# Ultimate Compressive Strength of H-Section Stub Columns Subject to Random Fitting Corrosion Damage
## 2 Numerical Modelling of H-Section Columns
### Randomly Pitted H-Section Columns  
According to the requirements of current specifications for corrosion inspection, the normal inspection can present a set of statistical data of pitting corrosion but not detailed corrosion map, usually including the mean values of the pit diameter and depth, \(\mu_{D}\) and \(\mu_{d}\), their standard deviations, \(\sigma_{D}\) and \(\sigma_{d}\), and the maximum values, \(D_{max}\) and \(d_{max}\). The degree of volume loss of corroded material, \(DOV\), is a key parameter that characterizes the pitting intensity of a corroded column, defined as:  
\[DOV=\frac{\Delta V}{V_{0}}\times 100\ \% \tag{1}\]  
where \(\Delta V\) represents the volume of corroded material caused by pitting corrosion, and \(V_{0}\) is the original volume of one intact plate of a column. Figure 2 illustrates the flowchart of numerically modelling the randomly pitted H-section columns. Figure 1: Steel columns with random pitting corrosion in a marine environment [9]. (**a**) Tubular section; (**b**) H-section. A set of pit data (\(N\)) with a random diameter and depth was firstly generated via the simple random number method, which follows a certain probabilistic distribution, such as the normal, log-normal or Weibull distribution. Note that the probabilistic models for the pit size (diameter and depth) are highly dependent on the stage of corrosion evolution in a specific marine environment, and they change according to the simulated environment. For each pit generated above, its shape was also randomly decided to be circular, conical or hemi-ellipsoidal in order to reflect the random nature of pit shape in actual corrosion. One pit of random size and shape was sequentially selected, and its volume was superposed onto the cumulative volume of corrosion pits, \(\Delta V\), until the target degree of volume loss of corrosion damage, \(DOV_{t}\), was reached, and then \(n\) (\(n<<N\)) pits with random diameter, depth and shape were determined. This was followed by the determination of the location of each of the pits. The random coordinates (\(x\), \(y\) and \(z\)) of each pit on the H-section columns were decided using the simple random number method, each of which was constrained on the column web or flanges. It is noteworthy that the coalescence of corrosion pits was not taken into account, because such pits can be modelled as one pit [23]. The aforementioned procedures to generate random pits can be implemented using any  
Figure 2: Flowchart of modelling the randomly pitted H-section column. finite element software package with a user-oriented secondary development function, such as ANSYS and ABAQUS, and the former was adopted in this paper. The corrosion data from the real plates [22] show that the mean and maximum diameters of the pits were \(\mu_{D}\) = 21.84 mm and \(D_{max}\) = 30.91 mm, respectively, and the mean and maximum depths of the pits were \(\mu_{d}\) = 3.04 mm and \(d_{max}\) = 4.89 mm, respectively. The diameter-to-depth ratios of the pits varied in the range from 4:1 to 8:1. The probabilistic models for the pit size (the diameter and depth of pits) were assumed to be normal distributions herein, and their standard deviations were decided to be 3.0 and 0.6 mm, respectively, based on the \"3\(\sigma\)\" principle indicating that the value of the pit size is within the range of \(\mu\pm 3\sigma\) by 99.7%. Five hundred random pits were generated to ensure that the target pitting intensity can be simulated in randomly pitted columns, as shown in Figure 3a,b. The FE element, SOLID 187, in ANSYS software was used to construct the finite element model of H-section stub columns with random pitting corrosion. Figure 3c,d display the size scheme of H-section and the numerical model of a randomly pitted column. Corrosion pits were involved on one side of the plate element, since the plate element has more adverse influence on the compressive strength and behavior of pitted plates because of extra bending induced by the thickness deviation in corroded areas.