Second international Coastal Symposium in Iceland 5 – 8 June 2005
Choice of safety levels for conventional breakwaters
Hans F. Burcharth
Aalborg University, Denmark
Contents
▪ Introduction
▪ Spanish Recommendations for Maritime Structures
▪ Objective of cost optimization study
▪ ISO prescription
▪ Safety classes
▪ Performance criteria
▪ Procedure in cost optimization study for rubble mound structures
▪ Results of study
▪ Conclusions on optimum safety levels for rubble mound structures
▪ Example of design to meet target safety levels
▪ Use of PIANC partial coefficients for design to meet target safety levels
Selection of type of breakwater
Damage
Hs
Damage
Hs
Main types of breakwaters and typical damage development
The optimum choice of type is very complicated, as wide ranges of both
functional and environmental aspects must be considered.
The main aspects to consider are listed below.
• Function (access road, installations, berths, wave reflection, and wave
transmission)
• Water depth
• Wave climate
• Material availability
• Foundation conditions (geotechnics)
• Conditions for construction (wave exposure, space on land/sea,
transport of materials, equipment, skill)
• Urgency in construction
• Ecological impact
• Visual impact
• Tectonic activity
The most common advantages and disadvantages between rubble mound
structures and monolithic structures like caissons are listed below.
Advantages of rubble mound structures:
• Construction simple in principle
• Ductile damage development
• Not sensitive to differential settlements
Constraints and disadvantages of rubble mound structures:
• Availability of adequate quarry needed
• Large quantity of material required in deeper water
• Transport of large amounts of materials
• Large space required for storing of materials (rock and concrete units)
• Separate structure needed to establish moorings
Advantages of caisson structures:
• Construction time short on location
• Relatively small amounts of materials for structures in deeper water
• Moorings are easily established along the caissons
Disadvantages of caisson structures:
• Brittle failures
• Sensitive to poor subsoil foundation conditions in terms of weak soils
prone to large settlements by consolidation
• High reflection of waves
However, because of the large number of aspects there are no simple rules for
the choice of type of breakwater. The actual combination of the functional and
environmental conditions vary considerably from location to location and
determines in practice the final choice.
Background
When the type of breakwater has been selected for further investigations one
has to select a safety level for the design.
Most national standards and recommendations introduce overall safety factors
on resistance to a specific return period sea state.
No safety level are given in terms of acceptable probability of a certain damage
within service life of the structure.
The exception is the Spanish Recommendations for Maritime Structures, in
which the given safety levels depend on the functional and economic
importance of the breakwater.
These safety levels must be regarded as tentative as they are not based on
more systematic investigations.
Example of safety levels specified in Spanish Recommendations for
Maritime Structures ROM 0.0
Economic repercussion index (ERI)
(cost of rebuilding and downtime costs)
Low economic repercussion
Moderate economic repercussion
High economic repercussion
ERI < 5
5 < ERI < 20
ERI > 20
Social and environmental repercussion index (SERI)
No social and environmental repercussion impact
Low social and environmental repercussion impact
High social and environmental repercussion impact
Very high social and environmental repercussion impact
SERI < 5
5 < SERI < 20
20 < SERI < 30
SERI > 30
From ERI is determined service lifetime of the structure
ERI
Service life in years
6 – 20
25
<5
15
> 20
50
From SERI is determined maximum overall probability of failure within
service lifetime, Pf
SERI
<5
5 - 19
20 - 29
>30
Serviceability 0.20
limit state
(SLS)
0.10
0.07
0.07
Ultimate limit
state
(ULS)
0.10
0.01
0.0001
0.20
Example a large breakwater in deep water protecting a container port and/or
berths for oil tanker would have ERI around 20. This means 50 years service
life time.
SERI might be low corresponding to 5 < SERI < 20 giving the Pf – values
SLS
ULS
0.10 in 50 years
0.10 in 50 years
Objective of present study
Capitalized costs (present value)
To identify the safety levels related to minimum total costs over the
service life. This includes capital costs, maintenance and repair costs,
and downtime costs.
Total costs
Construction costs
Maintenenance, repair
and economic loss due
to downtime etc.
Optimum safety level
Safety of breakwater
Studied influences on optimum safety levels
• Real interest rate, inflation included
• Service lifetime of the breakwater
• Downtime costs due to malfunction
• Damage accumulation
ISO prescription
The ISO-Standard 2394 on Reliability of Structures demands a safetyclassification based on the importance of the structure and the
consequences in case of malfunction.
Also, for design both a serviceability limit state (SLS) and an ultimate
limit state (ULS) must be considered, and damage criteria assigned to
these limit states.
Moreover, uncertainties on all parameters and models must be
taken into account.
Safety classes for coastal structures
In general there is very little risk of human life due to damage of a breakwater.
This is not the case for many other civil engineering structures.
A suitable classification could be:
Example of safety classes for coastal structures (Burcharth, 2000).
Safety class
Consequences of failure
Very low
No risk of human injury. Small environmental and
economic consequences
Low
No risk of human injury. Some environmental
and/or economic consequences
Normal
Risk of human injury and/or significant
environmental pollution or high economic or
political consequences
High
Risk of human injury and/or significant
environmental pollution or very high economic or
political consequences
Performance (damage) criteria related to limit states
Besides SLS and ULS is introduced Repairable Limit State (RLS) defined
as the maximum damage level which allows foreseen maintenance and
repair methods to be used.
Functional classification
Tentative performance criteria
I
Wave transmission
SLS: Hs, T = 0.5 – 1.8 m
Outer basin
Jetties
Damage to main armour
LargeD
distance
SLS: D = 5 %, RLS:
= 15 %
ULS: D = 30 %
Inner basins
Sliding distance of caissons
SLS: 0.2 m, ULS: 2 m
al port
Functional classification
II
Commercial port
Marina, fishing port
Tentative performance criteria
WaveMarina,
transmission
fishing port
SLS: Hs, T = 0.3 – 1.0 m
Damage to main armour
SLS: D = 5 %, RLS: D = 15 %
ULS: D = 30 %
Sliding distance of caissons
SLS: 0.2 m, ULS: 1 m
Functional classification
III
Tentative performance criteria
Wave overtopping
SLS: q = 10-5 - 10-4 m3/ms
ULS: q = 10-3 - 10-2 m3/ms
Damage to main armour
SLS: D = 5 %, RLS: D = 15 %
ULS: D = 30 %
Sliding distance of caissons
SLS: 0.0 m, ULS: 0.5 m
Functional classification
IV
Tentative performance criteria
Wave overtopping
SLS: q = 10-5 m3/ms
ULS: q = 10-2 m3/ms
Damage to main armour
SLS: D = 5 %, RLS: D = 15 %
ULS: D = 30 %
Sliding distance of caissons
SLS: 0.0 m, ULS: 0.5 m
Procedure in numerical simulation for identification of minimum cost safety
levels
• Select type of breakwater, water depth and long-term wave statistics.
• Extract design values of significant wave height HsT and wave
steepness corresponding to a number of return periods,
T = 5, 10, 25, 50, 100, 200 and 400 years.
• Select service lifetime for the structure, e.g. TL = 25, 50 and 100 years.
• Design by conventional deterministic methods the structure geometries
corresponding to the chosen HsT -values.
• Calculate construction costs for each structure.
• Define repair policy and related cost of repair.
• Specify downtime costs related to damage levels.
• Define a model for damage accumulation.
• For each structure geometry use stochastic models for wave climate
and structure response (damage) in Monte Carlo simulation of
occurrence of damage within service lifetime.
• Calculate for each structure geometry the total capitalized lifetime
costs for each simulation. Calculate the mean value and the related
safety levels corresponding to defined design limit states.
• Identify the structure safety level corresponding to the minimum total
costs.
Cross sections
Shallow water
Dn relates to main armour
4Dn
2Dn
1:1.5
1:2
min. 1.5m
3Dn
h
3Dn
Deep water
1.5Hs
1:2
2.3Dn
h
2Dn
3Dn
Dn relates to main armour
Only rock and concrete cube armour considered.
Crest level determined from criteria of max. transmitted Hs = 0.50 m
by overtopping of sea state with return period equal to service life.
Repair policy and cost of repair and downtime
Damage levels
S (rock)
Nod(cubes)
Estimated D
Repair
policy
Initial
2
0
2%
no repair
Serviceability
(minor damage,
only to armour)
5
0.8
5%
repair of
armour
Repairable
(major damage,
armour + filter 1)
8
2.0
15 %
repair of
armour +
filter 1
Ultimate
(failure)
13
3.0
30 %
repair of
armour +
filter 1 and
2
In costs of repair is taken into account higher unit costs of
repairs and mobilization costs.
Repairs are initiated shortly after exceedence of the defined
damage limits.
Downtime costs related to 1 km of breakwater is set to
18,000,000 Euro when the damage to the armour exceeds 15 %
displaced blocks.
Damage accumulation model
Simulations are performed with and without damage accumulation.
• Storms with Hs causing damage less than a set limit do not
contribute.
• Accumulation takes place only when the next storm has a higher Hs
– value than the preceeding value.
• The relative decrease in damage with number of waves (inherent in
the Van der Meer formulae for rock armour) is included.
Formulation of cost functions
All costs are discounted back to the time when the breakwater is built.
TL
min
T


C (T )  C I (T )   C R (T ) PR (t )  C R (T ) PR (t )  C F (T ) PF (t )
where
T
TL
CI(T)
CR1(T)
PR1(t)
CR2(T)
PR2(t)
CF(T)
PF(t)
r
t 1
1
1
2
2
return period used for deterministic design
design life time
initial costs (building costs)
cost of repair for minor damage
probability of minor damage in year t
cost of repair for major damage
probability of major damage in year t
cost of failure including downtime costs
probability of failure t
real rate of interest
1
1  r t
Case studies
Case study data
Case
Water
Depth
Armour
density
Waves
Orgin
y
H100
S,o
1.2
1.3
2.3
8m
15 m
30 m
Rock
2.65 t/m3
Cube
2.40 t/m3
Cube
2.40 t/m3
Distribution
Stability
formula
y
HS400
,o
Follonica
Weibull
5.64 m
6.20 m
Follonica
Weibull
5.64 m
6.20 m
Sines
Weibull
13.2 m
14.20 m
Built-in unit prices
core/filter 1/ filter 2/
armour
[EURO/m3]
van der Meer (1988)
10 / 16 / 20 / 40
van der Meer (1988)
modified to slope 1:2
10 / 16 / 20 / 40
van der Meer (1988)
modified to slope 1:2
5 / 10 / 25 / 35
Results
Optimum safety levels for rock armoured outer breakwater. 50 years service
lifetime. Shallow water depth 8 m. Damage accumulation included.
Real
Interest
Rate
(%)
Downtime
costs
Optimum design data
Optimum limit state
average number of events
within service lifetime
Optimized
armour
unit mass
W50
(t)
Optimum
design
return
period
T
(years)
HsT
(m)
Freeboard
Rc
(m)
SLS
RLS
ULS
Construction costs
for 1 km
length
(1,000
EURO)
Total lifetime
costs for 1 km
length
(1,000 EURO)
2
0
20
>6
4.40*
6.9
0.00
0.000
0.000
12,529
12,529
5
0
16
>6
4.40*
6.5
1.44
0.012
0.000
11,419
12,388
8
0
14
>6
4.40*
6.3
2.94
0.038
0.004
10,699
11,995
2
200,000
EURO
per day in
3 months
20
>6
4.40*
6.9
0.00
0.000
0.000
12,529
12,529
18
>6
4.40*
6.7
0.64
0.004
0.000
11,988
12,452
16
>6
4.40*
6.5
1.44
0.008
0.007
11,419
12,066
5
8
Total costs in 50 years lifetime. Rock armour. Shallow water of depth 8 m.
Damage accumulation included. Downtime costs not included.
Total costs in 1,000 Euro
22000
18000
2%
5%
8%
14000
10000
10
14
18
Design armour weight in ton
22
26
Optimum safety levels for concrete cube armoured breakwater. 50 years
service lifetime. 15 m water depth. Damage accumulation included.
Real
Interest
Rate
(%)
Downtime
costs
Optimum design data
Optimum limit state
average number of events
within service lifetime
Construction
costs for
1 km length
(1,000
EURO)
Total
lifetime
costs for
1 km
length
(1,000
EURO)
Optimized
design
return
period, T
(years)
HsT
(m)
Optimum
armour
unit mass
W
(t)
Freeboard
Rc
(m)
SLS
RLS
ULS
400
6.20
12.5
6.3
1.11
0.008
0.001
17,494
19,268
5
200
5.92
10.9
6.0
1.84
0.015
0.003
16,763
18,318
8
100
5.64
9.5
5.8
2.98
0.031
0.008
16,038
17,625
400
6.20
12.5
6.3
1.11
0.008
0.002
17,494
19,391
200
5.92
10.9
6.0
1.82
0.015
0.004
16,763
18,453
100
5.64
9.5
5.8
2.98
0.031
0.008
16,038
17,821
2
2
5
8
None
200,000
EURO per
day in 3
months
Total costs in 50 years lifetime. Concrete cube armour. 50 years
service lifetime. 15 m water depth. Damage accumulation included.
Downtime costs has no influence on total lifetime costs.
Total costs in 1,000 Euro
45000
40000
35000
2%
5%
8%
30000
25000
20000
15000
0
2
4
6
8
10
12
Design armour weight in ton
14
16
Optimum safety levels for concrete cube armoured breakwater.
30 m water depth. 50 years and 100 years lifetime. Damage accumulation
included. Downtime costs of 200,000 EURO per day in 3 month for damage
D > 15%.
Lifetime
(years)
50
100
Real
Interest
Rate
(%)
Optimum design data
Optimum limit state
average number of
events within structure
lifetime
Construction
costs for 1 km
length
(1,000 EURO)
Total lifetime
costs for 1 km
length
(1,000
EURO)
Optimized
design
return
period, T
(years)
HsT
(m)
Optimum
armour
unit mass
W
(t)
Freeboard
Rc
(m)
SLS
RLS
ULS
2
1000
14.7
168
14.8
1.21
0.008
0.001
76,907
86,971
5
400
14.2
150
14.8
1.84
0.016
0.003
73,722
81,875
8
100
13.2
122
14.8
3.39
0.052
0.012
68,635
78,095
2
1000
14.7
168
15.4
2.68
0.013
0.002
78,423
93,440
5
400
14.2
150
15.4
3.90
0.029
0.005
75,201
84,253
8
200
13.7
136
15.4
5.28
0.056
0.011
72,675
79,955
Case 2.3. Concrete cube armour. 30 m water depth. 50 years and 100 years
lifetime. Damage accumulation included. Downtime costs of 200,000 Euro per
day in 3 month for damage D > 15 %
Total costs in 1,000 Euro
210000
190000
170000
50 year - 2%
50 year - 5%
50 year - 8%
100 year - 2%
100 year - 5%
100 year - 8%
150000
130000
110000
90000
70000
50000
25
50
75
100
125
150
Design armour weight in ton
175
Conclusions
• The results show that optimum safety levels are somewhat higher than
the safety levels inherent in conventional deterministic designs,
especially in the case of depth limited wave height conditions and/or low
interest rates.
• The optimum safety levels depends on the repair cost. If doubbled the
optimum failure probability is about halved.
• Further, the results show that for the investigated type of breakwater
the critical design limit state corresponds to Seviceability Limit State
(SLS) defined by moderate damage to the armour layer. Designing for
SLS and performing repair when the SLS-damage is reached, imply that
the probability of very severe damage or failure is almost neglegeable,
and so will be the related cost of repair and downtime costs. This is
typical for structures with ductile damage development.
• The identified optimum safety levels correspond to exceedence of the
SLS-moderate damage level in average once to twice within a service
life of 50 years, given the yearly interest rates are 2-5 %. For higher
interest rates the optimum number of exceedences will increase
corresponding to less safe structures.
• The relations between total lifetime costs and the safety levels (e.g. in
terms of armour unit mass) show very flat minima. This means that
conservative designs involving fewer repairs are only slightly more
expensive than cost optimised designs.
• Knowledge about damage accumulation is important for the assessment of
optimum safety levels. Verification of the influence of choice of damage
accumulation model is ongoing.
• The obtained results indicate that optimum safety levels for rubble mound
breakwaters belonging to the functional classes III and IV (cf. Fig. 1) will be
almost the same as for classes I and II. This is because of the marginal
influence of downtime costs.
• It is expected that optimum safety levels for caisson breakwaters will be
relatively higher than for rubble mound structures due to the more brittle
failure of caissons. This is under investigation.
•The present and the coming investigations hopefully form a usefull
basis for national code makers to give advice on design safety levels
for breakwaters, related to both deterministic and reliability based
design procedures.
Example of stochastic analysis to check if a design meets target safety level
Cross section of La Coruña new breakwater
Design criteria
(From old spanish R.O.M.)
SLS
Max 30 % prob. of initiation of damage to main
armour, toe and rear slope within 50 years lifetime.
ULS
Max 15 % prob. of ”failure” of main armour, toe,
rear slope and superstructure within 50 years
lifetime.
Performance criteria
Structure part
Armour displacements
Main armour
Toe berm
Rear slope
Superstructure
displacement
Damage initiation
SLS
Failure
ULS
5%
5%
2%
15 %
30 %
5%
No
Any
displacement
Results of model tests at the Hydraulics and Coastal Engineering Laboratory at
Aalborg University
Failure probabilities Pf within 50 years structure lifetime based
on model tests and Monte Carlo simulations
Structure part
Damage initiation
SLS
Superstructure
sliding
slip failure
Armour
front slope
toe
rear slope
Failure
ULS
0.062
0.21
0.32
0.40
0.59
0.041
0.0011
0.51
Whole structure
ex. rear slope
0.21
Whole structure
incl. rear slope
0.54
Conclusion: Redesign of rear slope armour
The PIANC safety factor system for probabilistic design of breakwaters
(Burcharth 1991, Burcharth & Dalsgaard Sorensen 1999)
Examples
Armour stability (Hudson formula)
1 ˆ
1/ 3
0
Dn K D cot ˆ    H Hˆ ST
Z
Failure probability
within T-years
Coefficient of variation on Hs source data
0.05
0.20
Pf
H
Z
H
Z
0.01
0.05
0.10
0.20
0.40
1.7
1.4
1.3
1.2
1.0
1.04
1.06
1.04
1.02
1.08
2.0
1.6
1.4
1.3
1.1
1.00
1.02
1.06
1.00
1.00
Horizontal sliding of caisson on rubble foundation


1 ˆ ˆ
0
f FG  0.9 FˆU  H Hˆ ST   0.9 FˆH  H Hˆ ST 
Z
Failure probability
within T-years
Coefficient of variation on Hs source data
0.05
0.20
Pf
H
Z
H
Z
0.01
0.05
0.10
0.20
0.40
1.4
1.3
1.3
1.2
1.1
1.7
1.4
1.2
1.2
1.0
1.5
1.4
1.4
1.3
1.1
1.7
1.4
1.3
1.2
1.1
Acknowledgements
The authors appreciate the discussions in the PIANC Working Group 47 on
Criteria for the Selection of Breakwater Types and their Optimum Design
Safety Levels.