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.