Macromodeling of in- and out-of-plane behavior of unreinforced masonry infill walls

Abstract

Surveys on damaged and collapsed reinforced concrete (RC) buildings following recent earthquakes indicated that poor performance is associated with the influence of unreinforced masonry (URM) infill walls. In the event of an earthquake, a typical URM infill wall is subjected to a three-dimensional acceleration field and undergoes simultaneous in-plane (IP) and out-of-plane (OoP) loading. Depending on the direction of the seismic action, the observed damage mechanisms for URM infill walls may be classified as IP and OoP performance failures or a combination of both. Since the turn of the millennium, there have been a number of distinct experimental studies in the field of infilled frames, addressing the OoP response of URM infill walls. This has led to a number of numerical macro models able to represent the OoP behavior of the URM infill wall. The main limitation of the proposed models is the difficulty in using them as practical models, since all the proposed models were implemented in software tools without a graphical user interface (GUI), such as OpenSees. In this paper, one of the recently presented models is utilized and a methodology presented for a more practical and user-friendly implementation. The model previously validated using OpenSees is recalibrated and revalidated using the computer software SAP2000, which has a powerful GUI utilizing the material models and numerical elements available in the program library. The model considers the IP and OoP response as well as their interaction. For the determination of failure patterns, respective local damage grades for primary (frame) and secondary (infill wall) elements are defined. Finally, a four-story RC frame structure with URM infill walls, which was tested in the European Laboratory for Structural Assessment considering the IP response only, is used to assess the combined failure mechanism of URM infill walls through the concept of interaction curves.

Appendix: One-panel parameter calculations

The determination of the macromodel parameters for the model construction and post-analysis evaluation is presented here (Table 4). The example chosen is the second-story 6 m-long infilled panel of the structure tested in Negro et al. (1994).

Table 4 Material parameters and parameters of the macromodel

Post-analysis URM evaluation
IP limit (drift)	$\upbeta = \frac{{{\text{V}}_{\text{frame}} }}{{{\text{V}}_{\text{URM}} }} = \frac{270 kN}{163 kN} = 1.7 > 1.3$; $\frac{{{\text{L}}_{\text{URM}} }}{{{\text{H}}_{\text{URM}} }} = \frac{4000}{3050} = 1.3$	34 (mm)
	FEMA 356, Table 7–9, linear interpolation $\left\{ {\left. {\begin{array}{*{20}l} {\frac{{{\text{L}}_{\text{URM}} }}{{{\text{H}}_{\text{URM}} }}} \hfill \\ {\left[ - \right]} \hfill \\ {0.5} \hfill \\ {1.0} \hfill \\ {2.0} \hfill \\ \end{array} } \right|\begin{array}{*{20}c} {{\text{IP}}\;{\text{limit }}\left( {\text{drift}} \right)} \\ {\left[ \% \right]} \\ {1.5 } \\ {1.2} \\ {0.9} \\ \end{array} } \right\}$
	1.1% of story height (according to Kadysiewski and Mosalam (2009) and FEMA 356)
OoP limit (drift)	$min\left\{ {\begin{array}{*{20}c} {5\% } \\ {0.5*t_{URM} /H_{URM} } \\ \end{array} } \right\} = \left\{ {\begin{array}{*{20}c} {5\% } \\ {0.5*112/3050} \\ \end{array} } \right\} = \left\{ {\begin{array}{*{20}c} {5\% } \\ {1.83\% } \\ \end{array} } \right\}$	56 (mm)
	1.83% of story height (according to Kadysiewski and Mosalam (2009) and FEMA 356)
Linear interaction curve
UIPH_top, UIPH_bot:	IP top and bottom horizontal displacement of the URM infill panel, relative to the ground.
UIPV_top, UIPV_bot:	IP top and bottom vertical displacement of the URM infill panel, relative to the ground.
δIP_t:	IP relative displacement at each time step (according to Kadysiewski and Mosalam (2009)) $\delta_{IP\_t} = \left( {U_{IPH\_top } -_{ } U_{IPH\_bot } } \right) - \left( {\frac{{H_{col} }}{{L_{Bem} }} } \right)\left( { U_{IPV\_top} -_{ } U_{IPV\_bot } } \right)$
UOoP_top, UOoP_mid, UOoP_bot:	top, mid-, and bottom node out-of-plane displacement of the URM infill panel relative to the ground.
δOoP_t:	OoP relative displacement at each time step (according to Kadysiewski and Mosalam 2009) $\delta_{OoP\_t} = \left( {U_{OoP\_mid } } \right) - 0.5\left( { U_{OoP\_top} + U_{OoP\_bot } } \right)$