*Article* **Determination of Prestress Losses in Existing Pre-Tensioned Structures Using Bayesian Approach**

**Martin Moravˇcík and Jakub Kral'ovanec \***

Department of Structures and Bridges, Faculty of Civil Engineering, University of Zilina, Univerzitna 8215/1, 010 26 Zilina, Slovakia; martin.moravcik@uniza.sk

**\*** Correspondence: jakub.kralovanec@uniza.sk

**Abstract:** Deterioration of materials and structures is an unavoidable fact, and prestressed concrete structures are not an exception. The evaluation of load-carrying capacity and remaining service life includes collecting various information. However, one type of information is essential and the most important, the state of prestressing, which inevitably decreases over time. Currently, many possible methods for the evaluation of prestressing are available. These techniques are part of the structural assessment and provide residual prestressing force value which is later used in the evaluation process. Therefore, it is suitable to provide the value of prestressing force based on certain probabilistic backgrounds. This study addresses the determination of residual prestressing force in pre-tensioned railway sleepers one year after their production, using the so-called Bayesian approach. This technique is focused on the validation of results obtained from the application of the non-destructive indirect saw-cut method. The Bayesian approach considers analytic calculation as the primary method of prestressing determination. In this paper, Monte Carlo simulation was used to determine the total variability that defines all Bayesian systems of probability functions. Specifically, a total of 1000 simulations was applied, and the current random vector of prestressing force derived from the analytical calculation has been assumed as a normally distributed function. Finally, obtained results for different depths of saw-cuts are compared. The results of the experimental and statistical determination of residual prestressing force provide its value with a 95% confidence level. This study suggests that the implementation of the probability approach can be an effective tool for determining prestress losses.

**Keywords:** Bayesian approach; prestressing force; saw-cut method; assessment; pre-tensioned members
