# Deterioration Model for Corroded Circular Columns
## 1 Introduction  
A hysteretic model capable of capturing structural component deterioration is required for the study of the seismic performance of structures. The Ibarra-Medina-Krawinkler (IMK) plastic hinge model was initially introduced by [PERSON] et al. [1] [PERSON] et al. [2] proposed the modified IMK (ModIMK) model to address asymmetric component hysteretic behavior. Compared to alternative models [3], it is extensively utilized due to its good ability to efficiently simulate hysteretic characteristics.  
Nonlinear analytical models for reinforced concrete components under earthquake ground motions are usually based on either \"mechanics\" or \"phenomenological\" laws [4; 5; 6; 7]. The most typical mechanics-based model is the fiber model, the accuracy of which depends mainly on the definition of the constitutive laws of concrete and steel. In the case of serious damage, the deterioration in the component performance is associated with phenomena such as concrete crushing, reinforcement buckling, fracture, or slippage, and it is difficult to simulate the deterioration in the component performance in the fiber model due to the complex interaction of the geometric and material properties. The ModIMK model, on the other hand, is based on \"phenomenological\" laws, which describe the nonlinear behavior of the component in a simple moment-rotation form; the deterioration in the component's performance can be empirically simulated based on statistical analysis of a large amountof test data, and its computational speed is much faster than the fiber model. Due to its superiority, the ModIMK model is recommended by ASCE 41.  
By calibrating the model parameters of the components and subsequently regressing to derive the empirical equations for the model parameters, it is possible to make relatively accurate predictions regarding the hysteretic models of similar components [8; 9; 10]. Based on a test database for reinforced-concrete (RC) square columns failing in flexural or combined flexure-shear mode, [PERSON] et al. [11] calibrated the IMK model's parameters and derived the empirical equations for the model parameters. [PERSON] et al. [12; 13] created a database of steel and RC structural columns, modified the IMK model, and obtained prediction equations for the model parameters. [PERSON] et al. [14] gathered test data for corroded RC square columns, performed a calibration study for the ModIMK model parameters, and established model parameter prediction equation for corroded columns. [PERSON] et al. [15] developed a database of corroded concrete columns retrofitted with FRP (fiber-reinforced polymer) and determined its ModIMK model.  
The research above focuses primarily on reinforced-concrete square columns, whereas circular columns, which are extensively utilized in the fields of building engineering and bridge engineering, have received relatively little attention. [PERSON] et al. [16] collected test data for circular columns failing in flexural or combined flexure-shear mode, investigated the process for calibrating the parameters of the ModIMK model, and obtained prediction equations for each parameter. As for the calibration and prediction studies on the parameters of the ModIMK model for corroded circular columns, the authors of this work have not found any literature on the subject so far.  
Therefore, 35 sets of test data related to corroded circular columns were collected [17; 18; 19; 20; 21; 22; 23; 24; 25; 26]. After calibrating the model parameters for all the columns in the database, a set of empirical equations related to the model parameters was obtained using linear regression. Using this set of equations, a prediction method for the ModIMK hysteresis model was created. This prediction method allows the ModIMK hysteretic model to be applied to the seismic performance study of structures containing corroded circular RC columns.