Lifetime-Oriented Structural Design Concepts- P4 pptx

• information about the influence of the dynamic behaviour of the vehi-cles and the bridge structures including information about the pavementquality, • information about the different typ

• information about the influence of the dynamic behaviour of the

vehi-cles and the bridge structures including information about the pavementquality,

• information about the different types of bridge structures and the

corre-sponding influence surfaces,

• principles for the model calibration for ultimate limit and fatigue limit

states and the damage accumulation under consideration of different terials, methods for the exploitation of the currently available traffic data,

ma-• development of large capacity and heavy load transports not covered by

the normal traffic models,

• the influence of future political decisions with regard to new traffic

concepts

2.3.1.2 Basic European Traffic Data

With regard to the cross border trade, load models must be based on trafficdata which are representative for the European traffic For example the devel-opment of the models in Eurocode 1-2 [9] is based on data collected from 1977

to 1990 in several European countries [487, 720, 530, 37, 157, 361, 158] Themain data basis with information about the axle weights of heavy vehicles,about the spacing between axles and between vehicles and about the length ofthe vehicles came from France, Germany, Italy, United Kingdom and Spain.Most of the data relate to the slow lane of motorways and main roads and theduration of records varied from a few hours to more than 800 hours Anotherimportant point is the medium flow of heavy vehicles per day on the slowlane In order to analyse the composition of the traffic for the development ofthe load model in [9] four types of vehicles were defined for the European loadmodel for bridges Type 1 is a double-axle vehicle, Type 2 covers rigid vehicleswith more than two axles, Type 3 articulated vehicles and Type 4 draw barvehicles Figure 2.23 shows the typical frequency distribution of these fourtypes resulting from traffic records of the Auxerre traffic in France The database of different countries shows that the traffic composition is not identical

in various European countries The most frequent types of heavy vehicles are

1 and 3 Especially in Germany the traffic records in 1984 show that lorrieswith trailers (Type 4) dominated the traffic composition at that time Thetraffic records of the Auxerre traffic (Motorway A6 between Paris and Lyon)gave a full set of the required information for the development of an Euro-pean load model In addition the Auxerre traffic includes a high percentage

of heavy vehicles and gives a representative data base for the development

of a realistic European load model Figure 2.23 shows the distribution of theabove explained types of heavy vehicles based on the Auxerre traffic records.Figure 2.24 shows the gross vehicle weight and the axle load distributions

for the representative traffic in Auxerre and Brohltal (Germany) where n30

is the number of lorries with G ≥ 30 kN and n10 the number of axles with

P ≥ 10 kN Especially for the development of models for the fatigue resistance

Type 1 Type 2

Type 4 Type 3

20 30 40 50 60 70 80

40 60 80 100 120 140 160

N

N

per 24 hours based on traffic data of Auxerre in France (1986)

of structures further traffic records regarding the number of heavy vehicles perday are needed These data were taken for the load model in [9] from severaltraffic records in Europe From all the traffic records only the record locations

Auxerre Brohltal

PA[kN]

30n

n

10

nn

total weight of heavy vehicles axle loadsPériphérique

Doxey

Forth

Forth Doxey

Fig 2.24 Gross vehicle and axle weight distribution of recorded traffic data from

England, France and Germany

Table 2.3 Statistical parameters of the traffic records of Auxerre (1986)

4,1 6,4 3,6

7,2 69

78 45

68 196

443 254

429

Gl

28,0 30,4 17,1

48,1 78

79 60

54 220

463 265

440

Gl

1,3 2,2 0,3

1,0 45

43 46

38 107

257 123

251

Gl

17,2 10,4 13,3

9,4 33

34 35

28 64

195 74

183

Gl

Lane 2 Lane 1

Lane 2 Lane 1

Lane 2 Lane 1

relative frequency

% standard deviation V

kN mean value P of the total

vehicle weight kN

G 1

Type 2

Type 3 Type 4 Go G1

Fig 2.25 Histogram of vehicle Type 3 and approximation by two separate

distri-bution functions based on traffic data of Auxerre in France (1986 ) and frequency

of the different vehicle types in the lanes 1 and 2

with a high rate of heavy vehicle in the total traffic are of interest, for examplethe traffic records of Brohltal and Auxerre in Figure 2.24

The histograms acc to Figure 2.23 can be subdivided into two separateddensity functions, where the mean values correspond to loaded and unloadedvehicles The statistical parameters of these distribution functions are given inTable 3.6 For the vehicle of Type 3 the distributions are shown examplarily inFigure 2.25 Furthermore for the development of the load model the frequency

of the different vehicle types in the lanes 1 and 2 is needed The records based

on the Auxerre traffic are given in Figure 2.25

The number of axles per vehicle varies widely depending on the ent vehicle manufactures Nevertheless the frequency distributions of the axle

differ-Table 2.4 Relation between gross weight of the heavy vehicles and the axle weights

of the lorries of types 1 to 4 in % (mean values and standard deviation)

Axle 1 Axle 2 Axle 3 Axle 4 Axle 5 Type of

G o 50,0 8,0 50,0 8,0 Type 1

G l 35,0 7,0 65,0 7,0

G o 40,5 8,4 36,2 8,8 23,7 7,3 Type 2

G l 29,4 5,7 42,8 4,2 27,8 5,3

G o 30,6 5,8 27,5 4,4 16,2 3,6 13,6 3,1 12,1 3,1 Type 3

G l 17,1 2,4 26,9 4,4 19,9 3,0 19,0 2,8 16,7 3,8

G o 31,7 5,7 31,3 5,8 13,4 4,1 13,7 3,5 9,9 3,3 Type 4

G l 18,5 4,1 29,1 4,2 18,9 3,6 18,3 3,4 15,2 4,3

Table 2.5 Distance of axles in [m] of the different types of vehicles (mean values

and standard deviation)

Axle 1-2 Axle 2-3 Axle 3-4 Axle 4-5 Type of

4,27 0,40 4,12 0,31 4,00 0,42 1,25 0,03

pacings show three cases with peak values nearly constant and very smallstandard deviations (vehicles of types 2, 3 and 4 with a space of 1.3 m corre-sponding to double and triple axles and with a space of 3.2 m corresponding totractor axles of the articulated lorries) For the other spacings widely scattereddistributions were recorded resulting from the different construction types ofvehicles

As mentioned before, the traffic data given in Figures 2.23 and 2.24 arebased on the traffic records of the Auxerre traffic in France These data gave

no sufficient information about the distribution of gross vehicle weight G on

the single axles Additional information from the traffic records of the Brohltal-Traffic in Germany (Highway A61) was used to define single axles weightsand the spacing of the axles These data (mean values of axle weight andaxle spacing and corresponding standard deviations) are given in Tables 3.7and 3.8

A further important parameter is the description of different traffic tions For the development of load models the normal free flowing traffic as

) 1 (  D O

a[m]f(a)

A typical example for the distribution of distances measured at motorwayA7 near Hamburg is given in Figure 2.26 and compared with an analyticalfunction for high traffic densities given in [720] The density function is ap-proximated by a linear increase up to 20 m due to the minimum distance, aconstant part up to a distance of 100 m because of convoys and an exponen-tially decreasing part for distances greater than 100 m for covering free flowingtraffic Another possibility is the approximation of the intervehicle distance

by a log-normal distribution [305] which is based on new traffic data [314]

In Figure 2.26 the value α of the constant part between 20 and 100 m,

giving the probability of occurrence for lorry distances less than 100 m, and

the value λ were obtained from traffic records of 24 representative traffics

in Germany Additional information regarding the probability of occurrence

of convoys are given in [267] These accurate models apply mainly to thedevelopment of fatigue load models Regarding load models for ultimate andserviceability limit states simplified models for the vehicle distances can beused on the safe side In case of flowing traffic the distance between lorries isgiven by a minimum distance required, which results from a minimum reactiontime of a driver to avoid a collision with the front vehicle in case of braking

On the safe side a minimum braking reaction time T s of the driver of one

second is assumed Then the minimum distance a is given by a = v · (Ts)

where v is the mean speed of the vehicles With this assumption also convoys

are covered The distance is limited to a minimum value of 5 m in case of jamsituations

2.3.1.3 Basic Assumptions of the Load Models for Ultimate and

Serviceability Limit States in Eurocode

As mentioned before, the load model in Eurocode 1 is mainly based on thetraffic records of the A6 motorway near Auxerre with 2× 2 lanes because

these measurements were performed over long time periods in both lanes ofthe Highway and because these data represent approximately the current andfuture European traffic with a high rate of heavy vehicles related to the totaltraffic amount and also with a high percentage of loaded heavy vehicles (seealso Figure 2.24) The European traffic records had been made on variouslocations and at various time periods For the definition of the characteristicvalues of the load model therefore the target values of the traffic effects have to

be determined For Eurocode 1-2 it was decided, that these values correspond

to a probability p = 5% of exceeding in a reference period R T = 50 yearswhich leads to a mean return period of 1000 years

For the determination of target values of the traffic effects additional pects have to be considered The measurements of the moving traffic (e.g bypiezoelectric sensors) include some dynamic effect depending on the rough-ness profile of the pavement and the dynamic behaviour of the vehicles whichhas to be taken into account for modelling the traffic The dynamic effects

as-of the vehicles can be modelled acc to Figure 2.27 taking into account themass distribution of the vehicle, the number and spacing of axles, the axlecharacteristic (laminated spring, hydraulic or pneumatic axle suspension), thedamping characteristics and the type of tires [720, 530, 238, 99, 330, 331] Thenormal surface roughness can be modelled by a normally distributed station-

ary ergodic random process The roughness is a spatial function h(x) and the relation between the spatial frequency Ω and the wave length L is given by

Ω = 2π/L [1/m] In the literature many surfaces have been classified by power spectral densities Φ h (Ω) acc to Figure 2.27 Increasing exponent w results in

a larger number of wave length and increasing Φ h (Ω) results in larger tudes of h(x) For modelling the surface roughness of road bridges w = 2 can

ampli-be assumed The quality of the pavement of German roads can ampli-be classifiedfor motorways as ”very good”, for federal road as ”good” and for local roads

as ”average”

While for the global effects of bridge structures an average roughness profilecan be assumed, for shorter spans up to 15 m local irregularities (e.g locateddefault of the carriageway surface, special characteristics at expansion jointsand differences of vertical deformation between end cross girders and theabutment) have to be taken into account These irregularities were modelled

in Eurocode 1-2 by a 30 mm thick plank as shown in Figure 2.27

As mentioned above, the axle and gross weights of the vehicles of the erre traffic were measured by piezoelectric sensors The calculations with fixedbase and the vehicle model acc to Figure 2.27 showed for good pavementquality, that the characteristic values determined from the measured grossand axle weights include a dynamic amplification of approximately 15% of

spring and damper

of the vehicle body mass of the axle spring and damper

Modelling of the vehicles

ent )

h (:

o )=4

ve ry goo d pa m ent )

h (:

o )=1

w o o h

: : ) : )

:o=1 m -1

w=2

+h -h +x[m]

Table 2.6 Statistical parameters of the corrected static traffic records of Auxerre

(1986)

mean value P of the total vehicle weight [kN]

standard deviation V[kN] lane 1 lane 2 lane1 lane 2 Type 1 Go

Gl

74183

64195

3123

2928Type 2 Go

Gl

123251

107257

4031

3935Type 3 Go

Gl

265440

220463

5142

6865Type 4 Go

G

254429

196443

3755

6064

36,95 41,0m 32,35

Fig 2.28 Measurements of the eigenvalues of the first mode of steel and concrete

Bridges [169], and comparison of theoretically determined dynamic amplificationswith measurements

to Figure 2.27 results can be obtained by dynamic calculations of the bridgeand be compared with measurements at bridges Figure 2.28 shows an exam-ple of the calculated and measured dynamic amplification of the Deibel-Bridge[720]

With the assumptions and models explained above, a realistic tion of the dynamic and static action effects due to traffic loads is possible In

determina-a first step rdetermina-andom generdetermina-ations of lodetermina-ad files determina-and roughness profiles of the pdetermina-ave-ment surface can be produced Each load file consists of lorries with distancesbased on constant speed per lane The main input parameters are the numberand types of lorries, the probability of occurrence of each lorry type, the his-togram of the static lorry weights of each type, the distribution of lorries toseveral lanes For the load files simply supported and continuous bridges withone, two and four lanes and different span lengths between 1 and 200 m with

pave-a representpave-ative dynpave-amic behpave-aviour (mpave-ass, flexurpave-al rigidity, mepave-an frequencyacc to Figure 2.28 and damping) have to be investigated in order to get re-sults which are representative for the dynamic amplification of action effects

of common bridges Three different types of bridges with cross-sections withone, two and four lanes were investigated for the load model in Eurocode 1-2.For the different lanes the traffic types acc to 3.10 were assumed, wheretraffic type 1 is a heavy lorry traffic for which motorcars were eliminated fromthe measured Auxerre traffic The traffic type 2 is the measured traffic of lane

Table 2.7 Different cross-sections and traffic types for the random generations

4

Lane 2: Type 3 Lane 3:Type 3 Lane 4: Type 2

1 in Auxerre, including motorcars and traffic type 3 is the measured traffic oflane two in Auxerre Detailed information about the generation of these loadfiles are given in [720, 530]

With random load files the static and the dynamic action effects of thedifferent bridge types can be determined The comparison of the static anddynamic action effects gives information about the dynamic amplification and

the dynamic factor Φ, influenced by the dynamic behaviour of the lorries,

the bridge structure and by the quality of the pavement The results of thesimulations can be plotted in diagrams which give the cumulative frequency ofthe action effects A typical example is given in Figure 2.29 for a bridge with

convoy v= 80 km/h convoy v= 60 km/h convoy v= 40 km/h

of loaded lanes on the dynamic amplification In case of flowing traffic thedynamic amplification of action effects depends significantly on the quality ofthe pavement, the number of loaded lanes, the span length and the type ofthe influence line of the action effect considered.

bending moment

M

Fig 2.31 Influence of the span length and the number of loaded lanes on the

dynamic amplification factor ϕ

Figure 2.31 shows the envelope of the calculated dynamic factors ϕ for

flow-ing traffic as a function of the span length For the development of the loadmodel in Eurocode 1-2 it was decided, that the dynamic amplification of theaction effects should be included in the load model because otherwise differentparameters like the traffic situation (flowing traffic or traffic jam, the qual-ity of the pavement, the number of loaded lanes and the type of the influenceline) had to be considered separately The calculations show additionally, thatthe dynamic amplification due to flowing traffic is only relevant for shorterspan length up to 50 m because for greater span length the condensed trafficwith low vehicle spacings or the traffic jam lead to extreme action effects Asexplained above the dynamic effects due to local irregularities were modelled

by a 30 mm thick plank, which leads especially for shorter spans to a cant additional dynamic amplification factor Figure 2.32 gives the additional

signifi-dynamic factor Δϕ due to irregularities which has to be considered especially

for fatigue verifications for short spans, e.g for end cross girders and membersnear expansion joints (see Figure 2.32)

With the random load files the static and the dynamic action effects andthe characteristic values of the action effects can be determined As mentionedabove, the characteristic values in Eurocode 1-2 correspond to a probability

p = 5% of exceeding in a reference period R = 50 years which leads to a

return period of T R = 1000 years The procedure for the determination isshown in Figure 2.33 The simulation of different bridge types gives a cu-mulative frequency of the considered action effects The characteristic valuescan be determined by extrapolation Finally these characteristic values can

be compared with a simplified characteristic load model

The load model for global effects in Eurocode 1-2 [9] consists of uniformlydistributed loads and simultaneously acting concentrated loads, so that globaleffects in large spans and the local effects in short spans can be covered by

static values of simulations

of simulations

extrapolation for the determination of the characteristic values

E k,dyn

E k,stat

influence line for ME

dynamic amplification factor:

ME

stat , k dyn , k

E E

Fig 2.33 Determination of the characteristic values of the action effects from the

random generations of loads

the same model taking into account the dynamic amplification, where average

pavement quality is expected The carriageway with the width w is measured

between kerbs or between the inner limits of vehicle restraint systems For the

notional lanes a width of w l = 3,0 m is assumed, and the greatest possible

number n lof such lanes on the carriageway has to be considered The locations

of the notional lanes are not be necessarily related to their numbering Thelane giving the most unfavourable effect is numbered as Lane Number 1, thelane giving the second most unfavourable effect is numbered as Lane Number

2 and so on For each individual verification the load models on each notionallane and on the remaining area outside the notional lanes have to be applied

on such a length and longitudinally located so that the most adverse effect isobtained

The Load Model 1 in Eurocode 1-2 is shown in Figure 2.34 It consists

of a double axle as concentrated loads (Tandem System TS) and uniformlydistributed loads (UDL-System) For the verification of global effects it can beassumed that each tandem system travels centrally along the axes of notionallanes For local effects the tandem system has to be located at the mostunfavourable location and in case of two neighbouring tandem systems theyhave to be taken closer, with a distance between wheel axles not smaller

than 0,5 m With the adjustment factors α Qi and α qi the expected traffic ondifferent routes can be taken into account

The last step in the development of the load model is the comparison ofthe characteristic action effects caused by the normative load model withthe characteristic values of the dynamic values of the real traffic simulations.Figure 2.35 shows this comparison for a three span bridge girder with one,two and four lanes

For the verification of local effects a Load Model 2 is given in Eurocode1-2 This model consists of a single axle load equal to 400 kN, where the

Application of the Tandem System for global

Fig 2.35 Comparison of the Load Model 1 in Eurocode -2 with the characteristic

values obtained from real traffic simulations

dynamic amplification for average pavement quality is included In the vicinity

of expansion joints an additional dynamic amplification has to be applied for

Table 2.8 Traffic data of different locations and characteristic values of gross and

axle weight [720]

country location year number nl

of lorries per day

weight of one axle kN

tandem axles kN

tridem axles kN

gross weight

of vehicle kN Germany Brohltal 1984 4793 211 357 434 853 Belgium Chamonix 1987 1204 192 355 480 724 France Auxerre 1986 2630 245 397 527 811 France Angers 1987 1272 192 340 456 670

Table 2.9 Different design situations and corresponding return periods and fractiles

Design situation Return period TR

Fractile of the distribution of action effects in

%infrequent 1 year 99,997

quasi - permanent 1 day 99,240

taking into account the local irregularities at expansion joints The contactsurface of each wheel can be taken into account as a rectangle of sides 0,35 mand 0,6 m

The evaluation of the traffic data of different locations lead to static

char-acteristic axle values Q k given in Table 3.11, where the characteristic values

relate to a return period T R of 1000 years (probability p of 5% in 50 years)

It can be seen that the characteristic values are depending on the location.Taking into account the dynamic amplification for short spans (see Figure2.31), this leads to the axle weight given in Eurocode 1-2

For serviceability limit states like limitation of deflections, crack width trol and limitation of stresses to avoid inelastic behaviour, different designsituations have to be distinguished The Eurocodes distinguish between in-frequent, frequent and quasi permanent design situations characterised bydifferent return periods The return periods and the corresponding fractile ofthe distribution of the dynamic action effects are given in Table 3.12

con-A change of the return period is equivalent with a change of the fractile of

the distribution (see Figure 2.36) The representative values F repof the action

effects can then be written as F rep = ψ Fk, where Fkis the characteristic value

As explained above, the characteristic values were determined with

ad-verse assumptions regarding the quality of the pavement Φ(Ω h) = 16 acc to

static values of simulations

ME

stat , k dyn , k

E

E I

representative valuesErep=\ E k

stat , rep dyn , rep

E

E I representative values: characteristic values:

ME

2 lanes

4 lanes

pave-ment quality with Φ(Ω h) = 16

Figure 2.27, the composition of the traffic (100% lorries in the first lane) and

a probability of traffic jam of 100% The combination values taking into

ac-count these assumptions lead to values Ψ T R, which only cover the influence of

the return period T R Figure 2.37 shows an example for the frequent designsituation [37] for average pavement quality It can be seen that the values

Ψ T R are dependent on the span length, the traffic situation and the number

of lanes The condensed traffic and traffic jam give the greatest values Ψ T R

The values Ψ T R can be reduced by additional factors to be more close toreality As mentioned before the quality of the pavement has a significantinfluence on the dynamic action effects On the basis of a good pavement

quality with Φ(Ω h) = 4 acc to Figure 2.27 which can be assumed e.g for