Manual 21366537

Manual 21366537
Various
mathematical
and tested
these
using
and physical
the
models are
divided
non-linear
models,
used.
both cases
In
Sciences
(Nie et
and non-linear
the
prepared
regression
set
logarithmic
as
the
The values
from the
is
of
Figures A.2 and
evaluation,
The reason
with
it
for
the
are stored.
basin
scale,
like
slightly
and
analysis
the
Social
the choice
computer
of
system
Each of the models
results
are
plotted
on a
in Figure A.1, some guiding
of models can be used.
curved.
line,
althouih
Based on these
obser-
models as shown in Table A.1, were used.
related
parameters
regression
1975) for a typical
Linear
of regression
a tendency towards a straight
still
the
linear
The results
deflection
following
of
namely;
of
1984) was used to do linear
can be made as to what types
it
The discussion
in terms of the results.
linear
in general
shown,
vations.
of
versus
observations
There is
basin data sets
were selected
Package for
compatibility
discussed
a typical
Robinson,
analyses.
SPSS package was the
If
procedures
SPSS Statistical
1975;
where the deflection
sets.
two subgroups
based on the
al.,
used are briefly
RSD data
into
the
models available,
are
also
given
as derived
model in the SPSS package (Nie et al.,
data set.
these
models for
A.3.
Before
can be seen
typical
even
that
data
sets
considering
there
are
are
the
shown in
statistical
some shortcominis
in
some of these models.
Figure A.2 illustrates
that
A.1) are only applicable
models 1 and 2 (as
to the area of positive
2 is however able to be accurate
Figure A.3 shows that
that
if
lead to
an ill
in Table
curvature.
curvature
fit.
Model
over a wider area (10 to 300 mm).
model 1 is used over a wider area
covered by the positive
can easily
defined
of the deflection
For that
reason
than
basin,
it
models 1 and 2
~~
101
z
0
~
u
W
...J
lL.
W
0
~----.. .....
~
•••
E
E
x~
x
•
FITTED MODEL
MEASURED POINTS
__ .
~
••
I~
.~
16
. .~.
...
.
..
..
,..:~~
FIGURE A.I
TYPICAL LOG VERSUS LINEAR PLOT OF RSD DEFLECTION
BASIN MEASUREMENTS
200
HORIZONTAL
DISTANCE
(mm)
FIGURE A.2
TYPICAL PLOTS
OF LINEAR
REGRESSION MODELS FITTED
TO THE POSITIVE
CURVATURE
D
5
....
a
a
0,200
u
W
--J
tt
o
0,150
FIGURE
TYPICAL
A.3
PLOTS OF LINEAR REGRESSION MODELS FITTED
TO THE WHOLE DEFLECTION BASIN
Parameters for a
typical data set
l.
Y •••
A exp
(A
1
0
or y •••A
A
x2)
o
10(A1x2)
•••0,2959
A
0
o
-6
•••0,991 x 10
or log y •••log Ao + A1x2
2.
y •••A x2
3.
y •••exp (a x2
2
A
0
•••
a
1
x + a )
0
2
or y •••10(a2x +a'1x+ao)
a
0
0
•••
0,4578
•••
-0,4990
a1 •••
-0,4513 x 10-3
a2 •••
-0,1330 x 106
a
0
a1
•• 0,4467
••
0,7818 x 10 -3
a2 •••
6
0,2309 x 10-
a3 •••
-0,1021 x 10
were only applied to the first 200 rom.
wider than the normal width of positive
0,98
-9
This is covering an area
curvature
(Dehlen
1962)
but it does not lead to ill fits of model 1 (see Figure A.2).
A distinctive
feature of the deflection
basin curves as shown in
Figure A.3, is the peakedness of the area of the area of positive
curvature.
than
10
This area of positive
per
cent
deflection basin.
of
the
curvature
horizontal
is on average
distance
of
the
less
whole
The R-square values of model 1 and 2 are an acceptable 0,99.
The
goodness of fit was also calculated as follows:
n
i=l
T
- Y )2
(y
- E
i
i
*
100 %
n
-E
(y
i=l
where A
- A)2
i
= Average of measured values
Y.
= Measured data values
Yi
= Values from model fitted
~
The goodness of fit for a typical data set for models 1 and 2 is
95 per cent.
Both therefore have acceptable values of R-square
and goodness of fit for the positive curvature region.
Models 3 and 4 are polynomial functions of the order 2 and 3.
There is no real advantage gained in accuracy when the order of
the polynomial is increased above the third order.
tion takes longer and becomes costlier too.
of the second order polynomial
measurements
is 99 per cent.
The computa-
The goodness of fit
(model 3) for a typical set of
It can be seen in Table A.1 that
the R-square values for models 3 and 4 are also an acceptably
high 0,98.
This is very good, but visually it can be seen in
Figure A.3 that the deviance from the observed
values
in the
very small area near the origin (positive curvature) does lead
to some concern as to the applicability
deflection
basin.
This tendency
thereof for the whole
to give equal weight
to all
data points along the linear horizontal distance (x) is typical
of this linear regression model used in the SPSS package.
For
that reason
re-
it was decided to investigate
the non-linear
gression analysis with available models that would tend to give
a better description of the whole deflection basin.
Another point of interest in the vicinity of maximum deflection
(x-a) is the gradient of the tangent at x-a.
In Table A.2 the
gradient of the curve described by any of the 4 models is given
as first order differentials.
First order differentials
~
= A
dx
2. y" A o
x2
»
(Exp (Alx2
0
2Alx
~
- 2A x 0
~
= .a 1.- 2'2x) exp (a xl2+a
dx
dx
~
dx
X
o
+ a )
-
At the point of maximum deflection
(x-O) only models land
2
have a horizontal gradient as the first order differentials are
equal
to
dependent
zero.
The
gradient
on the values
given
by Models
3 and
of the constants when x-O.
4
This
are
is
another indication of ill fit of models 3 and 4 at the point of
maximum deflection.
As
indicated
earlier,
the
non-linear
model
of
regression
analysis used in the SPSS packaie (Robinson, 1984) tends to give
equal weight to each measurement on the deflection basin.
In
using this non-linear
is
regression
analysis package
the aim
then to minimize the sum of squares.
It is the sum squares of
the
model
difference
measured points.
between
the
fitted
and
the
observed
For this reason it is therefore important that
the
unnatural
"spikes
should
be
smoothed
out
before
curve
fitting is done.
There
are two options
in the non-linear
regression
analysis
package of SPSS (Robinson, 1984) namely using the Gauss method
or the Marquardt method.
The latter was selected as superior
due to its shorter computing time required.
two models
tested
by
the
two
options
In Table A.3 the
are
shown
with
the
calculated constants and sum of squares values.
Sum of squares
8,914 x 10
-1
3,768*10-3
Parameters for
a typical
data set
A ••3,321*10-1
A~ •• -9,991*10-1
a •• -1,066
3
o
a1 "" -1,134*10_7
a •• -2,796*10
2
As can be seen both models had been tested for curve fitting by
the linear regression analysis facility of SPSS before.
was
again
tested
here
on
an
area
wider
than
the
Model 1
positive
curvature by selecting the first 350 mm for curve fitting.
As
could be expected it did lead to a poor fit as reflected in the
rather high value of sum of squares.
The residuals
(difference between prediction and observation)
are also plotted.
goodness
of
Apart from giving a visual impression of the
fit, it also serves
as a monitor
patterns which indicate poor fitting models.
specific
In Figure A.4 the
residual plot of the model 1 fitting is shown.
pattern confirms the ill fit.
for
It re-emphasises
The definite
the fact that
model 1 can only be applied to the area of positive curvature
«
150 rom).
Model 2 (Table A.3) proved to be better suited for the fitting
of the whole deflection basin and particularly the large area of
0
0
0
15
0
en
en
L&J
0
<t
0
u
0
~
0
a:
UJ
0
lD
~
0
::l
0
Z
0
5
0
0
0
0
0
10
RESIDUALS
20
(X
30
16~
FIGURE" AA
RESIDUAL PLOT OF AN ILL FITTING MODEL
the reverse
curvature of the deflection
basin.
The good fit
thereof is reflected by the low value of the sum of squares in
table A.3.
The plot of residuals in Figure A.S also reflects no
specific patterns indicating a good fit.
the
area
of
deflection
positive
still
regression
curvature
persists
analysis
too.
as
The lack in fitting
in the
was
vicinity
indicated
in
of
the
maximum
linear
It would be possible though to use
these two models of table A.3 and limit the curve fitting of the
positive curvature to that by model 1 and the curve fitting of
the larger reverse curvature
to that of model
2 and achieve
satisfactory results.
The
non-linear
relatively
package
complex
of
models
SPSS
makes
it
possible
in the regression
to
analysis.
use
This
gives the opportunity to look at physical models which can be
adapted to the observed deflection basin.
that of beams of unlimited
concentrated
by Het~nyi
loading.
length on elastic foundations with
This model is described
and Fryba (1967).
(1971)
A promising model is
give a detailed description
in great detail
The intention is not to
of this theory here, but rather
concentrate on the use and manipulation of the derived solutions
in the curve fitting exercise.
In the analysis of bending of
beams on an elastic foundation H~tenyi (1971)
assumption
is
proportional
that
reaction
forces
of
states that the
the
foundation
are
at every point to the deflection of the beam at
that point based on the Winkler theory.
that deformation
This theory also states
exists only along the portion--d±·ree-t.ly--··under
loading and was verified in experiments for a variety of soils.
Het~nyi
(1971)
is quoted
as follows;
II
that the Winkler
theory, in spite of its simplicity may often more
represent
the actual
conditions
existing
accurately
in soil foundations
than do some of the more complicated analysis •••11
A short description
of the model is as follows;
Consider an
infinite beam subjected to a single concentrated force P at the
a point 0, which is the origin of the axis system as shown in
figure A.6.
The general solution for the deflection curve of a
•
••
•
.100
•
•
•
•
••
•
•
• •
•
•
• •
•
•
70
•
• •
•
•
•
•
•• •
• •
•
en
o;t
I
~
0
.;r
en
-10
i:::
•••••
G::
••
~
10
«
•
•
••
•
•
C
C
~
w
0::
::>
e"
IJ..
~
•••••
C
-5
~
<t)
•
• •
lA,J
~
••
•
•
•• •
•
••
•
•
••
•
•
•
•
-15
<:
•
•
•
•
m
-20
~
~
•
• •
•
(f)
ID
ID
C
§
•
•
~
-..J
••
•
.•.••.
l;j
• •
•
••
~
•
•....
•
•
•
• •
•
•
•
0
RESIDUALS
•
•
5
3
( x 10 )
•
•
•
10
Y
PA
-AX
= 2k e
(cos AX
.
to S In A X )
DOWNWARD
DEFLECTION
M= :A
BENDING
MOMENT
e-AX (cos AX - sin AX)
PAx'
Q =-2' e-
cos AX
SHEARING
FORCE
FIGURE A.6
POINT LOAD ON AN INFINITE BEAM ON AN ELASnC
FOUNDATION
beam subjected
to transverse
loading
is derived
by Hetenyi
(1971) as;
where
y is the deflection taken as positive downwards
x is the horizontal distance from the origin
C1, CZ' C3, C4 are constants
~ is the damping factor, and
k is the modulus of the foundation expressed in
kg/m2/m
E is the modulus of elasticity in kg/mn
I is the second moment of area of the beam
Without even going into further detail of the simplification
this model
between
of
it can be seen in Figure A.6 what the similarities
the
deflection
modelled
basin
deflection
curves
are.
curve
When
the
and
the
symmetry
measured
of
the
deflection curve and the equilibrium of the reaction forces are
considered this general equation reduces to;
Y
=
p
Zk
e
-).x
(cOSAX + sin~x), which gives the deflection curve
for the right side (x>o) of the beam.
the data preparations
preceding
sections.
case of no dampening
curve analyzed.
This correlates well with
of the deflection basin described in the
The form of the curve suggests that the
can be considered
for this part of the
Fryba (1967) gives the solution as follows for
such a situation;
e -blxl (a cosax + bsina Ixl)
This form is obviously similar to that derived by Hetenyi (1971.
In order to simplify the determination process of the constants
in these equations,
fitting model;
it was decided to use the following
curve
In figure A.7 a plot of a typical data set and the curve fitting
is shown.
Visually it can be seen that this model succeeds in
describing the observed deflection basin accurately. The sum of
squares value is low (4.15 x 10-3 for this typical data set) and
the plot of the residuals does not indicate any ill fit.
The
goodness of fit for such a typical data set is above 98 per
cent.
range
It was found that this mode is applicable
of variances
in load.
condition of pavements.
load repetitions
over a wide
and
structural
It is obvious though that although this
model gives the best fit of all models tested it still tends to
give an ill fit in the positive curvature area.
Although this
area is very small and very peaked in relation to the rest of
the deflection basin. it was decided to use the parabola of the
linear models
in this area of possible curvature
in order to
arrive at a true representation of the whole deflection basin.
E 0.2
E
Y = B 1e
82
X
(COS
B 3X + si n B 3X
)
z
Q
U
LOAD 60 kN
NO REPETITIONS
LL
W
x - PREDICTED
I-
w
...J
o
• - OBSERVED
FIGURE A.7
TYPICAL CURVE FITTING OF PHYSICAL
MODEL
SUHHARY ON CONDITION
DEFLECTION
SURVEYS ENHANCING
BASIN ANALYSIS
A condition survey is an important input in the non-destructive
testing of an analysis procedure.
In Figure B.1 it is shown how
this kind of visual survey greatly enhance the understanding of
the material characterization in a typical analysis procedure for
overlay
design.
Condition
surveys
are
non-destuctive
testing
procedures enhancing the other non-destuctive testing procedures
such as deflection basin analysis. In Figure 4.1 it was explained
how
in
the
South
African
mechanistic
rehabilitation
design
procedure (Freeme, 1983) it is important to identify the pavement
layer state. The discussion on
condition survey will therefore
focus on crack and rut classification related to the deflection
basin survey (see Figure B.1).
Ullidtz (1982) defines a functional and structural condition in
his model
on pavement
rehabilitation.
He
states
that;
"The
structural condition is of no immediate interest to the road user
but is is extremely important to the highway agency because the
future
functional
condition. "
condition
depends on
the present
structural
A visual condition survey can be seen as an aid to a
proper structural evaluation.
The standard
procedure
outlined
Draft
in
for conducting
TRH12
(NITRR.
a
1983),
condition
should
be
survey,
as
followed.
Normally the visual assessment precede the deflection basin survey
but it is suggested that the deflection basin survey and visual
assessment may be done simultaneously on smaller scale projects.
The results of both surveys should be plotted on the same scale.
By this means the obvious weak spots can be identified when other
relevant information such as drainage, cut or fill transition and
soil changes is taken into consideration.
Pavement
Evaluation
and
Overlay
Design Inputs
Destr u ct iv e Testi ng
raff ic
Data
In-situ Material Sampling
1esting Lab. Testing
Deflection
Survey
Analysis
Sections
Pavement Class Identification
Compute Deflection Basin
Parameter Function
Compute Distress Determi nants
Fatigue Cracking
Overlay Criteria
Overlay Thickness and System Selection
FIGURE 8.1
Mechanistic
overlay design flow diagram
B.3
Cracks in the existing asphalt concrete layer have a major inNormally pavements are
fluence on the overlay design procedure.
However,
the
majority of pavements fall somewhere between these extremes.
The
classified
as
either
cracked
or not
cracked.
aim of this section is therefore to establish quantitive procedures to
classify
cracked
pavements
in order
to
improve
the
rehabilitation design procedure.
Grant and Curtayne (1982) point out that fatigue is not necessarily the cause of cracking in asphaltic concrete layers in South
Africa.
Other factors, not necessarily traffic-related, should
also be considered as being possible causes of premature cracking
(Grant, et al (1979).
with
full
depth
Pronk
asphalt
and Buiter
pavements,
even
(1982) indicate that
in the Netherlands,
cracking does not necessarily begin at the bottom of the asphalt
layer.
Grant and Curtayne (1982) therefore stress that a study
of the past behaviour of the pavements can provide good clues in
this
respect.
complexity
of
The
preceding
crack
mechanisms
statements are
of
asphalt
to indicate
concrete
the
layers.
Different reasons for cracking are therefore discussed in order to
arrive at a classification for cracked pavements.
The aim of this is purely to simplify the analysis of such a
pavement by using the deflection basin parameters in the mechanistic approach.
First it is suggested that the difference in basic crack mechanism, due to the difference in pavement structure be considered.
For the
South African
condition it
is suggested
that on
the
grounds of as-built plans or matericiTsam-pting--procedure (Figure
B.1), a flexible pavement under survey be classified according to
the basic TRH4 (NITRR, 1985a) catalogue, i.e.
(a)
granular base pavements
(b)
bitumen base pavements (tar as an alternative)
(c)
cemented base pavements.
This basic classification is taken a step further by Freeme (1983)
by relating
the time-dependent behaviour of
different pavement
types to the concept of equivalent material state
Figure
B.2.
It
is
explained
in
Chapter
3
illustrated in
how
the
measured
deflection basin parameters can be used to accurately identify any
such pavement behaviour state.
Next, the degree of cracking should be defined.
In the light of
work done by Kilareski et al. (1982) and Treybig et al. (1978), it
is suggested
that
the AASHO
definition
of
cracking
could
be
applied. Jordaan and Servas (1983) give a very clear description
of three types of cracking and how it should be calculated.
types
are
crocodile
or
map
or
block
cracking,
These
longitudinal
cracking and other crack patterns or combinations of the preceding
types.
For these types each 100 m of road length is classified as
being in a sound, warning or severe condition.
This depends on
the percentage of 100 m being cracked and the road category.
Crack conditions can be improved by crack filling and repair of
the low percentage of severe cracking of the defined categories or
crack types.
The decision to repair cracks should be based on
economic comparisons,
improve possible
but it is obvious that crack repair will
crack attenuation behaviour in general.
Koole
(1979) suggests though that an overlay design based on the severe
condition of cracking might in some cases be the most economical
in the final analysis owing to the expensive nature of procedures
to upgrade the pavement in regard to the crack condition outlined
above.
In the final level of crack classification
methods should be considered.
more
sophisticated
This normally consists of analysis
procedures associated with the overlay design analyses.
researchers, such as Molenaar
Various
(1983) and Coetzee and Monismith
(1979) suggest the use of fracture mechanics principles and finite
element computer programs in the analysis stage.
In order to use
these procedures though, the previous crack classification would
have to be elaborated
crack
width
too.
in order to establish average values of
Molenaar
(1983)
states
the
following:
I
1940-4
-4760/9
B.D.
STATE .---..
VERY
I
STIFF
APPROXIMATE DEFLECTION
(mm)
LEVEL
STIFF
0,2
I
0,4
CONCRETE
EXAMPLES
OF CHANGE
OF STATE
PAVEMENT
OF DIFFERENT
TYPES
I
. FLEXIBLE
VERY
FLEXIBLE
0,6
~
CEMENT TREATED
•
BASE PAVEMENT
CRUSHED- STONE OR BITUMEN
CEMENT TREATED
SUBBASE
TREATED
BASE
OVER
BITUMEN TREATED BASE OVER
GRANULAR SUBBASE
GRANULAR BASE IGRANULAR
SUBBASE. LOW SUBGRADE
CBR VALUE
CONCRETE
ROAD
N2
HOORNSNEK (TVU
TYPICAL
IN
EXAMPLES
; BRONKHORSTSPRUIT
P67/1
(TVU;
N3 SWINBURNE (OFS)
P157/1 a PI57/2 JAN SMUTS AIRPORT nVU;PARADISE
N3 MARIANNHILL
(NTU
PRACTICE
P205/2
VALLEY (NTU
GI LLOOL Y (TVU
KOEBERG
(CAPE)
PI23 MAGALIESBURG nvu
P6/1 BABSFONTEIN
(TV L)
FIGURE B.2
DIAGRAMMATIC
REPRESENTATION OF THE TIME DEPENDENT BEHAVIOUR
OF DIFFERENT PAVEMENT TYPES (Freeme, /983)
"Although the fracture mechanic's approach has the potential to be
an excellent tool in solving the reflection crack problem, it has
not gained very much popularity.
In fact it can be stated that
it is still a research tool and that its practical application is
limited to only a few cases."
Recently the monitoring of crack movements, as described by Rust
(1984), has become another viable method that may be associated
with the classifications outlined above.
(CAM) that was developed
total
crack
movement.
The Crack Activity Meter
can measure amongst others the defined
Crack
activity
or total crack movement
normally has the typical peaking behaviour with axle repetitions
as shown in Figure B.3.
Rust (1985) was able to determine that
for a flexible pavement with a cemented base and under specific
conditions,
there
crack movement.
size
below
between block size and
The data indicated that there is a critical block
which
further decrease
Figure B.4.
is a good correlation
the
crack
movement
in block size.
increases
Typical
results
markedly
with
are shown
in
These concepts can be used effectively to enhance the
crack classification as given above.
In Appendix E the good correlation between the measured crackactivity and measured deflection basin parameters is illustrated
by means of an example. As will be shown there this greatly
enhances the rehabilitation analysis procedure.
One of the major aims of a rut survey is to determine the amount
of material needed for the levelling of the existing rut before an
overlay
is applied.
This is all related to ride comfort (PSI
values) and, in wet conditions
The extent of rutting
in particular,
to rider
safety.
is generally used in overlay design as a
major criterion of permanent deformation and the structural state
of the pavement.
The general procedure
is to limit rutting in
overlay designs by limiting the vertical subgrade strain (e:
This
approach
was
originally
developed
by Dorman
and
).
vs
Metcalf
•
JOINT 132
-x-
JOINT 131
WHEEL LOAD:
40 kN
E
-=IZ
llJ
400
-x .•..•.
....•• ...•.
::E
llJ
>
••.•x
0
.......
::E
:l<::
..•..
..•.. ....•.
U
<t
a:
u
...J
<t
I-
0
..•..
•....
....•.
,•....
"X
200
I-
o
o
200
400
REPETITIONS
(x
103)
FIGURE B.3
CHANGE IN TOTAL CRACK MOVEMENT DURING HVS
TESTING ON THE N2 CONCRETE ROAD-SECTION 258A2
(Rust
o
lD
If)
....
If)
If)
~
I
V
I
o
·v
I
1984)
BS
140-4-5097/2
400
.\
\
\
\
\
\
300
\
E
\
~
J-
.,,
\
\
.•..•
.',
\
\
z
•
•
\
\ •
w
:IE 200
w
>
0
:IE
\
~
0
«
0::
0
100
o
"-
,,
,,
"'-
.
tJ:l
......... .......-.
.....•.. -...-
.
• •
••
.
00
------ ---•
•
"........ -----
---- ---• --a-_
.
•
---
-- ---.••
•
•
-------------~----
o
4
BLOCK
SIZE
(m)
FIGURE 8.4
CORRELATION BETWEEN
CRACK MOVEMENT
AND BLOCK SIZE ON THE MR 27 (Rusf,1985J
(1963) in their analysis of the behaviour of the test sections of
the AASHO road test.
It is should be noted that rutting is not only related to the
subgrade but that contributions also come from the various layers
in the pavement.
For this reason Koole (1979) mentions that the
rut in the asphalt concrete layer should be treated separately.
The South African experience also indicates that such a direction
should be followed.
Freeme et ale (1982a) indicate that better
characterization of the bitumen layer in terms of volumetric and
shear properties
is necessary
to accommodate
phenomenon in the bitumen layer.
this deformation
Maree et ale (1982) show that
for granular base pavements tested with the Heavy Vehicle Simulator (HVS). most of the permanent deformation took place within
the granular base and subbase.
The subgrades never meaningfully
contributed towards the total deformation and were always well
protected.
strong
In the same report Maree et ale (1982) illustrate the
correlation
between
cracking,
excessive
rain, moisture
intrusion and deformation for typical granular base pavements;
this is shown Figure B.S.
The preceding statements make it obvious that a more qualitative
classification of rutting is needed than just a report of the
average rut.
In line with the classification outlined in the
previous section on cracking, it is suggested that the pavement
structure classification as defined be used also.
In fact it is
re-emphasized that no indicator like rutting or deflection should
be used
Freeme
in isolation.
(1983)
behaviour of
A
further
The concept is clearly illustrated by
in Figure
B.6
where
various indicators of the
typical granular layers are shown.
practical
classification
is needed
to discriminate
between various mechanisms of permanent deformation.
Molenaar
(1983) classifies two types of rutting (see Figure B.7).
The
first type is that without lateral displacement due to densification.
The second type is that with lateral displacement due to
Prandtl type of shear deformation.
ious discussion
This ties in with the prev-
on the South African
experience.
Grant
and
z
Q
ti
~
10
Q:
~
W
o
INGRESS OF WATER
\ \ \HIGH QUALITY
GI STANDARD
FIGURE 8.5
SCHEMATIC DIAGRAM OF THE RELATIVE
BEHAVIOUR
GRANULAR MATERIAL OF DIFFERENT QUALITIES
(Moree, of 01., 1982)
OF
PHASE 2
I
DENSIFICATION
E
E
STABLE
15
~
0::
OF WATER
tv<1:-
~
RATE OF INCREASE OF
DEFORMATION CAN REDUCE
AGAIN IF WATER IS REMOVED
~'i"
I
e,
0'<
<lot/;
~(j
WATER AND WATER-I
SUSCEPTIBLE
MATERIAL
I
I
10
OF INGRESS
I
I
I
o
~
I EFFECT
STATE
I
I
Z
~
I
PHASE 3
"
5
RATE OF INCREASE DEPENDENT
ON
QUALITY OF MATERIAL
AND STA BLE
MOISTURE· CONDITIONS
1LI
o
ESOs OR TRAFFIC
(a)
PERMANENT
••
DEFORMATION
IF WATER IS REMOVED
DEFLECTIONS
CAN
BECAUSE OF
REDUCE
INCREASE IN RESILIENT
MODULUS OF LAYER
~
~
- - ----
I-
Ua:
....•.
lLIlL1
-I)-
INGRESS
WATER
L&.<t
1LI-1
o
Z
1--
zJ:
DEFLECTION
REMAINS
LOW
IF LAY ER NOT SUSCEPTIBLE
TO WATER
e.g. CRUSHED- STONE BASE OR WATERBOUND MACADAM
1LI!::
::::;~
(f)
lLI
0::
(b)
ESOs
BEHAVIOU R
RESILIENT
OR TRAFFIC
••
0500
0..
MATERIAL
NOT SIGNIFICANTLY
SUSCEPTIBLE
TO THE INGRESS
OF WATER
~
(f)
/
:3
:>
I
~ 250
I
o
-- -~WATER
I
Z
lLI
------
,..,.
I
I-
REMOVED
I NGRESS OF WATER
AND WATER-SUSCEPTIBLE
MATERIAL
-I
(f)
lLI
0:: 0
ESOs
(c)
CHANGE
IN MODULUS
OR TRAFFIC
OF CEMENTED
LAYER
I INGRESS
~
I
g
I
I
m
........
z
2
0..
OF WATER
AND WATERSUSCEPTIBLE
MATERIAL
I
u~
00::
lLI
Z
lLI
o
w
(d)
STRENGTt-l
ESOs OR TRAFFIC
BEHAVIOUR
I
••
FIGURE 8.6
~
I
o
INDICATORS OF THE BEHAVIOUR OF GRANULAR LAYERS
~
lI'L
-_
MATERIAL
NOT SIGNIFICANTLY
SUSCEPTIBLE
TO THE INGRESS
0..
r-~
WATER~"""
REMOVED
I
I-
.......
.,.,....---...
_
..
IE r eeme. / !lE31
r
r
LORIGINAL
SURFAr
PROFILE
~-~
·
·
1
~
~
·
·
I
......•.....•.•
Type
I
~
A
Rutting without lateral displacement of the material. This
type of rutting is due to densification of the material .
.
_I
t~~
I
·
~-------.;I
·
I·
r
Type 8
Rutting with lateral displacement of the material.
Rutting can be judged to be a Prandtl type of shear
deformation.
FIGURE 8.7
TYPES
OF RUTTI NG WHICH CAN 8E DISCERNED
( Molenaar, 1983)
Curtayne (1982) note that shear in the subgrade is characterized
by wide rutting.
Shear in the base layer is characterized
narrow
displaced
ruts
with
material
appearing
like
a
by
mound
adjacent to the rut.
From the visual survey therefore a classification
of the type of
rutting that exists may be made. which will strongly influence the
overlay design analysis. The Draft TRH12 (NITRR. 1983) give clear
indications for rut criteria related to pavement class and
pavement type. It is suggested that those criteria and those
suggested by Jordaan and Servas(1983) be followed.
At any specific moment, an existing pavement has a certain amount of
accumulated
damage done to it by repeated traffic loading.
There
is normally also a certain amount of remaining damage which the
existing pavement can undergo before failure.
The severity of the
damage caused by each repeated traffic loading depends on the
structural strength of the existing pavement.
This is usually
expressed in terms of the equivalent number of standard axles
(E80s).
If the magnitude of the critical strains is reduced, then
the existing pavement can carry a larger number of standard axle
loads (E80s).
The function of an overlay is therefore to reduce
the magnitude of these critical load-induced strains or stresses,
depending on the distress determinants being used.
Remaining life has two meanings.
Without an overlay a pavement
normally has remaining life and with an overlay a pavement has a
remaining life, that is usually lengthened or prolonged.
For this
reason "remaining life" will refer to the remaining life of a
pavement without an overlay.
In the literature remaining life is usually analysed on the basis of
the phenomenological
theory of cumulative damage.
Attempts to
relate the structural condition, based on deflection basin measurements, in a different way to the life of the pavement, will also be
discussed.
The phenomenological
theory of cumulative damage is also referred to
as the linear summation of cycle ratios.
This was advanced by
Miner (1945) to predict the fatigue life of metals subjected to
fluctuating stress amplitudes.
Monismith et ale (1966, 1969) used
it to estimate fatigue life of bituminous layers in pavement structures and established
it as an acceptable and useful relationship.
n. ••number of applications at stress or strain level
Let
1
N. ••number of applications to failure at stress or strain
1
level
D.1 ••damage due to N.1 number of applications at stress
or strain level
Then the damage, D , is defined as the stress or strain cycle
i
ratio, i.e.
D
.
= n1·
1
N.1
Failure will occur when D. = 1.
1
Let r = number of different stress or strain levels involved
D = cumulative damage due to number of applications at
different stress or strain levels
Then the cumulative damage, D, is stated as the linear summation of
cycle ratios, i.e.
r
E
i=l
=
D
i
r
E
i=l
ni
N.
1
r
n.
or E 2i=l N.
= 1
1
Snaith et al. (1980) use the distress determinants vertical subgrade
strain (€vs)' and maximum horizontal aspahlt strain (ERA)' as
discussed in chapter 4 and 6 , to determine damage due to rutting
deformation and fatigue cracking respectively.
For both forms of
damage the strain-life relationship is given by the general
equation:
It is therefore possible to apply the cumulative damage theory to
both forms of damage.
applications
matically
The accumulation of damage from repeated
at various strain levels is illustrated diagram-
in Figure C.1.
In Figure C.1(a) the strain-life
diagram is shown with a typical strain-life curve, l-k.
On this
curve a strain level E1, for example, corresponds to a life N1.
Lines a-b, c-d, etc., represent n applications at strain level
1
E , and n applications at strain level E ' etc.
These lines,
l
Z
Z
represented
by arrows, are called damage paths.
The dashed
lines, b-c, d-e etc. are called iso-damage lines.
of damage at band
If the amounts
c are the same, then
This is represented more simply in a damage-life diagram (see
Figure C.1(b».
The damage scale ranges from 0 to 1.
The
damage paths can be plotted continuously as shown in Figure
C.1(c).
In this way, the cumulative damage arising from repeated
applications
is determined
in diagrammatic form.
In practice the number of repeated applications
(n.) is expressed
1
in terms of the equivalent number of standard axles (E80s).
This
reduces the analysis to only one strain level to determine remaining life.
In Figure C.1(a), therefore, at strain level E1
the damaged or consumed life is nl and total life is N .
1
Remaining life at this strain level is equal to:
Alternatively,
damage (D1) is often expressed as previously
defined and remaining life (R ) is then:
1
E',
a
b
,
'c
-..
DAMAGE
PATH
---
ISO-DAMAGE
LINE
.,
d
'" "' ••.._e
_
lll
n
I
N4
N--"
N4
N-....
n4
h
~
DAMAGE PATH
-
ISO-STRAIN
(c)
FIGURE
LINE
DAMAGE-PATH
DIAGRAM
C.I
GRAPHICAL
PRESENTATION
OF CUMULATIVE
DAMAGE THEORY (Snaith , et a I., 1980 )
R1
=
1-D
=
1
-
1
n1
N1
Using the same distress criteria, vertical subgrade strain (evs ) and
maximum horizontal asphalt strain and (eRA)' Anderson (1977) also
used this theory to determine remaining life.
though, that future environmental
It is pointed out,
or traffic changes cannot usually
be foreseen and therefore such a procedure should be seen as a guide
only.
In considering
the remaining life of a pavement with rutting
due to permanent deformation, Anderson (1977) reasons that the
damaged life or consumed life will be nullified when the surface
deformation
is removed by an overlay.
Koole (1979) supports this
view by Anderson (1977) in his description of the Shell overlay
design method.
The remaining life of a pavement with fatigue
cracking is determined
et ale
in accordance with the description by Snaith
(1980).
Treybig et ale (1978) also use the theory of cumulative damage in
order to determine remaining life for a pavement with fatigue
cracking and rutting due to permanent deformation.
As mentioned in
Appendix B, however, the cracked state of the existing pavement is
taken into consideration
asphalt).
in determining the material parameters (E
Chapter 4 described how these material parameters are
used to determine the distress determinants.
In a pavement with
fatigue cracking the maximum horizontal asphalt strain (ERA) is
calculated and used to determine the remaining life in terms of
standard axle (E80) repetitions,
(1980).
as described by Snaith et ale
It was shown in Chapter 6, Treybig et ale (1978) consider
the contribution
of all the structural layers to rutting due to
permanent deformation by determining the various stresses and
strains of each layer.
It is obvious that Kilareski et ale (1982) only considered fatigue
cracking when determining
not necessarily
remaining life.
be determined,
The strain (eRA) need
but as shown in Figure C.2 the
deflection basin parameter.
surface curvature index (SCI). is
related to the number of equivalent single-axle
loads (EAL).
In
this case the structural number has also been determined. based on
the AASHO Design Procedure (for the various test sections).
The 10
per cent fatigue cracking line is the same form as described above
for the general relationship.
N = A(l)b.
e:
The equation for
Kilareski
- n ).
1
1
et al. (1982) advance this one step further by relating remaining
remaining life is as described above. namely (N
life (in terms of equivalent axle loads) to the SCI for various
structural numbers (pavement strengths). as shown in Figure C.3.
Residual life determined from deflection measurements
lead to satisfactory
results.
Koole (1979) states:
alone does not
"It is not
possible to determine the residual life of a pavement solely from
deflection measurements".
The reasoq lies in the fact that the
change in a structural parameter. for example elastic modulus (E).
with an increase in load repetitions shows a sharp decrease in value
initially but thereafter there is a long period during which
virtually no change occurs and only at the end of the structural
life is there a definite sharp decrease to distress.
measurements
also reflect this typical behaviour.
Deflection
However. it is
possible to relate early life deflections empirically to the
critical life of particular types of pavement structures. as shown
in Figure C.4 using work done by Lister and Kennedy (1977).
Koole
(1979) also mentions that original design life can be determined
from FWD deflections.
FWD deflections
measured
A "crude" test on consumed life is to take
between the wheel tracks.
If the deflections
in the wheel tracks. are significantly
greater than those
measured between the wheel tracks the pavement is approaching the
end of its service life.
Pronk and Buiter (1982) mention the procedure in which the decline
in effective layer thickness is related to the structural strength.
This forms the basis of the structural performance model developed
by Molenaar (1983).
This principle is shown schematically
in
Figure C.5 where equivalent layer thickness (H ) decreases in
e
c:
1000
10
I
0
~
700
Section No.
• •
C,)
500
)(
Q)
400
c:
300
•...
200
Q)
-
~
10% Fatigue Crocking Line
8 (:3.14)
9(3.58 )
14 (3.65)
~,..,...
::s
___
1d (3.72 )
C
Ic (3.94) __
>
•...
::s
2 (4.38)
C,)
Q)
(,)
c
•...
::s
(J)
No.
H (2.70)
(J)
~
Structural
I
,........
.•,
"
"
7 (4.74)--
100
.•
.-#/1,
••.•
80
60
I x 10s
18-kip
2
3
(80-kN)
4
6
8
Ix 106
Equivalent Single-Axle
2
3
4
6
Loads
FIGURE
C.2
VARIATION
OF SURFACE CURVATURE
lNOEX-WITH EAL. (Kiloreski,
et 01.,1982)
STRUCTURAL NUMBER,
--l
5.0' 4.5
~
3.0
~
2.0
4.0 3.5
SN
3.0
W
lL.
--l
~
z
w
1.0
0.7
~
w
~
(,!)
z
z
0.2
<t
~
w
a::
O. I
0.07
0.05
50
SURFACE
100
150
CURVATURE
200
INDEX,
250
6
300
SCI<l6 IN.)
FIGURE C.3
REMAINING PAVEMENT LIFE BASED ON
FATIGUE CRACKING FOR BITUMINOUS
CONCRETE PAVEMENTS WITH SUBBASE.
(Kilareski,
et aI., 1982)
140-4-4760/38
ROAD BASE
Hot rolled asphalt
&
Dense bitumen macadam
Dense tarmacadam
Medium textured tarmacadam
x
Open textured tarmacadam
Readings still sound
AO
•
200
•
150
I
0
)(
E
E
"
•
N
100
•
80
.yAy
Z
0
.-
u
60
50
w
40
0
30
-I
LL
W
0
0
~
• A
• A
.
n
-0
y
A
0,2
0,3 0,4
0,6 0,8 1,0
1,5 2
3
CUMULATIVE STANDARD AXLES
4 5 6
(x 106)
8
10
15
FIGURE C.4
RELATION BETWEEN DEFLECTION AND CRITICAL LIFE OF
PAVEMENTS WITH BITUMINOUS AND TAR BOUND BASES
(Lister
and
Kennedy, 1978 )
20
(f)
(f)
w
z
:::c:
u
:c
I-~
0::-
W
Q)
>-:c
<X:...J
I-
Z
W
-J
<X:
>
~
o
W
LOAD
REPETITIONS
n
FIGURE C.5
HYPOTHESIZED DECREASE OF THE EQUIVALENT
LAYER THICKNESS (He) WITH RESPECT TO THE
NUMBER OF LOAD APPLICATIONS (n).
relation to the number of load applications(n).
The structural
condition of the pavement can be characterized by means of the
structural condition index p. which is defined as:
P = H
ecn
where
H
ecn
/H
eco
= equivalent layer thickness after n load
applications corrected for temperature and
environmental
H
eco
fluctuations
= equivalent layer thickness just after
construction corrected for temperature and
environmental fluctuations
In order to determine H
• deflection values between the wheel
eco
paths are measured as described above. Molenaar (1983) defines Heco
values determined in this way as "candidate" H
values since they
eco
would have been subjected to some loading between the wheel paths.
The amount of future deterioration depends on the expected number of
load applications.
the deterioration
Values for Sl
measurements.
og
the structural condition index P and the shape of
function characterized by Sl
N.
N should also be determined by means of deflection
Sl
og
N
can be calculated as follows:
2 2 2
S2
= a1 b1 S log He +
l.o.f(l
where
og
N 1
)
og - oge:
a1 = slope of fatigue relation
b1 = slope of H
S2
e
versus log e:relation (=2)
1.o.f. = lack of fit of the equation used to describe
the fatigue relation (=0,16)
In Figure 4.10 the typical relationship between H
e
and surface
curvature index (SeI) is shown from results of deflection basin
-
a..
-
1,0
x
w
0
z
z
0
I0
0,8
z
0
U
...J
<r
0::
:::>
f3
I-
u
:::>
0::
Ien
0,6
---
S\OgN
0,2
°
0,4
REPETITION
RAT\
n/ N
FIGURE C.6
COMPARISON
OF THE THEORETICALLY
DERIVED STRUCTURAL
PERFORMANCE
MODEL AND THE EQUIVALENT
LAYER
THICKNESS DETERIORATION
MODEL
(Molenaar,
1983)
plotted in relation to deterioration
Sl
og
(n/N) and the influence of
N can also be seen.
Molenaar
(1983) takes this even further by calculating
directly from deflection
curvature
P
P and SlogN
basin parameter values such as surface
index (SCI) as follows:
=
(SCI /SCI )d
o
S2 log N
where SCI
SCI
o
n
=
n
d2 2 2
2
1 c1 S 10gSCI+ Sl.o.f (log N-log €)
=
SCI at time of construction
=
SCI after n load applications
d1 = absolute value of the slope of the SCI versus He
relation
c
(a reasonable value is 0,53)
= slope of the 10g(SCI)-in relation to log N (=0,943)
1
All other variables have been defined before. However. Molenaar
(1983) warns as follows:
"Although the procedure to calculate P seems very simple, one should
be aware of the fact that in a number of cases the ratios H
and SCI /SCI
o
Remaining
n
ecn
/H
eco
might be larger than one.
life is determined
by this procedure as illustrated
in
Figure C.7.
Molenaar
(1983) modified the work done by the Belgian Road Research
Centre. He uses the following equation for permanent deformation
model:
where
u·
p
permanent deformation
(m)
Z
o
I-
o
Z-
o~
~ [j 0.9
_1__ I _-_n I_N_.....•••.
<:to
a:Z
::>IU
::>
a:
Ien
0.8
0.75
0.5
REPETITION
RATIO n/N
FIGURE C.7
PROCEDURE TO ASSESS THE REMAINING
LIFE (Molenaar,1983)
-......
¢
o
CD
~
¢
I
~
I
o
~
...
u
e
= elastic deformation
(m)
By means of regression analyses of a typical three-layered pavement
system Molenaar (1983) used the BISAR computer program to arrive at
values of bo' b1 and n for the various interfaces between the
layers.
The elastic deformation at the pavement surface must be
known in order to be able to determine the elastic deformation of
the top layer.
This deformation due to dual wheel loading can be
estimated from the maximum deflection (6 ) value of the falling
o
weight deflectometer
(FWD) by using the following equation:
log Ue surface = 0,09+0,948 log 60FWD
The elastic deformation of each layer can be calculated by subtracting the deformation at the lower interface from the deformation
at the upper interface.
The permanent deformation can then be
calculated by means of the permanent deformation model with
constants shown in Table C.1.
A correction factor is applied to relate observed rut depth to these
calculated values.
applications
By these means rut depth can be related to load
(n), and consumed rut life can be determined by
defining a terminal rut depth of for example 20 mm.
In chapter 4 and 6 it was concluded that the current mechanistic
design procedure in South Africa using distress determinants
vertical subgrade strain (€ ) and horizontal asphalt strain (€h )
vs
a
is a sound one. Proper fatigue relationships have been established
for these parameters.
This makes the use of the linear summation
of cycle ratios applicable to both distress criteria: fatigue
cracking and deformation rutting.
=
(l)b),
€
The generalized relationship,
described by Snaith et al. (1980) can thus be used to
(N
TABLE C.1.
Values forob
and b to be used in the calculation
1
of the permanent deformation (Molenaar. 1983)
b
=
Bituminous
layers
U *b n 1
e
0
U *4.49nO.25
e
U *2nO.3 if n<0.12 m
e
U *2nO.2 if n<0.12 m
e
Stone
base
Lean
concrete base
Granular
subbase
500
1 500
U *2nO.3
e
Subgrade
5 000 (summer)
200
5. 1O. 20. 40
U *(1+0.7 logn)
e
determine remaining life for both distress criteria.
The more
critical value can then be used in the selection of an overlay, as
described in Appendix D.
Although Freeme et al. (1982a) give a
fundamental basis to rehabilitation
the mechanistic
design procedure.
the case of establishing
design in their description of
it is felt that. particularly
in
criteria to determine consumed life due to
rutting, some advances can be made. This would again be possible
with the information available from HVS tests and observed field
data.
In this regard the approach by Treybig et al. (1978), where
the deformation contributions
of each layer is better rep~e$ented by~_
the computed stresses and strains of each layer, should be pursued
with the available data.
It is clear too that the approach to relate the remaining life of
the pavement to other structural indicators such as the equivalent
layer approach shows much promise.
model suggested by Molenaar
three-layered
The structural performance
(1983) was developed specifically
for a
pavement structure and therefore it is obvious that it
would not be possible to use this approach in all cases.
it is suggested that, with the previously mentioned
available on pavement performance
Instead
information
in South Africa, the performance
model be established with values determined from regression
analyses.
This approach would then take into consideration
factors
such as the deflection basin measuring device, deflection basin
parameter selected and pavement structure classification described
previously.
The model relating permanent deformation and elastic deformation to
the number of load applications seems a sound approach.
It would
also be possible to establish these relationships with the
regression analysis of the information available for the South
African condition.
This section is a logical continuation of the discussion in Appendix
C.
In general, the decision to overlay a pavement under analysis
will be based on criteria related to the remaining life or consumed
life.
The distress criteria, fatigue cracking and permanent
deformation rutting, are considered separately to determine the
remaining life of the pavement.
The decision to overlay the
pavement is based on the more conservative of the two criteria, but
both criteria are checked again to ensure that the prolonged life
(remaining life after the overlay) would indeed be achieved.
As in
any situation where various possible alternatives are generated,
sound engineering
considerations.
judgement is
influenced by
economic
The latter type of decision strongly indicates the
typical considerations
of a maintenance or pavement management
programme and should be viewed against that broader background
although the focus here is on a project level based on deflection
basin related criteria.
Snaith et al. (1980) describe how on the basis of the theory of
cumulative damage, the remaining life can be determined.
general this remaining life, as described in Appendix C,
=
In
would be
or R1 = 1-n /N .
Snaith et al. (1980) do
1 1
not mention any specific criteria related to this remaining life for
expressed as:
R1
N1-n
1
decisions to overlay or not.
Anderson (1977) bases the decision to
overlay or not on the length of the remaining life.
If the
anticipated or estimated future traffic is more than the remaining
life, an overlay is needed.
If the remaining life is more than the
anticipated traffic over the functional
no overlay is needed.
life
of
the
pavement,
An overlay may be required for other
functional reasons such as improving the skid resistance of the
riding surface.
It is in this regard that Anderson (1977) states
that even a nominal thickness of asphalt concrete placed on an
existing pavement gives the pavement a new "life" by removing the
surface deformation.
"There is no theoretical or practical
evidence which suggests that the permanent deformation which existed
before rehabilitation
will affect the future performance
of the
pavement."
In general Anderson (1977) does support the analysis procedure
described by Snaith et al. (1980).
For the generalized
fatigue
relationship
(N_(l)b) the aim of an overlay would be to reduce the
e:
strain level (e: ) to the level where the anticipated traffic would
vs
meet the prolonged life or remaining life after overlay.
This
process is shown in Figure 0.1 and in a more general form in Figure
0.2.
The formulation of the fatigue relationship
considered by
Treybig et al. (1978) (as discussed in chapter 6 and Appendix C) is
obViously more complicated.
Although no specific mention is made
of any criteria for overlays related to remaining life the reasoning
above was evidently followed.
Molenaar
(1983) does not use his permanent deformation model (see
Appendix C) in his proposed overlay design.
It is obvious though
that this model, if properly calibrated to field performances,
would
also be able to provide the same criteria based on remaining life as
described in Appendix C.
If an overlay is needed, the aim would be
to reduce the elastic deformation
deformation
(Ue ) and resulting permanent.
(Up ) of each layer
in order to meet the required
.
prolonged life.
Remaining
life (N1-n1) compared with the anticipated or future
traffic is the general criterion for overlays, based on analysis
using the cumulative damage (linear summation ratio) theory.
This
has already been briefly described on the basis of the discussion by
Snaith et al. (1980) (see Appendix C and sections 2).
In considering
the previously defined rema1n1ng life, Anderson
(1977) also considers the cracked state of the existing asphalt
concrete layer and whether the pavement has an asphalt concrete
layer when establishing
criteria for considering an overlay.
remaining life is automatically
zero if the pavement is cracked
The
_0_
:tI~
_0_
"':
:'4.
-0-
0_
FIGURE 0.1
CHANGES IN STRAIN LEVELS
2 "
DUE TO OVERLAY.
,
""
"",
"' .••..,
4
r>- O·
ISO-STRAIN
LINE
€2
(b) Damage- Life
Diagram
t
DOl
I.I
(c)
NOTE:
B.O. - BEFORE OVERLAY
Domage - Path Diagram
A.O. - AFTER
OVERLAY
N
~
.••..
FIGURE 0.2
o
U)
DAMAGE
~.
STRUCTURE
•.....
I
~
I
o
~
PROCESS IN A PAVEMENT
WITH
A SINGLE
( Snaith, et 01., 1980)
OVERLAY.
and warrants consideration
for an overlay, or if there is no
asphalt concrete layer yet.
the anticipated
If the remaining life is less than
traffic an overlay may be considered.
If the
remaining life is more than the anticipated traffic no overlay is
needed.
When an overlay is considered as was discussed in
section 2 (referring to Figures D.1 and D.2), the aim would again
be to reduce the strain level (ERA) to accommodate a prolonged
life or remaining life after the overlay, which would meet the
required anticipated
in this way, Anderson
traffic life.
Analysing various pavements
(1977) arrived at characteristic
shown in Figure D.3.
curves as
In this figure remaining life is expressed
as a percentage of the overlay thickness.
The latter value of
overlay thickness corresponds to the reduction in strain level
(ERA)'
Comparing these results with those of a fully cracked
asphalt concrete layer with no remaining life, Anderson (1977)
concludes that it will always be more economical to neglect any
existing asphalt when the remaining life is below 75 per cent.
In
this overlay design procedure, a "critical" remaining life of 50 per
cent was adopted, this being the point at which the existing life is
disregarded
in designing an overlay.
fatigue relationships
This approach, based on the
described in chapter 6, was also followed by
Monismith and Markevich
(1983).
The approach by Molenaar (1983), using the structural performance
model, obviously differs from the one described above.
Molenaar
(1983) is quoted as follows:
"Although Miner's law is applicable to the development of one crack,
further extension of cracks is dependent on the redistribution
of
the stresses, and in this case Miner's law may not be fully
applicable.
Furthermore Miner's law defines a clear failure
condition which occurs at e.g. the fracture of a test specimen.
Such a failure point does not exist in the case of pavements.
A
100 per cent cracked pavement surface can still be used as a
reasonable driving surface unless large deformations
pot-holes occur.
Therefore a straightforward
the estimation of overlay thicknesses
and/or
use of Miner's law in
is not considered to be a
proper approach, since this will result in an unrealistic
overlay
design especially in those cases where Miner's ratio comes close to
12
II
10
f/)
Q)
9
.J::
8
-
7
(,)
C
f/)
f/)
Q)
t*
t
Case 3
C
.¥.
(,)
.J::.
I~
0
6
5
~
Q)
>
0
*
4
~ Case 2
3
*
~ Case 6
t~t Case 1
t ,t Case 5
2
t*
t Case 4
25%
500/0
750/0
1000/0
Remaining Life
EFFECT
FIGURE 0.3
OF REMAINING LIFE ON OVERLAY
THICKNESS(Anderson, 1977)
This supports the reasoning of Anderson (1977), but also points to
the possibility of the structural performance model being used to
give a more realistic estimate of the structural life of a bitumen
pavement.
Molenaar (1983) does not give any specific indication
of criteria for
decisions on overlays.
It is evident from the
reasoning, however, that the remaining life determined in this
way, would also be used, but with different preconditions.
The two distress criteria, fatigue cracking and permanent deformation rutting have deliberately been considered separately.
The
reasoning behind this is explained by Koole (1979):
"In determining the thickness required for an overlay, the
subgrade-strain
separately;
and asphalt-strain
criteria should be considered.
it is quite possible that the design criterion that
did not govern the original pavement design will become limiting
for the overlay thickness."
In this section an overlay thickness is thus decided upon by means
of the limiting life of the two defined criteria described in
section 2 and 3.
The resulting lower distress criteria parameters
(ERA and E ) are usually calculated for the possible thicknesses
vs
considered. Anderson (1977) calculates these relationships for the
various thicknesses of overlays by means of the techniques described
in chapter 4.
This is shown in Figures D.4 and D.5 for reduction
in subgrade strain (E ) and asphalt tensile strain (ERA)'
In
vs
Figure D.3 only pavements with more than 50 mm of asphalt concrete
prior to overlaying are considered.
The reason was discussed in
chapter 6 and in Figure 6.2 what the effect of relatively thin
asphalt concrete layers (50 to 75 mm) on tensile strain in asphalt
concrete was shown.
From the quotation by Koole (1979) above it is
obvious that an overlay of for example 25 mm on the existing 25 to
40 mm of asphalt for rut requirements, could in fact shorten the
remaining life of the fatigue cracking requirements.
The desired
'"TV
"".-
""
,
""V',
'"T ""
I
8
-
v
Thickness of OVerIOY-f..
5
7
I
0
)(
c
6
..•..•...
c
c
-
5
0
~
en
Q)
4
.
"0
t:l
0
~
'-I
en
:J 3
.0
en
c
c
0
2
0
"0
:J
Q)
0::
2
4
6
8
Subgrade Strain Prior to Overlay (in lin x 10- 4
REDUCTION
10
)
FIGURE 0.4
IN SUBGRADE STRAIN DUE TO OVERLAY (Anderson,
1977)
fO- 4-4 7 60/45
i
V
I
o 2.5
)(
Thickness of Overlay (inches)
C
"'-
-.S 20.
c:
-•..
0
en
1.5
.t:'
0
00
.s:::.
Q.
en
0
1.0
-
0.5
o
::J
'0
4)
0::
234
Asphalt
strain
prior to overlay (in/in x 104)
FIGURE 0.5
REDUCTION IN ASPHALT TENSILE STRAIN DUE TO OVERLAY
( Pavements with more than 2" of asphalt concre~e prior to overlaying)
( Anderson 1 1977 )
reduction in strain level can also be expressed in terms of the
selected deflection basin parameters,
according to Anderson (1977).
as shown in Figure D.6,
Similarly the desired lower
deflection basin parameter such as surface curvature index
(SCl)
can be related to a higher equivalent layer thickness (H ) (see
e
Figure 4.10) according to the analyses of Molenaar (1983).
Treybig et al. (1978) established
the most comprehensive
procedure
for considering the effect of fatigue cracking and rutting simultaneously.
This is shown in Figure D.7 where the existing asphalt
concrete layer is regarded as uncracked.
The overlay thickness
required, is determined by selecting the thicker of the two thicknesses related to the various criteria for the desired load
repetitions.
Koole (1979) also describes how three separate overlay thicknesses
are determined.
This includes the previously discussed criteria
for fatigue cracking and rutting, and also a method of determining
thickness based on the assumption that the existing pavement has
deteriorated
to such an extent that the asphalt concrete layer is
treated as a granular layer and the overlay as a "new" asphalt
concrete layer.
The latter approach is also suggested by Thompson and Hoffman (1983)
when the asphalt concrete layer displays interconnected
Class 2
cracking.
Remaining life in relation to the distress criteria, rutting and
fatigue cracking, is the main criterion in the consideration
overlays.
of
The remaining life determined by methods described in
chapter 6 was determined for each of the distress criteria separately.
For the rutting criterion the views on remaining life vary
considerably.
The view that remaining life is completely restored
by an overlay removing the deformations
overlay design.
is Widely accepted in
Using the various models discussed in Appendix C
it is possible to determine the prolonged life by lowering the
-u:c 120
z
-><!
....J
0:::
OVERLAY
THICKNESS
110
100
W
>
0
90
0
I-
80
w
::>
0
70
N
0
I
0
0
.
t1
60
-
0
50
z
z 40
0
-
I-
u
::>
30
0
w 20
0:::
o
10 20
30
40·50
60 70 80 90 100 110 120 130 140 150
DO - 012 PRIOR TO OVERLAY (INCH)
FIGURE 0.6
REDUCTION IN 00- 012 DUE TO OVERLAY
(Anderson,
1977)
--;;;8
Cl)
.J::.
o
c:
•.....••
en6
(J)
Cl)
c
~
o
.J::.
I-
Fatigue---
4
:>;
o
~
Cl)
> 2
o
o
10
100
1,000
10,000
100,000
Allowable 18- Kip Equivalent Load Applications, N x 103
SAMPLE
FIGURE 0.7
OVERLAY THICKNESS
DESIGN CURVES
vertical subgrade strain (€
vs
) for example.
The more comprehensive
model proposed by Treybig et al. (1978) warrants a closer look if it
were to be related to the South African situation as were the other
proposals and recommendations
mentioned before.
This may all be
incorporated in a proposed catalogue of overlay designs, which would
be similar to the existing TRH4 (NITRR, 1985a).
In consideration of remaining life as a criterion for fatigue
cracking, the consideration of cracking only leads to some uneconomical overlay proposals.
Anderson (1977) indicates that a 50
per cent remaining life for fatigue cracking should be a critical
value.
The structural performance model by Molenaar (1983)
attempts to be more economical by considering the structural value
of the cracked asphalt layer.
of the use
It also offers better consideration
of other new materials like bitumen-rubber.
In the final selection of the thickness of the proposed overlay for
the critical strain parameter, the emphasis is on checking the other
parameter again in order to ensure that the overlay does not shorten
remaining life after overlay for the previously non-critical
parameter value.
From Anderson's (1977) work it is obvious that
this would be of particular importance with thin overlays on thin
asphalt concrete layers.
The approach by Treybig et al. (1978) to
plot overlay thickness for both criteria simultaneously
in relation
to remaining life gives a good graphical indication of such trends.
It has been stated that the selection of an overlay must be seen
against the background of maintenance or rehabilitation management
systems.
The models discussed for analysis are not always
applicable to the South African situation.
suggested that the recommendations
It is therefore
in regard to pavement per-
formance and structure were made in previous sections be extended .
to this area of overlay design in order to make the whole design
procedure mechanistically
sound.
This could easily be incor-
porated in the suggested catalogue of overlay designs, mentioned
above.
In Appendix B it was mentioned that there exists a good correlation
between
the measurements
deflection
basin
Deflectometer
of the
parameters
(RSD).
as
Crack-Activity-Meter
measured
with
(CAM)
the Road
and
Surface
The normal procedure of initial assessment
according to the draft TRH12 (1983) guidelines are carried out on a
typical cemented base pavement.
In the detailed assessment stage
the question whether the cracks recorded on specific sections are
active or not must then be addressed with
confidence.
The new
service of the NITRR where the CAM and the RSD are combined can then
give the required information to make a sound decision in regards to .
the rehabilitation option.
Various cracks with related block sizes
and degrees of severity are selected on such a section under investigation.
At the same point (crack) the CAM and RSD are set up and
measurements are taken with the Benkelmanbeam truck travelling over
the
crack
following
the
WASHO
procedure.
The
crack
activity
measurements are then ·correlated with various other parameters such
as block size and deflection basin parameters (Rust, 1984).
This
appendix therefore describes how such an analysis on the N4/3 was
used to verify the rehabilitation option selected in terms of its
crack attenuation.
The cemented base of N4/3 is cracked and urgently needs rehabilitation.
1986) .
Crack movement measurements were taken in October
(Rust,
It was found that there exists sections of road where the
crack movements are very high.
relatively large.
The block sizes were found to be
This means that the crack movements are likely to
increase as the block sizes break down to a smaller size.
The
rehabilitation option that was selected is to overlay the existing
pavement with a 100 mm G1 crushed stone base and 40 mm asphalt
surfacing.
The analysis described in this technical note
is to
determine what the effectiveness of the overlay is to reduce crack
movement.
In the analysis use was made
of measured
deflection
basins and the correlation thereof with crack movement measurements.
This was followed with a mechanistic analysis of the rehabilitation
option to calculate the deflection basin and predicted crack movements.
On each of the measuring points of the CAM the deflection basin was
also measured with the RSD.
The measurement of the wnole deflection
basin with the RSD makes it possible to determine various deflection
basin
parameters.
The
most
common
deflection
basin
parameters
(Rust. 1986) that can be calculated from RSD measurements
are listed
in Table 1.1 with their respective formula.
crack movements
(VETOT)
(HMAX)
and the maximum
in micro-meters
basin parameters.
were
correlated
The maximum horizontal
vertical
with
crack movements
various
The results were as follows:
904,271* (MAX. DEFL)2,6 - 9,483E-6*(SCI
)2,5
915
3,086E-3*(SCI
)I,5
610
9,81*(SCI
+
- 2,538E-2*(Dl )l,3
1
4931.765*(MAX. DEFL)5.2 - l,813E-12*(SCI
)5.1
915
4.312E-8*(SCI
)3.6
+ 1;65E-3*(Dl )1.9 -
)1.9
+ 49.713
610
1.887E-3*(SCI
305
=
+
+ 71.765
)l,4
305
Where: SCI
deflection
+
1
Surface curvature index with the subscripts
indicating
the offset for deflection in mm.
Dl1
=
Deflection
Index which is the difference in deflection
at 127 mm and 305 mm.
MAX. DEFL
VETOT
=
=
Maximum deflection in mm.
Total vertical movement in micrometer.
The regression analysis indicate that VETOT correlated better with
the deflection basin parameters than HMAX.
The reason for that can
clearly be related to the relatively large block sizes (Rust, 1986).
The pavement
structures as shown in Figure E.1 for the existing
pavement and the rehabilitated pavement were analysed mechanistically with the computer program ELSYM5.
indicated in the figure.
base was calculated
overlay.
The input values are as
The stress directly on top of the cemented
before and after the G1 crushed stone base
The calculated vertical stress was 374 kPa and after the
overlay it was reduced to 111 kPa.
This is a drastic reduction in
the calculated stress values and clearly indicates that the overlay
did indirectly reduce the possible crack movements.
During the mechanistic analysis the deflection basin was calculated
for the two pavement
flection
basin
structures.
parameters
are
In Table E.1 the relevant
indicated.
The
deflection
de-
basin
parameters on top of the old cemented base (now sub-base) and on top
of the overlayed pavement are shown.
Deflection basin parameters (mm)
MAX. DEFL
SCI915
SCI610
SCI305
0,253
0,230
When comparing
the deflection
basin parameters
calculated on the
surface directly it is shown in Table E.1 that the overlay reduces
the deflection basin parameters values drastically.
This reduction
in the respective deflection basin parameter values are even more
when the values calculated on top of the cemented base are compared.
i
2,4m
EXISTING PAVEMENT
I
I
3,7 m
3,7m
EXISTING
EXISTING
150 CI
<t.
EXISTING PAVEMENT
I
50
150
AC
CI
FIGURE E.!
REHABILITATION
OPTION ON N4 /3
3,7 m
rI
The regression analysis described earlier were also used to calculate the respective predicted crack movements.
These results are
shown in Table E.2.
The results in Table E.2 show that there is a drastic reduction in
the vertical and the horizontal crack movements.
In the case of the
vertical crack movements the reduction was more.
This
vertical
movement was the more severe case for crack movement due to the
relatively large block sizes.
(a)
The crack movements
(HMAX and VETOT) were correlated with
various deflection basin parameters as measured with the CAM
and the RSD.
(b)
The vertical stress calculated on top of the cemented base
show a drastic reduction in values when compared with the
vertical
stress values
calculated on top of the
sub-base of the overlayed pavement.
cemented
This reduction indicates
that there should be a reduction in crack movements too.
(c)
The
deflection
basin
parameters
were
calculated
existing pavement and the overlayed pavement.
for
the
These calcu-
lated deflection basin parameters were used in the correlation
relationships to determine the
calculated crack movements.
There is a drastic reduction in the crack movements on top of
the cemented base due to the overlay.
Odemark
(1949) equivalent
IS
layer thickness concept is used as a
simple method of approximation.
multi-layered
It enables the transformation of a
system into a single layer with equivalent thickness.
The principle is that the equivalent layer has the same stiffness as
the original layer, so as to give the same pressure distribution
underneath the layer.
This concept of classifying a pavement with
one number that represents more or less the bearing capacity of that
pavement is clearly illustrated by Molenaar and Van Gurp (1980) and
Molenaar (1983). The typical South African pavement structures that
were analysed in chapter 7 were also converted to
layer thickness.
the equivalent
The equivqlent layer thickness values calculated
were then rlated to various distress determinants and fatigue life
in
order
to
evaluate
this
concept
as
a possible
aid
in
the
mechanistic rehabilitation design procedure.
L-l
= aE
2
E.(l-v)
I].
~I
h.
]. E (I-v.)
s
].
II
3
where
= 0,9 for flexible pavements
a
=
E. =
].
E =
s
v. =
V =
s
h.].
].
thickness of layer i in m
elastic modulus of layer i in N/m2
2
elastic modulus of subgrade in Nlm
Poisson ratio of layer i
Poisson ratio of subgrade
layer with value equal to 0,35
L
=
Number of layers
Molenaar (1983) and Molenaar and Van Gurp (1980) analysed a typical
three-layered
pavement
structure.
The
typical
flexible
pavement
structures
referred
to in this Appendix
differ
from this three-
layered system in the sense that the pavement structures are either
four layered or five-layered systems with a different standard wheel
load
and
tyre
resemble
these
thickness
of
pressure.
The
three-layered
the
bitumen
bitumen
pavements
bases.
base
most
Most
of
pavements
closely
analysed
in terms
the typical
of
flexible
pavement structures analysed. though, have thin asphalt surfacings
(S 40
mm).
In Figures F.l and F.2 typical relationships of H
e
versus deflection
basin parameters, shape factor (Fl) and slope of deflection (SO) are
shown as calculated for bituminous base pavements.
The purpose
is
to show that some deflection basin parameters like SO, R. SCI, BCI
and BOI can discern
between
the various
subgrade
while others, such as F 1, F2, S, A and Q cannot.
elastic
moduli
In Figure F.3
surface curvature index (SCI) is shown for bituminous and granular
bases versus H.
In both cases SCI can discern between the various
e
subgrade effective elastic moduli.
The gradients for these functions of the bitumen base pavements correlate well with bitumen base
pavements with three layers (SCI with r
Gurp, 1980).
=
500 mm) (Molenaar and Van
The gradients for the relationships
of the granular
base pavements though, are shallow and reflect a greater sensitivity
to changes in H .
e
Flexible pavements in general were grouped together in Figure F.4 to
show that H
e
correlates well with vertical
subgrade strain (e:
vs
).
The various values of effective elastic moduli of the subgrade lead
to different
relationships
as shown in Figure F.4.
the other distress determinant,
(e:HA) , at the bottom
horizontal
of the bituminous
In Figure F.5
asphalt tensile
strain
base, is shown versus He'
Here again, there is a clear discernment between the elastic moduli
of the subgrade.
It is however not possible to develop the same
relationship between e:HA and He for the thin surfacings of granular
base pavements. One of the reasons for the latter situation seems
to be that the thickness, Poisson ratio and elastic modulus ratio of
the thin surfacing, compared to that of the base and even subgrade,
differ markedly
from that of a bituminous base pavement.
This is
IJ..
a::
0
I-
U
~
0,5
w
a..
<t
J:
CJ)
0,2
0,1
0, I
0,2
0,5
t
2
5
EQUIVALENT LAYER THICKNESS (He) (m)
10
FIGURE F. I
EQUIVALENT LAYER THICKNESS VERSUS SHAPE
FACTOR F!
0
en
Z
0
IU
W
...l
IJ..
W
0
IJ..
0
W
a..
0
...l
CJ)
CJ)
CD
•...•.
0
to
10
0,I
0,2
0,5
I
2
5
EQUIVALENT LAYER THICKNESS (He)(m)
(\J
10
I
.;t
I
0
.;t
en
FIGURE F.2
EQUIVALENT LAYER THICKNESS VERSUS SLOPE
OF DEFLECTION
GRANULAR
'"
~
"-
-
I- Es = 50 MPa
~
""'lIl
~
~
"'
"'"
~
10
0
~
\
\
tj
U')
,.\
, 1\\
\
\~.
BASES
Es=50MPa
Es=70
,
~
~
~
BITUMEN
~,.
~ ~~
~
~ ~
1\
\
E
::L
Es = 150 MPa
~
II
--
~
\' ,
\
•..
Es = 70 MPa
....•
..
100
I'f)
~
lC"""
'"
E
E
I
BASES---
~
"
MPa
"\~\
Es= 150 MPa
\
10
0,3
EQUIVALENT
I
LAYER
THICKNESS
,\
.
2
(Hel (ml
F.3
Equivalent
layer th i ckness versus
surface curvature
index
FIGURE
z
~
500
~
(J)
I
::i..
100
0,3
EQUIVALENT
I
LAYER THICKNESS
2
(HeJ (m)
FIGURE F.4
VERTICAL SUBGRADE STRAIN VERSUS
EQUIVALENT LAYER THICKNESS FOR
FLEXI BLE
.0
111
.•...
....
ut
o
to
I
~
I
o
'f
~--
PAVEMENTS
~ 100
<t
Q:
I(/l
I
::t
Es
= 50 MPo
Es
=
70 M Po
Es =150 MPo
10
O,~____
EQUIVALENT
I
LAYER
FIGURE
THICKNESS
2
(HeHml
F.5
EQUIVALENT
LAYER THICKNESS VERSUS
MAXIMUM
ASPHALT
STRAIN FOR
BITUMEN
BASE PAVEMENTS
clear when one looks at the formula for the calculation of H • given
e
Equivalent layer thickness (H ) can be used to indicate whether a
e
pavement structure with cemented subbases or bases is in the flexible state, with the cemented layers in the cracked phase exhibiting
equivalent granular behaviour according to the definition given by
Freeme
(1983).
pavements with
In
Figure F.6, H
e
for
the
pre-cracked
life
of
cemented subbases and bases is shown in terms of
standard 80 kN axle repetitions (E80s) determined as prescribed by
Freeme et al. (l982a).
A distinction can be made based on the
variance of the elastic modulus of the subgrade.
however,
that an H
It can be seen,
value of at least 1,1 m is required for a
e
subgrade modulus of 70 MPa to have any significant pre-cracked life
of cemented
layers.
This
is rather high and reaffirms that the
major portion of the structural life of typical TRH4 (NITRR, 1985a)
pavement structures
with cemented layers is in the cracked phase or
flexible behaviour state.
The recommended vertical subgrade strain (e ) criteria for diffevs
rent road categories (Freeme et al., 1982a) were used to calculate
the standard 80 kN axle repetitions for all the flexible pavement
structures for their respective values of H.
e
This relationship
between He and E80s is shown in Figure F.7 for all flexible pavement
structures.
In
this
figure
the
fatigue
life of
bitumen
base
pavements was also calculated with respect to maximum asphalt strain
(eRA) and correlated with the respective He value.
The recommended
fatigue life criteria for thick bitumen base pavements were used in
The recommended shift
the ca 1cu 1at·J.on (Freeme et al., 1982a).
factors shown in Table F.1 were applied to the calculated fatigue
lives.
Ul
0
CD
IJJ
CJ)
Z
0
!::
~
IJJ
Es
Cl.
IJJ
a:: 105
50 MPo
70 MPo
150 MPo'"
IJJ
...J
X
«
z
..lie:
0
CD
0
a::
«
0
z
«
~
CJ)
~
104
u
«
a::
u
IJJ
a::
Cl.
j
103
0,20
EQUIVALENT
1,0
LAYER THICKNESS
5,0
(He) (m)
FIGURE F.G
Initiation
of cracking of cemented
bases and su bbases in terms of
equivalent
layer thickness
'0
m
~
"'-
CD
o
II')
I
qI
o
'f'
-Q'I
I
_
-
I
E vs I FORI
r
FLEXIBLE
PAVEMENTS
I
I
I
I
I
I
TRH4 (NITRR 19850
TRAFFIC CLASSES
I
t
en
0
- E4
CO
W
C/)
107
-
z
0
I-
I-
E3
~
W
Cl.
W
0::
-
W
...J
X
«
I-
a
E2
,.,.
0::
«
a
z
«
I-
"'s
106
= 70 MPo
-
C/)
~EI
~
J
EO
105
-
-
E
FOR
HA
BITUMEN
BASE
PAVEMENTS
0,1
1,0
EQUIVALENT
LAYER
FIGURE
THICKNESS(He)
(m)
F.7
Pavement life for maximum
asphalt strain and vertical
subgrade strain criteria in
terms of equivalent layer thickness
-
to
I
V
I
o
V
--"""---------
The equivalent layer thickness (H ) concept proved to be a concept
e
that more
or less represents the structural capacity of flexible
pavements.
Deflection basin parameters correlate well with a value
such as H
e
in general, as calculated for flexible pavements.
however only such deflection
basin parameters,
It is
that normally use
points of deflection near each other in the calculation procedure
(e.g.
scr,
R, BCI, BDI and SD), that can discern the effect of
variance in subgrade elastic moduli.
Such relationships however do
not have much value except as for an interim step towards establishing relationships between the distress determinants (£RA and £VS)
and H .
e
He correlates well with subgrade vertical strain (£VS) for flexible
pavement structures and discerns the effect of variance of subgrade
elastic moduli.
Granular bases on the other hand do not give any
clear relationships between maximum asphalt strain (£RA) and He as
is the case with bitumen base pavements.
The reason seems to be the
ratios of the thickness, elastic modulus and Poisson ratio of the
surfacing and the base as well as that of the subgrade, in the
calculation of· H , which leads to this marked difference
e
between
granular and bitumen bases.
The value of H
e
can be used in a mechanistic design or analysis
procedure to establish the structural life of a flexible pavement
with regard to the distress determinants (£VS and £RA)'
The pre-
cracked life of a cemented base and subbase layer can be determined.
It must be remembered though, that in order to use H
the effective
elastic moduli
thicknesses have to be known.
e
in such a way,
of all the layers as well as the
This restricts H
e
to an interim value
in the determination of the distress determinants (£VS and £RA) in
the mechanistic analysis of a pavement.
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of pavement
design.
Parameter
.
Formula
I. Maximum
deflection
2. Radius
3.
of
80
curvature
Spreadability
4. Area
5. Shape
factors
6. Sur face
curvature
7. Base
curvature
8. Base
damage
9. Deflection
10. Bending
II. Slope
index
index
index
ratio
index
of deflection
12. Tangent
13. Radius
slope
of influence
r2
R
=
S
::
A
=
6[1+ 2 (SI/80)
F
=
(80- 82) I 81
SCI
=
8o'-:8r
BCI
=
8610 -8915
BDI
=
8305 -8610
Or
=
8r/80
BI
=
80/a
SO
=
tan-1 (80-8r)/r
ST
=
(8 o -8d/r
RI
=
R'/80
280 ( 80/8 r - \)
[( 80+81+82+ 83)/5]
80
r
,
,
where
)
=
127 mm
100 ,.
F2
=
=(
81""83
spaced
305mm
8, -83) 182
or
305
500 mm
8r ~ 80/2
where
,.
r
+2(82/801"83/80]
;
,
i
a = deflection
; where
where
r
=
r
shape of
road
~Point
surface
Positive
curvature
610 mm
to
poi nt
R I is the distance from
where
80 to whe re basin is tangent
to hori zontal.
P
/
=
distance
inflection
a or R'
Deflection basin length
Deflected
basin length
of
inflection
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