Social media platforms have become fundamental tools for sharing information during natural disasters or catastrophic events. This paper presents SEDOM-DD (Sub-Events Detection on sOcial Media During Disasters), a new method that analyzes user posts to discover sub-events that occurred after a disaster (e.g., collapsed buildings, broken gas pipes, floods). SEDOM-DD has been evaluated with datasets of different sizes that contain real posts from social media related to different natural disasters (e.g., earthquakes, floods and hurricanes). Starting from such data, we generated synthetic datasets with different features, such as different percentages of relevant posts and/or geotagged posts. Experiments performed on both real and synthetic datasets showed that SEDOM-DD is able to identify sub-events with high accuracy. For example, with a percentage of relevant posts of 80% and geotagged posts of 15%, our method detects the sub-events and their areas with an accuracy of 85%, revealing the high accuracy and effectiveness of the proposed approach.