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.     

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.     

IDENTIFICATION AND VERIFICATION OF SEISMIC DEMAND FROM DIFFERENT HYSTERETIC MODELS

The goal of this paper is to develop a modified Bouc-Wen hysteretic model from cyclic loading test data for reinforced columns, including the behavior of stiffness degradation, strength deterioration, pinching and softening effects of RC members. Seismic demands on this inelastic single degree of freedom system when subjected to both near-fault ground motion and far-field ground motion excitations were examined.

The cyclic loading test of reinforced concrete columns was experimentally observed and a system identification computer program was developed to solve each control parameter of the hysteretic model. A least-squared method for identifying parameters of the model is proposed in this paper. The hysteretic constitutive law produces a smoothly varying hysteresis such as the control-parameters for strength deterioration, stiffness degradation, pinching and softening effects. Two implementations of (1) flexure damage and (2) shear damage were conducted to provide better understanding of hysteretic behavior of RC structural members. A pseudo-dynamic experiment was also developed to verify the model parameters.

Based on the developed hysteretic model, the seismic demand of this inelastic model was investigated by using both near-fault ground motion data and far-field ground motion data as input motion. An R-μT inelastic response spectrum from different hysteretic models was generated.     

VERTICAL EARTHQUAKE GROUND MOTION RECORDS: AN OVERVIEW

Recent research clearly shows the importance of including the vertical component of earthquake ground motion in seismic analysis and design. In addition, pioneering studies [e.g., Elnashai and Papazoglou (1997)] have explored and documented the characteristics of available near-field vertical ground motion records. As a follow-up, this paper complements earlier studies, and investigates additional far-field records and available downhole array vertical motion records. A total of 111 free-field strong motion records (from California) and available downhole array records are employed. Compared to near-field records, far-field records generally contain more energy at longer periods. Based on the available data, response spectra are presented for near-field and far-field records respectively. The currently scarce downhole-array vertical motion records show that significant amplification may occur within the top 10-20 m soil layers. A simple one-dimensional (ID) vertical wave propagation model did not appear adequate for modelling the observed downhole array response. In using such a simplified model, very high viscous damping in the range of 15-25% was needed to match the recorded downhole vertical response, even for small tremors. Additional data and research are required [Beresnev et al., 2002] towards the development of a rational vertical motion site response analysis procedure.     

Sensitivity of the Earthquake Response of Tall Steel Moment Frame Buildings to Ground Motion Features

The seismic response of two tall steel moment frame buildings and their variants is explored through parametric nonlinear analysis using idealized sawtooth-like ground velocity waveforms, with a characteristic period (T), amplitude (peak ground velocity, PGV), and duration (number of cycles, N). Collapse-level response is induced only by long-period, moderate to large PGV ground excitation. This agrees well with a simple energy balance analysis. The collapse initiation regime expands to lower ground motion periods and amplitudes with increasing number of ground motion cycles.     

CALIBRATION OF FORCE REDUCTION FACTORS OF RC BUILDINGS

A comprehensive study is undertaken to assess and calibrate the force reduction factors (R) adopted in modern seismic codes. Refined expressions are employed to calculate the R factors “supply” for 12 buildings of various characteristics represent a wide range of medium-rise RC buildings. The “supply” values are then compared with the “design” and “demand” recommended in the literature. A comprehensive range of response criteria at the member and storey levels, including shear as a failure criterion, alongside a detailed modelling approach and an extensively verified analytical tool are utilised. A rigorous technique is employed to evaluate R factors, including inelastic pushover and incremental dynamic collapse analyses employing eight natural and artificial records. In the light of the information obtained from more than 1500 inelastic analyses, it is concluded that including shear and vertical motion in assessment and calculations of R factors is necessary. Force reduction factors adopted by the design code (Eurocode 8) are over-conservative and can be safely increased, particularly for regular frame structures designed to lower PGA and higher ductility levels.     

Impact of Vertical Ground Excitation on a Bridge with Footing Uplift

Ground motions recorded in the epicentral region of an earthquake often have a strong vertical component with dominant high frequencies. Damage to bridges in near-source regions due to strong vertical ground motion has been reported. The beneficial effects of footing uplift on structural performance in form of reduction of seismic response of structural members have been confirmed in previous research. The uplift of bridge piers has been utilised in a very limited number of bridge structures, e.g., the South Rangitikei railway bridge in New Zealand. However, the near-fault seismic behaviour of bridges with footing uplift has been even less addressed. In this study shake table investigations were carried out on the response of a single-span bridge model with footing uplift subjected to simultaneous vertical and horizontal excitations. Near-fault ground motions recorded in the Canterbury earthquake sequences of 2010 and 2011 were used. The experimental results show that inclusion of vertical ground motions produce stronger axial force in the pier and larger bending moment in the deck. Concurrent horizontal and vertical excitations may also cause more frequent footing uplift than the solely horizontal excitations.     

Modeling and Seismic Response Analysis of Italian Code-Conforming Single-Storey Steel Buildings

ABSTRACT

This article describes the structural design, nonlinear modeling, and seismic analysis of prototype single-storey non-residential steel buildings made of moment-resisting portal frames in the transverse direction and concentric braces in the longitudinal direction. Various design parameters (building geometry, seismic hazard, foundation soil category) and different modeling assumptions (bare frame model, model including cladding elements, ground motions including vertical accelerations, and modeling uncertainties) were considered to investigate their effects on the simulated seismic performance.     

SIGNIFICANT GROUND MOTION PARAMETERS FOR EVALUATION OF THE SEISMIC PERFORMANCE OF SLENDER MASONRY TOWERS

The evaluation of seismic risk of masonry monuments requires to study the combination of vulnerability and hazard. In the present work, the global seismic response of slender masonry towers has been studied by means of a specific 3-D fibre model. Accounting for the particular behaviour of such structures, the hazard should also be described by a suitable measure of intensity of the seismic action. A variety of different parameters relating with the ground acceleration recordings have been investigated for what regards their correlation with the damage indicators of the model. The combination of the peak ground velocity of the horizontal component and of the significant duration is an effective measure of intensity. This measure can be improved by considering the accord of the frequency content of the ground motion with the dynamical characteristics of the tower. Since in some cases the effect of the vertical component proved to be important, a further improvement can be obtained by taking into account also the vertical ground motion intensity.     

AN EVALUATION OF THE STRONG GROUND MOTION RECORDED DURING THE MAY 1, 2003 BINGÖL TURKEY,EARTHQUAKE

An important record of ground motion from a M6.4 earthquake occurring on May 1, 2003, at epicentral and fault distances of about 12 and 9 km, respectively, was obtained at a station near the city of Bingöl, Turkey. The maximum peak ground values of 0.55 g and 36 cm/s are among the largest ground-motion amplitudes recorded in Turkey. From simulations and comparisons with ground motions from other earthquakes of comparable magnitude, we conclude that the ground motion over a range of frequencies is unusually high. Site response may be responsible for the elevated ground motion, as suggested from analysis of numerous aftershock recordings from the same station. The mainshock motions have some interesting seismological features, including ramps between the P-and S-wave that are probably due to near- and intermediate-field elastic motions and strong polarisation oriented at about 39 degrees to the fault (and therefore not in the fault-normal direction). Simulations of motions from an extended rupture explain these features. The N10E component shows a high-amplitude spectral acceleration at a period of 0.15 seconds resulting in a site specific design spectrum that significantly overestimates the actual strength and displacement demands of the record. The pulse signal in the N10E component affects the inelastic spectral displacement and increases the inelastic displacement demand with respect to elastic demand for very long periods.     

ATTENUATION RELATIONSHIP FOR LOW MAGNITUDE EARTHQUAKES USING STANDARD SEISMOMETRIC RECORDS

Northwestern Italian weak-motion data were used to study attenuation characteristics of horizontal peak ground acceleration (PGA) and horizontal peak ground velocity (PGV) from earthquakes of local magnitudes (M _l ) up to 5.1. Data have been provided by the RSNI (Regional seismic network of Northwestern Italy) and RSLG (Regional seismic network of Lunigiana-Garfagnana) waveform database. The database consists of more than 14000 horizontal components recorded in the period 1999-2002 by both broadband and enlarged band seismometers. The accuracy of the procedure used to extract PGA values from the velocity recordings was verified comparing observed and derived PGA values at station STV2, which was equipped with both a temporary K2 Kinemctrtcs accelerometer and Guralp CMG40 broadband sensor. The attenuation of both peak ground acceleration and peak ground velocity was found to be logarithmically distributed with a strong attenuation for low distances (less than 50 km) and low M _l values (<3.0). The resulting equations are:

Log(PGA)=?3.19+0.87M?0.042M ²?1.92 Log(R)+0.249S,

Log(PGA)=?4.23+0.76M?0.018M²?1.56 Log(R)+0.230S,

where PGA is expressed in g, PGV is expressed in m/s, M is local magnitude, R is the hypocentral distance in kilometers and S is a dummy variable assuming values of 0 and 1 for rock and soil respectively. For increasing distance and magnitude, both PGA and PGV values show a linear distribution. The validity range of the obtained attenuation relationships is 0–200 km for distances and M _l up to 4.5. Sensitivity studies performed by analysis of residuals, showed that predicted PGA and PGV values are stable with respect to reasonable variations of the model and distances providing the data. Comparisons with attenuation relationships proposed for Italian region, derived from strong motion records, are also presented.     

Predicting the Seismic Response of Capacity-Designed Structures by Equivalent Linearization

An equivalent linearization procedure is developed for predicting the inelastic deformations and internal forces of capacity-designed structures under earthquake excitations. The procedure employs response spectrum analysis, and mainly consists of the construction of an equivalent linear system by reducing the stiffness of structural members that are expected to respond in the inelastic range. These members are well defined in structures designed with capacity principles. Maximum modal displacement demands of the equivalent linear system are determined either from the equal displacement rule, or from independent nonlinear response history analysis of SDOF systems representing inelastic modes.

Predictions obtained from the proposed equivalent linearization procedure are evaluated comparatively by using the results of nonlinear response history analysis as benchmark, linear elastic response spectrum analysis and conventional pushover analysis. The deformations and capacity controlled actions of a 12-story symmetrical plan concrete frame and a 6-story unsymmetrical plan concrete frame are obtained by each method under 96 strong ground motions. It is observed that the proposed procedure results in better accuracy in estimating the inelastic seismic displacement response parameters and capacity controlled forces than the other two approximate methods.     

A NON-PARAMETRIC APPROACH TO ATTENUATION RELATIONS

Abstract

A non-parametric multidimensional regression method is proposed for the prediction of seismic ground motion parameters. The main features which distinguish the method from standard regression procedures are: (1) The relationship between the input and output variables is not selected a priori by a prediction law, (2) an arbitrary number of input variables Can be taken into account, provided that an appropriate data base exists, and (3) the computational procedure is very simple. The results can be easily updated when new information becomes available. The method has been applied for the derivation of attenuation relations by using a combination of databases compiled by other researchers. In the majority of the cases discussed in this paper, the method was used for the prediction of horizontal peak ground acceleration as a function of magnitude and distance. In some cases, ground conditions were also taken into account. Some results on the attenuation relations of peak ground velocity and displacement, as well as Arias intensity, are also presented.     

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.     

EFFECTS OF SOIL LAYERING ON THE CHARACTERISTICS OF BASIN-EDGE INDUCED SURFACE WAVES AND DIFFERENTIAL GROUND MOTION

This paper studies the effects of soil layering in the basin based on the characteristics of basin-edge induced surface waves and associated differential ground motion. Seismic responses of various basin-edge models were simulated using software based on parsimonious finite difference staggered grid approximation of 2.5D eiastodynamic wave equation. Seismic responses of various models with different number of soil/soft rock layers but for a fixed thickness of deposit, fundamental frequency and impedance contrast revealed a decrease of surface wave amplitude with an increase in the number of layers in the basin. Shifting of dominant frequency towards the higher values was obtained with an increase of number of layers. An increase of dispersion of surface waves with an increase of number of soil layers in the basin was observed. A minor increase of Rayleigh wave velocity with an increase of number of soil layers was also obtained, but in the case of Love wave it was almost negligible.

Spectral analysis of the edge-induced surface waves revealed that the anomalous earthquake intensity may arise in a zone of width of 2.5–3.0 km, parallel to basin-edge and at an offset of 0.5–0.7 km from the edge. Maximum horizontal differential ground motion (HDGM) developed by Love wave (≈4.9×10^?2) was more than that of Rayleigh wave (≈9.4×10^?3). Large variation in HDGM caused by the surface waves was obtained with a change in the number of layers in the basin and maximum HDGM was observed when there were only two layers in the basin. It was inferred that the effect of soil layering in the basin was more on the Rayleigh wave as compared to the Love wave. Development of large HDGM near the basin-edge and its dependency on the number of soil layers reveals that basin-edge induced surface waves need special attention during seismic microzonation or seismic hazard prediction.     

Seismic Displacement Demands on Skewed Bridge Decks Supported on Elastomeric Bearings

The unseating of decks is one of the most prevalent failure modes of bridges after earthquake events, as observed in the 2010 Chile Earthquake. Damaged bridges in Chile often had skew angles and were supported on elastomeric bearings. Similar bridge construction practices with decks supported on elastomeric bearings are also common in the central and eastern U.S. (CEUS). The seismic displacement demands on skewed bridges are more complicated than those on bridges without skew angles due to the coupling of translational modes with the rotational mode of vibration. The study presented in this article seeks to understand the seismic response of skewed bridge decks supported on elastomeric bearings. The scope of the study is limited to one- and two-span bridges, which constitute a large portion of bridge inventory in the CEUS. The vibration modes of skewed bridge decks are derived in closed form and the modes are compared when the gaps between the bridge deck and the abutment are open and when one of the gaps is closed due to seismic excitation. Nonlinear response history analyses are carried out to understand the effects of vertical ground motion, skew angles, aspect ratios, and different ground motion types on the seismic displacement demand in these cases. Amplification factors that approximate the increase in the displacement demand due to the skew angle are proposed.     

MODELLING OF THE GROUND MOTION AT RUSSE SITE (NE BULGARIA) DUE TO THE VRANCEA EARTHQUAKES

An approach, capable of synthesising strong ground motion from a basic understanding of fault mechanism and of seismic wave propagation in the Earth, is applied to model the seismic input at a set of 25 sites along a chosen profile at Russe, NE Bulgaria, due to two intermediate-depth Vrancea events (August 30, 1986, M _ω=7.2, and May 30, 1990, M _ω=6.9). Accordingly to our results, once a strong ground motion parameter has been selected to characterise the ground motion, it is necessary to investigate the relationships between its values and the features of the earthquake source, the path to the site and the nature of the site. Therefore, a proper seismic hazard assessment requires an appro-priate parametric study to define the different ground shaking scenarios corresponding to the relevant seismogenic zones affecting the given site. Site response assessment is provided simultaneously in frequency and space domains, and thus the applied procedure differs from the traditional engineering approach that discusses the site as a single point. The applied procedure can be efficiently used to estimate the ground motion for different purposes like microzonation, urban planning, retrofitting or insurance of the built environment.     

Non-Iterative Equivalent Linearization Based on Secant Period for Estimating Maximum Deformations of Existing Structures

The capacity spectrum method of ATC-40 uses the secant period as the equivalent period of equivalent linear systems. Therefore, it results in a direct graphical comparison. The maximum inelastic displacement and acceleration demands of structures can be simultaneously obtained from the intersection of the demand and capacity diagrams. However, for evaluation of existing structures, the demands need to be determined through iterations since the equivalent period and damping of the equivalent linear systems currently available are both a function of the (displacement) ductility ratio, which is unknown and is the target of evaluation. In addition, the equivalent damping used in the capacity spectrum method is independent of periods of vibration. It may lead to poor estimations of maximum responses especially for short-period systems. This article proposes two equivalent linear systems based on the secant period to estimate the maximum displacement and acceleration responses of existing structures. Both the recommended equivalent period and damping are defined by the strength ratio (elastic lateral strength/yield lateral strength), rather than the ductility ratio. Because the strength ratio of existing structures is a known parameter, the maximum displacement and acceleration responses of these structures can be determined without iterations. Besides, effects of periods of vibration on the equivalent linear systems are also included in this study. The equivalent damping is derived from statistical analyses for bilinear single-degree-of-freedom (SDOF) systems with different periods of vibration, strength ratios and post-yield stiffness based on 72 earthquake ground motions recorded on firm sites. Procedures and examples for applications of the proposed equivalent linear systems on nonlinear static analysis procedures are also provided.     

Choices and Criteria for Seismic Strengthening

Risk assessment is affected by large uncertainties, depending on hazard, structure, damage, and loss analysis. Crucial problems and choices may refer to: (a) hazard parameters, including the definition of appropriate ground motion levels and of their probability to occur; (b) level of knowledge about materials, geometry, detailing; (c) assessed damage and failure modes; and (d) resulting potential for step changes in performances.

The cost of attaining a high level of knowledge may significantly reduce the remaining resources, it is therefore important to favor resilient solutions with a creative adoption of appropriate strengthening strategies.

In this framework, this article discusses the possible criteria for the mitigation of seismic risk and some of the alternative choices that may be adopted for strengthening, with reference to:

(a)?the modification of damage and collapse modes strengthening individual elements or locallyincreasing the deformation capacity;

(b)?the insertion of additional systems resisting to horizontal actions;

(c)?the introduction of base isolation, with the objective of capacity-protecting the existingstructure;

(d)?the reduction of displacement demand by added damping or introducing tuned masssystems.

Alternative strengthening choices lead to different protection levels and imply different performances that are, in general, represented by non linear or step functions of a cost parameter of the intervention. From these considerations, conceptual “structure driven” strengthening criteria, based on a logical use of resources, are discussed.     

Nonlinear Structural Performance of a Historical Brick Masonry Inverted Dome

ABSTRACT

Traditional domes are obtained by double curvature shells, which can be rotationally formed by any curved geometrical plane figure rotating about a central vertical axis. They are self-supported and stabilized by the force of gravity acting on their weight to hold them in compression. However, the behavior of inverted domes is different since the dome is downward and masonry inverted domes and their structural behaviors in the literature received limited attention. This article presents a nonlinear finite element analysis of historical brick masonry inverted domes under static and seismic loads. The brick masonry inverted dome in the tomb of scholar Ahmed-El Cezeri, town of Cizre, Turkey, constructed in 1508 is selected as an application. First, a detailed literature review on the masonry domes is given and the selected inverted dome is described briefly. 3D solid and continuum finite element models of the inverted masonry dome are obtained from the surveys. An isotropic Concrete Damage Plasticity (CDP) material model adjusted to masonry structures with the same tensile strength assumed along the parallel and meridian directions of the inverted dome is considered. The nonlinear static analyses and a parametric study by changing the mechanical properties of the brick unit of the inverted masonry dome are performed under gravity loads. The acceleration records of vertical and horizontal components of May 1, 2003 Bingöl earthquake (Mw = 6.4), Turkey, occurred near the region, are chosen for the nonlinear seismic analyses. Nonlinear step by step seismic analyses of the inverted dome are implemented under the vertical and horizontal components of the earthquake, separately. Static modal and seismic responses of the inverted masonry dome are evaluated using mode shapes, minimum and maximum principal strains and stresses, and damage propagations.