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Bridge code calibration and assessment of existing bridges require an accurate knowledge of traffic load patterns. WIM data are useful for these applications, either to account for the current traffic loads or to assess the potential impact of future loads. Traffic load effects were calculated on two composite bridges, using WIM data of a French motorway, and the effect of an increase of the gross weight limit from 40 to 44 tons was assessed by a micro-simulation. Extreme values and fatigue lifetimes are calculated and compared for the current traffic and a traffic with the increased weight limit. The lifetime of details sensitive in fatigue could be decreased by 20% if the weight regulation is changed.
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WIM data to assess consequences of new traffic
regulations
Franziska Schmidt, Bernard Jacob
To cite this version:
Franziska Schmidt, Bernard Jacob. WIM data to assess consequences of new traffic regulations.
The Fifth International Conference on Bridge Maintenance, Safety and Management, IABMAS
2010, Jul 2010, France. 6p, 2010. <hal-00949085>
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WIM data to assess consequences of new traffic regulations
F. Schmidt & B. Jacob
Laboratoire Central des Ponts et Chaussées, France
ABSTRACT: Bridge code calibration and assessment of existing bridges require an accurate knowledge of
traffic load patterns. WIM data are useful for these applications, either to account for the current traffic loads
or to assess the potential impact of future loads. Traffic load effects were calculated on two composite
bridges, using WIM data of a French motorway, and the effect of an increase of the gross weight limit from
40 to 44 tons was assessed by a micro-simulation. Extreme values and fatigue lifetimes are calculated and
compared for the current traffic and a traffic with the increased weight limit. The lifetime of details sensitive
in fatigue could be decreased by 20% if the weight regulation is changed.
1 INTRODUCTION
Bridge load effects, stresses or damage and lifetime
in fatigue are assessed either by measurements, us-
ing stain gauges, extensometers and other tech-
niques, or by calculation, using traffic load data and
bridge models such as influence line or surfaces, if
the dynamic interactions are neglected (Bailey &
Bez 1996, Nassif & Nowak 1996, Jacob 1998, Jacob
& Labry 2002). The development and implementa-
tion of WIM techniques allowed to collect traffic
load data on a large scale and to use them for bridge
assessment (Jacob et al. 2002), instead of using
simulated data (Hwang & Nowak 1991).
In the late 1980’s and early 1990’s, some exten-
sive works were developed in Europe using traffic
data of various EU member states (Vrouwenvelder
& Waarts 1993, Bruls et al. 1996, O’Connor et al.
1998) to design the Eurocode “Traffic loads on
bridges” (CEN EN1991-2, 2003). Extreme loads and
load effects were considered to calibrate the general
load models (Flint & Jacob 1996) and fatigue calcu-
lation were performed to design the fatigue load
models (Jacob & Kretz 1996).
All these models and assessment methods assume
that the traffic loads and models (Ditlevsen 1994)
are stationary. But the traffic loads and volume in-
crease with time because of the development of the
road freight transport, and the increases of the truck
legal weight limits. Thus it is necessary to periodi-
cally re-calibrate the bridge code load models and to
re-assess the reliability of existing bridges against
the traffic loads. That is one of the goal of the WIM
systems installed all around the world on highways
and motorways. The methodology and some tools
are briefly reported here, and an application to the
assessment of possible consequences of an increase
of the truck gross weight limit in France from 40 to
44 tons is presented.
2 WIM DATA
Traffic data and loads are collected in France for
bridge engineering by WIM systems since the early
1980’s. However, with the recent development of a
national WIM network for overload screening and
enforcement (Marchadour & Jacob 2008), more reli-
able and accurate data are collected continuously on
the main highways and motorways. The traffic data
used in this study were collected on two adjacent
traffic lanes of the French motorway A9 near Mont-
pellier in South France, over a month in June 2009.
Figure 1 shows the gross vehicle weight distribu-
tions on the slow lane over one and two weeks.
Figure 1. Gross weight distributions on the slow lane of the A9
motorway, 1 & 2 weeks in June 2009.
Axle loads and spacing, speed and time of pas-
sage in 1/100 s are also recorded for each truck in
both lanes. The accuracy of these data are at least in
class C(15), but mostly in class B(10) of the Euro-
pean specifications of WIM (Jacob et al. 2002), i.e.
app. 95% of the gross weights are within ±10% and
of axle loads within ±15% of the static values taken
as the reference.
3 CALCULATION TOOLS
3.1 Influence lines
The effects of traffic on a bridge are usually calcu-
lated by applying traffic loads, either measured by
WIM systems or simulated by software, on influence
lines or surfaces. For local effects sensitive to the
wheel transverse location, WIM data shall contain
this information and an accurate influence surface,
i.e. a two-dimensional calculation, must be used. For
most of the global or semi-global and longitudinal
effects, such as bending moments at mid-span or on
pier, shear forces or pier reactions, one or a set of
parallel longitudinal influence lines (one per traffic
lane) are sufficient, and the traffic data lane by lane
are used. That is the case in this study.
The influence lines or surfaces are obtained nu-
merically, through 1-D bridge model or 2-D finite
elements calculations, or on site through experimen-
tation (by strain measurement on a bridge under a
known truck). In this later case, several parameters
are taken into account, such as the stiffness of the
pavement surface, sidewalks and safety barriers, that
are neglected in the numerical method.
The effects considered in this study are, for two
bridges:
The bending moment stress at mid-span of a sim-
ple supported 40 m span bridge, near Auxerre.
This is a composite bridge with two main steel
girders and a concrete deck.
The bending moment stress at mid-spans and on
piers of the Libourne 4-span bridge (respectively
48, 60, 60 and 48 meters-long). This is also a 2-
steel girder composite bridge.
The influence lines are given in MPa/MN in Fig-
ures 2 and 3. The dominant effects are in the lower
flange at mid-span and in the upper flange on pier.
These influence lines are those calculated for a load
applied along a steel girder. To obtain the influence
surface, they have to be combined with the trans-
verse influence line, given by Courbon’s coefficient.
Figure 2. Influence line of the bending moment stress at mid-
span of the lower flange of a girder, Auxerre composite bridge.
Figure 3. Bending moment stress influence lines at mid-span
and on piers of the upper and lower flanges, Libourne bridge.
3.2 Traffic data adaptation
The WIM data presented in section 2 contain two
adjacent lanes in the same direction, i.e. one slow
lane and one fast (passing) lane. Auxerre bridge
supports 3 traffic lanes (each 3.50m in width), in-
cluding 2 slow lanes (one in each direction) and one
fast passing lane. Libourne bridge has 2 slow lanes
(one in each direction).
Thus, the recorded data are adapted to fit to the
bridge operation conditions. The natural data of the
slow lane are applied on one slow lane of each
bridge, and the data of the fast lane on the fast lane
of Auxerre. The slow lanes in the other direction are
filled with the slow lane data shifted by 10 minutes,
which simulate a traffic correlated (same peak and
low hours) but with independent trucks.
3.3 CASTOR and POLLUX softwares
The POLLUX software, developed by the LCPC, is
a new and extended version of the former CASTOR
software (Eymard & Jacob 1989). It uses WIM data
and load effect or stress influence lines of any
bridge, and calculates the effects of the whole traffic
on this bridge (Figure 4). The traffic record may be
on one lane or on multiple lanes, and the software
may use one influence line per lane, or an influence
surface for the whole deck.
Figure 4. Software POLLUX: main screen and parameters.
Different modules of POLLUX perform successive
tasks:
Traffic data cleaner: the traffic data files, pro-
vided by WIM systems, are first checked and
cleaned if necessary. If some anomalies are de-
tected, the involved vehicles are deleted. For ex-
ample, vehicles with a length below 1.5 m or over
25 m, or with only one axle or more than 8 axles,
are eliminated. If the gap between two successive
vehicles is greater than 90 minutes, the system is
assumed to have failed and the time period is de-
leted. All these limits are defined by the user.
CASTOR, which became a sub-routine of POL-
LUX, calculates the effects of the traffic loads.
For each effect (set of influence lines for each
traffic lane), the time history of the effect is cal-
culated with a constant time step, chosen by the
user with respect to the influence line shape. All
the vehicles are assumed to be at a constant speed
of 20 m/s. Thus for a 100 m bridge length, to
sample the influence line by steps of 1 m, the
time step will be 0.05 s. The output of CASTOR
is a set of three histograms, which represent the
variations of the effects: (i) the mini-max histo-
gram (successive local minima and maxima), (ii)
the level crossing histogram, and (iii) the rain-
flow histogram (AFNOR 1993), only used for fa-
tigue assessment. The class width of these histo-
grams are chosen by the user.
The sub-routine “Extrap” extrapolates the traffic
load effects over any time period longer than the
traffic record period, assuming that the traffic is
stationary, as explained in section 4.1.
The sub-routine “Durvie” calculates the damage
and lifetime in fatigue, for a detail submitted to
the stress history resulting of the traffic loads ap-
plied to a stress influence line, as explained in
section 4.2.
4 EXTREME EFFECTS AND FATIGUE
This section describes the methods used by CAS-
TOR and POLLUX to extrapolate the extreme ef-
fects and to calculate bridge lifetime in fatigue.
4.1 Extreme extrapolated effects
The extreme load effects or stresses over the whole
planned or conventional lifetime of a bridge, are ne-
cessary to calibrate the bridge code load models or
to assess the reliability of a bridge submitted to traf-
fic loads. Depending on the considered limit state -
ultimate or serviceability limit state - and the human
or economical consequences of the bridge or part of
a bridge failure, and on the status of the traffic ac-
tion – main action or secondary action in a combina-
tion of actions -, an adapted return period is chosen.
The return period Rx of x for a random variable X,
which is assumed to represent successive independ-
ent occurrences of a random phenomenon, is the
mean time period between two occurrences of x. It
may be proved that if P[Max1iN(Xi)<x
α
]=
α
,
αα
α
NN
Rx
)1ln( (1)
if N +, and then if N + and
α
0.
The return period for the traffic load characteris-
tic value is 2000 years in the Eurocode, which corre-
sponds to a probability
α
=5% to be exceeded in a
lifetime N=100 years.
The traffic load effect extrapolation method was
initially proposed by (Jacob et al. 1989). It consists
in fitting the upper part of a Gaussian distribution to
the upper tail of the level crossing histogram and
then using the Rice formula (Rice 1954). The traffic
load effect is assumed to be stationary and Gaussian
(Ditlevsen 1994), and thus the mean rate ν(x) of up-
crossings the level x>0 is given by:.
(Rice formula) (2)
where , and are respectively the standard var-
iation of , and the mean of the process. Then it
may be shown that:
(3)
The user chooses a return period and a confidence
level for the Kolmogorov test applied to check the
fit of the Gaussian distribution on the upper tail of
the level crossing histogram (Cremona 2001). Then
the value x with the chosen return period Rt is given
by Equation 3.
4.2 Fatigue
The fatigue damage D of a detail is assessed using
Miner’s rule:
(4)
where is the number of cycles in the class of
the stress rain-flow histogram; is the number of
cycles at failure corresponding to in the S-N
(Wöhler) two slope curve defined by:
(5)
in the Eurocode 1993 Part 1-9 (CEN EN 1993-1-9,
2005), corresponds to cycles, so
. The conventional lifetime (in years)
of the detail is 1/TD, where T is the length of the
time period which corresponds to the rain-flow his-
togram.
5 COMPARISON OF TRAFFIC LOAD EFFECTS
DEPENDING ON THE WEIGHT LIMIT
5.1 Weight limits in the current French legislation
and future plans
In France, and in Europe for international transport,
the standard gross vehicle weight limit is 40 tons.
Some countries allow higher weights, such as 44
tons in the UK for 6-axle articulated trucks. In
France, there are a couple of derogations which al-
low 44 tons for 5-axle articulated trucks if: (i) 40 ft
containers are transported in a multi-modal journey,
(ii) the freight comes from or goes to a maritime or
inland harbor, where it is carried by ship, (iii) some
specified agricultural goods are transported during
specific seasons. Moreover, log trucks are allowed
up to 48 tons on 5 axles and 57 tons on 6 axles by
decree.
In 2008, the French parliament voted a law called
“Grenelle de l’environnement” to reduce the CO2
emissions and the fossil energy consumption. An ar-
ticle stated that road transport regulation shall be
adapted for that. In February 2009, the parliament
asked to the government to study the positive and
negative impacts of increasing the gross weight limit
to 44 tons. The main criteria to consider were road
safety, CO2 emission and energy consumption, traf-
fic congestion, and infrastructure (bridges and
pavement...) lifetime and maintenance.
5.2 Impact of 44 t trucks on traffic and bridges
For bridges, the first task was to compare the ef-
fects of a single 44 t truck to those of a 40 t truck.
Because the axle load limit would not be increased,
only medium span (15 to 40 m) bridges could be af-
fected, or 10 m continuous span bridge for bending
moment on pier. Shorter spans could not support a
whole truck at once. Longer spans are not so much
sensitive to a single truck. For medium span bridges,
the load effects would be increased by less than
10%, which is not too much critical for the extreme
loads and load effects on healthy bridges. However,
the impact of multiple presences (truck crossing or
overtaking) of 44 t trucks, or the effect on the fa-
tigue lifetime was to be investigated more in depth.
Therefore, it is necessary to make some assump-
tion on how the whole traffic would change with
new regulations and to assess the effects of this
whole new traffic. The very simple and crude as-
sumptions done here are: (i) the gross weight of
every heavy vehicle laying between 36 and 44 tons
would be increased by 10%, the additional weight
being uniformly distributed on all axes; (ii) all the
other vehicles would have the same load as before
(volume limitation or not enough freight to carry).
With these assumptions, a micro-simulation gen-
erated a “modified” traffic file named “44 t” derived
from the natural traffic record of the WIM system on
the A9 motorway, named “40 t”. Both traffics were
used with the influence lines introduced in the sec-
tion 3.1, to obtain the effects and their histograms.
5.3 Extreme load effects
The minimum and maximum bending moment
stresses induced in the lower flange of a main girder
of Auxerre bridge under the two week traffic of the
A9 motorway are given in Table 1, for the natural
traffic and for the modified traffic with 44 ton
trucks. The minimum values are negative because of
the Courbon’s coefficient of the opposite lane of the
considered girder. With the 44 ton truck modified
traffic, the extreme values computed are increased
by 6.5% (minimum) and 8.5% (maximum), i.e. less
then the gross weight increase of the fully loaded
trucks, because these extreme values are obtained
while two trucks are crossing each other, one of
them may exceed the legal load.
Using the level crossing histogram of the same
effect, and the Rice formula as explained in section
4.1, the minimum and maximum values are extrapo-
lated for return periods of 25, 50, 500, 1000 and
5000 years (Table 2). For the three chosen Kolmo-
gorov thresholds, β=0.9, β=0.95 and β=0.99, the ex-
trapolated values are the same; that means that the
simulations has converged (Cremona 2001). The
maximum stresses for a 2000 year return period, as
specified in the Eurocode 0 (CEN EN1990, 2002)
for traffic load characteristic values, are close to 100
MPa, which seems to be coherent with the bridge
design. However, the real local traffic on this bridge
is much lower and lighter than the A9 motorway
traffic.
Table 1. Extrema of the computed stresses, Auxerre, main
girder mid-span bending moment, lower flange, A9 traffic and
modified traffic with 44 ton trucks (2 weeks).
______________________________________________
σmin (MPa) σmax (MPa)
______________________________________________
40 tons -6.1 35.3
44 tons -6.5 38.3
______________________________________________
Table 2. Extrapolated minimum and maximum stresses, Aux-
erre, mid-span bending moment, lower flange, A9 traffic, for
different return periods.
______________________________________
_____
Rt (yrs) σmin (MPa) σmax (MPa)
___________________________________________
25 -6.1 67.2
50 -6.7 74.1
500 -7.1 93.4
1000 -7.3 98.5
5000 -7.6 109.3
___________________________________________
5.4 Fatigue damage
To assess the fatigue damage and detail lifetime, the
rain-flow histograms are used, with the S-N curves
and the Miners’ law (section 4.2). Figure 5 gives the
rain-flow histograms of the bending moment stresses
in the lower flange at mid-span for both traffics (40
tons and 44 tons) on Auxerre bridge. An increase of
10% of the peak abscissa (18 to 20 MPa) is visible
when the 44 ton trucks are introduced. Reversely,
the distribution shows a drop at 18 MPa in this case,
because truck gross weights between 36 and 40 tons
were increased by 10%, and thus, there are no more
trucks in this weight interval.
Figure 5. Rain-flow distributions of the stresses in Auxerre
bridges at mid-span, lower flange, both traffics.
Then the fatigue damage is calculated for the S-N
curves 56, 63 and 71 MPa (Table 3). The detail is
classified in class 71 but the flange is 70 mm in
thick, and therefore a reduction factor of:
77.070/25
4= leads to the class 56.
The annual damage is obtained by multiplying
the weekly damage by 50. The conventional lifetime
is the inverse of the annual damage. The lifetimes
for Auxerre bridge are given in Table 3 for both traf-
fics. The values are very short, but the traffic of the
A9 motorway, one of the busiest in France, is much
more severe than the local traffic around Auxerre.
The most important finding is the reduction of the
lifetime by almost 20% when the 44 ton trucks are
introduced. That gives an estimation of the effect of
such a change in the regulation for bridges.
Table 3. Auxerre bridge lifetime for A9 traffic, 40 or 44 t gross
weight limit.
______________________________________________
Lifetimes (in years)
____________ _____________
Fatigue class 40 tons 44 tons
______________________________________________
Class 56 10.1 8.5
Class 63 14.3 12.0
Class 71 20.1 16.9
_____________________________________________
Similar results are given for Libourne bridge, and
more precisely for the weld of the vertical stiffener
on the girder lower flange at mid-span of the first
span. The fatigue class is 60 after the reduction due
to the flange thickness. The calculated lifetimes are
given in Table 4 for both traffics. The lifetime with
the natural traffic is app. 55 years, and reduced to 45
years with the 44 ton trucks.
Table 4. Libourne bridge lifetime, 1st span, bending moment of
it.
the lower flange, for A9 traffic, 40 or 44 t gross weight lim
______________________________________________
Lifetimes (in years)
____________ _____________
Fatigue class 40 tons 44 ton
______________________________________________
Class 50 34.6 28.9
Class 56 48.9 40.8
Class 63 69.0 58.8
_____________________________________________
These calculations show a decrease of the life-
time by app. 20% with the 44 ton trucks, as with
Auxerre bridge.
6 CONCLUSIONS
Bridge code calibration as well as assessment or re-
assessment of existing bridges under traffic loads
require an accurate knowledge of the load patterns.
WIM data are very useful for these applications, ei-
ther to give an account of the current traffic loads or
to forecast the potential impact of future loads.
With the computer software POLLUX developed
in the LCPC, the stresses induced in a fatigue sensi-
tive detail of two composite bridges, the weld be-
tween a vertical stiffener and the lower flange of a
main girder, were calculated. The traffic of a heavy
trafficked motorway in south of France, measured
over two weeks by an accurate WIM system, was
used. The same traffic was then modified to account
for a possible change in the gross weight limit in the
French law, being increased from 40 to 44 tons for
articulated 5-axle trucks and road trains. Extrapo-
lated extreme values and lifetime in fatigue were
calculated for both traffics and bridges.
The increase of the extreme stresses was limited
to 6.5 or 8.5%, on a 40 m simple supported span
(bending moment at mid span effect), carrying three
traffic lanes. The multiple presence of more than
one truck in adjacent lanes and the passage of excep-
tional or overloaded trucks explain that this increase
is less than 10% (40 to 44 t).
The computed lifetimes in fatigue for both
bridges are rather short, because the real traffics on
these bridges are local traffics and much lighter than
the motorway A9 one. However, the reduction of the
lifetime, whatever the fatigue resistance (S-N class)
and the bridge, is close to 20%. This value seems
reasonable because of the non linearity of the fatigue
damage with the load, while not all of the trucks are
affected by the weight increase. Moreover, the carri-
ers claim that increasing the weight limit by 10%
would slightly reduce the number of trucks on the
roads. Thus, we can estimate the lifetime reduction
for fatigue sensitive bridges between 10 and 20%, if
the weight regulation is changed.
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... This has been done recently for impact studies on bridges, of the possible introduction in Europe of EMS (European modular system, articulated trucks 25.25 m in length and up to 60 t), or of allowing GVW up to 44 t in France. For this study, WIM data files recorded at representative locations in France have been used and realistic assumptions of traffic evolution if authorized GVW were increased from 40t to 44t have been made [14]. Fatigue calculations on a set of concerned bridges have shown that a reduction in lifetime of 10% could be get with the introduction of GVW up to 44 t. ...
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WIM has developed greatly in the last ten years and confidence in the accuracy of recorded data has increased significantly. Traffic data recently obtained from a number of representative European sites are used to re-calibrate the codified main load model of the European bridge loading code, Eurocode 1 Part 3. A wide range of real and virtual bridge forms were chosen for the study. Simulations were performed using free-flowing and jammed traffic. Load effects generated were determined and statistical extrapolations were performed, where appropriate, to determine characteristic values for the load effects. Some of the assumptions used in the derivation of the original loading model were reassessed. Résumé Le pesage en marche s'est largement développé lors des 10 dernières années, et la qualité et la précision des mesures ont progressé. Des données de charges récemment collectées sur plusieurs sites représentatifs Européens sont utilisées pour réajuster le modèle de charge général de l'Eurocode 1 Partie 3 (charges du trafic sur les ponts routiers). Un très grand nombre de sollicitations sur des ponts réels ou théoriques est considéré. Les calculs sont réalisés par simulation du passage des trafics, fluides ou encombrés. Des extrapolations sont faites pour déterminer les valeurs caractéristiques d'effets. Certaines hypothèses utilisées lors de l'élaboration du modèle de charge initial sont réanalysées. Zusammenfassung WIM hat sich in den letzten 10 Jahren stark entwickelt, und die Qualität und die Genauigkeit der Messungen haben sich erheblich erhöht. Verkehrsdaten, die in der letzten Zeit von einer Anzahl europäischer repräsentativer Stellen erhalten wurden, wurden verwendet, um das Lastmodell vom Eurocode 1 Teil 3 (Verkehrslasten auf Strassenbrücken) nachzukalibrieren. Eine sehr grosse Anzahl Beanspruchungen auf realen oder virtuellen Brücken wurde für die Studie gewählt. Simulationen wurden bei fliessendem und gestautem Verkehr durchgeführt. Statistische Extrapolationen wurden durchgeführt, um die charakteristischen Werte für die Beanspruchung festzulegen. Einige Annahmen, die in der Erstellung des ursprünglichen Lastmodells verwendet wurden, wurden neu analysiert.
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Bridge dynamic load is defined as the ratio of dynamic increment to static response. Field measurements are performed to determine the actual truck load effects and to verify the available analytical models presented in other papers. The objective of this paper is to present the results of these studies. The tests are carried out on four steel girder bridges. Measurements are taken using a weigh-in-motion (WIM) system with strain transducers. For each truck passage, the dynamic response is monitored by recording strain data. The truck weight, speed, axle configuration, and lane occupancy are also determined and recorded. A numerical procedure is developed to filter and process collected data. The dynamic load factor (DLF) is determined under normal truck traffic of various load ranges and axle configurations. The field measurements confirmed the results of analytical studies. The stress due to dynamic load is nearly constant and is not dependent on truck weight. Therefore, the dynamic load factor is reduced for heavier trucks.
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This paper deals with the analysis of dynamic loads in bridges. Models are developed for trucks, road surface (roughness) and the bridge. The statistical parameters are based on the results of surveys, tests and analysis. Truck parameters include the body (mass), suspensions, and tires. Road profiles are simulated using stochastic processes (power spectral density function). A bridge is treated as a prismatic beam. The Monte Carlo method is used to simulate the traffic on the bridge. Random variables include the truck type, total weight, axle distances, and speed. Calculations are carried out for steel and prestressed concrete girder bridges. The dynamic load factors for a bridge design code are calculated based on the 75 year mean maximum loads. The analysis is performed for single trucks and for two trucks (side by side). Dynamic loads are lower for heavier trucks and also lower for two trucks. The calculated static and dynamic deflections are presented in tables and graphs as a function of gross vehicle weight, span and axle distance. Simulated deflections indicate that the dynamic component is not correlated with the static component. Therefore, the dynamic loads are lower for heavier truck. It is also found that the dynamic loads for two trucks are lower than for single trucks.
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Chief Engineer of State Public Works, in charge of national road freight transport control, 1994 to 2005. Since 2005 in charge of inter-national cooperation on road control, and project leader for the implement-tation of the National WIM network for overload screening and vehicle weight enforcement. Graduated from Ecole Poly-technique and Ecole Natio-nale des Ponts et Chaussées. Since 1982 with LCPC as bridge engi-neer, expert in WIM, and now technical director for the infra-structure, road safety, and opera-tions. Chaired the COST323 Action, WAVE project, and involved in several projects on trucks. Abstract Based on the research work carried out for more than 10 years by the LCPC and CETE Est, and on the recent developments and progresses in WIM technologies, the Division for Sea and Transport of the Ministry of Transport (DGMT) decided to install a network of WIM systems on National Highways and Motorways to efficiently screen and enforce overloaded and speeding heavy vehicles, to ensure a fair competition, safer roads, and lower infrastructure damage. A call for tender was launched in 2005 for a first phase of at least 10 fully equipped WIM sites. This paper describes the organization and implementation of this network and its devices in the context of a rapid increase of the heavy vehicle traffic in France. A close cooperation between the DGMT, the LCPC, the CETE Est and the selected supplied (STERELA) ensures the success of this ambitious program.
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This paper presents and compares bridge lifetimes in fatigue for several heavy traffics, using traffic data recorded by Weigh-In-Motion (WIM) systems, and computed with CASTOR-LCPC software. CASTOR-LCPC was developed to compute traffic load effects on bridges, in order to assess structural design, to calibrate load models to be used in bridge codes, or to evaluate fatigue damages and lifetimes. Load effects (such as stresses) vs time, are computed using multi-lane traffic data files and theoretical or experimental influence surfaces. Among others, CASTOR-LCPC provides a "rain-flow'" histogram of the stress cycles, used to calculate fatigue l~fetimes, once combined with Miner's law. One detail of a common bridge structure sensitive to fatigue is considered in this paper: the welded join between a vertical stiffener and the main girder upper or lower flanges, of composite (steel-concrete) bridges. Seven existing French bridges are considered as examples. Three traffics were chosen, with different vehicle flows and mean loads, measured by WIM systems on trafficked motorways in 1997 and 2001; one traffic recorded in 1986 on the A6 motorway at Auxerre, and which was used for the Eurocode "Traffic loads on road bridges" (EN 1991-3) is also used for comparison.
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A load effect from the traffic load on a large bridge with a large interval of slowly varying nonzero influence on the load effect can be modeled as a Gaussian random process. The mean value function and the covariance function that completely determines the process can be obtained by modeling the traffic load along each lane as a translating white-noise field. On the basis of a realistic traffic theoretical modeling of instantaneous random positions of single vehicles as represented by their random weights, the paper derives formulas for the mean and intensity of the white-noise traffic-load field in terms of traffic parameters and vehicle weight mean and variance. The formulas cover the entire range of traffic from free Poissonian traffic to congested traffic with the full stop queue as a limit case. The standard level crossing rate approximation method, used for the distribution of the maximal load effect over a given period of time due to moving traffic of any type, is taken as an example of an application of the white-noise traffic-load model. In a companion paper, Ditlevsen and Madsen (in press, 1994) used the model to obtain the distribution of the maximal load effect during a given period of time due to the formation of standing queues on the bridge.
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This paper proposes a method for determining optimal fittings of the Rice formula to the tails of outcrossing rate histograms related to traffic load effects. An optimal fitting is obtained through a series of statistical tests between successive fittings and the histogram tails. Optimality is found when a confidence level β0 for the Kolmogorov test is verified. That provides the optimal number of class intervals to take into account the load-effect extrapolation under the hypothesis that the process is stationary and Gaussian. Extrapolations are given for minimal and maximal load effects for any return period. Some examples highlight the use of the method.
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The results of a study are described which aimed at the derivation of a traffic load model for the design of road bridges. Attention is given to the Ultimate Limit State, the Serviceability Limit State and the Fatigue Limit State under static and dynamic conditions. A set of measurements done in 1978 in Rheden, The Netherlands, served as the basis for the vehicle model. Starting from the measurements of 16,000 vehicles, statistical models for the weight of 16 types of lorry configurations were derived. An additional set of measurements done in 1985 at Moerdijk, The Netherlands, was used to derive a statistical model for the axle loads, once the vehicle type and the total vehicle load is given. Based on various sources, a probabilistic traffic flow model was constructed, comprising traffic intensities, lorry distances and lorry speeds for three types of traffic: free, congested and full stop, each of which governs the traffic flow during some part of the day. Given both models, design values with predefined probabilities were derived for the axle, tandem, tridem and vehicle loads and for distributed loads on single and multiple lanes of various influence lengths. The axle and vehicle loads were derived by direct calculation. The distributed lane loads were derived using a simplified numerical traffic model. For short periods (1, 10 and 30 days), this simplified model was verified by Monte Carlo simulations on the full model. The values obtained in the way described above can not be used directly in design. The vehicle data is very limited and comes from one place and one time. The traffic flow model contains many simplifications and assumptions. These effects have been taken into account by an extensive trend and uncertainty analysis.
Conference Paper
In this section we use the representations of the noise currents given in section 2.8 to derive some statistical properties of I(t). The first six sections are concerned with the probability distribution of I(t) and of its zeros and maxima. Sections 3.7 and 3.8 are concerned with the statistical properties of the envelope of I(t). Fluctuations of integrals involving I2(t) are discussed in section 3.9. The probability distribution of a sine wave plus a noise current is given in 3.10 and in 3.11 an alternative method of deriving the results of Part III is mentioned. Prof. Uhlenbeck has pointed out that much of the material in this Part is closely connected with the theory of Markoff processes. Also S. Chandrasekhar has written a review of a class of physical problems which is related, in a general way, to the present subject.22