Seismic loss estimation of non‐ductile reinforced concrete buildings

Non‐ductile reinforced concrete buildings represent a prevalent construction type found in many parts of the world. Due to the seismic vulnerability of such buildings, in areas of high seismic activity non‐ductile reinforced concrete buildings pose a significant threat to the safety of the occupants and damage to such structures can result in large financial losses. This paper introduces advanced analytical models that can be used to simulate the nonlinear dynamic response of these structural systems, including collapse. The state‐of‐the‐art loss simulation procedure developed for new buildings is extended to estimate the expected losses of existing non‐ductile concrete buildings considering their vulnerability to collapse. Three criteria for collapse, namely first component failure, side‐sway collapse, and gravity‐load collapse, are considered in determining the probability of collapse and the assessment of financial losses. A detailed example is presented using a seven‐story non‐ductile reinforced concrete frame building located in the Los Angeles, California. Copyright © 2012 John Wiley & Sons, Ltd.     

A method of calculating the non‐linear seismic response of a building braced with viscoelastic dampers

Buildings are continually subject to dynamic loads, such as wind load, seismic ground motion, and even the load from internal utility machines. The recent trend of constructing more flexible high‐rise buildings underscores the importance of including viscoelastic dampers in building designs. Viscoelastic dampers are used to control the dynamic response of a building. If the seismic design is based only on the linear response spectrum, considerable error may occur when calculating the seismic response of a building; rubber viscoelastic dampers show non‐linear hysteretic damping that is quite different from viscous damping. This study generated a non‐linear response spectrum using a non‐linear oscillator model to simulate a building with viscoelastic dampers installed. The parameters used in the non‐linear damper model were obtained experimentally from dynamic loading tests. The results show that viscoelastic dampers effectively reduce the seismic displacement response of a structure, but transmit more seismic force to the structure, which essentially increases its seismic acceleration response. Copyright © 2003 John Wiley & Sons, Ltd.     

Comparative study of the inelastic response of base isolated buildings

This article presents a numeric comparative study of the inelastic structural response of base isolated buildings. The comparative study includes the following isolation systems: laminated rubber bearings, New Zealand one, pure friction and the frictional pendulum ones. The study is based on obtaining non‐linear response spectra for various design parameters using six earthquake records. Usually the base isolation of a new building seeks to maintain the structure in the linear elastic range. The response of old weak buildings or the response of new ones subjected to extreme earthquakes may not be, necessarily, in the aforementioned ideal elastic range. Consequently, it is important to characterize the response of isolated buildings responding inelastically. A conclusion from this research is that the isolators affect significantly the structural response of weak systems. Rubber isolators seem slightly less sensitive to plastification that may occur in the structure compared to friction isolators. Ductility demands in the structure are affected significantly by friction and neoprene protected systems, in particular sliding ones where larger demands are obtained. Copyright © 2002 John Wiley & Sons, Ltd.     

Sliding fragility of block‐type non‐structural components. Part 2: Restrained components

This paper focuses on seismic vulnerability assessment of restrained block‐type non‐structural components under sliding response on the basis of seismic inputs specified by current seismic codes. The general representation of restrained equipment considered in this study consists of a rigid block restrained by four post‐tensioned, symmetrically arranged cables. Two sliding‐related failure modes are considered: restraint breakage and excessive absolute acceleration. Fragility analysis is proposed as an appropriate tool to evaluate these failure modes. Sample fragility curves developed through Monte‐Carlo simulations show that the restraint breakage limit state is sensitive to the parameters of the equation of motion. For instance, fragility estimates obtained without taking into account vertical base accelerations can be significantly unconservative for relatively large values of the coefficient of friction. In contrast, the excessive absolute acceleration limit state exhibits little sensitivity to the parameters of the equation of motion. Peak absolute acceleration response is almost always equal to or greater than the horizontal peak base acceleration. Representative results suggest that reasonable response estimates for blocks located at stories other than the ground in multistorey buildings can in general be obtained by simply scaling the ground acceleration to the peak acceleration at the corresponding storey. Copyright © 2002 John Wiley & Sons, Ltd.     

Structure, soil–structure response and effects of damage based on observations of horizontal-to-vertical spectral ratios of microtremors

The microtremor horizontal-to-vertical-spectral-ratio (HVSR) technique is widely used in the urban environment to assess the fundamental frequency response of the ground. Extensive literature exists about case histories using HVSR for microzonation in several cities, but no systematic studies have been devoted to check the presence of soil–structure interaction effects, and even less attention to study building behaviour after earthquake damage. To evaluate the above-mentioned effects, a series of experiments are reported in this article.We first made a series of microtremor measurements on buildings and civil structures to evaluate the reliability of fundamental frequency determinations. Then, we considered several case studies to evaluate the effect of soil–structure interaction in estimates of site response in the presence of tall buildings. Finally, an experiment on the frequency change due to damage was performed. It was possible to confirm that HVSR is able to detect building fundamental modes and once known the building frequency, it is also possible to detect the presence of soil–structure interaction. Thus, once the presence of the building natural frequency is identified, it is possible to infer the site response from free field measurements. We also found that the HVSR technique is equally useful for detecting structural damage by determining the frequency shift of the buildings.     

Dynamic soil–structure interaction effects on the seismic response of asymmetric buildings

An approach is formulated for the linear analysis of three-dimensional dynamic soil–structure interaction of asymmetric buildings in the time domain, in order to evaluate the seismic response behaviour of torsionally coupled buildings. The asymmetric building is idealized as a single-storey three-dimensional system resting on different soil conditions. The soil beneath the superstructure is modeled as linear elastic solid elements. The contact surface between foundation mat and solid elements of soil is discretised by linear plane interface elements with zero thickness. An interface element is further developed to function between the rigid foundation and soil. As an example, the response of soil–structure interaction of torsionally coupled system under two simultaneous lateral components of El Centro 1940 earthquake records has been evaluated and the effects of base flexibility on the response behaviour of the system are verified.     

Approximate modal decomposition of inelastic dynamic responses of wall buildings

Two approximate methods for decomposing complicated inelastic dynamic responses of wall buildings into simple modal responses are presented. Both methods are based on the equivalent linear concept, where a non‐linear structure is represented by a set of equivalent linear models. One linear model is used for representing only one vibration mode of the non‐linear structure, and its equivalent linear parameters are identified from the inelastic response time histories by using a numerical optimizer. Several theoretical relations essential for the modal decomposition are derived under the framework of complex modal analysis. Various numerical examinations have been carried out to check the validity of the proposed modal decomposition methods, and the results are quite satisfactory in all cases. Fluctuating bending moment and shear at any location along the wall height contributed by each individual vibration mode can be obtained. Modal contributions to shear and flexural strength demands, as well as the corresponding modal properties, under various seismic loading conditions can also be identified and examined in detail. Furthermore, the effects of higher vibration modes on seismic demands of wall buildings are investigated by using the modal decomposition methods. Several new insights into the complicated inelastic dynamics of multi‐story wall buildings are presented. Copyright © 2004 John Wiley & Sons, Ltd.     

1971 San Fernando and 1994 Northridge, California, earthquakes: did the zones with severely damaged buildings reoccur?

This paper compares the distribution of damage from the San Fernando, 1971, and Northridge, 1994, earthquakes. Both events had similar size, occurred on blind thrust faults beneath the densely populated San Fernando Valley of the Los Angeles metropolitan area, and hence offer a rare opportunity to compare the effects of the two earthquakes. In a previous study of the distribution of red-tagged (‘unsafe’) buildings and of breaks in the water distribution system caused by the Northridge earthquake, the authors discovered that buildings were damaged less where the soil response was not linear (as indicated by the breaks in the water pipes), except in localized areas of very severe shaking (peak ground velocity exceeding 150 cm/s). The study in this paper shows that the same applies to the damage caused by the San Fernando earthquake, and that the areas with severely damaged buildings (so called ‘gray zones’) for both earthquakes overlapped. This reoccurrence of damage within the same area is interpreted to result from some specific properties of local soil and geology. These properties are not fully understood at present, but should be explored to provide a basis for a new tool for forecasting microzonation maps, and reducing future seismic hazard.     

Evaluation of predictors of non‐linear seismic demands using ‘fishbone’ models of SMRF buildings

Predictors (or estimates) of seismic structural demands that are less computationally time‐consuming than non‐linear dynamic analysis can be useful for structural performance assessment and for design. In this paper, we evaluate the bias and precision of predictors that make use of, at most, (i) elastic modal vibration properties of the given structure, (ii) the results of a non‐linear static pushover analysis of the structure, and (iii) elastic and inelastic single‐degree‐of‐freedom time‐history analyses for the specified ground motion record. The main predictor of interest is an extension of first‐mode elastic spectral acceleration that additionally takes into account both the second‐mode contribution to (elastic) structural response and the effects of inelasticity. This predictor is evaluated with respect to non‐linear dynamic analysis results for ‘fishbone’ models of steel moment‐resisting frame (SMRF) buildings. The relatively small number of degrees of freedom for each fishbone model allows us to consider several short‐to‐long period buildings and numerous near‐ and far‐field earthquake ground motions of interest in both Japan and the U.S. Before doing so, though, we verify that estimates of the bias and precision of the predictor obtained using fishbone models are effectively equivalent to those based on typical ‘full‐frame’ models of the same buildings. Copyright © 2003 John Wiley & Sons, Ltd.     

Elastic and inelastic drift performance optimization for reinforced concrete buildings under earthquake loads

This paper presents an effective optimization technique for the elastic and inelastic drift performance design of reinforced concrete buildings under response spectrum loading and pushover loading. Attempts have been made to develop an automatic optimal elastic and inelastic drift design of concrete framework structures. The entire optimization procedure can be divided into elastic design optimization and inelastic design optimization. Using the principle of virtual work, the elastic drift response generated by the response spectrum loading and the inelastic drift response produced by the non‐linear pushover loading can be explicitly expressed in terms of element sizing design variables. The optimization methodology for the solution of the explicit design problem of buildings is fundamentally based on the Optimality Criteria approach. One ten‐story, two‐bay building frame example is presented to illustrate the effectiveness and practicality of the proposed optimal design method. While rapid convergence in a few design cycles is found in the elastic optimization process, relatively slow but steady and smooth convergence of the optimal performance‐based design is found in the inelastic optimization process. Copyright © 2004 John Wiley & Sons, Ltd.     

Response analysis of rigid structures rocking on viscoelastic foundation

In this paper the rocking response of slender/rigid structures stepping on a viscoelastic foundation is revisited. The study examines in depth the motion of the system with a non‐linear analysis that complements the linear analysis presented in the past by other investigators. The non‐linear formulation combines the fully non‐linear equations of motion together with the impulse‐momentum equations during impacts. The study shows that the response of the rocking block depends on the size, shape and slenderness of the block, the stiffness and damping of the foundation and the energy loss during impact. The effect of the stiffness and damping of the foundation system along with the influence of the coefficient of restitution during impact is presented in rocking spectra in which the peak values of the response are compared with those of the rigid block rocking on a monolithic base. Various trends of the response are identified. For instance, less slender and smaller blocks have a tendency to separate easier, whereas the smaller the angle of slenderness, the less sensitive the response to the flexibility, damping and coefficient of restitution of the foundation. Copyright © 2008 John Wiley & Sons, Ltd.     

An investigation of earthquake induced pounding between adjacent buildings

The response of adjacent buildings in city blocks to several strong earthquakes is analysed, taking into account the mutual collisions, or pounding, resulting from insufficient or non-existing separation distances. The buildings are idealized as lumped-mass, shear beam type, multi-degree-of-freedom (MDOF) systems with bilinear force-deformation characteristics and with bases supported on translational and rocking spring-dashpots. Collisions between adjacent masses can occur at any level and are simulated by means of viscoelastic impact elements. Using five real earthquake motions the effects of the following factors are investigated: building configuration and relative size, seismic separation distance and impact element properties. It is found that pounding can cause high overstresses, mainly when the colliding buildings have significantly different heights, periods or masses. This suggests a possibility for introducing a set of conditions into the codes, combined with some special measures, as an alternative to the seismic separation requirement.     

Seismic performance of a block of buildings representative of the typical construction in the Eixample district in Barcelona (Spain)

Between the late nineteenth century and the early twentieth century, Barcelona was expanded, occupying the terrains connecting the old walled city and the nearby towns of the plateau of Barcelona. At that time, a large number of unreinforced masonry buildings were constructed and nowadays many of them are still used as dwellings. Though built individually, these buildings are connected to adjacent buildings, forming blocks composed of aggregates. In order to analyze the seismic behavior of isolated buildings and aggregates, two typical central buildings and one typical corner building have been chosen. The two central buildings and the corner building are referred as C1, C2, and E buildings. Two corner buildings and two central buildings have been connected in order to simulate a block side. This aggregate is referred as AGG and it is composed by the following sequence of individual buildings: E-C1-C2-E. Original plans and drawings of existing buildings are then used to model these buildings. The modeled buildings have five stories. Standard pushover analyses lead to evaluate their seismic performance by means of capacity spectra and fragility curves. The analysis has been carried out in the parallel (Ux) and transversal (Uy) directions to the street. Then, a capacity spectrum based method is used to analyze the seismic behavior of these buildings considered as individual buildings and as an aggregate. Two earthquake scenarios are considered. The first one is a deterministic scenario which is based on a historical earthquake occurred in 1,824, 25 km away from the city and the second one is a probabilistic scenario, which represents the ground motion with a probability of occurrence of 10% in 50 years. The soil local effects have been also considered and both scenarios have been used to assess the expected damage. Four non-null damage states are considered: slight (1), moderate (2), severe (3) and extensive-to-collapse (4). For the type of soil where most of the buildings are, and in the Ux direction, the four buildings show a similar behavior. The mean damage grade is 2.3 for the deterministic scenario and 2.7 for the probabilistic one. This means that moderate to severe damage is expected in both cases; furthermore, in the case of the deterministic scenario more than 10% of the buildings would suffer extensive-to-collapse damage and nearly 20% for the probabilistic scenario, confirming the high vulnerability of such buildings. The differences in the expected damage are due to the significant different characteristics of the response spectra of the earthquake scenarios in the range of the fundamental periods of the buildings.     

Damage evaluation models of reinforced concrete buildings based on the damage statistics and simulated strong motions during the 1995 Hyogo‐ken Nanbu earthquake

We have tried to estimate the yield shear strengths of reinforced concrete (RC) buildings based on the damage statistics in Kobe surveyed after the Hyogo‐ken Nanbu, Japan, earthquake of 1995 and the non‐linear response analyses for synthetic waveforms calculated from a complex seismic source and a three‐dimensional basin structure. First, a set of building models that represented the RC building stock in Kobe was constructed and plausible non‐linear multi‐degree‐of‐freedom models with four different numbers of stories were created based on the current seismic code and construction practice. For response analysis the damage criterion and the strength distribution should be assumed a priori. When the damage ratios for these standard models were calculated it was found that the damage ratios were so high that we had to increase the average yield strengths in order to match the calculated damage ratios to those observed. After searching the best models it was found that the estimated average yield strengths should be much higher than those based on the code, especially for low‐rise buildings. Using this set of building models we succeeded in reproducing the belt‐shaped area with high damage ratios in Kobe. One can apply the proposed methodology to different countries if there is enough damage data, strong motion records, and building statistics. If there is sparse damage data at several locations only, then our models can be adjusted to reproduce observed damage data and used for damage prediction as a first‐order approximation. Copyright © 2004 John Wiley & Sons, Ltd.     

The influence of dynamic soil–structure interaction on traffic induced vibrations in buildings

This paper deals with the dynamic response of buildings due to traffic induced wave fields. The response of a two-storey single family dwelling due to the passage of a two-axle truck on a traffic plateau is computed with a model that fully accounts for the dynamic interaction between the soil and the structure. The results of three cases where the structure is founded on a slab foundation, a strip foundation and a box foundation are calculated and a comprehensive analysis of the dynamic structural response is performed. A methodology is also proposed to calculate the structural response, neglecting the effects of dynamic soil–structure interaction. A comparison with the results of calculations where dynamic soil–structure interaction is accounted for shows that a good approximation is obtained in the case of a rigid structure resting on a soft soil.     

Effect of the variability in plan of concrete mechanical properties on the seismic response of existing RC framed structures

A proper characterization of concrete strength is essential to correctly model existing RC structures, whose seismic performance is affected by the poor quality of materials. The purpose of this work is to evaluate the effect of incorrect assumptions for concrete strength and the adequacy of current Codes provisions (Eurocodes, FEMA). Even the effects of the non homogeneity of concrete strength within the building is considered due to its high variability; in fact, buildings can experience an irregular seismic response, both in plan and in elevation. In this work the effects of irregularity in plan due to the strength variability of concrete is analyzed on a case study, a four storey RC framed building, designed for vertical loads only. The variability of concrete strength has been evaluated using the data of an extensive investigation developed by REGIONE TOSCANA on a large sample of RC framed buildings.     

Earthquake‐induced structural response output‐only identification by two different Operational Modal Analysis techniques

Output‐only system identification is developed here towards assessing current modal dynamic properties of buildings under seismic excitation. Earthquake‐induced structural response signals are adopted as input channels for two different Operational Modal Analysis (OMA) techniques, namely, a refined Frequency Domain Decomposition (rFDD) algorithm and an improved Data‐Driven Stochastic Subspace Identification (SSI‐DATA) procedure. Despite that short‐duration, non‐stationary, earthquake‐induced structural response signals shall not fulfil traditional OMA assumptions, these implementations are specifically formulated to operate with seismic responses and simultaneous heavy damping (in terms of identification challenge), for a consistent estimation of natural frequencies, mode shapes, and modal damping ratios. A linear ten‐storey frame structure under a set of ten selected earthquake base‐excitation instances is numerically simulated, by comparing the results from the two identification methods. According to this study, best up‐to‐date, reinterpreted OMA techniques may effectively be used to characterize the current dynamic behaviour of buildings, thus allowing for potential Structural Health Monitoring approaches in the Earthquake Engineering range.     

Experimental investigation on the seismic performance of masonry buildings using shaking table testing

Masonry buildings worldwide exhibited severe damage and collapse in recent strong earthquake events. It is known that their brittle behavior, which is mainly due to the combination of low tensile strength, large mass and insufficient connection between structural elements, is the main limitation for their structural implementation in residential buildings. A new construction system for masonry buildings using concrete blocks units and trussed reinforcement is presented here and its seismic behavior is validated through shaking table tests. Dynamic tests of two geometrically identical two-story reduced scale (1:2) models have been carried out, considering artificial accelerograms compatible with the elastic response spectrum defined by the Eurocode 8. The first model was reinforced with the new proposed system while the second model was built with unreinforced masonry. The experimental analysis encompasses local and global parameters such as cracking patterns, failure mechanisms, and in-plane and out-of-plane behavior in terms of displacements and lateral drifts from where the global dynamic behavior of the two buildings is analyzed comparatively. Finally, behavior factors for the design recommendations in case of unreinforced masonry are also evaluated.     

Seismic Vulnerability Assessment of Gravity Load Designed R/C Frames

The seismic vulnerability of some frame structures, typical of existing Reinforced Concrete buildings designed only to vertical loads, has been evaluated. They are representative of building types widely present in the Italian building stock of the last 30 years. A simulated design of the structures has been made with reference to the codes in force, the available handbooks and the current practice at the time of construction. The seismic response is calculated through non linear dynamic analyses with artificial and natural accelerograms. Three main types have been examined: bare frames, regularly infilled frames and pilotis frames. The results show a high vulnerability for the pilotis buildings: they can be assigned to the class B of the European Macroseismic Scale of 1998 (EMS98). On the contrary, a low vulnerability (class D of EMS98) can be attributed to the regularly infilled buildings: in this case collapse can be considered unlikely also with strong earthquakes. An intermediate seismic behavior is shown by buildings without infills, whose vulnerability can be placed between the classes B and C of EMS98. This revised version was published online in July 2006 with corrections to the Cover Date.     

Nonlinear soil response as a natural passive isolation mechanism. Paper II. The 1933, Long Beach, California earthquake

The areas that experienced large strains and differential motions in the soil (indicated by breaks in the water and gas pipe distribution systems) and the areas with severely damaged buildings showed remarkable separation during the March 10, 1933, Long Beach, California earthquake. With analogous results for the 1994 Northridge, California earthquake [Soil Dynam. Earthquake Engng. 17 (1998) 41], the observations summarized in this paper show the fallacy of simplistic and popular interpretations, such as those that hold that in the near field the damage to buildings is caused by ‘soft’ or ‘bad ground’ conditions. In fact, significant reduction in the potential damage to buildings may be expected in the areas where the soil experiences ‘moderate to large’ strains.