LEVERAGING PROBABILISTIC MODELLING OF UNCERTAINTIES TO MITIGATE REINFORCE CONCRETE STRUCTURAL ELEMENT FAILURE

Celestine Chukwudi UZOKA, Eghosa Akugbe IMARHIAGBE

Abstract


 

Abstract : This study evaluates the structural safety and reliability of a reinforced concrete beam using both deterministic and probabilistic approaches. The probabilistic properties of material strengths and applied loads form the basis for an analytical mean-value assessment and Monte Carlo simulation (MCS). Flexural resistance and demand are computed using standard reinforced concrete beam theory, while structural safety is quantified through a limit state function. The probability of failure is estimated from fundamental probability principles. Beam geometric dimensions are treated as deterministic variables, as construction tolerances (±5–10 mm) are relatively small and well controlled on site compared with the inherent variability of material properties and loads.Results from the analytical mean-value approach indicate that the beam design is structurally safe, with the mean bending resistance exceeding the mean bending demand by a large margin, reflecting a conservative design. However, assessment of the constructed beam using mean values shows only a small reserve capacity, highlighting the limitations of deterministic analysis in capturing uncertainty. Monte Carlo simulation of the design beam demonstrates high reliability, with no failure cases recorded in all thirty simulations and consistently positive limit state values. In contrast, probabilistic analysis of the constructed beam reveals nine failure cases out of thirty simulations, corresponding to a probability of failure of approximately 0.30. These failures occur under unfavourable combinations of high load effects and reduced material strengths and reinforcement areas. The findings demonstrate that while mean-value analysis may classify a beam as safe, probabilistic modelling provides deeper insight into structural reliability and exposes potential risks associated with real construction variability.

 

Keywords: Probabilistic modelling; Monte Carlo simulation; Reinforced concrete beam; Structural reliability; Probability of failure


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