Development of a method to calculate the probability of a berth failure under vertical stochastic load




port terminal, vessels with cargo, maximum pressure, front wall of a berth, risk of berth failure, risk insurance


We developed the method for determining the probability of achieving the maximum value of loads from the cargo that is stored at the port terminal warehouse on the front wall of the berth under conditions of uncertainty of the moments of vessel approach and their loading. The method is based on the construction and analysis of the stochastic model of operation of a port terminal, consisting of a single berth and a warehouse together with the reloading equipment. The process of the arrival of vessels with cargo is supposed to be described by the model of a complex Poisson process; the whole cargo unloaded from the vessels arrives at a warehouse and is transported from a warehouse by the land transport in a uniform way at constant intensity. The probabilistic model of the operation of the system "a warehouse – a berth" at the port terminal was constructed with the help of the mathematical theory of risk. We formulated the criterion of safe operation of a berth at its structural elements being influenced by the random load of the cargo, stored in a warehouse in the rear of the berth, as the probability of not exceeding the maximum admissible value of the pressure on the front wall of the berth (according to the Coulomb law). To find the probability of a berth failure, the linear integral equation of the convolution type, the solution to which was found for a series of particular cases, was derived. Based on the found probability for a berth failure, two practically important problems were stated and solved. First, the values of intensity of cargo transporting from a warehouse, which ensures the absence of a failure with the small enough assigned probability, were determined. Second, we stated the criterion of the economic viability of insuring the port losses as a result of elimination of consequences of a berth failure due to the maximum admissible value being exceeded by loads over the assigned period of time. The numerical illustration of the specified problems was presented

Author Biographies

Denys Bezushko, Odessa National Maritime University Mechnikov str., 34, Odessa, Ukraine, 65029

PhD, Associate Professor

Department of Engineering Constructions and Water Research

Konstantin Egupov, Institute of Fundamental and Applied Research Odessa National Maritime University Mechnikov str., 34, Odessa, Ukraine, 65029

Doctor of Technical Science, Professor, Director of Institute

Mykhaylo Postan, Odessa National Maritime University Mechnikov str., 34, Odessa, Ukraine, 65029

Doctor of Economic Sciences, Professor, Head of Department

Department of Management, Marketing and Logistics


  1. Kostyukov, V. D. (1979). Veroyatnostnye metody rascheta zapasov prochnosti i dolgovechnosti portovyh gidrotekhnicheskih sooruzheniy. Moscow: Transport, 154.
  2. Bolotin, V. V. (1984). Prognozirovanie resursa mashin i konstrukciy. Moscow: Mashinostroenie, 312.
  3. Thoresen, C. A. (2014). Port Designer’s Handbook. Thomas Telford Ltd. doi:
  4. Li, Q., Ye, X. (2018). Surface deterioration analysis for probabilistic durability design of RC structures in marine environment. Structural Safety, 75, 13–23. doi:
  5. Abu Taiyab, M., Alam, M. J., Abedin, M. Z. (2014). Dynamic Soil-Structure Interaction of a Gravity Quay Wall and the Effect of Densification in Liquefiable Sites. International Journal of Geomechanics, 14 (1), 20–33. doi:
  6. Chun, J., Song, J., Paulino, G. H. (2019). System-reliability-based design and topology optimization of structures under constraints on first-passage probability. Structural Safety, 76, 81–94. doi:
  7. Yáñez-Godoy, H., Schoefs, F. (2014). Probabilistic computational mechanics of structures with a ground anchor device: from identification by SHM to reliability assessment of quays. Journal of Civil Structural Health Monitoring, 5 (3), 307–320. doi:
  8. Xie, M., Ng, K. M., Habibullah, M. S., Kolowricki, K., Soszynska-Budny, J. (2012). A Study of Safety and Reliability of Maritime Transportation Systems. Life Cycle Reliability and Safety Engineering, 1 (1), 35–43.
  9. Mourillon, N. K. N., de Gijt, J., Bakker, K. J., Brassinga, H., Broos, E. (2017). Stability Analysis Quay Wall at The Amazonehaven, Port of Rotterdam. MATEC Web of Conferences, 138, 06001. doi:
  10. Poyzner, M. B., Postan, M. Ya. (1999). Ekspluatacionnaya nadezhnost' prichal'nyh sooruzheniy. Veroyatnostnye metody issledovaniya. Odessa: Astroprint, 148.
  11. Postan, M. Ya. (2006). Ekonomiko-matematicheskie modeli smeshannyh perevozok. Odessa: Astroprint, 376.
  12. Postan, M., Postan, M. (2013). Method of Assessment of Insurance Expediency of Quay Structures' Damage Risks in Sea Ports. Marine Navigation and Safety of Sea Transportation, 123–127. doi:
  13. Korolev, V. Yu., Bening, V. E., Shorgin, S. Ya. (2007). Matematicheskie osnovy teorii riska. Moscow: Fizmatlit, 544.




How to Cite

Bezushko, D., Egupov, K., & Postan, M. (2019). Development of a method to calculate the probability of a berth failure under vertical stochastic load. Eastern-European Journal of Enterprise Technologies, 1(3 (97), 21–27.



Control processes