Current approaches to assess the reliability and resilience of water infrastructure subject to seismic hazard typically use Repair Rate (RR) curves for the linear elements (pipelines), which estimate the expected number of repairs needed per unit length after the occurrence of an earthquake of a given intensity. The available RR curves are characterized by high levels of uncertainty being based primarily on expert judgment and on limited data. Also, they provide no distinction between the damage on the segments and on the joints. This paper develops probabilistic physics-based RR curves to quantify the damage to segmented pipelines due to earthquakes. First, a mechanical model for segmented pipelines is proposed. The model is then used to generate a set of synthetic data for the calibration of the model parameters. We compare the proposed RR curves with the ones available in the literature and discuss the advantages of the proposed model.