Ad Hoc Expert Meeting on Climate Change Impacts and Adaptation: A Challenge for Global Ports 29 – 30 September 2011 Sea Level Rise and the Increase in Rubble Mound Breakwater Damage By M. Esteban, H. Takagi, and T. Shibayama This expert paper is reproduced by the UNCTAD secretariat in the form and language in which it has been received. The views expressed are those of the author and do not necessarily reflect the views of the UNCTAD.
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Ad Hoc Expert Meeting on
Climate Change Impacts and Adaptation: A Challenge for
Global Ports
29 – 30 September 2011
Sea Level Rise and the Increase in Rubble Mound Breakwater Damage
By
M. Esteban, H. Takagi, and T. Shibayama
This expert paper is reproduced by the UNCTAD secretariat in the form and language in which it has been received. The views expressed are those of the author and do not necessarily reflect the views of the UNCTAD.
SEA LEVEL RISE AND THE INCREASE IN RUBBLE MOUND
BREAKWATER DAMAGE
Miguel Esteban1 Hiroshi Takagi
2 and Tomoya Shibayama
3
Sea level rise could threaten the stability of rubble mound breakwaters in the future, as greater water
depth will allow larger waves to reach these structures. Particularly worrying, however, is the
prospect of an acceleration in the pace of sea level rise as a result of climate change, especially after
2050. This could lead to a change in the philosophy behind the design of breakwaters and ports,
leading to substantial increases in the cost to build and maintain these costly structures. Particularly
there would have to be a shift in the main parameter used to calculate breakwater sections from the
significant wave height (Hs) to the limiting breaker height (Hb), due to future uncertainties in wave
climate. The likely increases in breakwater costs due to this shift in design philosophy were
evaluated for 4 different rates of sea level rise showing that for the more extreme cases of sea level
rise (for a sea level rise of 1.3m over 50 years) a breakwater designed in 2050 would be between
around 8% and 66% more expensive than one designed in the 20th century not taking into account
sea level rise.
INTRODUCTION
As a consequence of global warming due to increasing concentrations of
greenhouse gases in the atmosphere sea level rise is expected to accelerate in the
course of the 21st century. During the 20
th century global average sea level rose
by an average of around 1.7mm per year, with satellite observations showing
increases of 3mm since 1993, according to the Fourth Assessment Report of the
Intergovernmental Panel on Climate Change, or IPCC 4AR. Future IPCC
projections show that by the end of the 21st century sea level could be between
0.18 and 0.59m higher than at present. More extreme scenarios, such as those by
Vermeer and Rahmstorf (2009), argue that sea level rise could be in the range of
0.81 to 1.79m by 2100.
Sea level rise and other effects of climate change, such as an increase in tropical
cyclone intensity (Knutson and Tuleya, 2004, Elsner et al., 2008, Landsea et al.,
2006, Webster and Holland, 2005) could alter future wave patterns (Mori et al,
2010) and this could lead to increased damage to coastal structures. Generally, it
has been proven that the damage due to winds increases exponentially with
regards to the maximum wind speed, though a number of variables complicate
the assessment of economic damages (Hallegate, 2007, Pielke, 2007)
Typically nowadays the effect of climate change is ignored when designing
breakwaters, which could lead to them being under-designed towards the end of
1Dept of Civil and Environmental Engineering, Waseda University, Ookubo, Shinjuku-ku, Tokyo 169-8555,
Japan 2 Japan International Cooperation Agency, Disaster Management Division 1, Nibancho Center Building 5-25,
Niban-cho, Chiyoda-ku, Tokyo 102-8012, Japan 3 Dept of Civil and Environmental Engineering, Waseda University, Ookubo, Shinjuku-ku, Tokyo 169-8555,
Japan
their life for the cases of rapid increases in sea levels. The effect of sea level rise
on caisson breakwaters was investigated by Okayasu and Sakai (2006), who
found that the probability of sliding failure could increase by up to 50% in the
period ranging from 2000 to 2050 (assuming a design life of 50 years), and that
the adaptation cost could correspond to between 0.5 and 2.3% of the sectional
area of the caisson. Takagi et al. (2010) used a SWAN-based model to show
how a 10% potential increase in the future wind speed of typhoons resulting
from the warming of surface sea temperatures can lead to a 21% increase in the
significant wave height generated by these winds. This effect, together with the
rise in sea level detailed in the IPCC 4AR could make the expected sliding
distances for the breakwaters at Shibushi Ports in Japan up to three times greater
than at present.
However, to the authors’ knowledge, no research has been carried out on the
effect that climate change induced acceleration in sea level rise can have on the
design of rubble mound breakwaters. To do so, the present paper will introduce
a variety of sea level scenarios, which will be assumed to take place during the
design life of the structure (50 years).
The purpose of the present work, however, is not to evaluate the potential
increase in damage to a single breakwater, as this would require an in-depth
assessment of the wave conditions present at that particular breakwater. Rather,
the authors argue that an increase in water depth could result in an increase in
the future damage potential to breakwaters in general, and the objective of the
present paper is to provide a general idea of the magnitude of the increase in
cost (in terms of the cross sectional area of breakwater required) to adapt to this
specific problem of climate change. Currently, the wave depth in front of a
breakwater limits the height of the waves that can reach it, and thus an increase
in future water depth could result in higher potential damage to breakwaters,
provided that the wind speed is enough to generate the required waves. Although
this might not apply to all areas in the world, expected increases in tropical
intensity (see Knutson and Tuleya, 2004) make it likely that this will be the case
in areas affected by tropical cyclones. Furthermore, the patterns of wave action
in different parts of the world are likely to change in the future (Mori et al,
2010). The authors will thus conclude how it will be necessary to shift the
current design methodology from one which focuses on the significant wave
height (Hs) to the limiting breaker height (Hb).
METHODOLOGY
Breakwater Design according to Van der Meer Formula
Rubble mound breakwaters consist of several layers of stones, with the centre of
them typically made of quarry run and the outer layer consisting or armour units.
The present study uses the Van der Meer formula (1987) for the design of a
variety of breakwater sections. This formula uses the significant wave height
(Hs) as the main design parameter and derives two different expressions
according to the type of breaker. For plunging breakers
(1)
For surging breakers
(2)
Where Ns is a parameter knows as the stability number, a is the relative
underwater density of the armour, Da is the nominal armour unit diameter, Pb is
the overall porosity of the breakwater, Nw is the number of waves acting on the
breakwater, is the angle of the front slope of the structure with respect to the
horizontal and Sa is the armour damage, defined as
(3)
where Ae is the erosion area of the breakwater profile between the still water and
plus/minus one wave height. For Sa=0 an infinite Da would be required, and
hence Van der Meer recommends using Sa=2 as an equivalent for zero damage.
Limiting Breaker Height
This parameter will have a crucial influence on the behaviour of a rubble mound
breakwaters in the event of rapidly rising seas, as it will increase the height of
the waves that will be able to reach the structure. In the present study, the
following equation proposed by Goda [1985] is used for evaluating the limit
wave height that is possible in front of the breakwater Hb.
(4)
in which h is the water depth at the breakwater, L0 is the deep water wave length
and is the slope of the sea bottom.
Estimation of Run-Up
In order to adequately compute the required size of a breakwater it is necessary
to calculate the estimated run-up of the waves. It is important to note that sea
level rise will cause an increase in Hb, and hence the heights of the wave
reaching the breakwater could also be increased. Hence, the potential run-up on
the breakwater will also increase and will require engineers to design the
structures with higher crests that at present so that there is not significant
overtopping towards the end of their working lives. Van der Meer (1993)
provides a relatively simple estimate of run-up, for ξp<2:
(5)
Or for ξp≥2:
(6)
Where r2% is the runup exceeded by 2% of the waves, rf is the factor which takes
into account friction, any horizontal berm sections in the front face, the angle of
approach and whether the waves are short crested (for simple rock breakwater
with waves coming normal to the face rf=0.5). The surf similarity parameter, ξp,
is based on the peak period of the wave spectrum.
Breakwater Sections Considered
The effects that sea level rise will have on rubble mound breakwaters will vary
greatly depending on factor such as the geometry of the breakwater, the
bathymetry in front of it or the wave climate. A total of 12 breakwaters sections
were calculated, in water depths ranging from 3 to 25m. Each section was then
calculated for a variety of significant wave heights (Hs), ranging from 3 to 15m.
Each Hs was calculated for a total of 5 wave periods (from 6 to 14 sec).
Furthermore, all breakwater sections were calculated for 4 different bottoms
slopes in front of the breakwater (). Other parameters, such as the slopes of the
seaside and portside of the structure, the breadth of the top section, or the storm
duration were not changed, in order to simplify the results. Another crucial
parameter that was not changed was the type of armour used. Again, for the sake
of simplicity and ease of comparison only rock armour was used, though for the
case of the deeper sections it is normally very difficult to find rock of adequate
size to fulfil the requirements of Van der Meer (1987) and hence concrete units
such as tetrapods or accropods are used. These units also have better
interlocking capabilities and can contribute to a decrease in the required armour
weight. However, these units also have other associated costs, such as the
formwork and labour to make them. The current approach of only using rock is
simplistic, but allows for an intuitive understanding of the problem, by providing
an insight into the increase in armour requirements according to the Van der
Meer formula (1987). Nevertheless, all the combinations summarised in Table 1
resulted in a total of 5440 breakwater section calculations.
Sea Level Rise Scenarios
Future patterns in sea level rise are highly uncertain due to a lack of
understanding of the precise working of global climate and its interaction with
the physical environment. A lot of this is down to uncertainty in the response of
the big ice sheets of Greenland and Antarctica (Allison et al., 2009). In fact, it is
currently believed that sea level in the 21st century is likely to rise much more
than the range of 0.18-0.59m given in the IPCC 4AR. In this report, the coupled
models used for the 21st century sea level projections did not include
representations of dynamic ice sheets, only including simple mass balance
estimates of the contributions from Greenland and the Arctic ice sheets. In fact
the IPCC 4AR assumed that ice was accumulating over the Antarctic ice sheet,
though it is currently losing mass as a consequence of dynamical processes, as
shown in Allison et al., (2009). Recent research such as that by Vermeer and
Rahmstorf (2009) show how sea level rise for the period 1990-2100 could be in
the 0.75 to 1.9m range.
Table 1. Summary of Parameters of Breakwater Sections Considered
Parameter Symbol
(unit)
Conditions Calculated Notes
Water Depth h (m) 3, 5, 7, 9, 11, 13, 15, 17,
19, 21, 23, 25
Effect of sea level rise for
deeper sections where
h>25 is very small
Significant Hs (m) For h=3, Hs=3. 5
Wave Height
For h=5, Hs=3. 5, 7
For h=7, Hs=3. 5, 7, 9
For h=7, Hs=5, 7, 9, 11,
13
All others, Hs= 5, 7, 9, 11,
13, 15
Wave Period T (s) 6, 8, 10, 12, 14
Slope of sea
bottom 1:10, 1:20, 1:30, 1:40
Sections considered by
Goda (1985)
Run-up friction rf 0.5 for all cases See Van der Meer (1993)