The well-being of society can be severely impacted by infrastructure disruptions. This study proposes a novel mathematical model to estimate the societal impact of water disruption quantitatively from two aspects: the percentage of people who can perform certain water-related activities and the percentage of people intolerant to disrupted activities. The model begins by incorporating the tolerance level (TL) to establish a suffering level function of the disrupted activity. Then, from the individual's perspective, an activity estimation model is developed to predict an individual's activity choices when water is limited due to infrastructure disruptions, and this model is mainly driven by prioritizing activities with the maximum suffering level. To quantify the societal impact in regions, a Monte Carlo simulation is adopted to generate simulated residents with randomly sampled TL following lognormal or Weibull distributions, and the activity estimation model is conducted for each simulated resident; consequently, societal impacts can be aggregated and derived. Additionally, an illustrative case study of Osaka and sensitivity analyses are performed; the results validate the model's effectiveness and applicability. The proposed model provides insightful information to support emergency management and can be integrated with infrastructure resilience models to better build human-centric sustainable and resilient cities.