## 1 Introduction  
Half-through and through concrete-filled steel tubular (CFST) arch bridges are broadly exploited in China, and as their service life grows, the high-strength steel suspenders (referred to as suspenders) [1] connect the bridge deck system to the arch ribs break more frequently for various reasons. Some bridges have suffered from serious accidents due to the lack of robustness of the suspension deck system, leading to bridge collapses and even car damage. For instance, in 2001, the Xiaonanmen Bridge in Yibin, Sichuan collapsed due to the fracture of short suspenders at both ends [2]. In 2011, a bridge deck collapsed because of the fracture of the second suspender of the main span of the Kongque River Bridge in Korla, Xinjiang [3], and in 2019, a bridge collapsed continuously as a result of the fracture of the sixth suspender from the right of the Nanfang'ao Cross Harbour Bridge in Taiwan [4]. According to the structure and force characteristics of CFST-base arch bridges, the suspension deck system can be divided into three major types, as demonstrated in Figure 1. The first type of deck system is often utilized in the arch girder combination system, whose robustness is best. The second type of deck system is supported by a crossbeam with a stiffened longitudinal beam, which has better robustness. The third type of deck system is without a longitudinal beam, whose robustness is the worst [5]. The third type of bridge deck system is mostly employed in several half-through and through arch bridges with suspender-breaking accidents. According to the learned experiences and lessons from China's engineering practice, the Technical code for concrete-filled steel tubular arch bridges [6] states that the third type of bridge deck system is no longer allowed. In fact, it is stipulated that such a system should be appropriately strengthened and reconstructed according to the service conditions of the bridge. However, due to the lack of sufficient theoretical basis and specific calculation methods, the existing bridge design codes also lack specific requirements on the relevant robustness design theory and calculation methods; hence, the robustness design of suspension deck systems for half-through and through arch bridges is limited to conceptual design. In recent years, the problem of bridge deck collapse caused by broken suspenders of the half-through and through CFST-base arch bridges has also attracted extensive attention from researchers. [PERSON] suggested that the continuous collapse analysis method, similar to that of suspension bridges, should be employed to examine the suspender breakage of half-through and through arch bridges [7]. There are some people who exploited the finite element method (FEM) to analyze the static and dynamic responses of the remaining structures when different suspenders were broken. Further, the effects of load, damping ratio, and suspender breaking time on the dynamic characteristics of suspender breaking were taken into account [8; 9; 10; 11; 12]. Additionally, the other scrutinized the suspender fracture process and bridge structure failure mode by implementing the FEM. It was revealed that the robustness of the suspension bridge deck system of the through CFST arch bridge is the main reason to prevent severe consequences such as beam falling after suspender breaking, and then the safety of the corresponding bridges was evaluated [13; 14; 15; 16]. [PERSON] and [PERSON] carried out the scale specimen test of tied-arch bridges to examine the influence of single suspender fracture on the residual suspender internal force of tied-arch bridges [17; 18]. To sum up, at present, scholars often use static and dynamic FEMs or specimen tests to analyze the suspender failure of half-through and through arch bridges.