## 1 Introduction  
Unreinforced masonry (URM) buildings are the most representative construction system since the early ages of mankind. The increasing interest in this construction technique in the last few decades has resulted in many experimental tests on URM subassemblages [1; 2; 3; 4; 5] and on complete URM buildings [6; 7; 8; 9; 10; 11; 12]. These studies have provided significant valuable insights into the seismic performance of URM buildings. However, many characteristics of URM buildings are yet to be fully understood, and URM buildings are always severely damaged when an earthquake occurs [7; 8; 10; 11; 12]. On the other hand, most masonry buildings are less than three-story, and most of them are constructed without the consideration of earthquake design requirements or reference to any design code [13; 14; 15; 16; 17; 18]. According to experimental studies on two-story masonry buildings conducted in the United States [4; 19; 20], URM walls exhibited a ductile behavior with a clear yield point and constant strength after yielding, even though no reinforcing bars were used. In the experimental studies by [PERSON] et al. [21] and [PERSON] et al. [22], deformation capacities of masonry walls with aspect ratio \(h/l\) (\(h\): wall height, \(l\): wall length) of 0.67 to 1.33 and 0.75 to 2.25 were found to be 2.0% to 5.0% and greater than 1.5 % of the lateral drift angle, respectively. Such ductile behavior of URM walls appears when the walls fail by rocking behavior or bed joint sliding behavior, from Figure 1 below. Based on these experimental results, in various seismic performance design guidelines [23; 24; 25],deformation-dominant hysteresis models in nonlinear analysis are allowed for the rocking and bed joint sliding failures of URM walls. The representative failure modes of URM walls resisting in-plane lateral loads are divided into four types, as shown in Figure 1: (a) rocking failure mode, (b) toe crushing failure mode, (c) bed joint sliding failure mode, and (d) diagonal tensile failure mode. The rocking failure mode and the bed joint sliding failure mode can be categorized as the ductile failure mode, as mentioned in the previous paragraph, whereas the toe crushing failure mode and the diagonal tensile failure mode can be categorized as the brittle failure mode [13; 26; 27; 28]. The dominant failure mode of a URM wall depends on the aspect ratio of the wall, the material properties of the masonry unit and the joint mortar, and the axial load. According to the study by [PERSON] et al. [29], since the axial load is generally not high in one- or two-story masonry buildings, the dominant failure mode of URM walls is mainly determined by the aspect ratio of the wall; the rocking failure or toe crushing failure are dominant at an aspect ratio greater than 1.8, and the bed joint sliding failure mode is dominant at an aspect ratio less than 1.8. In particular, the walls in low-rise masonry buildings have various openings such as doors and windows. Therefore, since the aspect ratios of most masonry walls with openings exceed 1.5, the walls in low-rise masonry buildings with openings mainly show the rocking failure or toe crushing failure. On the other hand, the toe crushing failure generally occurs at the compression end of walls after the rocking failure [19]. In addition, the toe crushing failure for a masonry wall with low axial load is defined as residual behavior after rocking failure in nonlinear analysis, according to ASCE 41-17 [25]. Therefore, it is important to understand the in-plane rocking behavior occurring in URM walls, and to quantitatively evaluate the strength, stiffness, and deformation capacity for the in-plane rocking behavior in order to reasonably assess the seismic performance of low-rise masonry buildings. Figure 1: Representative failure modes of unreinforced masonry wall: (**a**) rocking failure mode; (**b**) toe crushing failure mode; (**c**) bed joint sliding failure mode; (**d**) diagonal tension failure mode.