## 1 Introduction  
Embankment dams are hydraulic structures constructed from natural materials available near the construction site. Depending on the type of material used, they may be classified as earthfill dams (with either homogeneous or heterogeneous cross-sections) or rockfill dams. According to ICOLD data [1], there are over 58,000 high dams worldwide, of which approximately 75% fall into the category of embankment dams. The safety assessment of such dams is a critical issue due to the potentially catastrophic consequences that a failure could entail, both in terms of human lives and economic losses. In the broadest sense, the failure of an embankment dam represents a catastrophic scenario in which the structure is unable to withstand the applied loads, leading to at least one of the following incidents: the uncontrolled release of reservoir water or a complete loss of structural integrity of the dam and/or its foundation. It is clear that the embankment dams (due to their large size, complex geotechnical conditions, and the potentially catastrophic consequences of failure) are structurescharacterized by a very high level of risk. As outlined in Eurocode 7 [2], they fall under Geotechnical Category 3, which demands in-depth investigations and advanced engineering practices. ICOLD standards further highlight the necessity of ongoing monitoring and risk evaluation to ensure the safety and performance of these critical infrastructures. ICOLD in its Bulletin 154 [3] states the following principle: \"The fundamental dam safety objective is to protect people, property and the environment from harmful effects of mis-operation or failure of dams and reservoirs. Accordingly, a dam must have an acceptable level of safety at all times\". For that reason, one of the most important activities in dam-safety management, both for existing dams and during the design phase, is the continuous safety review. The ICOLD Bulletin 154 [3] states that the safety review must provide an answer to the question \"Does the dam system conform to current regulatory requirements, current national and international standards and practices, and to current requirements with respect to acceptable and tolerable risk criteria?\". Analyzing its behavior and assessing the safety of a dam rely on conducting computational simulations of relevant physical processes, which are most commonly performed using the finite element method (FEM). Material parameters that serve as an input for a FEM model are most often derived from two primary sources of known (measured) data: preliminary investigation and monitoring data. The preliminary investigation typically includes results from laboratory testing and in-situ experiments conducted during the design or investigation phases, which provide insight into the behavior of individual materials usually on a much smaller scale compared to the structure as a whole. Nevertheless, these tests are very useful, as they provide engineers with a certain understanding of material behavior in controlled conditions. The long-term safety of a dam depends as much on systematic monitoring during its operation as on a sound design and construction. The data monitored on dams directly reflect the structure's response to external actions, revealing both its overall displacements, and the changes in its internal seepage and stress-strain state. ICOLD Bulletin 154 [3] emphasizes that the operational phase poses the greatest safety challenge and therefore requires a structured management system in which monitoring data are collected (automatically or manually), checked and interpreted in a timely manner to support risk-informed decisions. Each monitoring scheme is unique, tailored to a particular dam of a particular structural type and foundation setting. The dam's response that is being captured by monitoring data is inherently stochastic.