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Degree Project in Civil Engineering and Urban Management Second cycle, 30 credits Assessment of ice loads on piled structures based on local conditions ASTRID LINDBLOM ELIN ÅNGER Stockholm, Sweden 2022 Assessment of ice loads on piled structures based on local conditions Astrid Lindblom & Elin Ånger June 2022 Master Thesis, 2022 TRITA-ABE-MBT-22403 ISBN: 978-91-8040-308-5 ©Astrid Lindblom & Elin Ånger 2022 KTH Royal Institute of Technology Department of Civil and Architectural Engineering Division of Concrete Structures Stockholm, Sweden, 2022 Abstract This master report studies structural design methods for ice loads and the impact of local conditions. Ice loads occur due to ice movements or expansion of the ice sheet. Specifically, this study analyses ice loads on piled structures and ten different design methods and handbooks to calculate the ice load. There are five Swedish methods among these, and the remaining are developed in Denmark, Finland, Norway, and Germany. The methods are developed for different types of structures. For example, dams, bridge supports, traffic piers, ports and piles The ice loads have been divided into different categories; vertical ice loads and horizontal loads caused by thermal expansions, water level changes, or drifting ice. Some methods depend on local conditions parameters for the input data. These methods have been investigated in a parametric study to shed light on how different inputs affect the ice load. Some input data from local conditions have been developed and are presented to facilitate the design. Temperature and ice thickness are the parameters where most data are accessible. Furthermore, an evaluation has been performed on whether the methods are applicable for piles, if local conditions are considered, and if the method is practically applicable for ice load design. The size of the ice load is reported for different ice load types for three Swedish cities, namely Halmstad, Mora and Umeå. The overall result was that Mora generated the highest ice load magnitudes and Halmstad the lowest. A Finite Element (FE) analysis has been performed to address the affect that ice loads has on the dimensions of the piles. In general, more knowledge is needed about ice loads and their magnitude. Studies on what safety factors are included in each method need to be carried out to counteract unnecessarily applied safety factors in several stages. In addition, studies from a statistical perspective are required, where the return period of the input data used in the methods is studied. A statistical study would evaluate which values are justified in relation to the return period of the ice load. Keywords: Ice loads, Local conditions, Structural design, Piled structures v Sammanfattning I denna masteruppsats studeras dimensioneringsmetoder för islaster och hur lokala förhållanden inverkar på dessa. Islaster uppstår till följd av isens rörelser och expansion. Specifikt studeras islaster på pålade konstruktioner och tio olika handböcker och dimensioneringsmetoder för att bestämma islasten. Av dessa metoder är fem svenska metoder och de återstående är utvecklade i Danmark, Finland, Norge och Tyskland. Metoderna är anpassade för olika typer av konstruktioner; till exempel dammar, brostöd, trafik bryggor, hamnar och pålar. De studerade metoderna och dess tillvägagångssätt för att bestämma islast presenteras i examensarbetet. Islasterna har delats in i olika kategorier, vertikala islaster och de horisontella lasterna från termiska expansioner, vattenståndsförändringar och drivande is. En parameterstudie har genomförts för att belysa hur olika indata påverkar islasten storlek för de metoder som beaktar lokala förhållanden. Viss indata från lokala förhållanden har tagits fram samt presenteras för att underlätta islastberäkningar där temperatur och istjocklek är de parametrar där mest data finns att tillgå. Vidare har en utvärdering gjorts huruvida metoderna är applicerbara för pålade konstruktioner, om lokala förhållanden beaktas såväl som om metoderna är praktiskt tillämpbara vid islastdimensionering. Islastens storlek redovisas för olika islasttyper för de svenska städerna Halmstad, Mora och Umeå. Det övergripande resultatet av detta var att Mora genererade den största islasten och Halmstad den lägsta lasten. En Finita Element (FE) analys har genomförts för att belysa islastens påverkan på pålarnas dimensioner. Generellt behövs mer kunskap om islaster och dess storlek. Närmare studier skulle behöva genomföras gällande de säkerhetsfaktorer som inkluderas i respektive metod för att inte använda onödigt mycket säkerhetsfaktorer i fler led. Utöver detta behövs studier från ett statistiskt perspektiv där återkomstperioden av den indata som används i metoderna studeras och vilka värden som är befogade att använda i förhållande till islastens återkomstperiod. Nyckelord: Islaster, Lokala förhållanden, Dimensionering, Pålade konstruktioner vii Preface This master thesis has been performed as the final part of our Master’s Programme in Civil and Architectural Engineering. The work has been performed at the division of Concrete Structures, KTH, and in cooperation with the consulting company ELU Konsult AB. We want to thank our supervisor Richard Malm at KTH, Royal Institute of Technology, for the support and guidance he has provided. In particular, we would like to express our sincere gratitude to our supervisors at ELU Konsult AB, Henrik Posay Mayor and Gustav Norén for all their support. They have especially contributed with knowledge about the problem of ice loads for consultants, and their advice has been a great asset while writing this thesis. Stockholm, May 2022 Astrid Lindblom & Elin Ånger ix Contents Abstract v Sammanfattning vii Preface ix 1 Introduction 1 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Aim and purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Adaptation to marine structure . . . . . . . . . . . . . . . . . . . . . 3 1.4 Research questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.5 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.5.1 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Ice loads 7 2.1 Ice growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 The failure modes of ice . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Horizontal ice loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.4 2.3.1 Thermal expansion . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3.2 Water level changes . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3.3 Drifting ice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3.4 Pack ice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Vertical ice loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.4.1 2.5 Water level changes . . . . . . . . . . . . . . . . . . . . . . . . 14 Previous measurements of ice loads . . . . . . . . . . . . . . . . . . . 14 xi 3 Design methods for ice loads 3.1 15 General information . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.1.1 Trafikverket . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.1.2 Löfquist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.1.3 Waxholmsbolaget . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.1.4 Stockholms hamnar . . . . . . . . . . . . . . . . . . . . . . . . 16 3.1.5 Svensk Energi . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.1.6 Vejdirektoratet . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.1.7 RIL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.1.8 Statens vegvesen . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.1.9 Port Designer’s handbook . . . . . . . . . . . . . . . . . . . . 18 3.1.10 EAU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.2 3.3 Horizontal ice loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.2.1 Methods without classification of load type 3.2.2 Thermal expansion . . . . . . . . . . . . . . . . . . . . . . . . 21 3.2.3 Water level changes . . . . . . . . . . . . . . . . . . . . . . . . 24 3.2.4 Drifting ice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Vertical ice loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4 Local conditions & applicability 4.1 . . . . . . . . . . 20 43 Parametric study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.1.1 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.1.2 Ice thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.1.3 Ice strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.1.4 Water level variation . . . . . . . . . . . . . . . . . . . . . . . 60 4.1.5 Support design . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.2 Input data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.3 Applicability and comparison of three cities . . . . . . . . . . . . . . 74 4.4 Pile dimensions and capacity . . . . . . . . . . . . . . . . . . . . . . . 81 xii 5 Evaluation 87 5.1 Categorisation and treatment of ice loads . . . . . . . . . . . . . . . . 87 5.2 Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.2.1 Safety margins and return periods . . . . . . . . . . . . . . . . 89 5.2.2 Input parameters . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.3 Pile dimensions and capacity . . . . . . . . . . . . . . . . . . . . . . . 93 5.4 Compilation of methods . . . . . . . . . . . . . . . . . . . . . . . . . 94 6 Conclusion 101 6.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 6.2 Further research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Bibliography 103 A Translation 109 A.1 English to Swedish . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 B Analytical calculations 111 B.1 Löfquist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 B.2 Waxholmsbolaget . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 B.3 Stockholms hamnar . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 B.4 Svensk Energi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 B.5 Vejdirektoratet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 B.6 RIL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 B.7 Statens vegvesen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 B.8 Port Designer’s handbook . . . . . . . . . . . . . . . . . . . . . . . . 127 B.9 EAU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 B.10 Pile capacity - Received from ELU . . . . . . . . . . . . . . . . . . . 132 C Blueprints 137 xiii Chapter 1 Introduction 1.1 Background In countries with cold winters, such as Sweden, ice settles on rivers, lakes, seas and other bodies of water. Although, it should be considered that the climate varies substantially from the north to the south of Sweden. For example, SMHI claims that the mean ice thickness varies between 0 and 0.8 m in Sweden (Eklund, 1998). As ice is formed, moves and expands, ice loads arise. These loads act on and affects structures which must be designed to withstand this. Ice loads are often categorised as static or dynamic loads and may induce horizontal or vertical force component. The static ice loads typically occur due to expansion during temperature changes and water level variations. Dynamic loads usually originate from drifting ice floes (Hellgren et al., 2022). The differentiation between horizontal and vertical loads originates from the direction of the load action. The ice load’s direction depends on the ice’s movements and the load type. Ice load types can, for example, be due to thermal expansions, water level variation, drifting ice from the ship and currents (Wikenståhl et al., 2012). The magnitude of the ice load depends on several factors, such as the strength of the ice, friction and thickness, and the dynamic ice load also depends on the kinetic energy (Burcharth, 2004). The ice thickness, in turn, is a consequence of several factors, such as meteorological ones and the size of the body of water. Moreover, the load also depends on currents, wind, the rate of water level changes, etc. (Eklund, 1998). The information and guidelines provided in Eurocode regarding ice load design are limited to EN 1991-1-6, chapter 4.9, "Actions due to ice, including floating ice, should be taken into account where relevant" (EN 1991-1-6, 2005). No other information is available about the ice load in the additional documents EKS 11 (Boverket, 2019) and TSFS (Transportstyrelsen, 2018). Sweden, on the other hand, has guidelines where ice loads are adapted for bridge supports, (Löfquist, 1987) and (Trafikverket, 2021), and dam structures (Svensk Energi, 2011). These guidelines have limited adaptions to local conditions, even though Mayor et al. (2020) specif- 1 CHAPTER 1. INTRODUCTION ically state that local conditions should be taken into account. More specific information and guidance can also be found, for example Stockholms hamnar (2016) and Wikenståhl et al. (2012) which are only applicable in the archipelago of Stockholm. Further, other countries where ice load also is important have their own handbooks and guidelines. According to Mayor et al. (2020), the different methods and calculating procedures result in widely different magnitudes of ice loads and do not treat the same load types. The horizontal ice load is divided into different ice load types depending on what causes the load. The types of horizontal ice load studied in this report are ice load caused by thermal expansion, water level changes and drifting ice. The vertical ice load also has different load types, but these types have not been studied, then most of the method does not specify what causes the vertical load. In harbours and coastal areas, many structures are constructed on piles that are exposed to open seawater. For example, pile-based structures can be piers, ports, and more. Previous research has mainly focused on dams, bridge supports and offshore structures. Consequently, there is a lack of knowledge regarding ice loads on piled structures. It is concluded by Mayor et al. (2020) that further research on ice load on piled structures is needed. More Swedish standards are adapted for bridge supports, but it is unclear to what extent the guidelines can be used on piled structures. There are also uncertainties about how bridge supports and piles relate to each other. As marine structures usually are less heavy than bridge structures, vertical ice loads have a greater impact on these structures (Mayor, 2022). According to Johansson et al. (2013), it is difficult to measure the ice load in the field, since the measuring device is located a bit outside the structure, whilst the thermal expansion tends to result in uneven values. This means that the in-situ measurements rarely result in accurate values. According to Adolfi and Eriksson (2013), the majority of the design methods for ice loads in dams recommends a line load due to the difficulties of field measurements. Due to the lack of an industry standard regarding ice loads, the structural safety can be questioned and the dimensions that may be unnecessarily conservative. Which is further emphasised as the different methods generate vastly different values of the ice load. Higher ice loads call for larger dimensions of the piled structure and thus more material. There are few known cases where piled marine structures have reached failure due to buckling induced by ice load (Mayor et al., 2020). Overall, this could indicate that the design is too conservative, but also that the design is correct as the structures should rarely fail. Löfquist (1987) argues that the safety margin for ice loads on bridges must be high, but there is an indication that the recommended values are too high compared to what the bridges are exposed to. Local conditions can be used to determine the ice load that a structure should withstand. According to Hellgren (2022), there are three factors that has a significant effect on the ice load on dam structures. These variables, which are affected by local conditions, are the thickness of ice, the water level variation and the geometry of the dam structure. Hellgren (2022) claims that, if the guidelines for dam structures would have been updated to consider local conditions, at least these three factors should be included. If local conditions are used, the structure is adapted to the 2 1.2. AIM AND PURPOSE prevailing circumstances at the project’s location. While using local conditions, the return period of the input data needs to be kept in mind. The return period of the ice load is also of importance when determining how large safety factors should be used. 1.2 Aim and purpose The purpose of this master report is to facilitate and clarify the design process of ice loads on piled structures, as there is a lack of this information today. Further, facilitating how local conditions can be accounted for is also of interest to better adapt the design loads to each situation. The overall purpose is to gain and provide better knowledge about ice loads and the resulting design process. As the previous research on this topic of ice loads on piled structures is limited and no Swedish standard is available, this is of particular interest. The aim is to demonstrate how ice load is considered in different design methods. According to Mayor et al. (2020), there are only a few cases of reported failures due to buckling. This fact is remarkable considering the uncertainty of the magnitude of ice loads, suggesting that the design loads might be unnecessarily conservative considering the prevailing circumstances. Hence, an additional purpose of this report is to evaluate how the local conditions influence the ice load. This will be achieved by evaluating some of the methods that are currently used in ice load design. The input information that is needed and how it affects the ice load will also be evaluated. Some useful input information will be presented and developed in this report to assist the use of local conditions. An assessment of which methods that are applicable for piles, account for local conditions and are suitable to use during ice load design will also be performed. This assessment will be performed for each load type individually. Knowledge of ice loads and local conditions would likely facilitate the method choice in ice load design and rationalise the structures to obtain better resource efficiency. In addition to this, a simple FEM analysis will be performed to demonstrate how the ice load affects the pile dimensions. The analysed methods will be discussed and compared to each other. This report is conducted together with the company ELU Konsult AB, and likewise, their goal is to facilitate their design process of marine structures. 1.3 Adaptation to marine structure Marine structures are often located in protected areas and thus not exposed to strong winds and currents. The occurrence of pack ice is thus low. Ship movements may result in loads as ice floes are pushed against the structure when a ship approaches the marine structure. This load type contributes to an additional, non-natural, load on the structure due to the conversion of kinetic energy as the ship collides with the ice floes. The most critical situation occurs when ice gathers inside the port, but 3 CHAPTER 1. INTRODUCTION ice barriers can decrease that effect (Ruiz de Almirón de Andrés et al., 2018). Large ice floes colliding with marine structures are not that common because of the protected location. Consequently, ice floes are usually divided into smaller floes before colliding with the structure. Methods to calculate the ice load due to large ice floe are not disregarded in this project because it may occur in some cases and the degree of protection provided for a structure varies. Further, the affects of an ice cover frozen stuck to the structure are considered in this report, if a method to determine this is available. As previously presented, the ice cannot cause loads larger than it can withstand itself. Hence, the ice’s strength is limiting, and the lowest value can be chosen. On the other hand, several ice behaviours can act during the structure’s lifetime, and the highest value of these should be considered during design. For example, the highest generated horizontal ice load caused by thermal expansion, drifting ice and water level movements should be considered. The studied calculating procedures do not all describe the load for the same ice load types. The loads from each procedure and there assigned load type will be presented in this report. This will highlight the differences between the methods which will be followed up in the discussion. More on this note, all calculations procedures are not specifically adapted and developed for piled structures but are still used in lack of better methods. In these cases, the source will be applied as given in the guideline but to the dimensions of a piled structure. This applicability will also be discussed in this project. 1.4 Research questions The provided background and purpose above and the resulting aim led to these research questions. RQ1 How are ice loads considered and categorised in the design methods? Which load cases are considered in the design methods? RQ2 Which of these methods are adapted to piled structures and applicable for design and considers local conditions? RQ3 How does the result differ between the design methods, load cases and local conditions when determining the ice load? RQ4 How do the input parameters affect the ice loads on piled structures? RQ5 How can input data dependent on local conditions be found and determined? RQ6 How are pile dimensions affected by the magnitude of the ice load? 4 1.5. SCOPE 1.5 Scope This master report will study and evaluate some existing methods used to determine ice loads. There will be a distinction between different types of ice loads and the evaluation will be performed for each load type presented in Chapter 2. Whether the methods are applicable for piles and are could be used in design will also be evaluated and discussed. The parameters used in each method and for each load type will be presented in a parametric study that will be performed to evaluate the impact of each input parameter. This parametric study will also provide information on to what degree the local conditions affect the results in each case and affect the method choice if some information is absent or uncertain. Input information for the local conditions affecting the ice loads will be presented and produced for this report, along with information on where further data can be found. The needed information for the local conditions will be presented. Considering the presented information, the discussion will reason about which method is most effective for piled structures and if some specific parts in each method are particularly advantageous during design. In the list below, the methods which will be evaluated are presented. • Trafikverket, Sweden: TRVINFRA-00227 (Trafikverket, 2021). • Löfquist, Sweden: Ice load on bridge support (Löfquist, 1987). • Waxholmsbolaget, Sweden: Guidelines for Traffic piers in the archipelago (Wikenståhl et al., 2012). • Stockholms hamnar, Sweden: Technical handbook, Designing port constructions (Stockholms hamnar, 2016). • Svensk Energi, Sweden: RIDAS Power companies guidelines for dam safety (Svensk Energi, 2011). • Vejdirektoratet & Banedanmark, Denmark: Appendix DK:2015 Ice load (Vejdirektoratet & Banedanmak, 2015). • Finnish Association of Civil Engineers, Finland: RIL 2013, Design criteria and structural loads. Water structures (RIL, 2013). • Statens vegvesen, Norway: Handbook N400 Bridge design (Statens vegvesen, 2015). • Port Designer’s handbook, Norway (Thoresen, 2014). • Committee for waterfront structures, Germany: EAU 2012 (Committee for waterfront structures, 2012). 5 CHAPTER 1. INTRODUCTION 1.5.1 Limitations In the list below, the limitations of this project are presented. • Only seasonal ice will be studied, not multi-year ice or glacier ice. • Offshore structures and ice on open sea will not be considered specifically in this project. Consequently, pack ice is not studied. • Marine structures, hence not bridges, will be studied. In cases where no information about marine structures and piles is provided, the guidelines given will be used but applied to the dimensions of the structure of interest. • Wear of piles is not accounted for in this project. • The local conditions presented apples to Sweden. Data to produce information for input variables will be obtained from Swedish sources and measurements. • It is likely to assume that the amount of ice will be affected by global warming, but this is not considered in this report. How global warming will affect the ice load’s magnitude is unknown. The probability of a magnitude of a load occurring has to be acceptable at the beginning of the structure’s lifetime and over its entire lifetime. 6 Chapter 2 Ice loads Ice loads have two main components, horizontal and vertical. The magnitude of the ice load is limited by the strength of the ice, external forces, temperature, friction between the structure and the ice, and the kinetic energy from current and wind. Furthermore, the size of the ice load depends on the failure type of the ice, its deformations properties, the geographic location, the geometry of the reservoir, and more (Burcharth, 2004). 2.1 Ice growth Ice growth and settling of an ice cover occurs when the temperature of the water is equal to its freezing point, which for freshwater is 0 ◦ C. Ice growth primarily occurs on the bottom of the ice cover when the water is cooled and heat is transported to the air through the ice and potential snow. Flooded snow or water on the ice’s surface allows for freezing from the top of the ice cover as well (Eklund, 1998). The speed of the ice growth depends on the thermal conductivity of the ice and the ice thickness, as it in itself is insulating. However, ice has a relatively low thermal conductivity (Fransson, 2009). A snow layer on the ice slows down the ice growth significantly, as the snow has an insulating capacity (Eklund, 1998). On the other hand, snow can be flooded and cause snow-ice. In these cases, the ice freezes from above and can cause multiple layers of ice (Fransson, 2009). The energy exchange is important for ice growth and is also affected by radiation (Bergdahl, 1978). Eklund (1998) states that several factors such as ice thickness, amount of snow, wind speed, humidity affect the ice growth, where amount of snow and temperature are the most important factors. Ice growth also depends on other factors, in addition to meteorological ones. The size of the body of water and the flow rate are important. For example, a lake with a larger volume has slower ice growth than a smaller one (Eklund, 1998). If the flow rate stirs the water enough to affect the stratification of the water, this leads to a lowered ice growth. Stratification is the separation of water, usually caused by a higher density of water at a specific temperature. Stratification results 7 CHAPTER 2. ICE LOADS in lower temperatures in shallow water when the air temperature is lower than the temperature at which maximum density is reached. On the other hand, it should be considered that lakes that receive cooler waters from rivers freeze quicker (Eklund, 1998). According to Hüffmeier and Sandkvist (2008), ports and harbours with high traffic of ships are commonly less likely to freeze, and the ice thickness is usually less thick. Because the water is often in motion and the ice is difficult to settle. Furthermore, ice growth depends on the salinity of the water, where a higher degree of salinity leads to a lowered freezing point. Thus, the ice grows quicker in lakes with freshwater than at sea. The relation between salinity and freezing point can be seen in Figure 2.1. It should also be noted that the salinity affects other aspects of the ice. For example, the bending strength is affected where freshwater has a higher bending strength than seawater (Burcharth, 2004). Further, the salinity also impacts the temperature at which the maximum density is obtained. If the temperature when maximum density is reached and the freezing temperature are closer to each other, the water is more easily stirred. Consequently, the temperature in the seawater is approximately the same over the depth when ice is formed (Bergström et al., 1966). The amount of salinity for different types of water is presented in Table 2.1. Freezing temperature [◦ C] 0 −1 −2 −3 0 10 20 30 Salinity [‰] 40 Figure 2.1: Freezing point of the water in relation to its salinity (Burcharth, 2004). Table 2.1: Salinity degrees in waters (Vatteninformationssystem Sverige, 2022). Freshwater ≤2‰ 2.2 Brackish water ≤ 30 ‰ Saline water ≥ 30 ‰ The failure modes of ice Ice can fail in several ways and there are six failure modes, according to Løset et al. (2006). The failure modes are creep, crushing, bending, buckling, splitting, 8 2.2. THE FAILURE MODES OF ICE and spalling. The failure mode with the lowest load capacity is the one that is most prone to occur. It should be noted that more than one failure mode can occur simultaneously. Crushing, bending fracture, and splitting are the most crucial failure modes for piled and pile like structures, according to Mayor et al. (2020), which in turn refers to (Burcharth, 2004). Moreover, Løset et al. (2006) state that the recognised design scenarios are stress, bending moment, force and splitting, which should be considered during design. The ice load cannot exceed the bearing capacity of the ice, which is the compressive, shear, tensile, flexure, or buckling strength (Løset et al., 2006). When ice fails due to crushing, the compressive strength of the ice is the crucial capacity. The compressive strength of the ice is higher than its bending strength, which means that crushing failure requires higher ice loads to fail than bending failure (Mayor et al., 2020). Moreover, ice is a brittle material and crushing is a common failure mode (Fransson, 2009). Several factors affect the strength of the ice, such as salinity, temperature, loading direction and loading rate. For freshwater, the bending strength of ice varies between 0.2 MPa to 3 MPa and between 0.1 MPa to 1.5 MPa for seawater (Timco and O’Brien, 1994). Note that freshwater provides higher values of bending strength. According to Malm et al. (2017), the compressive strength of ice varies between 1 MPa to 5 MPa and Löfquist (1987) states that field measurements using ice from an ice cover have resulted in values between 0.5 MPa and 2 MPa. According to Fransson (2009), the theoretical compressive strength can vary between 3 MPa to 10 MPa using a linear elastic model subjected to high loading rates and small stress levels, and ice cube measurements have generated values between 5 MPa to 10 MPa. The maximum pressure of the ice is limited by pressure melting, although the pressure usually is lower than the melting pressure of the ice, according to Fransson (2009). Crushing usually occurs when ice floes are pushed against vertical structures (Mayor et al., 2020). Sopper et al. (2017) conclude that the conditions of the contact area is of great importance when determining the compressive strength of ice. The compressive strength also depends on whether the ice is dry or submerged, as it affects the contact area. Further, this mainly occurs at high speeds against both narrow and wide structures (Løset et al., 2006). Figure 2.2 illustrates the failure mode crushing against a pile. The arrow demonstrates the movement of the ice cover. 9 CHAPTER 2. ICE LOADS Figure 2.2: Crushing failure against a pile, elevation view. If an ice floe or ice cover is pushed against an inclined structure, it is more likely to fail due to bending. Bending failure occurs instead of crushing failure when the structure has 45◦ sloping (Thoresen, 2014). Furthermore, Løset et al. (2006) state that this change of failure mode is obtained as the ice cover is bent when pressed upon the slope. This is also stated by Xu et al. (2022), where the importance of considering this positive aspect during design is stressed. In Figure 2.3, an ice cover’s failure against an inclined pile is illustrated. The arrow demonstrates the direction of movement of the ice cover. Figure 2.3: Bending failure against a structure, elevation view. Splitting failure is most likely to occur when the ice cover meets slender structures (Mayor et al., 2020), like piles. In this case, the ice cover or ice floe is split into two separate pieces. Factors such as the width of the structure, the drifting speed of the 10 2.3. HORIZONTAL ICE LOADS ice flow or cover, the brittleness of the ice, and the geometry of the structure affect if the ice fails due to splitting or crushing. Generally, splitting is most common at low speeds when the ice yields (Løset et al., 2006). Splitting failure is demonstrated in Figure 2.4, where the arrow demonstrates the movement of the ice. Figure 2.4: Splitting failure against a pile, plan view. As presented in this section, the geometry of the structure is important for how the ice cover behaves and thus fails. The properties of the ice depend on several factors. During the design of a structure, the failure mode of ice is significant, then the failure load of crushing is higher than bending. Hence, a geometry of the structure and dimensions and the properties of the ice should be considered (Løset et al., 2006). For narrow structures, such as piles, the ice tends to fail in crushing or splitting, since the ice interacting with the structure is limited by the surrounding ice. This results in high loads. For wider structures, flexural failure or failure due to buckling commonly occur in the ice, which results in lower pressure. This is because failure can occur non-simultaneously over a wide structure Hellgren (2022). 2.3 2.3.1 Horizontal ice loads Thermal expansion When water freezes to ice, the volume increases by 9 % (Fransson, 2009), and the volume of the ice is also affected by the thermal expansion. The bottom of the ice cover has a constant temperature of 0 ◦ C, while the top of the ice cover varies due to the sun, the air temperature, wind and water currents. If the air temperature decreases, an ice cover of freshwater ice (Löfquist, 1987) will contract and vice versa if the temperature increases (Bergdahl, 1978). If the temperature is decreased rapidly, the top of the ice cover will contract quickly, which leads to stresses in the ice cover as the volume change is inhomogeneous through the ice. In contrast, saline ice expands when the temperature is lowered and thus acts differently than freshwater ice (Löfquist, 1987). Stress due to temperature changes can cause fractures in the ice if its strength is exceeded. The volume changes at the top surface of the ice and the magnitude of the tension depends on the temperature change rate and the span of the temperature change. Rapid and large temperature changes contribute to larger stresses in the ice cover (Ekström, 2002). 11 CHAPTER 2. ICE LOADS When cracks are formed in the ice cover, they can be filled with water and snow, which can freeze. As previously mentioned, this causes a volume expansion that can move the ice cover (Fransson, 2009). These movements will cause pressure on structures, shores or other ice covers. However, thermal loads caused solely on reduced temperature results in quite small loads compared to other thermal loads. On the other hand, an ice cover of freshwater will expand if the temperature is raised. A larger load will be obtained if this happens after a contraction due to reduced temperature and the cracks are filled with water or snow (Bergdahl, 1978). It is stated by Bergdahl (1978) that the thermal ice pressure depends on the rate of temperature change, thermal expansion coefficient, to which extents possible cracks have been filled, the ice thickness and restrictions on the ice cover from shores. A characteristic value of thermal ice load is difficult to determine due to the local climate, where the amount of snow acts as insulating layer and provides shade, also affects the rate of temperature change (Ekström, 2002). 2.3.2 Water level changes Horizontal ice load can occur due to water level changes. The longitudinal expansion of the ice cover can develop an arching action between supports when the water level changes. This kind of arch action can also occur due to thermal expansion in the ice (Wikenståhl et al., 2012). The structure is not affected by ice loads if it is surrounded by stationary ice (Wikenståhl et al., 2012). Likewise, the Finnish civil engineers association, (RIL, 2013), states that the ice load can be lowered if the structure has ice loads acting on all sides. However, the ice load due to water level changes can be high for certain combinations of pile distances and water level changes. The size of the load depends on local conditions (Wikenståhl et al., 2012). According to Comfort et al. (1993), water level variations can be divided into three classes. Namely, small changes with slow rises, large changes where the water level is lowered recurrently and mid high rises that occur relatively often. The small raises are between 10 and 15 cm and occur 0 to 0.5 times per day, which have little to no effect on the ice load. The mid-high raises are between 10 and 30 cm and occur 1 to 2 times per day, generating the highest impact on the ice load (Comfort et al., 1993). For ice loads to occur due to water level changes, several factors need to be achieved. First, the water level changes need to vary around the mean water level and be sufficiently large to develop cracks. The water level changes can, on the other hand, not be too large as the ice cover has to be frozen and stuck to the structure (Malm et al., 2017). Noteworthy is that this is information regarding dams, not a structure surrounded by ice from all sides. 12 2.3. HORIZONTAL ICE LOADS 2.3.3 Drifting ice Drifting ice load is defined as the total contact force from ice pressed against the marine structure. The collision occurs from the impact of wind and current forces, which can cause crushing failure of the ice on structures. Drifting ice is often the characteristic load on the open sea and on large lakes (Ekström, 2002). Large drifting ice floes can develop large forces. For example, this force was measured in 1971 at Torne älv, Sweden, to 120 kN/m, at a bridge pillar that was found to be damaged due to large ice floes. The characteristic value has been calculated with respect to the compressive strength of the ice floe and the contact area. The compressive strength, for example, also depends on the temperature of the ice (Löfquist, 1987). In cases where ships berth in harbours, brash ice can be pushed against the structure. This ice can cause access problems for the ship if an ice cap is frozen to the structure and creates loads. In this project, the resulting load is of interest and is classified as drifting ice, even though the drifting is forced from berthing ships (Ruiz de Almirón de Andrés et al., 2018). Frozen stuck ice cover According to Løset et al. (2006), an especially complicated situation is created if a structure is frozen into the ice cover and the cover begins to move due to currents or wind. This load case is considered a type of drifting ice, as wind and currents generate this load even if it acts on an entire cover. If the ice thickness is larger around the structure, the severity of the load increases. The contact surface is increased, for example, if the structure has ice built up around it, which can be achieved if the structure’s thermal conductivity is higher than the surrounding ice. In various pulling and pushing of the cover, the structure is affected largely (Løset et al., 2006). 2.3.4 Pack ice When a large amount of ice is drifting at high speeds, ice can gather at structures and be stacked on each other as ridges or ice jams. This behaviour can be caused by winds and currents acting on ice floes or on an ice cover, where cracks naturally occur. Ice ridges are most common in open sea and in less protected areas (Mayor et al., 2020). Ice accumulation on piles may increase the effective width of the pile, which the ice load act on, and therefore also the total ice load (Løset et al., 2006). 13 CHAPTER 2. ICE LOADS 2.4 2.4.1 Vertical ice loads Water level changes Vertical ice loads occur when the ice cover is frozen and the water level changes. A rise in the water level causes the ice cover to rise, which can cause a lifting force on the structure (Ekström, 2002). Usually, light structures are more sensitive to vertical forces, as they are easier to lift. If piles are lifted, soil can fill the positions underneath the pile, which results that the structure can not settle back to its original position when the water level is back to normal level again. The process can be repeated, so the structure is successively lifted (Thoresen, 2014). Water level changes can also cause bending stress when the water level is lowered, creating cracks in the ice cover. When the water level then rises, the ice growth in the cracks creates a perpendicular force and a vertical lifting force on the structure (Ekström, 2002). A downwards directed load is also a possible load case. Mayor et al. (2020) states that this type of load is significantly smaller than the upwards directed and can thus be neglected. The downwards directed load is limited by the ice cover’s weight above its equilibrium in water. 2.5 Previous measurements of ice loads According to Johansson et al. (2013), most of the field measurements of static ice load on structures has been conducted indirectly, by measuring the in-situ pressure of ice. The most common measurement technique is to place an oil-filled sheet metal cushion and the pressure is measured continuously. But these measurements are unreliable because the pressure is redistributed around the sensor, if the deformation differs from the ice. In addition, the oil expands with increasing temperature, which results in increased oil pressure. Despite this, Johansson et al. (2013) states that if several sample measurements are preformed during a long time period, a better idea of the magnitude of the ice loads can be obtained. Adolfi and Eriksson (2013) have performed a literature study on field measurements of ice load. Which resulted in yearly maximum ice loads between 7 kN and 374 kN in Canada and the United States of America. Adolfi and Eriksson (2013) have used this input data to determine a global distribution of ice load with a log-normal distribution. The result is that there is a probability of 4% that the ice load reaches values above 253 kN/m once every 25 years. The report also recommends ice load values for the north, middle and south of Sweden, 253 kN/m, 181 kN/m and 118 kN/m, respectively. 14 Chapter 3 Design methods for ice loads In this chapter, the calculation methods in several design guidelines are presented. The equations have been homogenised as some variable symbols have been changed to be the same for all methods. These changes have been performed in order to simplify for the reader. Some equations have also been multiplied with the structural width or circumference to obtain the same point load output. In the studied references, the terms compressive strength of ice and crushing strength of ice appear. These have been assumed to be the same parameter, in accordance with Mayor et al. (2020). In this report, the term compressive strength is used. 3.1 3.1.1 General information Trafikverket The Swedish Transport Administration recently presented a new design guideline, TRVINFRA, for bridges and bridge-like structures (Trafikverket, 2021). The new guidlines replaces the previous code from 2019 (Krona, 2019). The new guidelines specifically state that it replaces the guidelines written by Löfquist (1987), which have been widely used in Sweden to determine and understand ice loads (Mayor, 2022). As the new guidelines only present a magnitude of the ice load, both Trafikverket (2021) and Löfquist (1987) will be considered separately and compared in this report. The Swedish Transport Administration’s new bridge guideline for ice load design is limited as only one value for horizontal ice loads is presented and none for vertical ice loads. If the supports have a total span 25 m and are placed in Dalarna, Gävleborg, Jämtland, Norrbotten, Värmland, Västerbotten or Västernorrland it is up to the client to decide a suitable design value of the ice load. It is stated that horizontal ice loads parallel and perpendicular to the support do not act simultaneously. The ice load can be assumed to act on levels mean high water level, MHW, and mean low water level, MLW, and the magnitude should be evaluated, although there are no specifications how to determine the magnitude. Furthermore, several ψ-factors for 15 CHAPTER 3. DESIGN METHODS FOR ICE LOADS variable loads are presented to be used in different load combinations (Trafikverket, 2021). 3.1.2 Löfquist The guidelines presented by Löfquist (1987) are adapted for bridge supports and were produced for the Swedish Road Administration, which is an old authority and now part of the Swedish Transport Administration. Löfquist (1987) state that the ice load should be considered to act between the mean high water (MHW) and the mean low water (MLW). Further, it is stated that local conditions should be considered. While considering thermal expansions, a bridge support behind another bridge support along the stream can be designed to withstand one-third of the magnitude affecting the first support, according to Löfquist (1987). 3.1.3 Waxholmsbolaget Waxholmsbolaget’s guideline (Wikenståhl et al., 2012) is applicable and specifically written for traffic piers in the inner archipelago of Stockholm, Sweden. For cases where nothing specifically is stated, the horizontal ice load should be equal to 200 kN per pile, while piles behind other piles, in the direction of the force, should be considered to be unloaded. According to Wikenståhl et al. (2012), the ice load acts between MHW and MLW if no pack ice occurs. The superstructure should be build above MHW to avoid large ice loads. Wikenståhl et al. (2012) state that the largest ice thickness in the inner archipelago in Stockholm, on average, is about 0.3 m. During extreme winters, the ice thickness can reach 0.6 m. It is also stated that the ice load is highly affected by local conditions (Wikenståhl et al., 2012). 3.1.4 Stockholms hamnar According to Ports of Stockholm (Stockholms hamnar, 2016), the ice load should be evaluated based on local conditions. Different types of ice loads do not act simultaneously and the point of action should be assumed between MHW and MLW. The load combination factor, ψ, from Karlsson et al. (2011), which now is outdated and replaced, should be used while performing load combinations. This Swedish, Stockholm-based handbook is developed for ports and values for concrete elements, sheet-pile walls and piles are presented. It should be noted that Stockholms hamnar does not provide any particular procedures for specific failures and ice load types. It instead provides guiding values for ice loads in different directions to the quay (Stockholms hamnar, 2016). 16 3.1. GENERAL INFORMATION 3.1.5 Svensk Energi The Swedish guideline for dam safety presented in RIDAS (Svensk Energi, 2011) is not extensive and is produced for dams, hence not for piled structures. On the other hand, it is stated that slender structures can be exposed to values higher than 200 kN/m and this information refers to Ekström (2002). It is not specifically presented what type of horizontal ice load is described in this guideline. A range of values is presented and the chosen value should be based on geography, altitude and local conditions. The ice thickness is 0.6 m below a line through Stockholm and Karlstad and 1 m above this, note that these are guiding values according Svensk Energi (2011). The load acts at a third of the ice’s thickness from the top of the cover. The top of the ice cover is considered to be at the maximum water level. 3.1.6 Vejdirektoratet The Danish handbook, Appendix DK:2015 Ice load , is developed by Vejdirektoratet & Banedanmak (2015), but will in the following only be referred to one of the authors, Vejdirektoratet. The local variations of ice thickness should be used and if no information on the local conditions is available, the ice thickness, d, can be chosen to 0.57 m, see Equation 3.1. However, it should be noted that the thickness is usually less in port areas. Combined with the ice strengths, the ice thickness results in an ice load with a return period of 50 years. These values are applicable for saline and freshwater according to Vejdirektoratet & Banedanmak (2015). d = 0.57 m (3.1) Furthermore, the ice load should be decided based on local conditions, namely water depth, salinity, wind conditions, the currents and the dimensions and geometry of the structures. It is applicable for bridges and other structures. The ice load should normally be considered to act at the annual mean water level measured during January and April, according to Vejdirektoratet & Banedanmak (2015). 3.1.7 RIL When determining the ice load, the Finnish association of civil engineers states that one should consider the local conditions and firstly use statistics in their design criteria for water structures (RIL, 2013). The applied data of the area should at least be from 10 ice-occurring winters. If this information is absent, the equations and methods presented in this chapter should be used. The ice load should not exceed a safety level of 98 % of the structure’s life span. The point of action for the horizontal ice loads is considered to be a third of the thickness of the ice from its top. The maximum ice thickness, d, of a fixed ice cover is given for geographically divided 17 CHAPTER 3. DESIGN METHODS FOR ICE LOADS areas in Finland. The thickness of ice varies from 0.7 m in the south to 1.1 m in the north, and the ice thickness along the coast is generally lower compared to the inland. The values can be linearly interpolated. The ice thickness on floating ice and open ice ridges should be decided separately (RIL, 2013). 3.1.8 Statens vegvesen According to the Public Road Administration in Norway’s handbook, Handbook N400 Bridge design (Statens vegvesen, 2015), the ice thickness, d, is can be determined by Equation 3.2 (Statens vegvesen, 2015). This equation uses a parameter F D [h◦ C], describing the numbers of hour with cold climate. This value can, in turn, be found in the Norwegian handbook of road construction (Statens vegvesen, 2014), which presents a design value for specific areas in Norway. For permanent structures, the return period for F D should be 100 years and for temporary structures, a return period of 10 years should be used (Statens vegvesen, 2015). Statens vegvesen (2014) presents different amounts of hours of frost, F D, for permanent and temporary structures. For permanent structure, the number of hours with frost is higher than for temporary structures and the ice thickness varies between 0 m and 1.8 m. For temporary structures, the ice thickness varies between 0 m and 1.5 m. √ d= FD 175 (3.2) According to the Norwegian handbook, Statens vegvesen (2015), the local conditions and variations should be considered to archive a better estimate of the ice load. The width of the support, can under certain conditions, be increased to an effective width. The point of action for the ice load should, for drifting ice, be the most unfavourable position between the highest astronomical tide (HAT) and the lowest astronomical tide (LAT). Regarding regulated reservoirs and lakes, the point of action should be between the highest and lowest regulated water levels (HRW) and (LRW) respectively. The point of action should be separately evaluated for rivers, respectively. Even though the handbook is primarily developed for bridges, it also concerns quays and piles (Statens vegvesen, 2015). 3.1.9 Port Designer’s handbook The Port Designer’s handbook (Thoresen, 2014) includes guidelines and recommendations for port design and structures. The handbook is adapted for port design and is based on port and harbour projects in Norway (Thoresen, 2014). The handbook has not specified where the load acts, but has clearly stated the importance of local conditions for ice loads. Water level variation, type of structure, ice conditions and properties should be evaluated and the effect on the structure should be determined (Thoresen, 2014). 18 3.1. GENERAL INFORMATION 3.1.10 EAU The method to calculate ice load according to the German handbook EAU 2012 (Committee for waterfront structures, 2012), which is explicitly valid for piles. The load is applied between 0.5 to 1.5 m above MHW and should be reduced if an air bubble system, heating or thermal device is used. The ice thickness can also be reduced due to the amount of water flow, which also reduces the ice load (Mayor et al., 2020). The ice load calculations according to Committee for waterfront structures (2012) are applicable for both sea ice, with a salinity degree higher than 50 ‰ and for freshwater. Brackish water is calculated with the same equation as freshwater. The handbook provides different procedures or values of parameters for coastal areas and inland areas. The porosity of the ice is dependent on the salinity and the mean temperature of the ice and calculated according to Equation 3.3 for saline waters. If the porosity is unknown, the mean ice temperature is assumed to be linear between the ice’s top and bottom. The temperature at the bottom of the ice cover is approximately -2◦ C for the German North Sea coast and approximate -1◦ C for the German Baltic Sea coast, but the temperature variates with the air temperature and the salt content. φp = 19.37 + 36.18 · SB0.91 · |Tm |−0.69 (3.3) where, φp SB Tm Porosity of the ice [‰] Salinity [‰] Mean temperature of the ice [◦ C] The horizontal ice compressive strength, σk , is calculated according to Equation 3.4 for saline water. In freshwater, the compressive strength is calculated according to Equation 3.5 and depends on the mean ice temperature if no more specific strength is known (Committee for waterfront structures, 2012). The compressive strength should not exceed 1.5 MPa for the North Sea, 1.8 MPa for the Baltic Sea and 2.5 MPa for freshwater, according to Committee for waterfront structures (1996). In coastal areas, the bending strength can be assumed to one-third of the compressive strength, and the shear strength to one-sixth of the compressive strength (Committee for waterfront structures, 2012). σk = 2700 · ε1/3 · φ−1 p (3.4) ( 1.10 + 0.35 · |Tm | If 0◦ > Tm > −5◦ σk = 2.85 + 0.45 · |Tm + 5| If Tm < −5◦ (3.5) 19 CHAPTER 3. DESIGN METHODS FOR ICE LOADS where, φp ε Tm Porosity of the ice [‰] Specific rate of expansion, ε = 0.001 s−1 ] Mean temperature of the ice [◦ C] 3.2 3.2.1 Horizontal ice loads Methods without classification of load type Trafikverket Trafikverket (2021) does not provide any specification of the horizontal load type, only a value of the ice load is given, see Equation 3.6. This value is applicable for Sweden in specific locations, see Section 3.1.1. Otherwise, the client should prescribe a magnitude of the ice load. Ih.1 = 200 kN (3.6) Stockholms hamnar Stockholms hamnar does not provide any specification of the horizontal load type. The values presented in Equation 3.7 can be used to determine the horizontal ice load for sheet-pile walls, concrete elements and piles, slabs respectively (Stockholms hamnar, 2016). The parameter i1-2 , is an ice line load parameter and b is the width of the support. Ih.1 ( i1 · b For sheet-pile walls and concrete elements = i2 · b For piles and slabs where, Away from quay 50 kN/m i1 = 50 kN/m Parallel to the quay 100 − 200 kN/m Towards the quay ( 100 kN/m Parallel to the quay i2 = 200 kN/m Towards the quay 20 (3.7) 3.2. HORIZONTAL ICE LOADS Svensk Energi The horizontal ice load, according to Svensk Energi (2011), is presented in Equation 3.8. South of Sweden is defined as Blekinge, Bohuslän, Halland, Skåne and Västergötland and the middle part of Sweden is considered to be the area north of the stated and south of a line through Karlstad and Stockholm. Areas north of this line are considered to be north of Stockholm. The variable, b, is the width of the support, and i is a line load parameter. Ih.1 = i · b (3.8) where, 50 kN/m In the south of Sweden i = 100 kN/m In the middle of Sweden 200 kN/m North of Stockholm It should be noted that slender structures can be affected by loads larger than 200 kN/m, according to Svensk Energi (2011) which in turn refers to (Ekström, 2002). The limiting value for the line load, i, is 2000 kN/m for arch action on supporting structures. According to Svensk Energi (2011), the line load for arch action is based on experiments performed by Löfquist (1987). 3.2.2 Thermal expansion Löfquist Equation 3.9 presents how to calculate the thermal ice load according to Löfquist (1987). If the support length, a, is smaller than 4 m, it should be defined as 4 m. The ice load parameter, i1 , normally varies between 50 kN/m to 300 kN/m for freshwater. It should be noted that no guidance for saline water is given in Löfquist (1987). Ih.1 = i1 · a (3.9) where, a≥4m 50 kN/m ≤ i1 ≤ 300 kN/m For a support behind another one in the stream direction, the ice load parameter, i1 , can be reduced as presented in Equation 3.10. This reduction is for cases where a large value of i1 initially is applied on the first row of piles relative to the current 21 CHAPTER 3. DESIGN METHODS FOR ICE LOADS line. If needed, the case where the ice loads only act on one side of the support could be considered (Löfquist, 1987). i1 i1 = max 3 50 kN/m (3.10) Waxholmsbolaget Wikenståhl et al. (2012) states that the values presented in Equation 3.11 should be used for horizontal loads per support or pile. The equation should be used for all the horizontal ice load types, not only for the thermal ice load. The equation is adapted for slender structures, where the ice thickness and width of the supports are approximately the same. The horizontal load is limited by the compressive strength, σk . It is stated that the ice thickness can reach a magnitude of 0.6 m during extreme winters. The thermal ice load can reach a maximum of 400 kN if the there is a current line or flat beach which ice can slide on. Otherwise, the thermal load should be limited to 200 kN. Ih.1 ( 400 kN Current line or flat beach which ice can slide on = min 200 kN Other cases σk · d · b Applicable for slender structures, d≈b (3.11) where, σk b d Compressive strength defined as 2 MPa Width of the support [m] Thickness of ice [m] If there are piles behind other piles, in relation to the stream, the ice load on these should be considered to be 0 kN. Vejdirektoratet The ice load due to thermal expansion, according to Vejdirektoratet & Banedanmak (2015), affects the support in the bridge’s direction horizontally. The load can be considered to act on one side and evenly distributed along the support’s width. This load multiplied by the support’s width, b, gives the total ice load, see Equation 3.12. σk is the ice’s compressive strength and d the ice thickness in meters. 22 3.2. HORIZONTAL ICE LOADS Ih.1 = 0.04 · σk · d · b (3.12) where, σk = 1900 kPa RIL The thermal horizontal ice load is, according to RIL (2013), limited by different load magnitudes for different parts of Finland. These values vary from 400 kN/m in the north to 200 kN/m in the south. This value should be multiplied by the width of the support, b, to obtain a point load. The combined width of all the piles should, in the loading direction, be at least 4 m. The presented values can be assumed lower if the ice cover’s length is larger than 50 m. In these cases, the load can be multiplied by a form factor. This form factor can be interpolated up to 0.6 when the cover is 150 m. In addition, the thermal ice load can be reduced if the structure is flexible, the support on the opposite shore is limited, and thermal expansions are equal around the pile and thus cancel each other out. Lastly, if the area is wind protected, it can be assumed that there is snow on the ice, which lowers the load. Statens vegvesen The thermal expansion and the resulting ice load is according to Statens vegvesen (2015) calculated as presented in Equation 3.13. A separate evaluation should be performed if there is a risk of one-sided structure loading. Ih.1 ( (300 · d + 2.5 · |T |) · b = min i·b kN (3.13) where, d T b i Ice thickness [m], and defined as d ≤ 0.5 Lowest average daily temperature, of a return period of 50 years [◦ C] The width of the support [m] Ice load parameter [kN/m], and defined as i = 250kN/m Port Designer’s handbook Thoresen (2014) does not provide any value or equation for thermal ice loads. 23 CHAPTER 3. DESIGN METHODS FOR ICE LOADS EAU The German handbook does not provide a method to calculate the thermal ice load that is explicitly valid for piles. In Section 3.2.3, a method to calculate the horizontal ice load is presented that is explicitly valid for piles. Although, the method is not adapted specifically for thermal ice loads. The thermal ice line load, i, determined using Figure 3.1, is a static load on bank structures or other planar structures caused by rapid temperature changes. This ice load depends on the temperature rate change, Tr , the ice thickness, d, and the mean ice temperature, Tm , according to Committee for waterfront structures (2012). Figure 3.1: Thermal ice load, i, as a function of temperature rate change, Tr . Reproduced figure from Committee for waterfront structures (2012). The thermal load, Ih.1 , in Equation 3.14, is dependent on the width of the piles and thermal ice line load for planar structures, i. Ih.1 = i · b 3.2.3 (3.14) Water level changes Löfquist According to Löfquist (1987), the horizontal ice load caused by water level changes is calculated similarly to the thermal ice loads, see Section 3.2.2. Regarding this load type, the maximum i1 , an ice load parameter, can be defined as 200 kN/m. Further, Löfquist (1987) also states that this load type can be considered to act on one side of a support. 24 3.2. HORIZONTAL ICE LOADS Waxholmsbolaget The ice load caused by water level changes is described in Equation 3.15 and reach a maximum of 200 kN. Note that the equation for slender piles is used for all the horizontal ice load types (Wikenståhl et al., 2012). Ih.1 ( σk · d · b Applicable for slender structures, d≈b = min 200 kN (3.15) where, σk = 2 MPa Piles behind other piles should be considered to be unaffected by the ice load. Vejdirektoratet The Danish guidelines (Vejdirektoratet & Banedanmak, 2015) does not provide any specific method to calculate the horizontal load caused by water level changes. RIL RIL (2013) does not provide any specific method to calculate the horizontal ice load from water level changes. Statens vegvesen See Section 3.2.2, as the procedure is identical. Port Designer’s handbook Thoresen (2014) does not provide any value or equation for ice loads caused by water level changes. EAU The Committee for waterfront structures (2012) does not provide any value or equation for ice loads caused by water level changes. 25 CHAPTER 3. DESIGN METHODS FOR ICE LOADS 3.2.4 Drifting ice Löfquist The Swedish handbook written by Löfquist (1987) provides a specific method to calculate the drifting ice load. The horizontal ice load caused by a small ice floe can be calculated with Equation 3.16. The ice load parameter, i2 , varies between 10 kN/m and 30 kN/m normally according to Löfquist (1987). The variables, L1 and L2 , are the distances between surrounding supports. Ih.1 = i2 · (L1 + L2 ) 2 (3.16) The resulting ice load from larger ice floes can be obtained using Equations 3.17 and 3.18, depending on the geometry of the support. Equation 3.18 should be used in cases with an inclined or pointed support. The variable d, is the thickness of the ice, b is the width of the support and the following parameters σk , C1 , C2 and C3 are presented in Tables 3.1 to 3.4 (Löfquist, 1987). Figure 3.2 explains the support’s geometry and angles in order to decide C2 and C3 . Equations 3.17 and 3.18 should be used when the current and floes primarily move parallel to the support’s width. A perpendicular pressure also acts on the support, which is considered as 15 % to 20 % of the total pressure. If the current is floating with an angle towards the support, Equation 3.17 can be divided into vectors. If the angle between the support width and current is larger than 30◦ , a special investigation regarding the ice load’s magnitude is required. Further, the dynamic ice load with temporary high pressure and the resulting potential resonance should be considered if the support has a low stiffness (Löfquist, 1987). Piles are affected by this due to their slender geometry. Ih.2 = C1 · σk · d · b (3.17) Ih.3 = C1 · C2 · C3 ·σk · d · b | {z } (3.18) ≥0.5 Table 3.1: Guiding values of the compressive strength of the ice, σk , (Löfquist, 1987). σk [kPa] 500 700 1400 Context Saline water at the Swedish west coast Regulated rivers in the middle and north of Sweden Heavy ice breakage, large ice floes of kernel ice flows at high speed 26 3.2. HORIZONTAL ICE LOADS Table 3.2: The form factor, C1 , due to support width, b, and the ice thickness, d, (Löfquist, 1987). C1 [-] 0.80 0.90 1.00 1.10 1.30 1.80 (a) b/d ≥4 3 2 1.5 1 0.5 (b) Figure 3.2: (a) The support’s sharpness, θ. Elevation view. (b) The support’s inclination, β. Section view. Table 3.3: The form factor, C2 , due to the support’s front sharpness (Löfquist, 1987). C2 [-] 0.54 0.59 0.64 0.69 0.77 1.00 Sharpness, θ 45◦ 60◦ 75◦ 90◦ 120◦ 180◦ Table 3.4: The form factor, C3 , due to the support’s front inclination (Löfquist, 1987). C3 [-] 0.50 0.75 1.00 Inclination, β 30◦ - 45◦ 15◦ - 30◦ 0◦ - 15◦ 27 CHAPTER 3. DESIGN METHODS FOR ICE LOADS Waxholmsbolaget Drifting ice is a horizontal load type that can reach values up to 1200 kN according to Wikenståhl et al. (2012), but is also limited by the crushing strength of the ice, see Equation 3.19. Note that the equation for slender piles is used for all the horizontal ice load types. (Wikenståhl et al., 2012) Ih.1 ( σk · d · b Applicable for slender structures, d≈b = min 1200 kN (3.19) where, σk = 2 MPa If there are several rows of piles, the load on the piles behind others, in the direction of the stream, can be set to 0 kN. Vejdirektoratet Equation 3.20 determines the vertical ice load due to drifting ice floes. This procedure is also used to obtain loads from a larger floating ice layer affected by currents and wind. Three different scaling factors, C1 , C2 and C3 are used, where C1 is a form factor dependent on the cross-section of the support, C2 is a contact factor since the ice is not in contact with the entire support, C3 is a factor accounting for the three-dimensional action of tension (Vejdirektoratet & Banedanmak, 2015). The variable, σk , is the compressive strength of ice, d is the ice thickness and b is the width of the support. Ih.1 = C1 · C2 · C3 · σk · d · b where, ( 0.9 For circular cross-sections of the support C1 = 1.0 For rectangular cross-sections of the support 0.5 For drifting ice floes C2 = 1.0 For ice frozen to the structure 1.5 For an increasing ice thickness around the structure r d C3 = 1 + 5 · b σk = 1900 kPa 28 (3.20) 3.2. HORIZONTAL ICE LOADS RIL The ice load due to drifting ice floes is according to RIL (2013), The Finnish Association of Civil Engineers, expressed in Equations 3.21 and 3.22. The former is the maximum static load if a vertical structure cuts a moving ice field or floe and the latter is when the ice is adhering to the structure. If the front of the structure is vertical, either equation may be used. Further, a dynamic load can be produced where either equation can be used and an oscillation frequency can vary between 0.5 Hz to 10 Hz and 0 Hz to 1 Hz for compression and bending, respectively. For dynamic ice loads, structural dynamics should be considered. Perpendicular to the movements of the ice, the loading should be assumed to be at least 10% of Equation 3.21, 3.22 or 3.37. Ih.1 = C1 · C2 · C3 · C5 · b · d · σk (3.21) Ih.2 = C2 · C4 · C5 · tan(β) · σb · d2 (3.22) where, C1 C2 C3 C4 C5 b d σk β σb Form factor [-], see Table 3.5 Contact coefficient between ice and structure [-] Factor for the ratio between ice thickness and the width of the structure [-] Factor for the geometry of the structure [-] Contact factor between the ice and the structure ice cover [-] Support width [m] Ice thickness [m] Compressive strength of ice [MPa], see Table 3.6 Inclination of the front wall to the horizontal plane. [◦ ] Bending strength of ice [MPa] with, C2 = 0.5 C3 = 1 + b 0.2 · max d C4 = 1.0 b 1 + 0.05 · d ( 1 C5 = 1.5 to 4.0 1.5 · d b If the structure’s front is a wall If the structure’s front is a semicircle For drifting ice floes For ice frozen to the structure 29 CHAPTER 3. DESIGN METHODS FOR ICE LOADS σb = 0.65 · σk Table 3.5: Form factor, C1 , due to the structure’s shape at the level of action (RIL, 2013). C1 [-] 0.9 1.0 0.5 0.6 0.7 0.8 1.0 Shape of the structure’s front Semicircle Rectangle A triangle with vertex, ≤ 45 ◦ A triangle with vertex, 60 ◦ A triangle with vertex, 90 ◦ A triangle with vertex, 120 ◦ A triangle with vertex, ≥ 150 ◦ Table 3.6: Compressive strength of the ice, σk , (RIL, 2013). σk [MPa] 1 1.5 2.5 3 Context Weakened ice due to melting during spring Intact, moving ice during melting at spring Intact, slowly moving ice due to thermal effects at coldest winter Intact, moving ice due to wind and currents, at coldest winter Ice loads due to ships moving and berthing against marine structures pushing ice against the structure should also be considered according to RIL (2013). It should be noted that this horizontal load type does not act simultaneously with other ice loads. Equation 3.23 demonstrates this ice load caused by berthing ships for piles, columns and solid walls. Piles should be designed to withstand a point load acting between one meter above the MW and two meters below it. The parameter, i, describes a line load and Ih.3.1 describes a point load dependent on the type of structure. Ih.3 ( max i · b = Ih.3.1 200 kN Solid wall (3.23) Piles and columns where, Ih.3.1 i = 100 kN/m ( 350 kN/1 · 1 m2 For connecting berths = 500 kN/1 · 1 m2 For sea piers Ice loads due to ice cover movements according to RIL (2013) is calculated according to Equation 3.24. Generally, the area of an ice floe should be considered the maximum possible but not larger than five times the width of the riverbed. If the 30 3.2. HORIZONTAL ICE LOADS area is wind protected, it can be assumed that there is snow on the ice, which would lower the load. Ih.4 = Ih.4.1 + Ih.4.2 + Ih.4.3 + Ih.4.4 + Ih.4.5 Ih.4.1 = µtop · q · B Ih.4.2 = µbottom · B · γw · v 2 2·g Ih.4.3 = G · θ Ih.4.4 = ζk · B · γw · v 2 2·g where, Ih.4.1 Ih.4.2 Ih.4.3 Ih.4.4 Ih.4.5 µtop q B µbottom γw v g G θ ζk b ν Wind load on the ice cover [kN] Water flow load on the cover’s bottom side [kN] Horizontal component due to the floes weight [kN] Flow load on the edge of a floe [kN] Wave load on the floe’s side [kN] Friction coefficient of top surface [-], see Table 3.7 Wind load [kN/m2 ] Area of the ice field or floe [m2 ] Friction coefficient of bottom surface [-], see Table 3.8 Volume weight of water [kN/m3 ] Water current rate [m/s] Gravitational constant [m/s2 ] Weight of an ice floe [kN] Inclination of the water surface [◦ ] Hydrodynamic form factor [-], see Figure 3.3 Structure width [m] Kinematic viscosity [m2 /s] Table 3.7: Friction coefficient, µtop , (RIL, 2013). µtop [-] 0.0010 0.0015 0.0020 0.0030 Surface roughness Smooth ice surface Snowy ice surface Coarse ice surface Narrow ice field 31 (3.24) CHAPTER 3. DESIGN METHODS FOR ICE LOADS Table 3.8: Friction coefficient, µbottom , (RIL, 2013). µbottom [-] 0.005 0.015 0.01 - 0.1 Surface roughness Smooth surface, for example ice Rough surface, for example concrete Uneven surface 1.5 ζk [-] 1 0.5 0 3 10 104 105 106 v·b Reynolds number [-] ν 107 Figure 3.3: The hydrodynamic form factor, ζk , as a function of Reynolds number (RIL, 2013) (Johannesson and Vretblad, 2011). Statens vegvesen Equation 3.25 is used to determine the ice load due to drifting ice according to Statens vegvesen (2015). Reductions of the structural width, b, to the effective width, beff , can be performed if the centre-to-centre (c.t.c) distance is larger than five times the width of the structural component. Regarding structures with inclined supports, the ice load is limited by the ice’s bending strength. If the inclination is less than 70◦ , Statens vegvesen refers to ISO 1906:2010 (E) section A.8.2.4.4.3 (Statens vegvesen, 2015). Ih.1 −0.16 n b d · = A · d · beff · d d1 where, 32 (3.25) 3.2. HORIZONTAL ICE LOADS A b beff d d1 n Ice load parameter [kN/m2 ] Width of the support [m] Effective width of the support [m] Ice thickness [m] Transformation factor of the ice thickness [m] Exponent [-] A = 1800 kN/m2 d1 = 1.0 m n= d If d ≤ 1.0 m 5 If d > 1.0 m −0.3 ( Total structure width If c.t.c. < 5 · b = Structural component’s width If c.t.c. > 5 · b beff −0.5 + If pack ice is present in the area, an individual evaluation should be performed. An evaluation of the dynamic effects should be implemented if the displacement of the structure at the point of action of the ice load is greater than 10 mm (Statens vegvesen, 2015). Port Designer’s handbook Equation 3.26 is one of the methods used to determine the horizontal ice load due to drifting ice, according to Thoresen (2014). The method is based on the distance between the piles or the size of the ice floe, D and a characteristic number of the ice load per meter, i for different locations. The method is mainly used for single pile structures. Ih.1 = i · D (3.26) where, 10 - 20 kN/m In rivers or berth structures under traffic i = 30 kN/m For narrow rivers 50 - 100 kN/m For structures heavily exposed to ice Equation 3.27 is used when the floating ice reaches failure due to crushing against the structure (Thoresen, 2014). The ice load is calculated by global pressure pG , which is based on an ISO standard (ISO 19906, 2010). The global pressure is determined based on the strength coefficient and empirical factors. The standard is valid specific for Arctic offshore climate. The handbook recommends reducing the force to one 33 CHAPTER 3. DESIGN METHODS FOR ICE LOADS third for structures with 45◦ sloping since the ice tends to fail in bending instead of crushing. Ih.2 = pG · d · b pG = A · d d1 (3.27) n m b · d The strength coefficient, A, is equal to 1.8 MPa for the Baltic Sea and 2.8 MPa for the Beaufort Sea, d1 is a reference for ice thickness that is equal to 1 meter, m is an empirical exponent. According to Mayor et al. (2020), there is a printing error in Port Designer’s Handbook, where the coefficient, m, is defined as (-0,16), not (0,16). The parameter, n [-] is also an empirical exponent explained below. ( 1.8 MPa Baltic Sea A= 2.8 MPa Beaufort Sea n= -0.5 + -0.3 d If d < 1.0 m 5 If d > 1.0 m Some scenarios would increase the ice load, Ih.2 , which happens when ice is frozen around the structure, this is presented in Equation 3.27. In this case, the ice load, Ih.2 , should be multiplied with a coefficient, kAdfreeze , which increases the effective width of the piles, see Equation 3.28 (Thoresen, 2014). Ih.3 = Ih.2 · kAdfreeze (3.28) Where the coefficient kAdfreeze is approximately 2.9 for low ratios of b/d and is between 1.75 to 2 for ratios larger than 20. EAU The German handbook, written by Committee for waterfront structures (2012), has one equation to determine the horizontal ice load on vertical piles. Although, there are different empirical contact coefficients, k, for ice floes or tightly lying ice cover. The horizontal ice load, Ih.1 , is calculated according to Equation 3.29. The calculating procedure is also dependent on the shape of the piles and the arrangement. The equation is valid if the piles have a width, b, up to 2 m and a ratio between the pile and the ice thickness, d, of b/d < 12. The inclination of the piles should also be steeper than 80◦ . The ice compressive strength, σk , should be calculated according to Equation 3.4 for saline water and Equation 3.5 for freshwater in Section 3.1. 34 3.3. VERTICAL ICE LOADS Ih.1 = k · σk · b0.5 · d1.1 If b/d < 12 (3.29) where, Ih.1 k σk b d Horizontal ice load [MN] Empirical contact coefficient [m0.4 ] Ice compressive strength [MPa] Width of piles [m] Ice thickness [m] ( 0.793 In the occurrence of tight lying ice cover k= 0.564 In the occurrence of ice floes 3.3 Vertical ice loads Trafikverket Trafikverket (2021) does not provide any guidance regarding vertical ice loads. Löfquist The vertical ice load, uplift, should be calculated as presented in Equation 3.30 for both piles or dolphin structures and bridge supports according to Löfquist (1987). The parameter A is used to calculate the uplift, dependent on local factors such as salinity. The lowest value is applicable for saline waters on the Swedish west coast and the highest value is applicable for freshwater. The bending strength of ice, σb , varies between 1000 kPa in freshwaters to 2000 kPa in saline waters on the Swedish west coast (Löfquist, 1987). Iv.1 2 For separate piles, dolphins A · d p = 2 · (a + b) · 0.6 · d · σb · w · kg For bridge supports | {z } iv where, 35 (3.30) CHAPTER 3. DESIGN METHODS FOR ICE LOADS d A a b iv σb w kg Ice thickness [m] Uplift parameter [kN/m2 ] Length of the support [m] Width of the support [m] Maximum ice lift along a straight wall [kN/m] The bending strength of ice [kPa] Water level rise [m] Uplift module [kN/m3 ] with, 800 kN/m2 ≤ A ≤ 1600 kN/m2 d ≤ 0.6 m 1000 kPa ≤ σb ≤ 2000 kPa kg = 10 kN/m3 Furthermore, according to Löfquist (1987), the uplift caused by water level changes is limited to a third of the horizontal value, Ih.1 , see Equation 3.31. The procedure to calculate the horizontal load due to water level changes is presented in Section 3.2.3. The lowest value obtained from Equations 3.30 and 3.31 should be chosen as the vertical ice force in the design. It should be considered that this is an interpretation by the authors of what is presented by Löfquist (1987), as it is not clear. Iv.2 = Ih.1 3 (3.31) Waxholmsbolaget If the ice cover is frozen around the piles and the water level rises, an uplift force occurs. This load is only limited to the bending strength, σb , and the weight of the water under the pier, see Equation 3.32 (Wikenståhl et al., 2012). Iv.1 ( √ 60 · b · d · σb · w = min γw · B · w where, b d σb w γw B The width of the support [m] Ice thickness [m] Bending strength of ice [MPa] Water level change [m] Weigth of water [kN/m3 ] Area under the pier [m2 ] 36 kN (3.32) 3.3. VERTICAL ICE LOADS For a pile behind another pile, along the direction of the force, the load should be equal to 0 kN. Stockholms hamnar Equation 3.33 describes the vertical ice load upwards, uplift, on quays and piers acting on piles and slabs (Stockholms hamnar, 2016). The support width, b, is multiplied with an ice load parameter for a line load, i. Iv.1 = i · b · π (3.33) where, i = 20 kN/m Svensk Energi Svensk Energi (2011) does not provide any value or equation for vertical ice loads. Vejdirektoratet The vertical ice load upwards can be obtained by Equation 3.34 for piles and smaller structures, respectively (Vejdirektoratet & Banedanmak, 2015). The parameter σb is the bending strength of the ice, d is the ice thickness, b is the width or diameter of the support, kg is an uplift module and w is the water level change. Iv.1 = 0.8 · σb · d1.75 · b0.25 If 0.5 ≤ π · b · 0.4 · d · pk · σ · w g b b If > 7 d b ≤7 d (3.34) where, σb = 500 kPa kg = 9.81 kN/m3 w=1m Vejdirektoratet & Banedanmak (2015) also presents a vertical load downwards and the magnitude is determined by Equation 3.35. The value is defined as half the uplift, as the magnitude of the downwards directed load usually is less, according to Vejdirektoratet & Banedanmak (2015). Iv.2 = 37 Iv.1 2 (3.35) CHAPTER 3. DESIGN METHODS FOR ICE LOADS RIL The vertical load due to water level changes according to RIL (2013) is expressed in Equation 3.36. RIL also presents a bending moment caused by the vertical ice load, but this is not presented here, as only the ice load is of interest. Equation 3.36 is applicable for both upwards and downwards directed loads. For Finnish conditions, in cases of snow on the ice cover, the ice surface temperature usually is less than -5 ◦ C according to RIL (2013). Iv.1 ( √ 4 ks · v · t · d3 · V = kv · σb · d2 Wall structures, [kN] Individual structure, [MN] (3.36) where, ks v t d V kv σb σk Coefficient depending on temperature and time [-], see Figure 3.4 Water level change rate [m/h] Time from the beginning of water level change [h] Ice thickness [m] Length of support in contact with ice [m] Coefficient dependent on ice thickness and support width [-], see Table 3.9 Bending strength of ice [MPa] Compressive strength of ice [MPa], see Table 3.10 σb = 0.65 · σk 38 3.3. VERTICAL ICE LOADS Figure 3.4: The coefficient, ks , given from the ice’s surface temperature [-]. Reproduced from RIL (2013). Table 3.9: The coefficient, kv , is equal to a ratio between structure width and ice thickness (RIL, 2013). kv [-] 0.16 0.18 0.22 0.26 0.30 0.36 0.43 0.63 1.1 39 b/d 0.1 0.2 0.5 1 2 3 5 10 20 CHAPTER 3. DESIGN METHODS FOR ICE LOADS Table 3.10: The compressive strength of ice, σk , (RIL, 2013). σk [MPa] 1 1.5 2.5 3 Context Weakened ice due to melting at spring Intact, moving ice during melting at spring Intact, slowly moving ice due to thermal effects at coldest winter Intact, moving ice due to wind and currents at coldest winter Further, the vertical ice load on an inclined surface can be determined using Equation 3.37, where Ih.2 is the horizontal force on the structure expressed in Section 3.2.4 and β is the inclination of the front wall. Iv.2 = Ih.2 tan(β) (3.37) Statens vegvesen Uplift due to water level changes can reach a third of the horizontal component’s magnitude, see Equation 3.38. The calculation procedure for the horizontal ice load, Ih.1 , is presented in Section 3.2.3 (Statens vegvesen, 2015). Iv.1 = Ih.1 3 (3.38) An additional calculation procedure to determine the ice load uplift is presented in Equation 3.39 (Statens vegvesen, 2015). Iv.2 = V · 0.6 · | p 0.7 · d · A · w · kg {z } qv where, V d A w kg Length of support in contact with ice [m] Ice thickness [m] Ice load parameter [kN/m2 ] Water level change [m] Uplift module [kN/m3 ] with, A = 1800 kN/m2 kg = 9.81 kN/m3 40 kN (3.39) 3.3. VERTICAL ICE LOADS For an individual placed pile, the vertical ice load can be calculated according to the simplified Equation 3.40, where qp is a distributed load, and d is the thickness of the ice cover (Statens vegvesen, 2015). Iv.3 = qp · d2 (3.40) where, qp ≤ 1600 kN/m2 d ≤ 0.6 m Port Designer’s handbook The vertical ice load, Iv.1 , is determined based on the width of the piles, b, and the ice line load, i, determined in Figure 3.5. The line load is based on the ice thickness, d, and the diameter of the piles but is also inversely dependent on the tidal variation. The inscribed circle should be used for squared shaped piles. The bending strength of the ice is equal to 2000 kN/m2 , according to Thoresen (2014). Iv.1 = π · b · i Figure 3.5: Vertical uplift force. Reproduced figure from (Thoresen, 2014). 41 (3.41) CHAPTER 3. DESIGN METHODS FOR ICE LOADS EAU Equation 3.42 determines the vertical loads, Iv.1 , directed upwards or downwards, on an individual pile (Committee for waterfront structures, 2012). In the equation, d represents the thickness of the ice and b is the width of the piles. The compressive strength of the ice, σk , should be calculated according to Equation 3.4 for saline water and Equation 3.5 for freshwater in Section 3.1. If the distances between the piles, L, are less than the characteristic length of ice cover, Dc , the vertical ice load should be decreased. In cases of closely placed piles, should the vertical load, Iv.1 , be multiplied with a geometric factor, fg . The variable, L1-4 , is half the distance between the surrounding piles. If it is not surrounding piles on all sides, the characteristic length Dc should be used instead of the missing L1-4 . Iv.1 0.15 · b · 0.4 · σk · d2 · fg = 0.6 + d where, fg = L21 1 + L22 + L23 + L24 4 · Dc2 Dc ≈ 17 · d 42 If L ≥ Dc If L < Dc (3.42) Chapter 4 Local conditions & applicability In all studied methods, it is stated that the local conditions should be considered while determining the design value for ice loads. However, it is not always apparent how it should be considered, to what degree, and regarding which parameters. Several local conditions affect the ice load as presented in Chapter 2. This chapter will address the conditions needed as input in the methods presented in the previous chapter, Chapter 3, and evaluate the methods’ applicability for design of piles. In addition, the ice load in three cities will be presented and the ice loads effect on pile dimensions is also reported. In Table 4.1 the summary of the studied methods are presented and it is highlighted if they consider vertical ice load and which direction of vertical ice loads it concerns. An X represents that the load type is considered. Table 4.2 shows the methods treating horizontal ice loads. All studied methods treat horizontal ice loads, but all of them do not have specific values or methods for different types of loads. Whether the methods treat different types of horizontal load actions differently and what methods they consider is also presented in the table with an X for thermal expansion, water level changes and drifting ice, respectively. Table 4.1: Methods which accounts for vertical ice load and each load direction. Iv Upwards Method Trafikverket Löfquist Waxholmsbolaget Stockholms hamnar Svensk Energi Vejdirektoratet RIL Statens vegvesen Port Designer’s handbook EAU Not considered X X X Not considered X X X X X 43 Downwards X X X X X X X X X X X CHAPTER 4. LOCAL CONDITIONS & APPLICABILITY Table 4.2: Methods which accounts for horizontal ice load. Whether and which load cases the methods concerns. Method Trafikverket Löfquist Waxholmsbolaget Stockholms hamnar Svensk Energi Vejdirektoratet RIL Statens vegvesen Port Designer’s handbook EAU 4.1 Thermal expansion Ih Water level changes Drifting ice X X X X X X X X X X X X X X X X X X X X X X X X X X Parametric study The parameter study is based on variables that consider local conditions, where one parameter at a time is varied and the other parameters are held constant. The parametric study is conducted on four different variable that are commonly used in the methods; temperature, ice thickness, ice strength and water level variations. The input data for the studied parameters are present in Table 4.3, which presents the input value used when the parameter is held constant and the range of the parametric study. The same input is used for all methods and in all studies, when the parameter is held constant. In several of the analysed methods, some parameters are given recommended value, this is not considered in this section as the input for each parameter is set to the same values. If the method provides a limitation of what magnitude the ice load can reach, it is demonstrated in the study. In cases where specific assumptions are needed, this is stated in each section. Likewise, if there are several equations to calculate the ice load within one method, the equation used in this parametric study is stated. Note that all methods are not dependent on all parameters. The salinity degree equals 50‰ but not all methods are developed for saline waters. In addition, the only method that requires a salinity degree is EAU, where the limited value of saline water is 50‰. The calculation example is a vertical pile, where the c.t.c distance is equal to 4 m, and the point load on each pile is calculated. 44 4.1. PARAMETRIC STUDY Table 4.3: Input data used in the parameter study. Parameter Air temperature, T Ice bending strength, σb Ice compressive strength, σk Ice thickness, d Water level change, w Salinity, SB Width of pile, b 4.1.1 Units ◦ C MPa MPa m m ‰ m Input -20 1 1.5 0.5 0.5 0/50 0.35 Range -60 – 0 0.5 – 2 0.5 – 3 0.1 – 1 0 – 1.5 Not studied Not studied Temperature Of the method studied in this report, three methods are dependent on temperature when determining the ice load. These methods are presented in Table 4.4. Which load types of these three methods depend on the temperature are presented in Table 4.5. Of the three methods which require the temperature to determine the ice load Statens vegvesen (2015) is the one where the return period of this input parameter is stated, but also that it is the lowest daily temperature that is of interest. EAU requires the mean temperature of the ice but does not state a return period, described more in the sections below. On the other hand, RIL requires the surface temperature of the ice, and a value of 10 ice seasons should be used to determine this. Table 4.4: Methods dependent on temperature. Method Trafikverket Löfquist Waxholmsbolaget Stockholms hamnar Svensk Energi Vejdirektoratet RIL Statens vegvesen Port Designer’s handbook EAU 45 T X X X CHAPTER 4. LOCAL CONDITIONS & APPLICABILITY Table 4.5: Methods to calculate ice load dependent on the temperature. Methods RIL Statens vegvesen EAU Horizontal Thermal Water level expansion changes Drifting ice Vertical X X X X X Thermal expansion Two methods are dependent on the temperature when the thermal ice load is determined, Statens vegvesen (2015) and EAU (Committee for waterfront structures, 2012). Figure 4.1 shows the horizontal thermal ice load in relation to temperature change. According to Statens vegvesen (2015) and Equation 3.13 in Section 3.2.2, the thermal expansion depends on the lowest daily temperature with a return period of 50 years. Statens vegvesen (2015) reaches a maximum value of 87.5 kN at -40◦ C. The thermal ice load according to EAU (Committee for waterfront structures, 2012) is determined by Figure 3.1. The figure is dependent on the mean ice temperature, and the temperature change rate, where the highest and the lowest load have been evaluated from Figure 3.1 and the temperature change is between 1 and 10◦ C/h. The mean ice temperature are either -20◦ C and -30◦ C, corresponding to an air temperature of -40◦ C and -60◦ C, respectively. An air temperature of -60◦ C has not been measured during SMHI’s measurement period of 30 years (SMHI, 2022c). The air temperature is based on the assumption that the ice temperature has a linear behaviour and the bottom of the ice cover is 0◦ C. In Figure 4.1 the temperature is varied linearly between -60◦ C and -40◦ C, even though it is only given to two data points. Hence, the correlation is not necessarily linear to the air temperature, but the intermediate values are unknown. 46 4.1. PARAMETRIC STUDY Statens vegvesen EAU 120 Horizontal ice load [kN] 110 100 90 80 70 60 50 40 −60 −55 −50 −45 −40 −35 −30 −25 −20 −15 −10 Air temperature [◦ C] Figure 4.1: Horizontal ice load due to thermal expansion dependent on the temperature. Drifting ice Figure 4.2, based on Equation 3.29 according to Committee for waterfront structures (2012), present how the ice load due to ice floes varies dependent on the air temperature. This equation is dependent on the ice compressive strength, which in turn depends on the mean ice temperature, see Equation 3.4 and 3.5 in Section 3.1.10. The equation for saline is divided into two equations. One equation for colder temperatures and another for warmer temperatures, but at 5◦ C both equations are valid and do not result in the same load, hence the hack in the graph. As previously mentioned, the compressive strength has a limitation in the previous edition, which is presented alongside the value generated by EAU 2012 where no limitation is given. The absence of a limitation results in high values, 1300 kN instead of 400 kN when the air temperature is -35◦ C. 47 CHAPTER 4. LOCAL CONDITIONS & APPLICABILITY 1,400 EAU-saline water EAU-freshwater EAU 1996-freshwater Horizontal ice load [kN] 1,200 1,000 800 600 400 200 −35 −30 −25 −20 −15 −10 ◦ Air temperature [ C] −5 0 Figure 4.2: Ice load due to drifting ice as a function of the temperature. Vertical The vertical ice load has two methods that are dependent on the temperature, RIL and EAU. Figure 4.3 shows the vertical ice load in relation to the temperature variation. The method RIL has a coefficient, ks , that is dependent on the surface temperature of the ice, see to Equation 3.36 in subsection RIL in Section 3.3. The surface temperature is assumed to be equal to the air temperature. The other method, EAU, depends on the ice compressive strength, σk , when calculating the vertical ice load using Equation 3.42. The ice compressive strength depends on the mean ice temperature according to Equation 3.4 and 3.5, which are found in Section 3.1.10. The mean ice temperature is assumed to be linear, and the temperature at the bottom of the ice cover is assumed to be 0 ◦ C for freshwater and -1 ◦ C for saline water. Thus, the vertical ice load according to EAU is dependent on the surface temperature of the ice, which is assumed to be equal to the air temperature. The salinity of the water is determined to 50‰ in the comparison. The compressive strength is limited in EAU 1996 (Committee for waterfront structures, 1996) to 2.5 MPa for freshwater and 1.5 MPa for saline water. However, this restriction does not exist in EAU 2012 (Committee for waterfront structures, 2012), which means that the compressive strength increases to 8.5 MPa for -35◦ C in freshwater. This results in an ice load of 600 kN for EAU 2012 and ice load of 176 kN for EAU 1996. The limited value given in EAU 1996 is demonstrated alongside EAU 2012 in order to demonstrate the large difference. 48 4.1. PARAMETRIC STUDY According to RIL, there are two equations to calculate the vertical ice load, depending on the structure. One equation is adapted to wall structures and the other one for individual structures, where the equation for wall structures depends on the surface temperature, thus used in Figure 4.3. 350 RIL EAU-saline water EAU-freshwater EAU 1996-freshwater Vertical ice load [kN] 300 250 200 150 100 50 0 −35 −30 −25 −20 −15 −10 ◦ Air temperature [ C] −5 0 Figure 4.3: Vertical ice load dependent on the temperature. 4.1.2 Ice thickness The thickness of the ice is the information required in most methods, except for the three methods that only provide a value of the ice load. In Table 4.6, the methods requiring ice thickness are presented. In addition, Table 4.7 specifies which load types that depend on the ice thickness. All methods that require the ice thickness to determine the ice load do not specify what type of ice thickness it concerns, whether it is maximum ice thickness or the mean ice thickness, nether, and what return period should be used. Except for RIL and Statens vegvesen. RIL states that data from 10 winters with ice would be used, but it is not stated whether it is the maximum obtained ice thickness from this time period or if another value should be used (RIL, 2013). Statens vegvesen (2015) states that a return period of 100 years should be used for the amount of frost, which is used to determine the ice thickness. The authors interpret this as if the ice thickness should have a return period of a hundred years, even if this is not explicitly stated. 49 CHAPTER 4. LOCAL CONDITIONS & APPLICABILITY Table 4.6: Methods dependent on ice thickness. Method Trafikverket Löfquist Waxholmsbolaget Stockholms hamnar Svensk Energi Vejdirektoratet RIL Statens vegvesen Port Designer’s handbook EAU d X X X X X X X Table 4.7: Methods dependent on the thickness of the ice. Methods Löfquist Waxholmsbolaget Vejdirektoratet RIL Statens vegvesen Port Designer’s handbook EAU Horizontal Thermal Water level expansion changes X X X X X X Drifting ice X X X X X X X Vertical X X X X X X X Thermal expansion Four methods are dependent on the thickness of the ice when determining the horizontal ice load due to thermal expansion. The ice load dependent on the ice thickness is shown in Figure 4.4. Waxholmsbolaget (Wikenståhl et al., 2012) presents a maximum value of 400 kN for horizontal ice loads caused by thermal expansion, which can be reached in the occurrence of a current line, in other cases, the ice load is limited to 200 kN. At an ice thickness of 0.7 m, this limit is reached, as presented. According to the guidelines of Waxholmsbolaget, the largest average ice thickness is 0.3 m, but during extreme winters, the ice thickness can reach 0.6 m in the archipelago of Stockholm. However, there is no limited value according to Wikenståhl et al. (2012). Statens vegvesen (2015), on the other hand, is limited by an ice thickness of 0.5 m, which results in a maximum ice load of 70 kN in this study. The thermal ice load, according to EAU (Committee for waterfront structures, 2012), is determined by Figure 3.1 in Chapter 3. The figure depends on the temperature rate and does only provide two ice thicknesses, 0.5 m and 1 m. When the temperature rate change is high, the resulting line load of the ice is higher for a thinner ice thickness. As opposed to this, if the temperature change rate is low, thicker ice 50 4.1. PARAMETRIC STUDY results in higher ice loads than thinner ice. It is therefore difficult to present how the ice load depends on the ice thickness in a manner that is representative of how the method handles ice load. Consequently, this method is excluded in Figure 4.4. The magnitude of the ice load varies between 100-400 kN/m for ice thickness between 0.5 and 1 m. The mean ice temperature varies also between -20◦ C and -30◦ C, is a lower air temperature than used in the other methods where -20◦ C is used. The thermal ice load largely depends on the temperature rate change. 600 Horizontal ice load [kN] 500 Waxholmsbolaget Vejdirektoratet Statens vegvesen 400 300 200 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Ice thickness, d [m] 0.8 0.9 1 Figure 4.4: Horizontal ice load due to thermal expansion dependent on the thickness of the ice, d. Water level changes Two methods depends on ice thickness when determining the ice load caused by water level variations, Waxholmsbolaget and Statens vegvesen. Both provide the same equations resulting in ice loads dependent on the ice thickness as for thermal expansion. Thus, this result can be found in Figure 4.4. The difference is that the Waxholmsbolaget has a maximum limit of 200 kN for ice loads caused by water level variations. Drifting ice Seven methods depends on the ice thickness while determining the horizontal ice load due to drifting ice. Figure 4.5 presents the ice load correlated with the thickness of 51 CHAPTER 4. LOCAL CONDITIONS & APPLICABILITY the ice. Two of the methods use the same equation, Statens vegvesen (2015) and Port Designer’s handbook (Thoresen, 2014). 1,400 Horizontal ice load [kN] 1,200 1,000 Löfquist Waxholmsbolaget Vejdirektoratet RIL Statens vegvesen Port Designer´s EAU 800 600 400 200 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Ice thickness, d [m] 0.8 0.9 1 Figure 4.5: Horizontal ice load due to drifting ice, dependent on the thickness of the ice, d. Vertical Figure 4.6 presents the vertical ice load depending on the thickness of the ice. RIL (2013) provides two equations for the vertical load, where the equation adapted for an individual structure is used and not for all structures. In Port Designer’s handbook (Thoresen, 2014), the vertical ice load is determined by a figure in section 3.3. The figure has four different thicknesses of the ice, and the resulting ice loads are presented in Figure 4.6. This means that there does not have to be a linear relation between the four determined values of ice loads. When the ice thickness is 0 m the ice load is set to 0 kN. Löfquist (1987) and Statens vegvesen (2015) provides two equations for the vertical ice load, where the equations for bridge supports are used in Figure 4.6. This decision was made because it considers more local conditions, other than ice thickness. Consequently, these equations has been used in the other parts of the parametric study. It is convenient to use the same equation for all the methods in the entire parametric study to be able to obtain a better comparison. The ice thickness is limited to 0.6 m for both the methods. 52 4.1. PARAMETRIC STUDY 700 Vertical ice load [kN] 600 500 400 Löfquist Waxholmsbolaget Vejdirektoratet RIL Statens vegvesen Port Designer´s EAU 300 200 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Thickness of ice, d [m] 0.8 0.9 1 Figure 4.6: Vertical ice load dependent on the thickness, d. Löfquist (1987) and Statens vegvesen (2015) both provides equations to determine the vertical ice load on separate supports, which is an equation that is often used during design of piled structures. These two methods provides identical equations. As the equations for bridge supports consider more local conditions, these are used in the parametric study, as previous stated. The equation for separate supports is instead presented in Figure 4.7 together with the resulting ice load from the equation adapted for bridge supports, to be able to compare the equations. Löfquist presents values which are recommended for saline and fresh water respectively, which Statens vegvesen does not. However, the range of values for the methods are the same. In Figure 4.7 both the vertical ice load for saline and fresh water are presented after Löfquist’s recommendations for A. Both methods, on the other hand, are limited to one-third of the horizontal load, which is approximately 250 kN according to Löfquist (1987) and for Statens vegvesen (2015), the horizontal load is always limiting and hence the design value. 53 CHAPTER 4. LOCAL CONDITIONS & APPLICABILITY 800 Vertical ice load [kN] 700 Löfquist Statens vegvesen Seperate support, Fresh water Seperate support, Saline water 600 500 400 300 200 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Thickness of ice, d [m] 0.8 0.9 1 Figure 4.7: Vertical ice load dependent on the thickness, d. 4.1.3 Ice strength The strength of ice is divided into bending strength and compressive strength. The vertical ice load is mainly dependent on the ice’s bending strength and the horizontal load is mainly dependent on the ice’s compressive strength. However, there is one exception, the vertical ice load is dependent on the compressive strength, σk according to EAU . It should also be noted that Port Designer’s handbook (Thoresen, 2014) presents a value A, which is a strength coefficient, though this is not included as dependent on the ice strength. Table 4.8 presents the methods that are dependent on the ice strength, both the bending strength and the compressive strength. Table 4.9 presents which type of ice load depends on the ice strength. 54 4.1. PARAMETRIC STUDY Table 4.8: Methods dependent on strength of ice. Method Trafikverket Löfquist Waxholmsbolaget Stockholms hamnar Svensk Energi Vejdirektoratet RIL Statens vegvesen Port Designer’s handbook EAU σb σk X X X X X X X X X Table 4.9: Methods to calculate ice load dependent on ice strength. Methods Horizontal, σk Thermal Water level expansion changes Drifting ice Löfquist X Waxholmsbolaget X X X Vejdirektoratet X X RIL X EAU X * = calculated using σk instead Vertical, σb X X X X * Thermal expansion The horizontal ice load according to Wikenståhl et al. (2012) is calculated with the same equation for all ice types, thermal expansion, water level changes and drifting ice. However, there are different maximum ice loads for the different ice load types, where the maximum ice load due to thermal expansion is 400 kN. Figure 4.8 presents the thermal ice load in correlation to the compressive strength. 55 CHAPTER 4. LOCAL CONDITIONS & APPLICABILITY 600 Waxholmsbolaget Vejdirektoratet Horizontal ice load [kN] 500 400 300 200 100 0 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 Ice compressive strength, σk [MPa] 3 Figure 4.8: Horizontal ice load due to thermal expansion dependent on the compressive strength, σk . Water level changes Waxholmsbolaget is the only method where the ice load due to water level changes is dependent on the ice compressive strength. The maximum load for ice load caused by the water level changes is equal to 200 kN and is reached when compressive strength is equal to 1.15 MPa. Figure 4.9 presents the horizontal ice load, dependent on the water level changes, both with the limit and without it. 56 4.1. PARAMETRIC STUDY 400 Waxholmsbolaget Horizontal ice load [kN] 350 300 250 200 150 100 50 0 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 Ice compressive strength, σk [MPa] 3 Figure 4.9: Horizontal ice load due to water level changes dependent on the compressive strength, σk . Drifting ice Figure 4.10 presents the horizontal ice load, caused by drifting ice, in relation to the ice compressive strength. The figures show the ice load due to drifting ice and thermal expansion, respectively. Löfquist (1987) has several equations to calculate the ice load caused by drifting ice. Equation 3.17 and 3.18 depend on the ice compressive strength and are valid for larger ice floes. In Figure 4.10, Equation 3.17 is used for vertical piles. Vejdirektoratet & Banedanmak (2015) and RIL (2013) both has a similar equation as Löfquist (1987) to calculate the ice load due to drifting ice with several form factors, these equations are used in the study. The ice compressive strength is according to RIL (2013) dependent on the season. The weakest ice compressive strength equals 1 MPa and occurs during the melting in spring. The highest ice compressive strength occurs in the coldest winter and is equal to 3 MPa. The contact factor, C5 , in Equation 3.21 in Section 3.2.4, is a factor that considers the constraint of the ice cover, which for drifting ice is assumed to be 1, as the ice should not contribute with any constrains in this case. 57 CHAPTER 4. LOCAL CONDITIONS & APPLICABILITY 900 800 Horizontal ice load [kN] 700 Löfquist Waxholmsbolaget Vejdirektoratet RIL EAU 600 500 400 300 200 100 0 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 Ice compressive strength, σk [MPa] 3 Figure 4.10: Horizontal ice load due to drifting ice dependent on the compressive strength, σk . Vertical The vertical ice load depends on the bending strength, σb , in four methods, (Löfquist, 1987), Waxholmsbolaget (Wikenståhl et al., 2012), (Vejdirektoratet & Banedanmak, 2015) and RIL (2013). Löfquist (1987) provides two equations to calculate the vertical ice load, one for separate piles and dolphins and another for bridge support. The equation for bridge support is dependent on the ice bending strength and is therefore used in Figure 4.11. The one for separate piles and dolphins uses an unspecified parameter A instead. RIL (2013) presents two cases used for vertical piles, where the one for individual structures is dependent on the ice’s bending strength and thus presented in Figure 4.11. 58 4.1. PARAMETRIC STUDY 400 Löfquist Waxholmsbolaget Vejdirektoratet RIL 350 Vertical ice load [kN] 300 250 200 150 100 50 0 0.6 0.8 1 1.2 1.4 1.6 Ice bending strength, σb [MPa] 1.8 2 Figure 4.11: Vertical ice load as a function of the bending strength, σb . It is only in EAU where the vertical ice load depends on the compressive strength, σk (Committee for waterfront structures, 2012). The ice compressive strength, in turn, depends on the temperature and the salinity of the ice. The correlation between the ice compressive strength and the vertical ice load is presented in Figure 4.12 59 CHAPTER 4. LOCAL CONDITIONS & APPLICABILITY 250 EAU Vertical ice load [kN] 200 150 100 50 0 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 Ice compressive strength, σk [MPa] 3 Figure 4.12: Vertical ice load dependent on the compressive strength, σk . 4.1.4 Water level variation Half of the analysed methods are dependent on water level change in order to calculate the ice load, which is presented in Table 4.10. Four methods are dependent on the variable, w, water level difference in meter and RIL is dependent on the variable, v, water level variation rate [m/h]. The water level variation rate is multiplied by the time from when the water level change began. The vertical ice load is the only ice load type that is dependent on the water level change, which is presented in Table 4.11. According to the studied methods, the water level changes cause horizontal and vertical loads, but the actual variations as an input parameter only affect the vertical loads. 60 4.1. PARAMETRIC STUDY Table 4.10: Methods dependent on water level change, w, and water level change rate,v . w [m] Method Trafikverket Löfquist Waxholmsbolaget Stockholms hamnar Svensk Energi Vejdirektoratet RIL Statens vegvesen Port Designer’s handbook EAU v [m/h] X X X X X Table 4.11: Procedures dependent on the water level changes. Methods Horizontal Thermal Water level expansion changes Drifting ice Vertical X X X X X Löfquist Waxholmsbolaget Vejdirektoratet RIL Statens vegvesen Vertical Figure 4.13 presents the methods that are dependent on the water level variation. Four of five methods are presented in the figure since Vejdirektoratet & Banedanmak (2015) provides an equation that is not applicable for the dimensions used in this parametric study. The equation is valid if b/d > 7, which means that the dimensions need to be ten times larger. Hence, the method is excluded from Figure 4.13. Statens vegvesen (2015) provides an equation that depends on the water level changes to calculate the vertical ice load. The equation is non-linear dependent on the ice thickness. However, the equation should only be used if the load is maximum one-third of the horizontal ice load due to thermal expansion. One-third of the horizontal ice load is equal to 23 kN, this upper limit is also presented in Figure 4.13 though this is not dependent on water level changes. Löfquist (1987) provides two equations to calculate the vertical ice load, one for separate piles and dolphins and another for bridge support. The equation for bridge supports depends on the water level change, thus this equation is used in Figure 4.13. 61 CHAPTER 4. LOCAL CONDITIONS & APPLICABILITY 90 Löfquist Waxholmsbolaget Vejdirektoratet RIL Statens vegvesen 80 Vertical ice load [kN] 70 60 50 40 30 20 10 0 0.2 0.4 0.6 0.8 1 1.2 Water level variation, w [m] 1.4 Figure 4.13: Vertical ice load dependent on the water level change, w. 4.1.5 Support design The methods that account for the support’s dimensions are presented in Table 4.12. Most methods consider the width or circumference of the support at the level where the load acts. Note that this width, in some cases, is added to the methods to achieve a point load output. Some methods also consider other aspects of the support, such as the inclination of the support’s front or sharpness, as the ice fails due to bending instead of crushing in this case. No parametric study is conducted on the support design as it is not considered a local condition. Table 4.12: Methods dependent on the support width or other form factors. Method Trafikverket Löfquist Waxholmsbolaget Stockholms hamnar Svensk Energi Vejdirektoratet RIL Statens vegvesen Port Designer’s handbook EAU 62 b Other X X X X X X X X X X X X X X 4.2. INPUT DATA 4.2 Input data During the design of a structure intended to withstand ice loads, a return period of 50 years should be used, according to Eurocode EN 1990 (2002). This also affects the input data that should be used and their return periods. Return periods will be discussed further in Chapter 5. In some cases, the method itself specifies what return period to use. Note that long return periods and more extreme input values do not necessarily lead to high ice loads as the method affects this. Seldom do the methods specify explicitly and clearly what input information should be used. Temperature As lower temperature results in larger ice loads, the largest temperature obtained in an area would be reasonable to use. However, the temperature must also have time to affect the ice, its thickness and consequently the resulting load (Norén, 2022). Thus, deciding what specific temperature to use is not apparent since the input a method calls for is not always specified. For example, if it is a record value or if it is a daily average temperature. SMHI, the Swedish Meteorological and Hydrological Institute, has extensive data on the temperate in Sweden and different types of temperature data. For example, the minimum average temperature per day for a time period of 30 years at several positions in Sweden is available. A period of 30 years is, according to SMHI (2021c), considered a normal period and refers to the World Meteorological Organization, while stating that 30 years is decided to be a long enough time frame to determine typical values. The normal period which is valid now, in 2022, is 1991 to 2020 according to SMHI (2021a). This data from SMHI can be used to evaluate the temperature at different positions, Figure 4.14 presents the minimum daily temperature per county between 1991 and 2020. All measuring points have been divided into counties and for each county, the lowest daily temperature found is obtained. The values have also been divided into temperature spans of 5◦ C. If more specific and local information regarding the temperature is of interest, it can be found at SMHI’s website. Data from several normal periods are available. Figure 4.15 shows the stations used in the normal period between 1991 and 2020 and where more specific information can be found, it should though be noted that all stations have not been active for the entire normal period of 30 years. The coordinates for each measuring position have been used to create Figure 4.15 and this figure, as well as Figure 4.14, have been produced in Excel. 63 CHAPTER 4. LOCAL CONDITIONS & APPLICABILITY Figure 4.14: Minimum daily temperature, T , at different counties in Sweden between 1991 and 2020. 64 4.2. INPUT DATA Figure 4.15: The positions of SMHIs temperature measuring stations in Sweden between 1991 to 2020. Ice thickness Ice thickness depends on several factors, such as salinity, temperature, amount of snow, etc. as presented previously in Chapter 2. SMHI has previously measured the ice thickness of some Swedish lakes and the results have been summarised in a report by Eklund (1998). A reconstruction of the result and the mean value of the ice’s maximum thickness per year is presented in Figure 4.16 and note that this information is applicable for freshwater. The data in the figure is from approximately 40 years and the line demonstrating 80 cm ice thickness is uncertain, but it is more conservative than 70 cm, thus presented in this thesis. 65 CHAPTER 4. LOCAL CONDITIONS & APPLICABILITY Figure 4.16: Mean value of each years maximum ice thickness, d, in freshwater in different parts of Sweden. Reproduced from Eklund (1998). Fransson and Bergdahl (2009) presents different ice thicknesses in the Baltic Sea and on the Swedish west coast. This information is based on data from 1963 to 1979 gathered from SMHI and Havsforskningsinstitutet, which have been summarised by Fransson and Bergdahl (2009). Ice was not present at all positions in all the measured years. The mean value of each year measured maximum presented by Fransson and Bergdahl (2009) around the Swedish coast is reconstructed and presented in Figure 4.17. This information applies to saline or brackish water and the measurements were performed three days each month. 66 4.2. INPUT DATA Figure 4.17: Mean value of the maximum ice thickness, d, in saline and brackish water in different parts of Sweden. Reproduced from Fransson and Bergdahl (2009). In order to obtain more information about the ice thickness, data from SMHIs Oceanographic observations of sea ice in the Baltic Sea has been analysed (SMHI, 2022b). The studied positions in Sweden are presented in Figure 4.18, this included positions along with the Swedish coast as well as positions in the lakes Mälaren and Vänern. The positions have been chosen to obtain values distributed over Sweden and as far into each harbour as possible, as most marine structures are located there. In cases where the measuring seasons were few, a position somewhat further out has been chosen, this is for example the case outside Slite. All data have been analysed using Excel. 67 CHAPTER 4. LOCAL CONDITIONS & APPLICABILITY Figure 4.18: Selected measuring points in Sweden based on data from SMHI (2022b). Table 4.13 presents the city located closely to each measurement point, alongside how many years measurements have been performed at each position between the years 1987 to 2021. How large the share of each season an ice cover is reported is also presented at each location. The ice data is presented as a four-digit number, where each position in the number refers to a specific property and the value in each position refers to something within this property. The first position in the four-digit number indicates the ice concentration, where the values 5 to 8 are considered an ice cover since SMHI stated that this can be considered stable or relatively stable ice in communication with them. 1 to 4 is considered drifting ice. This information is the basis for the ratios given in Table 4.13. Measurements have not been performed periodically or started on the same date each year or the same date for all locations. Measurement points without information have been excluded while determining the shares where an ice cover is present. 68 4.2. INPUT DATA Table 4.13: SMHI (2022b) measuring series length between 1987-2021 and the percentages of each series where an ice cover is frozen per city. City Luleå Umeå Sundsvall Gävle Nynäshamn Slite Kalmar Malmö Göteborg Strömstad Köping Karlstad Lidköping Years measured 35 35 35 31 17 8 17 8 14 13 35 34 30 Part of season with ice cover 88.1 % 43.8 % 51.9 % 57.6 % 30.9 % 3.3 % 49.4 % 4.8 % 4.0 % 14.3 % 79.7 % 77.2 % 64.3 % Data presented by SMHI (2022b) of ice thickness has also been used to obtain the mean, maximum and the mean of each year’s maximum at the measurement locations presented above. The values have been divided into thicknesses for an ice cover and for drifting ice to use more customised values for each load type, see Table 4.14. The data from SMHI is presented as a span of the ice thickness. While calculating the mean thickness, both the total mean and for each annual maximum, the mean value of the span is used. When the resulting value is obtained, the values are again divided into spans. The standard deviation for the ice thickness of all measurements and the number of measurements for both an ice cover and drifting ice is presented in Table 4.15. As previously described, the mean value is based on a span, where the middle of the span is used to obtain the mean value. The number of measurements varies between locations, but it is especially prominent that the number of measurements where an ice cover is reported are few at some locations. More of this type of information and in several other locations in Sweden can be produced using SMHIs ice data. 69 CHAPTER 4. LOCAL CONDITIONS & APPLICABILITY Table 4.14: Ice thickness of different types of ice at some Swedish ports and lakes produced from ice data from SMHI (2022b). City Luleå Umeå Sundsvall Gävle Nynäshamn Slite Kalmar Malmö Göteborg Strömstad Köping Karlstad Lidköping Ice cover thickness, d [cm] Mean of Mean Max yearly max 30 – 50 50 – 70 30 – 50 15 – 30 50 – 70 15 – 30 15 – 30 30 – 50 15 – 30 10 – 15 30 – 50 15 – 30 10 – 15 30 – 50 15 – 30 10 – 15 10 – 15 10 – 15 10 – 15 50 – 70 15 – 30 5 – 10 5 – 10 5 – 10 10 – 15 10 – 15 10 – 15 10 – 15 15 – 30 10 – 15 15 – 30 50 – 70 15 – 30 15 – 30 50 – 70 15 – 30 10 – 15 30 – 50 15 – 30 Drifting ice thickness, d [cm] Mean of Mean Max yearly max 10 – 15 50 – 70 15 – 30 5 – 10 50 – 70 15 – 30 5 – 10 30 – 50 10 – 15 5 – 10 30 – 50 10 – 15 5 – 10 15 – 30 5 – 10 5 – 10 10 – 15 5 – 10 5 – 10 15 – 30 5 – 10 5 – 10 10 – 15 5 – 10 5 – 10 15 – 30 5 – 10 5 – 10 10 – 15 5 – 10 10 – 15 50 – 70 15 – 30 5 – 10 50 – 70 15 – 30 5 – 10 15 – 30 10 – 15 Table 4.15: Mean ice thickness, standard deviation and number of measurements for an ice cover and drifting ice. Produced based on data from SMHI (2022b) based on all messurments. City Luleå Umeå Sundsvall Gävle Nynäshamn Slite Kalmar Malmö Göteborg Strömstad Köping Karlstad Lidköping Ice cover Drifting ice Standard Standard Mean n Mean n deviation deviation [cm] [-] [cm] [cm] [-] [cm] 34.1 5135 17.0 12.9 555 13.3 16.6 1633 9.5 8.7 1888 6.8 16.1 1513 10.3 7.9 1261 6.1 14.6 1301 7.1 8.9 847 5.3 13.2 274 6.1 8.2 564 4.1 12.5 7 0.0 6.9 201 4.0 13.0 305 10.5 7.2 274 4.0 5.8 6 2.4 6.2 97 3.6 12.5 15 0.0 6.2 323 3.6 11.1 52 4.1 7.8 286 3.6 18.2 2805 11.2 10.2 640 8.0 18.4 2548 11.8 8.9 626 6.8 13.4 952 5.7 7.1 424 4.6 n = Number of measurements 70 4.2. INPUT DATA Ice strength The ice strength is explicitly stated in many methods regarding compressive and bending strength and in some cases, a span or values for different cases are presented. However, it is difficult to state or find statistics on what ice strength is achieved at different locations of Sweden and thus find the highest value or mean value, even though it is known that the ice strength increases with decreasing temperature and salinity. Consequently, it would be reasonable to assume that the strength is higher in the north of Sweden or lakes and rivers than at sea. Table 4.16 presents the recommended ice strength for the methods studied. The ice bending strength, according to RIL (2013) is 65% of the ice’s compressive strength. According to Thoresen (2014), it is one-third of the ice compressive strength, though this is not used in the equations. On the contrary, the ice bending strength according to Löfquist (1987) has a higher bending strength interval than the compressive strength, which is opposite to the other methods. But when the ice starts to drift, the compressive strength usually decreases because the ice has started to melt. The bending strength is instead related to a solid frozen ice cover (Mayor, 2022). RIL provides values for the ice’s compressive strength for different times of the winter season and how the ice is moving. Löfquist (1987) gives guiding values for saline water, freshwater and how the ice is moving. The other methods, which provide guidance for the ice strength, only suggest a specific value. Committee for waterfront structures (2012), on the other hand, provides an equation to obtain σk based on temperature and salinity but does not provide any guidance for σb , which is not a used parameter in the handbook. Committee for waterfront structures (2012) generates high values of σk , even though it accounts for local conditions affecting the ice. This value has been limited in the calculation examples since the values are considered unrealistic (Mayor, 2022). Fransson (2009) states that the bending strength can reach 10 MPa, but this is applicable for low stress levels and high load rates. Hence, the applicability of this in situ is questionable and the values presented by Malm et al. (2017) where the highest compressive strength value is 5 MPa are more similar to the values presented in the methods presented in this report. Table 4.16: Ice strength according to the methods. σb σk [MPa] [MPa] Löfquist 1<σb <2 0.5<σk <1.4 Waxholmsbolaget 1.4 2 Vejdirektoratet 0.5 1.9 RIL 0.65 ·σk 1< σk < 3 EAU * ** * = Not applicable (NA), ∗∗ = Calculated by Equation 3.4 or 3.5 Method 71 CHAPTER 4. LOCAL CONDITIONS & APPLICABILITY Water level variations The water level varies typically with the seasons. These variations are due to recurring and similar variations of wind and water over the year. For example, the water level varies more during the winter season than during the summer, usually due to stronger wind in winters (SMHI, 2021b). The water level changes, water level change time and water level change rate are of interest when determining the vertical ice load. Water level changes is the distance of the change, the water level change time is the time elapsed when water level changes occurs and water level change rate is the speed of the water level change. Statens vegvesen (2015) provides a guiding value of 1 m. In RIL (2013), the water level change rate is multiplied by the time from the beginning of the water level change. On the other hand, the load also depends on the factor ks which is larger if less time has passed from when the water level change started. Note that some methods only account for vertical uplift force and only inquire the water level rises. The input that should be used for water level change and the changes time period is not always apparent in each method. As mentioned, the variation range is significant over the year and if the lowest water level and highest water level were accounted for, the change would be extensive. As previously mentioned, the ice loads tend to reach higher values when the variations are middle-high and occur once or twice a day, according to Comfort et al. (1993). Noteworthy is that this applies to horizontal load and that this is not the case according to the design methods where the load increases with larger variations. In Table 4.17, the daily variation of the water levels mean, maximum and mean of each year’s maximum is presented for five cities along the Swedish coast. The information is obtained from SMHIs hourly oceanographic observations of the water level and processed to obtain the desired information. The locations where the measurements have been performed are presented in Figure 4.19. The difference between the daily highest and the daily lowest water levels was calculated using Excel. The mean, maximum, and mean of each year’s maximum were obtained from this. Table 4.18 shows the standard deviation, the number of messurments and the mean value of all daily variations. Note that the information on water level differences is based on variations over the entire year. Thus, the variations might be conservative, as ice is not expected all year round, but as stated, the variations are usually larger during the winter season. 72 4.2. INPUT DATA Figure 4.19: Locations of selected positions with studied water level variation in Sweden. Based on water level observations from SMHI (2022a). Table 4.17: Daily variations of water level. Produced from data from SMHI (2022a). City Kalix Umeå Stockholm Kalmar Halmstad Measuring period [-] 2009 – 2021 2009 – 2021 2009 – 2020 2009 – 2021 2009 – 2021 Mean Max [cm] 15.5 10.5 8.8 14.5 28.7 [cm] 98.0 91.4 61.9 105.8 208.3 Mean of yearly max [cm] 80.5 57.5 41.5 77.5 117.3 Table 4.18: Standard deviation, number of messurments and the mean value of daily water level variations. Based on the mean value of all variations and data from SMHI (2022a). City Kalix Umeå Stockholm Kalmar Halmstad Mean value [cm] 15.5 10.5 8.8 14.5 28.7 Number of mesurments [-] 4512 4632 4718 4632 4632 73 Standard deviation [cm] 13.0 8.1 6.3 10.1 14.6 CHAPTER 4. LOCAL CONDITIONS & APPLICABILITY 4.3 Applicability and comparison of three cities The evaluation of methods is intended to eliminate methods that are not applicable for pile structures, that are not applicable for structural design or do not consider local conditions. Several methods have not been explicitly developed for piled structure. However, in the elimination, the question is if it is explicitly stated that the method is not applicable for design of piled structures. Methods that consider local conditions are the methods which include some of the variables in the parametric study. The local condition variables which were studied was; temperature, the thickness of ice, the ice strength and water level variations. In Table 4.19 to 4.22 in Section 4.3, it is specified whether the methods may be applicable for piles, if they are useful or reasonable to follow during structural design and if they consider local conditions. The methods which live up to these points are then studied further for three Swedish cities, see Figure 4.20 and the similar figures for the horizontal and vertical ice loads in Section 4.3. Umeå, Mora and Halmstad are cities used to study the methods closer and are chosen based on their geographical positions. Umeå is located on the Swedish east coast at the Gulf of Bothnia and is the northernmost of the cities studied. Mora is located inland at the lake, Siljan, approximately in the middle of Sweden. To the far south, Halmstad is studied and is placed towards the west coast. The input data for the resulting ice load in Figure 4.20 to 4.24 were the same for all the methods, unless the method provided an assigned value or had a recommended span of values. The mean thickness of the yearly maximum thickness was used to determine the ice thickness. The results were 28 cm for Umeå, 50 cm for Mora and 11 cm for Halmstad, see Figures 4.16 and 4.17. The minimum daily temperature during a 30-year measurement period was used to determine the temperature for the cities. The values can be found in Figure 4.14 where the highest value in each span was chosen based on the county of each city. This resulted in -40◦ C in Umeå and Mora, -25◦ C in Halmstad. The ice load are determined for a piled structure with a diameter of 0.35 m for the piles. Additional values used for the calculations can be found in Appendix B. Thermal ice load The procedures providing a method to determine thermal horizontal ice load is evaluated in Table 4.19. In turn, the methods which are confirmed for the three cases are presented and calculated for the three different cities Umeå, Mora and Halmstad, see Figure 4.20. Löfquist (1987) is considered to be not applicable as insufficient guidance is given on how to apply the ice load parameter i1 . As no value or guidance is given at all for saline water, it does not account for local conditions. Furthermore, RIL presents a map over Finland with an ice load, per meter, within a geographic area, making it difficult to determine the load in Sweden. Hence, RIL is considered to be inapplicable 74 4.3. APPLICABILITY AND COMPARISON OF THREE CITIES for structural design in Sweden and can not account for our local variations. The method to determine the thermal ice load according to EAU is not applicable for piles, as it is adapted for planer structures. In additions, the temperatures used are not compatible with a Swedish climate and the presented ice thicknesses are too limited. Table 4.19: Applicability of the methods for horizontal ice loads due to thermal expansion. May be applicable for piles X X X X X Method Horizontal ice load [kN] Löfquist Waxholmsbolaget Vejdirektoratet RIL Statens vegvesen EAU Applicable in design Considers local conditions X X X X X X X Umeå Mora Halmstad 300 200 100 n ten sv egv ese Sta irek tor a Vej d Wa xho lm sbo lag et tet 0 Figure 4.20: Horizontal ice load due to thermal expansion calculated in Umeå, Mora and Halmstad Water level changes Löfquist (1987), Wikenståhl et al. (2012) and Statens vegvesen (2015) are the only methods that provide a value or equation to determine the horizontal ice load due to water level changes. Table 4.20 presents the applicability of the methods that are dependent on the water level changes and Figure 4.21 presents the resulting values 75 CHAPTER 4. LOCAL CONDITIONS & APPLICABILITY of the ice load in three cities in Sweden. All three sources use the same equations to calculate horizontal ice load due to water level changes as due to thermal expansion. Several methods have one equation to calculate the horizontal ice load and have not divided them into specific load cases such as thermal expansion, water level changes and drifting ice. Waxholmsbolaget, on the other hand, has a limitation of the ice load due to water level changes. Löfquist (1987) does not consider local conditions based on the reasons stated above for thermal ice loads, as the methods are identical. Table 4.20: Applicability of the methods for horizontal ice loads due to water level changes. Method Löfquist Waxholmsbolaget Statens vegvesen May be applicable for piles X X X Considers local conditions X X X X Umeå Mora Halmstad 200 Horizontal ice load [kN] Applicable in design 150 100 50 Sta t Wa xh ens olm s bol veg ves e age t n 0 Figure 4.21: Horizontal ice load due to water level changes calculated in Umeå, Mora and Halmstad Drifting ice load The analysed methods that provide a specific method for drifting ice are evaluated in Table 4.21. The methods considered acceptable have been calculated and the resulting ice load caused by drifting ice for the three cities is presented in Figure 4.22. 76 4.3. APPLICABILITY AND COMPARISON OF THREE CITIES Similar equations calculate the horizontal ice caused by drifting ice in Port Designer’s handbook and Statens vegvesen, the equations are based on ISO 19906:2010. According to ISO 19906 (2010), two criterias should be fulfilled, which are that b/d > 2 and a displacement lower than 10 mm. However, it is unlikely that the diameter of the pile is twice as large as the ice thickness and that the deformation is less than 10 mm for light constructions (Mayor, 2022). The methods of the handbooks are thus not valid for piles. Though, this is not explicitly mentioned in any of the handbooks. Löfquist (1987) is only applicable regarding the method for large ice floes. In the occurrence of small drifting ice floes or a drifting ice cover, the handbook does not provide any adaption to the local conditions. For RIL (2013) all methods are not rational to use during design as one procedure, Equation 3.24, is unreasonably extensive. The method requires many specific parameters which are difficult to obtain, this complicates the calculations. The application to local conditions is not possible for drifting ice moved by a berthing ship. RIL is, despite this, considered acceptable since some equations are admissible. Table 4.21: Applicability of the methods for horizontal ice loads due to drifting ice. Method Löfquist Waxholmsbolaget Vejdirektoratet RIL Statens vegvesen Port Designer’s handbook EAU May be applicable for piles X X X X X 77 Applicable in design X X X X X X X Considers local conditions X X X X X X X CHAPTER 4. LOCAL CONDITIONS & APPLICABILITY Umeå Mora Halmstad Horizontal ice load [kN] 400 300 200 100 EA U RIL ate t irek tor Vej d Wa xho lms Löf q uis bol age t t 0 Figure 4.22: Horizontal ice load due to drifting ice calculated in Umeå, Mora and Halmstad Highest design value Figure 4.23 presents the horizontal design load for the three cities according to all methods studied in this project. The design load is the highest horizontal ice load and is only valid if the structure is subjected to all ice load types, which means thermal ice load, drifting ice load and ice load due to water level changes. The calculations to obtain the values are presented in Appendix B. The ice load according to Trafikverket (2021), Stockholms hamnar (2016) and Svensk Energi (2011) have not been presented in any previous figures with comparisons of the three cities. The explanation for this is that they only present a general calculation or value of the horizontal ice load and the ice loads have not been divided into load cases of their cause. Because of this, these methods have been eliminated, as they do not consider local conditions and are not dependent on input parameters. According to Trafikverket (2021) the design load should be 200 kN for regions in the south of Sweden. The horizontal ice load in Mora and Umeå should be decided by the project’s client, but how this should be performed is not specified. All the design values in Figure 4.23 obtained by Trafikverket (2021) is determined to 200 78 4.3. APPLICABILITY AND COMPARISON OF THREE CITIES kN. As this value is for southern Sweden this is probably less than what is intended for Mora and Umeå. Löfquist (1987) presents a method to calculate the horizontal ice load due to thermal expansion and water level changes, which has an ice load per meter that varies between 50-300 kN/m for the thermal load, but does not provide any information on how to apply these values. For the ice load due to water level changes, the ice load per meter should be set to 200 kN/m. The equation also states that structures smaller than 4 m should be calculated as for 4 m, which then results in a value of 800 kN. According to Svensk Energi (2011), the force from the arch action can reach a maximum of 2000 kN/m, but it is not described how the load should adapted to local conditions. According to Malm (2022), arch action is unlikely to occur for piled structure in a marine area, but rather on a dam structure with a gap. As a result, this thesis does not consider this value. Umeå Mora Halmstad 600 400 200 ign er’s han d boo k EA U veg ves en ens Por t Des Sta t RIL et rat gi Vej dir ekt o kE ner nar Sve ns ham lms ckh o Sto Wa xh olm Löf sb o qui lag et st 0 TR V Horizontal ice load [kN] 800 Figure 4.23: Horizontal design ice load for Umeå, Mora and Halmstad 79 CHAPTER 4. LOCAL CONDITIONS & APPLICABILITY Vertical ice load Table 4.22 presents the methods which are used to determine vertical upward ice loads. Vejdirektoratet & Banedanmak (2015), RIL (2013) and Committee for waterfront structures (2012) also provides methods to determine vertical ice loads directed downwards. The load is set to the same as the value upwards and half the upwards directed ice load for Vejdirektoratet. Stockholms hamnar (2016) does not consider local conditions, the vertical ice load is therefore not calculated. Thoresen (2014) is not applicable in design because of the chart which is used to determine the vertical ice load, as it is difficult to read for piles smaller than 1 m. Table 4.22: Applicability of the methods for upwards vertical ice loads. Method Löfquist Waxholmsbolaget Stockholms hamnar Vejdirektoratet RIL Statens vegvesen Port Designer’s handbook EAU May be applicable for piles X X X X X X X X Applicable in design X X X X X X X Considers local conditions X X X X X X X The vertical upwards directed ice loads for the three cities, Umeå, Mora and Halmstad, are presented in Figure 4.24. Two results from Löfquist (1987) are presented, one result obtained from the equation adapted for bridge supports and another from the equation adapted for separate piles and dolphins. This is to illustrate the differences between the equations. Statens vegvesen (2015) also has two equations to calculate the vertical load, one for separate supports and another one for supports in pair or group. However, the handbook writes that the vertical load can reach a maximum of one-third of the horizontal load, which also becomes the design value for all the cities. 80 4.4. PILE DIMENSIONS AND CAPACITY Umeå Mora Halmstad Vertical ice load [kN] 250 200 150 100 50 EA U n ten sv egv ese Sta RIL t Vej d irek tor ate t Wa xh olm s pile Löf qui st, qui Löf bol age s st 0 Figure 4.24: Vertical ice load upwards calculated in Umeå, Mora and Halmstad 4.4 Pile dimensions and capacity A simple FE-model has been performed to evaluate the ice loads impact on piles and their resulting dimensions. The used model is a simplification of a pile pair. In reality, both piles are connected to a foundation, but in the model, the piles are considered to be connected to each other by a hinge. The blueprint on which the simplified model is based is presented in Appendix C. In the blueprint, a section of a pier is presented and the pier is placed on two piles. The water level line, MW, is located along the pier foundation. Thus, the piles are extended two meters vertically from the water level line and are considered interconnected with a hinge at the top. The ice load is assumed to act at the water level. The two analysed and simplified load cases are presented in Figure 4.25. The load cases are identical, except for the loads, where the point load acts on one of the piles in load case 1 and in load case 2, a point load affects both piles. Both point loads in load case 2 have the same magnitude as the load in load case 1. However, the magnitudes of the ice load are varied and the studied magnitudes are 20 kN, 50 kN, 100 kN and 200 kN. The two bottom boundary conditions at the separate ends of the piles are defined 81 CHAPTER 4. LOCAL CONDITIONS & APPLICABILITY as hinges, which allow for rotation in the paper’s plane. A hinge that also allows for rotation in the paper’s plane was placed as the two piles’ connection. The connection hinge itself was allowed to move sideways. The piles were modelled with a circular hollow cross-section, where the thickness was 12.5 mm and the diameter was varied between 220 mm, 270 mm and 320 mm. The piles were performed in steel in the FE model. (a) (b) Figure 4.25: (a) Load case 1, with one point load. (b) Load case 2, with two point loads. In order to determine the pile’s normal load capacity as a result of the maximum internal bending moment, a mathcad calculation sheet were used. The calculation sheet was previously produced by ELU Konsult AB but were revised and adapted for this project. These calculation sheets are presented in Appendix B.10 and is in Swedish. In this case, a single vertical pile were studied. A first-order linear analysis was performed without accounting for the pile’s imperfections. The rust thickness was assumed to be 4 mm. The chosen steel class was S 420 and the steel’s yielding strength was 420 MPa. The obtained maximum internal bending moment, as well as the maximum internal normal force, are presented in Table 4.23 and 4.24 for load cases 1 and 2, respectively. Values for the left and right piles are presented separately. A negative normal force indicates that the pile is in compression. 82 4.4. PILE DIMENSIONS AND CAPACITY Table 4.23: Maximum bending moment and normal force in load case 1 for the left and right piles. Load [kN] 20 50 100 200 Pile diameter [mm] 220 270 320 220 270 320 220 270 320 220 270 320 Max moment [kNm] Left pile Right pile 39 8 40 10 40 12 93 8 94 10 94 12 183 8 184 10 184 12 363 8 364 10 364 12 Max normal force [kN] Left pile Right pile 36 -50 36 -53 35 -57 92 106 92 109 91 112 186 199 186 202 185 205 374 384 374 387 373 391 Table 4.24: Maximum bending moment and normal force in load case 2 for the left and right piles. Load [kN] 20 50 100 200 Pile diameter [mm] 220 270 320 220 270 320 220 270 320 220 270 320 Max moment [kNm] Left pile Right pile 39 33 40 32 40 32 93 87 94 86 94 86 183 177 184 176 184 176 363 357 364 356 364 356 Max normal force [kN] Left pile Right pile 73 -88 73 -91 72 -94 185 -200 185 -203 184 -206 372 -387 371 -390 371 -393 745 -760 745 -763 745 -767 The resulting normal force capacity in the left and right pile for load cases 1 and 2 are presented in Table 4.25 and 4.26. As presented above, the left pile is exposed to tension in load cases 1 and 2. The favourable effect of this on the pile’s capacity is not accounted for when buckling is of interest. If the pile has no remaining capacity No value is presented if the pile’s remaining normal force capacity is less than zero. 83 CHAPTER 4. LOCAL CONDITIONS & APPLICABILITY Table 4.25: Remaining normal load capacity of the right and left pile in load case 1. Remaining normal load capacity [MN] Left pile Right pile 220 1.6 2.1 20 270 2.3 2.7 320 3.0 3.2 220 0.8 2.0 50 270 1.6 2.6 320 2.4 3.2 220 – 1.9 100 270 0.4 2.5 320 1.4 3.0 220 – 1.8 200 270 – 2.3 320 – 2.9 – demonstrates that no capacity is remaining. Load [kN] Pile diameter [mm] Table 4.26: Remaining normal load capacity of the right and left pile in load case 2. Remaining normal load capacity [MN] Left pile Right pile 220 1.6 1.7 20 270 2.3 2.3 320 3.0 3.0 220 0.8 0.7 50 270 1.6 1.5 320 2.4 2.3 220 – – 100 270 0.4 0.2 320 1.4 1.1 220 – – 200 270 – – 320 – – – demonstrates that no capacity is remaining. Load [kN] Pile diameter [mm] The remaining normal load capacity for the different pile diameters is presented in Figure 4.26. When the normal load capacity is less than 0 MN, the pile fails due to the ice load itself. As can be seen, the relation between ice load and the normal capacity is linear, even if each pile dimension results in different inclinations in the figure. 84 4.4. PILE DIMENSIONS AND CAPACITY 3 220 mm LC 2 270 mm LC 2 320 mm LC 2 Normal load capacity [MN] 2.5 2 1.5 1 0.5 0 0 20 40 60 80 100 120 Ice load [kN] 140 160 180 200 Figure 4.26: Normal load capacity in the right piles in load case 2 as a function of the ice load. 85 Chapter 5 Evaluation 5.1 Categorisation and treatment of ice loads This section will discuss research question 1. Division of ice load types It is clear that ice loads are treated differently in the methods analysed in this project. Some methods do not provide any adaptation to specific load cases, and some methods do not consider vertical ice loads. Whether vertical ice loads are essential to account for is debated, especially for heavier structures. Downwards directed ice loads are even more questioned. Methods adapted to specific horizontal ice load types, such as drifting ice, water level changes, or thermal expansion, allow for adaptation to the situation and the location. For example, if an icebreaker frequently breaks the ice in a specific harbour or if the ice cover never is allowed to settle, it would be reasonable to disregard loads from a moving ice cover. Furthermore, ice loads due to thermal expansion could be neglected if the ice cover never fully freezes and drifting ice would be more of an issue. While neglecting ice load types, it should be considered that this has to be valid for the entire structural lifespan. The input data can also be adapted to the load case if different load types have been presented. For example, the ice thickness data from SMHI is separated into two different thicknesses, one for an ice cover and one for drifting ice. In this thesis, the division between load types has been vertical ice load and horizontal ice load. The horizontal load has then been divided into three load types based on their origin; thermal expansion, water level changes, and drifting ice. Some methods provide more specific load cases as well. RIL (2013) provides an approach to determine the ice load from moving vessels and the ice pushed against a structure during berthing. Ice loads from berthing vessels are, in this thesis, considered drifting ice, but it is also the only method that provides information on this load type. This thesis also considers a moving ice cover as drifting ice, even though this is not drifting ice floes. Hence, a more specialised analysis regarding the load type 87 CHAPTER 5. EVALUATION could be conducted, where the division between load types was stricter and more multifaceted. If the ice load is divided into load types it allows for adaptions to each case, project, and location and this enables to design for lower loads. Not all load types must originate from the same source during design as some methods are not applicable in Sweden, or some load types are complicated to account for as the information is limited. We think it is surprising that Trafikverket, in their new guidelines (Trafikverket, 2021), states that the method proposed by Löfquist (1987) is replaced. Especially since the adaptation to local conditions and the structure’s geometry are removed in the new guidelines. According to Mayor (2022), Löfquist’s guidelines are the most commonly used and accepted source for ice loads in Sweden. Moreover, Trafikverket’s new guidelines (Trafikverket, 2021) are not applicable for all bridge spans in all counties of Sweden. It is unclear how the ice load should be determined when the guidelines are inadequate since Löfquist’s method has been replaced. An advantage of removing the reference to Löfquist’s method is that other methods may be used in Trafikverket’s projects. However, as the customer should prescribe which method to use, extensive knowledge of ice loads is required. Trafikverket’s guidelines do not provide any guidance regarding vertical ice loads. It is more conservative to account for vertical ice loads than not, excluding this would be less suitable for light weight structures. It should be noted that the guidelines from Trafikverket (2021) are for bridges. The methods to determine the horizontal ice load due to water level changes use the same equations and procedures as for the thermal ice load, apart from changing some variable or input. Further, it is interesting that the methods do not depend on the water level changes and no method has a separate procedure to calculate the horizontal ice load due to water level changes. Only Waxholmsbolaget and Statens vegvesen (2015) are methods that consider local conditions and are applicable in design. However, both methods have an identical calculation procedures for thermal expansion. This may be because the water level changes cause cracks in the ice cover, which are filled with water that expands during freezing. The volume change creates a force when the water level returns to the previous level. The action causing the ice load could thus be included in the thermal ice load. Structure geometry In Chapter 2, it is clearly stated that the geometry of a support affects the ice load, as the ice will fail differently. Primarily, inclined support results in ice failing in bending instead of compression, resulting in lower ice loads. Since this affects the behaviour of the ice and the load, it would be logical to account for this while determining the ice load. The methods that consider the support’s inclination and sharpness are presented in Section 4.1.5. For example, Statens vegvesen (2015), accounts for the centre-to-centre (c.t.c) distance while determining the drifting ice load, where the effective width of the piles is increased if the piles are closely placed. This approach is easy to follow and understand. If the piles are closely placed, it behaves more or 88 5.2. INPUT less like a wall structure instead. For example, RIL (2013) instead presents different equations for wall and piled structures. If possible, it would be efficient to place piles so ice accumulation is avoided, but how this should be conducted and accounted for during design is unclear. Adaptation of methods The division of ice load types and how the method should be treated can to some extent be regarded as an interpretation. Thus the original source should be studied during design. The project includes methods adapted to wall structures, resulting from the lack of methods for piled ones. Thus, the methods adopted for wall structures are also implemented for piles. According to Malm (2022), the stiffness of piles is lower than for example a concrete dam, and thereby the ice load acting on piles is likely lower since the ice load occurs as a result of restrained deformation. Hence, Malm (2022) states that it is considered likely that ice loads should be lower on piles than on concrete dams. The ice load is treated as a point load in this project. To obtain the point load, the width of the pile or the pile’s circumference is, in some cases, multiplied by the line load presented in the respective methods. The pile’s circumference is mainly used for the vertical load, which is essential for the grip surface. The width is used for the horizontal ice loads, where the load acts mainly on one side of the pile. This results in a linearity between the ice load and the pile width. The c.t.c distance could, in some cases, have been appropriate to use. For example, if an ice floe is crushed against a pile, the size of the ice floe that affects one pile is more decisive than the width of the pile. This distinction is under the assumption that the width of ice floes and the kinetic energy affect the load. On the other hand, if piles are closely placed, the structure can act more like a wall structure. As mentioned, the ice load is also limited by the ice strength. 5.2 Input In this section, research question 5 will be analysed and evaluated. 5.2.1 Safety margins and return periods Whether the methods include safety margins or not has not been analysed in this thesis. The use of safety margins is an uncertainty as well as a possible and partial explanation of the different magnitudes of the ice loads. Uncertainties of which and how large safety margins are included are an issue, as this results in questions about whether additional safety factors are required. The lack of knowledge likely results in unnecessary large safety margins to ensure safety, especially as margins would be added in several steps of the calculation procedure. Implementing unnecessarily 89 CHAPTER 5. EVALUATION large safety margins results in low material efficiency, which is expensive and negatively affects the environment. In order to sort these questions out, more knowledge on the topic is required. For example, the sources of each respective method could be studied. All methods do not state what they are based on, whether they are based on a scientific study or likewise. This vagueness makes it difficult to determine the original source and thus whether and to what degree safety margins have been included. While performing this study, it is also essential to consider whether a method is intended to determine design values, maximum ice loads or if it is the expected ice load or an average value. An additional question, closely related to safety margins, is regarding which input each method require and which return period that should be used. Some methods require input, for example temperature, water level changes or ice thickness, in order to determine the ice load. This input can be from measured local conditions. The degree of precision and definition regarding the input parameter varies between the methods. For example, if a 30-year period should be used as the basis for the lowest daily mean temperature, or if the mean temperature during the winter months should be applied. It is seldom clearly stated in the methods which information they require and because of this, different interpretations of the needed input data may arise. This is the case for all input data, temperature, ice strength, ice thickness and water level changes. If the return period of the ice load should be 50 years, as stated, this means that the magnitude should be obtained for a 50-year period. However, the input data are stochastic variables and whether all variables demand a return period of 50 years is unclear. If parameters with long return periods are used, the need for extensive safety margins should be less. Further, parameters with a return period of 50 years are not always available as it requires long measurement series. The measurements would also have to have been performed in many places to obtain the desired value and to be able to choose a measurement series based on local conditions. This report presents standard deviations along with the mean values. By using this, a confidence interval could be obtained which makes it possible to obtain the load with a desired return period and thereby make different measurement series comparable even if they vary in length. In some cases, the measurement series are too short and the variation is non-existent, this gives questionable results. Note that one has to consider the period of time from which the confidence interval was obtained. A 98% confidence interval based on daily measurements does not result in a 50 year return period. Confidence intervals can be used to ensure that the measurement series are comparable, even though their length may vary. Since it is unlikely that all input parameters with a 50-year return period occur simultaneously, it also raises the question whether this would correspond to an ice load that returns once in 50 years. According to RIL (2013), the used ice load should be from 10 ice occurringwinters, suggesting that the time frame for the input data could be from 10 years as well. Further research is needed about suitable safety margins in ice load design methods and on ice loads from a statistical perspective, analysing return periods and the resulting need for safety margins. The issues presented in this section is also impor- 90 5.2. INPUT tant to keep in mind while implementing statistics for the input parameters, both the input developed specifically for this study and other data. Knowledge on the topic of safety margins and return periods would better justify the margins used and counteract extensive dimensions and ineffective material use. In contrast, a certain degree of conservatism and caution is justified during design to be on the safe side, especially as the knowledge of ice loads remains limited. The usage of local conditions as input data can be challenged by the uncertainties regarding its use. The uncertainties are, for example, during what time period the measurements should have been performed and what return periods the input data should have. Further, it is often unknown what type of value to use, for example if it is the mean or maximum value. 5.2.2 Input parameters Temperature According to RIL (2013), it is reasonable to assume that the surface temperature of the ice does not exceed -5 ◦ C if there is snow on the ice cover. Since this is applicable in Finland, it is reasonable to assume this is applicable in Sweden as the conditions are similar. RIL (2013) also states that if an area is wind protected, as it can be assumed to be in many quays and harbours, there is snow on the ice cover. However, it is not always snow on an ice cover, not even in protected areas during the whole winter season. While studying Committee for waterfront structures (2012), two temperatures are presented where -60◦ C is highly unlikely to occur and the value -40◦ C could be used in Sweden. In many cases -40◦ C would also be considered conservative. However, since no other information exists, it is unknown if lower values can be used or how intermediate ones should be treated. Regarding the temperature, there is a lot of information and data available that can be used. While determining the temperature to use when calculating the ice load, it should be considered that choosing the lowest temperature measured is conservative. The temperature must have time to affect the ice, thus a mean daily temperature would be more plausible. The input that the source specifies should be used, but as presented in Section 5.2.1, it is not always clear which input that is requested. A negative correlation between the temperature and thermal ice loads is shown in the parametric study. This correlation is interesting as fresh water ice contracts with decreasing temperature. Thus, it was expected that the result should have shown the opposite. On the other hand, the ice strength is increased with lower temperatures. Ice thickness In the Norwegian handbook, Statens vegvesen (2015), a method where the ice thickness can be determined based on the number of hours with cold climate is presented, 91 CHAPTER 5. EVALUATION see Equation 3.2 in Chapter 3. However, the ice thickness according to this equation is not investigated in this thesis. Information on hours with cold climate can, for example, be found in the report by Ställ (1983). There is data available that can be used in ice load design regarding the ice thickness. For example, SMHI has presented such data, see Section 4.2. Ice strength As with all input parameters, it is not evident which values to use. Thus, preferably the recommended values for each method would be used, see Table 4.16. If this information is non-existent, the values presented in RIL (2013) are situation dependent, which is preferable as it allows for adaptations to each situation and the prevailing circumstances. Further, as expected the bending strength according to RIL is less than the compressive strength, and the values are realistic and rational in relation to the information stated in Chapter 2. Further, the Finnish conditions can be considered similar to Swedish. While deciding the ice strength, the salinity could be considered and the values could be decreased slightly for seawater. EAU presents an equation to calculate the compressive strength dependent on the ice temperature and the salinity. However, the equation results in high compressive strength in freshwater with cold temperatures, in comparison with the other methods, using EAU 2012. The earlier version, EAU 1996, provide limitations of the compressive strength, which results in values similar to those in the other methods. It is peculiar that these restrictions have been removed in the newer version. Some method uses a contact factor to account for the contact between the ice cover and the structure. The factor is used to reduce the ice load for drifting ice and increase the load with the risk of pack ice. In some cases, a contact factor is used when the ice strength is the same for all types of ice load. Water level variations In the parametric study, it is concluded that the vertical ice load increases with increasing water level variations. This correlation is in contrast to the information stated in Section 2.3.2 that the medium variations that occur one to two times a day result in the highest ice loads and that large variations will break the ice cover. Thus, the ice load should decrease with high water level variations. However, it is unclear what input to use and over what time frame the variations should be studied. The information about medium rises indicate that the variations should not be the maximum over an entire year but rather smaller variations occurring once or twice a day. Furthermore, note that the ice load magnitude studies are horizontal ice loads due to changes in water levels. Only the vertical ice loads depend on the water level changes among the analysed methods. Hence, the load situation differs even if the mechanism is identical. 92 5.3. PILE DIMENSIONS AND CAPACITY Non-analysed parameters None of the studied methods accounts for the size of the water body even though it is a known factor affecting the cooling time (Eklund, 1998). Nevertheless, this is indirectly accounted for if ice thickness based on statistics is included in the method. Eklund (1998) also states that the maximum ice thickness tends to be unaffected by this since the ice cover settles later in the season when the air temperature is colder and no protecting snow has covered the ice. The salinity of the water is only directly considered in EAU (Committee for waterfront structures, 2012). However, this is to a high degree considered by other parameters, for example, the ice strength and the ice thickness. If one differentiates between sea and lakes while choosing input data for the ice thickness based on local conditions, the salinity is considered to some degree. The amount of snow is not considered directly in any method. RIL (2013) proposes that the minimum surface temperature of the ice is limited if there is snow on the ice cover. However, the amount of snow is not considered in the methods, which is interesting since it is stated as one of the essential factors for ice growth, according to Eklund (1998). The snow amount is, to some degree, considered if statistical values of ice thickness from the surrounding area are implemented, as the snow amount also varies based on location. Wind and currents are only accounted for in the method presented by RIL (2013) for drifting ice, Equation 3.24. However, this equation not considered suitable during design because it required knowledge about variables that are unrealistic to determine. Additional parameters that affect the ice growth and the ice loads are not presented in this section. 5.3 Pile dimensions and capacity Research question 6 will be evaluated and analysed in this section about the pile’s capacity and dimensions. The FE model is created to highlight the impact of ice loads on the pile dimensions. It is limited and only presents the ice loads due to four horizontal magnitudes. Despite the simplifications in the model, the analysed magnitudes demonstrate the ice load’s impact on the pile dimensions. Therefore, it can be concluded that the ice load to a large degree affects the piles. For example, neither of the three dimensions of piles in load case 1 or 2 could withstand an ice load of 200 kN. In contrast, the right pile withstands the ice load of 200 kN in load case 1, where only the left pile is affected by the load. This result highlights the importance of reducing the ice load for piles behind others, if possible, to reduce material use and cost. For example, the reduction of ice load for piles behind others is presented in methods from Wikenståhl et al. (2012) and Löfquist (1987). Note that the ice load can act 93 CHAPTER 5. EVALUATION in different directions, as this affects the possibility to reduce the load. The main limitation of the FEM study is the model itself. Additional factors that would affect the dimensions of the piles are the length of the piles, how the piles are joined, the boundary conditions, different inclinations, and whether more piles were used. The action point of the ice load on the piles would also affect the load situation. Thus, more and different models could be performed to better understand how ice loads affect the dimensions and how the pile plan could be performed to reduce the impact of the ice loads. It is also essential to consider that the ice can act in different directions and be acting to a side or behind a structure. 5.4 Compilation of methods This section will discuss and evaluated research questions 2, 3 and 4 divided info one section per method. According to the author’s investigation, a method that does not fulfil all the conditions in this thesis is not recommended to be used for design of piles. The three conditions are if the method; considers local conditions, is applicable in design, and is applicable for piles. If the method did not fulfil the three requirements, the reason for this would be discussed in this chapter. Likewise, the result of the parametric study and resulting ice load for the three cities are analysed in this part. Among the three studied cities in Section 4.3, Mora often results in the highest ice load, Umeå the second-highest, and Halmstad the lowest. These results are reasonable, as Halmstad and Umeå are coastal cities with saline water, even if the waters around Umeå are brackish. Mora is an inland city located by a lake and has also almost twice as thick ice thickness as Umeå, since the ice thickness in Umeå is measured at a harbour. It is also important to consider that larger bodies of water balance the temperature and that inland area tends to be colder than coastal ones, as seen in Figure 4.14 in Section 4.2. The horizontal design load for Mora varies between 70 kN and 800 kN for the studied methods. The lowest load is achieved by the methods without adaption to local conditions and are adapted for wall structures, Svensk Energi (2011) and Stockholms hamnar (2016), which is might because the load behaves differently for wall structures. The lowest horizontal ice load, calculated from methods that take local conditions into account, is 350 kN, determined according to Wikenståhl et al. (2012). The majority of the methods that consider local conditions generates results between 370 kN and 440 kN for the horizontal ice load in Mora, which is a high magnitude of the ice load. As seen in Section 4.4, piles with a dimension of 320 mm fail due to an ice load of 200 kN. In Mora, the temperature is low and the inland lake, Siljan has thick ice. This results in higher loads for the methods that consider the local conditions compared with the methods that do not. The largest magnitude of the ice loads is due to drifting ice, which may not be a big problem in an inland lake due to low current flow compared to a river, for example. However, the current 94 5.4. COMPILATION OF METHODS flow is not taken into account in any of the methods. Trafikverket The Swedish Transport Administration’s method is a handbook that does not fulfil the three conditions of applicability because it does not consider local conditions. In addition, the method only recommends one magnitude of the ice load, which may be valid in the south of Sweden. How the ice load should be considered in the north of Sweden when this value is not applicable is unclear, especially since it is stated that the method presented by Löfquist (1987) is replaced. Löfquist The method written by Löfquist (1987) is a handbook that considers local conditions, is applicable in design and is applicable for piles, even if it is adapted to bridge supports. It is noticeable that the method is adapted for bridge supports for two types of ice load types; ice load due to thermal expansion and water level changes. The support should be set to at least 4 m, which results in extensive ice loads and is therefore not applicable for piles for these load types. In addition, the method does not consider local conditions for these two ice load types. On the other hand, the equation for small drifting ice floes depends on the thickness of the ice, the ice strength, and the geometry and inclination of the piles. According to Löfquist (1987), drifting ice load generates a lower ice load than the other methods in all the cities. However, the drifting ice load in the parametric study results in high magnitudes of the ice load when the ice thickness and the ice strength are varied separately. This result might occur because Löfquist recommends the lowest range of compressive ice strength, even lower than the bending strength. However, this does not have to be wrong because the ice strength is usually less when the ice is drifting. The vertical ice load results in average values for all cities, and likewise, the parametric study results in average values for all variables. This was when the equation for bridge supports was used instead of the equation for separate piles and dolphins. The equations for separate supports result in extensive vertical ice loads, especially in Mora. The methods’ dependency on ice thickness could explain this, which is shown in the parametric study. The equation for separate piles is more affected by the ice thickness than the equation for bridge supports. Despite this, the equation for separate supports and dolphins is mostly used in the design of piled structures according to Mayor (2022). Waxholmsbolaget The method written by Wikenståhl et al. (2012) considers local conditions and is applicable in design of piles, as the method is adapted for smaller traffic piers in 95 CHAPTER 5. EVALUATION the archipelagos of Stockholm. The equations to calculate the horizontal ice load considers the thickness of the ice cover and the strength of ice. The equation to calculate the vertical ice load also consider the water level variation. In other words, several parameters depend on local conditions. All horizontal ice load types are calculated using the same equation for slender piles, but with different maximum values according to Wikenståhl et al. (2012). The same equation for all the different ice load types results in high ice load due to thermal expansion and water level changes compared to the other methods. In contrast, the drifting ice load results in an average load. This result is also the case for the parametric study, where drifting ice generates low to average loads, and the thermal ice load generates high. The vertical load results in the lowest loads for all cities compared to the other methods. This is also the case for the parametric study, where Waxholmsbolaget has the lowest vertical ice load for all the cases when the ice thickness, the ice strength, and the water level variation are varied separately. Stockholms hamnar The method from Ports of Stockholm (Stockholms hamnar, 2016) does not fulfil the three conditions of applicability because it does not consider local conditions. However, the handbook is adapted to be applicable in Stockholm, which means that the handbook considers the local conditions in Stockholm. But the requirement of local conditions was to make the handbook applicable to different geographical locations. However, the handbook describes that local conditions should be considered, but it does not specify how. The method only recommends two magnitudes of the horizontal ice load, depending on whether the load is parallel or toward the quay, and one magnitude for the vertical load. Svensk Energi RIDAS (Svensk Energi, 2011) does not fulfil the three conditions of applicability because it does not consider local conditions nor vertical ice loads. Instead, the method recommends magnitudes of the ice load per meter adapted for dam structures. The method does not provide a guideline for different ice load types, only a value based on the geographic location. Svensk Energi (2011) states that the line load can achieve a limiting value of 2 000 kN/m due to arch action, which is an extreme high line load compared to the other methods. Since it is near 5 times as large as the second-highest line load compared to the other methods. Even though Löfquist (1987) results in a higher point load of 800 kN compared to 700 kN for a pile with a width of 0.35 m. But the extensive load that Löfquist (1987) result in is because of the requirement that the width should be equal to 4 m. However, this type of load is not considered in this report since it was judged unlikely that such an arch action could occur for piled structures. 96 5.4. COMPILATION OF METHODS Vejdirektoratet The method from The Danish road directorate considers local conditions and is applicable for design of piles. The equations to calculate the horizontal and vertical ice load consider several variables of the local conditions, such as the thickness of ice and the strength of ice. The contact between the pile and the ice is also considered for drifting ice. In other words, several parameters that depend on the local conditions are considered. The thermal load is the lowest compared to the other methods for all cities. This is also the result of the parametric study, where the ice thickness and ice strength are varied separately. The thermal load, according to Vejdirektoratet, seems to generate low loads, and a possible explanation for this could be the reduction factor of 0.04 that is included in the equation. The equation is similar to Equation 3.11 provided by Waxholmsbolaget, which is not reduced by this factor of 0.04. On the other hand, the drifting ice load results in a high load in Mora and an average load in Halmstad. In the parametric study, the ice load results in average ice loads, but the graph is exponential and the ice load increases rapidly with increased ice thickness. The drifting ice load due to the ice strength in the parametric study results in average ice loads compared to the other methods. The vertical ice load also results in a higher load than average for Mora and an average value for Halmstad. The vertical ice load due to the ice thickness is exponential, as shown in the parametric study and results in really high loads when the thickness of ice is increased. RIL The method from the Finnish Association of Civil Engineers (RIL, 2013) considers local conditions, is applicable in design and is applicable for piles. However, the method does not apply to countries other than Finland regarding thermal expansion. RIL has the most parameters that consider local conditions of all studied methods. The parameters can even be so many that it instead becomes difficult to determine and thus this influence the applicability of the method. The slope of the river, wave load and flow load on the edge and the bottom ice cover, are example of parameters that are difficult to determine. The drifting ice load is quite high for all the cities compared to the other methods. Due to the berthing load, the loads must also be set to at least 200 kN. The drifting ice load is also clearly the highest in the parametric study when the ice thickness increases, and due to the ice strength. These results indicate that RIL results in high ice loads for drifting ice. Regarding the parametric study of the ice thickness for drifting ice, the load reaches over 1 MN for ice thicknesses above 0.9 m. This is extremely high ice loads, given that the method recommends ice thicknesses between 0.7 m and 1.1 m (RIL, 2013). One procedure to determine the ice loads due to drifting ice is considered difficult to used in design since it includes several variables which cannot easily be determined. 97 CHAPTER 5. EVALUATION The vertical ice load results in average values for RIL compared to the other methods for all the cities. Likewise, the vertical ice load in the parametric study is in the average for all the parameters. One aspect that should be noted regarding this method is uncertainties associated with the translation from Finnish. Statens vegvesen The method from the Norwegian Public Road Administration considers local conditions and is applicable for design. The method is also applicable for piles, except for ice loads due to drifting ice, as the method is not applicable according to the original source, ISO 19906 (2010). The handbook is valid if the width of the piles is greater than two times the thickness of the ice. This ratio is often not achievable in Swedish conditions for smaller structures, but in cases where the ice thickness is slim, the equation for drifting ice may be valid. However, the equation results in high ice loads compared to other methods. The same equation determines the ice load due to thermal expansion and water level changes. All cities result in average values among the studied methods in this report. Likewise, the parametric study results in average results. However, few methods were available for comparison of the ice load caused by water level changes. In addition, no method has an adapted a sole equation for the ice load due to water level changes. The vertical ice loads result in the average loads for all the cities. The parametric study shows that the vertical ice load is to a small extent dependent on the ice thickness and to a higher degree on the water level variation. It should be noted that the vertical ice load is limited to one-third of the horizontal ice load, which often becomes the limiting value. Statens vegvesen also has another equation to calculate the vertical ice load, which is adapted for separate supports and dolphins. This equation is often used when calculating the vertical load for piled structures, but the equation results in high values and are in most cases limited to one third of the horizontal load. Port Designer’s handbook The Port Designer’s handbook (Thoresen, 2014) is not applicable for piled structures. This because the vertical ice load is difficult to determine from the graph for structures with a diameter of less than 1 m, as the graph is exponential. In addition, the horizontal ice load is not applicable for all cases according to the original source, ISO 19906 (2010). This is the same reason as for Statens vegvesen. 98 5.4. COMPILATION OF METHODS EAU The method from the Committee for waterfront structures, EAU (Committee for waterfront structures, 2012), considers local conditions, is applicable in design and is applicable for piles. Except for the ice load due to thermal expansion, which is not applicable for piles or the Swedish climate. This is because the ice load method is adapted for banks or planar structures and is valid for air temperatures between -40◦ C and -60◦ C, which rarely occurs in Sweden. EAU is the only method explicitly adapted for piled structures and where the ice strength depends on the salinity and the ice temperature. The ice strength results in significant ice loads unless the former edition, EAU 1996, is used as a limitation of the strength. The salinity degree is also remarkable high, the salinity should be at least 50 ‰ for water to be classified as saline water. The highest salinity degree in Sweden on the west coast is approximately 30‰. The drifting and vertical ice loads result in high loads compared to the other method, but the loads are around the average values regarding Halmstad. These values are obtained because the ice strength results in a high load, even though the limitation is applied. This is visible in the parametric study, where the ice load results in low values when the ice thickness and the ice strength are varied. 99 Chapter 6 Conclusion 6.1 Conclusion The methods studied in this thesis treats the ice loads differently. All methods do not propose a procedure to determine the ice load but rather specify a value. Only values are not desirable as this does not allow for adaptation to the specific project. Although, the methods presenting a value are not necessarily more conservative than methods accounting for local conditions. Some methods do not consider vertical ice loads and this may be an issue for light-weight structures such as piers. Determining the vertical ice load could be performed using another method. Further, not all methods divide the horizontal ice loads into different load types. Division of the ice load into load types allows for better adaptation of how the marine structure will be used and better adaptation of the input parameter to the load type. The ice load magnitudes varies significantly between the methods and different ice load types. The methods that are considered to be applicable for piles, suitable for design of piles and account for local conditions are; Löfquist (1987), Wikenståhl et al. (2012), Vejdirektoratet & Banedanmak (2015), RIL (2013), Statens vegvesen (2015) and Committee for waterfront structures (2012). Note that these methods are only suitable to use according to the applicability study, with the requirement of being applicable for design of piles and considering some local conditions investigated in the parametric study. However, this does not mean that the calculation procedures for all the ice load types are appliable in the specific methods. The methods with a procedure to determine the ice loads depend on different input data types. It is however unclear to a large extent how these input data should be derived. The input data which affects the ice load varies between the methods. This is presented in Section 4.1 where the effect of each parameter on the ice load’s magnitude is presented. The input data used in the methods are local conditions and can be adapted to the situation and project location. There is a limited possibility to find information based on local conditions regarding the ice strength. Information from for example SMHI is available to derive local conditions such as ice thickness, temperature and water level changes. Some guiding values provided by the methods has been used in this report when calculating the ice loads, primely regarding the 101 CHAPTER 6. CONCLUSION ice strength. It is unclear which time period that should be used for the water level variations, likewise if it is the maximum, mean or minimum value that is requested in the methods. It is also concluded that the ice load affects the pile dimensions, where larger ice loads require larger dimensions of the piles. Thus, it is of interest not to have too high design loads as it is ineffective regarding material usage. On the other hand, sufficiently high safety factors are required, especially since the knowledge of ice loads is limited. According to some methods, piles behind others should be considered less exposed to ice loads. This reduction could allow for less material use. 6.2 Further research An overall conclusion from this project is that further research on ice loads is needed. Information about the safety margins used in all methods is needed along a study of each handbook’s original source. This is essential because some methods may contain safety margins while others do not, and it is unclear whether additional margins should be applied. The information would indicate the total, combined, safety factor and what margins are reasonable to further apply in design. Further, what specific input information should be used in each method needs to be sorted out, especially concerning whether all input information should have a return period of 50 years. This knowledge should be combined with knowledge about safety margins. The effect of ice loads on pile dimensions could be more closely studied. This knowledge would further highlight the importance of ice loads and its magnitude. Additional pile dimensions could be studied, as well as more extensive FEM analysis and more complex models with more piles and different inclinations of the piles. Measurements from actual ice loads would be useful for all ice load studies, especially measurements over a more extended period of time and several winters. In addition, ice load measurements on piles would have been interesting for this thesis, as many measurements are performed on dams and more rigid structures. The direct response of the piles exposed to ice load could also be studied, where the forces and elongation in the pile would be measured. 102 Bibliography Adolfi, E., Eriksson, J., 2013. Islastens inverkan på sannolikheten för halka och vältningsfel för betongdammar (svenska: Islastens inverkan på brottsannolikheten för glidning och stjälpning av betongdammar. Ph.D. thesis, KTH, Royal Institute of Technology, Sweden. 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Offshore Mechanics and Arctic Engineering Vol. 144, No. 1. 107 Appendix A Translation A.1 English to Swedish English Svenska Bathymetry Batymetri Brackish water Bräckt vatten Coastal area Kustnära område County Län Current line Strömfåra Freshwater Sötvatten Ice floe Isflak Ice jams Packis, isansamling Ice ridges Isrygg Kernel ice Kärnis Maximum water level Dämningsgräns Pack ice Packis Quay Kaj Ridges Vallar Saline water Saltvatten Wear Nötning 109 110 Appendix B Analytical calculations B.1 Löfquist Input b ≔ 0.35 m ⎡ 0.28 m ⎤ d ≔ ⎢ 0.5 m ⎥ ⎢ ⎥ ⎣ 0.11 m ⎦ Width of pile [m] Umea� Mora Halmstad Ice thickness [m] a ≔ 0.35 m Support length [m] ⎡ 1500 ⎤ σb ≔ ⎢ 2000 ⎥ kPa ⎢ ⎥ ⎣ 1000 ⎦ Bending strength [kPa] w ≔ 0.5 m Water level rise [m] Thermic ice load Ih.1 ＝ i1 ⋅ a Thermal ice load [kN] i1 Ice load parameterdependent on local variations [kN/m] a Support length [m] kN i1 ≔ 200 ― m Varies between 50 - 300 kN/m Ih.1 ≔ i1 ⋅ max (4 m , a) = 800 kN 111 Water level changes Ih.1 ＝ i1 ⋅ a Ice load, water level changes [kN] i1 Ice load parameter dependent on local variations [kN/m] a Support length [m] kN i1 ≔ 200 ― m Ih.1 ≔ i1 ⋅ max (4 m , a) = 800 kN Floating ice, larger ice floe Ih.2 ＝ C1 ⋅ σk ⋅ d ⋅ b Ice load from flowing ice [kN] Ih.2 ＝ C1 ⋅ C2 ⋅ C3 ⋅ σk ⋅ d ⋅ b Ice load from flowing ice, support shape [kN/m] C1 Formfactor, (b/d) [-] C2 Formfactor, pointyness of supports front [-] C3 Formfactor, incilnation of support front [-] σk Cruching strength of ice [kPa] ⎡ 1.2 ⎤ C1 ≔ ⎢ 1.6 ⎥ ⎢ ⎥ ⎣ 0.882 ⎦ C2 ≔ 1 C3 ≔ 1 ⎡ ⎤ σk ≔ ⎢ 700 ⎥ kPa ⎣ 500 ⎦ Input: 500, 700 or 1400 kPa Umea� 112 Non-Commercial Use Only Umea� Ih.2 ≔ C1 (0) ⋅ σk (0) ⋅ d (0) ⋅ b = 82.32 kN Mora Ih.2 ≔ C1 (1) ⋅ σk (0) ⋅ d (1) ⋅ b = 196 kN Halmstad Ih.2 ≔ C1 (2) ⋅ σk (1) ⋅ d (2) ⋅ b = 16.979 kN Verical ice load -For bridge supports Iv ＝ 2 ⋅ (a + b) ⋅ 0.6 ⋅ d ⋅ ‾‾‾‾‾‾‾ σ b ⋅ w ⋅ kg Uplift caused by ice [kN] a Length of support [m] b Width of support [m] σb Bending strength [kPa] w Water level rise [m] kN kg ≔ 10 ―― m3 Uplift module [kN/m^3] Umea� ⎛ Ih.1 ⎞ Iv ≔ min ⎜2 ⋅ (a + b) ⋅ 0.6 ⋅ d (0) ⋅ ‾‾‾‾‾‾‾‾‾ σb (0) ⋅ w ⋅ kg , ―― ⎟ = 20.369 kN 3 ⎠ ⎝ Mora ⎛ Ih.1 ⎞ Iv ≔ min ⎜2 ⋅ (a + b) ⋅ 0.6 ⋅ d (1) ⋅ ‾‾‾‾‾‾‾‾‾ σb (1) ⋅ w ⋅ kg , ―― ⎟ = 42 kN 3 ⎠ ⎝ Halmstad ⎛ Ih.1 ⎞ Iv ≔ min ⎜2 ⋅ (a + b) ⋅ 0.6 ⋅ d (2) ⋅ ‾‾‾‾‾‾‾‾‾ σb (2) ⋅ w ⋅ kg , ―― ⎟ = 6.534 kN 3 ⎠ ⎝ -For seperate piles and dolphins 113 Non-Commercial Use Only -For seperate piles and dolphins ⎡ 800 ⎤ kN A ≔ ⎢ 1600 ⎥ ―― ⎢ ⎥ m2 ⎣ 1200 ⎦ Umea� 2 I ⎛ ⎞ h.1 Iv.2 ≔ min ⎜A (0) ⋅ d (0) , ―― ⎟ = 62.72 kN 3 ⎠ ⎝ Mora 2 I ⎛ ⎞ h.1 Iv.2 ≔ min ⎜A (1) ⋅ d (1) , ―― ⎟ = 266.667 kN 3 ⎠ ⎝ Halmstad 2 ⎛ ⎞ Iv.2 ≔ min ⎝A (2) ⋅ d (2) , Ih.1⎠ = 14.52 kN 114 Non-Commercial Use Only B.2 Waxholmsbolaget Input b ≔ 0.35 m Width of pile [m] ⎡ 0.28 m ⎤ d ≔ ⎢ 0.5 m ⎥ ⎢ ⎥ ⎣ 0.11 m ⎦ Umea� Mora Halmstad Ice thickness [m] ⎡ 1500 ⎤ σb ≔ ⎢ 2000 ⎥ kPa ⎢ ⎥ ⎣ 1000 ⎦ Bending strength of ice [kPa] w ≔ 0.5 m Water level rise [m] kN γw ≔ 10 ―― m3 Heavyness of water [kN/m^3] B ≔ 16 m 2 Area under pier [m^2] kN kg ≔ 10 ―― m3 Uplift module [kN/m^3] Thermal expansion/water level changes/drifting ice σk ≔ 2 MPa ⎡ 196 ⎤ Ih ≔ σk ⋅ b ⋅ d = ⎢ 350 ⎥ kN ⎢ ⎥ ⎣ 77 ⎦ Maximum Ih : Umea� Mora Halmstad 400 kN for thermal expansion 200 kN for water level changes 1 200 kN for drifting ice Vertical Umea� ⎛ ⎞ I ≔ min ⎝0.60 ⋅ b ⋅ d (0) ⋅ ‾‾‾‾‾‾‾‾‾ σb (0) ⋅ w ⋅ kg , γw ⋅ B ⋅ w⎠ = 5.092 kN Mora ⎛ ⎞ I ≔ min ⎝0.60 ⋅ b ⋅ d (1) ⋅ ‾‾‾‾‾‾‾‾‾ σb (1) ⋅ w ⋅ kg , γw ⋅ B ⋅ w⎠ = 10.5 kN Halmstad ⎛ ⎞ I ≔ min ⎝0.60 ⋅ b ⋅ d (2) ⋅ ‾‾‾‾‾‾‾‾‾ σb (2) ⋅ w ⋅ kg , γw ⋅ B ⋅ w⎠ = 1.633 kN 115 Mora ⎛ ⎞ I ≔ min ⎝0.60 ⋅ b ⋅ d (1) ⋅ ‾‾‾‾‾‾‾‾‾ σb (1) ⋅ w ⋅ kg , γw ⋅ B ⋅ w⎠ = 10.5 kN Halmstad ⎛ ⎞ I ≔ min ⎝0.60 ⋅ b ⋅ d (2) ⋅ ‾‾‾‾‾‾‾‾‾ σb (2) ⋅ w ⋅ kg , γw ⋅ B ⋅ w⎠ = 1.633 kN B.3 Stockholms hamnar Input Non-Commercial Use Only b ≔ 0.35 m Width of pile [m] Vertical kN i ≔ 20 ― m I ≔ π ⋅ b ⋅ i = 21.991 kN Thermal expansion/Drifting ice kN i ≔ 200 ― m I ≔ i ⋅ b = 70 kN B.4 Svensk Energi Input b ≔ 0.35 m Width of pile [m] kN iNorth ≔ 200 ― m kN iSouth ≔ 50 ― m I ≔ iNorth ⋅ b = 70 kN I ≔ iSouth ⋅ b = 17.5 kN 116 B.5 Vejdirektoratet Input b ≔ 0.35 m ⎡ 0.28 m ⎤ d ≔ ⎢ 0.5 m ⎥ ⎢ ⎥ ⎣ 0.11 m ⎦ Width of pile [m] Umea� Mora Halmstad Ice thickness [m] Thermal ice load Ih.1 ＝ 0.04 ⋅ σk ⋅ d ⋅ b Thermal ice load [kN] σk Cruching strength [kPa] d Ice thickness [m] b Support width [m] σk ≔ 1900 kPa ⎡ 7.448 ⎤ Umea� Ih.1 ≔ 0.04 ⋅ σk ⋅ d ⋅ b = ⎢ 13.3 ⎥ kN Mora ⎢ ⎥ Halmstad ⎣ 2.926 ⎦ Drifting ice Ih.2 ＝ C1 ⋅ C2 ⋅ C3 ⋅ σk ⋅ d ⋅ b Ice load from flowing ice [kN] C1 Form factor [-] C2 Contact factor [-] C3 Dimensioning factor [-] σk Cruching strength [kPa] d Ice thickness [m] b Support width [m] C1 ≔ 0.9 Circular cross-section C2 ≔ 0.5 117 Drifting ice C2 ≔ 0.5 Drifting ice ⎡ 2.236 ⎤ ‾‾‾‾‾‾ d ⎢ C3 ≔ 1 + 5 ―= 2.854 ⎥ b ⎢⎣ 1.604 ⎥⎦ σk ≔ 1900 kPa Ih.2 ≔ C1 ⋅ C2 ⋅ C3 ⋅ σk ⋅ d ⋅ b Umea� Ih.2 ≔ C1 ⋅ C2 ⋅ C3 (0) ⋅ σk ⋅ d (0) ⋅ b = 187.36 kN Mora Ih.2 ≔ C1 ⋅ C2 ⋅ C3 (1) ⋅ σk ⋅ d (1) ⋅ b = 426.965 kN Halmstad Ih.2 ≔ C1 ⋅ C2 ⋅ C3 (2) ⋅ σk ⋅ d (2) ⋅ b = 52.785 kN Verical ice load Iv ＝ 0.8 ⋅ σb ⋅ d 1.75 ⋅ b 0.25 Uplift caused by ice [kN] If 0.5<b/d<7 Iv ＝ π ⋅ b ⋅ 0.4 ⋅ d ⋅ ‾‾‾‾‾‾‾ kg ⋅ σ b ⋅ w Uplift caused by ice [kN] If b/d>7 σb Bending strength [kPa] d Ice thickness [m] b Support width [m] kg Uplift module [kN/m^3] w Water level change [m] σb ≔ 500 kPa kN kg ≔ 9.81 ―― m3 w≔1 m 118 Non-Commercial Use Only kN kg ≔ 9.81 ―― m3 w≔1 m Umea� | b Iv.Umeå ≔ if 0.5 ≤ ―― ≤7 | = 33.159 kN d (0) | ‖ 1.75 | 0.25 ( ) ⋅b ‖ | ‖ 0.8 ⋅ σb ⋅ d 0 | b else if ―― >7 | d (0) | ‖ | ‾‾‾‾‾‾‾ ( ) ‖ π ⋅ b ⋅ 0.4 ⋅ d 0 ⋅ kg ⋅ σb ⋅ w | Mora | b Iv.Mora ≔ if 0.5 ≤ ―― ≤7 | = 91.469 kN d (1) | ‖ 1.75 | ( ) ⋅ b 0.25 ‖ | ‖ 0.8 ⋅ σb ⋅ d 1 | b else if ―― >7 | d (1) | ‖ kg ⋅ σb ⋅ w || ‖ π ⋅ b ⋅ 0.4 ⋅ d (1) ⋅ ‾‾‾‾‾‾‾ Halmstad | b Iv.Halmstad ≔ if 0.5 ≤ ―― ≤7 | = 6.464 kN d (2) | ‖ 1.75 | 0.25 ( ) ⋅b ‖ | ‖ 0.8 ⋅ σb ⋅ d 2 | b else if ―― >7 | d (2) | ‖ | ‾‾‾‾‾‾‾ ( ) ‖ π ⋅ b ⋅ 0.4 ⋅ d 2 ⋅ kg ⋅ σb ⋅ w | Downwards vertical load ⎡ Iv.Umeå ⎤ ⎢ ⎥ ⎢ Iv.Mora ⎥ ⎡ 16.58 ⎤ ⎢⎣ Iv.Halmstad ⎥⎦ ⎢ Iv.2 ≔ ―――― = 45.735 ⎥ kN ⎢ ⎥ 2 ⎣ 3.232 ⎦ 119 Non-Commercial Use Only B.6 RIL Input b ≔ 0.35 m ⎡ 0.28 m ⎤ d ≔ ⎢ 0.5 m ⎥ ⎢ ⎥ ⎣ 0.11 m ⎦ Width of pile [m] Umea� Mora Halmstad Ice thickness [m] Thermic ice load Ih.1 ＝ f (d) ⋅ b Thermal ice load [kN] f Varies: 80 - 400 (Finland). Dependent on width of ice field, ice thickness & latitude [kN/m] d Ice thickness [m] b Support width [m] Not considered as the method is considered non applicable in Sweden Floating ice Ih.1 ＝ C1 ⋅ C2 ⋅ C3 ⋅ C5 ⋅ σk ⋅ d ⋅ b Ice load from flowings cutt by vertical structure [kN] C1 Form factor [-] C2 Contact factor [-] C3 Dimensioning factor [-] C5 Contraint of ice [-] σk Cruching strength [kPa] d Ice thickness [m] b Support width [m] σk ≔ 1500 kPa 120 σk ≔ 1500 kPa C1 ≔ 0.9 Circular cross-section, semicircular front C2 ≔ 0.5 Contact coefficient ⎡ 2.2 ⎤ d ⎢ = 3.143 ⎥ C3 ≔ 1 + 1.5 ― b ⎢⎣ 1.471 ⎥⎦ C5 ≔ 1 For no constraints Ih.3 ≔ 200 kN Ice load due to ships moving and berthing [kN] Umea� Ih.1 ≔ max ⎛⎝C1 ⋅ C2 ⋅ C3 (0) ⋅ C5 ⋅ σk ⋅ d (0) ⋅ b , 200 kN⎞⎠ = 200 kN Mora Ih.1 ≔ max ⎛⎝C1 ⋅ C2 ⋅ C3 (1) ⋅ C5 ⋅ σk ⋅ d (1) ⋅ b , 200 kN⎞⎠ = 371.25 kN Halmstad Ih.1 ≔ max ⎛⎝C1 ⋅ C2 ⋅ C3 (2) ⋅ C5 ⋅ σk ⋅ d (2) ⋅ b , 200 kN⎞⎠ = 200 kN Vertical load, upwards and downwards I v ＝ kv ⋅ σ b ⋅ d 2 Uplift caused by ice [kN] ks Coefficient [-] kv Coefficient [-] v Water current rate [m/s] t Water level change time [h] σk Cruching strength [kPa] 121 Non-Commercial Use Only σk Cruching strength [kPa] σb Bending strength [kPa] d Ice thickness [m] b Support width [m] ks ≔ 150 Surface temperature -20 ° C and time 2 h ⎡ 0.27 ⎤ kv ≔ ⎢ 0.236 ⎥ ⎢ ⎥ ⎣ 0.36636 ⎦ Due to b/d t ≔ 2 hr m v ≔ 0.25 ― hr σb ≔ 0.65 ⋅ σk = 0.975 MPa Umea� 2 Iv ≔ kv (0) ⋅ σb ⋅ d (0) = 20.639 kN Mora 2 Iv ≔ kv (1) ⋅ σb ⋅ d (1) = 57.525 kN Halmstad 2 Iv ≔ kv (2) ⋅ σb ⋅ d (2) = 4.322 kN 122 Non-Commercial Use Only B.7 Statens vegvesen Input b ≔ 0.35 m Width of pile [m] ⎡ 0.28 m ⎤ d ≔ ⎢ 0.5 m ⎥ ⎢ ⎥ ⎣ 0.11 m ⎦ Umea� Mora Halmstad ⎡ -40 ⎤ T ≔ ⎢ -40 ⎥ ⎢ ⎥ ⎣ -25 ⎦ Umea� Mora Halmstad Ice thickness [m] Temperature [ ° C] Water level change [m] w ≔ 0.5 Thermic ice load/Water level changes Ih.1 ＝ (300 d + 2.5 |T|) ⋅ b Thermal ice load [kN] d Ice thickness [m] T Lowest average daily temperatur of 50 years[ ° C] b Support width [m] Umea� dUmeå ≔ 0.28 ⎛b⎞ Ih.1.Umeå ≔ min ⎛⎝⎛⎝300 ⋅ min ⎛⎝dUmeå , 0.5⎞⎠ + 2.5 |T (0)|⎞⎠ , 250⎞⎠ ⋅ ⎜―⎟ ⋅ kN = 64.4 kN ⎝m⎠ Mora dMora ≔ 0.5 ⎛b⎞ Ih.1.Mora ≔ min ⎛⎝⎛⎝300 ⋅ min ⎛⎝dMora , 0.5⎞⎠ + 2.5 |T (1)|⎞⎠ , 250⎞⎠ ⋅ ⎜―⎟ ⋅ kN = 87.5 kN ⎝m⎠ Halmstad dHalmstad ≔ 0.11 ⎛b⎞ Ih.1.Halmstad ≔ min ⎛⎝⎛⎝300 ⋅ min ⎛⎝dHalmstad , 0.5⎞⎠ + 2.5 |T (2)|⎞⎠ , 250⎞⎠ ⋅ ⎜―⎟ ⋅ kN = 33.425 kN ⎝m⎠ Floating ice 123 Floating ice ⎛ b ⎞ -0.16 ⎛ d ⎞ n Ih.2 ＝ A ⋅ d ⋅ beff ⋅ ⎜― ⋅ ⎜―⎟ ⎟ ⎝d⎠ ⎝ d1 ⎠ Ice load from flowing ice [kN] A Ice load parameter [kPa] d Ice thickness [m] beff Effective support width [m] d1 Transformation factor [m] n Help parameter [-] A ≔ 1800 kPa | beff (Ctc , η) ≔ if Ctc > 5 ⋅ b | ‖b ‖ | else if Ctc < 5 ⋅ b| | ‖ Ctc ⋅ η + b | ‖ Ctc is the centre-to-centre distance [m] η is the number of piles [-] beff ≔ beff (4 m , 4) = 0.35 m d1 ≔ 1 m Umea� | = -0.444 nUmeå ≔ if d (0) ≤ 1 m | ‖ d (0) ‖ ―― | | m ‖ -0.5 + ―― | ‖ 5 ‖ | else if d (0) > 1 m| ‖ -0.3 | | ‖ ⎛ b ⎞ -0.16 Ih.2.Umeå ≔ A ⋅ d (0) ⋅ beff ⋅ ⎜―― ⎟ ⎝ d (0) ⎠ nUmeå ⎛ d (0) ⎞ ⎜―― ⎟ ⎝ d1 ⎠ = 299.54 kN Mora 124 Non-Commercial Use Only Mora | = -0.4 nMora ≔ if d (1) ≤ 1 m | ‖ d (1) | ‖ ―― | m ‖ -0.5 + ―― | ‖ 5 ‖ | else if d (1) > 1 m| ‖ -0.3 | | ‖ ⎛ b ⎞ -0.16 Ih.2.Mora ≔ A ⋅ d (1) ⋅ beff ⋅ ⎜―― ⎟ ⎝ d (1) ⎠ nMora ⎛ d (1) ⎞ ⎜―― ⎟ ⎝ d1 ⎠ = 440.055 kN Halmstad | = -0.478 nHalmstad ≔ if d (2) ≤ 1 m | ‖ d (2) ‖ ―― | | m ‖ -0.5 + ―― | ‖ 5 ‖ | else if d (2) > 1 m| ‖ -0.3 | | ‖ ⎛ b ⎞ -0.16 Ih.2.Halmstad ≔ A ⋅ d (2) ⋅ beff ⋅ ⎜―― ⎟ ⎝ d (2) ⎠ nHalmstad ⎛ d (2) ⎞ ⎜―― ⎟ ⎝ d1 ⎠ = 165.394 kN Verical ice load Iv.1 ＝ V ⋅ 0.6 ⋅ ‾‾‾‾‾‾‾‾‾‾‾ 0.7 ⋅ d ⋅ A ⋅ w ⋅ kg Uplift caused by ice [kN] V Length of support in contact with ice [m] d Ice thickness [m] A Ice load parameter [kPa] w Water level change [m] kg Uplift module [kN/m^3] b Support width [m] ⎡ 0.28 ⎤ d ≔ ⎢ 0.5 ⎥ ⎢ ⎥ ⎣ 0.11 ⎦ 125 Non-Commercial Use Only ⎡ 0.28 ⎤ d ≔ ⎢ 0.5 ⎥ ⎢ ⎥ ⎣ 0.11 ⎦ V ≔ b ⋅ π = 1.1 m A ≔ 1800 kg ≔ 9.81 ⎡ 27.444 ⎤ kN 0.7 ⋅ d ⋅ A ⋅ w ⋅ kg ⋅ ― = ⎢ 36.674 ⎥ kN Iv.1 ≔ V ⋅ 0.6 ⋅ ‾‾‾‾‾‾‾‾‾‾‾ m ⎢⎣ 17.202 ⎥⎦ -Vertical component cause by water level changes ⎡ Ih.1.Umeå ⎤ ⎡ 64.4 ⎤ ⎢ ⎥ Ih.1 ≔ ⎢ Ih.1.Mora ⎥ = ⎢ 87.5 ⎥ kN ⎢ ⎥ ⎢⎣ Ih.1.Halmstad ⎥⎦ ⎣ 33.425 ⎦ ⎡ 21.467 ⎤ Ih.1 ⎢ = 29.167 ⎥ kN Iv.2 ≔ ―― 3 ⎢⎣ 11.142 ⎥⎦ Maximum one-third of the horizontal load Vertical ice load for seperate piles kN A ≔ 1600 ―― m2 ⎡ 125.44 ⎤ Iv3 ≔ A ⋅ (d ⋅ m) = ⎢ 400 ⎥ kN ⎢ ⎥ ⎣ 19.36 ⎦ 2 Umea� Iv ≔ min ⎛⎝Iv.1 (0) , Iv.2 (0) , Iv3 (0)⎞⎠ = 21.467 kN Mora Iv ≔ min ⎛⎝Iv.1 (1) , Iv.2 (1) , Iv3 (1)⎞⎠ = 29.167 kN Halmstad Iv ≔ min ⎛⎝Iv.1 (2) , Iv.2 (2) , Iv3 (2)⎞⎠ = 11.142 kN 126 Non-Commercial Use Only B.8 Port Designer’s handbook Input b ≔ 0.35 m ⎡ 0.28 m ⎤ d ≔ ⎢ 0.5 m ⎥ ⎢ ⎥ ⎣ 0.11 m ⎦ Width of pile [m] Umea� Mora Halmstad Ice thickness [m] Thermal ice load Port Designer´s handbook does not provide any value or equations. Water level changes Port Designer´s hanbook does not provide any value or equations. Floating ice Same equation as Ha� ndbok N400 - Statens vegvesen ih ＝ pG ⋅ d ⋅ b ⎛ d ⎞n ⎛ d ⎞m pG ＝ A ⋅ ⎜―⎟ ⋅ ⎜― ⎟ ⎝ d1 ⎠ ⎝ b ⎠ A Strength coefficient [kPa] d1 Reference ice thickness[m] n Empirical cofficient [-] m0 Empirical cofficient [-] A ≔ 1800 kPa Given value m ≔ -0.16 Given value d1 ≔ 1 m Given value Umea� 127 Umea� | = -0.444 nUmeå ≔ if d (0) ≤ 1 m | ‖ d (0) ‖ ―― | | m ‖ -0.5 + ―― | ‖ 5 ‖ | else if d (0) > 1 m| ‖ -0.3 | | ‖ nUmeå ⎛ d (0) ⎞ Ih.Umeå ≔ A ⋅ d (0) ⋅ b ⋅ ⎜―― ⎟ ⎝ d1 ⎠ Mora | = -0.4 nMora ≔ if d (1) ≤ 1 m | ‖ d (1) | ‖ ―― | m ‖ -0.5 + ―― | ‖ 5 ‖ | else if d (1) > 1 m| ‖ -0.3 | | ‖ nMora ⎛ d (1) ⎞ Ih.Mora ≔ A ⋅ d (1) ⋅ b ⋅ ⎜―― ⎟ ⎝ d1 ⎠ m ⎛ d (0) ⎞ ⋅ ⎜―― ⎟ = 321.711 kN ⎝ b ⎠ m ⎛ d (1) ⎞ ⋅ ⎜―― ⎟ = 392.589 kN ⎝ b ⎠ Halmstad | = -0.478 nHalmstad ≔ if d (2) ≤ 1 m | ‖ d (2) | ‖ ―― | m ‖ -0.5 + ―― | ‖ 5 ‖ | else if d (2) > 1 m| ‖ -0.3 | | ‖ nUmeå ⎛ d (2) ⎞ Ih.Halmstad ≔ A ⋅ d (2) ⋅ b ⋅ ⎜―― ⎟ ⎝ d1 ⎠ m ⎛ d (2) ⎞ ⋅ ⎜―― ⎟ = 222.22 kN ⎝ b ⎠ ⎡ Ih.Umeå ⎤ ⎡ 321.711 ⎤ ⎢ ⎥ Ih ≔ ⎢ Ih.Mora ⎥ = ⎢ 392.589 ⎥ kN ⎢ ⎥ ⎢⎣ Ih.Halmstad ⎥⎦ ⎣ 222.22 ⎦ Verical ice load Not possible to calculate with small dimensions. 128 Non-Commercial Use Only B.9 EAU Input b ≔ 0.35 Width of pile [m] ⎡ ⎤ SB ≔ ⎢ 4 ⎥ ⎣ 32 ⎦ Saline promille [‰] ⎡ -20 ⎤ Tm ≔ ⎢ -20 ⎥ ⎢ ⎥ ⎣ -12.5 ⎦ Umea� Mora Halmstad Ice temperature [ ° C] ε ≔ 0.001 Specific rate of expansion [1/s] ⎡ 0.28 ⎤ d ≔ ⎢ 0.5 ⎥ ⎢ ⎥ ⎣ 0.11 ⎦ Umea� Mora Halmstad Ice thickness [m] Saline water φp ＝ 19.37 + 36.18 ⋅ SB 0.91 ⋅ ||Tm|| -0.69 φp.Umeå ≔ 19.37 + 36.18 ⋅ SB (0) 0.91 φp.Halmstad ≔ 19.37 + 36.18 ⋅ SB (1) ⋅ ||Tm (0)|| 0.91 -0.69 ⋅ ||Tm (2)|| = 35.537 -0.69 = 167.72 1 ― 3 σk ＝ 2700 ⋅ ε ⋅ φp -1 1 ⎛ ⎞ ― 3 -1 ⎜ σk.Umeå ≔ min ⎝2700 ⋅ ε ⋅ φp.Umeå , 2.5⎟⎠ = 2.5 1 ⎛ ⎞ ― 3 -1 ⎜ σk.Halmstad ≔ min ⎝2700 ⋅ ε ⋅ φp.Halmstad , 1.5⎟⎠ = 1.5 Fresh water | , 2.5⎞ = 2.5 σk ≔ min ⎛ if 0 > Tm (1) > -5 | ⎜ ‖ ⎟ | ⎜ ‖ 1.1 + 0.35 ⋅ ||Tm (1)|| ⎟ | ⎜ else ⎟ | ⎜ ‖ ⎟ ||Tm (1) + 5|| | 2.85 + 0.45 ⋅ ⎟⎠ | ⎝⎜ ‖ Drifting ice 129 Drifting ice Ih.1 ＝ k ⋅ σ0 ⋅ b 0.5 ⋅ d 1.1 Ice load, drifting ice [kN] d Ice thickness [m] k Empirical contact factor [m^0.4] b Support width [m] σk0 Ice compressive strenght [MPa] k ≔ 0.564 In occurence of ice floe Umea� Ih ≔ k ⋅ σk.Umeå ⋅ b 0.5 ⋅ d (0) 1.1 ⋅ 1 MN = 205.649 kN Mora Ih ≔ k ⋅ σk ⋅ b 0.5 ⋅ d (1) 1.1 ⋅ 1 MN = 389.153 kN Halmstad Ih ≔ k ⋅ σk.Halmstad ⋅ b 0.5 ⋅ d (2) 1.1 ⋅ 1 MN = 44.151 kN Vertical load ⎛ 0.15 ⋅ b ⎞ 2 Iv.1 ＝ ⎜0.6 + ――― ⎟ ⋅ 0.4 ⋅ σk ⋅ d ⋅ fg d ⎠ ⎝ Uplift caused by ice [kN] σk Compressive strenght [kPa] d Ice thickness [m] b Support width [m] fg Geometric factor [-] ⎡ 4.76 ⎤ Lc ≔ 17 ⋅ d = ⎢ 8.5 ⎥ ⎢ ⎥ ⎣ 1.87 ⎦ Characteristic length of ice cover [m] r1 ≔ 2 Half the space between piles [m] ⎡ 4.76 ⎤ r2 ≔ Lc = ⎢ 8.5 ⎥ ⎢ ⎥ ⎣ 1.87 ⎦ r1 2 + r2 2 + r3 2 + r4 2 fg ＝ ―――――― 4 ⋅ Lc 2 130 Non-Commercial Use Only r1 2 + r2 2 + r3 2 + r4 2 fg ＝ ―――――― 4 ⋅ Lc 2 The ice load is determined at the middle pile Umea� 2 4 ⋅ r1 2 + 2 ⋅ r2 (0) = 0.677 fg ≔ ―――――― 2 4 ⋅ Lc (0) 2 ⎛ 0.15 ⋅ b ⎞ Iv.1 ≔ ⎜0.6 + ――― ⋅ 0.4 ⋅ σk.Umeå ⋅ d (0) ⋅ min ⎛⎝1 , fg⎞⎠ ⋅ MN = 41.77 kN ⎟ d (0) ⎠ ⎝ Mora 2 4 ⋅ r1 2 + 2 ⋅ r2 (1) = 0.555 fg ≔ ―――――― 2 4 ⋅ Lc (1) 2 ⎛ 0.15 ⋅ b ⎞ ( ) Iv.1 ≔ ⎜0.6 + ――― d 1 ⋅ ⋅ min ⎛⎝1 , fg⎞⎠ ⋅ MN = 97.883 kN σ ⋅ 0.4 ⋅ k ⎟ d (1) ⎠ ⎝ Halmstad 2 4 ⋅ r1 2 + 2 ⋅ r2 ((2)) = 1.644 fg ≔ ―――――― 2 4 ⋅ Lc ((2)) 2 ⎛ 0.15 ⋅ b ⎞ ( ) Iv.1 ≔ ⎜0.6 + ――― d 2 ⋅ ⋅ min ⎛⎝1 , fg⎞⎠ ⋅ MN = 7.821 kN σ ⋅ 0.4 ⋅ k.Halmstad ⎟ d (2) ⎠ ⎝ 131 Non-Commercial Use Only Stockholm Dokumentnamn K1-BE-22800-004 Uppdragsnummer 50206 B.10 Pile capacity - Received from ELU Dimensionering - Stålrörspåle Erhållen av ELU Konsult AB. Reviderad av Astrid Lindblom och Elin A� nger Sidomotsta� ndet ger ett tilla� ggsmomet i pa� len. Mtillägg ≔ 0 kN ⋅ m Beräknade tvärsnittsegenskaper Geometri för rörpåle Ro� rpa� lens ytterdiameter: (Varieras mellan 220 mm, 270 mm och 320 mm) Dy ≔ 320 mm Utva� ndig avrostning: Ru ≔ 4.0 mm = 4 mm Inva� ndig avrostning: Ri ≔ 0 mm = 0 mm Grundtjocklek pa� ro� r: trör ≔ 12.5 mm Foderro� rets godstjocklek efter avrostning: tred ≔ trör - Ru - Ri = 8.5 mm Ro� rpa� lens ytterdiameter mht avrostning: dy ≔ Dy - 2 ⋅ Ru = 312 mm Ro� rpa� lens innerdiameter: di ≔ Dy - 2 ⋅ trör + 2 ⋅ Ri = 295 mm Ro� rpa� lens ytterradie mht avrostning: dy ry ≔ ―= 156 mm 2 Ro� rpa� lens innerradie: di ri ≔ ―= 148 mm 2 Generellt för rörpåle 132 Stockholm Dokumentnamn K1-BE-22800-004 Uppdragsnummer 50206 Generellt för rörpåle Reduktionsfaktor fo� r flytgra� ns fo� r hantering lagring, slagning: [PKR 96:1 3.2.2a] μs ≔ 1.0 Reduktionsfaktor fo� r elasticitetsmodul mht egenspa� nningar: [PKR 96:1 3.6.1] β ≔ 0.9 Initialkrokighet fo� r pa� len (geometrisk): Rakhetskontroll fo� rutsa� tts. [PKR 96:1 3.4.1] 1 flk ≔ ―― 600 Fiktiv initialkrokighetskoeficient fo� r sta� lro� r: [PKR 96:1 Tabell 3.6.1a, 3.6.1b] 1 fδf ≔ ―― 750 n≔1 Antal skarvar per kna� ckla� ngd: Pilho� jd relaterad till skarv bela� gen inom kna� ckla� ngden: [PKR 97:1 4.3.11.4 (6)] Osa� kerhet i pilho� jd, vid rakhetskontroll 1,0 annars 2,0 : [PKR 96:1 3.4.1.] Sta� lkvalite� fo� r ro� r γδ ≔ 1 fyk ≔ 420 MPa Partialkoefficient ba� rfo� rma� ga [TRVFS 2011:12, kap 8 7§]: γM0 1 fδskarv ≔ n ⋅ ――― = 8.333 ⋅ 10 -4 4 ⋅ 300 γM0 ≔ 1.0 fyk fyd ≔ μs ⋅ ―― fyd = 420 MPa Elasticitetmodul fo� r sta� l. [SS-EN 1993-1-1:2005 3.2.6] Esk ≔ 210 GPa Ea ≔ β ⋅ Esk Ea = 189.0 GPa Excentricitet i pa� lspets. [PKR 104 3:3] ⎛ Dy ⎞ e0 ≔ max ⎜20 ⋅ mm , ―⎟ 30 ⎠ ⎝ e0 = 20.0 mm Tvärsnittsegenskaper 133 Stockholm Dokumentnamn K1-BE-22800-004 Uppdragsnummer 50206 Tvärsnittsegenskaper Stål: dy 2 - di 2 Aa ≔ π ⋅ ――― 4 Aa = 8105 mm 2 dy 4 - di 4 Ia ≔ π ⋅ ――― 64 Ia = 9338.9 cm 4 π 1 Wel ≔ ―⋅ ⎛⎝ry 4 - ri 4 ⎞⎠ ⋅ ― 4 ry Wel = 598.6 cm 3 4 ⋅ ry ⎛ ri ry ⎞ 2⋅π ⎛ 2 ⋅ ⎝ry - ri 2 ⎞⎠ ⋅ ―― ⋅ ⎜―+ ――⎟ Wpl.1 ≔ ―― 2 3 ⋅ π ⎝ ry ry + ri ⎠ Wpl.1 = 783.2 cm 3 Wpl.2 ≔ 1.25 ⋅ Wel Wpl.2 = 748.3 cm 3 Wpl ≔ Wpl.2 Wpl = 748.3 cm 3 Inverkan av lokal buckling av stålprofil [EK 1994-1-1:2005 Tabell 6.3 (vid betongfyllt tva� rsnitt) EK 1993-1-1:2005 Tabell 5.2 klass 1 (vid tomt ro� r) Faktor ≔ 90 [faktor 90 vid betongfyllt ro� r annars 50] 235 ⋅ MPa störstavärde ≔ Faktor ⋅ ―――― fyd störstavärde = 50.4 dy kvotdt ≔ ―― tred kvotdt = 36.7 ‖ || Kontrollbuckling ≔ ‖ if kvotdt ≤ störstavärde || ‖ ‖ “OK!” || ‖ ‖ || ‖ else || ‖ ‖ “EJ OK Lokal buckling” | | ‖ | ‖ Kontrollbuckling = “OK!” Rörtvärsnittets bärförmåga [EK3-1-1:2005(6.2.4, 6.2.5)]: NRd ≔ Aa ⋅ fyd NRd = 3404 kN Mel ≔ Wel ⋅ μs ⋅ fyk Mel = 251.4 kN ⋅ m Mpl ≔ Wpl ⋅ fyd Mpl = 314.3 kN ⋅ m Beräkning av brottgränskapacitet 134 Stockholm Dokumentnamn K1-BE-22800-004 Uppdragsnummer 50206 Mpl ≔ Wpl ⋅ fyd Mpl = 314.3 kN ⋅ m Beräkning av brottgränskapacitet NRd ⋅ me nbrott (me) ≔ NRd - ―― Mpl mebrott ≔ 0 , 100 ⋅ N ⋅ m ‥ Mpl Beräkning av bruksgränskapacitet NRd ⋅ me nbruk (me) ≔ NRd - ―― Mel mebruk ≔ 0 , 100 N ⋅ m ‥ Mel Resultat 3850 3500 3150 2800 2450 Normalkraft [kN] 2100 1750 nbruk nbrott 1400 1050 700 350 0 0 35 70 105 140 175 210 245 280 315 350 Moment [kNm] Normalkraftskapacitet = nbrott (Maximalt moment i pålen) - Tryckande normalkraft i påle Snittkrafter från vänster och höger påle hämtas från RSTAB 135 APPENDIX B. ANALYTICAL CALCULATIONS 136 Appendix C Blueprints 137 TRITA – ABE-MBT-22403 ISBN: 978-91-8040-308-5 www.kth.se