The use of Internet of Things (IoT) technologies is becoming a preferred solution for the assessment of tailings dams' safety. Real-time sensor monitoring proves to be a key tool for reducing the risk related to these ever-evolving earth-fill structures, that exhibit a high rate of sudden and hazardous failures. In order to optimally exploit real-time embankment monitoring, one major hindrance has to be overcome: the creation of a supporting numerical model for stability analysis, with rapid-enough response to perform data assimilation in real time. A model should be built, such that its response can be obtained faster than the physical evolution of the analyzed phenomenon. In this work, Reduced Order Modelling (ROM) is used to boost computational efficiency in solving the coupled hydro-mechanical system of equations governing the problem. The Reduced Basis method is applied to the coupled hydro-mechanical equations that govern the groundwater flow, that are made non-linear as a result of considering an unsaturated soil. The resulting model's performance is assessed by solving a 2D and a 3D problem relevant to tailings dams' safety. The ROM technique achieves a speedup of 3 to 15 times with respect to the full-order model (FOM) while maintaining high levels of accuracy.