## 1 Introduction
Recognizable trends within the dam's behavior do exist, yet the complex interplay of variable external loads and the structure's non-linear response mean that nominally similar conditions rarely yield identical readings. Further scatter in monitoring data arises from instrument precision limits, measurement error and data-handling noise. Consequently, the monitoring observations should be treated as random variables and described by appropriately assigned probability distributions, not as single deterministic values. Finally, not all types of monitoring data carry the same level of reliability or significance [4]. Certain instruments provide more accurate or consistent measurements than others, and some monitoring points are more critical due to their location or relevance to the dam's behavior. As a result, the interpretation of monitoring data should consider the contextual importance of each measurement point. Methods for the safety assessment can be deterministic and probabilistic, where these terms illustrate the treatment of model input variables in calculations. The deterministic approach is the traditional way of solving safety problems, where the computational parameters of materials and/or loads and hydraulic boundary conditions are defined as constant values. Many current design codes still prescribe deterministic safety criteria expressed through minimum factors of safety (FS). These requirements are rooted in long standing engineering practice and empirical experience. Although widely used in design and evaluation, the global factor of the safety approach has inherent limitations: it neither distinguishes among different sources of uncertainty nor provides a direct estimate of failure probability. By the second half of the twentieth century, the dam-engineering community recognized the need for a systematic treatment of uncertainty. The arrival of probability theory and structural reliability concepts opened the door to a broad family of probabilistic analysis methods [5]. These methods model the stochastic behavior of key variables and deliver measurable quantities such as the probability of failure (p\({}_{\text{f}}\)) and the reliability index (\(\beta\)), which can be compared with target values specified in reliability-based standards. ISO guidelines [6] and Eurocodes [7] now define target \(\beta\)-values that structures must meet. Numerous studies have expanded the reliability assessments of dam and slope stability by incorporating advanced probabilistic methods into conventional analysis frameworks [8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21], but these efforts generally overlook the incorporation of actual dam monitoring data. The problem of integrating the monitoring data into the analysis has been addressed theoretically in several works [22; 23], in which it is either treated deterministically, or, in the case of a probabilistic attempt, by using full Bayesian updating. The examples of using the Bayesian updating approach have been reported for smaller or less-complex geotechnical systems such as landslides and rock slopes [24; 25; 26; 27; 28; 29; 30]. For large embankment dams, whose instrumentation produces high-dimensional stochastic data, a full Bayesian integration is very computationally challenging [31]. Several studies have explored techniques to reduce the computational burden, including surrogate modeling approaches or reduced-order models in geotechnical problems [17; 28; 29]. This paper introduces a methodology that implicitly integrates monitoring data, with their inherent stochastic character, directly into a Monte Carlo probabilistic safety assessment. Although this methodology is developed in the context of embankment dam safety, its applicability extends to other geotechnical systems where systematic long-term monitoring is implemented (e.g., the safety assessment of large natural or engineered slopes, in which surface displacement and pore pressures are monitored).