PSI - Issue 84

Vittorio Palma et al. / Procedia Structural Integrity 84 (2026) 1318–1325

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1. Introduction The integrity and load-carrying capacity of prestressing systems are key factors for the safety and durability of prestressed concrete (PC) structures, particularly in existing assets, where ageing, aggressive environments, and construction defects may compromise the effectiveness of post-tensioned tendons (CEN 2023b, 2023a; Fib 2002; FHWA 2013). In such contexts, information on tendon condition is generally obtained through special inspections and in situ testing, often destructive or semi-destructive, performed on a limited number of sampled elements (Fib 2002). The inspection sample size directly affects both the statistical accuracy of defectiveness estimates and the economic, logistical and time-related costs of inspection campaigns, with direct implications for management decisions such as continued operation, intervention or usage restrictions. Current technical standards and engineering practice, including the Eurocodes (CEN 2023b, 2023a), provide safety models and structural verification criteria but offer limited quantitative guidance on inspection planning and sample size selection. This issue is particularly relevant for post-tensioned systems, where the inspectable population is finite, exposure conditions and construction details are heterogeneous, and diagnostic methods are characterised by imperfect detection, i.e. non-unit sensitivity and specificity. In the absence of quantitative criteria, inspection planning is often based on expert judgement, with the risk of oversized campaigns yielding marginal informational benefits or undersized campaigns leaving residual uncertainty incompatible with robust decision-making. Existing literature addresses these aspects from complementary perspectives. Several studies focus on degradation mechanisms in post-tensioned systems, including grouting defects, voids and corrosion processes (Celati et al. 2025), while others investigate the performance of non destructive diagnostic techniques and their dependence on the inspection scenario and adopted technology (Yee et al. 2023). In parallel, within the fields of Bayesian decision analysis and Life-Cycle Management, Value of Information (VoI) criteria have been developed to quantify ex ante the informational benefit of measurements and inspections and to optimize sampling designs as a function of costs and decision consequences (Kharroubi et al. 2011; Thöns e Stewart 2019; Verzobio et al. 2022; Thöns et al. 2025). However, an operational formulation that explicitly links inspection sampling planning to the reduction of epistemic uncertainty and to structural reliability assessment within a risk-based decision-making framework is still limited. This paper proposes an approach for determining the optimal number of inspections on post-tensioned tendons, combining probabilistic modelling of tendon defectiveness, Bayesian updating of inspection information, and structural reliability assessment within a Value of Information–based decision framework. The objective is to provide a practice-oriented formulation in which the inspection sample size results from a quantitative balance between inspection costs, reduction of epistemic uncertainty and the impact of risk management decisions. The paper is organized as follows. Section 2 introduces the proposed methodology. Section 3 describes the Bayesian updating of tendon condition and the construction of the pre- and post-inspection quantities required for sampling planning. Section 4 applies the approach to a case study of a prestressed concrete beam, analyzing the evolution of structural safety with varying sample size, the effect of diagnostic quality, and the identification of the optimal inspection effort. Conclusions discuss implications, limitations and future developments. 2. Structural Reliability, Risk and Expected Cost Analysis Structural reliability assessment requires distinguishing between aleatory variability and epistemic uncertainty, as these arise from different sources and affect both the analysis results and the resulting decisions differently (Verzobio et al. 2022). Aleatory variability reflects the inherent randomness of actions, material properties, and geometric imperfections, and is therefore irreducible. Epistemic uncertainty, by contrast, arises from incomplete knowledge and may be reduced through additional information. In post-tensioned prestressed concrete structures, a major source of epistemic uncertainty is tendon condition, which may be affected by grouting defects, voids, water ingress, corrosion, and the imperfect performance of inspection methods. Accordingly, this study considers tendon defectiveness in a finite population through the discrete system-state variable , representing the number of defective tendons. Inspection outcomes , , characterized by non-unit sensitivity and specificity, are incorporated through Bayesian updating of the state probabilities ( ) . The updated probabilities ( ∣∣ , ) are then propagated through the limit state function (⋅) to evaluate failure probability under alternative management actions . Since these actions modify the post-action structural state, the decision problem is formulated in extensive form and the system variables are updated to represent the post-action structural state. Inspection planning is finally defined as a Bayesian decision problem, in which the value of predicted information balances uncertainty reduction, inspection costs, and failure