also presented.     

STRONG GROUND MOTIONS AND DAMAGE PATTERNS FROM THE 1999 DUZCE EARTHQUAKE IN TURKEY

The M _w , 7.1 Duzce earthquake occurred on 12 November 1999 along the North Anatolian Fault in northwestern Turkey. This paper documents observations from a field reconnaissance team, addressing two principal aspects of this significant earthquake: the recorded ground motions and the distribution and severity of the earthquake effects on the built environment. In general, the recorded ground motions from this earthquake were smaller than predicted by ground motion predictive equations available at the time of the event. One anomalous recording is presented and potential causes for this irregular motion based on observations from field reconnaissance are discussed. The effects of rupture directivity on the near-fault recordings are assessed and the effects of soil conditions on the recorded ground motions are examined. The patterns of building damage based on post-earthquake reconnaissance are presented for the most strongly shaken cities in the near-fault region: Duzce, Kaynasli, and Bolu. Damage in Duzce was concentrated in the southern part of the city, which is underlain by softer sediments. Damage in Bolu was distributed evenly throughout the city; whereas damage was concentrated on more recent alluvial sediments in Kaynasli. No evidence of liquefaction or ground failure was observed in the populated areas surveyed after the earthquake.     

MODELLING OF RC MEMBERS UNDER CYCLIC BIAXIAL FLEXURE AND AXIAL FORCE

A model is proposed for the incremental force-deformation behaviour of reinforced concrete sections and members, under generalised load or deformation histories in 3D, including cyclic loading, up to ultimate deformation. At the section level the model is of the Bounding Surface type and accounts for the coupling between the two directions of bending and between them and the axial direction. For the construction of the member tangent flexibility matrix on the basis of the section tangent flexibility matrix, a piecewise-linear variation along the member is assumed for the nine terms of the tangent section flexibility matrix. Model parameters are derived on the basis of available test results for: (a) the force-deformation response under cyclic biaxial bending with normal force; (b) the hysteretic energy dissipation; (c) the secant-to-yield member stiffness, and (d) the ultimate deformation of the member under cyclic biaxial load paths.     

Constant Ductility Energy Factors for the Near-Fault Pulse-Like Ground Motions

This study is focused on the constant ductility energy factors for bilinear system under the near-fault pulse-like ground motions. The variation of energy factors is studied in consideration of the earthquake magnitude, rupture distance, damping ratios, and post-yield stiffness ratios. The results indicate that the near-fault pulse-like ground motions would increase the energy dissipation of structures. The energy factors are significantly influenced by the earthquake magnitude. The damping ratios have more obvious influences on the energy factors than the post-yield stiffness ratios. A predictive model is proposed for the application of constant ductility energy factors for near-fault pulse-like ground motions.