PIANC MMX Congress Liverpool UK 2010

STRUCTURAL RELIABILITY ANALYSIS OF QUAY WALLS WITH STEEL SHEET PILES by 1

by P. Osório , C. Odenbreit2 and T. Vrouwenvelder3

ABSTRACT This paper shows the first results of the reliability analysis of a steel sheet pile wall located in the Port of Hamburg, North of Germany. The wall was designed according to EAU 2004 and the First Order Reliability Moment (FORM) was used to perform the reliability analyses. Blum’s model of interaction soil/structure, which was used in the design of the wall, was also used in the reliability analyses. To have a basis of comparison, another model was used: the sub-grade reaction model, or beam in an elastic foundation model. The results show a fair approximation between both models in the outcome of the reliability analyses. The stochastic properties of the variables were based on the recommendations of the Joint Committee for Structural Safety (JCSS) and corrosion was also included in the analyses through a probabilistic model. The results show that the sheet pile wall has a probability of failure below the limit given by the Eurocode EN 1990 for a service life of 50 years.

1. INTRODUCTION 1.1

Quay walls with steel sheet piles

A sheet wall is by definition a retaining wall of thin cross section that resists loads by bending (BS 6349-2:1988) It consists on the connection of sheet piles by the means of interlocks and driven into the soil. It is possible to fabricate sheet piles with reinforced concrete, prestressed concrete and even wood, but steel is the material most commonly used. Roughly 2 million tons of steel is consumed per year for this purpose, according to Smoltczyk, U. (2003). Steel offers several advantages such as the variety of cross-section with a wide range of strength, economy, lack of buckling under heavy driving, availability in different combinations to increase wall section modulus, re-usability for temporary works, relatively light weight, and the possibility of increasing the pile length by welding or bolting, Clayton C. et al (1993). Another advantage is that the repair of a corroded or damaged pile can be easily made by welding a new portion of steel to it. Quay walls with steel sheet piles and relieving platforms are a common solution in coastal engineering. The concrete relieving platform enables the wall to retain higher values of soil and thus the berthing of ships of higher tonnage. To keep up with the growing demand for container transportation, the Port of Hamburg in Germany decided to expand its capacity and construct the Predöhlkai Liegeplatz 2 in recent years. The quay wall that is object of the analysis in this paper is sited there. Figure 1 shows a schematic view of it. In Germany, quay walls are designed according to EAU 2004. The approach to design of these recommendations is based on the Eurocodes, i.e., verification of limit states and the use of partial safety factors for actions and resistances. According to EAU 2004, there are 4 limit states that must be verified: •

LS 1A: limit state of loss of support safety

•

LS 1B: limit state of failure of structures and components

•

LS 1C: limit state of loss of overall stability

•

LS 2: limit state of serviceability.

For this paper, only the verification of the limit state of failure of structures and components is presented. Within this limit state, only the failure of steel sheet pile was verified, not taking in account the failure of the anchor, the failure of the reinforced concrete elements or the failure of the soil. 1

Assistant, University of Luxembourg, Luxembourg, [email protected] Professor, University of Luxembourg, Luxembourg 3 Professor, Technical University of Delft, The Netherlands 2

1 of 11

PIANC MMX Congress Liverpool UK 2010

Relieving platform

Water level Retaining height

Anchor

Dredge line Concrete piles

Soil

Figure 1: Schematic view of the quay wall analyzed To model the interaction between soil and wall, the Blum’s method is commonly used in Germany. It is based on the principle that a failure situation occurs in which the deformations are so large that the minimum active pressure and the maximum passive pressure are present. It is a simple and easily applicable method but has the disadvantage that the actual pressures on site may differ considerably from the assumed ones (active and passive). An alternative method is considering the soil modeled as set of elasto-plastic springs, making the pressure of the soil on the wall dependent of its deformation. It is called the sub-grade reaction model, elasto-plastic model or beam on elastic foundation model. Although it is a more realistic model, it is also more complex. This method is commonly used, for example, in France and Netherlands. 1.2

Reliability Analysis

Structural Reliability can be defined as the degree in which it is likely that a structural element functions as it should. It depends on the margin between the resistance to failure and the loads. No structure is 100% safe, and so the question is always “how safe is safe enough”? There are values of probability of failure that are accepted as being good enough depending on the horizon of time that the structure is supposed to function, as well as its importance. This is defined in Eurocode Basis of Structural Design, EN 1990. When the probability distribution of all the parameters involved in the design of a structure is known, then the probability of failure can be determined as follows:

pf =

∫ f (x).dx x

(1)

G(X) ≤ 0

where the vector X={X1, ...,Xn} represents the resistance and load random variables acting on the system and fx(X) is the joint probability density function of vector X. The function G(X) ≤ 0 is the socalled “limit state” function, which represents the region of failure. The Reliability Index (β) is related to the probability of failure pf through:

pf = Φ(-β)

(2)

where Φ(-β) represents the cumulative distribution function of the standard normal distribution. To determine the probability of failure of a complex system with non-linear behaviour, there are several methods available. The Monte Carlo simulation method is based on the repetitive application of a set of random values of each variable to the system. The main problem with this method is that for low probability failures, there is the need of application of a very high number of simulations, which for complex systems can be too much time-consuming. Other methods like First Order Reliability Moment 2 of 11

PIANC MMX Congress Liverpool UK 2010

(FORM) can simplify the task but are based in simplifications that in some cases can result in inaccurate values of pf. To perform the reliability analyses, a probabilistic program called Prob2B, developed at TNO Department of Built Environment and Geosciences, in Netherlands was used. This program performs the probabilistic operations necessary to apply the methods of reliability analysis above mentioned, as well as others. However, it does not perform structural analyses of the sheet pile wall, and so it was necessary to couple it with other programs. To perform structural analyses according with Blum’s Method, a German program called DC-Pit was used and to perform the structural analyses according to the sub-grade reaction model, a Dutch program MSheet was used. Since these programs cannot incorporate the effects of corrosion on the analyses, then Microsoft Excel was used as an intermediate tool to perform this task. The way the programs interact is describe in Figure 2.

DC-Pit or MSheet Manual definition of the structural system (number of soil layers, wall type and geometry, etc.)

Prob2B Manual definition of - the stochastic properties of the variables. - limit state function. - Method to perform the reliability analysis (R.A.) Initiation of R.A.

Structural analysis of the system using the variables generated.

Generation of a set of random variables

Output of results (bending moments, internal forces, displacements).

Transfer of the results of the structural analysis to Excel.

1. Limit state verification. 2. Next limit state verification? Microsoft Excel Incorporation of the effects of corrosion in the cross-section (reduction of thickness and increase in the stresses)

No

Yes

Output of the Reliability Analysis (probability of failure, Reliability Index, etc.)

Figure 2: Flowchart of the procedure used to perform the reliability analyses After manually define the structural layout of the system in the DC-Pit or MSheet and after the definition of all the probabilistic options in Prob2B, all the procedure is automatic and controlled by Prob2B. 1.3

Corrosion models

Corrosion is a complex phenomenon and its effects on steel sheet pile walls are dependent on many different parameters. In the case of sheet piles in marine environment, according to (ECSC, 2004), the effect of corrosion depends mainly on:

•

endogenous parameters that define the properties of the steel material, like for example, chemical composition, microstructure, inclusions content,

•

exogenous parameters that define the properties of the marine environment, like for example, the ionic content of the water (chlorides, sulphates, etc.), water pH, water temperature, dissolved oxygen in water, water agitation, etc.

•

a dynamic parameter, i.e. the effect of time on the corrosion loss.

3 of 11

PIANC MMX Congress Liverpool UK 2010

These parameters can vary significantly according to the location of the port, and even within different areas of the same port. This originates a high level of uncertainty on the effect that corrosion has on sheet piles, i.e., the reduction of plate thickness of the section. The gathering of data concerning the values of thickness loss in steel sheet piles is a slow and expensive task, because it requires diving professionals that are frequently encountering highly strained conditions (muddy and turbid water), Heeling, A. et al (2006). For this reason, only few of the biggest ports and also public institutions have possibility of undertaking campaigns of measurements of thickness losses due to corrosion. For this paper, data from two different sources were used to model the effect of corrosion in the steel sheet piles:

•

recommended values in EAU 2004 for the semi-probabilistic design.

•

values from the Report “Design Method for Steel Structures in Marine Environment including the Corrosion Behaviour”, (ECSC 2004) for the reliability analyses.

1.4

Model of corrosion from EAU 2004

EAU 2004 recommends the separation of the exposed height of the sheet pile wall in 4 different zones:

•

splashing water zone (SpWz)

•

intertidal zone (WWz)

•

low water zone (LWz)

•

permanent immersion zone (UWz)

Figure 3 shows a qualitative diagram of the corrosion zones for North Sea.

Figure 3: Qualitative diagram of the corrosion steel sheet piling for North Sea, EAU 2004 The mean and maximum values of thickness loss for each zone of steel sheet piles in contact with the North Sea and Baltic Sea can be withdrawn from figure 4. The maximum values (Figure 4, b) are used to verify the occurrence of pitting corrosion in serviceability limit states.

4 of 11

PIANC MMX Congress Liverpool UK 2010

15,9

5,8 3,9 1,9

Figure 4: Decrease in thickness as a result of corrosion in the sea-water zone and determination of thickness loss for 50 years of service life, EAU 2004 Table 1 resumes the values determined in Figure 4 for a service life of 50 years.

Mean values of thickness loss (mm)

Maximum values of thickness loss (mm)

splashing water zone (SpWz)

1,9

8

intertidal zone (WWz)

1,9

5,8

low water zone (LWz)

3,9

15,9

permanent immersion zone (UWz)

1,9

5,8

Zone

Table 1: Mean and maximum values of corrosion for a sheet pile in Northe Sea and Baltic Sea for a service life of 50 years, EAU 2004 After corrosion measurements in the Port of Hamburg, Shoener, M., et al (2009) determined that the mean value of thickness loss for a service life of 50 years is 3,8 mm in the zone of higher corrosion, that is quite close to the mean value of 3,9 mm recommended in EAU 2004. 1.5

Probabilistic model of corrosion

The Report “Design Method for Steel Structures in Marine Environment including the Corrosion Behaviour”, (ECSC 2004), has a significant amount of corrosion data, including a model obtained through corrosion measurements in steel sheet piles of 13 different United Kingdom sites (in contact with North Sea and Irish Sea). The conditions present there can be considered representative of the conditions for North of Europe (ESCS 2004). For this reason, it was used for modeling the corrosion in the Port of Hamburg. The probability density function and the stochastic properties of the thickness loss after 50 years of service life are shown in Figure 5. The separation of zones along the sheet pile is identical to the separation used in EAU 2004, with 4 different zones (splash, tidal, low water and immersion). The pattern of corrosion along the sheet pile of this probabilistic model is slightly different from the model of EAU 2004. The zone with highest mean value of thickness loss in the probabilistic model is the splash zone, whilst in EAU 2004 is the low water zone. Nevertheless, in the probabilistic model the standard deviation of thickness loss at the low water zone is higher than the one at the splash zone. 5 of 11

PIANC MMX Congress Liverpool UK 2010

Probability density function

This makes the curve for the low water zone to be wider and consequently to have higher values of corrosion loss at the right-end percentiles. For example, the 95%-percentile at the low water zone is at 5,4 mm of thickness loss against 5,1 mm at the splash zone.

Zone

Distribution

Mean (mm)

Std. Dev. (mm)

Splash

Lognormal

2,55

1,35

Tidal

Lognormal

1,2

0,75

Low water

Lognormal

2

1,9

Immersion

Lognormal

1,3

0,9

Corrosion thickness loss after 50 years (mm) Splash Zone

Tidal Zone

Low water Zone

Immersion Zone

Figure 5: Probability density function and stochastic properties of the corrosion loss at 50 years for all the zones of the sheet pile

1.6

Effect of corrosion in the resistance of the cross-section

All the reliability analyses have been conducted assuming that the corrosion affected the section of the wall homogeneously, i.e. the same value of thickness loss was assumed to occur in all the extension of the wall in contact with water. This is a simplified model because in reality corrosion can have a highly irregular effect along the sheet pile. The thickness reduction has a direct effect on the reduction of the section modulus (W) and of the cross-section area (A). A simplified model of representing the variation of these parameters with uniform corrosion is given by Equation (3) for the section modulus and Equation (4) for the crosssection area (ECSC, 2004).

Wcorr = W0 – K1.tcorr

(3)

Acorr = A0 – K2.tcorr

(4)

Where: Wcorr and Acorr

section modulus and area of the corroded section

W0 and A0

the initial section modulus and area (non-corroded state)

K1 and K2

coefficients that depends on the properties of the section

tcorr

thickness loss due to corrosion

6 of 11

PIANC MMX Congress Liverpool UK 2010

2. RELIABILITY ANALYSIS OF THE SHEET PILE WALL 2.1

Methodology

The schematic structural layout of the sheet pile wall is in Figure 6. The sheet pile is single-anchored and a slope of inclination 1:4 was defined to relieve pressure over the wall.

Water level Water level Retaining height

Dredge line

Soil

Figure 6: Schematic structural layout of the sheet pile wall analysed There are 6 layers of soil and 5 soils (layers 2 and 4 share the same soil), see Figure 7. The sheet pile has 32,40 m long. +3.40 +2.80

+2.00 1:4

0.00 mNN

-2.00

-2.50

Water level

Layer 2 (Soil 2)

Sheet pile

Layer 1 (Soil 1) -1.50 Water level

30 °

Anchor

-14.00 -13.50 -16.00

Layer 4 (Soil 2)

Layer 3 (Soil 3)

Layer 5 (Soil 4) Design dredge line

-20.80

-20.80

Layer 6 (Soil5) -29.00

Figure 7: Schematic structural layout of the sheet pile wall analysed

7 of 11

PIANC MMX Congress Liverpool UK 2010

Before the reliability analyses, the sheet pile wall was designed according to EUA 2004. The software DC-Pit was used to perform the structural analysis applying Blum’s Method. The characteristic values listed in Table 2 were used in the design. The design values of bending moment MEd and normal force NEd obtained for the most unfavourable load case were MEd = 3334 kN.m/m and NEd = 1243 kN/m.

Variables Steel yield strength fy (MPa) Surcharge (kPa) 3 Reinforced concrete unit weight γconc (kN/m ) Soil 1 (in layer 1) Internal friction angle φ (°) Friction angle soil/wall δ (°) 3 Soil unit weight γ (kN/m ) 3 Soil saturated unit weight γsat (kN/m ) Cohesion c (kPa) 2 Modulus sub-grade reaction K (MN/m /m) Soil 2 (in layers 2 and 4) Internal friction angle φ (°) Friction angle soil/wall δ (°) 3 Soil unit weight γ (kN/m ) 3 Soil saturated unit weight γsat (kN/m ) Cohesion c (kPa) 2 Modulus sub-grade reaction K (MN/m /m) Soil 3 (in layer 3) Internal friction angle φ (°) Friction angle soil/wall δ (°) 3 Soil unit weight γ (kN/m ) 3 Soil saturated unit weight γsat (kN/m ) Cohesion c (kPa) 2 Modulus sub-grade reaction K (MN/m /m) Soil 4 (in layer 5) Internal friction angle φ (°) Friction angle soil/wall δ (°) 3 Soil unit weight γ (kN/m ) 3 Soil saturated unit weight γsat (kN/m ) Cohesion c (kPa) 2 Modulus sub-grade reaction K (MN/m /m) Soil 5 (in layer 6) Internal friction angle φ (°) Friction angle soil/wall δ (°) 3 Soil unit weight γ (kN/m ) 3 Soil saturated unit weight γsat (kN/m ) Cohesion c (kPa) 2 Modulus sub-grade reaction K (MN/m /m)

Characteristic value

Stochastic properties Coefficient Mean of variation 462,3 0,07 25,8 0,10 0,03 25

430 30 25

Probabislitic Distribution Lognormal Normal Normal

32,5 21,7 18 20 0 40

Lognormal Lognormal Lognormal Lognormal Lognormal Lognormal

32,5 21,7 18 20 0 40

0,10 0,10 0,05 0,05 0 0,20

3,25 2,17 0,9 1,0 0 8

35 23,3 18 20 0 50

Lognormal Lognormal Lognormal Lognormal Lognormal Lognormal

35 23,3 18 20 0 50

0,10 0,10 0,05 0,05 0 0,20

3,5 2,33 0,9 1,0 0 10

20 13,3 13 13 12,5 0,5

Lognormal Lognormal Lognormal Lognormal Lognormal Lognormal

20 13,3 13 13 12,5 0,5

0,10 0,10 0,05 0,05 0,20 0,20

2,0 1,33 0,65 0,65 2,5 0,1

37,5 25 19 21 0 100

Lognormal Lognormal Lognormal Lognormal Lognormal Lognormal

37,5 25 19 21 0 100

0,10 0,10 0,05 0,05 0 0,20

3,75 2,5 0,95 1,05 0 20

32,5 21,7 21 21 25 150

Lognormal Lognormal Lognormal Lognormal Lognormal Lognormal

32,5 21,7 21 21 25 150

0,10 0,10 0,05 0,05 0,20 0,20

3,25 2,17 2,1 2,1 5 30

Standard Deviation 32.4 2,58 0,75

Table 2: Properties of the variables used in the analyses The stochastic properties of the variables used in reliability analyses should result from tests and measurements performed at the structures and its materials. If no information of this type exists, then a second way (and not so accurate) is to find approximations in published information. The Joint Committee for Structural Safety (JCSS) is developing a Model Code (JCSS, 2006) to assist structural engineers in performing reliability analyses, and it gives information related to typical values of stochastic properties and distribution types. All the values of the stochastic properties (distribution types, mean values coefficient of variation and standard deviation) in Table 2 were chosen from the recommended values by the Model Code. According to this publication, in order to avoid negative values in geotechnical properties, its distribution should be lognormal. According to EAU 2004 (and other publications as for example Smoltczyk, U., 2003), the characteristic value for geotechnical properties should be equal to the nominal value, which is the mean value of the results of the tests conducted to its determination. For this reason, for soil properties, all the mean values were considered to be equal to the characteristic ones.

8 of 11

PIANC MMX Congress Liverpool UK 2010

The stochastic properties of steel were determined with the expression (JCSS, 2006): Mean: μ(fy) = fy.EXP(1,64 x cov) – 20, with cov = 0,07 (coefficient of variation)

(5)

Concerning the surcharge, the mean value was determined in a way that the characteristic value could correspond to the 95-percentile of the Normal distribution. The stochastic properties of concrete bulk density were also according to JCSS Model Code. 2.2

Ultimate Limit State verification

No second order effects were taken in account in the verification of the ultimate limit state and so the expression used was

σEd = MEd/Wel + NEd/A < fyd

(6)

The ultimate limit state verification using the Peiner combined-wall PSp 1006/PZi 675/11,5 (with an elastic section modulus Wel = 10635 cm3/m, cross section area A = 306 cm2/m and steel grade S430 GP) is resumed in Table 3.

Design values of maximum bending moment and normal force

Section properties

Verification

Wel (cm3/m)

A (cm2/m)

fyk (MPa)

MEd (kN.m/m)

NEd (kN/m)

σEd (MPa)

fyd (MPa)

σEd / fyd

10635

306

430

3334

1243

354,1

390,9

0,91

Table 3: Ultimate limit state verification for the most unfavourable load case without the effect of corrosion If the effect of corrosion is taken in account, then the cross-section properties are altered according to Equation (3) and Equation (4). The value of thickness loss considered was the mean value recommended by EAU 2004 for a period of 50 years, i.e. the value of 3,9 mm for the low water zone and 1,9 mm for the others. No safety factor was applied to the value of thickness loss. The critical point of analysis was located in the immersion zone (same point as in the verification without corrosion), and the values obtained are resumed in Table 4.

Design values of maximum bending moment and normal force

Section properties

Verification

Wcorr 3 (cm /m)

Acorr 2 (cm /m)

fyk (MPa)

MEd (kN.m/m)

NEd (kN/m)

σEd

fyd (MPa)

σEd / fyd

10280

297

430

3334

1243

366,2

390,9

0,94

Table 4: Ultimate limit state verification for the most unfavourable load case taking the effect of corrosion in account As expected, the effect of corrosion increases the maximum design stress in the cross-section σEd, but it remains below the design yield strength fyd, and so, for this model of corrosion, the sheet pile is considered to be safe for 50 years of service life. 2.3

Reliability analysis of the sheet pile wall

The reliability analysis of the sheet pile wall was performed using Blum’s model and the sub-grade reaction model. The limit state function G(X, z) used in the analyses was dependent on the vector of random variables X and it was verified along the height of the sheet pile, being also dependent on the distance to the top of the pile z.

G(X,z) = fy – (M(X,z)/W(z) + N(X,z)/A(z))

(7)

The limit sate function was analyzed at every 15 cm of the sheet pile’s length. The section modulus W(z) and the cross-section A(z) were only dependent of z when corrosion was taken in account and varying according to the corrosion zones. 9 of 11

PIANC MMX Congress Liverpool UK 2010

The method used to perform the reliability analyses was the First Order Reliability Moment (FORM). Monte Carlo Method was not used because preliminary analyses revealed small values of probability of failure (pf ≈ 1x10-8) for this structure. A first estimate of the number N of simulations for a 95% confidence level, can be determined using the following expression of Broding et al. cited in Melchers, R (1999):

N > 3/pf

(8)

In this case, it would be required to perform N = 3x108 simulations, that with approximately 4 seconds for each simulation, would take several years to complete. The results (Reliability Index β and probability of failure pf) of the application of FORM are shown in Table 5.

Soil Model

Results without corrosion

Results with corrosion

β

pf

β

pf

Blum’s model

5,8

3,3x10-9

5,1

1,3x10-7

Sub-grade reaction model

6,8

5,65x10-12

5,3

6,8x10-8

Table 5: Results of the reliability analyses with FORM

Reliability Index β

As expected, the effect of corrosion causes an increase in the probability of failure of the steel sheet pile wall, but it remains below the limit recommended by the Eurocode Basis of Structural Design, EN 1990, that is pf = 7,3x10-5 (or β = 3,8) for structures with a service life of 50 years and a Reliability Class RC2, see Figure 8.

Soil/structure interaction model

Figure 8: Reliability Index of the wall using FORM Method taking and without taking corrosion in account The difference between the results of both models of interaction soil/structure is caused by the distinct distribution of the internal forces and bending moments along the sheet pile in both methods. Blum’s model is based on the limit pressures (active and passive) of the soil and for every limit state verification in the FORM routine, a new depth of wall is determined. On the contrary, for the sub-grade 10 of 11

PIANC MMX Congress Liverpool UK 2010

reaction model, the wall depth is fixed and the soil pressures depend on the conditions present, where intermediate pressures between active and passive are possible. This means that for the same values of the random variables, the distribution of bending moments, normal forces and shear forces have slightly different values (usually higher) if using Blum’s model rather than sub-grade reaction model. Despite all these factors, the results show an approximation between the application of both methods, especially in the case where corrosion was taken in account.

3. CONCLUSION The work shown in this paper is part of a research project now in progress at the University of Luxembourg in cooperation with the Technical University of Delft that approaches the design of steel sheet piles in marine environment. The analyses shown here are the first of a thorough planned study of reliability of steel sheet piles with the effect of corrosion. A reliability analysis of a certain structure should be performed with the structural model as close as possible to the one that is built or planned to be built. The application of Blum’s model fails this principle because, as said before, for every limit state verification the wall’s depth is re-determined. Nevertheless, the results shown in this paper indicate a fair approximation in relation to sub-grade reaction model. More research must be done, namely by using other reliability methods and also a finite elements model, but with basis in the shown results, it can be said that Blum’s model can be used to perform preliminary analyses, since it is much simpler to use in an algorithm than the subgrade reaction model. The limit for the probability of failure (or on the other hand the Reliability Index) that Eurocode EN 1990 defines for a safe structure with 50 years of service life was not exceeded in the present case, even if the effect of corrosion is taken in account. However, It must be noted that the stochastic properties of the variables were not based in actual measurements and tests in the real structure but in published recommendations, that although were based in many real situations, are not as accurate as real tests would be.

4. ACKNOWLEDGEMENTS The authors would like to thank the Port of Hamburg for the information related to the design of the quay walls in Predöhlkai Liegeplatz 2, and also Wim Courage from TNO - Department of Built Environment and Geosciences, in Netherlands, for the cooperation in coupling Prob2B with DC-Pit and MSheet.

5. REFERENCES BS 6349-2:1988, British Standards Institute, Maritime Structures – Design of Quay Walls, Jetties and Dolphins, BSI, 1999 Clayton, C., Milititsky, J, Woods, R. (1993), Earth Pressure and Earth-retaining Structures, Taylor & Francis, EAU 2004, Committee for Waterfront Structures of the Society for Harbour Engineering and the German for Soil Mechanics and Foundation Engineering, Recommendations of the Committee for Waterfront Structures Harbours and Waterways – EAU 2004, 8th Edition, Ernst & Sohn, Berlin, 2006 European Coal and Steel Community (2004), Design Method for Steel Structures in Marine Environment Including the Corrosion Behaviour, ESCS European Committee for Standardization (2002), European Standard EN 1990:2002, Brussels Heeling, A. & Alberts, A. (2006), Beschreibung und Beurteilung des Korrosionszustandes korrodierter Stahlspundwände, 31st PIANC Congress, Estoril Joint Committee for Structural Safety (2006), JCSS Model Code, Zurich Melchers, R (1999). Structural Reliability Analysis and Prediction. Chichester : John Wiley & Sons Shoener, M., Nickels, H., Plath, M. (2009), Wanddickenmessungen an Spundwänden im Hamurger Hafen, Workshop Spundwände – Profile, Tragverhalten, Bemessung, Einbringung un Wiedergewinnung, Technical University of Hamburg, Hamburg Smoltczyk, U. (2003), Geotechnical Engineering Handbook - Volume 3, Ernst & Sohn, Berlin

11 of 11