Lifetime-Oriented Structural Design Concepts- P24 ppt

FE calculations with stochastically fluctuating fields of the initial void ratio: a dimensions and an example of a field e x, b differential settlement due to cyclic loading as a function of

Correlation length 0.5 m 2.0 m 20.0 m

Δ s

s σ

sstat scyc

σ av

( Δ s/s)cyc( Δ s/s)stat

a =

Nc = 105 cycles

Fig 4.182 FE calculations with stochastically fluctuating fields of the initial void

ratio: a) dimensions and an example of a field e( x), b) differential settlement due

to cyclic loading as a function of the differential settlement due to static loading

different fields e( x ) (see an example in Figure 4.182a) were tested Let s land

s rbe the settlements of the left and the right foundation, respectively (Figure

4.182a) The differential settlement Δs = |s l − s r | was divided by the mean

value ¯s = (s l + s r )/2 The ratio (Δs/¯ s)stat due to static loading up to σav

was compared to the ratio (Δs/¯ s)cyc describing the additional differential tlement accumulated during the subsequent 105cycles Independently of the

set-correlation length the differential settlement (Δs/¯ s)cyc resulting from cyclic

loading was observed to be approximately three times larger than (Δs/¯ s)stat

caused by static loading (Figure 4.182b) This finding can be attributed tothe fact that the settlement due to monotonic loading is proportional to theload, while the accumulation rate under cyclic loading is proportional to thesquare of the strain amplitude, i.e approximately proportional to the square

of the load Therefore, a cyclic loading has a smaller range of influence than a

monotonic loading and inhomogeneities of the field e( x) near the foundationshave a larger effect (i.e the differential settlements are larger due to averagingover a smaller region)

Keßler [428] used the high-cycle model to simulate a vibratory compaction

in a certain depth (Figure 4.183a, the pulling-out of the vibrator was notmodelled yet) The initial densitiy and the frequency were varied In thatcase, the implicit steps of the calculation were performed dynamically.Canbolat [168] determined the settlements of the abutment of a bridge(”H¨unxer Br¨ucke”) under 53 years of traffic loading The geometry of theproblem and the FE mesh are given in Figure 4.183b The profile of voidratio with depth was chosen in accordance with in-situ CPT measurementsusing correlations A special calculation strategy was used in order to applythe initial stress within the embankment [168] The traffic loading was esti-mated based on the general development of traffic in the period 1951 - 2004,with traffic measurements for similar streets and with an information about

4.6 Application of Lifetime-Oriented Analysis and Design 649

void ratio

e0 = 0.715

ID0 = 0.4

Nc = 4,000 infinite elements

vibrator

4 6 8 10

Fig 4.183 a) FE calculation of a vibratory compaction see Keßler [428], b) FE

calculation of the settlements of a bridge cp Canbolat [168]

the percentage of the different classes of vehicles The varying amplitudesdue to different classes of vehicles were collected in packages of a constantamplitude

The accumulation model was also used by Niemunis et al [580] for thecalculation of excess pore water pressures and settlements in a water-saturatedsand layer under earthquake loading This problem was studied using theFinite Difference Method A special numerical strategy was tested (Figure4.184a) The fast processes (propagation of shear wave) were decoupled fromthe slow processes (accumulation of the mean values, e.g excess pore water

pressure) for one period T of the harmonic excitation of the rock bed The

dynamic calculation of the shear wave propagation in the sand layer during the

first period T of excitation was performed with fixed values of σav (average

effective stress), uav (average excess pore water pressure) and eav (averagevoid ratio) At the end of the period, the change of σav, uav and eav during

T was calculated by means of the accumulation model For this purpose the strain amplitude εampl was obtained from the dynamic calculation The porewater dissipation was also calculated in a separate step, i.e decoupled from

the ”dynamic” and the ”cumulative” mode The values uav and σav were

modified over a period T (consolidation) The dynamic calculation of the wave

propagation during the second period of excitation followed using the modifiedvalues ofσav, uav and eav, and so on The introduction of special boundaryconditions lead to a reflection of the shear wave at liquefied layers Figure4.184b presents an example of a calculation, i.e the distributions of shear

strain γ, shear strain amplitude γampland excess pore water pressure uav with

depth z for 15 calculated periods T (N = 15) It has to be critically remarked, that the shear strain amplitudes mostly exceed γampl= 10−3(Figure 4.184b)

and thus lay in a range, which was scarcely covered by laboratory tests up tonow

0 T 2T 3T

Time t

Number of cycles N

−σv0

−σ v0

−σ v0

z

Fig 4.184 Calculation of the pore water pressure accumulation in a

water-saturated sand layer under earthquake loading (displacement amplitude uampl =

1 cm at the rock bed in a depth z = 100 m) after Niemunis et al [580]: a) numerical strategy, b) profiles of shear strain γ, shear strain amplitude γampl and excess pore

water pressure u with depth

Geogrid-reinforced soil structures under cyclic loading were studied by wanitaki & Triantafyllidis [65] (Fig 4.185a) In particular, a geogrid-reinforcedembankment on piles in soft ground was investigated In such systems the ver-tical loads are conducted into the piles via stress arches developing in the baselayer The cyclic loading was applied on the soil surface simulating traffic load-ing caused by trains Arwanitaki & Triantafyllidis demonstrated that cyclicloading leads to a weakening of the stress arches causing large settlements

Ar-A reduction of accumulated settlements with increasing number of geogridlayers was observed (Fig 4.185b)

The high-cycle model has been also applied to predict the long-term mations of wind power plant foundations The construction of many offshorewind parks is planned in the North Sea and the Baltic Sea during the nextyears The foundations of OWPPs are subjected to a high-cyclic loading due

defor-to wind and waves During its life time apart from many (millions or billionsof) cycles with small to intermediate amplitudes an OWPP is also subjected

to a few load cycles with large amplitudes (due to strong storms) Both the

large and the small cycles may cause permanent deformations However, the

small cycles may theoretically lead to a ”self-healing” of the structure, i.e.large deformations occuring during strong storms may be reduced due to

4.6 Application of Lifetime-Oriented Analysis and Design 651

t

10 20 30 40 50 60 Settlement s [mm]

70

control cycles

Fig 4.185 FE calculation of a geogrid-reinforced embankment under traffic loading

see Arwanitaki & Triantafyllidis [65]: a) geometry and loading, b) comparison of the

curves of settlement s(N c) for an embankment with three geogrid layers and a reinforced embankment

-35 -30 -25 -20 -15 -10 -5 0 5

Packege No.

1 2 3 4 5 6 7 8 9 10 12 14 16 18

210,000,000 49,000,000340,000,000 24,000,000 14,000,000 11,000,000

Fig 4.186 FE calculation of a monopile foundation of an offshore wind power plant

in the North sea compare Wichtmann et al [843]: a) geometry of the foundation, b)

FE model, c) idealized cyclic loading, d) increase of the horizontal displacement of

the monopile with increasing N c, calculation of load package No 16

subsequent millions of cycles with small amplitudes The long-term tion behaviour of the foundations of OWPPs is not well-understood yet Littleoperating experience exists and no established methods for a prediction of the

deforma-serviceability (e.g tilting after 20 years of operation) are available in the erature Experiences from existing offshore or onshore wind power plants orconventional offshore foundations cannot be easily adapted due to the largedimensions and large loads of the new OWPPs.

lit-Figure 4.186a presents an example of a monopile foundation, i.e the wind

power plant is founded on a single steel pile with a large diameter (usually >

5 m) The FE mesh is given in Figure 4.186b Since an uni-directional cyclicloading was studied the symmetry of the system could be utilized The ideal-ized loading resulting from wind and waves was grouped into packages withsimilar average value and amplitude (Figure 4.186c) Figure 4.186d exhibitsthat the high-cycle model predicts an increase of the horizontal deformations,

i.e an increase of the tilting of the OWPP with the number of cycles N c.The aim of future research will be to exploit the limits of foundation designfor extreme load events

Future Life Time Oriented Design Concepts

Authored by Friedhelm Stangenberg, Dietrich Hartmann, Tobias Pfister

5.1 Exemplary Realization of Lifetime Control Using Concepts as Presented Here

Authored by Friedhelm Stangenberg, Dietrich Hartmann, Tobias Pfister

In the following two possible applications of the lifetime control conceptsproposed within this book are examplarily presented

5.1.1 Reinforced Concrete Column under Fatigue Load

Authored by Friedhelm Stangenberg and Tobias Pfister

In this first example, a reinforced concrete column under static and fatigueload is investigated It is subjected to a static load case, which is assumed toappear once a year and a fatigue load case with one million cycles per year.The reliability of the structure as the major design matter is investigated inthe initial state and during the scheduled lifetime of 80 years The column isshown in Figure 5.1

A basic quantity for the estimation of the reliability is the scatter of terial and model properties and of the load: the compressive strength, thetensile strength, the stiffness, and fracture energy are assumed normally dis-

ma-tributed and fully correlated The scatter of the lifetime Nf according the

S-N -approach, as the basic quantity for the fatigue model, is correlated to

the scatter of the compressive strength like described in Section 3.3.1.2.2.1,see e.g eq (3.125) The static load is assumed normally distributed

staticcyclic

h = 4.00 m

e

P

P f

6 elments, each 10 concrete layers

Fig 5.1 Reinforced concrete column under fatigue loading

Fig 5.2 Degradation of the load-carrying-capacity and response surfaces atT = 0 a

and T = 80 a together with Monte Carlo simulation points

The reliability in the initial state is estimated with the response surfacemethod according to Section 4.4.2.3 The original design with 3 bars of di-

ameter 16 mm on each side results in Pf = 0.532 ×10 −6 and could thus be

accepted

The time-dependent reliability is estimated with the time-discretizationapproach according to Section 4.4.3.2 The failure rate is evaluated with theresponse surface method for each time instant and integrated over the number

of load events Figure 5.2 (left diagram) shows the simulated degradation

of the load-carrying capacity of the column due to increasing deformationand damage The right diagram shows the resulting response surfaces in the

5.1 Exemplary Realization of Lifetime Control 655

Fig 5.3 Time-dependent hazard function and time-dependent reliability: original

design (left) and improved design (right)

initial state and after 80 years lifetime, together with a cloud of Monte Carlosimulation points The developing of the values of the hazard function aswell as of the time-dependent reliability are shown in the left diagram in

Figure 5.3 After 50 years, EC1 demands a safety index of β = 3.8 Under

assumption of a normal distributed limit state function, this corresponds to

a failure probability of Pf = 7.24 ×10 −5 Like indicated in the diagram, this

failure probability is missed, so the design has to be changed As one possiblealternative, the number of reinforcing bars has been changed from 3 to 4 oneach side The resulting values of the hazard function and of the reliabilityare shown in the right diagram in Figure 5.3 This design could be accepted

5.1.2 Connection Plates of an Arched Steel Bridge

The lifetime-oriented design of an arched steel bridge has been discussed ready in Section 4.6.4, at full length Here, therefore only the general approachfor the lifetime analysis is recapitulated with respect to an implementationinto the practice The bridge contemplated in Section 4.6.4 is an arched steelbridge erected in M¨unster, Germany, in 2001 Structural details of this struc-ture, which are sensitive to fatigue, are the plates connecting the vertical tierods with the main girders

al-During the design phase of this bridge, the checking methods for fatigue cording to the German standard EC3 have been applied indicating that thestresses in the connecting plates are not exceeding the corresponding limit val-ues However, several connecting plates of the real structure showed macrocracks, already two years after the construction Hence, more sophisticated

ac-Par alle

l / dis tributed software sys tem

Level of optimization

e l a

s e m

i

t o r c i M

e l a

s e m

i

t o r c M

Loading / Load capacity

Damage model

Strucural detail

Damage evolution

F t

Level of reliability

Total structure

Load model

EA EI

Fig 5.4 Multi-level system approach followed during the lifetime analysis of the

arched steel bridge [826]

lifetime-oriented design concept methods have been developed to estimate liable lifetime values and, furthermore, investigate possible structural improve-ments

re-The design concept, suggested in Subsection 4.6.4, comprises two mainapproaches (Figure 5.4 and 5.5) which are to be explained more detailed Asdepicted in Figure 5.4, a multi-level system approach is chosen having thefollowing sublevels:

• Level of load model where external loads are described analytically

• Level of total structure where those structural members are identified that

are most sensitive with respect to fatigue

• Level of structural member for which a structural analysis and a

compu-tation of stress-time histories is carried out

• Level of fatigue in the critical structural components of the bridge

identi-fied according to used verification concepts for fatigue

• Reliability level for the time-variant limit state of fatigue

• Optimization level of the total structure as well as the identified weak

5.1 Exemplary Realization of Lifetime Control 657

F(t)

t

X 2

X 1

Fig 5.5 Multi-scale modeling and analysis of fatigue-related structural problems

tasks structural analysis and reliability analysis For that, different time scales

in the micro and macro scale are introduced and analyzed in an interlocked

fashion, as demonstrated in Figure 5.5 Within the micro time scale single load

events, i.e 10-min wind processes or vehicle crossing, are analyzed with regard

to their structural impact The numerical results of the structural analyses,carried out by means of a Finite Element Analysis for different parametersets of the corresponding load event, are stored in a file-based lookup table.Subsequently, the random sequence of these single load events is modelled in

the macro time scale represented by stochastic pulse processes Here, partial

damage values induced by each load event are estimated using stochasticallydefined S-N-curves Finally, the partial damages are accumulated analogously

to the pulse process until a predefined damage limit state is reached

The numerical methods, used in the above-named sublevels, have alreadybeen explained in section 4, together with exemplary results in Subsection4.6.4 In the given context, only the achieved lifetime increase of the ex-emplarily researched structural problem is highlighted For that, Figure 5.6shows the time-dependent evolution of computed failure probabilities of theconnection plate The comparison of the two plotted curves substantiates thedrastically increased lifetime of the optimized plate shape E.g at a reliability

level of Pf= 2.3%, the lifetime of the original shape (TL= 0.025 a) has been improved to TL= 5.6 a for the optimized plate shape.

Finally, the main benefits of the proposed multi-scale and multi-level

ap-proach can be summarized as follows: According to the multi-level system

approach, a well-organized and simplified model of the initially complex tural design problem is provided By that, suitable analytical solution methods

Service lifetime TS [a]

Welding perpendicular to plate

Bulk material Initial shape Improved shape

Fig 5.6 Comparison of resulting time-dependent failure probabilities of the

re-searched connection plate

for each different system level can be developed and considered efficiently A

benefit resulting from the multi-scale approach is a lifetime-oriented modelling

of actions and, additionally, a runtime-efficient analysis of the correspondentlifetime of the structure Particularly, the combination of this multi-scale ap-proach with parallelization techniques, as explained in Subsection 4.5.4, allowthe numerical analysis in a comparatively short response time

5.1.3 Conclusion

These short examples show, how the models and methods presented in thisbook can be applied to extend the design process according to standard designcodes These applications are time-consuming and need extensive knowledge.Thus, they can be applied only selectively for specific problems They canonly be established in engineering practice by degrees going along with en-hancement and improvement of the applied models and methods

5.2 Lifetime-Control Provisions in Current

Standardization

Authored by Friedhelm Stangenberg

In the Eurocodes (ECs) and other codes, links are implemented for ing later detailing of regulations concerning lifetime control

provid-5.3 Incorporation into Structural Engineering Standards 659

E.g EC1 mentions five “building classes” distinguishing different “designworking life”:

• temporary buildings,

• renewable structural components (e.g bearing elements),

• agricultural or similar structures,

• residential and business buildings,

• monumental and engineering structures (particularly bridges).

EC2 has chapters about “durability of reinforced concrete”, particularly withrespect to “environmental conditions” as well as to “chemical and physicalattacks” For steel reinforcement, EC2 mentions, in context with reinforcedconcrete structural longtime resistance: “Where required, the products shallhave adequate fatigue strength”

EC3, for steel structures, gives regulations for taking into account dation effects due to “fatigue”

degra-Further references to structural lifetime control can be found in other ern building codes

mod-However, these hints are only regulatory frames, which must be filled bydetailed precisions, in the next future The research work documented in thisbook aims to contribute to a scientific basis for lifetime control and to deriva-tions of regulations and specifications for later practical use There is a com-mon understanding that lifetime control—of course, combined with qualityassurance on a high level—must be introduced into structural design pro-cesses and into the management of existing structures

A reasonable and sufficiently simplified handling of the resulting tools ofthese lifetime related structural control concepts will be the next step in acontinuing development

5.3 Incorporation into Structural Engineering Standards

Authored by Friedhelm Stangenberg

The realization of lifetime control in structural engineering practise will befollowed by:

• effecting a change in structural engineering mentality;

• pointing out the significance of a reliable service-life control to owners,

users, licensing authorities, insurance companies, designing and controllingengineers;

• integrating service-life control aspects in quality assurance systems;

• transfer into codes, model codes and international regulatory principles of

structural engineering

1 DIN EN 206-1 Festlegung, Eigenschaften, Herstellung und Konformit¨at

2 DIN 1072 Straßen- und Wegbr¨ucken, Belastungsannahmen (1952)

3 DIN 1045 Bestimmungen f¨ur die Ausf¨uhrung von Bauwerken aus Stahlbeton

- Teil A (1959)

4 DIN 1045 Beton- und Stahlbeton: Bemessung und Ausf¨uhrung (1978)

5 DIN V ENV 1992-1-1 EC 2: Planung von Stahlbeton- und erken, Teil 1-1: Grundlagen und Anwendungsregeln f¨ur den Hochbau, Entwurf(1989)

Spannbetontragw-6 DIN 4030-1 Beurteilung betonangreifender W¨asser, B¨oden und Gase - lagen und Grenzwerte (1991)

Grund-7 EC 3: Design of steel structures Part 1.9: Fatigue, CEN (1993)

8 DIN V ENV 1994-1-1 EC 4: Bemessung und Konstruktion von werken aus Stahl und Beton, Teil 1-1: Allgemeine Bemessungsregeln und An-wendungsregeln f¨ur den Hochbau (1994)

Verbundtrag-9 EN 1991 Actions on structures - Part 2: Traffic loads on bridges (1995)

10 EN ISO 13918 Welding - Studs and ceramic ferrules for arc stud welding (1998)

11 EN ISO 14555 Welding - Arc stud welding of metallic materials (1998)

12 EN 206-1 Concrete - Part 1: Specification, performance, production and formity (2000)

con-13 DIN 1045-1 Tragwerke aus Beton, Stahlbeton und Spannbeton - Teil 1: messung und Konstruktion (2001)

Be-14 DIN 1045-2 Tragwerke aus Beton, Stahlbeton und Spannbetonn - Teil 2: Beton

- Festlegung, Eigenschaften, Herstellung und Konformit¨at - Anwendungsregeln

zu DIN EN 206-1 (2001)

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Raumtem-16 EN 1990 Grundlagen der Tragwerksplanung (2002)

17 prEN 12390 Testing hardened concrete - Part 9: Freeze-thaw resistance, ing (2002)

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27 DIN 18800-5 Stahlbauten, Teil 5: Verbundtragwerke aus Stahl und Beton,Bemessung und Konstruktion (2005)

28 EC 2: Design of concrete structures Part 1-1: General rules and rules forBridges (2005)

29 EC 2: Design of concrete structures Part 2 : Concrete Bridges-Design anddetailing rules (2005)

30 EC 3: Steel Structures Part 1-9: Fatigue (2005)

31 EC 3: Steel Structures Part 2: Steel bridges (2005)

32 EN 1991-1-4 EC 1: Action on structures - Part 1-4, General actions, Windactions, German version (2005)

33 EN 1992-1-1 EC 2: Design of concrete structures, Part 1-1: General rules andrules for buildings (2005)

34 E DIN EN 1994-1-1/NA1:2007-06 Nationaler Anhang - National festgelegteParameter, Eurocde 4: Bemessung und Konstruktion von Verbundtragwerkenaus Stahl und Beton, Teil 1-1: Allgemeine Bemessungsregeln und Anwen-dungsregeln f¨ur den Hochbau; 6 Entwurf (2006)

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