The Dutch Structural Design Method for Jointed Plain Concrete Pavements

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The Dutch Structural Design Method for
Jointed
Plain Concrete
Pavements


Houben, L.J.M.

Delft University of Technology, Section Road and Railway Engineering,

P.O. Box 5048, 2600 GA Delft, the Netherlands, email:
l.j.m.houben@tudelft.nl






Abstract

In the Netherlands the analytical structural design of
jointed
plain concrete pavements has
developed

since the early eighties. The latest version of the design method was released early 2005 by CRO
W as
the software package VENCON2.0. This package not only includes
jointed
plain concrete pavements but
also continuously reinforced concrete pavements.

This paper describes the backgrounds of VENCON2.0

as far as it concerns jointed plain concrete
pavemen
ts
. First the inputs are briefly outlined: traffic loadings, temperature gradients, substructure and
concrete properties. The thickness design of
jointed
plain concrete pavements is based on Miner’s fatigue
damage analysis, applied for various critical loc
ations of the pavement, taking into account the traffic load
stresses and the temperature gradient stresses. The traffic load stresses are calculated with the ‘new’
Westergaard equation for edge loading, including load transfer at the edge

or
joint. The te
mperature
gradient stresses are calculated with a modified Eisenmann method.

Finally, for a case study the design results according to VENCON2.0 are presented, illustrating the effects
of various input parameters. For
jointed
plain concrete pavements the
only design result is the thickness
of the concrete slabs.




Keywords: Structural design, plain concrete pavements


1

Introduction

In this paper the backgrounds of the current Dutch method for the structural design of
join
ted
plain concrete pavements,
subjected to normal road traffic, are explained (STET,
2004; HOUBEN et al., 2006; STET et al., 2006). The design method is available as a
software package called VENCON2.0 (CROW, 2005) that was released early 2005 by
CROW.

The structural design of plain co
ncrete pavements is based on a fatigue strength
analysis, performed for various potentially critical locations on the pavement, i.e. the
free longitudinal edge, the longitudinal joint(s) and the transverse joint in the centre of
the wheel tracks. The analy
sis includes the traffic load stresses (calculated by means of
a Westergaard
-
equation, taking into account the load transfer in the joint or at the edge)
and the temperature gradient stresses (calculated by means of a modified Eisenmann
theory). Van Cauwel
aert’s multi
-
layer slab model is used to calculate the traffic load
stresses in bound bases (VAN CAUWELAERT, 2003).

Figure 1 gives an overview of the input and calculation procedure of the VENCON2.0

design method.




















Figure 1
-

Flow cha
rt of the structural design of plain/reinforced concrete pavements


according to the VENCON2.0 design method (HOUBEN et al, 2006)


As can be seen in Figure 1 the VENCON2.0 design method covers the structural design
of both jointed plain concrete pav
ements and continuously reinforced concrete
pavements. This paper only deals with jointed plain concrete pavements, which means
that the items 1 to 7 from Figure 1 are subsequently discussed in the chapters 2 to 8. In
chapter 9 some calculation results of
the VENCON2.0 design method are presented for
a jointed plain concrete pavement case study.


1. TRAFFIC LOADINGS:

Axle loads

Directional factor

Design traffic lane

Traffic at joints

2. CLIMATE:

Temperature



gradients




3. SUBSTRUCTURE:

Modulus of substructure


reaction




5. TRAFFIC LOAD


STRESSES:

Load transfe
r at joints

Westergaard equation

6. TEMPERATURE


GRADIENT STRESSES:

Eisenmann/Dutch method




7. THICKNESS PLAIN/REIN
-


FORCED PAVEMENT:

Miner fatigue analysis



9. REINFORCEMENT OF


REINFORCED PAVEMENTS:

Shrinkage and temperature

Tension bar m
odel

Crack width criterion

8. ADDITIONAL CHECKS


PLAIN PAVEMENTS:

Robustness (NEN 6720)

Traffic
-
ability at opening

10. ADDITIONAL CHECKS


REINFORCED PAVEMENT:

Robustness (NEN 6720)

Traffic
-
ability at opening

Parameter studies

4. CONCRETE:

Stre
ngth


Parameters

Elastic modulus




2

Traffic loadings

The traffic loading is calculated as the total number of axles per axle load group (> 20
kN) on the design traffic lane during the desired lif
e of the concrete pavement. In the
calculation is included:



the division of the heavy vehicles per direction; for roads having one carriageway the
directional factor depends on the width of the carriageway, for roads having two
carriageways the directional

factor is taken as 0.5;



in the case that there is more than 1 traffic lane per direction: the percentage of the
heavy vehicles on the most heavily loaded lane (the design traffic lane); this
percentage varies from 100% (1 lane per direction) till 80% (4
lanes per direction);



the average number of axles per heavy vehicle (Table 1).

In the case that no real axle load data is available, for a certain type of road the default
axle (wheel) load frequency distribution, given in Table 1, can be used. These frequ
ency
distributions are based on axle load measurements on a great number of provincial
roads in the Netherlands in the years 2000 and 2001. In the design method all the truck
axles are taken into account. Note that the highest axle load group in Table 1 is

200
-
220
kN!

Table 1 makes clear that also in the Netherlands there are quite some overloaded axles
and these really should be taken into account when designing a concrete pavement.


Table 1
-

Default axle load frequency distributions for different types o
f road


Axle load

group

(kN)

Average

wheel load
P (kN)

Axle load frequency distribution (%) for different types of road

heavily

loaded
motorway

normally

loaded
motorway

heavily

loaded

provincial
road

normally

loaded

provincial
road

municipal

m
ain
road

rural

road

public

transport

bus lane

20
-
40

15

20.16

14.84

26.62

24.84

8.67

49.38

-

40
-
60

25

30.56

29.54

32.22

32.45

40.71

25.97

-

60
-
80

35

26.06

30.22

18.92

21.36

25.97

13.66

-

80
-
100

45

12.54

13.49

9.46

11.12

13.66

8.05

-

100
-
120

55

6.51

7.91

6.50

6.48

8.05

2.18

100

120
-
140

65

2.71

3.31

4.29

2.70

2.18

0.38

-

140
-
160

75

1.00

0.59

1.64

0.83

0.38

0.38

-

160
-
180

85

0.31

0.09

0.26

0.19

0.38

0.00

-

180
-
200

95

0.12

0.01

0.06

0.03

0.00

0.00

-

200
-
220

105

0.03

0.01

0.03

0.00

0.00

0.00

-

Av
era
ge

n
umber

of
axles per heavy vehicle

3.5

3.5

3.5

3.5

3.5

3.1

2.5


Different types of tire are included in the VENCON2.0 design method:



single tires, that are mounted at front axles of heavy vehicles;



dual tires, that are mounted at driven axles, and somet
imes at trailer axles;



wide base tires, that are mostly mounted at trailer axles;



extra wide wide base tires, that in future will be allowed for driven axles.

Every tire contact area is assumed to be rectangular. In the Westergaard equation for
calculation

of the traffic load stresses, however, a circular contact area is used. The
equivalent radius a of the circular contact area of the tire is calculated by:


a = b √(0.0028*P + 51)



(Equation 1)


where:

b = parameter dependent on the type of tire (Table 2)

P = average wheel load (N) of the axle load group


Some tire type default frequency distributions are included in the design method (Table
2).


Table 2
-

Value of paramete
r b (equation 1) for different types of tire


Type of tire

Width of
rectangular
contact area(s)


(mm)


Value of
parameter b
of Equation 1

Frequency distribution (%)

roads

public transport bus
lanes

Single tire

200

9.2


39

50

Dual tire

200
-
1
00
-
200

12.4


38

50

Wide base tire

300

8.7


23

0

Extra wide


wide base tire

400

9.1


0

0


3

Climate

With respect to the climate especially the temperature gradients in the concrete
pavement are important. In the years 2000 and 2001 the temper
ature gradient has
continuously been measured on a stretch of the newly build motorway A12 near Utrecht
in the centre of the Netherlands. The
(
continuously reinforced
)

concrete pavement has a
thickness of 250 mm and the measurements were done before the po
rous asphalt
wearing course was constructed. Based on these measurements it was decided to
include the default temperature gradient frequency distribution shown in Table 3 in the
current design method.


Table 3
-

Default temperature gradient frequency dist
ribution


Temperature gradient class


(ºC/mm)

Average temperature
gr
adient ΔT (ºC/mm)
=
䙲equen捹⁤楳瑲ibu瑩tn
=
†††††=††
⠥E
=
M⸰MM=

=
M.MM5
=
†††††=†
M.MM25
=
†††††=††=

=
M⸰M5=

=
M.MN5
=
†††††=†
M.MN
=
†††††=††=

=
M⸰N5=

=
M.M25
=
†††††=†
M.M2
=
†††††=††=†
T.5
=
M⸰25=

=
M.MP5
=
†††††=†
M.MP
=

††††=††=†
5.5
=
M⸰P5=

=
M.M45
=
†††††=†
M.M4
=
†††††=††=†
4.5
=
M⸰45=

=
M.M55
=
†††††=†
M.M5
=
†††††=††=†
N.M
=
M⸰55=

=
M.MS5
=
†††††=†
M.MS
=
†††††=††=

M.5
=
=
=
4

Substructure

The rate of support of the pavement by the substruct
ure is an important parameter in
the structural design of concrete pavements. The substructure includes all the layers
beneath the concrete pavement, so the base, the sub
-
base and the subgrade. The rate
of support is represented by the modulus of substruct
ure reaction k at the top of the
base.

Starting point for the calculation of the k
-
value is the modulus of subgrade reaction k
o
at
the top of the subgrade. Among other things Table 4 shows the k
o
-
values that are used
in VENCON2.0.


Table 4
-

Modulus of sub
grade reaction k
o

of Dutch subgrades


Subgrade

Cone resis
-

tance q
c

(N/mm
2
)

CBR
-
value

(%)

Dynamic modulus of

elasticity E
sg

(N/mm
2
)

Modulus of subgrade
reaction k
o

(N/mm
3
)

Peat

0.1
-

0.3

1
-

2

25

0.016

Clay

0.2
-

2.5

3
-

8

40

0.023

Loam

1.0
-


3.0

5
-

10

75

0.036

Sand

3.0
-

25.0

8
-

18

100

0.045

Gravel
-
sand


10.0
-

30.0


15
-

40

150

0.061


To obtain the modulus of substructure reaction k at the top of the base, equation 2 has
to be applied for each layer (first the sub
-
base, then the bas
e):


k= 2.7145.10
-
4

(C
1

+ C
2
.e
C3

+ C4.e
C5
)


(Equation 2)


where:

C
1

= 30 + 3360.k
o

C
2

= 0.3778 (h
b



43.2)

C
3

= 0.5654 ln(k
o
) + 0.4139 ln(E
b
)

C
4

=
-
283

C
5

= 0.5654 ln(k
o
)

k
o

= modulus of su
bgrade/substructure reaction at top of underlying layer (N/mm
3
)

h
b

= thickness of layer under consideration (mm)

E
b

= dynamic modulus of elasticity of layer under consideration (N/mm
2
)

k = modulus of substructure reaction at top of layer under conside
ration (N/mm
3
)


The boundary conditions for Equation 2 are:

1.

h
b

≥ 150 mm (bound material) and h
b

≥ 200 mm (unbound material)

2.

every layer has an E
b
-
value that is greater than the E
b
-
value of the underlying layer

3.

log k ≤ 0.73688 log(E
b
)


2.82055

4.

k ≤ 0.16 N/mm
3



5

Concrete

Various concrete grades are applied in the to
p layer of concrete pavements (Table 5). In
the old Dutch Standard NEN 6720 (1995), valid until July 1, 2004, the concrete grade
was denoted as a B
-
value where the value represented the characteristic (95%
probability of exceeding) cube compressive strengt
h after 28 days for loading of short
duration* (f’
ck

in N/mm
2
). In the new Standard NEN
-
EN 206
-
1 (2001), or the Dutch
application Standard NEN 8005 that is valid since July 1, 2004, the concrete grade is
denoted as C
-
values where the last value represents
the characteristic (95% probability
of exceeding) cube compressive strength after 28 days for loading of short duration and
the first value represents the characteristic cylinder compressive strength at the same
conditions (Table 5).


Table 5
-

Dutch concr
ete grades used in road construction



Concrete grade

Characteristic (95% probability of exceeding) cube compressive
strength after 28 days for loading of short duration, f’
ck

(N/mm
2
)

B
-
value

C
-
values

B35

B45

C28/35

C35/45

35

45


Generally on heavily
loaded
jointed
plain concrete pavements, such as motorways and
airport platforms, the concrete grade C35/45 is used. On lightly loaded
jointed
plain
concrete pavements (bicycle tracks, rural roads, etc.) mostly concrete grade

C28/35
and sometimes C35/45 is

applied.


According to both CEB
-
FIP Model Code 1990 (1993) and Eurocode 2 (prEN 1992
-
1
-
1,
2002) the mean cube compressive strength after 28 days for loading of short duration
(f’
cm
) is:


f’
cm

= f’
ck
+ 8 (N/mm
2
)



(Equation 3)


For the structural design of concrete pavements not primarily the compressive strength
but the flexural tensile strength is important. In accordance with both NEN 6720 (1995)
and the Eurocode 2 (prEN

1992
-
1
-
1, 2002), in the VENCON2.0 design method the
mean flexural tensile strength (f
brm
) after 28 days for loading of short duration is defined
as a function of the thickness h (in mm) of the concrete slab:


f
brm

= 1.3 [(1600


h)/1000)] [1.05 + 0.05 (f’
ck

+ 8)]/1.2 (N/mm
2
)


(Equation 4)


The mean flexural tensile strength (f
brm
) is used in the fatigue analysis (see chapter 8).



___________

* loading of short duration:

loading during a few minutes


loading of long duration: static
loading during 10
3

to 10
6

hours, or



dynamic loading with about 2.10
6

load cycles


Except the strength also the stiffness (i.e. Young’s modulus of elasticity) of concrete is
important for the structural design of co
ncrete pavements. The Young’s modulus of
elasticity of concrete depends to some extent on its strength. According to NEN 6720
(1995) the Young’s modulus of elasticity E
c

can be calculated with the equation:


E
c

= 22250 + 250 ∙ f’
ck

(N/mm
2
) with 15
≤ f’
ck

≤ 65


(Equation 5)


For the two concrete grades applied in concrete pavement engineering, Table 6 gives
some strength and stiffness values. Besides some other properties are given, such as
the Poisson’s ratio (that pl
ays a role in the calculation of traffic load stresses, see
chapter 6) and the coefficient of linear thermal expansion (that plays a role in the
calculation of temperature gradient stresses, see chapter 7).


Table 6
-

Mechanical properties of (Dutch) con
crete grades for concrete pavement
structures


Property

Concrete grade

C28/35
(B35)

C35/45
(B45)

Characteristic* cube compressive strength after 28 days for
loading of short duration, f’
ck

(N/mm
2
)

35

45

Mean cube compressive strength after 28 days for
loading of
short duration, f’
cm

(N/mm
2
)

43

53

Mean tensile strength after 28 days for loading of short duration,
f
bt
(N/mm
2
)

3.47

4.01

Mean flexural tensile strength after 28 days for loading of short
duration, f
brm

(N/mm
2
): concrete thickness h = 180 mm




h = 210 mm



h = 240 mm



h = 270 mm



4.92

4.82

4.71

4.61


5.69

5.57

5.45

5.33

Young’s modulus of elasticity, E
c

(N/mm
2
)

31
,
000

33
,
500

Density (kg/m
3
)

2300
-

2400

Poisson’s ratio
ν
=
M⸱5=

=
M⸲M
=
Coefficient of linear thermal expansion α (°C
-
1
)

1∙10
-
5


=
1.2∙10
-
5

* 95% probability of exc
eeding


6

Traffic load stresses

The tensile flexural stress due to a wheel load P at the bottom of the concrete slab
along a free edge, along a longitudinal joint

or

along a transverse joint
of a jointed
plain
concrete pavement is calculated by means of t
he ‘new’ Westergaard equation for a
circular tire contact area (IOANNIDES, 1987):










3
2 4
3 1
4 1
1.84 1.18 1 2
3 100 3 2
cal
c
P
P
E h a
l n
h k a l


  
 
 

 

 
     
 
 

 
 
 



(Equation 6)


where:


P

= flexural tensile stress (N/mm²)

P
cal

= wheel load (N), taking into account the load transfer (Equation 7)

a
= equivalent radius (mm) of circular contact area (Equation 1 and Table 2)

E
c

= Young’s modulus of elasticity (N/mm²) of concrete (Equation 5 and Table 6)



= Poisson’s ratio of concrete (usually taken as 0.15)

h = thickness (mm) of concrete sla
b

k = modulus of substructure reaction (N/mm
3
) (Equation 2)

l =
3
4
2
12(1 )
c
E h
k



= radius (mm) of relative stiffness of concrete slab


The load transfer W at edges/joints is incorporated in the design of
jointed plain
concrete pavement s
tructures by means of a reduction of the actual wheel load P to the
wheel load P
cal

(to be used in the Westergaard equation) according to:




1 0.5/100 1
200
cal
W
P W P P
 
   
 
 




(Equation 7)


The contribution of the base
to the load transfer W has been determined by means of
the model for a slab on a Pasternak
-
foundation (VAN CAUWELAERT, 2003).

In the VENCON2.0 design method the following values for the load transfer W are
included:



free edge

of
jointed
plain concrete pav
ement (at the outside of the carriageway):

-

W = 20% in the case that a unbound base is applied;

-

W = 35% in the case that a bound base is applied;



longitudinal joints

in
jointed
plain concrete pavements:

-

W = 20% and 35% respectively at non
-
profiled c
onstruction joints without tie bars in


jointed
plain concrete pavements on a unbound and a bound base respectively;

-

W = 50% and 60% respectively at non
-
profiled construction joints with tie bars and


dowel bars respectively in
jointed
plain concrete p
avements;

-

W = 35% at contraction joints without any load transfer devices in
jointed
plain



concrete pavements;

-

W = 70% and 80% respectively at contraction joints with tie bars and dowel bars


respectively in
jointed
plain concrete pavements;



transve
rse joints

in
jointed
plain concrete pavements:

-

W = 20% and 35% respectively at non
-
profiled construction joints without dowel


bars in
jointed
plain concrete pavements on a unbound and a bound base



respectively;

-

W = 60% at construction joints with
dowel bars in
jointed
plain concrete pavements;

-

W = 80% at contraction joints with dowel bars in
jointed
plain concrete pavements;

-

W according to Equation 8 at contraction joints without dowel bars in
jointed
plain



c
oncrete

pavements:



W = {5.
log(k.l
2
)

0.0025.L

25}.logN
eq

20 log(k.l
2
)+0.01.L+180



(Equation 8)


In Equation 8 is:

W = joint efficiency (%) at the end of the pavement life

L

= length (mm) of concrete slab

k

= modulus of substructure reaction (N/mm
3
)

l

= r
adius (mm) of relative stiffness of concrete slab

N
eq

= total number of equivalent 50 kN standard wheel loads in the centre of the
wheel
track during the pavement life, calculated with a 4
th

power, i.e. the load
equivalency

factor l
eq

= (P/50)
4

with whee
l load P in kN


7

Temperature gradient stresses

In VENCON2.0 the stresses due to positive temperature gradients are only calculated
along the edges of the concrete slab (as, from a structural point of view, the weakest
point of the pavement always is some
where at an edge and never in the interior of the
concrete slab). Starting point for the calculation of the temperature gradient stresses is
a beam (of unit width) along an edge of the concrete slab (LEEWIS, 1992).

In the case of a small positive temperatu
re gradient

T the maximum upward
displacement due to curling of the beam is smaller than the downward displacement
due to the compression of the substructure (characterised by the modulus of
substructure reaction k) because of the deadweight of the beam.
In this case the beam
remains fully supported over the whole length. The flexural tensile stress σ
T
at the
bottom of t
he concrete slab along the edge or

joint is then equal to (Figure 2


left):



Figure 2
-

Effect of small (left)

and great (right) positive temperature gradient on the
behavior of a

concrete pavement


2
c
T
h T
E
 






(Equation 9
)


where:

σ
T

= flexural tensile stress
(N/mm
2
) at the bottom of the concrete slab due to a small


positive temperature gradient
Δ
T (°C/mm)

h = thickness (mm) of the concrete slab

α = coefficient of linear thermal expansion of concrete (usually taken
as 1.10
-
5

º
C
-
1
)

E
c

= Young’s m
odulus of elasticity (N/mm²) of concrete (Equation 5 and Table 6)


In the case of a
large

positive temperature gradient

T the maximum upward
displacement due to curling of the beam is greater than the downward displacement
due to the compression of the su
bstructure because of the deadweight of the beam. In
this case the beam is
only supported over a certain length C at either end. The flexural
tensile stress σ
T
at the bottom of the concrete slab along the edge

or

joint (assuming a
volume weight of the concrete of 24 kN/m
3
) is then equal to (Figure 2


right):


longitudinal edge:

5'2
1.8*10/
T
L h






(Equation 10a)


transverse edge:

5'2
1.8*10/
T
W h






(Equation 10b)


The slab span in the longitudinal direction (L’) and in the transverse

direction (W’) is
equal to:


C
L
L
3
2
'






(Equation 11a)


'
2
3
W W C
 






(Equation 11b)

where:

L = length (mm) of the concrete slab

W = width (mm) of the concrete slab

C = supporting length (mm), which is equal to (EISENMANN, 1979):


C = 4.5
h
k T


if C << L





(Equation 12)


The actually occurring flexural tensile stress at the bottom of the concrete slab due to a
temperature gradient ΔT at a free edge

or

joint is the smallest value resulting from the
Equations 9 and 10a (free edge or longitudinal joint) or the smallest value
resulting from
the Equations 9 and 10b (transverse joint.




8

Slab thickness of
jointed
plain concrete pavement

In the case of
jointed
plain concrete pavements on a 2
-
lane road the fatigue strength
analysis is carried out for the following locations of t
he design concrete slab:



the wheel load just along the free edge of the slab;



the wheel load just along the longitudinal joint between the traffic lanes;



the wheel load just before the transverse joint.

In the case of a multi
-
lane road (e.g. a motorway) th
e strength analysis is also done for:



the wheel load just along every longitudinal joint between the traffic lanes;



the wheel load just along the longitudinal joint between the entry or exit lane and the




adjacent lane.


T
he flexural tensile stress (

Pi
) at the bottom of the concrete slab due to the wheel load
(P
i
) in each of the mentioned locations is calculated by means of the Westergaard
equation (Equation 6), taking into account the appropriate load transfer (joint efficiency
W, Equations 7 and 8)

in the respective
edge/
joints.


T
he flexural tensile stress (

Ti
) at the bottom of the concrete slab due to a positive
temperature gradient (ΔT
i
) in each of the mentioned locations is calculated by means of
the Equations 9 to 12.

In the case of
jointed
p
lain concrete pavements the horizontal slab dimensions (length
L, width W) are predefined.


T
he structural design is based on a fatigue analysis for all the mentioned locations of
the pavement. The following fatigue relationship is used (CROW, 1999):


max
max
min
12.903 (0.995/)
log 0.5/0.833
1.000 0.7525/
i
i
brm
brm
i
brm
f
N with f
f




  





(Equation 13)


where:


N
i

= allowable number of repetitions of wheel load P
i

i.e. the traffic load stress

Pi
till


failure when a temperature gradient stress

Ti

is present


mini
= minimum occurr
ing flexural tensile stress (=

Ti
)


maxi

= maximum occurring flexural tensile stress (=

Pi

+

Ti
)

f
brm

= mean flexural tensile strength (N/mm
2
) after 28 days for loading of short duration


(Equation 4)


The design criterion (i.e. cracking oc
curs), applied on every of the above
-
mentioned
locations of the plain or reinforced concrete pavement, is the cumulative fatigue damage
rule of Palmgren
-
Miner:


i
i
i
N
n


= 1.0





(Equation 14)



where:

n
i

= occurring number of repetitions of wheel load P
i
, i.e. the traffic load stress

Pi
,



during

the pavement life combined with a temperature gradient stress

Ti

due to



the

temperature gradient
ΔT
i


N
i

= allowable number of repetitions of wheel load P
i
, i.e. the traffic load stress

Pi
, till


failure combined with a temperature gradient stress

Ti

due to the temperature


gradient ΔT
i



Lateral wander within a traffic lane is taken int
o account when analyzing a transverse
joint or crack, with 50% to 100% of the traffic loads driving in the centre of the wheel
track.

When analyzing a longitudinal free edge or longitudinal joint the number of traffic loads
just along the edge or joint is
limited to 1% to 3% (free edge) or 5% to 10% (every
longitudinal joint) of the occurring total number of traffic loads on the carriageway (so
not the design traffic lane).


9


Design examples for case study

In this chapter, design results obtained by means

of the program VENCON2.0 for a
specific case will be presented. The case concerns a
jointed plain concrete pavement
for a
7.5 m wide 2
-
lane provincial road.


Because the width of the pavement is more than 4.5 to 5 m a longitudinal contraction
joint is req
uired in the road axis to prevent uncontrolled (‘wild’) l
ongitudinal cracking. T
ie
bars are applied in the longitudinal joint
, yielding a
load transfer W = 70% (see chapter
6).


The following
jointed
plain concrete pavement structure is taken into account:



plain concrete slabs, width 3.75 m (equal to the lane width) and length 4.5 m (to limit
the ratio of length and width of the slabs); the transverse contraction joints are
provided with dowel bars, which means that the load transfer W = 80% (see chapter
6)
;



250 mm thick cement
-
bound base (E = 6000 MPa), that is not bonded to the
concrete slabs (safe assumption); the bound base results in a load tranfer at the free
edge of the pavement W = 35% (see chapter 6);



500 mm sand sub
-
base (E = 100 MPa);



subgrade wit
h E = 100 MPa which equals a modulus of subgrade reaction k
o

= 0.045
N/mm
3
.

The modulus of substructure reaction (k
-
value of subgrade, sub
-
base plus base) is
equal to the maximum value k = 0.16 N/mm
3

(see chapter 4, Equation 2).


The default temperature gr
adient frequency distribution of VENCON2.0 is applied
(Table 3).


With respect to the traffic loading, it is assumed that heavy vehicles are driving on the
road on 300 days per year. The heavy traffic is equally divided over the 2 traffic lanes.
The traffi
c growth is 3% per year. On average a heavy vehicle has 3 axles. The default
frequency distribution of the types of tire of VENCON2.0 is used (see Table 2, one but
last column).

It is assumed that 50% of the heavy vehicles on a traffic lane drives exactly
in the centre
of the wheel track. It is furthermore assumed that 2% of the heavy vehicles on the road
drives exactly along the edge of the pavement and that 10% of the heavy vehicles on
the road drives exactly along the longitudinal joint.


In the calculat
ions the following parameters are varied:



the concrete grade: C28/35 (B35) or C35/45 (B45) (see chapter 5);



the axle load frequency distribution on the provincial road: heavily loaded provincial
road (Table 1, 5
th

column) or normally loaded provincial road

(Table 1, 6
th

column);



the number of heavy vehicles per day on a traffic lane in the 1
st

year: 10, 100 or
1000;



the design life of the pavement: 20, 30 or 40 years.


The
numerical
calculation results (
required
thickness of the concrete slabs) for the
join
ted
plain concrete pavement are given in Table
7
.
The calculation results are
graphically presented in Figure 3 and Figure 4.

The mentioned thicknesses include 15 mm extra concrete on top of the minimum
thickness calculated by means of the VENCON2.0 p
rogram.



In this case study the centre of the free edge of the pavement is always governing the
thickness design of the
jointed
plain concrete pavement. The centre of the longitudinal
joint and the centre of the wheel track at the transverse joint are

never decisive for the
design.


Table
7



Design thickness (mm) of plain concrete pavement for 2
-
lane provincial road
according to VENCON2.0


Concrete grade

C28/35 (B35)

C35/45 (B45)

Axle load frequency
distribution on
provincial road

Heavy

Normal

Heavy

Normal

Number of heavy
vehicles per day on
traffic lane in 1
st

year

10

100

1000

10

100

1000

10

100

1000

10

100

1000

Design life 20 years

234

247

263

224

238

253

208

221

235

199

212

227

Design life 30 years

237

250

267

227

241

258

211

225

239

202

215

231

Design life 40 years

239

254

271

230

244

262

213

227

243

205

218

234


plain concrete pavement, effects of concrete grade and axle load
frequency distribution
200
210
220
230
240
250
260
20
25
30
35
40
design life (years)
concrete slab thickness (mm)
C28/35, heavy, 100
C28/35, normal, 100
C35/45, heavy, 100
C35/45, normal, 100


Figure
3

-

Effect of
concrete grade, axle load frequency distribution and design life on


the required thickness of a jointed plain concre
te pavement; 100 heavy
vehicles on design traffic lane in 1
st

year


plain concrete pavement, effects of concrete grade and number of
heavy trucks per day
200
210
220
230
240
250
260
270
280
20
25
30
35
40
design life (years)
concrete slab thickness (mm)
C28/35, heavy, 10
C28/35, heavy, 100
C28/35, heavy, 1000
C35/45, heavy, 10
C35/45, heavy, 100
C35/45, heavy, 1000


Figure
4

-

Effect of
concrete grade, number of heavy vehicles on design traffic lane in 1
st



year and design life on
the required thickness of a jointed plain concrete
pavement; heavy axle load frequency distribution



It appears from
Table 7
, Figure 3 and Figure 4
that the most influencing factors on the
required jointed
plain concrete pavement thickness are:



the concre
te grade: concrete C35/45 results in 25 to 30 mm thinner slabs compared
to concrete C28/35 (due to the better fatigue behaviour, see Table 6 and Equation
13);



the heavy axle load frequency distribution (highest axle load group 200
-
220 kN, see
Table 1) requ
ires about 10 mm thicker concrete slabs than the normal axle load
frequency distribution (highest axle load group 180
-
200 kN);



the number of heavy vehicles: a 10 times greater number of heavy vehicles requires
about 15 mm thicker concrete slabs;



the desi
gn life: a 2 times longer design life requires only 5 to 10 mm thicker concrete
slabs.


References


CAUWELAERT, F. VAN.
Pavement Design and Evaluation.

ISBN 2
-
9600430
-
0
-
6,
Federation of the Belgian Cement Industry, Brussels, Belgium, 2003.


COMITE EURO
-
I
NTERNATIONAL DU BETO
N.
CEB
-
FIP

M
odel Code 1990.

Bulletin
d’information 213/214,
London, Thomas Telford, 1993.


CROW.
Uniform e
valuation method for concrete pavements (in Dutch).

Publication
136, CROW, Ede, the Netherlands, March 1999.


CROW.
VENCON2.0 soft
ware for the structural design of plain and continuously
reinforced concrete pavements (in Dutch).

CROW, Ede, the Netherlands, January
2005.


EISENMANN, J..
Concrete Pavements: Design and construction (in German).

Wilhelm Ernst & Sohn, Berlin
-
München
-
Düsse
ldorf, Germany, 1979.


HOUBEN, L.J.M.; BRAAM, C.R.; LEEST, A.J. VAN; STET, M.J.A.; FRENAY, J.W.;
BOUQUET, G.Chr..
Backgrounds of VENCON2.0 software for the structural design
of plain and continuously reinforced concrete pavements.
Proceedings 6
th

Internati
onal DUT
-
Workshop on Fundamental Modelling of Design and Performance of
Concrete Pavements, held September 15
-
16,
2006 in Old
-
Turnhout, Belgium. Delft
University of Technology, Section Road and Railway Engineering, Delft, the
Netherlands, 2006.



IOANNIDES
, A.M.; THOMPSON, M.R.; BARENBERG, E.J..
The Westergaard
Solutions Reconsidered.
Workshop on Theoretical Design of Concrete Pavements, 5
-
6 June 1986, Epen. Record 1, CROW, Ede, the Netherlands, 1987.


LEEWIS, M..
Theoretical knowledge leads to practical re
sult (in Dutch).

Journal

BetonwegenNieuws’ no. 89, September 1992, pp. 20
-
22.


NEN 6720:1995, TGB 1990.
Concrete Standards


Structural requirements and
calculation methods (VBC 1995), 2
nd

edition with revisions A2:2001 and A3:2004
(in Dutch).

NNI, Delft,

the Netherlands, 1995.


NEN
-
EN 206
-
1:2001.
Concrete


Part 1: Specifications, properties, manufacturing
and conformity (in Dutch).

NNI, Delft, the Netherlands, 2001.


prEN 1992
-
1
-
1, EUROCODE 2.
Design of concrete structures


Part 1: Genera
l
rules and rul
es for buildings.

Comitée Européen de Normalisation (CEN), Brussel,
July 2002.


STET, M.J.A..
Software for the structural design of elastically supported
pavements of plain and continuously reinforced concrete. Technical report on the
design models and for
mulae used in VENCON2.0 (in Dutch).

CROW, Ede, the
Netherlands, 2004.


STET, M.J.A.; LEEST, A.J. VAN; FRENAY, J.W..
Dutch design tool for jointed and
continuously reinforced concrete road pavements.

10
th

International Symposium on
Concrete Roads, Brussels,

Belgium, 2006.