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ISSN 0347-6049
i V//särtryck 153
Resilient modulus by indirect tensile testSafwat F. SaidPrepared for presentation and publication at the Fourth Inter-national Symposium RULEM, 24 - 26th October, 1990 inBudapest, Ungern
Vag-och Trafik- Statens väg- och trafikinstitut (VT!) * 581 01 Linköping
'Institutet swedish Road and Trattic Research Institute * S-581 01 Linköping Sweden
-
ISSN 0347-6049
___ K1/särtryck153 1990
Resilient modulus by indirect tensile test
Safwat F. Said
Prepared for presentation and publication at the Fourth Inter-
national Symposium RIÅLEM, 24 - 26th October, 1990 in
Budapest, Ungern
f, Väg"00h a /(' Statens vag- och trafikinstitut (VTI) * 581 01 Linkoping
[ St]tlltet Swedish Road and Traffic Research Institute * S-581 01 Linkoping Sweden
-
Samhall Klintland Grafiska, Linköping
-
RESILIENT MODULUS BY INDIRECT TENSILE TEST"
SAFWAT F. SAID
Swedish Road and Traffic Research Institute
Linköping, SWEDEN
Abstract
With developments in analytical design of pavement structu-
re, there is an increasing demand for knowledge of the
mechanical properties of various pavement elements under
different conditions encountered in roads, such as tensile
strength, stiffness modulus, and repeated-load fatigue re-
sistance of the asphalt concrete mixtures. These parameters
provide a good basis for analytical design and performance
evaluation of flexible pavements.
In this study, Indirect Tensile Test has been conducted
because of its validity and simplicity. However, modifica-
tions of the test apparatus and test procedure have been
introduced.
Three different types of asphalt concrete mixtures have
been examined using indirect tensile method. Two of the
mixes are blended with 3% rubber content by total weight.
i.e. Rubit (RUBI2), which is a dense asphalt concrete used
for surfacing, and a porous mix called Rubdrain (RUBD12) .
The third mix is a conventional dense asphalt concrete
(HAB12T) used for surfacing. The maximum size of the aggre-
gate was 12 mm for all types.
Stress-deformation-strain relationships have been estab-
lished in order to examine the effect of stress and/or
strain level on the resilient modulus found by the indirect
tensile test and to define an approximate linear viscoelas-
tic zone for bituminous mixtures at different temperatures.
Resilient modulus has been measured using the modified in-
direct tensile method for mixtures studied at four different
temperatures.
Keywords: Asphalt Material, Rubberized Asphalt, Indirect
Tensile Test, Resilient Modulus, Linear Viscoelastic,
Stress-Strain Relation, Temperature.
*This job has been conducted by the Dept. of Highway
Engineering, Royal Inst. of Technology in cooperation with
the Swedish Road and Traffic Research Inst.
-
1 Introduction
With developments in analytical design of pavement structu-
re, there is an increasing demand for knowledge of the
mechanical properties of various pavement elements under
different conditions encountered in roads, such as tensile
strength, stiffness modulus, and repeated-load fatigue re-
sistance of the asphalt concrete mixtures. These parameters
provide a good basis for analytical design and performance
evaluation of flexible pavement.
In the last three decades a lot of research has been
focused on the response of various layers and materials sub-
jected to possible conditions in the field by using a wide
variety of methods and apparatus, which have a provided
valuable knowledge platform for further investigation.
Indirect tensile test has been conducted in this study
because of its validity and simplicity. However, modifica-
tions of the test apparatus and test procedure have been
introduced.
Three different types of asphalt concrete mixtures have
been examined using indirect tensile method. A conventional
mix HABl2T, which is a dense asphalt concrete used for
surfacing, Rubit (RUBI2)], which is a rubber granular blended
asphalt mix with 3% rubber content, and a porous mix, called
Rubdrain (RUBD12) also containing 3% rubber used as a drain-
age layer, have been used. The maximum size of the aggregate
was 12 mm for all types. Rubit and Rubdrain mixtures are
marketed by the ABV (NCC) company. The specimens were
supplied by the ABV laboratory.
Stress-deformation-strain relationships have been estab-
lished in order to examine the effect of stress and/or
strain level on the resilient modulus found by the indirect
tensile test and to define an approximate linear viscoelas-
tic zone for bituminous mixtures at different temperatures.
Resilient modulus has been measured using the modified
indirect tensile method for mixtures studied at four
different temperatures.
2 Test apparatus
Due to its simplicity and validity the Repeated-1load Indi-
rect Tensile Test [1-8], with modification in test apparatus
and test procedure, has been used to study the mechanical
properties of bituminous mixtures. The principle of this
test is that a cylindrical specimen is loaded in the verti-
cal diametral plane, the compressive load is applied through
a couple of curved loading strips. The resultant deformation
is measured at horizontal diameter.
The expressions given by Schmidt [2] andKennedy et .al.
[1] for tensile stress at the center of specimen, resilient
modulus, Poisson's ratio and strain across horizontal diame-
ter are the following:
-
. + v v + + + + k k k k k k k k W k ok WoW k ok k k k k k ok k k k k d k k k k k k k k (1)Q [1
5 11 3.4 [ÄH/AV]- 0427 4 v 4 4 v k kW kk kk kk k k k k k k k k k k k k k k k k k (2)
(P/t. AH)[4/n+n-1] = P(n+0.27)/t.AH. . . .. . + + + ++ + ++. (3)Mr
E. =(2P/MantD)[ (4D*n-16D?x2)/(D2+4x2)2+(1-n)]. .... . + +. (4 )
Tensile stress (MPa)
Applied load (N)
specimen thickness (mm)
specimen diameter (mm)
Poisson's ratio
Total resilient horizontal deformation (mm)
Total resilient vertical deformation (mm)
Resilient modulus (MPa)
Tensile strain at horizontal diameter
SU
ctU
Q
AH
NV
Mr
Ex
d
By substituting Equation (1) in Equation (3) and solving for
resilient modulus:
Mr = (KD/2) (0/AH)]) (n+0.27) i i i v v v v k k k k k k k k k k k k e k k k k k k a (5)
To find the tensile strain at the center of the specimen
(x=0), substituting Equation (3) in Equation (4) and solving
for strain we get:
Co = (2AH/D)[(I+3n)/(4+KM+T)] ] + + + + + + + + + + + * + & * k ok k k k k k k k a (6 )
If n = 0.35 then
Co = 2.1 (AH/D) ....................................... (7)
where, AH and D are defined as before.
The testing machine is capable of applying compressive
pulse loads over a range of frequencies and load durations
for repeated load testing.
In this investigation the repeated load pulse was applied
at a frequency of 0.33 Hz with 0.2 sec loading time and 2.8
sec rest period. The load applied in the vertical diameter
plane is sensed by a load cell under the specimen. Deforma-
tion across the horizontal diameter of the specimen is
sensed by one extensometer instead of two LVDTSs, which are
normally used. Instron dynamic strain gauge (2620-601, with
resolution of 20+*107-5 mm and weight 20 grams), and MTS
extensometer (632-11l1c, resolution 8*10-7-5 mm and weight 25
grams) have been shown to be adequate. The strain gauge is
fixed to two curved zinc strips (2 mm thick, i0 mm wide and
80 mm long) which are glued at opposite sides of the hori-
zontal diameter. The total weight of extensometer and the
-
two deformation strips is less than 75 gm (See Plate 1 and
Figure 1). However, a couple of LVDTs with the frame which
carry out the two LVDTs is more than 700 gm which might
influence the recorded deformation.
Plate 1. Horizontal] extensiometer mounted on the specimen.
_| (ts d US If 4)
FPL
/_/_ __J
Fig.l. Deformation strips.
-
The deformation is measured at the same points where the
two zinc strips are glued in order to avoid any error in re-
cording deformations due to specimen movement or inadequate
contact between extensometer (strain gauge) and specimen.
Brown and Cooper [9] have mentioned the shortcomings of
indirect tensile test, using LVDTs, in deformation measure-
ment. The recorded deformation was found to be influenced
by the strength of the spring used to keep the LVDT core in
contact with the specimen, and by the vibration of the frame
which carries the deformation transducers. In addition, it
is easier to use just one extensometer rather than two
LVDTS .
The loading device is shown in Plate 2 and Figure 2. The
upper steel loading strip is not fixed on the upper platen
of loading device in order to bring a good contact between
loading strips and specimen even at low stresses and high
stiff asphalt specimens. An alignment bar is fixed to the
upper aluminum platen to bring the loading strips into the
same vertical plane. Figure 3 shows three different cases
which could happen depending on the contact between loading
strips and specimen when the loading strips are fixed on the
platens. Case 1 shows a good contact, while cases 2 and 3
show insufficient contact which is a result of a rough
surface. For more details see reference 22.
Plate 2. Loading device and specimen in place.
-
0 :sug Z 12
© organ %& / C J_
© 7/77 NZ / . -/// /" , z* sär
\ ( \| 22 _£ _/ __z Im
O_ y k 0 | [
Å,
di / en
_ _ /
| \ // 9)
GRK w ] & |- 1
#NWM r®\\\ n Xskäl .
o s I _._]
|
210
All dimensions in mm
1 Precision Pillar2 Ball Bushing3 Upper Plate4 Float Loading Strip
Fig. 2.
twCO
-IOy
Un SpecimenAlignment BarFixed Loading StripBottom PlateHardened Disk
Loading device for indirect tensile test.
-
Case 1 0
Case 2
Case 3
Fig.3. Contact between strips and specimen.
3 Viscoelastic property of bituminous materials
Various investigators have emphasized the effects of stress
or strain levels on the modulus of asphalt concrete mixtures
[2,10-21]. The increasing use of elastic theory in pavement
evaluation and for comparing various asphalt materials in
terms of their rheological characters makes the fundamental
properties in stress-strain relationship an important param-
eter [16]. With regard to the non-linear viscoelastic behav-
ior of bituminous materials, the stress or strain level has
an essential influence when measuring the moduli. Sayegh
[17] does not exceed a strain value of 4.107* when measuring
moduli. Monismith et. al. [11] consider the stiffness of
asphalt mixtures independent of applied stress at strains
less than 1.1073 in/in. Bonnaure et .al. [13] determine
stiffness modulus for strains 5.107 at -159C and +92C;
20.107 at +302C. Bonnaure et .al. also report that the phe-
nomenon of non-linearity appears at strains close to
100.107. Kennedy and Anagnos [1] and ASTM [3] recommend a
load range to induce 10 to 50 percent of the tensile
-
strength as determined in the static indirect tensile test,
or in lieu of tensile strength data, loads ranging from 4 Ib
(25 Ib according to Kennedy) to 200 Ib per inch of specimen
thickness can be used. Schmidt [2] uses a stress range from
about 1 psi up to 15 psi at the specimen center at 73 PF (24
°C). So a wide variety of limits have been recommended.
Therefore, an approximate linear zone (the resilient
modulus is independent of applied stress or strain level)
should be well defined to make the modulus more reliable.
4 Linearity
The test series consist of testing three specimens from each
type of asphalt mixture at temperatures of -10, +5, +25 and
+40 degrees Celsius and at a loading frequency of 0.33 Hz.
Totally, 36 specimens have been tested with this method.
The test procedure is the following:
* The test specimens were stored in a temperature cabinet
for 24 hours at testing temperature. ( A dummy specimen
has shown that it takes at least four hours to bring the
specimen from room temperature to -10eC) .
* Repeated-load pulse, at a frequency of 0.33 Hz, was ap-
plied with 0.2 sec loading time and 2.8 sec rest period
* The load level was increased gradually up to a level
which resulted in a recordable deformation by
extensometer.
* -A minimum of 50 load repetitions were applied before the
first reading.
* The load level was increased gradually to a higher level
with about 25 load repetitions at each load level. The
maximum load level used was about 4000 N.
* Stresses and strains were calculated at each load level,
a curve was fitted by regression analysis for all three
specimens, which represent the material response at de-
fined temperature. The zero point has normally been ad-
justed due to surface irregularities.
The isochronous stress-horizontal deformation-strain
diagrams were produced for bituminous mixtures to study the
stress and strain effect on resilient modulus using repeated
load indirect tensile test. Figure 4 shows isochronous dia-
gram for HABl27T mix. Similar curves have been found for the
other two mixtures (See Figure 5 and 6). The stress was
calculated at the center of the specimen by Equation 1.
These diagrams are represented by stress-deformation-strain
-
0.40aoe | //l
| +5 °C0.35 s
l/ /// "(u gset 0.30
TENS
ILE
STRE
SS(M
Pa)
"7 a
| \ 0.20
sl |/ _-
|/ s
I
//+40°C
0.10
|
pameM
. //// ///////,/
/
/
o L-- . -o ul
0 50, 100. 150, 200. 250, 300 x10
OEFORMATION (mm)
(0 " 200 / 5,00 " 600 x 10%
STRAIN
Fig.4. Stress-deformation-strain relationships for HABl27T.
curves and not only by the more familiar stress-strain
curves, hence the deformation distribution on the horizontal
diameter is not uniform [2,4,5,23]. This is done in order
to eliminate the effect of using an assumed value for the
Poissons ratio for strain calculation at the center of the
specimen, which might affect the strain value. However, for
the sake of comparison, the tensile strain at the center of
the specimen is calculated by Equation 7.
The correlation coefficients (R) are higher than 0.94,
except for the porous graded mix tested at 25 degrees
Celsius, which is 0.83. In all the cases, the stress-
deformation relationships show curves which are concave
downwards. This means that strain increases faster than
stress and results in a reduction in resilient modulus. The
nonlinearity relationships are obvious even at low stress
and deformation levels. The non-linear viscoelastic rela-
tionships confirm the importance of stress and deformation
levels when measuring the resilient moduli of asphalt
mixtures .
The above discussion shows the dominance of viscous prop-
erties at high strain and stress levels. Therefore, and in
order to measure the resilient moduli of bituminous materi-
als with consistent in results, a viscoelastic linear zone
should be defined in which the effect of stress or strain
levels on the resilient modulus is negligible. If resilient
modulus is measured at higher stresses or strains, it could
be justified in some cases in order to simulate field
-
- 0.40
&
0 0.35
E 3 n 10°C //+S°C / -
§ 0.30 o
% / *ZSOC
- 025 /////,////
0.15 A/ ///
I| | aoe_|_0.10 7 Tee|__---*x
0.05 // / ////; * A ___/_l",//
0- -4
0 50 100 150. 200. 250, 300. 350 400. x 10
JEFORMATION (mm)
-- } + i } -6
0 200 400 600 800 x10
STRAIN
Fig.5. Stress-deformation-strain relationships for RUB1l2.
0.40
0.35
0.30
TENSILE
STRESS
(MPa)
0.25
0 20
0 15
0 10
0 05
Fig.6. Stress-deformation-strain relationships
10
|
1~10°C
/
¥ +5 °C// /////
// / e/
_- 25°C
/ _l
/| / cV/
// 7/
________._ 4|U
/ // ---|_| see/ / nonafuse
//L-/"/ Louk
0 50 100 150. 200, 250 300 350 500 x 10
DE FOR2MATION (mm)
0 200 400 600 800 = 10
STR AIN
for RUBD12 .
-
p Linear zone is at
o=A/B *100 © 10%
Fig.7. Isochronous stress-deformation curve.
conditions, in this case the stress or strain level should
be reported.
The viscoelastic linear zone is defined, in this study,
as the zone where stress in the stress-deformation curve
divergqges with less than 10 percent from the rectilinear
stress-deformation relation shown in Fiqure 7. The recti-
linear stress-deformation relation is represented by the
slope of the curve at the origin.
The 10 percent divergence of stress cause a 10 percent
reduction in resilient modulus from the initial modulus
value (modulus at origin). This variation is believed to be
acceptable because of the hetrogeneity and unisotropy of
asphalt concrete mixtures.
Figure 4 through 6 also show the limits of deformations
and stresses at 10 percent reduction of resilient modulus.
The stress limits decrease with increased temperatures but
for deformations it is the opposite, i.e., the deformation
limits increase with increased temperatures. A similar con-
clusion is reported by other investigators [24,25 ,26] when
exposing asphalt mixture specimen to different deformation
rates, using the tensile strength method, higher elongation
is reported at lower deformation (high temperatures
correspond to low deformation rates) and vice versa. At low
temperatures the bituminous mixtures are stiff and brittle.
They tolerate low strains with high stresses. At high
temperatures these mixtures have low stiffness and high
flexibility. They tolerate high strains but with very low
stresses.
Figure 8 shows a relation between temperatures and the
logarithm of deformation limits, as defined before for
1 1
-
- 1000
600 - I 300
Log(D) = exp(0.0138T+0.313) &g | e00
2007 -400
mm
-6TE
NSIL
EST
RAIN
x10
- - 20080 -
D]x
10
60 7
- 1000 7
- 80
DEFO
RMAT
ION
(
60
ad - 40
- 30 - 10 0 10 20 e
TEMPERATUR (T) 2C
Fig.8. Relationship betweenn the logarithm of deformation
and temperature.
tested mixtures (with 0.2 sec loading time, and a frequency
of 20 cycle/min.).The correlation coefficient (R) for all
materials together is 0.986, using regression Equation 8.
Log(D) = exp(0.0138T+0.,313) . | / . v v v v v & v k k v k k k k k k k k k k a k a (8 )
where
D= Horizontal deformation in mm x 107-74
T= Temperature in Celsius.
5 Resilient modulus
In accordance with the discussion in the above section
regarding stress-strain relationships and the effect of
irregularites of specimen surface the following procedure
has been used for resilient modulus measurement. Indirect
tensile test has been used on cylindrical bituminous sample.
* The test specimens were stored in a temperature cabinet
to the proper temperature.
* Repeated-load pulses at a frequency of 0.33 Hz were
applied with 0.2 sec loading time.
12
-
Ä minimum of 50 load repetitions were applied before the
first reading and until the resilient deformation became
constant .
The resilient horizontal deformation were measured at
the maximum allowable load level and at 50 and 75% of
this value. The test began at the lowest load level and
increased gradually to higher load levels with about 25
load repetitions at each load level.
After the test had been completed, the tensile stress
was calculated at each load level according to Equation
(1) .
Stress-resilient horizontal deformation curve was
plotted. Curve fitting by linear regression analysis
was used. In such cases, the zero point was adjusted as
shown in Figure 9 to compensate for surface irregulari-
ties and insufficient contact between loading strips and
specimen .
The resilient modulus was calculated with constant
Poisson'!s ratio according to Table 1 at different
temperatures by Equation 5:
/
LN
Fig.9. Correction of the stress-strain curve.
1 3
-
Table 1. Constant Poisson's ratio
TeC n
- 1 0 0 . 20
d- 55 0 . 25
+2 0 0 . 35
+4 ( 0 . 4 0
10000 +
8000 -
6000 -
$ 4000 -£
92)
-3DCM
2- 2000 +
C
gä[I x
1900 ---HAB12T n
1000 - - - RUBA2 ä
- - -RUBD 12 *xgjxx
500 he~10 0.0 +10 +20 +30 +40
TEMPERATURE °C
Fig.l10. Effect of temperature on resilient modulus.
14
-
Figure 10 shows the resilient modulus at different
temperatures. The relationship between temperature and the
log of resilient modulus is not linear. The rubberized mix
(RUB1I2) shows lower moduli than conventional mix (HABl27T), a
fact which indicates the higher flexibility of the rubber-
ized mix. The porous mix (RUBD12) has shown, as expected,
the lowest moduli. Furthermore, there were no problems in
measuring resilient modulus for the porous mix.
Conclusions
An approximate linear viscoelastic zone for practical use
has been defined for asphalt mixtures at different
temperatures (with 0.2 loading time and 20 cycles/min.).
The upper loading strip should be free in order to create
satisfactory contact between loading strips and specimen
even at low stresses and stiff asphalt specimens.
One extensometer may be used instead of two LVDTs with
carryirig frame. In that case the recorded deformation
will not be influenced by the following: (1) the strength
of the spring that keeps the LVDT cores in contact with
the specimen, (2) the vibration of the frame which car-
ries the deformation transducers, and (3) the extensive
load on the specimen.
References
Kennedy T.W and Anagnos J.N, "Procedures for the Static
and Repeated-Load Indirect Tensile Tests, "Research Re-
port 183-14, Center for Transportation Research, The Uni-
versity of Texas at Austin, 1983.
Schmidt R.J, "A Practical Method for Measuring the Resil-
ient Modulus of Asphalt-Treated Mixes", Highway Research
Record, 404, 1972 .
; American Society for Testing and Materials,ASTM D 4123-82, Method of Indirect Tension Test for Re-silient Modulus of Bituminous Mixtures, 1984.
Wallace K. and Monismith C.L, "Diametral Modulus Testingon Nonlinear Pavement Materials", Proceedings, The Asso-ciation of Asphalt Paving Technologists, Vol. 49, 1980,p. 633.
. Kennedy T.W, "Characterization of Asphalt Pavements Mate-
15
-
1 0
1 1
1 2
1 3
1 4
15
16
rials Using the Indirect Tensile Test" Proceedings of the
Association of Asphalt Paving Technologists, Vol. 46.
1977 .
Baladi G.Y, Harichandrun R.S and Lyles R.W, "New Rela-
tionships Between Structural Properties and Asphalt Mix
Parameters", Paper presented at the Transportation
Research Board, 67Jth Annual Meeting, Jan 1988.
Hondros G., "The Evaluation of Poisson's Ratio and the
Modulus of Materials of a low Tensile Resistance by the
Brazilian (Indirect Tensile) Test with Particular Refe
rence to Concrete", Australian Journal of Applied Sci
ence, Vol. 10, No. 3, 1959.
Baladi G.Y., Harichandrun R. and De Foe J.H., "The Indi-
rect Tensile Test, a New Apparatus". Interim Report,
College of Engineering, Michigan State University 1987.
Brown S.F and Cooper K.E, "The Mechanical Properties of
Bituminous Materials for Road Bases and Base courses"
Proceedings of the Association of Asphalt Paving
Technologists, Vol. 53, 1984.
. Pell P.58 and Taylor I.F, "Asphaltic Road Materials in
Fatigue", Proceedings of the Association of Asphalt
Paving Technologists, Vol. 38, 1969.
. Monismith C.L, Epps J.A and Finn F.N, "Improved Asphalt
Mix Design" Proceedings, The Association of Asphalt
Paving Technologists, Vol. 54, 1985, p. 347.
.Deacon J.A and Monismith C.L, "Laboratory FlexuralFatigue
Testing of Asphalt-Concrete with Emphasis on Compound-
Loading Tests", Highway Research Record, No. 158, 1967.
. Bonnaure F., Gest G., Gravious A. and Uge P., "A new
Method of Predicting the Stiffness of Asphalt Paving
Mixtures" Proceedings, The Association of Asphalt
Paving Technologists, 1977, p. 64 .
. Kallas B.F. and Riley C., "Mechanical Properties of As-
phalt Pavement Materials", Proceedings, 2nd International
Conference on the Structural Design of Asphalt Pavements,
Ann Arbor 1967, p. 931.
. Kallas B.F and Puzinauskas V.P, "Flexure Fatigue Tests on
Asphalt Paving Mixtures", American Society for Testing
and Materials, STP 508, 1972, p. 47.
. Witczak M.W. and Root R.E., "Summary of Complex Modulus
Laboratory Test Procedures and Results", American Society
for Testing and Materials, STP 561, 1973, p.67.
16
-
17 .
18 .
19
20
21
22 .
23
24
25 .
26
Sayegh G., "Viscoelastic Properties of Bituminous
Mixtures", Proceedings, 2nd International Conference
on the Structural Design of Asphalt Pavements, Ann
Arbor 1967, p. 743.
Takallou H.B., McQuillen J. and Hicks R.G., "Effect of
Mix Ingredients on Performance of Rubber Modified Asphalt
Mixtures", FHWA-AK-RD-86-05, Federal Highway
Administration, May 1985.
.Lee M.A. and Emery J.J., "Improved Methods for Character-
izing Asphaltic Concrete", Proceedings, Canadian Techni-
cal Asphalt Association, Vol. 22, 1977, p.109.
.Vinson T. "Fundamentals of Resilient Modulus Testing"
Workshop on Resilient Modulus Testing, Oregon State
University, Corvallis, OR, 1989.
. Furber B. "Strain and Temperature Effects on Resilient
Moduli" Workshop on Resilient Modulus Testing, Oregon
State University, Corvallis, OR, 1989.
Said S.F, "Tensile and Fatigue properties of Bituminous
Mixtures Using Indirect Tensile Method", Ph.D.
Dissertation, Department of Highway Engineering
Royal Inst. of Technology, 1989.
. Kennedy T.W and Hudson W.R, " Application of the Indirect
Tensile Test to Stabilized Materials", Highway Research
Record 235, 1968.
. Eriksson R. "Dragprov på sandasfalt", Meddelande 85,
Statens Väginstitut, Stockholm, 1954 .
Sugwara T. "Mechanical Response of Bituminous Mixtures
under Various Loading Condations", Proceedings, 3rd In-
ternational Conference on the Structural Design of As-
phalt Pavements, London 1972, p. 343.
. Linde S. "Investigations on the Cracking Behavious of
Joints in Airfields and Roads" SP Rapport 1988:23,
Polymerteknik, Borås 1988.
17
-
L" ANALYSE D'EXTENSION INDIRECTE DES MODULES RESILIENTS
SAFWAT FP. SAID
L' Institut National Suédois de Recherches Routiéres et de la
Circulation
Linképing, Suéde
Résumé
Les progrés faits dans le domaine du design analitique des
structures de pavé ont rendu necessaire un croissant besoin
de connaissances sur les propriétés mécanique des différents
composants du pavé dans les conditions des routes; telles que
la résistance a l'extension; la rigidité des modules et la
résistance a plusieures réprises des mélanges de pavé en bé-
ton. Ces paramétres constituent une base convenable pour le
design analytique et l'évaluation des performances du pavé
flexible.
Dans ce rapport-ci on a choisi l'analyse d'extension indi-
recte a cause de sa validité et simplicité. En tout cas; on a
éffectué des modifications de l' appareillage et des
procedures d'analyse.
On a examiné trois types différents de mélanges de pavé en
béton par utilisant la méthode d'extension indirecte. Deux
d'entre les mélanges sont mélés a 3% de contenu de caoutchouc
par le poids total, c'est a dire le Rubit (RUB12), qui est un
asphalt dense en béton, utilisé pour la réféction des routes,
et un mélange poreux appéllé Rubdrain (RUBD12) . Le troisiéme
mélange est un asphalt dense conventionnel en béton (HABI2T),
utilisé pour la réféction des routes. La dimension maximum de
l' aggrégat a été 12 mm pour tous les types.
La relation entre la tension et la déformation (stress-de-
formation-strain) a été établie pour examiner l' influence du
niveau de la tension et/ou la déformation sur le module rési-
lient trouvé par l'analyse d'extension indirecte et pour dé-
finir une zone viscoélastique approximativement linéaire pour
les mélanges de bitume a temperatures différentes. Les modu-
les résilients ont été mésurés par utilisant la méthode d'ex-
tension indirecte, modifiée pour les mélanges analysés a 4
temperatures différentes.
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