# Ultimate Compressive Strength of H-Section Stub Columns Subject to Random Fitting Corrosion Damage
## 2 Numerical Modelling of H-Section Columns
### Validation of Numerical Models  
In this section, the numerical models of pitted H-section stub columns were validated against the test results [24]. The experiments involved axial compression tests on perforated steel H-section stub columns, where the presence of perforations signifies severe pitting corrosion damage. The detailed material and dimensional information of the tested columns were introduced in the above section. Six of the columns were retrieved, each of which had three identical circular holes regularly and equidistantly assigned on the column web. The diameters of the openings of the six columns were 40, 50, 60, 70, 80 and 90 mm,  
Figure 4: Schematic diagram of corrosion pattern of H-section columns: (a) single-flange corrosion (SF); (b) double-flange corrosion (DF or AF); and (c) web corrosion (W). respectively. Additionally, the distance between the center of the first opening to the column bottom (designated as DI) was 112 mm. Each column was assigned a label to indicate its size information, including the dimensions of each section and its opening. For example, H11.5 \(\times\) 7.5\(-\)D70\(-\)D112 represented an H-section column with a flange thickness (\(t_{f}\)) of 11.5 mm, a web thickness (\(t_{w}\)) of 7.5 mm, a circular hole diameter of 70 mm and a distance (DI) of 112 mm. For the initial study of the mesh convergence of finite element models, a tested column with a moderate-sized (70 mm) hole (H11.5 \(\times\) 7.5\(-\)D70\(-\)D112) was selected, since the test results, such as test load and failure mode, of this kind of column has been reported in detail, making it convenient for the validation. Figure 5 demonstrates the load-displacement curves and ultimate loads of the column under different mesh sizes. It is evident that there was no significant difference observed in the load-displacement curves when the mesh size was less than 16 mm, and convergence appeared with the decrease in mesh size. Notably, for mesh sizes of 4 and 6 mm, the ultimate loads were nearly identical, but the former resulted in an approximately three-times-longer computing time than the latter. Specifically, it took approximately 45 min to compute the 4 mm meshes, while it took about 15 min for the 6 mm meshes (these calculations were performed on a personal computer equipped with a 12 th Gen Intel(r) Core(tm) i5-12600K processor and 16 GB of RAM). However, a finer mesh allows for a more detailed representation of corrosion pits. As a result, a relatively fine mesh with a size of 6 mm was adopted for following numerical analyses. In Figure 6, a comparative study between the results of tests and numerical analyses of the six tested columns was illustrated, focusing on the ultimate loads, load-displacement curves, and typical failure modes. Figure 5(a),b reveal the significant impact of the opening size in H-section columns on their ultimate load and load-displacement behavior. It is observed that larger opening sizes correspond to lower ultimate loads. For example, with an opening size of 40 mm, the perforated column demonstrated an ultimate load of 1966 kN, resulting in a reduction in strength of approximately 1.5% compared to the intact column. As the opening size increased to 70 mm, the strength reduction reached approximately 6.8%, with an ultimate load of 1860 kN. Similarly, for a 90 mm opening, the strength reduction increased to around 10.8%, with an ultimate load of 1780 kN. Moreover, Figure 5(a) indicates that the maximum relative error between the numerical models and experimental results for the ultimate loads of the six columns was less than 5.3%. The numerical models exhibited a slight underestimation of the test results, which is consistent with the findings of the original paper [24]. Several factors may contribute to this discrepancy, including the absence of residual stress and a significant but imprecisely measured initial geometric deflection being incorporated into the numerical models. Figure 5: Mesh convergence study: (**a**) load–displacement curves; (**b**) ultimate loads and computing time.