Stochastic modeling of forces on jacket-type offshore 2 structures colonized by marine growth 3

: The present paper deals with the stochastic modeling of bio-colonization for the computation of stochastic hydrodynamic loading on jacket-type offshore structures. It relies on a 14 multidisciplinary study gathering biological and physical research fields that accounts of 15 uncertainties at all the levels. Indeed, bio-colonization of offshore structures is a complex 16 phenomenon with two major but distinct domains (i) marine biology whose processes are modeled with biomathematics methods and (ii) hydrodynamic processes. This paper aims to connect these two domains. It proposes a stochastic model for the marine organism’s growth and then continues with transfers for assessment of drag coefficient and forces probability density functions that 20 accounts for marine growth evolution. A case study relies on the characteristics (growth and shape) of the blue mussel (Mytilus edulis) in northeastern Atlantic. biocolonization as a cumulative deterioration process and defines two phases for it: an initiation phase and a propagation phase. It reviews meta-models, describes database construction which consists of the influencing factors. It proposes a stochastic modeling of biofouling based on non-stationary, state-dependent Gamma process for the blue mussel Mytilus edulis . The developed Gamma process provides individual shell length time series for blue mussels in the first year of 51 colonization. The results reveal that the method can capture the distribution and especially extreme 52 values of observed shell length. Thereafter, the study focuses on the drag term of the Morison’s 53 equation. It reviews a response surface method to model the drag force as well as the effect of 54 physical characteristics of structural members such as surface roughness ( k ) and average thickness of 55 marine growth ( Th ). Moreover, the drag force exerted by extreme waves for colonized structural 56 members during the typical macro-colonization years is determined. The probabilistic 57 macro-colonization, shell length time-series considering the occurrence probability of typical 58 macro-colonization years are provided. The evolution of the drag coefficient with regard to the probabilistic shell length time series is evaluated and the results are discussed.


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Actual challenges for requalification of existing offshore structures through the reassessment 27 process emphasizes the importance of updating information about the state of structural safety. One 28 of the most important phases during the design or re-assessment level is a re-evaluation of

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The model should be able to capture the initiation phase and then simulate a propagation phase 144 (macro-colonization). The latter allows for obtaining the individual size and accordingly the physical 145 characteristics of the colonized surface needed for the hydrodynamic calculations [6]. The initiation 146 phase includes spawning date, larval survival, development, and settlement. We considered that 147 this phase was mainly driven by temperature while the propagation phase (macro-colonization) 148 corresponding to the juvenile growth was driven by both, the temperature and the concentration of 149 chlorophyll-a, proxy of the food available in the water column for mussels. These drivers are related 150 to the bivalve ecophysiology, which is detailed in the following paragraph. this temperature. Above this temperature, the spawning dates are not modeled but forced with factors such as storms, shock, rain, etc., which can randomly trigger bivalve's spawning, were not 185 considered. The second important step following spawning is the larval survival and development.

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For mussels, Bayne (1965) [27] observed that M. edulis larvae could reach its development within 20 187 to 40 days, depending on the temperature. A slower (S) larval growth and metamorphosis can take

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As mentioned before geometrical parameters (thickness and roughness) are required for load 195 computation. They depend on geometrical specifications (shape) of organisms colonizing the 196 structure. In this study, these parameters are linked to the shell length of blue mussel individuals.

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Shell growth of blue mussel has an asymmetric sigmoid shape curve ([28]; [29]). The growth rate of 198 blue mussel individuals is, therefore, neither monotonic nor stationary, and the growth curve can be

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In order to model bio-colonization and to standardize the time intervals of data acquisition, 223 each month has been divided into three 10-days periods. The database used hereafter has been 224 therefore constructed from periodic observations at established time intervals τ equal to 10 days. It 225 should be noted that the water temperature could not change abruptly in each 10-days period. The  observations each year depending on the data acquisition time intervals τ; in our case N=17, t=37 and 229 τ=10. The long-term time-variant modeling of input factors being out of the scope of this work, we 230 assumed that N is statistically sufficient for computing the frequency of each macro-colonization 231 scenario. Therefore, the database has been constituted from the regular measurements of water 232 temperature (T) and Chl. a (C), and can be denoted as:

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Hereafter, T i t,τ, is used for the initiation phase determination and C i t,τ for the modeling of the 235 propagation phase. Four types of larval development combining the slow (S) and fast (F) growth 236 possibilities are presented in the Table 1 for the three initiation times (corresponding to the three 237 spawning periods) obtained from the database considering key factors and thresholds described in 238 the previous section. The first larval development is always slow due to water temperature below 239 14°C during early spring, and the third one can be slow only if the second one is also slow (because 240 the water temperature cannot fluctuate abruptly). These results come from the natural seasonal 241 variations of temperature during one year. These frequencies will be considered as discrete 242 probabilities for the modeling. At the end of this larval growth period, we considered that larvae 243 settled on the structures, and that was the start of the propagation phase (macro-colonization) 244 described in Table 1 for the 17 annual chronicles.  Table 2 shows the date of start of macro-colonization, expressed in 10-days periods (1 = first 10 250 days of January), for three main spawning events of blue mussel between March and June.

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Occurrence and probability were calculated from the 17-year time-series of temperature data at the

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The relationship between the start of macro-colonization and the concentration of Chl. a is 314 presented in Figure A3 in Appendix A. There is no significant correlation between these two

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The complete Gamma process function is defined by two parameters: a shape function αS and a scale 359 function βS (4). We discredited time horizon into equal intervals of length τ=10 days. Then, the

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Once the Gamma process has been estimated, the DEB data are not needed anymore and we 386 can use the Chl. a database to predict the growth rate of mussels. The macro-colonization can be then             macro-colonization year. Therefore, 30,000 simulations (10,000 simulations for each 583 macro-colonization inception time in one year) have been performed to provide the individual shell 584 length of blue mussels for each typical macro-colonization year.

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The individual shell length time-series S(t) of the blue mussels are simulated from developed 586 Gamma process (section 2.8) from the inception times for typical macro-colonization years. No 587 correlation between macro-colonization inception time conditioned by the temperature and the 588 aggregate Chl. a (Ct) levels are observed (section 2.6). Therefore, they are simulated independently.

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Hence, all of the time-series of aggregate C(t) could be used for the simulation of individual shell 590 length time-series S(t)) for each typical macro-colonization year.

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The individual shell length time-series simulation procedure is as follows: the typical

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This study highlights the site-specific property of biofouling and therefore, constructs a well and hence increases the prediction accuracy. For some structures, it may not be necessary to 720 clean all members completely to allow a macro-fouling community to develop and create artificial 721 reefs that would be useful for fisheries and biodiversity. This work can be extended to floating 722 structure once the correlation between thickness and weight is known.