Corrosion and Corrosion Protection of Wind Power Structures in Marine Environments: Volume 1: Introduction and Corrosive Loads

By Andreas Momber

Corrosion and Corrosion Protection of Wind Power Structures in Marine Environments: Volume 1: Introduction and Corrosive Loads offers the first comprehensive review on corrosion and corrosion protection of offshore wind power structures. The book provides extensive discussion on corrosion phenomena and types in different marine corrosion zones, including the modeling of corrosion processes and interactions between corrosion and structural stability. The book addresses important design issues, namely materials selection relative to performance in marine environments, corrosion allowance, and constructive design. Active and passive corrosion protection measures are emphasized, with special sections on cathodic corrosion protection and the use of protective coatings.

Seawater related issues associated with cathodic protection, such as calcareous deposit formation, hydrogen formation and fouling, are discussed. With respect to protective coatings, the book considers for the first time complete loading scenarios, including corrosive loads, mechanical loads, and special loads, and covers a wide range of coating materials. Problems associated with fouling and bacterial-induced corrosion are extensively reviewed. The book closes with a chapter on recent developments in maintenance strategies, inspection techniques, and repair technologies. The book is of special interest to materials scientists, materials developers, corrosion engineers, maintenance engineers, civil engineers, steel work designers, mechanical engineers, marine engineers.

Offshore wind power is an emerging renewable technology and a key factor for a cleaner environment. Offshore wind power structures are situated in a demanding and challenging marine environment. The structures are loaded in a complex way, including mechanical loads and corrosive loads. Corrosion is one of the major limiting factors to the reliability and performance of the technology. Maintenance and repair of corrosion protection systems are particularly laborious and costly.

• Explores the literature between 1950 and 2020 and contains over 2000 references
• Offers the most complete monograph on the issue
• Covers all aspects of corrosion protection in detail, including coatings, cathodic protection, corrosion allowance, and constructive design, as well as maintenance and repair
• Delivers the most complete review on corrosion of metals in marine/offshore environments
• Focuses on all aspects of offshore wind power structures, including foundations, towers, internal sections, connection flanges, and transformation platforms

• Language: English
• Publisher: Academic Press
• Release date: Apr 6, 2024
• ISBN: 9780323857437

Andreas Momber

Andreas Momber is the head of R&D of a surface protection service company which focusses on marine applications. He has over twenty years experience in surface protection and has managed numerous funded projects with respect to marine and offshore wind corrosion. Dr. Momber is a regular contributor to relevant conferences, workshops, meeting etc. on offshore wind power. Research on universities in the US, Australia, Germany and UK on surface technology. He has published over 200 scientific papers, as well as several well-known works including: Hydroblasting and Coatings of Steel Structures and Hydrodemolition of Concrete Surfaces and Reinforced Concrete. Dr. Momber is an active member of NACE, SSPC and GFKORR.

Book preview

Front Cover for Corrosion and Corrosion Protection of Wind Power Structures in Marine Environments - Volume 1: Introduction and Corrosive Loads - 1st edition - by Andreas Momber

Corrosion and Corrosion Protection of Wind Power Structures in Marine Environments

Volume 1: Introduction and Corrosive Loads

Andreas Momber

Muehlhan AG/Muehlhan Holding GmbH, Hamburg, Germany

Privatdozent Faculty of Geo-Resources and Materials Technology, University of Aachen, Aachen, Germany

Table of Contents

Cover image

Title page

Copyright

Foreword

Chapter 1. Introduction

Abstract

1.1 Offshore wind power structures

1.2 Corrosion as an economic parameter

1.3 Corrosion as a design parameter

1.4 Corrosion protection

Chapter 2. Corrosion

Abstract

2.1 Some basic relationships

2.2 Corrosion systems

2.3 Types of corrosion

2.4 Corrosion effects and damages

2.5 Corrosion models

2.6 Atmospheric marine corrosion

2.7 Corrosion in the splash zone

2.8 Corrosion in the intermediate (tidal) zone

2.9 Corrosion in seawater

2.10 Corrosion in sediment/seawater interface

2.11 Corrosion in soil/sediments

2.12 Corrosion in compartments

2.13 Corrosion under insulation

2.14 Corrosion in dissimilar corrosive environments

2.15 Pitting corrosion

2.16 Crevice corrosion

2.17 Corrosion fatigue

2.18 Mechanically induced corrosion

2.19 Erosion corrosion

2.20 Correlation between laboratory data and field data

Chapter 3. Biofouling

Abstract

3.1 Introduction

3.2 Macrofouling

3.3 Biofilms

3.4 Sulfate-reducing bacteria

3.5 Effects of sulfate-reducing bacteria on coating performance

3.6 Fungal attack

Bibliography

Further reading

Index

Copyright

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Foreword

The energy sector is undergoing an important transition to meet the world’s energy needs, reduce greenhouse gas emissions, support climate change mitigation, and protect our planet for future generations. A major element of the energy transition is the integration of large-scale renewable energy sources, including wind energy, in the energy mix of countries.

For millennia, humanity has harnessed the wind for mobility with sailboats, whereas the wind has been used for centuries to perform mechanical work using large surfaces that interact with the passing airflow. More recently, wind power has achieved technological maturity, and, along with solar energy and bioenergy, wind energy is poised to play a significant role in the energy transition.

In support of the global research community and the commercial wind energy sector, the Wind Energy Engineering Series publishes research and application-oriented books on the overarching subjects related to wind energy engineering, focusing on scientific and technical content that supports all stages of research and application.

While still in its infancy, offshore wind energy is the next focus in developing wind power as a reliable and affordable source of renewable energy. Building on the experiences of onshore wind power developments, offshore wind energy is constrained by demanding and challenging work environments, with corrosion being one of the major limiting factors to the reliability and performance of offshore wind power structures and equipment.

Building on his broad expertise in corrosion research and industrial applications, Dr. Andreas Momber has produced a comprehensive two-volume set on corrosion and corrosion protection, specifically targeted for wind power structures in marine environments. Well anchored in the theoretical and fundamental concepts of corrosion, the two-volume set transposes these concepts to design and operational issues specifically applied to offshore wind power systems.

Volume 1, Corrosion and Corrosion Protection of Wind Power Structures in Marine Environments: Introduction and Corrosive Loads, presents a comprehensive review of corrosion specifically focused on wind power structures and equipment operating in marine environments, where corrosion is viewed as design and economic parameters. Following a broad coverage of fundamental corrosion phenomena, the book provides, with details, the types of corrosion and their effects and damages to marine structures and equipment. Building on this foundation, this book introduces various corrosion models induced by the atmospheric marine conditions, splash zones, seawater, soils, sediments, and operational conditions. This book concludes with a broad coverage of biofouling applied to marine environments. For its part, Volume 2 focuses on corrosion protection measures in wind energy applications.

Unique in the scientific and technical literature on wind energy, the two-volume set of Corrosion and Corrosion Protection of Wind Power Structures in Marine Environments constitutes a masterpiece on corrosion of wind power structures operating in marine environments. There are no doubts that this contribution by Dr. Andreas Momber, a leading authority on the subject of corrosion, will be a reference for the offshore wind energy research, manufacturing, development and operational communities.

Prof. Yves Gagnon PEng, DSc

Université de Moncton, Canada

Series Editor, Wind Energy Engineering Series

Chapter 1

Introduction

Abstract

This chapter describes the elements of offshore wind farms and the structure of individual wind power constructions for the use in marine environments. Corrosion is discussed as an economical parameter and a design parameter. With respect to the economic effects of corrosion, cost models are presented for wind farm erection, operation, and maintenance. The design effects of corrosion and corrosion protection are discussed for a number of relevant loading scenarios and mechanical parameters. The general principles of corrosion protection for offshore wind power constructions are presented.

Keywords

Corrosion; wind turbine; substation; wind farm; substructure; foundation

1.1 Offshore wind power structures

1.1.1 General structure

1.1.1.1 General structure of an offshore wind farm

A wind farm is an energy producing facility, comprising all its main assets to produce power and transfer it into the power grid (DNVGL, 2015b). The configuration of an offshore wind farm is illustrated in Fig. 1.1. Two general types of structures (or assets) can be distinguished with respect to offshore wind power constructions (Fig. 1.2):

• wind turbine.

• substation.

Figure 1.1 Structure of an offshore wind farm (courtesy of Stiftung Offshore Windenergie, Varel, Germany).

Figure 1.2 General structures of offshore wind power structures. (A) Wind turbines (DNVGL, 2016e. Support Structures for Wind Turbines. DNVGL-ST-0126, Fig. 1.1, DNVGL AS, April 2016. Modified version of original work owned by copyright holder DNV AS, included with permission from DNV AS. Modifications are made by the author and for the author’s account only. DNV does not take responsibility for any consequences arising from the use of this content.). (B) Substation (DNVGL, 2016f. Manufacturing and Commissioning of Offshore Substations, Fig. 1.1, DNVGL-RP-0423, DNVGL AS, March 2016. Modified version of original work owned by copyright holder DNV AS, included with permission from DNV AS. Modifications are made by the author and for the author’s account only. DNV does not take responsibility for any consequences arising from the use of this content.).

1.1.1.2 Wind turbines

Per definition, the wind turbine is a system which converts kinetic wind energy into electrical energy (DNVGL, 2015b). An offshore wind turbine basically consists of the following parts (Fig. 1.2A and Fig. 1.3A):

Figure 1.3 Detailed structures of offshore wind power structures. (A) Foundation (monopile) and transition piece—internal (Nielsen, 2016). (B) Substation. 1: jacket foundation; 2: platform; 3: boatlander; 4: ladder; 5: crane; 6: deck cover; 7: working deck (courtesy of Ramboll Denmark A/S).

whereby foundation, substructure and tower form the support structure.

According to DNVGL (2015b), the support structure of a wind turbine is defined as the structure below the yaw system of the rotor-nacelle assembly. It includes tower structure, substructure, and foundation.

The substructure refers to the part of the support structure for a wind turbine which extends upwards from the soil and connects the foundation and the tower (DNVGL, 2015b).

The foundation is the part of the support structure for a wind turbine or substation that transfers the loads acting on the structure into the soil (DNVGL, 2015b).

For an offshore wind farm with 140 turbines in the North Sea, 84,000 tons of steel are required for foundations (monopiles), and 35,000 tons of steel are required for transition pieces (Bortels et al., 2010). Table 1.1 lists weights for numerous constructive parts, illustrating the very high amount of steel consumed. Table 1.2 provides baseline parameters for a 10-MW offshore wind power turbine.

Table 1.1

Table 1.2

The design of foundations depends primarily on the water depth and the weight of the other parts of the structures (Table 1.3). A number of foundation types can be distinguished; some are illustrated in Figs. 1.2A and 1.4. Foundation types include the following:

• monopiles (Brennan and Tavares, 2014; Yeter et al., 2018a).

• jackets (Natarajan et al., 2019).

• tripods (Plodpradit et al., 2019; Yeter et al., 2015).

• tripiles.

• floating foundations (Bento and Fontes, 2019; Carbon Trust, 2020; Castro-Santos and Diaz-Casas, 2016).

• buckets (Bagheri and Kim, 2019).

• gravity foundations (Esteban et al., 2019).

Table 1.3

Figure 1.4 Types of offshore wind power foundations (De Vries, 2011).

Fig. 1.5 illustrates three types of floating foundations. An important part of floating foundations is the mooring system. Reviews on offshore wind power foundation constructions are provided by Oh et al. (2018), Soares-Ramos et al. (2020), and Wu et al. (2019b). Details of transition piece and tower design are provided in Figs. 1.3A and 1.6. Fig. 1.7 illustrates the design of a nacelle. Weights for two foundation types (monopile, jacket) for a 10-MW offshore wind power turbine are listed in Tables 1.4 and 1.5. Weights and lengths of mooring systems for floating offshore wind power foundations are presented in Table 1.6.

Figure 1.5 Floating offshore wind power foundations (courtesy of Acteon Group Ltd., UK).

Figure 1.6 Structure of transition piece and tower (courtesy of Matthias Ibeler, Germany). 1: transition piece; 2: access platform; 3: boatlander; 4: tower section; 5: flange connection; 6: accessories.

Figure 1.7 Structure of a nacelle. Seidel, M., 2007. Tragstruktur und Installation der Offshore-Windenergieanlage Repower 5M. Stahlbau 76(9), 650–656. Reprinted by permission of Wiley & Sons, Inc.

Table 1.4

Table 1.5

Table 1.6

This monograph focuses preliminary on foundation, transition piece, tower, and accessories. Rotor blades are not considered.

1.1.1.3 Substations

Substations can be subdivided further into the following types (DNVGL, 2015b):

• transformer stations.

• converter stations.

• accommodation platforms.

A transformer station is an installation at which electricity is received from the offshore wind turbines of a wind farm and converted from medium voltage to high voltage in order to facilitate transmission of electricity to an onshore transformer station or to an offshore converter station using AC cables (DNVGL, 2015b). A converter station is an installation at which electricity is received from the offshore wind turbines of a wind farm and/or one more substation (DNVGL, 2015b). Converter stations are used for the conversion from high-voltage alternating current to high-voltage direct current. Accommodation platforms are installations used to accommodate a number of people for a longer period of time.

A substation basically consists of the following parts (Figs. 1.2B and 1.3B):

• foundation.

• substructure.

• topside.

• installations/equipment.

Table 1.7 summarizes the weights of offshore wind power substation components. Fig. 1.8 illustrates the amount of steel consumed, and to be protected, during the manufacture of parts of the topside of a substation.

Table 1.7

Figure 1.8 Steel surfaces of a section of a topside of an offshore wind power substation (courtesy of Muehlhan Holding GmbH, Hamburg, Germany).

1.1.2 Structural parts of offshore wind power structures

With respect to the function of structural parts of offshore wind power structures, DNVGL (2015b) distinguishes between three types of structural parts:

• primary structure.

• secondary structure.

• special structure.

Steel thickness limitations for the three structural categories for wind power structures (onshore and offshore) and for general offshore structures can be found, among others, in DNVGL (2015a) and DNVGL (2016e).

1.1.2.1 Primary structural parts

The primary structure consists of the load-bearing structure that transfers permanent loads, life loads, and environmental loads, caused by gravity and environment and actions of the support structure, to the soil. Structural parts, the failure of which will have substantial consequences to the structural integrity, shall be classified as primary structure (DNVGL, 2015b). For wind power structures, primary structural parts include: tower structures, monopile (foundation) structures, and their transition pieces (DNVGL, 2016e). Examples are provided in Fig. 1.9.

Figure 1.9 Primary, secondary, and special parts of an offshore wind power structure (De Jong, M.P., 2010. Results of corrosion inspections offshore wind farm Egmond aan Zee, 2007–2009, Fig. 2, Report 50863231-TOS/NRI10-2242, KEMA Nederland, B.V., Arnhem, Netherlands, 20 October, 2010. Modified version of original work owned by copyright holder DNV AS, included with permission from DNV AS. Modifications are made by the author and for the author’s account only. DNV does not take responsibility for any consequences arising from the use of this content.).

1.1.2.2 Secondary structural parts

Secondary structural parts are parts where failure will be without significant consequence (DNVGL, 2015c). Secondary structures for wind power structure are, for example, boat landings, access ladders, access platforms, internal platforms, internal ladders, J-tubes, landing points at transition piece, and hosting point (DNVGL, 2015b, 2016e). Examples are provided in Fig. 1.9.

1.1.2.3 Special structural parts

Special structures are the same as primary structures; but in addition, the special structural parts are subject to particularly arduous conditions, for example, stress conditions that may increase the probability of brittle fracture or multiaxial stresses (DNVGL, 2015c). Certain elements of the primary structure of offshore constructions, such as cans of tubular nodes, ring flanges of tubular towers, thick-walled deck-to-leg and column connections, may be classified as special structures (DNVGL, 2015b). For wind power structures, special structural parts include tubular joints, flange connections in primary structures, and transition pieces in jacket foundations (DNVGL, 2016e). Examples are provided in Fig. 1.9.

1.2 Corrosion as an economic parameter

1.2.1 Loading collective for offshore wind power structures

1.2.1.1 Stress regime for offshore wind power structures

Wind power constructions performing under marine conditions are exposed to a harsh environment. As can be seen in Table 1.8, the probability of failure of a girder structure is much higher in a marine atmosphere compared to an urban atmosphere, which can mainly be attributed to corrosion processes.

Table 1.8

Offshore wind power constructions experience a complex stress regime, which includes the following types of stresses:

• corrosive stress.

• physical stress.

• biological stress.

A detailed loading collective for an offshore wind power structure is displayed in Fig. 1.10. An example for the combined action for different types of loading was provided by Ray et al. (2009), who described the contribution of biological loads (microbial), chemical loads and physical loads (ice scouring) to the corrosion of steel pilings in a marine (harbor) environment.

Figure 1.10 Loading collective for offshore wind power structures (Momber, A.W., Plagemann, P., Stenzel, V., Schneider, M., 2009. Beurteilung von Korrosionsschutzsystemen für Offshore-Windenergietürme - Teil 1: Problemstellung und Versuchsdurchführung. Stahlbau 78(4), 259–266. Reprinted by permission of Wiley and Sons, Inc.).

1.2.1.2 Inspection and repair

The fact that corrosion is a mutual factor for the reliable performance of offshore wind power structures is illustrated in Tables 1.9 and 1.10, showing monitoring/inspection regimes for the operation of offshore wind power structures. It can be seen that repeating examinations of corrosion-related issues are recommended for numerous vital components of the structure.

Table 1.9

Table 1.10

The durability with respect to corrosion is the time during which a corrosion system meets the requirements for serviceability, whereby serviceability is the ability of a corrosion system to perform its specified functions without impairment due to corrosion (ISO 8044, 2015).

Corrosion protection systems for offshore wind power structures must exhibit a high reliability. In addition, the systems must be capable to protect the structure for a sufficient period of time if the corrosion protection system is mechanically damaged. The expected durability for corrosion protection systems for offshore wind power structures is often mentioned to be more than 25 years. The definition for durability (for protective coating systems) according to ISO 12944-1 (2018) is: Durability: the expected life of a protective paint system to the first major maintenance painting. Maintenance is usually required once 10% of the coating system show a degree of rusting Ri3 (1.0%) as per ISO 4628-3 (2016) (see 8.13.1.2). Durability is a planning parameter that/planning parameter that can help the owner set up a maintenance programme (ISO 12944-1, 2018). A durability of more than 25 years would correspond to the designation very high/VH (>25 years) as per ISO 12944-1 (2018).

1.2.1.3 Failure analysis

Li et al. (2020b) identified failure causes for offshore wind power structures and found that material degradation due to fatigue and corrosion occupied a considerable proportion among the top 16 failure causes. Fault three analysis of floating offshore wind power structures revealed the following main reasons for gearbox failure (Kang et al., 2019b):

• corrosion of pins.

• abrasive wear.

• abnormal vibrations.

• fatigue.

Important measure (IM) values suggested that extreme sea conditions were the main causes of structural malfunctions. Marine conditions, namely salt spray and high wind speed, showed the most significant impact on floating offshore wind power structures, reliability and availability (Kang et al., 2019b).

1.2.2 Cost issues

1.2.2.1 Cost structure

The cost structure of an offshore wind farm is shown in Fig. 1.11. If costs due to corrosion are considered, a distinction must be made between corrosion protection costs and corrosion damage costs (Fig. 1.12). Corrosion protection costs include initial costs for the application of, and planned maintenance costs for, the corrosion protection system. Corrosion damage costs, however, include costs for the replacement of corroded parts, costs for unplanned maintenance and repair, and costs for downtimes. In case of offshore wind power structures, the costs for downtimes cover interruptions in electric power delivery, and the associated costs can make up the majority of all costs. Costs due to corrosion damage cannot be planned, but it is obvious that the likelihood of a corrosion damage increases if a low-quality corrosion protection system is applied.

Figure 1.11 Cost structure of an offshore wind farm. Redrawn from Soares-Ramos, E.P., de Oliveira-Assis, L., Sarrias-Mena, R., Fernández-Ramírez, L.M., 2020. Current status and future trends of offshore wind power in Europe. Energy 202, 117787.

Figure 1.12 Corrosion costs. Redrawn and translated from Kunze, E. (Ed.), 2009. Korrosion und Korrosionsschutz. Wiley-VCH, Berlin. Reprinted by permission of Wiley and Sons, Inc.

A life cycle cost analysis for protective coatings on offshore wind power structures was provided by Bjoergum et al. (2015).

In order to evaluate the lifetime costs of offshore wind power structured, the levelized cost of energy (LCOE) approach is frequently used (e.g., Myhr et al., 2014; Rubert et al., 2018; Yeter et al., 2020b):

Equation (1.1)

Here, LCOE is the levelized cost of energy in €/MWh, NPVtotal is the net present value of lifetime costs in €, and NPVyield is the lifetime generated energy in MWh. LCOE estimation requires two sets of input, namely a turbine's expected yield and the estimated expenditure over the asset's design lifetime (Rubert et al., 2018):

Equation (1.2)

Equation (1.3)

In the equations, CAPEX are the costs accrued of capital, OPEX are the operational expenditure costs, AEP is the annual energy production, n is the year of energy production, and i is a discount factor. Yeter et al. (2020b) added an additional term DECEX to Eq. (1.2) to cover costs for decommissioning. CAPEX and OPEX were defined as follows (Rubert et al., 2018):

Equation (1.4)

Equation (1.5)

In the equations, CE is the exwork expenditure, CC is the civil expenditure, CG is the grid connection expenditure, CO are other capital costs, R is the rated power, CF are the fixed O&M expenditure, CI are insurance costs, CU is the connection and use of systems charge, AEP is the annual energy production, CV is the O&M expenditure, and n is the year of energy production. The annual energy production depends, among others, on the number of turbines, losses, running hours per year, and machine availability. A scheme of a lifetime model based on the LCOE approach is provided in Fig. 1.13. Detailed procedures for the calculation of CAPEX, OPEX, and LCOE for offshore wind power structures are provided in Ioannou et al. (2018a,b). Yeter et al. (2018b) have shown that the LCOE for an offshore wind power foundation (monopile) depended on the structural reliability index (see 1.3.2.2); LCOE showed minimum values at a reliability index of about β=3.4.

Figure 1.13 Schematic overview of lifetime extension levelized cost of energy methodology. Redrawn from Rubert, T., McMillan, D., Niewczas, P., 2018. A decision support tool to assist with lifetime extension of wind turbines. Renew. Energy 120, 423–433.

1.2.2.2 Impact of anticorrosion solutions on costs

The OPEX for corrosion-related issues can be assumed as follows (Nessie, 2019):

Equation

(1.6)

In the equation, OPEXC is the percentage change to the total OPEX due to the combined effect of OPEXC.ch and OPEXC.i, is the percentage of OPEX initially spent for corrosion-related issues (percentage of total OPEX; it was assumed to be between 25% and 35%), and OPEXC.ch is the percentage change of OPEXC.i due to improved corrosion protection management (potential savings in percentage of OPEXC.i). Different scenarios for offshore renewable devices (wave, tidal, wind power) are listed in Table 1.11. The pessimistic scenario considered the lowest savings when applying novel anticorrosion solutions. This scenario assumed an 8% CAPEX increase (+8%) related to the application of the improved anticorrosion solutions. The OPEXC.i was the higher value in the range found in the reference literature for OPEX spent on corrective corrosion, namely 35%. The OPEXC.ch was the lowest of the range (−15%), indicating the low impact of the anticorrosion solutions. According to Eq. (1.6), OPEXC becomes 0%, and improved corrosion protection management methods did not result in a change of the total OPEX. The optimistic scenario covered the most positive impact on the cost of energy when tackling corrosion issues. In that case, the corrosion solution did not have any additional cost related to its application; therefore CAPEXC is +0%. The OPEXC.ch, or the cost reduction due to improved corrosion management, was the highest value in the assumed range, being −35%. For the OPEXC.i, a potential value of 5% was chosen for the most optimistic scenario based on industry discussions (Nessie, 2019). For offshore wind power structures, the optimistic scenario indicated a cost reduction of approximately 8%. The CAPEXC did not increase for this scenario; thus the reduction in the OPEXC lead to a reduction in the LCOE. As indicated in Table 1.11, all scenarios assumed increases in CAPEX with the introduction of improved corrosion mitigation. Potential decreases in CAPEX, for example, through the application of less-expensive protective coating systems, were not assumed in Nessie (2019).

Table 1.11

1.2.2.3 Life cycle costs for floating offshore wind farms

A cost model for floating offshore wind farms was introduced by Maienza et al. (2020). The structures were subdivided into turbine (CT), floating platform (CP), transmission system (CTS), and mooring (CM) and anchoring system (CA), and the costs were:

Equation (1.7)

For a turbine, the costs were approximated as follows:

Equation (1.8)

Here, CT are the costs for one turbine in €, PT is the installed power in MW, and nT is the number of turbines in the park. For the floating platform, the costs were approximated as follows:

Equation (1.9)

Here, CP are the costs of the platform in €, rP is the industrial profit, and nT is the number of turbines. The term CPi covers: CP1=material costs; CP2=direct labor costs; and CP3=activity costs. The material costs include the following:

Equation (1.10)

Here, CP11 covers the costs for steel, CP13 covers the material costs for ballast material, and CP12 covers the following costs:

• material for steel preparation.

• material for painting (coating application) of the platform.

The direct labor costs cover the following:

Equation (1.11)

Here, CL are the hourly fixed costs. The term hLi covers hours of labor, whereby hL1 covers the hours for the preparation, prefabrication, and construction of the platform, and hL2 covers the following hours:

• surface preparation (blasting and priming).

• coating application.

• corrosion control.

For the other parts of the structures, no corrosion-related costs were assumed.

A detailed CAPEX cost calculation model for substructures of offshore wind power turbines was presented by Hübler et al. (2020). The substructure was considered the parts that carry the nacelle of the turbines. The impact of different monopile designs on the stochastic cost-efficiency of an offshore wind farm was investigated. Monopiles were considered as foundations (for 5 MW turbines), and they were varied with regard to diameter and wall thickness; creating designs with increased lifetimes, but higher capital expenditures. The costs were subdivided as follows:

Equation (1.12)

Here, Csub are the costs of the substructure, Cmono are the costs of the monopile, CTS are the costs of the transition piece, Ctower is the costs of the tower, and Cadd are the costs of additional parts, such as boat landings. The monopile costs were further specified:

Equation (1.13)

Here, Cmono are the monopile costs, Cmat are the material costs (related to weight), Cweld are the welding costs (related to weld volume), Cprod are the fixed production costs, and Ccoat are the coating costs (related to monopile area). For the coating costs, an initial (onshore) coating (down to 5 m below mudline) and an additional (offshore) patch coating of 2% of the surface area were assumed, which led to relatively high costs per m². No other corrosion protection was considered.

1.2.2.4 Costs for repair and maintenance

Costs for coating maintenance on offshore wind power structures were assumed to consist of three parts (Bjoergum et al., 2015):

Equation (1.14)

Here, Cmaint are the maintenance costs, CCM are the costs for coating application, CAC are the costs for accessing the structure, and CPL are the costs for production losses during the maintenance work. The coating application costs were assumed as follows:

Equation (1.15)

Here, ACM is the area to be maintained, and cCM are the specific application costs. The costs for accessing the offshore wind power structure were assumed as follows:

Equation (1.16)

Here, tW is the waiting time, NP is the number of workers, cP is the hourly rate for one worker, tV is the number of hours a transfer vessel is required, and cV is the hourly rate for the transfer vessel. It was assumed that the travel time to the wind farm was negligible compared to working and waiting time. The costs due to production loss were assumed as follows:

Equation (1.17)

Here, tPL is the number of nonproductive hours, PP is the average power production during the maintenance period, and pEL is the price for electricity tariff.

It was claimed that the costs for the repair of corrosion protection systems of land-based wind power devices are 5–10 times as high as the initial coating application costs (Mühlberg, 2010). A parameter that can characterize repair efforts is the cost ratio:

Equation (1.18)

In the equation, RCost is the cost ratio, CR are the costs for the repair of a damaged coating system, and CN are the costs for the initial coating application. Examples provided in Table 1.12 indicated high values, whereas the ratio was higher for repair under offshore conditions compared with repair onshore prior to the offshore transport.

Table 1.12

aRatio between repair costs offshore and repair costs on land.

Results reported in Knudsen et al. (2020) can be approximated with a power-law regression for the effects of the corrosivity category on the repair costs of steel structures:

Equation (1.19)

Here, CM are the maintenance costs in €/(m² years) and C is the corrosivity category according to Table 2.64.

1.2.2.5 Future trends in offshore wind power

Costs for the erection and maintenance of offshore wind farms depend strongly on water depth and on distance to the shore. For European waters, the average water depth was claimed to increase linearly from 12 m (2008) to 53 m in 2030, and the average distance to the shore was projected to increase linearly from 10 km (2008) to ca. 100 km in 2030 (Soares-Ramos et al., 2020). Important offshore wind farm parameters were projected as follows (Soares-Ramos et al., 2020):

Equation (1.20)

Equation (1.21)

Equation (1.22)

Equation (1.23)

In the equations, NWF is the number of offshore wind farms, APF is the average wind farm power in MW, IC is the installed capacity in GW, NWT is the number of wind turbines, and t is the year of projection. Based on an extensive review, Diaz and Guedes Soares (2020) introduced a number of regressions for performance parameters of offshore wind power structures:

Equation (1.24)

Equation (1.25)

Equation (1.26)

Equation (1.27)

In the equations, PT is the wind turbine power in kW, HT is the turbine height in m, Dr is the rotor blade diameter in m, NT is the number of turbines in an offshore wind farm, and PF is the installed capacity of the offshore wind farm in MW. The coefficients of regressions (R²) varied between 0.762 and 0.868.

1.3 Corrosion as a design parameter

1.3.1 Introduction

For offshore structures, two major design methods are introduced:

• Working stress design method (DNVGL, 2015c).

• Load and resistance factor design (DNVGL, 2015a,b,c,d).

Both methods require the consideration of corrosion effects. With regard to the loading type, two main limit states can be distinguished for offshore wind power structures (DNV, 2013; Shittu et al., 2020):

• ultimate limit state=loss of static equilibrium of the structure.

• fatigue limit state=cumulative damage due to repeated loads.

Examples for a 10-MW offshore wind power turbine are provided in Table 1.2.

Among others, corrosion affects the following design and stability parameters of offshore (wind power) structures:

• maximum displacement of monopile foundations (Yeter et al., 2018a).

• axial stress of steel members (Melchers, 2005a).

• bending of steel plates and beams (Melchers, 2005a; Wang et al., 2020b).

• shear resistance of plates (Paik et al., 2004a).

• bending strength of plates (Paik et al., 1998a).

• tensile elongation (Sheng and Xia, 2017).

• uniaxial compression strength (Silva et al., 2013).

• butt-welded joints (Wang et al., 2018f).

• buckling of plates (Khedmati et al., 2011; Wang et al., 2018g).

• stress concentration (Starokon and Ermakov, 2019).

• seismic performance (Zheng et al., 2019).

• free vibrations (Eslami-Majd and Rahbar-Ranji, 2017).

A review on corrosion-related design issues for marine steel structures was provided by Tekgoz et al. (2020). Fig. 1.14 provides a framework for the structural integrity assessment of corroded steel structures.

Figure 1.14 Proposed framework for the structural integrity assessment of corroded structures. Adasooriya, N.D., Hemmingsen, T., Pavlou, D., 2020b. Environment-assisted corrosion damage of steel bridges: a conceptual framework for structural integrity. Corros. Rev. 38 (1), 49–65. Reprinted by permission of Walter de Gruyter and Company.

Fig. 1.15 illustrates design fatigue curves for a butt weld under different corrosive conditions. As can be seen, typical fatigue strengths (horizontal lines) do not exist under corrosive conditions, and fatigue design parameters must be varied accordingly.

Figure 1.15 Fatigue lines for a butt weld under different conditions (Schaumann and Kleinadam, 2002). EC3: Kerf category 125; onshore (Eurocode). DIBT: Kerf category 125; onshore (DIBt-Guideline, 2018). GL-A: Category 125, with corrosion protection; offshore wind (GL-Guideline). GL-B: Category 125; noncorrosive; constant stress swing widths; offshore wind (GL-Guideline). GL-C: Category 125; in seawater without corrosion protection; offshore wind (GL-Guideline). N-CP: Category C; in seawater with cathodic corrosion protection; offshore (Norsok, 2004). N-FC: Category C; in seawater without corrosion protection; offshore (Norsok, 2004). N-AIR: Category C; in air; offshore (Norsok, 2004).

Early investigations into the effects of corrosion on the performance of constructive elements of offshore structures were performed by Oberparleiter (1986) and Oberparleiter and Schütz (1988). On welded low-carbon steel elements, Oberparleiter (1986) noted a clear decrease in the fatigue stress cycles (between 30% and 40%), leading to fracture, if the elements were tested in seawater instead of air. Oberparleiter and Schütz (1988) reported an increase in the crack growth rate in offshore steels in seawater compared to that found in air. More information on this particular issue is provided in 2.17.

Fig. 1.16 illustrates effects of uniform (general) corrosion and localized corrosion on the stress–strain behavior of marine steels. Strength deteriorating effects of both corrosion types on the shapes of the stress–strain curves can clearly be recognized (see also Wang et al., 2018a; Sultana et al., 2015). The critical effect of localized corrosion (pitting) is particularly highlighted. To quantify corrosion effects on stress–strain curves, Adasooriya et al. (2020b) introduced a susceptibility index:

Equation (1.28)

Here, IS the susceptibility index in %, and αR represents ratios of stress–strain curve characteristic parameters:

Equation (1.29)

Here, xcorr is the value for the parameter in a corrosive medium, or a corrosive environment, and xair is the value of the parameter in air. Respective stress–strain curve parameters included yield strength, tensile strength, percentage elongation, and percentage reduction of the cross-sectional area (Adasooriya et al., 2020b).

Figure 1.16 Effects of corrosion on stress–strain curves of marine steel plates under axial compressive load (Wang et al., 2018a). (A) Degree of pitting. (B) Depth of corrosion.

1.3.2 Structural reliability

1.3.2.1 Performance indicators

To assess the performance of structures, quantitative performance indicators can be selected, which express physical states that can be used in relation to the performance requirements. Performance indicators can be the following (ISO 2394, 2015):

• structural characteristics (e.g., stiffness/flexibility, load bearing capacity).

• response parameters (e.g., internal forces, stresses, deflections, accelerations, crack sizes).

• utilization factors.

• functionalities (e.g., safety for people, energy consumption, robustness, usability, availability, failure probabilities).

1.3.2.2 Structural reliability index

Structural reliability is the ability of a structure or structural member to fulfil the specified requirements, during the working life, for which it has been designed (ISO 2394, 2015). Reliability is often expressed in terms of probability. Reliability can be related to a reliability index (ISO 2394, 2015):

Equation (1.30)

Here, β is the reliability index, Φ−1 is the inverse standardized normal probability distribution, and Pf is the probability of failure. The reliability index can be compared with a target reliability, which corresponds to acceptable safety or serviceability. The reliability index was utilized, among others, by Adasooriya et al. (2020a) for corrosion fatigue in marine environments (2.17.11), Boero et al. (2012) for harbor infrastructures (1.3.15), Gomes et al. (2020) for mooring chains (1.3.25), Han et al. (2019a) for steel plates in seawater (1.3.19.2), Lardier et al. (2008) for corrosion fatigue of mooring lines (1.3.13.7), Nie et al. (2019) for corroded steel beams (1.3.6.2), Shittu et al. (2020) for pitting corrosion of offshore wind power structures (1.3.13.6), and Silva et al. (2014) for distributed and localized corrosion of marine vessels. The reliability index was shown to linearly decrease with exposure (operation) time for tankers and FPSOs (Paik et al., 2003). ISO 2394 (2015) provides exemplary values for target reliabilities (between β=3.1 and 4.7). The probability of failure is defined as follows (ISO 2394, 2015; Melchers and Beck, 2018):

Equation (1.31)

Here, g(x) is the limit state function, whereby limit state is the state beyond which a structure no longer satisfies the design criteria (ISO 2394, 2015). The probability of failure shall not exceed a specified target value:

Equation (1.32)

Here, Pf is the probability of failure and Pft is the specified target probability. ISO 2394 (2015) provides values for exemplary target probabilities (between 10−6 and 10−3).

With respect to corrosion in marine environments, the probability of failure approach was utilized, among others, by Arzaghi et al. (2018) for corrosion fatigue (2.17.3), Boero et al. (2012) for steel sheet sea walls (1.3.15), Chaves and Melchers (2018) for steel welds (1.3.24), Gholami et al. (2018) for offshore jackets (1.3.19.1), Gomes et al. (2020) for mooring chains (1.3.25), Guedes Soares and Garbatov (1999a) for FPSO plates (9.1.4), Lardier et al. (2008) for corrosion fatigue of mooring lines (1.3.13.7), Melchers (2005a) for the pitting corrosion of offshore pipes (1.3.11.12), Neumann et al. (2019) for corroded marine structures (2.5.17.3), and Zhang et al. (2010) for offshore structures (1.3.19.1).

1.3.2.3 Limit state functions

Limit states include the following (DNV, 2014; DNVGL, 2016a,c,d; ISO 2394, 2015):

• accidental limit state.

• condition limit state.

• fatigue limit state (e.g., Shittu et al., 2020).

• serviceability limit state.

• ultimate limit state.

Examples for the ultimate limit state for general offshore structures and for offshore wind power structures include the following (DNV, 2014; DNVGL, 2015a):

• loss of structural resistance (excessive yielding and buckling).

• failure of components due to brittle fracture.

• loss of static equilibrium of the structure, or of a part of the structure.

• failure of critical components of the structure caused by exceeding the ultimate resistance.

An example for the fatigue limit state is cumulative damage due to repeated loads (DNV, 2014; DNVGL, 2015a). Examples for the accidental limit state for offshore wind power structures include the following (DNV, 2015a):

• structural damage caused by accidental loads.

• ultimate resistance of damaged structures.

• loss of structural integrity after local damage.

Examples for the serviceability limit state for offshore wind power structures include the following (DNV, 2015a):

• excessive vibrations producing discomfort or affecting nonstructural components.

• differential settlements of foundations soils causing intolerable tilt of the wind turbine.

• temperature-induced deformations.

• deflections that may alter the effect of the acting forces.

Limit state functions are defined as follows:

Equation (1.33)

The variables x are basic (randomly distributed) variables, including the following (ISO 2394, 2015):

• physical quantities, which characterize actions, environmental influences, material, and geometrical dimensions.

• model parameters that specify the model itself.

• parameters that describe requirements related to the performance of the structural system (serviceability limits).

Random variables can either be steady or discrete. Probability distributions for discrete random variables include binomial distribution, hypergeometric distribution, and Poisson distribution (Bronstein and Semendjajew, 1987). Distributions for steady random variables include normal distribution, lognormal distribution, exponential distribution, and Weibull distribution (Bronstein and Semendjajew, 1987).

Simple limit state functions can be expressed as follows (ISO 2394, 2015):

Equation (1.34)

Here, x is the design parameter, Rd(x) is the design value for the resistance, and Sd(x) is the design value for the action (load) effect. The case g(x)<0 defines an undesirable domain. Methods for the estimation of Rd are provided in ISO 2394 (2015). The two functions Rd(x) and Sd(x) are either functions of deterministic (fixed) values or functions of random (distributed) values. The situation shown in Fig. 1.17A illustrates the case of a steadily decreasing resistance function and an unsteady load function. Fig. 1.17B, in contrast, shows a fixed value for the load function, Sd(z)=constant, and a steadily decreasing resistance function for a randomly (normal) distributed parameter.

Figure 1.17 Graphical representations of limit state functions. (A) Time-variant decreasing resistance function and random load function (based on Melchers, 2003d). Designate limit states: g(x)=0. (B) Time-invariant load function and time-variant decreasing resistance function of a randomly distributed corrosion loss (based on Neumann et al., 2019).

With respect to corrosion in marine environments, limit state functions were utilized, among others, by Adasooriya et al. (2020a) for corrosion fatigue in marine environments (2.17.11), Arzaghi et al. (2018) for corrosion fatigue (2.17.3), Bharadwaj et al. (2012) for offshore wind assets (1.3.19), Boero et al. (2012) for steel sheets (1.3.15), Chaves and Melchers (2018) for welds (1.3.24), Gholami et al. (2018) for offshore jackets (1.3.19.1), Guedes Soares and Garbatov (1999a) for plate buckling, Guo et al. (2008) for tanker deck plates (1.3.7), Han et al. (2019a,b) for steel plates (1.3.19.2), Melchers (2005a) for the pitting corrosion of offshore pipes (1.3.11.12), Momber et al. (2021a,c) for the local corrosion of wind power structures (9.2.2), Neumann et al. (2019) for corroded marine structures (2.5.17.3), Nie et al. (2019) for plate yielding (1.3.6.2), Silva et al. (2014) for distributed and localized corrosion of marine vessels, Sun and Bai (2003) for FPSO structures, Straub and Faber (2007) for corrosion failure, Zhang and Zhou (2014) for submerged pipes, and Zhang et al. (2010) for offshore jacket structures (1.3.19.1).

In a general way, the limit state function for corrosion was expressed as follows (Straub and Faber, 2007):

Equation (1.35)

Equation (1.36)

In the equations, hT is the total corrosion depth, hC is the corrosion depth due to uniform corrosion, hCr is a critical corrosion depth, hP is the corrosion depth due to localized corrosion (e.g., pit depth), tE is the exposure time, x is the location, rcorr is the corrosion rate, and tI is an initiation time. Failure occurs for hT>hCr. Some of the parameters involved in the equations were assumed to be randomly distributed (corrosion rate, initiation time, measured corrosion depth).

Failures due to corrosion are failures due to cumulative deterioration. In such cases, the time dependency of failure may be accounted for by subdividing the considered time reference period into intervals (ISO 2394, 2015).

1.3.2.4 Reverse strength ratio

A reserve strength ratio is defined as follows (ISO 2394, 2015):

Equation (1.37)

Here, RSR is the reserve strength ratio, RC is a characteristic value of base capacity, and SR is the design load corresponding to ultimate limit states. The reserve strength is related to a residual influence factor that characterizes structural redundancy (ISO 2394, 2015):

Equation (1.38)

Here, RIFi is the residual influence factor, RSRfail,i is the value of the structure where one member "i" has failed, and RSRintact is the value for the intact structure. Values for the residual influence factor are 0≤RIF≤1.0, whereby larger values indicate higher redundancy.

Based on the work of Frangopol and Curley (1987), ISO 2394 (2015) introduced a reliability-based redundancy index:

Equation (1.39)

In the equation, RI is the redundancy index, Pf(damaged) is the probability of failure for a damaged structural system, and Pf(intact) is the probability of failure of an intact structural system. The index takes values between zero and infinity, with smaller values indicating larger robustness (ISO 2394, 2015).

With respect to corrosion in marine environments, the reserve strength ratio approach was applied, among others, by Ahmmad and Sumi (2010) for tensile loads (1.3.11.2), Bai et al. (2016) for jacket structure degradation (1.3.16), Feng et al. (2020) for compressive loads (1.3.11.3), Jiang and Guedes Soares (2016) for biaxial compressive loads (1.3.11.3), Kainuma et al. (2014) for tensile fatigue loads (1.3.13.3), Kim et al. (2017a) for jacket degradation (1.3.23), Nie et al. (2019) for yield loads (1.3.6.2), Paik et al. (2004a) for shear loads (1.3.11.1), Sultana et al. (2015) for compressive loads (1.3.11.3), Wang et al. (2018a) for compressive loads (1.3.11.3), and Zhang et al. (2010) for general offshore structures (1.3.19.1).

1.3.3 Design of steel structures for offshore applications

1.3.3.1 General fatigue design

In general, the classification of structural details for offshore structures and their corresponding Δσ-NF curves in air, in seawater with adequate cathodic protection, and in free corrosion conditions can be taken from DNVGL (2016b). The basic design Δσ-N curve is given as follows (DNVGL, 2016b):

Equation (1.40)

In the equation, NF is the predicted number of cycles to failure for a stress range Δσ, Δσ is the stress range in MPa, m is the negative inverse slope of the curve, and Equation is the intercept of the log NF axis. The fatigue strength of welded joints is assumed to depend on plate thickness to some extent, whereby the thickness effect is accounted for as follows (DNVGL, 2016b; DNVGL, 2016e):

Equation (1.41)

Here, T is the plate thickness through which a crack will most likely grow (T=TRef for thickness less than TRef), TRef is the reference thickness (DNVGL, 2016e: for welded connections other than tubular joints: 25 mm; for tubular joints: 32 mm; for bolts: 25 mm), and k is a thickness exponent on fatigue strength. Values for the thickness exponents are tabulated in DNVGL (2016b) for air exposure, free corrosion in seawater, and for seawater with cathodic protection. They are typically between K=0.15 and 0.25. Examples are provided in Tables 1.13 and 1.14.

Table 1.13

Table 1.14

aCurves can be found in Figs. 1.2–1.9 in DNVGL (2016b).

For the design of offshore wind power structures, DNVGL (2016b) introduced a design fatigue factor (DFF). This factor is a safety factor to be applied to the characteristic cumulative fatigue damage to obtain the design fatigue damage of the structure. As illustrated in Table 1.15, the design fatigue factor depends on the assumptions for the corrosive environment, but also on the accessibility of the respective structural part for inspection and repair. It is lower when accessibility is provided.

Table 1.15

aAccessibility for inspection and repair of initial fatigue and coating damages.

bThe basic NF–Δσ curve for unprotected steel in the splash zone is free corrosion. The basic NF–Δσ curve for coated steel is in air.

For general offshore structures, GL (2007) introduced a correction factor for design fatigue curves:

Equation (1.42)

Here, ΔσRc is the corrected value of the reference stress range, ΔσR is the reference stress range, ft is a thickness effect factor, fc is a corrosion effect factor, fw is a weld shape effect factor, fm is a material effect factor, fr is a mean stress effect factor, fi is a structural element safety factor, and fs is a hot spot effect factor. The corrosion effect factor can be taken as fc=0.7 if corrosion is assumed (GL, 2007).

1.3.3.2 Tubular members of offshore structures

Norsok (2004) considered the strength of tubular members for offshore applications with severe localized corrosion by treating the corroded part of the cross-section as noneffective, and by using provisions given for dented tubulars. An equivalent dent depth can be estimated as follows (Norsok, 2004):

Equation (1.43)

In the equation, Equation is the equivalent dent depth, DM is the tube diameter, Acorr is the corroded part of the cross-section, and A0 is the full cross-section. Dented tubular members under combined loading should be assessed to satisfy the following two conditions (Norsok, 2004):

For tension:

Equation (1.44)

For compression:

Equation

(1.45)

In the equations, NSd is the design axial force on the dented section, M1,Sd is the design bending moment about an axis parallel to the dent, M2,Sd is the design bending moment about an axis perpendicular to the dent, NE,dent is the Euler buckling strength of the dented section for buckling in line with the dent, Δy1 is the member out-of-straightness perpendicular to the dent, Δy2 is the member out-of-straightness in line with the dent, and Cm1, Cm2 are moment reduction factors. The power exponent α depended on the dent depth, thus on corrosion effects, as follows:

Equation (1.46)

Here, δ is the dent depth and DM is the tube element diameter.

1.3.3.3 Fatigue reassessment for lifetime extension

Ziegler (2018) and Ziegler and Muskulus (2016) used the elementary effect method to analyze the global sensitivity of residual fatigue lifetimes for offshore wind power structural parts (turbine: 5.0 MW; foundation: monopile; water depth: 20 m) to environmental, structural, and operational parameters. With respect to the location, they considered tower bottom and mud line. Results are shown in Fig. 1.18. Availability, turbulence intensity and free corrosion were found to have strong influences, whereby free corrosion introduced a severe negative influence on the fatigue lifetime for both situations.

Figure 1.18 Results of one-parameter sensitivity results for offshore wind power structural parts. (A) Tower bottom. (B) Mudline. Redrawn from Ziegler, L., Muskulus, M., 2016. Fatigue reassessment for lifetime extension of offshore wind monopile substructures. J. Physics: Conf. Ser. 2016, 753, 092010.

1.3.4 Axial loads

1.3.4.1 Axial stress on steel members

An example for corrosion effects on general design parameters is the axial stress on steel members in seawater as illustrated in Fig. 1.19. The corrosion effect can be expressed as follows (Melchers, 2005a):

Equation (1.47)

Figure 1.19 Cross-section of a bar under axial stress showing corrosion loss. Redrawn from Melchers, R.E., 2005a. The effect of corrosion on the structural reliability of steel offshore structures. Corros. Sci. 47, 2391–2410.

In the equation, R is the resistance, σM is the axial stress, AS is the cross section, PS is the perimeter area exposed to seawater, hS is the corrosion loss, and tE is the exposure time. The higher the corrosion loss, the less is the resistance of the structural part.

1.3.4.2 Compressive strength under axial loads

Silva et al. (2011) simulated different degrees of corrosion by Monte Carlo simulation to investigate effects of random, nonuniform corrosion on the ultimate compressive strength of steel plates in marine environments. Based on finite element model (FEM) calculations, they derived an empirical model for the compressive strength reduction over time due to corrosion. The assessment parameter was a strength ratio:

Equation (1.48)

Here, RS is the strength ratio, σU is the ultimate compressive strength, and σY is the yield stress. The dependence of the strength ratio on exposure (service) time was modeled as follows (R²=0.977):

Equation (1.49a)

Equation (1.49b)

In the equations, RS is the strength ratio, σU0 is the initial ultimate compressive strength, σY is the yield stress, tE is the exposure (service time), tC is the coating lifetime, tT is a transition time, and n is a distribution parameter. Silva et al. (2011) estimated: n=1.42, tC=10.54 years, and tT=50 years. Eq. (1.49b) and the parameters tC and tT correspond to the structure of the corrosion model introduced by Guedes Soares et al. (2009) (see 2.5.10.1).

Ok et al. (2007) performed a finite element simulation of the uniaxial in-plane compressive strength of steel plates (yield strength: 235 MPa) with pitting corrosion. The pitting corrosion depth was assumed to be 20% of the plate thickness. Parameters varied included plate slenderness, plate width, pit depth and pit width, pitting corrosion length, and pit location. The numerical simulations led to the following relationship:

Equation (1.50)

In the equation, σC is the ultimate strength with pitting corrosion in MPa, σ0 is the ultimate strength without pitting, Y is a complex function, and C1 and C2 are constants. The constants were found to be C1=4.886, C2=5.786 for single-edge pitting, and C1=3.066, C2=3.966 for both-edge pitting. The function Y was estimated with an empirical artificial neural networks (ANN) approach:

Equation (1.51)

The four variables were: x1=plate slenderness, x2=ratio pit width/plate width, x3=ratio pit length/plate length, and x4=ratio pit depth/plate length. Length, width, and depth of pitting corrosion exhibited weakening effects on the ultimate strength