## 3 Framework Development
### Analysis of Corrosion-Induced Degradation  
After assigning the mechanical parameters to the models and applying the boundary conditions, each model was subjected to increasing shear stress until failure. Crack patterns were observed at the capacity stress level during the structure's lifecycle, captured at each time interval on the surface where the rebar appears as circular features, illustrating the various stages of this process. Figure 5 illustrates the progression of cracking on the concrete surface surrounding the rebar at various stages in the structure's life cycle, with the estimated cracking relative to the total cross-sectional area increasing over time. Using the areal fracture intensity method, we quantified the extent of fracturing to assess its impact. Using the measurement technique, developed by [72], to quantify fractures in discrete fracture analysis. The intensity of the areal fracture, denoted as \(P_{21}\), is the ratio of the total length of the fracture traces to the cross-section (see for a schematic measurement of the fracture trace). Figure 6 shows that in the initial stages (t = 0-30 years), \(P_{21}\) is 0.000469 mm/mm\({}^{2}\), indicating minimal cracks. As time progresses (t = 50 years), early-stage cracking increases to \(P_{21}\), reaching 0.0154 mm/mm\({}^{2}\), showing visible cracks forming around the rebar. By the mid-stage of the structure life cycle (t = 60 years), the cracking extends further from the rebar \(P_{21}\), increasing to 0.0255. In the advanced stage (t = 70 years), the cracks spread significantly, with \(P_{21}\) reaching 0.0538 mm/mm\({}^{2}\). This trend continues into the severe stage (t = 90 years), where the cracking area grows to \(P_{21}\) = 0.073 mm/mm\({}^{2}\), reflecting severe structural degradation due to ongoing corrosion and mechanical stress. Figure 5: Crack patterns at different stages of the structure’s life cycle under capacity stress are shown at 10 years, 30 years, 50 years, 70 years, and 90 years. On the free surface, in the shear direction, shear cracks are observed, as depicted in Figure 7.  
Figure 7 depicts the development of these shear cracks on the free surface in the shear direction, distinct from the corrosion-induced cracking visible on the cross-section where the rebar appears as a circle. Next, we evaluated the shear capacity for each model from the resulting shear stress-displacement curves. The models represent different stages in the structure's lifecycle, where the shear capacity at time \(\text{t}_{\text{i}}\) and \(\text{t}_{\text{i+1}}\) was divided by the shear capacity at t = 0, thereby determining the deterioration of capacity over time, as depicted in Figure 8.  
Figure 8: Deterioration patterns in the shear capacity of the structure over time for different corrosion intensities. Figure 6: Schematic representation of fracture trace measurement. Figure 7: Shear crack development on the free surface in the shear direction. Figure 8 illustrates the degradation of shear capacity over time for a wall subjected to a seismic event, considering three different levels of corrosion: intensive, moderate, and minor. The results demonstrate a clear trend of decreasing shear capacity as corrosion advances, with the reduction rate varying significantly across corrosion levels, ranging from a 20 percent reduction to an over 80 percent loss in capacity at 120 years. As the primary purpose is to achieve material degradation while keeping the simulations feasible, we implemented several simplifications in the modeling approach. We modeled only a small section out of the wall, reducing computational expense while providing insights into shear capacity and localized corrosion effects. Although the direct impact of the reinforcing steel on the concrete's structural behavior was ignored, the steel's corrosive pressure action on the concrete was accounted for, recognizing its significant role in the degradation process.