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The 2016 Kumamoto earthquake (main-shock: Mw 7.0, April 16th) has induced a widespread disruption of lifeline systems across the affected area. In Uki City (Kumamoto prefecture, Japan), water supply had been intermittently cut off for several days: as a result, around 50 repair operations on various locations of the underground pipeline system have been carried out by municipal services. In order to better constrain the vulnerability of such infrastructure with respect to future earthquakes, the collected empirical data is exploited to derive repair-rate functions for ductile pipelines (ductile iron and polyvinyl chloride) of small diameter (less than 100 mm). Due to the relatively low number of data points over a limited range of seismic intensity, the derivation of purely empirical damage function appears to be subject to significant statistical biases. Therefore, a Bayesian updating framework is adopted, where prior information on the parameters of the repair-rate function is estimated from existing damage functions from the literature. Moreover, the uncertainty related to the characterization of the Peak Ground Velocity at the location of the pipelines is taken into account by: (i) the generation of shake-maps with different assumptions on ground-motion prediction equations or fault models, and (ii) the inclusion of a spatially correlated field of the intra-event shake-map error term (i.e., modelling of the inherent variability of the seismic intensity). The results show that the derived repair-rate equation is consistent with some existing functions for ductile and earthquake-resistant pipeline segments. The effect of specific land conditions (e.g., topographic/geological factors) is also investigated, with the possibility to further parametrize the repair-rate function. Finally, the developed damage functions are applied to stochastic simulations of the seismic performance of the water network, while keeping track of various sources of uncertainties and quantifying their impact on the system's loss distribution. [ABSTRACT FROM AUTHOR]