PSI - Issue 84

Simone Celati et al. / Procedia Structural Integrity 84 (2026) 127–134

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4.1. Load modelling The ship impact load is proportional to the ship's speed ( ~ (3 / , 1 / ) ), mass ( ~ (20000 , 40000 ) ), and stiffness ( ~ (15 / , 3 / ) ), according to (JCSS_part.2 2001): = √ ∙ (12) The parameters of Eq. (12) are modelled Log-Normal distributed, thus, the impact load is also treated as Log Normal distributed with a coefficient of variation ( ) of 0.82 derived from Eq. (12). The original design documentation is used to evaluate the shear effect induced by the impact load. In particular, the shear value reported in the documentation is interpreted as the 99th quantile of the shear probability distribution, and the mean shear value is back-calculated, assuming a Log-Normal distribution with = 0.82 , leading to a mean value equal to 31,15 . 4.2. Definition of the time-dependent shear capacity Based on Morsh truss theory, as reported in the Fib concrete model code (fib concrete model code 2010), the time dependent shear capacity is evaluated as follows: ( ) = 0.8 ( ) cot + 0.8 √ (13) where = 1200 is the width of the concrete strut, accounts for the longitudinal strain in the member and is equal to 0.4/(1 + 1500 ) , with longitudinal strain at the mid-depth of the member estimated from: = / . The mean compressive force in the section, = 5.29 , is provided in the design documentation, and the Young Modulus, , is evaluated using the Eurocode 2 formulation: =9500 1 /3 . The steel yield stress ( ) is modelled as a Normal variable ( ~ (610 ; 30 ) ), based on the steel class 550 KS (JCSS_part.3 2001). Concrete compressive strength ( ) is considered time independent (i.e., the long-term strength development of concrete is disregarded) and follows a Log-Normal distribution with a characteristic value of 45MPa, mean 53MPa, and a of 0.19. To remain consistent with the design assumptions, the concrete strut inclination is derived using Eq. (19), where 2 = 155 correspond to the stirrup shear capacity reported in the design documentation for the section at level -2 metres, resulting in cot ≅ 1.44 . In Eq. (13), 0.8 ∙ is the inner lever arm considered with = 18652 , and is the reinforcement ratio per meter equal to 4 25 with spacing 150 . The description and probabilistic models are reported in Table 1. The model considered for the capacity model uncertainties refers to shear resistance. The variable ℎ refers to the time to corrosion initiation, accounting only for chlorides diffusion. Table 2 shows the probabilistic models adopted for the variables of the corrosion model. Based on the probabilistic models from Table 2, the mean value of the time to initiation is 122 years, with a standard deviation of 92 years and a kernel distribution is used to model it (see also Table 1). Table 1: Random variables and relative probabilistic models for the propagation phase Variable Description Distribution Mean Standard Deviation 0 [mm 2 ] Initial steel area per meter D 490 - (fib 2015) pitting factor LN 9.28 4.04 [mm/y] (DuraCrete 2000)* Corrosion rate Weib. 0.004 0.003 [MPa] (JCSS_part.3 2001) Steel yielding stress N 610 30 [MPa] (JCSS_part.3 2001) Concrete compressive strength LN 53 10.1 Θ C (JCSS_part.3 2001) Capacity model uncertainties LN 1 0.1 ℎ [years] Time to initiation Kernel 122 92 where is equal to Stirrups spacing: 150 mm, and only the external reinforcements (2 out of 4) are considered corroding. * Considered for wet/rarely dry because it is not given for submerged structures. 4.3. Structural reliability quantification over time A Monte Carlo analysis is conducted based on the probabilistic models described in the previous sections to evaluate the limit state function, and subsequently, the failure probability and reliability index. The following limit