Choice of safety levels for conventional breakwaters 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 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 ERI < 5 Moderate economic repercussion 5 < ERI < 20 High economic repercussion ERI > 20 Social and environmental repercussion index (SERI) No social and environmental repercussion impact SERI < 5 Low social and environmental repercussion impact 5 < SERI < 20 High social and environmental repercussion impact 20 < SERI < 30 Very high social and environmental repercussion impact SERI > 30

From ERI is determined service lifetime of the structure Service life in years 15 25 50 From SERI is determined maximum overall probability of failure within service lifetime, Pf SERI < 5 5 - 19 20 - 29 >30 Serviceability limit state (SLS) 0.20 0.10 0.07 Ultimate limit state (ULS) 0.01 0.0001

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 0.10 in 50 years ULS 0.10 in 50 years

Objective of present study 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.

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 safety-classification 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.

Consequences of failure 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 Damage to main armour SLS: D = 5 %, RLS: D = 15 % ULS: D = 30 % Sliding distance of caissons SLS: 0.2 m, ULS: 2 m

Functional classification Tentative performance criteria II Wave transmission 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 Tentative performance criteria III 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 Tentative performance criteria IV 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.

Only rock and concrete cube armour considered. Cross sections Shallow water Deep water 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 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. where T return period used for deterministic design TL design life time CI(T) initial costs (building costs) CR1(T) cost of repair for minor damage PR1(t) probability of minor damage in year t CR2(T) cost of repair for major damage PR2(t) probability of major damage in year t CF(T) cost of failure including downtime costs PF(t) probability of failure t r real rate of interest

Built-in unit prices core/filter 1/ filter 2/ Case studies Case study data Case Water Depth Armour density Waves Stability formula Built-in unit prices core/filter 1/ filter 2/ armour [EURO/m3] Orgin Distribution 1.2 8 m Rock 2.65 t/m3 Follonica 5.64 m Weibull 6.20 m van der Meer (1988) 10 / 16 / 20 / 40 1.3 15 m Cube 2.40 t/m3 van der Meer (1988) modified to slope 1:2 2.3 30 m Sines 13.2 m 14.20 m 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 Construc-tion costs for 1 km length (1,000 EURO) Total lifetime costs for 1 km length Optimized armour unit mass W50 (t) Optimum design return period T (years) HsT (m) Free- board Rc SLS RLS ULS 2 20 > 6 4.40* 6.9 0.00 0.000 12,529 5 16 6.5 1.44 0.012 11,419 12,388 8 14 6.3 2.94 0.038 0.004 10,699 11,995 200,000 EURO per day in 3 months 18 6.7 0.64 11,988 12,452 0.008 0.007 12,066

Total costs in 50 years lifetime. Rock armour Total costs in 50 years lifetime. Rock armour. Shallow water of depth 8 m. Damage accumulation included. Downtime costs not included.

Optimum safety levels for concrete cube armoured breakwater 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 Optimized design return period, T (years) HsT (m) Optimum armour unit mass W (t) Free- board Rc SLS RLS ULS 2 None 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 16,038 17,625 200,000 EURO per day in 3 months 0.002 19,391 1.82 0.004 18,453 17,821

Total costs in 50 years lifetime. Concrete cube armour 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.

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) 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 Optimized design return period, T HsT (m) Optimum armour unit mass W (t) Free- board Rc SLS RLS ULS 2 1000 14.7 168 14.8 1.21 0.008 0.001 76,907 86,971 50 5 400 14.2 150 1.84 0.016 0.003 73,722 81,875 8 100 13.2 122 3.39 0.052 0.012 68,635 78,095 15.4 2.68 0.013 0.002 78,423 93,440 3.90 0.029 0.005 75,201 84,253 200 13.7 136 5.28 0.056 0.011 72,675 79,955

Case 2. 3. Concrete cube armour. 30 m water depth 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 %

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 • 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 Damage initiation SLS Failure ULS Armour displacements Main armour Toe berm Rear slope 5 % 2 % 15 % 30 % Superstructure displacement No Any displacement

Results of model tests at the Hydraulics and Coastal Engineering Laboratory at Aalborg University

Conclusion: Redesign of rear slope armour Failure probabilities Pf within 50 years structure lifetime based on model tests and Monte Carlo simulations Structure part Damage initiation SLS Failure ULS Superstructure sliding slip failure Armour front slope toe rear slope 0.32 0.40 0.59 0.062 0.21 0.041 0.0011 0.51 Whole structure ex. rear slope 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) Failure probability within T-years Coefficient of variation on Hs source data 0.05 0.20 Pf 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 1.02 1.08 2.0 1.6 1.1 1.00

Horizontal sliding of caisson on rubble foundation Failure probability within T-years Coefficient of variation on Hs source data 0.05 0.20 Pf H Z 0.01 0.05 0.10 0.20 0.40 1.4 1.3 1.2 1.1 1.7 1.0 1.5

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.