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.
Bergdahl, L., 1978. Thermal Ice Pressure in Lake Ice Covers. 1978, Chalmers
Tekniska Högskola, Göteborg, ISSN: 0348-1050.
Bergström, M., Blomqvist, E., Clason, G., Gierts, L.-M., Heimbürger, G., Jondal,
B., Nessen, N., Näslund, B., Reinius, L., Rosén, K.-G., Schültz, F., Strokirk, E.,
Tengvika, N., Whålin, E., 1966. Build handbook for house, road and water construction (Swedish:Bygg handbok för hus-, väg och vattenbyggnad), 3rd Edition.
AB Byggmästarens förlag, Stockholm.
Boverket, 2019. The Swedish National Board of Housing, Building and Planning’s
handbook on design rules, EKS 11 (Swedish: Boverkets konstruktionsregler, EKS
11), 1st Edition. Boverket, Karlskrona.
Burcharth, H. F., 2004. Ice loads on structures (Dannish: Islaster på konstruktioner)
(4th Edition). 2004, Aalborg Universitet, Denmark.
Comfort, G., Abdelnour, R., Gong, Y., 1993. Phase II; Static ice loads on hydroelectric structures; field measurements and large-scale tests conducted during the
1992-93 winter. Cea project 9038 g 815, Fleet Technology, Kanata, ON.
Committee for waterfront structures, 1996. Recommendations of the committee for
waterfront structures harbours and waterways EAU 1996, 7th Edition. Ernst &
Sohn, Berlin.
Committee for waterfront structures, 2012. Recommendations of the committee for
waterfront structures harbours and waterways EAU 2012, 9th Edition. Ernst &
Sohn, Berlin.
Eklund, A., 1998. lce thickness of lakes -a statistical processing of the Swedish
Meteorological and Hydrological Institute’s measurements (Swedish: lstjocklek
på sjöar -en statistisk bearbetning av SMHls mätningar). 1998, SMHI, Sweden.
Ekström, T., 2002. Elforsk report 02:03 Ice loads against hydraulic structures: focus on concrete dams (Swedish: Elforsk rapport 02:03 Islaster mot hydrauliska
konstruktioner: inriktning mot betongdammar). Elforsk, Stockholm.
103
BIBLIOGRAPHY
EN 1990, 2002. Eurocode - Basis of structural design. EN 1990. The European
Union, Brussels.
EN 1991-1-6, 2005. Eurocode 1: Actions on structures - Part 1-6: General Actions
- Action during execution. EN 1991-1-6. The European Union, Brussels.
Fransson, L., 2009. Ice Handbook for Engineers, 1.2th Edition. Luleå Tekniska Universitet, Luleå.
Fransson, L., Bergdahl, L., 2009. Recommendations for design of offshore foundations exposed to ice loads, Elforsk report 09:55. Elforsk, Lund.
Hellgren, R., 2022. A systems approach to ice loads on concrete dams. Doctoral
thesis in civil and architectural engineering, KTH Royal Institute of Technology.
Hellgren, R., Petrich, C., Arntsen, B., Malm, R., 2022. Ice load measurements
on rätan concrete dam using different sensor types. Cold Regions Science and
Technology 193, 103425, ISSN:0165-232X, [Accessed: 23-02-2022].
URL
https://www.sciencedirect.com/science/article/pii/
S0165232X21002068
Hüffmeier, J., Sandkvist, J., 2008. Ice Control Measures in Swedish Harbours. Report 2007 4693-1, SSPA Sweden AB, Göteborg, ISSN: 1402-1528.
ISO 19906, 2010. Petroleum and natural gas industries - Arctic offshore structures,
1st Edition. International Organization for Standardization, Borlänge.
Johannesson, P., Vretblad, B., 2011. Building formulas and tables (Swedish: Byggformler och tabeller), 11th Edition. Liber AB, Stockholm, ISBN: 978-91-4710022-4.
Johansson, F., Spross, J., Fransson, L., 2013. Elforsk report 13:56. Ice load against
dam structures - Compilation of the state of knowledge and proposals for research
and development (Swedish: Islast mot dammkonstruktioner - Sammanställning av
kunskapsläget samt förslag till forskning och utveckling). Elforsk, Stockholm.
Karlsson, M., Eklund, B., Lundman, P., 2011. The Swedish Transport Administration’s Requirements Bridge, TRVK Bridge 2011: 08 (Swedish: Trafikverkets Krav
Bro, TRVK Bro 2011:085). Trafikverket, Borlänge, ISBN: 978-91-7467-153-7.
Krona, K.-M., 2019. Requirements Bridge design TDOK 2016: 0204 (Swedish: Krav
Brobyggande TDOK 2016:0204), 3rd Edition. Trafikverket, Borlänge.
Løset, S., K.N Shkhinek, O. G., Høyland, K., 2006. Action from ice on Arctic offshore
and coastal structures. LAN, St. Petersburg, ISBN: 5-8114-0703-3.
Löfquist, B., 1987. Ice load on bridge support (Swedish: Istryck mot bropelare).
Publication 1987:43, Vägverket, Sweden.
Malm, R., 2022. Personal communication with Richard Malm, KTH.
104
BIBLIOGRAPHY
Malm, R., Fransson, L., Nordström, E., Westberg-Wilde, M., Johansson, F., Hellgren, R., 2017. Load conditions regarding ice pressure (Swedish: Lastförutsättningar avseende istryck). 2017:439, Engergiforsk AB, Göteborg, ISSN:978-917673-439-1.
Mayor, H., 2022. Personal communication with Henrik Mayor, ELU Konsult AB.
Mayor, H., Sagemo, A., Johansson, P.-O., 2020. Ice loads on piles (Swedish: Islaster
mot pålar). Tekniskt PM, Pålkommisionen.
Norén, G., 2022. Personal communication with Gustav Norén, ELU Konsult AB.
RIL, 2013. 201-3-2013 Design criteria and structural loads. Water structures
(Finnish: RIL 201-3-2013 Suunnitteluperusteet ja rakenteiden kuormat. Vesirakenteet), 1st Edition. Suomen Rakennusinsinöörien Liitto RIL ry, Helsinki, ISBN:
978-951-758-580-4 .
Ruiz de Almirón de Andrés, C., Saarinen, S., Uuskallio, A., 2018. Review of ice
challenges and ice management in port areas. Coastal Engineering Proceedings
1 (36), Papers 79.
URL
https://icce-ojs-tamu.tdl.org/icce/index.php/icce/article/
view/8660
SMHI, 2021a. Data series with normal values for the period 1991-2020 (Swedish:
Dataserier med normalvärden för perioden 1991-2020). [Accessed: 18-03-2022].
URL
https://www.smhi.se/data/meteorologi/
dataserier-med-normalvarden-for-perioden-1991-2020-1.167775?l=null
SMHI, 2021b. Seasonal variations in the water level (Swedish: Vattenståndets
årstidsvariationer). [Accessed: 12-04-2022].
URL
https://www.smhi.se/kunskapsbanken/oceanografi/
vattenstand-i-havet/havsvattenstandets-arstidsvariationer-1.25961
SMHI, 2021c. What are normal periods? (Swedish: Vad är normalperioder?).
[Accessed: 26-04-2022].
URL
https://www.smhi.se/kunskapsbanken/klimat/normaler/
vad-ar-normalperioder-1.4087
SMHI, 2022a. Download oceanographic observations - Sea level RW, hourly value
(Swedish: Ladda ner oceanografiska observationer - Havsvattenstånd RW,
timvärde). [Accessed: 27-04-2022].
URL
https://www.smhi.se/data/oceanografi/
ladda-ner-oceanografiska-observationer#param=sealevelrw,stations=
all
SMHI, 2022b. Oceanographic observations - Baltic Sea Code for sea ice (Swedish:
Oceanografiska observationer - Östersjökoden för havsis). [Accessed: 22-03-2022].
URL
https://www.smhi.se/data/utforskaren-oppna-data/
oceanografiska-observationer-ostersjokoden-for-havsis
105
BIBLIOGRAPHY
SMHI, 2022c. Swedish temperature record (Swedish: Svenska temperaturrekord).
[Accessed: 28-03-2022].
URL
https://www.smhi.se/kunskapsbanken/meteorologi/
svenska-temperaturrekord/svenska-temperaturrekord-1.5792
Sopper, R., Daley, C., Colbourne, B., Bruneau, S., 2017. The influence of water,
snow and granular ice on ice failure processes, ice load magnitude and process
pressure. Cold Regions Science and Technology 139, 51–64, ISSN: 0165-232X.
URL
https://www.sciencedirect.com/science/article/pii/
S0165232X1730191X
Statens vegvesen, 2014. Handbook N200 Road construction (Norwegian: Håndbok
N200 Vegbygging). Statens vegvesen, ISBN: 978-82-7207-672-5.
Statens vegvesen, 2015. Handbook N400 Bridge design (Norwegian: Håndbok N400
Bruprosjektering). Statens vegvesen, ISBN: 978-82-7207-680-0.
Stockholms hamnar, 2016. Technical handbook, Designing port constructions
(Swedish: Teknisk handbok Projektering hamnkonstruktioner), 1.1 Edition.
Stockholms hamnar, Borlänge.
Ställ, J., 1983. Design instructions for ground insulation of unheated buildings
(Swedish: Dimensioneringsanvisningar för markisolering av ouppvärmda byggnader). Rapport R132:1983, Göteborgs Universitet, Sweden, ISBN: 91-540-40426.
Svensk Energi, 2011. RIDAS Power companies guidelines for dam safety (Swedish:
RIDAS Kraftföretagens riktlinjer för dammsäkerhet). Avsnitt 7.3, Betongdammar,
Tillämpningsvägledning. Svensk Energi.
Thoresen, C. A., 2014. Port Designer’s Handbook, 3rd Edition. ICE Publishing,
London, ISBN: 978-0-7277-6004-3.
Timco, G., O’Brien, S., 1994. Flexural strength equation for sea ice. Cold Regions
Science and Technology 22 (3), 285–298, ISSN: 0165-232X.
URL
https://www.sciencedirect.com/science/article/pii/
0165232X9490006X
Trafikverket, 2021. Bridge and bridge-like structures, Construction TRVINFRA00227 (Swedish: Bro och broliknande konstruktion, Byggande TRVINFRA00227), 2nd Edition. Trafikverket, Borlänge.
Transportstyrelsen, 2018. Swedish Transport Agency Constitution Collection, TSFS
2018: 57, Swedish Transport Agency regulations and general guidelines on the application of Eurocode (Swedish: Transportstyrelsen Författningssamling, TSFS
2018:57, Transportstyrelsens föreskrifter och allmänna råd om tillämpning av eurokoder), 1st Edition. Transportstyrelsen.
Vatteninformationssystem Sverige, 2022. Glossary (Swedish: Ordlista). [Accessed:
17-02-2022].
106
BIBLIOGRAPHY
URL
http://extra.lansstyrelsen.se/viss/Sv/ordlista/Pages/
ordlistas.aspx
Vejdirektoratet & Banedanmak, 2015. Appendix DK:2015 Ice load (Danish: Tillæg
DK:2015 Islast).
Wikenståhl, T., Granström, A., Milchert, T., Kedeby N.-Å., Wiberg, K., 2012.
Guidelines for Traffic piers in the archipelago (Swedish: Riktlinjer för trafikbryggor i skärgården). 2012, Waxholmsbolaget, Sweden.
Xu, N., Zhang, H., Wang, Y., 2022. Cracking pattern of indented ice sheet bending
failures. 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