5 5.5. Discussion, conclusions and future work 119 For cracks (BAB), complex degradation patterns are observed, with DTMCs not fully capturing these changes (e.g., Cohort CMW in Figure 5.2(c)). It is also unlikely to find cracks in states k =2,3,4†. For infiltration (BBF), Figure 5.2(d) shows an initial probability of roughly 25% for pipes in Cohorts CMW and CR to experience at least mild infiltrations (i.e., k>1). Comparing Cohorts PMW and PR Figure 5.2(f) shows that Cohorts PMW(PVC pipes carrying mixed and waste content) and PR (PVC pipes carrying stormwater) exhibit similar patterns under surface damage (BAF), with a maximum expected severity of k <2 over 125 years. No significant di!erences were found between these cohorts for cracks and infiltration†. Comparing Cohorts CdL and CdG Figure 5.2(g) compares Cohorts CdL (Concrete pipes, width<500 mm) and CdG (Concrete pipes, width⇒500 mm). Narrow pipes show more severe surface damage (BAF) than wider ones. The same pattern is observed under cracks (BAB)†. For infiltration (BBF), wider pipes tend to reach severe states faster, though with considerable uncertainty†. Comparing Chains “Multi” and “Single” When comparing Chains “Multi” and “Single”, we generally observed no significant di!erences. However, for certain cases, such as Cohort CdG and surface damage (BAF) in Figure 5.2(h), Chain “Single” transitions to more severe states faster than Chain “Multi” when PipeAge >60 years (see Pij in Figure 5.1, ∆t =3 years). We hypothesise this occurs because Chain “Multi” may converge towards diagonal values in Pij close to 1 (e.g., Figure 5.1(a), p3,3 =p4,4 =0.9999), making these states nearly absorbing, a behaviour not seen in Chain “Single” (Figure 5.1(b)). 5.5 Discussion, conclusions and future work We model sewer main deterioration in a large-scale case study in Breda using Discrete-Time Markov Chains (DTMCs). We describe a methodology to calibrate DTMCs and visually† compare deterioration patterns across cohorts (groups of sewer mains with similar characteristics) for three damage types: infiltration, surface damage, and cracks. Our DTMCs e!ectively project and estimate future deterioration states of sewer mains, enabling comparisons across cohorts, such as expected severity classes. For instance, we conclude that concrete pipes carrying mixed and waste content †All comparative figures and scripts are available at zenodo.org/record/6535853
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