## 6 Conclusions  
An original methodology for integrating the stochastic monitoring data into the Monte Carlo probabilistic safety assessment procedure without recalibrating the input parameters' distributions has been presented. The concept of \"weighted\" simulations according to how closely they match the monitoring data has been introduced. The described methodology was tested on a case study of CD triaxial testing of the rockfill material, with the idea that the triaxial test specimen mimics the real structure, whose safety is under investigation. Input variables for the baseline probabilistic analysis were based on material parameters calibrated from recreated laboratory tests in the FEM environment using the Mohr-Coulomb material model. Based on the presented methodology and case study, the following conclusions can be made:  
1. Incorporating monitoring data systematically shifts results toward the behavior actually observed in the field and narrows their scatter. For the triaxial-test specimen, the mean factor of safety (FS) dropped from 1.69 to 1.48 and its standard deviation fell by roughly one-quarter after weighting, revealing a more conservative--and better defined--safety estimate. 2. A meaningful overlap between baseline and monitoring distributions is essential. If the observed data lie completely outside the prior envelope, all weights collapse to zero and the analysis cannot converge; conversely, if monitoring uncertainty spans the entire prior envelope, the update is uninformative. 3. The tighter the monitoring distribution, the stronger (and more localized) the update, but the larger the baseline sample required for convergence. Quasi-deterministic monitoring in the case study (\(\sigma\approx 0.1\%\) of baseline range) obtained best results but demanded the order of \(10^{6}\) baseline simulations. 4. Practical success depends on aligning monitoring uncertainty with prior variability. If the monitoring range is overly narrow, too few simulations receive meaningful weight and convergence falters; if it is excessively wide, the weights become nearly uniform, and the update adds little new information. The case study demonstrated this statement. 5. Preserving correlations among input parameters is critical; otherwise, the weighting step may keep and even exaggerate physically impossible combinations. In the case \begin{table}
\begin{tabular}{c c c c} \hline \hline \(\sigma/\varepsilon_{1,\text{range}}\) & \(\mu\) (FS) & \(\sigma\) (FS) & **KL (FS)** \\ \hline
0.1\% & 1.45 & 0.06 & 1.99 \\
1\% & 1.48 & 0.08 & 1.56 \\
10\% & 1.62 & 0.10 & 0.13 \\
100\% & 1.69 & 0.11 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Effects of monitoring data span on FS statistical measures. study, embedding the negative \(\varphi^{\prime}\)-E and positive \(\varphi^{\prime}\)-\(\Downarrow\) correlations ensured realistic parameter combinations and prevented uninformative weighting. 6. The procedure remains computationally tractable for routine problems. With a monitoring standard deviation equal to \(\sim\)1% of the baseline spread in the case study, 10,000 baseline simulations yielded \(\sim\)200 effectively weighted simulations; these are sufficient for smooth posterior histograms and stable statistics. The presented methodology offers a transparent and computationally tractable route for embedding monitoring data into routine engineering calculations, thus producing more realistic safety estimates of actual structural behavior. Although this methodology is developed in the context of embankment dam safety, it can be applied to other structural systems where systematic long-term monitoring is implemented. It must be pointed out that the structural monitoring data usually reflect the operating conditions (far from the failure state); therefore, analyses must mirror the actual operating conditions. If extreme design scenarios have not occurred during the observed period, monitoring records cannot validate them directly.