Time-varying ultimate strength of aging sheet pile considering corrosion effect
Balegh Benamar
LGCE Civil Engineering and Environmental Laboratory, Djillali Liabes University, BP 89.
DZ 22000 Sidi Bel Abbes, Algeria balegh.benamar@yahoo.com
Trouzine Habib
LGCE Civil Engineering and Environmental Laboratory, Djillali Liabes University, BP 89.
DZ 22000 Sidi Bel Abbes, Algeria h_trouzine@yahoo.fr
Abstract—-Steel Sheet pile walls are widely used in excavation support systems, cofferdams, cut-off walls under dams, slope stabilization, water front structures, and floodwall. Corrosion in sheet pile leads to severe degradation processes which usually affect both the ultimate and serviceability limit state performance of the structure. Recent developments in mathematical modeling strategies, in association with in situ thickness measurements, have significantly enhanced the qualitative understanding of the corrosion processes at various locations within marine structures. A comprehensive mathematical model is developed that allows capturing all the main effects of corrosion.
Keywords—Sheet pile; Corrosion; Mathematical; modeling
I. INTRODUCTION
Sheet pile wall structures are widely used in excavation support systems, cofferdams, cut-off walls under dams, slope stabilization, waterfront structures, and floodwalls [1]. Sheet pile walls are classified as flexible walls and have relatively much lower system stiffness compared to other in-situ walls, such as slurry walls [2-3]. They can also be exposed to the seawater environment or aggressive soils, and are at higher risk of corrosion, particularly after many years in service (beyond 5–100 years).
Knowledge about the corrosion rate is also important in case of verifying the remaining bearing capacity of existing structures, and estimating the remaining service life time according to bearing capacity. In terms of structure oversizing, a certain corrosion rate (mm/year) is assumed. The corrosion is also assumed to be even all over the surface but pit corrosion or other types of uneven corrosion are not accounted for. In practice the corrosion rate is also assumed to be a linear function of time.
The loss of thickness which is due to atmospheric corrosion may be taken as 0,01 mm per year in normal atmospheres and as 0,02 mm per year in locations where marine conditions may affect the performance of the structure [4].
The soil corrosion rates are affected by the type of soil, the variation of the level of the groundwater table, the presence of oxygen, contaminants, and the organic matter. The corrosion effect of the organic matters depend on their compositions and concentrations [4,6] while the loss of thickness of carbon steel
in red clay soils, for example, is above 1mm/year [7].
It is also commonly found that the most severe corrosion in sheet pile structures appears in the splash zone, while much lower corrosion rates are found in a couple of meters below mean water level [5].
It is found that for sheet piling with similar wall thickness profiles throughout the earlier perforation of the in- and out- pans of U shaped steel sheet piling, the webs of Z and I- shaped steel piling, and the earlier perforation of the corner regions correlated with localized segregation and differences in metal composition [8]. Several case are studies in marine concentrated corrosion, and corrosion rate measurements in steel sheet pile walls in a marine environment, and much debate on whether a corrosion model should rely on mechanistic principles or actual corrosion data collected from structures marine surveys [9]. Recent researches and developments realized in mathematical modeling strategies, in association with in situ thickness measurements, have significantly enhanced the qualitative understanding of the corrosion processes at various locations within marine structures [10-14].
The aim of the present on-going work is to analyze results of some empirical corrosion models with recommendations of the European design code in terms of design values on corrosion rate in the sheet pile wall subject of atmospheric, soil and/or marine corrosion.
Nomenclature
d(t) t d∞ T0 Tt C1, C2 d∞ Tst β η s C bf tf
ε Mpl
Mpl
Φpl.c
φ fy
mean value of corrosion depth (mm) structural age (year)
long-term thickness of the corrosion wastage (mm) period without corrosion(year)
transition between coating durability and corrosion initiation (year) statistical corrosion data
long-term thickness of the corrosion wastage (mm) the period without corrosion in Qin and Cui model (year) statistical value of random variable in Qin and Cui model statistical value of random variable in Qin and Cui model thickness of web of sheet pile (mm)
corrosion percentage flange width of sheet pile (m) flange thickness of sheet pile (m) yield strength factor
plastic moment resistance (kNm/m) wall yield moment (kNm/m)
member rotation; with subscript y, yield; pl, plastic member plastic rotation capacity
yield stress (kN/m2)
II. ANALYTICAL MODELS AND DESIGN VALUES ON CORROSION RATES A. Empirical models
Assuming a constant corrosion rate from the various corrosion mechanisms and the scattered corrosion data available within the published research literature, seems insufficient to predict the corrosion damage for certain structures as ships age [9]. A variety of empirical mathematical models have been proposed to predict corrosion.
Initially, simple linear relationships of corrosion wastage against time were proposed by Southwell et al. (1979) [9,10] :
d(t) = 0.076 + 0.038t (1)
Where d(t) is the mean value of the structural thickness reduction (mm), and t is the time (year)
However, this linear model tends to overestimate the corrosion wastage at the initial stages of the corrosion process, probably, due to the exclusion of coating effects. Thus, a modified Southwell’s model is proposed by Melchers (1999) [9,11]:
d(t) = 0.084t0.823 (2)
Guedes Soares and Garbatov (1999) proposed a similar model (Eq. (3)) which also proposing including no corrosion and transition between coating durability, and corrosion initiation.
However, they believed that the corrosion would gradually come to a halt at a depth of d1, since corrosion products on the plate surface will hinder the corrosion process. Any disturbance, or indeed removal, of this oxide layer could lead to a re-initiation of the corrosion process [9,15].
d(t) = d∞[1 − exp (−t−TT0
t )] (3)
Where d∞ is the long-term thickness of the corrosion wastage (mm), T0 is the coating life and Tt is transition between coating durability and corrosion initiation.
Paik, Kim and Lee (1998), and Paik and Thayamballi (1998) proposed a linear probabilistic model, which was later modified by Paik and Thayamballi (2002) by separating the corrosion process into three successive stages: (1) no corrosion T0; (2) transition between coating durability and corrosion initiation Tt ; (3) general corrosion. For the third stage, they suggested three types of corrosion rate : the convex type (gradual build-up of rust layer will prevent metal from further corrosion), the concave type (likely to happen under dynamically loaded structures due to flexing exposing fresh areas to corrosion) and the linear type (rust layer are continually removed due to abrasion or wear) [9, 16-18].
In Paik and Thayamballi model, the coating duration was described using a lognormal distribution by Yamamoto and Ikegami (1998), Paik and Thayamballi (2002) and Ahmmad and Sumi (2010). The corrosion rate is no longer constant [9,16,18]:
d(t) = C1 (t − T0− Tt)C2 (4)
Where obtaining C1 and C2 is based on collected statistical corrosion data.
Qin and Cui (2002)(2003) proposed a more flexible model for general corrosion of mild steels using a Weibull function.
Unlike the corrosion process described by Guedes and Garbatov (1999) and Paik, Kim and Lee (1998), they believed
that after the ‘no corrosion’ period (0_Tst), corrosion would accelerate (Tst, TA) until general corrosion is initiated, and then decelerate (TA_TL) over the service life. It has the advantage of being a more flexible model and can describe the previously published models by applying certain parameters values. However, this model was fitted to an assumed corrosion data set instead of real measurements, which makes it difficult to determine the degree of accuracy and rationality [9,15,16].
d(t) = d∞{1 − exp [− (t−Tηst)β]} (5)
Where d∞ is the long-term thickness of the corrosion wastage (mm), Tst is the period without corrosion and β and η are determined by the least-squares method.
Fig. 1. Empirical corrosion models
B. Design values on corrosion rates of sheet pilling according to the Eurocode 3
In terms of strength verification of sheet piles for both serviceability and ultimate limit states, the European Committee for Standardization [4] has determined the loss of thickness for parts of sheet pile walls which are in contact with water or with soil (with or without groundwater), dependent upon the required design working life of the structure. Where sheet piles are in contact with soil or water on both sides, the corrosion rates is applied to each side. If the aggressiveness of the soil or water is different on opposite sides of a sheet pile wall, then corrosion rates given in this section should be considered as for design only. The loss of thickness due to atmospheric corrosion may be taken as 0,01 mm per year in normal atmospheres and as 0,02 mm per year in locations where, marine conditions may affect the performance of the structure. The following have a major influence on the corrosion rates in soils [4]: the type of soil, the variation of the level of the groundwater table, the presence of oxygen, and the presence of contaminants.
The recommended value of the loss of thickness due to corrosion for piles and sheet piles in soils with or without groundwater is estimated for 5, 25, 50, 75 and 100 years, for the following cases [4]:
Undisturbed natural soils (sand, silt, clay, schist, ….) Polluted natural soils and industrial sites
120 100 80 60 40 20 0
5
4
3
2
1
0 5
4
3
2
1
0
Structural age (years)
Corrosion depth (mm)
Southwell (1979) Melchers (1999) Paik and Thayambali (2002) Guedes and Garbator (1999) Qui and Cui (2002)
Aggressive natural soils (swamp, marsh, peat, …)
Non-compacted and non-aggressive fills (clay, schist, sand, silt, ...)
Non-compacted and aggressive fills (ashes, slag, ....)
In cases of presence of fresh water or sea water the cases defined are [4]:
Common fresh water (river, ship canal, ….) in the zone of high attack (water line).
Very polluted fresh water (sewage, industrial effluent, ….) in the zone of high attack (water line).
Sea water in temperate climate in the zone of high attack (low water and splash zones)
Sea water in temperate climate in the zone of permanent immersion or in the intertidal zone.
Fig. 2. Recommended value for the loss of thickness (Eurocode 3 - Part5) III. INVESTIGATED CASES In designing sheet piling, several aspects are to consider : geotechnical conditions, structural systems, state criteria, material properties and aggressiveness of the media.
A fully fixed anchored sheet pile wall is the focus of our study.
The most commonly used sheet piles sections are Z profiles.
In case of designing sheet pile wall, factors that influence the corrosion rate should be taken in consideration : temperature, oxygen concentration, salinity etc... Six empirical corrosion models are applied in this study.
Fig. 3. Steel sheet pile for classification for ultimate strengthss (Eurocode 3 - Part5)
This part of the project involved an investigation to define the cross-section classification sections (i.e. the determination of bf /tf /ε ratios, the ratio of flange width bf to flange thickness tf , where ε =(235/fy)0,5, the corresponding rotational behaviour, and level of plastic resistance for such sections.
Physical testing (47 bending tests on forme z sections)was undertaken in order to define the boundaries between the cross-section classifications required for plastic design (Fig.
4).
Class 4 sections (bf /tf /ε≥ 66 for z section) are incapable of mobilising plasticity in the member, as buckling dominates the available resistance at stress levels less than first yield. No plastic rotations are,therefore, allowed to develop.
Class 3 sections (45≤bf/tf/ε≤66 for z section may reach first yield but, again, buckling effects dominate the avail able moment resistance and only partial plastification can occur
Class 2 sections (bf/tf/ε ≥ 45 for z section lie on the boundary between Class 3 and Class 1 type sections. The full theoretical plastic moment resistance can be mobilised, but this cannot be maintained if plastic rotation develops.
Class 1 sections (25 ≤ bf/tf/ε ≥ 45 for z sections can become fully plastic and the full theoretical plastic moment can be maintained in association with plastic rotation up to a limiting value as defined by the 100% line in Fig. 4.
Fig. 4. Plastic rotation capacity in sheet pile - z section [19]
IV. RESULTS AND DISCUSSIONS In Fig. 1, schematics of the corrosion models process of Southwell et al, Melchers, Paik and Thayambali, Guedes and Garbator and Qui and Cui, are illustrated.
Southwell et al is a simple linear model which gives the maximum value of corrosion depth for a structural age between 25 and 100 years, the corrosion process also starts at initial time. Melchers model gives corrosion depth values greater than Southwell model until 75 years. For Guedes and Garbator model, the no-corrosion period is about 1.5 years, the transition between coating durability and the corrosion initiation is about 4 years.
For Paik and Thayambali model, the coating duration is described using lognormal distribution, the transition between coating durability and corrosion initiation is about 7.5 years.
For Qin and Cui model, the non corrosion period is about 1.4
100 80 60 40 20 0
8 7 6 5 4 3 2 1 0 8
7 6 5 4 3 2 1
0
Time (year)
Recommended loss of thickness (mm)
Undisturbed natural soils Polluted soils and sites A ggressiv e natural soils Non-compacted and non-aggressiv e fills Non-compacted and aggressiv e fills C ommon fresh w ater
V ery polluted fresh w ater in the zone of high attack Sea w ater in the zone of high attack Sea w ater in the intertidal zone
years than the corrosion accelerates to 25 years than a decelerate is noted, Qin and Cui model gives the lowest values of corrosion depth until 70 years.
Fig. 2 gives the recommended values for the loss of thickness (Eurocode 3 - Part 5) for different types of soils and waters versus required design working life from 5 to 100 years, values depend on aggressiveness of soils or waters. The loss of thickness due to corrosion at 5 years from 0.00 to 0.55 mm, are respectively for undisturbed natural soils and sea water in temperate climate in the zone of high attach. After 100 years, the loss of thickness due to corrosion for sea water in temperate climate in the zone of high attack, can reach 7.50 mm. As presented in Eurocode 3- Part 5 the highest corrosion rate is usually found in the splash zone or at the low water level in tidal waters. However, in most cases, the highest pending stresses occur in permanent immersion zone.
V. CONCLUSION
Eurocode 3 Part 5 allows for the use of plasticity in the design of teel sheet piles, at the ultimate limit state. How the occurrence of plasticity affects the structure’s behaviour, compared with the response when only elastic deformation is allowed, and how the ultimate limit state can be verified,when simple methods of design are used In the context of plastic design, the required z section can be sized based on the first mobilisation of the plastic moment.
Corrosion of sheet pile influence on the thickness tf and therefore on a new classification of steel sections (classe 1,2,3 or 4).
It is expected that this procedure can be easily applied to assist the risk-based inspection. Time to when sheet pile fail by ultimate strength varies in a wide range depending on the initial designs and corrosion severity at both local and global places.
A values which is given by Southwell et al, Paik et al, Melchers, Guedes and Garbator, Qui and Cui models can be defined, using a various experiences are consequently lower than recommended values of the loss of thickness due to corrosion according to the European standard.
Sheet pile wall movement and stress distribution depend on support conditions, and care should be taken to ensure that the maximum bending moments do not occur at the same level as the main corrosion zones.
References
[1] G. King, “Analysis of cantilever sheet-pile walls in cohesionless soils,” J Geotech Eng 121(9), 1995, 629–35.
[2] G.W. Clough, T.D. O’Rourke, “Construction induced movements of in situ walls,” In: ASCE specialty conference on design and performance of earth retaining structures, Ithaca (NY), 1990, p. 439–70.
[3] Ö. Bilgin, “Numerical studies of anchored sheet pile wall behavior constructed in cut and fill conditions,” Computers and Geotechnics 37, 2010, 399–407
[4] Eurocode 3 - “Design of steel structures - Part 5: Piling - EN 1993-5:2007 (E) ,” European Committee for Standardization, Brussels, 2007.
[5] H. Wall, L. Wadsö, “Corrosion rate measurements in steel sheet pile walls in a marine environment,” Marine Structures 33, 2013, 21-32.
[6] C. Soriano, A. Alfantazi, “Corrosion behavior of galvanized steel due to
typical soil organics,” Construction and Building Materials 102, 2016, 904–
912
[7] M. Yan, C. Sun, J. Xu, J. Dong, W. Ke, “Role of Fe oxides in corrosion of pipeline steel in a red clay soil,” Corrosion Science 80, 2014, 309–317 [8] R.E. Melchers, R.J. Jeffrey, K.M. Usher, “Localized corrosion of steel sheet piling,” Corrosion Science 79, 2014, 139–147.
[9] Y. Wang, J.A. Wharton, R.A. Shenoi, “Ultimate strength analysis of aged steel-plated structures exposed to marine corrosion damage,” A review, Corrosion Science 86, 2014, 42–60.
[10] C.R. Southwell, J.D. Bultman, J.C. Hummer, “ Estimating of service life of steel in seawater,” Seawater Corrosion Handbook, 1979, 87–374
[11] R.E. Melchers, “Corrosion uncertainty modelling for steel structures,”
Journal of Construction Steel Research 52, 1999, 3–19.
[12] R.E. Melchers, “Probabilistic models for corrosion in structural reliability assessment,” Part 2: Models based on mechanics,” Journal of Offshore Mechanics and Arctic Engineering 125, 2003, 272–280.
[13] Y. Garbatov, S.C. Guedes, G. Wang, “Nonlinear time dependent corrosion wastage of deck plates of ballast and cargo tanks of tanker,” Journal of Offshore Mechanics and Arctic Engineering 129, 2007, 48–55.
[14] R.E. Melchers, “Condition assessment of aged structures, Wood head Publishing Limited, 2008.
[15] S.C. Guedes, Y Garbatov, “Reliability of maintained corrosion protected plates subjected to non-linear corrosion and compressive loads,” Marine Structures 12, 1999, 425–445.
[16] J.K. Paik, S.K. Kim, S.K. Lee, “Probabilistic corrosion rate estimation model for longitudinal strength members of bulk carriers,” Ocean Engineering 25, 1998, 837–860.
[17] J.K. Paik , A.K. Thayamballi, “The strength and reliability of bulk carrier structures subject to age and accidental flooding,” SNAME Transactions 106, 1998, 1–40.
[18] J.K. Paik, A.K. Thayamballi, “Ultimate strength of ageing ships,”
Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment 216, 2002, 57–78.
[19] R.Hartmann-Linden, A. Kort, M. Meyrer, A.Schmitt, G.Sedlacek, F.Van tol, “Development of Unified Design Rules for Steel Sheet Piles and Introduction in Eurocode 3,Part 5,” CEC Agreement 7210-SA 127/523/840, Report to European Coal and Steel Community, 1997.
