Lifetime-Oriented Structural Design Concepts- P23 potx

labora-4.6.5.1.1 Experimental Investigation on Mechanical Concrete Properties According to the available construction drawings the concrete used for allstructural members tested now was

5,68 5,68 5,68

Fig 4.157 Location of drilling cores

drilled out from various sections of the structure for further laboratory ings (Figure 4.157) The total number of drilling cores was limited by logisticalreasons within the deconstruction process and in order to ensure the structuralstability also during and after the core-drilling

test-In order to get information on the actual concrete properties, tory tests were performed according to the same methods described in Sec-tion 3.2.1.2

labora-4.6.5.1.1 Experimental Investigation on Mechanical Concrete Properties

According to the available construction drawings the concrete used for allstructural members tested now was conform to the formerly strength grade

B 450 [3], which correlates at time of construction more or less with a C 30/37according to the current standards Due to lack of more detailed information

it was assumed that the concrete composition in all parts of the bridge was thesame The maximum size of aggregates could be determined on the drillingcores to 32 mm

4.6.5.1.1.1 Non-Destructive Tests

In order to determine the concrete’s stiffness, resp the dynamic elastic

Table 4.17 Dynamic elastic moduli Edyn (mean) and their standard deviations(SD) of the concrete after a service life of 50 years for the different members of thebridge

structural member number of specimens Edyn SD

of laboratory concretes tested at an age of 28 days without former loadings In

Thus, it can be assumed, that a main part of the determined standard

due to testing and materials inhomogeneities – by deviations due to concrete’spost-hydratation, environmental impacts and mechanical effects raised by thecyclic loading itself

4.6.5.1.1.2 Destructive Tests

In addition, static compression tests were performed on a couple of mens from the main structural members, mainly to determine the stress-strainrelation The results reveal that the mean values of the Young’s Modulus

speci-Estat, the ultimate strain  u as well as the compressive strength f care imately on the same level for the different structural members (Table 4.18).(This would confirm the assumption, that in all investigated members nearlythe same concrete had been used) On the other hand the scatters, e.g a three-

as well as their standard deviations (SD) after a service life of 50 years for thedifferent structural members of the bridge

structural

member

number ofspecimens

[-] [N/mm2] [N/mm2] [%0] [%0] [N/mm2] [N/mm2]main girder 7 38,800 6,700 2.17 0.33 72.4 18.5cross girder 6 39,400 6,300 2.02 0.27 70.6 13.7

comparison to results of common static compression 28 days-tests on commonseparately fabricated concrete specimens.

years Assuming, that the concrete has fulfilled the requirements to a B 450,resp C 30/37, at construction time, a post-hardening of 80 100 % can be

the value of a C 30/37 at an age of 28 days (Figure 4.158) At first, theseresults seem to be in contrast to the typical stress-strain relations of laboratoryconcrete at an age of 28 days (Figure 4.158) In the latter, the ultimate strain

post-hardening effect on the one hand leads to a significant increase in strength inthe bridge’s in-situ concrete, on the other hand the cyclic loadings reduced –analogue to investigations on laboratory test concretes – the ultimate strain

impaired by cyclic loadings only barely) Additionally also the shape of thestress-strain relation diverges significantly between laboratory concretes (at

28 days) and the in-situ concrete of the 50 year old bridge (Figure 4.158) Thetypical concave shape towards the strain axis was not observable at the in-situ concrete Thus, it could be proved also by these tests, that cyclic loadings

Fig 4.158 Comparison of stress-strain curves between bridge concrete (dashed

line) and laboratory concretes with different strengths at the age of 28 days (solidlines) [193]

300 µm

Fig 4.159 LM-micrograph of in-situ concrete

change the stress-strain curve from a concave form towards the strain axis to

a straight line, as it was also observed in cyclic tests on laboratory concretes(Section 3.2.1.2)

4.6.5.1.1.3 Microscopic Analysis

Furthermore, microscopic analyses partly proved the existence of cracks within the concrete microstructure caused by cyclic loading (Fig-ure 4.159) The path of these microcracks are similar to those of laboratoryconcretes (Section 3.2.1.2), which were subjected to about 600,000 load cy-

microcrack-ing starts in the transition zone between cement paste and coarse aggregategrains By the continuous cyclic loadings a prolongation of these microcracksthrough the cement paste was raised However, it must be emphasised that theexistence of microcracks significantly was depending on the extraction pointwithin the respective drilling core, i.e samples without any microcracks wereobserved as well

justed to 0.675 f c and 0.10 f c, respectively Altogether, sixteen specimens weresubjected to cyclic loading using the test setup described in Section 3.2.1.2

Seven of these in-situ specimens failed already within a comparatively lownumber of load cycles between 652 and 307,000 Other ones, however, resistedmillions of load cycles without any occurrence of failure In comparison tothese in-situ specimens, none of the laboratory concrete specimens of grade

C 30/37 failed before applying about 800,000 load cycles at the same testregime Hence, it can be revealed that the bridge’s in-situ concrete has a moresensitive behaviour to further cyclic loading in comparison to laboratory con-crete of C 30/37 at an age of 28 days

specimens during the cyclic tests is illustrated (Figure 4.160, left) On three

of these specimens the cyclic tests were carried out as long-term tests for12.0 millions to 27.8 millions load cycles (The others were tested only up to600,000 load cycles) At first, it became evident that the initial strains scatterwithin a wide range In order to reveal these differences it is more suitable

to take into account only the increase in strains during the cyclic loadings(”fatigue strains”, see also Section 3.2.1.2) For this purpose the fatigue strains

of the nine in-situ specimens up to 600,000 cycles are separately illustrated

in Figure 4.160, right The development of the fatigue strains within the first600,000 cycles are quite differently shaped for each specimen, which indicatesalso a wide scattering in the maximal bearable number of cycles up to failure

N f

Before the cyclic tests were started the mean value of the compressive

adjusted to 0.675 and 0.10, respectively

60 65 70 75 80

Fatigue strainefat,max [‰]

cyclic tests (Section 3.2.1.2), it was possible to calculate almost the actual

maxamount to 0.55 (QT 3-1, HT 11) as well as 0.64 (O 3)

Cyclic loadings lead to degradation processes combined with changes inthe mechanical concrete properties An adequate description of the changes inthe Young’s modulus, referred to the fatigue strain, is given in Section 3.2.1.2.Following this approach here, the Young’s modulus as well as the dynamicelastic modulus versus the fatigue strain are illustrated in Figure 4.161 for thethree long-term cyclic tests Thereby, it has to be considered, that the concretespecimens in this case are already about 50 years old and had imprintedalready a certain amount of fatigue strain within this period However, thisamount of the accumulated fatigue strains remains unknown in value and issurely different for each specimen

Nevertheless, at first roughly an almost linear relationship between theresidual Young’s modulus/dynamic elastic modulus resp and the fatiguestrain has been observed Although, the actual stress levels of the appliedloads on each specimen are not equal, the changes in the stiffness can be ap-proximated adequately by a common trendline This underlines again thatthe linear relationship between the residual stiffness and the fatigue strain

at S ∗

(Sec-tion 3.2.1.2) Furthermore, it could be proved that quite different accumulatedfatigue strains – as it can be assumed within the 50 years of service lifetime

Fig 4.162 Three dimensional Finite Element model of the road bridge at H¨unxe

Table 4.19 Number of elements of structural members

elements

of the bridge – have no significant influence on further development of theratios between residual stiffness and fatigue strain Additionally, it could beobserved that the dynamic elastic modulus is quite more influenced by thecyclic loading than the Young’s one In comparison to investigated normal andhigh strength laboratory concretes without any pre-loadings (Section 3.2.1.2),the development of the residual Young’s modulus versus fatigue strain of thebridge’s concrete follows nearly the same trendline

4.6.5.1.2 Finite Element Model

A three dimensional finite element model of the bridge has been developedfor numerical analysis of the structural state after 50 years of service (Fig-ure 4.162) To match the geometrical shape of the bridge as well as possibleand to model the connections of all structural members correctly, a quitelarge number of elements according to Table 4.19 has been required The size

of the resulting stiffness matrix is about one billion entries, which only could

be handled using bandwidth optimization and sparse storage schemes offered

by the finite element program [788] A three dimensional shell element able for geometrically and physically nonlinear analyses has been implementedfor calculation purposes (see e.g [421, 443]) This element employs a layeredapproach to combine the both composites of reinforced concrete The for-mulation of the finite element allows for up to four uniaxial steel layers tomodel reinforcement bars as well as the prestressing tendons in an accordantposition

suit-4.6.5.1.3 Material Model

To mirror the complex material behaviour of concrete correctly, a three

[444]) was used for the nonlinear finite element simulations of the structure

To avoid mesh-dependencies, the crack band and fracture energy approachhas been incorporated into the material model [95] Both, reinforcementsteel bars as well as the prestressing tendons are predominantly subjected

to tension Therefore, they are modeled, according to the layered elementconcept, as dimensionless steel layers, using an uniaxial elasto-plastic material

law with a damage component d Hence, the resulting stress-strain relations

for reinforcement bars and tendons read:

σ s = E s(1− d) s σ s = E s(1− d)( s +  ps) (4.423)

for the Young’s modulus of steel

4.6.5.1.4.1 Corrosion of the Reinforcement Steel Bars

A first impact of corrosion on structural response is the reduction of thereinforcement bars’ cross-section during time Assuming a constant corrosion

A s=π(D0− 2k s (t − t i))2

Within that time the corrosion attack front is presumed to permeate throughthe concrete cover to the steel bars If concrete cracks appear in structuralelements due to mechanical loading, corrosion initiates immediately thereafter

Fig 4.163 Applied corrosion model

as follows:

experiments of [181] and depicted here on the right hand side of Figure 4.163:

4.6.5.1.4.2 Fatigue of the Prestressing Tendons

The second long-term damage mechanism, namely fatigue of the steel

struc-tural design codes [182] The failure criterion is defined by the bilinear S-N

Δσ Rsk= Δσ

∗ Rsk1[106

S-N curves

This relationship has been modified to account for uncertainties of the

Fig 4.164 Modified S-N curves for steel and fatigue damage evolution function

in the brackets reflects a normalized fatigue life accumulated at different stress

account by a reduction of the material stiffness as follows:

E s f at= (1− d f at

4.6.5.1.5 Modelling of Uncertainties

During an ordinary design process, all input parameters are usually treated in

a deterministic way using just mean values as input Such an approach deniesthe stochastic character of material properties and damage driving forces abinitio In the context of generating input data for numerical simulations twoimportant questions arise The first one is, how many data sets have to begenerated to ensure a good representation of the population characteristics,namely mean value, standard deviation and type of distribution Thereby,

it should be considered, that the higher the number of sets is chosen, themore expensive – in terms of computation time – the presented approach will

be The second question concerns the method to be used for this purpose.Therefore the statistical moments mean, standard deviation, skewness andkurtosis have been regarded (Figure 4.165) Obviously, an impressive smallnumber of simulations seems to be sufficient for generation of input data withthe postulated characteristics taking Latin Hypercube sampling instead ofpure Monte Carlo method This even holds for the higher order statisticalmoments skewness and kurtosis Further, the generated data sets have beencompared to the expected values in Figure 4.166 The Gaussian shape of thedistributions of expected and generated values are in great accordance Justlittle differences in mean and standard deviation of the material parameterscompressive strength and elastic modulus were found

It is assumed that all material parameters obtained by testing reflect thebridge’s structural state after 50 years of service, shortly before its deconstruc-tion Therefore, the properties have to be transformed back to the structuralvirgin state, to serve as realistic input data for the lifetime simulations

Fig 4.166 Validation of input data

4.6.5.1.5.1 Long-Term Developement of Concrete Strength

cement type, the curing conditions and the ambient temperature For a

f c5% f cm f c95%

drilling cores CEB-FIP Modelcode 90 f c,50a ~ 1.28 x f c

Fig 4.167 Evolution of compressive strength and histogram of concrete strength

Table 4.20 Determination of compressive strength at time of construction

structural member cross girder main girder arches

Additionally, some data on long-term evolution of the compressive strength

is available in the literature Three long-time test series initiated about

100 years ago at the University of Wisconsin-Madison provide data ofvarious concrete mixtures A wide range of cement types, mix proportionsand ambient conditions has been investigated [819] An increase of thecompressive strength occurs predominantly in the first ten years Thereafter,the concrete strength remains nearly at a constant level of about 160% withrespect to its initial value This corresponds to the model code prediction,which is contrasted to the mean value of the experimental data stemmingfrom the long-time test series C in Figure 4.167 Due to lack of information

on the cement type of the bridge’s structural concrete, the measured concretestrength given in Table 4.20, is reduced by a factor of 1.60 to account forits evolution in time Differences between geometric shape of specimens andstandardised cylinders have been regarded as well

Table 4.21 Concrete strength grades according to German standards

DIN 1045 [1959] DIN 1045 [1978] DIN 1045-1 [2001]

4.6.5.1.5.2 Determination of Material Properties

According to the expertise and declarations on the available constructiondrawings, concrete conform to the formerly strength grades B 300 and B 450has been used to build the bridge As a side note, the lower grade B 300 hasonly been used for the concrete hangers These strength grades were defined

as mean values of at least three test specimen in the former German standardDIN 1045 [3]

To determine a realistic mean value for material parameter concretestrength, the notation there has to be transformed to the recent definition

of concrete strength classes The cube strength according to the six definedconcrete strength classes given in the old standard represent a mean value ofminimal three test cubes Since the fourth edition of the German standard re-leased in 1959 the classification of concrete classes has changed twice [4, 13]

By contrast, the classification of concrete today uses the 5%-fractile value

of the concrete strength to set the crucial limits The classification of bothused concrete types according to the different definitions in German standardsthrough time can be taken from Table 4.21

Assuming the compressive strength to be Gaussian distributed, the fractile value allows the calculation of the corresponding expected mean valueusing eq (4.431):

5%-f c,cyl,5% ≡ f c,cyl = 30 [N/mm2]

f cm,cyl = 30 + 1· 1.645 · s ≈ 38 [N/mm2]

f c,cyl,95%= 30 + 2· 1.645 · s ≈ 46 [N/mm2]

(4.431)

wherein s denotes the standard deviation of the compressive strength which is

cast-in-place concrete structures [694] In Figure 4.167 a histogram of the resultingconcrete strength population is given Obviously, the results gained by testingthe drilling cores fit to this population quite well

Further, the material properties Young’s modulus and tension strength aremodeled as fully correlated to the compressive strength Again the Model Code

1990 provides eq (4.432) and eq (4.433) to estimate those quantities with

parameters as small as possible

E(f ck) = 21500·

f ck+ 810

4.6.5.1.5.3 Modelling of Spatial Scatter by Random Fields

The spatial variability of relevant material properties and damage drivingforces can be described by the use of random fields To create the randomfields of those input parameters the midpoint approach, a type of the pointdiscretization methods, has been used to determine the input values for allelements in all simulations [863, 521] This procedure leads to an element-wiseconstant representation of each parameter in one simulation The isotropic

∞ is also known as linear dependency of values The other limit l H → 0 stands

for uncorrelated or stochastically independent behaviour A visualization ofthe effect of different correlation lengths on the bridges element mesh is given

in Figure 4.168 In this study the calculation of all random fields has beenperformed assuming the correlation length equal to the largest dimension of

the bridge - its length of 62.50 m Additionally, all parameters were assumed

to be independent and Gaussian distributed

of 20 eigenvalues only as depicted in Figure 4.168 [586] Thereby, the use

of even a limited number of Latin Hypercube samples grants an accuraterepresentation of the required statistical distribution

Fig 4.168 Random field dependency on correlation length and eigenvalues used

for reconstruction of correlation matrix

Each random field is finally represented as a sum of the mean value

4.6.5.1.6 Lifetime Simulation

In general, structural degradation modelling in our concept follows a two stepprocedure, displayed in Figure 4.169 First, the structure is stepwise subjected

to a design load combination consisting of dead (G) and traffic (Q) load as well

as the prestressing (V ) of the tendons At that load level, the external forces

are kept constant A further augmentation of the external load would lead

to structural failure due to static overloading The corresponding tangentialstiffness relation in the first domain reads:

where u, Δu denote the vectors of the system node displacement and its

vector of internal forces, both depending on the current system u and damage

d states The low indices (n + 1) indicate values incremented on step (n + 1).

A nonlinear structural simulation over the lifetime T , under the fixed load combination G + V + Q and the long-term degradation mechanisms described

above, follows in the second step The corresponding time-dependent systemgoverning eq (4.439) reads [622]: