The 2016 Kumamoto earthquake (main-shock: M_w 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.

2016年熊本地震（主震：M _w7.0，4月16日）在整个灾区引发了生命线系统的广泛破坏。在宇气市（日本熊本县），断断续续地供水了几天：结果，市政部门对地下管道系统的各个位置进行了约50次维修。为了更好地限制此类基础设施在未来地震中的脆弱性，利用收集到的经验数据得出了小直径（小于100毫米）延性管道（延性铁和聚氯乙烯）的修复率函数。由于在有限的地震烈度范围内数据点数量相对较少，纯经验损坏函数的推导似乎受到很大的统计偏差。因此，采用贝叶斯更新框架，其中从文献中现有的损伤函数中估算出修复率函数参数的先验信息。此外，通过以下方式考虑了与管道位置处的峰值地速特征相关的不确定性：（i）在地面运动预测方程或断层模型上具有不同假设的振动图的生成，以及（ii ）包含事件内抖动映射误差项的空间相关字段（即，地震强度固有变化的建模）。结果表明，所推导的维修率方程与延性和抗震管段的某些现有函数一致。还研究了特定土地条件（例如地形/地质因素）的影响，有可能进一步参数化修复率功能。最后，将开发的损伤函数应用于水网抗震性能的随机模拟，同时跟踪各种不确定性来源并量化其对系统损失分布的影响。