Engineering Structures 64 (2014) 52–67

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Engineering Structures

journal homepage: www.elsevier .com/locate /engstruct

Unreinforced and confined masonry buildings in seismic regions:Validation of macro-element models and cost analysis

http://dx.doi.org/10.1016/j.engstruct.2014.01.0140141-0296/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author at: Engineering Department, Pontifical Catholic Univer-sity of Peru, Av. Universitaria 1801, San Miguel, Lima 32, Peru. Tel.: +51 1 626 20004605; fax: +51 1 626 2000 2813.

E-mail address: marquesmnc@sapo.pt (R. Marques).

Rui Marques a,b,⇑, Paulo B. Lourenço b

a Engineering Department, Pontifical Catholic University of Peru, Av. Universitaria 1801, San Miguel, Lima 32, Perub Institute for Sustainability and Innovation in Structural Engineering, University of Minho, Campus de Azurém, 4800-058 Guimarães, Portugal

a r t i c l e i n f o a b s t r a c t

Article history:Received 30 April 2013Revised 29 December 2013Accepted 8 January 2014

Keywords:Macro-element modelsQuasi-static testsUnreinforced masonryConfined masonrySeismic assessmentCost analysis

Modern design of buildings requires accounting for sustainability aspects using a life-cycle perspective,but also the early design phase where earthquake actions have a significant influence concerning thestructural design. Recently, the seismic evaluation of masonry buildings using macro-element modelingapproaches became popular, by applying performance-based assessment procedures through nonlinearstatic (pushover) analysis methodologies. This work addresses the validation for these approaches refer-ring to two full-scale masonry structures tested under quasi-static lateral loading and almost unknown inthe literature. The experimental behavior of tested unreinforced masonry (URM) and confined masonry(CM) structures is compared against the pushover response of the corresponding computational models.Then, referring to typical housing in southern Europe and its usual design with a reinforced concrete (RC)structure, the validated assessment tools are employed to evaluate the earthquake-resistant possibilitiesof URM and CM solutions, namely in terms of maximum applicable ground accelerations. The masonrysolutions are also compared in terms of construction costs against the RC typology. The considered anal-ysis tools present a good agreement when predicting, satisfactorily, the experimental test behavior, thusbeing able to be used in performance-based design. With respect to the studied housing, the predictedpushover responses for the masonry structures denote capacity to resist earthquakes adequately. Thesestructures allow also a significant cost reduction (up to 25%) against the RC, thus appearing to be com-peting alternatives.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

The building sector has a large influence in the economy, total-izing about 10% of the GDP in European countries. Moreover, peo-ple live most of their lives inside buildings, while housing has amajor weight in the budget of families and of the banking system.Low-to-medium rise buildings (up to 3 storeys) are the more fre-quent typology for housing, requiring then particular attention indeveloping sustainable solutions for construction. The adoptedstructural solution represents itself an important initial investmentfor housing and is the focus of the present paper.

Buildings need to provide for welfare, health and safety of occu-pants. The occurrence of strong earthquakes in the Euro-Med re-gion, see Fig. 1, even in moderate seismicity zones (e.g., the 2011Lorca earthquake in Spain), highlighted the consequences of poorly

designed earthquake resistance structures regarding: damages, in-jured people, deaths, post-earthquake traumas and reconstructioncosts. It is known that earthquakes can take place all over theworld causing large losses. The seismic action needs then to beadequately considered in the design of buildings, as addressed inrecent methodologies and codes for seismic safety assessment ofstructures, e.g. [1–3].

There is an important challenge to be addressed today, which iscombining sustainability and earthquake resistance. Cost-effectivestructural solutions can present higher vulnerability to earth-quakes, as is typically the case of unreinforced masonry (URM)when compared to reinforced concrete (RC), which became thedominant structural solution in many countries, even for smallhouses in low seismicity regions. Still, in many cases and takinginto account the seismic performance, URM or confined masonry(CM) structural solutions can be alternatively used for low-risebuildings.

The sustainability concept is often applied in the fields of con-struction economy or green building as whole, with less consider-ation of the adopted structural typology, also in terms of

(a) (b)

Fig. 10. Building tested by Zavala et al. [27]: (a) structural plan and (b) test set-up.

Fig. 11. Geometrical and computational models in 3DMacro of the building.

R. Marques, P.B. Lourenço / Engineering Structures 64 (2014) 52–67 57

element probably provides a more accurate approximation.According to Cappi et al. [14], the damage in the walls was typi-cally by diagonal cracking and was initiated in the center spandrel(Fig. 7b).

The predicted sequence for the wall deformed shape and dam-age is summarized in Fig. 8, for every model and in correspondencewith wall displacement levels of 7.5 mm (yielding), 18.5 mm (endof the first yielding stage) and ultimate displacement (strength lossof 20%). A wider sequence for the wall predicted behavior is pre-sented in Marques [21]. The known experimental results describ-ing the wall deformed shape and damage are limited, butaccording to Cappi et al. [14] the wall response incorporates wall-and frame-type behavior patterns. Due to the wall-type behavior,the overturning action generates tension in the left piers andcompression in the right piers, while the spandrels are essentiallysubjected to shear. Due to the frame-type behavior, the four bot-tom-to-top columns are subjected to similar moments, while thecross members are compressed and bent.

Concerning the deformed shape, the SAM II and 3Muri modelsprovide a similar trend by deforming linearly along the height.On the other hand, the TreMuri and 3DMacro models present anidentical first level mechanism. In terms of damage the samegroups are identified, with the first group (SAM II and 3Muri) pre-senting initial damage mostly by flexure, even if some panels fail

latter by shear, and the second group (TreMuri and 3DMacro) pre-senting shear damage in selected panels (e.g. the lower pier on thewall right), associated with rocking of piers at the first level on thewall left. In the experimental test, the earliest damage was due toshear on the intermediate horizontal cross member, and which re-sulted seriously damaged at the end of the test. Damage to thismember is identified by all the models.

The model grouping in terms of the predicted response seems tobe associated to the assumptions adopted by the models, as thefirst group considers one-dimensional elements with a bilinear re-sponse, while the second considers a bi-dimensional domain forthe material constitutive law. From the experimental and analyti-cal results presented in Cappi et al. [14], namely the identifieddiagonal shear damage for the central spandrel and a stronger de-formed shape at the first level, it seems that the second modelgroup better agrees with the experimental response. For this rea-son, Fig. 8c and d is assumed to represent the best approximationto the experimental damage.

2.2. Models for confined masonry (CM)

CM is a particular case of masonry structures, even if it presentssome similarity with reinforced concrete (RC) structures due to thepresence of a frame. CM is characterized by casting of the RC ele-

Fig. 12. Experimental against predicted damage in the South wall for three drift levels.

North point South point Central point ········ Predicted at roof centroid

-1500

-1000

-500

0

500

1000

1500

-40 -20 0 20 40

Bas

e sh

ear

forc

e (k

N)

1st storey displacement (mm)

-1500

-1000

-500

0

500

1000

1500

-40 -20 0 20 40

Bas

e sh

ear

forc

e (k

N)

Building displacement (mm)

Fig. 13. Comparison of the predicted envelopes in 3DMacro against the experimental response. (For interpretation of color in this figure, the reader is referred to the webversion of this article.)

58 R. Marques, P.B. Lourenço / Engineering Structures 64 (2014) 52–67

ments only after the masonry works, which provides a good con-nection between the confining elements and the masonry panelsdue to the combination of bond effects, shrinkage of the RC ele-ments and the fact that the vertical dead load is transferred tothe walls. The interaction behavior between the confining ele-ments and masonry through the existing interface is a specific as-pect that needs to be considered in the response of CM walls underlateral loading. Some models have been implemented for CM struc-tures based on a wide-column approach, e.g. [22,23], consideringthe interaction behavior between the confining elements and themasonry implicitly in the wall shear response.

Micro-modeling strategies can also be used, namely based inthe finite element method, to model explicitly the concrete-masonry interface, e.g. Calderini et al. [24]. Alternatively, a discrete

element approach is also applicable, such as that idealized byCaliò et al. [25] originally for URM and which has beenextended in the 3DMacro software [11] to model RC/steel/masonry mixed structures. This last approach uses an interface(constituted by nonlinear springs) between the masonry panels(Fig. 9a), which in the case of two neighboring CM panels isinterposed by a frame modeled through nonlinear beam finiteelements with concentrated plasticity (Fig. 9b). For the beamelements and in agreement to a given type of interaction (axial,flexural or axial-flexural), the corresponding hinges are consid-ered according to the respective N–Mx–My domain (such as inFig. 9c). This approach has already been used for the simulationof a CM structure built in southern Italy after the 1908 Messinaearthquake [26].

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4. Conclusions

The present work offers a contribution regarding the design andconstruction of cost-effective buildings in seismic regions. For thispurpose, the tools available for the seismic design of unreinforcedand confined masonry buildings are presented and validatedagainst experimental evidence. With reference to an actual caseof a single family housing, simulations are carried to assess itsearthquake-resistant capabilities and an evaluation of the con-struction costs of masonry solutions is made in comparing withthe usual RC frame structure.

In general and referring to the validation of experimental tests,the analysis tools available allowed a satisfactory prediction of thecapacity curve from the pushover analysis, namely in terms of ini-tial stiffness, base shear strength and displacement capacity, thusbeing accurate to use in performance-based design. Furthermore,the software codes allow simulating the specificities of real ma-sonry building configurations.

Using a typical house in the southern Europe as case study,structural masonry solutions allowed ensuring seismic safety upto large ground acceleration levels, namely 0.15g and 0.20g forURM and CM structures, respectively. Furthermore, these solutionsallow a cost reduction of the structure respectively of 24% and 16%when considering the RC structure as reference. For the URM struc-ture, it was demonstrated that a very conservative design is ob-tained using the force-based method specified in EC8 [1], due tothe consideration of very conservative values for the behaviorfactor.

The simulation of the real dynamic behavior of a masonrybuilding is a very complex task. In order to simplify, the validationof the presented macro-element models against experimental re-sults and also its application to a typical building allows to obtainan approach to the pushover response of the studied structures,which is assumed to provide a representative indication of the seis-mic behavior, particularly regarding the application of seismiccodes.

Acknowledgement

The first author acknowledges the financial support from thePortuguese Foundation for Science and Technology (FCT) throughthe Ph.D. Grant SFRH/BD/41221/2007. This paper is in honor ofEngineer Ángel San Bartolomé Ramos, Professor and Researcherof the Pontifical Catholic University of Peru, for his contributionin the field of masonry structures.

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