## 1 Introduction  
Large-span bridges have been widely adopted because of their great crossing ability [1; 2; 3]. The saddle structure is an important part of a large-span suspension bridge as it helps to realize the large span and crossing function [4; 5]. It is used as the main support component for the suspension cable or diagonal cable to pass through the top of the tower and transfer the cable force. It plays an important role in reasonably reducing the maximum bending moment at the bottom of the tower, effectively adjusting the load-carrying capacity of the tower and the scale of the foundation, as well as equalizing the cable force of the main cable [6]. At present, the main saddle structure used in large-span bridges can be divided into an anti-slip saddle and a rolling saddle. The anti-slip saddle is generally set up as an anti-slip device in the saddle balance system, to avoid the slip phenomenon in a suspension cable or cable-stayed cable during the bridge operation process [7]. The rolling saddle is optimized and designed based on the anti-slip saddle structure. A row of rollers is set below the saddle base, which changes the original form of friction from sliding friction to rolling friction, and leads to the automatic equalization of the cable system [8]. To date, many researchers have carried out several in-depth studies and research on the anti-slip function of the cable saddle [9; 10; 11; 12]. [PERSON] et al. [13] proposed a combination of horizontal and vertical friction plates in the saddle groove and investigated the anti-slip problem between the saddle and the main cable in the main tower saddle of the Wenzhou Oujiang Beikou Bridge in China. [PERSON] et al. [14] set polytetrafluoroethylene (PTFE) slip plates on the lower part of the tower saddle body on both sides of the Jinan Phoenix Yellow River Bridge and the top fixed joint of the cable tower to reduce the top thrust friction resistance. They were also lubricated to adapt to the relative positional difference generated in the construction process. In the test study of the friction coefficient between the main cable and the cable saddle, the field bridge test values of the friction coefficient of the George Washington and Forth Road bridges in America are 0.3 [15]. The test result of the Delaware River bridge is between 0.19 and 0.21. The test value of the Kanmon bridge in Japan is between 0.15 and 0.21. The test value of the Honshu-Shikoku bridge is between 0.16 and 0.44 [16]. Researchers at Southwest Jiaotong University tested the friction coefficients between different numbers of strand bundles and test saddles through model tests, and the friction coefficients of ordinary saddles and those setting vertical friction plates were found to be 0.473 and 0.552, respectively [17]. For research into a new rolling saddle, [PERSON] et al. [18] analyzed its internal force in Wanxin Bridge, and the results showed that the wall thickness of the saddle should not be too large, and especially the radius of the inner tangent circle of the saddle groove part should not be too large. In the outdoor test simulation of the main bridge of the Jinshajiang River Bridge over Tiger Leaping Valley, it is confirmed that in the case of unbalanced cable force, the saddle can be rolled using the roller shaft to achieve the adjustment of the two ends of the cable force [19]. The cable force system tends to be balanced through the bias load test of the saddle structure. To ensure the anti-slip safety of the main cable in the main saddle of a long-span suspension bridge, contact and slip behaviors of the main cable of a long-span suspension bridge were investigated [20]. From the above research, it can be seen that there are differences between the slip-resistant saddle structure and rolling saddle structure in many aspects, which has an important impact on the structural force system and service performance of large-span bridges.