# A Review of Prediction Methods for Ultra-Low Cycle Fatigue Damage of Steel Piers Under Earthquakes
## 1 Introduction  
Steel structure bridges are known for their lightweight, high strength, compact area, and low energy consumption [1, 2]. As steel production and labor costs rise, the advantages of steel bridges become more apparent. Recently, the number of steel bridges in China has increased significantly [3, 4]. When compared to traditional reinforced concrete piers, steel bridge piers offer high strength, excellent seismic performance, and rapid construction, making them widely utilized in the United States, Japan, and Taiwan [5, 6]. With China's rapid economic growth and rising seismic performance standards for steel bridges, the application of steel bridge piers is expected to expand further. Despite their benefits, steel piers remain vulnerable during earthquakes [7]. Past seismic events have shown that steel bridge piers primarily suffer from the local buckling failure of the steel plates near the bottom [8] and ultra-low cycle fatigue failure at welded joints [9]. There are three main reasons for the local buckling of the pier. First, the earthquake causes the horizontal movement of the pier, which causes the axial force at the top of the pier to become the eccentric axial force. Second, ground motion causes the resonance of the bridge pier, which changes the shape of the pier. Finally, the material becomes less strong in earthquakes. Notably, thick-walled steel bridge piers may experience ultra-low cycle fatigue failure prior to local buckling, representing a typical mode of seismic damage. Under the action of earthquakes, steel piers are not only subjected to axial load, but also to horizontal seismic load. Therefore, the welded joints of steel piers are subjected to axial force, horizontal shear force, and bending moment simultaneously, placing them in a complex stress state. For instance, during the 1995 Kobe earthquake in Japan, complex stress states at the joints of many steel piers led to ultra-low cycle fatigue failures, as illustrated in Figure 1 [9; 10]. Due to the characteristics of temperature transfer, the welded joints have obvious gradient distribution of mechanical properties [11], which has an adverse effect on the fracture properties of welded joints. So far, researchers both domestically and internationally have extensively studied local buckling in steel plates and ultra-low cycle fatigue failure in welded joints. They have effectively addressed the local buckling issues by implementing longitudinal stiffeners, increasing plate thickness, and infilling concrete at the bases of steel bridge piers [12; 13; 14; 15; 16]. Recently, scholars identified ultra-low cycle fatigue failure as a failure mode characterized by high strain levels and fatigue lives ranging from just a few cycles to even less than ten. This mode is different from low cycle fatigue failure [17; 18; 19]. Through various studies on the failure mechanisms of ultra-low cycle fatigue and low cycle fatigue in steel, researchers have clarified that ultra-low cycle fatigue failure is fundamentally different. It is primarily a ductile failure, while low cycle fatigue failure tends to be brittle. In 2006, [PERSON] [20] and [PERSON] [21] observed, using scanning electron microscopy of the fracture surface (Figure 2), that cracks resulting from ultra-low cycle fatigue failure exhibit bluntness, noticeable width, and significant opening. The fracture surface displays distinct ductile dimples, indicating a ductile failure morphology. In contrast, cracks due to low cycle fatigue failure are sharp, narrow, and deep, typically resulting in a cleavage fracture indicative of brittle failure. Based on the characteristics of ductile failure in steel, [PERSON] et al. [22] in 2005 and [PERSON] et al. [17] in 2007 proposed the microvoid coalescence fracture mechanism to explain the microscopic processes involved in ultra-low cycle fatigue failure. The research on the mechanism of ultra-low cycle fatigue failure in structural steel reveals that this failure is characterized by ductile cracking [23].