## 1 Introduction  
Timber structures have been widely used in the construction of palaces, temples, and civil dwellings in ancient China because timber is very easy to obtain and process. The famous Buddha Tower, also known as YingXian Timber Tower, is a typical traditional Chinese timber structure as shown in Figure 1. It can be seen that the tower was erected by columns, beams, and bracket sets [1]. Timber frame, consisting of beams and columns, is the basic structural component and also the structural skeleton of the timber structures. The columns and beams are connected by the mortise-tenon joints, and two typical types of the joints are presented in Figure 2.  
Figure 1: The Buddha Tower. Tamber frame is the main component of resisting the lateral force such as earthquake actions and strong winds. Therefore, the mechanical properties of the timber frame, especially the mortise-tenon joints, have prominent effects on the seismic performance of the whole structures [2]. [PERSON] et al. [3,4] carried out some pseudo-static tests and shaking table tests on timber structures with mortise-tenon joints and found that most of the input energy is dissipated by the mortise-tenon joints. [PERSON] et al. [5] used a synchronous loading technique to study the hysteresis behavior of a full-scale Chinese timber structure and revealed the effects of vertical loads and gaps in the mortise-tenon joint. Some tests on the timber frame with straight mortise-tenon joints [6,7] or with dovetail joints [8, 9, 10, 11] have been conducted and the pulling-out of the tenon were frequently observed. [PERSON] [12] studied the seismic and lateral resistance of column-and-tie wooden buildings, the global slip of the framework and the slip of the column footing were observed. [PERSON] et al. [13] used multi-scale modelling method to simulate a timber frame with mortise-tenon joints and received good results. Some analytical models were proposed [6,7] and can predict the hysteresis behavior of the timber frame. [PERSON] et al. [14] studied the moment-rotation angle curve of aluminum alloy mortise-and-tenon joints, and proposed a hybrid beam element model which can well reflect the semi-rigid characteristics of the joints. Most of these experiments and numerical simulations are based on the intact timber structure specimens or models. However, in real situation, the damage of the mortise-tenon joint is often encountered in timber frame, especially in the ancient structures. Two typical damages of the mortise-tenon joint are shown as follows: (1) Gap between the mortise and tenon (Figure 3a); (2) defect in the tenon (Figure 3b). Traditional timber frames often undergo lateral displacement during the action of earthquake or strong wind [15,16], which will lead to a gap between mortise and tenon in the longitudinal direction of the beam. Besides, in some moist districts, the tenon may suffer from fungi or termites and eventually become incomplete. These adverse influences are likely to weaken the connection between the beam and the column and hence reduce the seismic resistance of the frame. To study the influence of damage caused by termites and fungi, different types of holes were drilled in the dovetail and straight mortise-tenon joints, and the results compared with the intact joints revealed that these damages can significantly influence the seismic performance of these joint [17,18]. [PERSON] et al. [19,20] carried out some tests on the through-tenon joints and dovetail joints by cutting the tenon size to simulate looseness, and the hysteresis behavior of these joints was remarkably affected. [PERSON] et al. [21] conducted the low-cycle reciprocating load test on the straight-tenon joint wood frame with column foot damage, the results showed that this damage can decrease the fullness and peak of the hysteresis curves as well as the energy dissipation ability of the frame. Figure 2: Timber frame with mortise-tenon joints: (**a**) Straight joint; (**b**) dovetail joint.