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
=
†††††=††=
㔹
=
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
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ISBN 2

9600430

0

6,
Federation of the Belgian Cement Industry, Brussels, Belgium, 2003.
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I
NTERNATIONAL DU BETO
N.
CEB

FIP
M
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Uniform e
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Publication
136, CROW, Ede, the Netherlands, March 1999.
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VENCON2.0 soft
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reinforced concrete pavements (in Dutch).
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