Development of a method to calculate the probability of a berth failure under vertical stochastic load
Keywords:port terminal, vessels with cargo, maximum pressure, front wall of a berth, risk of berth failure, risk insurance
AbstractWe 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
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