Definition of Seismic Input for Out-of-Plane Response of Masonry Walls: I. Parametric Study

Response of masonry walls to out-of-plane excitation is a complex, yet inadequately addressed theme in seismic analysis. The seismic input expected on an out-of-plane wall (or a generic “secondary system”) in a masonry building is the ground excitation filtered by the in-plane response of the walls and the floor diaphragm response. More generally, the dynamic response of the primary structure, which can be nonlinear, contributes to the filtering phenomenon. The current article delves into the details and results of several nonlinear dynamic time-history analyses executed within a parametric framework. The study addresses masonry structures with rigid diaphragm response to lateral loads. The scope of the parametric study is to demonstrate the influence of inelastic structural response on the seismic response of secondary systems and eventually develop an expression to estimate the seismic input on secondary systems that explicitly accounts for the level of inelasticity in the primary structure in terms of the displacement ductility demand. The proposed formulation is discussed in the companion article.     

Seismic Performance and Modeling of a Half-Scale Base-Isolated Wood Frame Building

The concept of base isolation is a century old, but application to civil engineering structures has only occurred over the last several decades. Application to light-frame wood buildings in North America has been virtually non existent with one notable exception. This article quantitatively examines issues associated with application of base isolation in light-frame wood building systems including: (1) constructability issues related to ensuring sufficient in-plane floor diaphragm stiffness to transfer shear from the superstructure to the isolation system; (2) evaluation of experimental seismic performance of a half-scale base-isolated light-frame wood building; and (3) development of a displacement–based seismic design method and numerical model and their comparison with experimental results. The results of the study demonstrate that friction pendulum system (FPS) bearings offer a technically viable passive seismic protection system for light-frame wood buildings in high seismic zones. Specifically, the amount and method of stiffening the floor diaphragm is not unreasonable, given that the inter-story drift and accelerations at the upper level of the tested building were very low, thus resulting in the expectation of virtually no structural, non structural, or contents damage in low-rise wood frame buildings. The nonlinear dynamic model was able to replicate both the isolation layer and superstructure movement with good accuracy. The displacement-based design method was proven to be a viable tool to estimate the inter-story drift of the superstructure. These tools further underscore the potential of applying base isolation systems for application to North America's largest building type.     

Simulation of Shake Table Tests on Out-of-Plane Masonry Buildings. Part (VI): Discrete Element Approach

ABSTRACT

Although many experimental tests and numerical models are available in the literature, the numerical simulation of the seismic response of existing masonry buildings is still a challenging problem. While the nonlinear behavior of masonry structures is reasonably predictable when the out-of-plane behavior can be considered inhibited, when the in-plane and out-of-plane responses coexist and interact, simplified models seem unable to provide reliable numerical predictions. In this article, taking advantage of the experimental tests carried out in a shaking table on two masonry prototypes at LNEC, a macro-element approach is applied for the numerical simulations of their nonlinear response. The adopted approach allows simulating the nonlinear behavior of masonry structures considering the in-plane and out-of-plane responses. Since it is based on a simple mechanical scheme, explicitly oriented to representing the main failure mechanisms of masonry, its computational cost is greatly reduced with respect to rigorous solutions, namely nonlinear FEM approaches. Two modeling strategies are adopted, namely a regular mesh independent from the real texture of the prototypes and a detailed one coherent with the units disposal. The numerical results are discussed and the correlation between the nonlinear static analyses and the dynamic response is provided.     

Simulation of Shake Table Tests on Out-of-Plane Masonry Buildings. Part (IV): Macro and Micro FEM Based Approaches

ABSTRACT

This article presents a study on the out-of-plane response of two masonry structures without box behavior tested in a shaking table. Two numerical approaches were defined for the evaluation, namely macro-modeling and simplified micro-modeling. As a first step of this study, static nonlinear analyses were performed for the macro models in order to assess the out-of-plane response of masonry structures due to incremental loading. For these analyses, mesh size and material model dependency was discussed. Subsequently, dynamic nonlinear analyses with time integration were carried out, aiming at evaluating the collapse mechanism and at comparing it to the experimental response. Finally, nonlinear static and dynamic analyses were also performed for the simplified micro models. It was observed that these numerical techniques correctly simulate the in-plane response. The collapse mechanism of the stone masonry model is in good agreement with the experimental response. However, there are some inconsistencies regarding the out-of-plane behavior of the brick masonry model, which required further validation.     

Predictive Tri-Linear Benchmark Curve for In-Plane Behavior of Adobe Walls

In the present study, numerical simulations are conducted to estimate the in-plane response of adobe walls subjected to pseudo-static cyclic loading based on the finite element code ABAQUS. The simplified micro-modeling approach is adopted and an interface model reported in ABAQUS material library is applied as material model for zero-thickness interface elements. The comparison between obtained results and field test data results in good agreement. Parametric studies are carried out to evaluate the effectiveness of independent parameters changes on response of adobe walls. It is noted that mechanical properties of joints and adobe units play an active role on in-plane behavior of walls. A tri-linear benchmark curve is proposed to predict the response of aforementioned walls. In this regard, a statistical study is performed to derive the predictive tri-linear benchmark curve. The regressive analysis on 59 numerical models resulted in proposing predictive models. Finally, by comparing tri-linear curves obtained from the regressive analysis, numerical analysis, and experimental study, appropriate accuracy of theoretical model can be found.     

Performance of Wall to Diaphragm Anchors for Use in Seismic Upgrade of Heritage Masonry Buildings

Performance of wall to diaphragm (WD) anchors in heritage unreinforced masonry (URM) buildings during the recent New Zealand earthquake series is commented on, detailing typical failure modes. Current building code provisions for the design of masonry anchors are discussed and overview of an associated experimental program investigating the effectiveness of a relatively new type of retrofit WD anchors is presented. A total of 40 anchors were tested for pull out capacity (POC), of which 30 were installed in salvaged heritage material assemblages and 10 were tested in-situ at a heritage URM building. The POC of anchors ranged from 13.01 kN to 23.12 kN when installed in a heritage URM wall and between 9.54 kN and 12.16 kN when driven from side into two consecutive floor joists of a heritage timber diaphragm. Investigated also were the effects of embedment length, installation quality, anchor location, condition of masonry, and condition of substrate materials on anchor performance.     

Simple Models for Inelastic Seismic Analysis of Asymmetric Multistory RC Buildings

A simple stick model is presented for the inelastic seismic analysis in 3D of two-way eccentric multistory RC buildings. It has 3 DoFs per floor, point hinges at the ends of the vertical elements connecting floors, elastic story stiffness derived from the corresponding story force-interstory deformation relations of the elastic 3D structure under inverted-triangular floor loading (by torques for torsional stiffness, by horizontal forces for the lateral ones), story yield forces derived from the total resistant shear of the story vertical elements, but no coupling between lateral and torsional inelasticity. It is evaluated on the basis of comparisons of response histories of floor displacements to those from full nonlinear models in 3D of four actual buildings. Alternative locations of the story vertical element with respect to the floor mass center are examined: (a) the floor “center of twist” of the elastic 3D building under inverted-triangular floor torques; (b) the story “effective center of rigidity,” through which application of inverted triangular lateral forces does not induce twisting of floors; (c) the centroid of the secant stiffness of the story vertical members at yielding and (d) the centroid of the lateral force resistance of story vertical elements. Among alternatives (a)–(d), the floor “center of twist” provides the best agreement with floor displacement response-histories from full 3D nonlinear models. This means that the static eccentricity that matters for torsional response may be taken as that of the floor “center of twist.” The center of resistance comes up as the second-best choice.     

Dynamical Assessment of the Work Conditions of Reinforcement Tie-Rods in Historical Masonry Structures

Tie-rods are essential structural elements, which have been employed for centuries in masonry historical buildings, either during the construction or in successive strengthening interventions, with the aim of containing dangerous horizontal actions. The actual work conditions of these tie-rods, which are strongly influenced by their load history, are difficult to be quantified theoretically, and an effective method for their measure is of great importance in order to ensure the efficiency of these elements during the time and the stability of the entire building. Common measurements are often carried out adopting models based upon significant simplifications, like, for example, hinges at the extremities. These assumptions, rarely represent the real work conditions for anchorages. In this work, a non-destructive testing method is presented, based upon sophisticated dynamical models that can take into consideration many of the circumstances neglected by the simplified models. Four case studies are extensively described, trying to embrace the most common situations in term of peculiar features of the building, structural configuration, and load history. The discussion of the results yields the safety margin of the rod with respect to the material failure and provides important indications about the overall stability of the whole building.     

Simplified Seismic Sidesway Collapse Capacity-Based Evaluation and Design of Frame Buildings with Linear Viscous Dampers

This article describes a simplified procedure for estimating the seismic sidesway collapse capacity of frame building structures incorporating linear viscous dampers. The proposed procedure is based on a robust database of seismic peak displacement responses of viscously damped nonlinear single-degree-of-freedom systems for various seismic intensities and uses nonlinear static (pushover) analysis without the need for nonlinear time history dynamic analysis. The proposed procedure is assessed by comparing its collapse capacity predictions on 272 different building models with those obtained from incremental dynamic analyses. A straightforward collapse capacity-based design procedure is also introduced for structures without extreme soft story irregularities.     

Comparison of Numerical and Experimental Seismic Responses of FREI-Supported Un-reinforced Brick Masonry Model Building

Comparative study of numerically and experimentally obtained seismic responses of un-reinforced masonry building supported on in-house designed un-bonded fibre reinforced elastomeric isolator (U-FREI) are presented in this article. The effectiveness of U-FREI is established very clearly in terms of controlled dynamic response of the model building. Experimental studies are carried out on a shake table with elaborate instrumentations for measurement of acceleration and displacements at different floor levels. Numerical study of the model building supported on U-FREI is carried out to compare the results with experimental investigation. Multi-linear pivot hysteretic plasticity model is used to simulate the behavior of FREI, while plate elements are used for brick-masonry walls. Experimentally obtained force-displacement curves of FREI are used for defining the properties of multi-linear model representing FREI. The dynamic responses obtained from the numerical studies are compared with those from experimental investigations. This study indicates that the seismic responses of building supported on U-FREI can be numerically evaluated with quite reasonable accuracy. A good numerical model can be judiciously used at the preliminary design stage, followed by actual testing and construction of the base isolated building.     

A SIMPLIFIED METHOD FOR ELASTIC SEISMIC ANALYSIS OF HILL BUILDINGS

Abstract

Buildings on hill slope are highly irregular and asymmetric in plan and elevation. They are subjected to severe torsion in addition to lateral forces under the action of earthquakes. In the present study, simplified 3D dynamic analysis of hill buildings based on transformation of stiffness and mass of various components about a common arbitrarily-chosen reference axis is presented. Few actual hill building problems have been analysed with the simplifed method and the rigorous method of analysis. The results of the two methods of analysis advocate the use of the simplified method in the Code of Practices of different countries. With the use of the simplified method, the configurations for buildings on hill slope can be decided by taking various trial configurations so as to obtain the most economical and safe design from the seismic point of view.     

Nonlinear Static Procedure for Multi-Story Asymmetric Frame Buildings Considering Bi-Directional Excitation

The present article focuses on a nonlinear static procedure (NSP) for a multi-story asymmetric frame building with regular elevation subjected to bi-directional ground motion. In this procedure, two simplified models—an equivalent single-story model and an equivalent single-degree-of-freedom (SDOF) model—are used to predict the peak response of multi-story asymmetric buildings. The peak response is predicted through pushover analysis of an equivalent single-story model considering the effect of bi-directional excitations and an estimation of the nonlinear response of equivalent SDOF models. The predicted results are compared with the nonlinear dynamic analysis results, and satisfactory predictions can be obtained by the proposed procedure.     

Influence of Diaphragm Flexibility on Seismic Response of Unreinforced Masonry Buildings

The effects of diaphragm flexibility on the seismic response of low-rise unreinforced masonry buildings are examined using one-way stiffness- and strength-eccentric single-story systems subjected to unidirectional ground excitation. A wide range of diaphragm stiffnesses are considered. Results show that diaphragm flexibility can induce different effects depending on the configuration of the system and the level of diaphragm flexibility. When diaphragm is relatively stiff, amplified displacement demands can be imposed on the flexible side of the structure. When diaphragm is relatively flexible, peak displacements of in-plane loaded walls generally reduce. A diaphragm classification is developed to capture these salient effects.     

Nonlinear Static and Dynamic Behavior of a 16-Story Torsionally Sensitive Building Designed According to Eurocodes

A 16-story building under construction in Bucharest has been designed according to the provisions of EC2 and EC8, using elastic spectral modal analysis. Considering that the building is torsionally sensitive in the nonlinear range, it was further checked and verified using nonlinear dynamic and static procedures, using a detailed space-frame model. Specifically, time-history analysis for seven different excitations, as well as respective inelastic static analysis taking into account torsional effects were performed. The results are examined regarding structural (global) and member (local) response and various issues concerning the adequacy of the original elastic design and the applicability of advanced analysis methods are discussed.     

Inelastic Displacement Ratios for Nonstructural Components Subjected to Floor Accelerations

This paper describes a study on the characterization of the Inelastic Displacement Ratios (IDRs) of inelastic acceleration-sensitive nonstructural components subjected to floor accelerations obtained from the linear analysis of multistory building structures under far-field ground accelerations. Several building models having different structural systems and a number of stories were considered. IDRs were obtained from the displacement response of elastic and inelastic single-degree-of-freedom systems subjected to floor accelerations. Similarities and differences between floor acceleration IDRs and ground acceleration IDRs were identified, and efforts were made to explain the differences. Finally, a predicting equation for floor acceleration IDRs is proposed and validated.     

MODELLING OF STRUCTURAL ACCELERATIONS AND APPLICATION TO CONTROLLER DESIGN

In this paper a method for the identification of simplified linear models for building structures is applied to the case when acceleration, rather than displacement, is measured. A frame from benchmark structural controller studies is simulated, and from the input-output data of these simulations, simplified models for the acceleration response of the frame are obtained that have far fewer degrees of freedom. One of these simplified models is used to design a controller, which is tested using an evaluation model from the benchmark controller studies and found to be effective.     

Floor Spectra of Inelastic RC Frame Buildings Considering Ground Motion Characteristics

A range of reinforced concrete frame buildings with different levels of inelasticity as well as periods of vibration is analyzed to study the floor response. The derived floor acceleration response spectra are normalized by peak ground acceleration, peak floor acceleration, and ground response spectrum. The normalization with respect to ground response spectrum leads to the lowest coefficients of variation. Based on this observation as well as previous studies, an amplification function is proposed that can be used to develop design floor spectra from the ground motion spectrum, considering the building’s dynamic characteristics and level of inelasticity.     

The Effect of Stiffened Floor and Roof Diaphragms on the Experimental Seismic Response of a Full-Scale Unreinforced Stone Masonry Building

An extensive experimental program was carried out at EUCENTRE, within a research project on the evaluation and reduction of the seismic vulnerability of stone masonry structures. The main part of the experimental program has been devoted to the shaking table tests on three full-scale, two-story, single-room prototype buildings made of undressed double-leaf stone masonry. The first building tested was representative of existing unreinforced stone masonry structures with flexible wooden diaphragms, without any specific anti-seismic design nor detailing. In the second and third buildings, strengthening interventions were simulated on structures theoretically identical to the first one, improving wall-to-floor and wall-to-roof connections and increasing diaphragm stiffness. In particular, in the third specimen, steel and r.c. ring beams were used to improve the diaphragm connection to the walls and collaborating r.c. slab and multi-layer plywood panels were used to stiffen floor and roof diaphragms, respectively. This article describes the strengthening interventions applied to the third building prototype and presents the experimental results obtained during the shaking table tests. The results obtained permitted the calibration of a macroelement model representative of the nonlinear behavior of the structure.     

Simplified Mechanical Model to Estimate the Seismic Vulnerability of Heritage Unreinforced Masonry Buildings

Traditional or historic masonry structures occur in large populations throughout the world, particularly in preserved historical city clusters. Being non-engineered and aging these structures are in urgent need of assessment and seismic repair/rehabilitation. However, traditional masonry presents important challenges to computational modeling, owing to complexity of structural system, material inhomogeneity, and contact interactions that collectively can only be addressed through detailed 3D nonlinear representation. In this article, a simple performance assessment model is developed in order to address the need for preliminary assessment tools for this class of structures. The objective is to be able to rapidly identify buildings that are at higher risk in the event of a significant earthquake, potentially justifying a second round of more detailed evaluation. The proposed model defines the characteristics of a Single Degree of Freedom representation of the building, formulating consistent 3D shape functions to approximate its fundamental mode of vibration considering both in-plane and out-plane wall bending as a result of insufficient diaphragm action. Parametric expressions for the dynamic properties are derived in terms of the important geometric, material, and system characteristics, and are used to express local demand from global estimates. Acceptance criteria are established both in terms of deformation and strength indices to guide retrofit. An application example of the proposed assessment methodology is included to demonstrate the ability of the model to reproduce the essential features of traditional masonry buildings under seismic action.     

Seismic performance of historical vaulted adobe constructions: a numerical case study from Yazd,Iran

Past earthquakes have demonstrated that historical vaulted adobe buildings are highly vulnerable to seismic actions. Hence, it is crucial for such building typologies to be evaluated in terms of seismic capacity. To this end, this article deals with the seismic performance of historical vaulted adobe houses from the city of Yazd, Iran as one of the seismically active areas of the world and possessing a very rich adobe heritage. Thus, and based on a detailed geometrical survey, a representative sample of adobe houses from Yazd was studied using a simplified in-plane analysis based on three geometric indexes. Concerning the out-of-plane behavior, a deeper assessment was conducted by performing a numerical study, where the main influential parameters on the seismic behavior of vaulted adobe buildings were considered. The numerical analyses were carried out by adopting the limit analysis theory implemented in the Block2D software. The results obtained indicate the safe in-plane behavior of most of the houses and the safe out-of-plane response of the sample under gravitational loads. However, the sample out-of-plane safety under earthquake-induced loads seems to be a matter of concern.