# A Review of Prediction Methods for Ultra-Low Cycle Fatigue Damage of Steel Piers Under Earthquakes
## 2 Research Status and Development Trend at Home and Abroad
### Seismic Performance and Seismic Response Calculation Model of Steel Pier
#### 2.5.2 Seismic Response Calculation Model of Steel Bridge Pier  
The primary seismic failure modes of steel piers include local buckling of steel plates and ultra-low cycle fatigue failure of welded joints. To address local buckling while ensuring calculation efficiency and accuracy, most researchers use shell elements to model the local buckling zones of steel piers and beam elements for other undamaged areas. This method has demonstrated effectiveness in calculating the seismic response and horizontal bearing capacity of steel piers [86; 87]. However, simulating the ultra-low cycle fatigue failure of welded joints presents challenges, particularly in modeling fatigue crack propagation. As a result, the current seismic response calculation models for steel bridge piers often overlook the influence of crack propagation. This leads to discrepancies between the displacement hysteresis curve and skeleton curve of the steel bridge pier during the crack propagation stage and the corresponding experimental results [83].  
The coexistence of ultra-low cycle fatigue failure in welded joints and local buckling failure in steel plates is common. The sequence of these failures is unpredictable, and their interaction affects the seismic response of steel piers. For instance, in 2012, [PERSON] et al. conducted various reciprocating displacement load tests on nine unstiffened box steel piers. They discovered that most thick-walled pier specimens developed fatigue cracks before experiencing local buckling. Notably, horizontal loads had not reached their maximum when these cracks appeared [39]. In 2019, [PERSON] et al. performed quasi-static tests on two box-type steel bridge piers. Their findings indicated that welded joints underwent ultra-low cycle fatigue cracking following the local deformation of the steel plate. Once the cracks grew to a certain length, the structural bearing capacity decreased [81].  
Using mixed-element models is necessary to improve computational efficiency during the seismic analysis of steel bridge piers. This model requires the use of beam or plate shell elements in regions wherein ultra-low fatigue damage has not occurred and that of solid elements in regions wherein ultra-low cycle fatigue damage has occurred. The CDM programs representing ultra-low cycle fatigue damage are written in programming software, such as FORTRAN. Subsequently, the damage attributes are assigned to solid elements in finite element software, such as ABAQUS 6.14. Finally, the ultra-low cycle fatigue damage of steel bridge piers is calculated on the basis of multiscale models. The CDM model is successfully applied to predict the ULCF damage of steel beam-to-column connections [88].  
In summary, current predictions for ultra-low cycle fatigue damage in steel bridge piers, based on crack initiation, lack accuracy. The predictions vary depending on the seismic performance evaluation indicators and seismic response calculation models for steel bridge piers. Existing models do not account for the effects of ultra-low cycle fatigue crack propagation and their interaction with local buckling, limiting their theoretical applicability in predicting damage.