Simulation Of The Response Of Cracked Flexible Pavements To Surface Loads
M.S.A. Hardy
Department of Civil Engineering, University of Edinburgh, United Kingdom
ABSTRACT
Flexible pavements frequently show a loss of stiffness
prior to any visible surface distress or marked loss of
serviceability.
This loss of stiffness is detected by
stationary, or very slow moving, devices such as the Falling
The loss of
Weight Deflectometer or Deflectograph.
stiffness is frequently linked with the growth of fatigue
cracks from the bottom of the pavement's bound layers
towards the surface.
This paper contains finite element simulations of the
response of cracked pavements to loads applied to their
surfaces where, in practice, only the surface deflections can
be monitored. The aim is to investigate whether single
cracks originating from the bottom of the bound layers can
be detected by the response at the surface and under what
loadings.
INTRODUCTION
It is common practice to use surface deflection methods
to assess the structural condition of a pavement. In the UK
the most common systems in use are the Deflectograph and
Falling Weight Deflectometer. Both of these methods aim
to identify "the loss of structural strength due to repetitive
loading causing cracking and deformation and consequently
ingress of water" [1]. However, as the strength (stiffness)
of asphalt is very dependent on its temperature it is
necessary to correct the measured deflections for
temperature. This variation of surface deflection with
parameters other than structural condition leads to a range
of interpretations of any particular set of measurements.
When simulations of these tests have been made, they
have generally been carried out with programs that assume
that the pavement is uniform in its material properties along
any horizontal plane.
The modelling of structural
degradation is therefore interpreted as a reduction in the
stiffness of the layers where the cracking is taking place.
This averaging-out of the effect of cracking through the
layer disguises one property of a crack in the pavement that
makes it distinct from a reduction in stiffness due to
temperature effects. The presence of a crack in a pavement
leads automatically to a pavement response that varies as
the crack itself is traversed by a load. If it is possible to
detect these variations in response with position of load then
it may be possible to infer the presence of a crack directly
from the results, and distinguish it from an increase in
response due to changes in temperature.
Pavements with cracks have been analysed before [2-5]
but the focus of these studies has been the growth of cracks
in pavements and not their detection. The theory used,
. therefore, concentrates on analysis of stress concentrations
around crack tips, and does not easily give rise to analysis
of surface deflections.
One recent study has investigated the effects of cracks
on pavement deflections using finite element analysis (FEA)
[6]. The cracks, however, penetrate the full depth of the
asphalt layers, giving large effects on the measured
deflection.
The aim of this paper is to investigate the ch;mges in
surface deflections that might be caused by the appearance
of a crack at the bottom of the asphalt layers without
penetrating the surface, and to investigate what sort of
surface loadings might be used to enhance the ease of
detection of cracks.
CRACKED PAVEMENT MODELS
TIiE PAVEMENTS
Two basic pavement constructions have been
investigated. Pavement A would be typical of a minor road
and pavement B a motorway in the UK.
Both of these pavements were analysed using twodimensional, static, plane strain FEA with a range of
different crack sizes and configurations. This simplified
model would not be replicated in practice, but it has been
shown [7] that simplified, two-dimensional pavement
models can give good simulations of the true tbreedimensional case.
Road transport technology--4. University of Michigan Transportation Research Institute, Ann Arbor, 1995.
213
ROAD TRANSPORT TECHNOLOGY-4
'is
~5
fu
],4
c
] 3
Layered Half-Space
Plate
---_.-_.
Beam
----.
Table I. Pavement specifications
Young's
Poisson's
moduluslMPa
ratio
.
u
:; '2
Depth/m
Pavement A
Asphalt layers
Foundation
3000
140
0.35
0.4
0.2
1.9
Pavement B
Asphalt layers
Foundation
3000
140
0.35
0.4
0.4
(3
ID
u
0
't:
::0
11>
16.0
1.0
O.S
1.S
2.0
1.9
Distance from loDd (m)
Figure I a. The responses of pavement A from other
simulations [7J
1E-6
OOE+Q
~
-IE-Q
5
-2E-6
.§
-3E-6
g
-4E-6
~ -5E-6
-7E-6
+-____~------+-----~
.~,______
-2.0
-1.0
0.0
1.0
2.0
Distance from load (m)
Figure I b. The FEA response of pavement A.
Previous studies have shown that the response of a
pavement to oscillating or moving loads is smaller than the
response to a static, stationary load [8).
The material parameters chosen for the models here
were those fitted to real responses at low (between zero and
10Hz) frequencies [9} when the load is not travelling over
the surface. Whilst this may not be ideal for finding the
response of this particular pavement to moving loads, the
range of stiffnesses that are possible for asphalt mixtures,
and the variation that can be found with varying
temperature during the day, obviates the need to
characterise any particular pavement more accurately..
The FE mesh generated for the analysis contained a
total of 768 8-noded quadratic elements with a high
concentration of elements around the crack, especially the
crack tips. In practice, however, only surface measurements
can be made on roads and, as long' as the crack does not
approach the surface too closely St Venant's Principle
indicates that precise modelling in the region of the crack
tips does not have a serious effect on the surface
defonnation, as long as the overall effect of the crack is
modelled adequately.
The model extends to 10m each side of the crack, where
it is restrained to move only in the vertical direction. There
was negligible movement at this distance under any of the
loading conditions examined. The base of the model was
restrained in both horizontal and vertical directions.
214
The load is applied unifonnly over a 200mm wide strip.
This is likely to give an overestimate of the true surface
deflections as the load in this model extends infinitely,
rather than just over a small patch of the road surface.
The model parameters for the minor road (pavement A)
were taken from a previous investigation into modelling
road responses [7}. The parameters for the motorway
construction (pavement B) are based on the material
properties obtained from the minor road model, but with the
asphalt thickness increased to typical UK motorway
standards. The material parameters and geometry of the
models are shown in table I.
The surface deflections due to vertical surface loads
obtained using FEA for pavement A with no crack compare
favourably with those predicted for this pavement by other
verified models (see figure I). There is a small increase in
the .peak response which may be attributable to the plane
stram model used here with no adjustment for the
cylindrical symmetry of the real loading, as described
above.
EFFECT OF CRACK GEOMETRY
When a crack appears at the bottom of the asphalt
layers it will effectively grow both upwards into the asphalt
layers and also downwards into the granular layers. If this
downward growth did not occur there would be a large
tensile stress concentration at the interface of the asphalt
and granular layers. A granular material is unable to sustain .
tensile stresses so the material must be pulled apart, fonning
a downward propagating crack. This section investigates
the size of this crack and the sensitivity of the surface
deflection to its correct modelling.
Cracks extending parallel with the interface of granular
and asphalt layers were also simulated, but is was found that
these delaminating cracks are held closed by the application
of vertical surface loads, and therefore sliding betwe~n the
layers will be limited by friction.
In order to investigate the effect of vertical crack
penetration into the granular layers, pavements A and B
have been analysed with a crack penetrating 100mm into
the asphalt, and a variety of depths into the sub-base: 10, 30,
60 and 150mm. These pavements are referred to as
A 100/1 0, A 100/30, A100/60, A100/150, BIOO/IO, B100/30,
B I00160, and B 100/150.
Figure 2 shows the deviation in response of models
AIOO/30, AI00/60 and A 100/1 50 from A 100110. These
differences are approximately 1% of the total observed
MODELING PAVEMENT RESPONSE AND PERFORMANCE
deflection for the uncracked road showing a lack of
sensitivity to this depth of penetration.
Figure 3 shows the deviation of models BI00/30,
B 100/60 and B 100/150 from the B 100/1 0 response. Again
these differences are less than 1% of the total observed
deflection for the uncracked road (see figure 5 below).
In the rest of this paper the crack penetration into the
granular layers has been fixed at 100mm. The penetration
into the asphalt layers is varied for the two pavements
giving a total of nine different pavements for consideration.
These are referred to by the letter identifying the pavement
construction CA or B) and the penetration of the crack into
the asphalt layers e.g. Pavement B150 is pavement B with a
crack penetrating the asphalt layer by 15Omm.
g
E
5
c
.9
<J
.
t;:;
Cl.)
Cl
I
u
1--Al00/30
1' __ ' __ ' AlOO/6Q
____ Aloo/ 150 1
cc
c.. -4£.8
.~
-6£.8
-0
.E
-8£08
Q)
0.0
c
-2
'"
U
.c
-I
2
0
Distance (m)
1&6
0080
-1&6
5c
-213-6
.9
<J
-3&6
0:::
-4&6
....
Cl
.... _.. 8100 .
____ 8150
_ _ 8200
-5£..6
-6E-6
-2
-I
o
2
Distance (m)
Figure 5. Pavement B responses to loading over a crack.
AIOO/30; AIOO/60 3,IlQ AIOO/150 from AIOO/IO. These
differences are approximately 1% of the total observed
deflection for the uncracked road showing a lack of
sensitivity to this depth of penetration.
.,
-2&8
E
<>
----AIOOI
_ _ AlSO
Figure 4. Pavement A responses to loading over a crack.
~
.§.
5 OOE+O
C
<>
I
60E-8
2E-8
E
-5£..6
-6E-6
-2
4£08
~
I-AO
I....... A50 .
-8E-6
E
CENTRALLY APPLIED LOADS
When a vertical load is applied directly over a crack in
a pavement the crack will open up and the deflection of the
surface of the road will be larger than that found for an
uncracked pavement.
The deflection under the load for the nine pavements
are shown in figures 4 and 5. The deflection increases as
the crack grows, as expected, by as much as 20% for cracks
that are severe. However, it may be very difficult in
p@ctice t9 cJj~tinguish between the increase in deflection
due .to the crack compared with the changes due to
temperature, for example.
Figure 2 shows the deviation in response of models
-213-6
-3&6
-4&6
-7&6
g
RESPONSE TO VERTICAL WADS
1&6
0080
-1&6
-1
0
40E-8
20E-8
~
OOE+O
E
E
-20E-8
'"
<:
-40E-8
>.
-60E-8
-2
2
-I
2
0
Distance (m)
Distance (m)
Figure 6. Asymmetry in pavement A response caused by a
crack 100mm from the load
Figure 2. Change in pavement A responses with crack
penetration into the granular layers.
30£08
IE-8 """._ _ _ _ _ _ _ _ _ _ _ _ _ _ _-,
~
!
1_ -: :-:---:: ._.
50E-IO
0080 ~...
Q;
~ -50E-IO
~
Q.
'"
is
.:
~
c
~
U
--':--;"
p--
;,_.,- -•• -- -':-"::-:-:i~
••
I
I
I
1-
I
I
-IE-8':''
i-_BlOO/30
-2E-8 -"-
I······ - Bl00I6O I
I
-2E-8
1 ____
j
BlOOII50
g
20£08
E
10£08
5
~
0080
E
E
-10£08
<:
·20£08
<J
.,>.
. ____ ._ 8100
____ 8150
_ _ 8200
-30£08
-2
-2
-I
0
Distance (m)
Figure 3. Change in pavement B responses with crack
penetration into the granular layers.
2
-I
o
2
Distance (m)
Figure 7_ Asymmetry in pavement B response caused by a
crack 100mm from the load.
215
ROAD TRANSPORT TECHNOLOGY-4
~~~----------------~----------~
D
30&8
~ 20~
E
.s
c:-
OO£+<)
-10&8
'"
<:
-20&8
-30&8
-40~
~
~~
~.~
r---
10&8
;:;
5
S
>.
,:
, :'
VI
+--__-'-__
-2
-1
\!
15&8
.-.,
E
S
.s
'~
10&8
~
..... "IOO
i ____ AlSO,
5E-8
c:- OOE+{)
I
_ASO
E
S
-5E-8
<'"
-10&8
>.
_______ AlOO
I ____ AISO
~>lL---=:;==::::::.~
o
\
\
-15&8
-2
2
-1
Distance (m)
Figure 8. Asymmetry in pavement A response caused by a
crack 200mm from the load
~~
20&8
~
1O~
E
.:=-
15E-8
€
S
~
(I)
<:
~
5
·5
-10E-8
-20~
5E-8
____ B1S0
c:- OOE+O
_ _ _ 8100
5
:::
1 __
·2
·1
0
-5E-8
>.
<'" -10&8
____ B1S0
I
-40&8
8100
2
Distance (m)
Figure 9. Asymmetry in pavement B response caused by a
crack 200mm from the load
NON-CENTRAL LOADS
When a vertical load is applied to one side of a crack in
a pavement the crack may open up, giving rise to a response
that is not symmetrical about the load, or it may close which
will then give the same response as an uncracked pavement.
Whilst changes in the maximum deflection under the load
may be difficult to distinguish from environmental
influences over the time of the crack growth, it may be
possible to identify the changes in symmetry that occur due
to the existence of a crack. Figures 6 to 11 show the
asymmetry in the cracked road responses for loads applied
at distances 100mm, 200mm and 500mm from the crack. In
all figures the horizontal axis is measured from the crack
and the load is moved to the right. The asymmetry is
defined to be the response to the load minus the response
reflected about the load. If there was no asymmetry in the
response the response and its reflection would be identical
and the plot would show a zero, horizontal line.
When the load is close to the crack, as in figures 6
and 7, the load tries to open the crack and the. deflection at
the crack is larger than the symmetric deflection on the
other side of the load. Whilst the changes in response are
still small compared with the overall response, especially
for pavement B with small cracks, the asymmetry produced
may be more reliably detected than the overall change in
response that might be expected.
Figures 8 and 9 show the asymmetry produced when
the load is 200mm from the crack. The responses are very
similar in magnitude to the responses when loaded at
216
... ____ Bl00
;:;
____ ._. Bl00
-30E-8
(
_ _ BSO
10&8
'-'
OOE+O
2
0
Distance (m)
Figure 10. Asymmetry in pavement A response caused by a
crack 500mm from the load
30&8
""'
~
,
;:;
-15E-8
·2
-1
0
Distance (m)
Figure 11. Asymmetry in pavement B response caused by
a crack 500mm from the load
10Omm. This lack of sensitivity to distance of the load from
the crack is to be expected as there is no asymmetry when
the load is directly over the crack or when the load is a long
way from the crack.
Figures 10 and 11 show part of the response when the
load is 500mm from the crack. The analysis when the load
is this far from the crack is limited due to the construction
of the FE mesh and the software used. However, the small
part of the response shown is quite illuminating. In
figure 10 the response appears to go positive to the left of
the load, unlike the responses from this pavement when the
load was closer to the crack. Further examination of this
case reveals that the crack is in fact closing. The FE model
does not have any contact elements, and therefore this case
appears to show the road overlapping itself as the crack
opening becomes negative. This is clearly nonsense. A
correct interpretation when the crack appears to close is that
the response would be the same as for the uncracked road
and no asymmetry would result.
When pavement B is loaded in this way, however, the
crack is still observed to open and could be detected by the
asymmetry.
Whilst the asymmetry in the cracked pavement
responses are of similar magnitude to the changes observed
in the centrally loaded case, the differences are more clearly
identified in these cases because no reference is needed to a
response that must be theoretically derived or recorded from
the undamaged pavement.
2
MODELING PAVEMENT RESPONSE AND PERFORMANCE
8OE-8
6OE-8
~ 4OE-8
E
5 20E-8
,2
" OOE+O
U
., -20E-8
c::
-40E-8
0"
-60E-8
-80E-8
2E-8
g
E
lE-8
--'
OOEtO
..
,;;.-..._.
-.-~
.~
,S -1E-8
-2
-I
~
-2E-8
..
-<
-3E-8
a;
E
E
.••.••• ASO
____ AlOO
_ _ AlSO
>.
0
,
, .
-4E-8
',j
-5&8
-2
6OE-8~
~
I"' .. "
Al00
____ AlSO
-6&8
2
Distance (m)
Figure 12. Vertical deflection of pavement A subjected to a
shear load over the crack.
________________________________
_ _ ASO
-1
2
0
Distance (m)
Figure 14. Asymmetry in pavement A response caused by a
crack 100mm
from a shear load
____________________
2£..8~------
4OE-8
~
IE-8~~-=
~
20E-8
oB.,"'"
OOE+O
gE
,§,
..
c:::
Cl
-20E-8
-40E-8
,S -1E-8
.....•• BlOO
____ BlSO
a;
E
E
~
_ _ B200
-I
0
-2E-8
___ BSO
-3E-8
.•.•..• Bl00
____ BISO
-4&8
-< -5£-8
-60E-8
-2
__
OOEtO ~=----~::a..._
_ _ BSO
~
~
Distance (m)
Figure 13. Vertical deflection of pavement B subjected to a
shear load over the crack.
RESPONSE TO SHEAR LOADS
In order to investigate how the effect of the crack can
be exaggerated, the responses to surface shear loads have
been investigated. It was hoped that shear loads opening a
crack when applied in one direction but closing it when
applied in the reverse direction could be used more
effectively than the simple vertical loads which mayor may
not open the crack. The practicalities of applying these
loads are discussed in a later section of this paper.
When a shear load is applied directly over a crack there
is no tendency to open or close the crack at all because of
the symmetry of the situation. There is a tendency to
produce shear motion across the crack and in practice this
would be resisted by friction. The largest difference in
response to different crack sizes will be produced when the
coefficient of friction is zero. The responses of the two
pavements to shear loads applied directly over the crack and
to the right, are shown in figures 12 and 13.
For both pavements there is barely any visible effect of
increasing crack size. The deflections are also small
compared with the deflections due to vertical loads
(approximately 1%).
When loads are applied to one side of the crack there
will be a tendency for the crack to either open or close,
depending on the location and direction of the load and the
size of the crack. Figures 14 to 19 show the response of the
cracked pavements minus the response of the uncracked
pavement in each case.
Figure 14 shows that there is more deflection at the
crack for a load 100mm away when the crack is 50 or
100mm into the asphalt. However, when the crack is
_ _ B200
-6E-8+-____~--__~----~====~
2
-2
-1
o
2
Distance (m)
Figure 15. Asymmetry in pavement B response caused by a
Crack 100mm from a shear load
150mm (~ of the way through 'the asphalt) the response
between the crack and the load is increased, but the
response beyond the crack is reduced.
I~.----------------------------.
g
E
,s
~
a;
E
E
.
>.
<
14&8
12E-8
A
'I
10E-8
I \
8&8
I I
6£-8
4E-8
I
2E-8
I
OOEtO -I-_.-:!"".....,...:-=:o:.---7":':':'
I \
_ _ ASO
....... Al00
____ AlSO
-2£..8
-4E-8+-_____________-+______
-2
-1
~-----~
o
2
Distance (m)
Figure 16. Asymmetry in pavement A response caused by a
crack 200mm from a shear load
~
,s"
~
1i
§
>.
<'"
lE-8
lE-8
OOE+{)
-IE-8
-lE-8
-3E-8
-4E-8
-SE-8
-6E-8
-7E-8
____ BSO
....... Bloo
____ B1S0
___ B2oo
-2
-I
0
Distance (m)
2
Figure 17. Asymmetry in pavement B response caused by a
crack 200mm from a shear load
217
ROAD TRANSPORT TECHNOLOGY--4
4OE-8
~
I':
I
c
u
E
I':
1&6
I~I
30E-8
1 __
1\
/\
20E-8
A50
!....... AIOO
\\
/:
;:.
~.
-<'" OOE+{)
8OE-8
E
6OE-8
.,cE
4OE-8
E-
____ AlSO
I'~\
: '\
10E-8
g
E
>.
,\
I
20E-8
j
ell
-< 0080
-2
-1
0
-2
2
5&8
"'-.
-1
g
____ BI50
3E-8
E
_ _ B200
2&8
1E-8
3&8
C
2&8
-1E-8
-2
-I
o
I
....... BlOO
____ BISO
IE-8
E
>.
'"
0080
-<
---
-<'"
_ _ B50
4E-8
EuI':
I':
2
0
SE-8
....... BlOO
;:. 0080
-1E-8
2
Distance (m)
Figure 19. Asymmetry in pavement B response caused by a
crack 500mm from a shear load
This lack of response of a damaged pavement can be
explained by the fact that the load is not fully transferred
beyond the crack. The lack of response is therefore not a
reaction to strengthening by the crack but a response to lack
of load transfer beyond the crack.
All the other responses show increased deflection in the
region of the crack, with the responses increasing with crack
size. The asymmetry observed is up to 10% of the total
deflection.
Figures 16 and 17 show the same responses but with the
load 200mm from the crack. Again the anomalous results
for pavement A I 00 can be explained by a lack of load
transfer across the crack.
The reponse of pavement A I 00 is similar to the
responses when the load is 500rnm from the crack and these
are discussed below.
The lack of load transfer effect is not apparent on the
stiffer, deeper pavement B until loads 500mm from the
crack are examined.
The responses to loading 500mm from the crack are
shown in figures 18 and 19. In both these simulations there
is now a tendency for the crack to close rather than open.
As discussed above, this cannot occur. However, in
contrast to the vertical loading case above, it is possible to
reverse the load direction when this happens due to shear
loads and maintain an open crack giving asymmetry. The
results presented here are therefore possible, but should be
considered in the context of a reversed load.
218
\
Figure 20. Asymmetry in pavement A response caused by a
crack 100mm from a combination of loads
_ _ B50
4E-8
E
\
Distance (m)
Figure 18. Asymmetry in pavement A response caused by a
crack 500mm from a shear load
u
1
\
_/
Distance (m)
!C
I
I
••••... AlOO!
____ Alsol
-20E-8
-IOE-8
~
_ _ ASO!
jI
,I
-2
-1
0
2
Distance (m)
Figure 21. Asymmetry in pavement B response caused by a
crack 100mm from a combination of loads
PRACTICAL IMPLEMENTATION
It is not practicable to apply a shear load to a pavement
in isolation of a vertical load. The coefficient of friction
between a tyr~ and a dry road can be as high as 0.8 [10] and
it is therefore possible to generate combined lateral and
vertical loads in the road by, for example, using a
misaligned wheel running on a vehicle.
If two wheels were directed at opposite yaw angles to
the same line of travel, one of the tangential forces will tend
to close the crack, whilst the other will tend to open it
(unless both wheels pass directly over the crack). If the
crack closes then the response will be the same as the road
in its undamaged condition. A third wheel running along
the same line of travel but aligned with it could also be used
to assist in the analysis of the responses.
If a pavement is not cracked then the response to a
tangential load can be calculated from the response to a
combined tangential and vertical load and the response to a
vertical load. If two different combined loads are analysed
with the tangential components equal and opposite then the
tangential component of the response will be equal and
opposite, and antisymmetric about the load.
The cracked roads have been simulated with a vertical
load and with a combined vertical and tangential load. The
tangential load is half the magnitude of the vertical load, i.e.
mobilising a friction coefficient of 0.5. The tangential
components have been applied both towards and away from
the crack. Under each of these loadings the crack has been
MODELING PAVEMENT RESPONSE AND PERFORMANCE
80E-8
70E-8
6OE-8
C SOE-8
:::
-:::. 4OE-8
t:> 30E-8
~ 20E-8
~ IOE-8
<"' OOE+O
-IOE-8
-20E-8
j\
:I ~\
g
,
-2
-I
Such large deviations over such a wide range of
distances from a crack make investigation and
implementation of this sort of analysis more practicable.
There are obvious advantages over existing practice with
the penalty of mush more complex loading arrangements.
I-_ASO
....... AlOO
AlSO
\\ i ____
-A
CONCLUSIONS
o
2
Distance (m)
Figure 22. Asymmetry in pavement A response caused by a
crack 200mm from a combination of loads.
25E-8
_ _ B50
20E-8
~
lSE-8
t:>
IOE-8
E
5E-8
S
~
>.
-<
...••.. Bl00
____ BISO
_ _ B200
OOE+O
-5E-8
-2
-1
0
2
Dis tance (m)
I. FEA can be used to investigate the effects of cracks on
the surface response of pavements. Two dimensional
plane strain models may overestimate the true response
of the pavement, but are useful for examining trends and
investigating the initial feasibility of crack detection.
2. When a cracked pavement is loaded vertically at a
distance from the crack, there is a possibility of the
crack opening up and producing an asymmetric
response. The crack may, however, alternatively be
pressed closed by the load and a symmetric response
would result. An asymmetric response may be used to
identify a crack, but a symmetric response to vertical
loads does not indicate that no crack is present.
3. Shear loads at the surface give rise to antisymmetric
responses if the load is over the crack. If the load is not
over the crack the response will not be antisymmetric if
the crack opens and the presence of a crack can be
detected by the asymmetry.
4. For some pavement constructions, loadings and crack
Figure 23. Asymmetry in pavement B response caused by a
crack 200mm from a combination ofIoads.
examined and the response of the uncracked pavement has
been substituted if the crack appears to close.
The responses to the tangential components of the load
have been calculated as described above and the difference
between the theoretically perfectly antisymmetric responses
found. The asymmetry discovered is due to the opening or
closing of the cracks under the three different loading
conditions. The asymmetry discovered in this way could be
used in practice as these loads are all possible to apply to a
road surface.
Figures 20 and 21 show the asymmetl)' of the two
pavements when analysed in this way when loaded 100mm
from the crack. The asymmetry observed is of similar
magnitude to that observed when the shear load alone is
used except for the response of pavement A with a 150mm
crack. This gave an almost discontinuous response when
loaded with a shear load alone. With this combined load
analysis the response is more continuous as the crack is
opened by the vertical load with the shear loads not
managing to close it when acting in either direction.
Figures 22 and 23 show the asymmetry when the load is
200mm from the crack. As with the shear loading alone,
there is an increase in the asymmetry compared with the
previous results.
Figures 24 and 25 show the asymmetry when the load is
500mm from the crack. The asymmetry is still very large at
this distance from the crack and is greater than 10% of the
deflection measured under a single vertical load.
~
E
5
C
-.;
E
E
>.
Cl)
<:
70:&8
60£-8
5OE-8
40£-8
30£-8
20E-8
10£-8
OOE+O
-10:&8
-20£-8
-30£-8
I-_ASO i
•..•••• AlOO
ii ____ AlSO
-2
-I
2
0
Distance (m)
Figure 24. Asymmetry in pavement A response caused by a
crack 500mm from a combination of loads
5 r n & 8 , - - - - - - - -_ _ _ _ _ _ _- ,
45£-8
40£-8
~ 35£-8
I
30£-8
t:>
25£-8
-.;
20£-8
§
15£-8
_ _ B50
I....... BlOO
~ 10£-8
<
5£-8
1____
BISO
1--B200
OOE+O
-5£-8+-------+-------~------~------~
-2
-1
o
2
Distance (m)
Figure 25. Asymmetry in pavement B response caused by a
crack 500mm from a combination of loads
219
ROAD lRANSPORT TECHNOLOGY--4
5.
6.
-
7.
geometry there is a tendency for the crack to close. This
results in a symmetric response. The asymmetry can be
returned by reversing the shear load causing the crack to
open.
Vertical or combined vertical and shear loads can be
applied to the road in practice. Analysis of the response
to a vertical load, and a vertical load combined with
shear loads in both directions can reveal asymmetry due
to the presence of a crack.
Over a wide range of distances and crack sizes,
combined loads can reveal large asymmetries in
response indicating the presence of cracks. These
asymmetries will be revealed by the combination of
loads even if some loads close the crack and others open
it.
Further work is required to investigate more realistic
three-dimensional loading conditions for a larger range
of pavements. An experimental investigation into the
technique is also required before much further progress
can be made.
REFERENCES
1. Anon, 'Bituminous mixes andflexible pavements - an
introduction' British Aggregate Construction Materials
Industries, London, 1992.
2. Folias, E.S., 'On a plate supported by an elastic
foundation containing a finite crack' Int. J. Fracture
Mechanics, Vo1.6, No. 3, Sept., 1970.
3. Wnuk, M.P., 'Subcritical growth offracture (Inelastic
fatigue)' Int. J. Fracture Mechanics, Vo1.7, No. 4, Dec.,
1971.
220
4. Lin, S-T., Folias, E.S., 'On thefracture ofhighway
pavements'Int. 1. Fracture Mechanics, VoUl, No. 1,
Feb., 1975.
5. Ramsamooj, D.V., 'Fracture ofhighway and airport
pavements' Engineering Fracture Mechanics, Vol.44,
No ..4, pp.609-626, 1993.
6. Uddin, W., Zhang, D., Femandez, F., 'Finite element
simulation ofpavement discontinuities and dynamic load
response'TRR 1448, TRB, 1994.
7. Hardy M.s.A., Cebon, D., 'Flexible pavement response
models for assessing dynamic axle loads' Heavy
vehicles and roads:technology safety and policy, Proc.
3rd Int. Symp. Heavy Vehicle Weights and Dimensions,
University of Cambridge, UK, 1992, ed. D. Cebon &
c.G.B. Mitchell, pub. Thomas Telford, London.
8. Hardy M.S.A., Cebon, D., 'Importance ofspeed and
frequency in flexible pavement response' J. Eng.
Mechanics, ASCE, Vo1.l20, No.3, Mar. 1994.
9. Hardy M.S.A., 'Response offlexible pavements to
dynamic tyre forces' PhD thesis, University of
Cambridge, UK, 1990.
10. Ervin RD, 'Measurements of the longitudinal and lateral
traction properties oftruck tires.' Braking of road
vehicles, IMechE, London, 1976.
ACKNOWLEDGEMENTS
The author is grateful for assistance of Prof. J .M. Rotter
of the Department of Civil & Environmental Engineering,
University of Edinburgh, UK., in developing the model and
for permitting the use of his own FE code.