Development of a Hollow Cylinder Tensile Tester To Obtain Mechanical Properties of Bituminous Paving Mixtures

by

William G. Buttlar, Ph.D., P,E. Assistant Professor

Department of Civil and Environmental Engineering UniverSity of Illinois at Urbana-Champaign

205 North Mathev.rs Avenue 1212 Newmark Laboratory

Urbana,l l 61801 Ph, (2 I 7) 333·5966 Fax, (217) 333·1924

buttlar@uiuc.edu

Ghazi G. A1-Khateeb, M.S.C.E. Graduate Research Assistant

Department of Civil and Environmental Engineering University of Il linois at Urbana-Champaign

1208 Newmark Laboratory Urbana, IL 6180 I

Diyar Bozkurt, M.S .C.E. Graduate Research Assistant

Department of Civil and Environmental Engineering University of Illinois at Urbana-Champaign

1208 Newmark Laboratory Urbana, IL 6180 1

Submitted for Publication in the Journal of the Association of Asphalt Paving Technologists

December 9, 1998

Buttlar, AI-Khateeb, and Bozkurt

Abstract

A new hollow cylinder tensile test (HCT) device was de\'eloped. which can be used 10 obtain fundamental properties of asphaltic paving mixtures, such as creep compliance, tensile strength, and dynamic modulus, at low and intermediate temperatures. The device was originally developed to be a compact, portable, and operationally simple surrogate test to obtain similar properties as the Superpave Indirect Tensile Tester (JOT), but is capable of obtaining properties at both low and intermediate pavement service temperatures. The device produces strain in an asphalt cylinder by appl~'i ng pressure to the inner cylinder \\'all . causing tensile or 'hoop' stress to develop in the cylinder The load system is also used to

measure specimen deformation, which makes specimen preparation and device operation \'et\'

simple. Three·dimensional finit~ element analyses were conducted to model practical test

conditions in the HCf, including effects of eccentrically cored test specimens. A series of simple formulas are presented, which allow stresses and strains to be accurately determined from test measurements, based upon finite element results and the elastic·viscoelastic correspondence principle, Formulas for tensile strength and creep compliance are presented, the lauer of which requires that creep tests are conducted in the linear viscoelastic range.

Preliminary tests have been conducted using a prototype HCf, which have ShOlI11 very promising results. A reference material was measured to within one percent of expected modulus, and tests on asphalt concrete have produced very reasonable properties. Measurement resolution, even for very stiff materials, has be~n found to be exceptionally good. This is due to the la rge gage area of HCf spedmens, e.g .. the cylindrical cavity wall. A comprehenSive validation program is now needed to verify the accuracy and repeatability of the HCT.

Key Words: Hollow Cylinder, HCT, SupelJl3ve JOT, Creep Compliance. Tensile Strength, Dynamic Modulus, Resilient Modulus, Asphah Mixture, Asphah Concrete, Tensile Test, Thermal Cracking

Introduction

Mechanical testing of asphaltic paving mixtures has long been recognized as a vital step in mixture deSign, production control. and forensic investigation of this most important construction material. Over the past several decades. there has been movement away from devices that measure empirical binder and mixture properties (penetration, stability and now, etc.) and an increased emphasis on devices that obtain fundamental material properties. such as dynamic modulus, creep compliance, and tensile strength. Fundamental material properties, combined with mechanics·based pavement response and distress models. can be calibrated to pavement performance with far fewer observations than empirical test results. and can handle changes in traffic, materials, and production techniques with little or no model re-calibration.

Increases in traffic volume, vehicle loads, tire pressures, and ti re stiffnesses, have resulted in the need to reevaluate the types of mixtures that are appropriate for present and future transportation faci lities. More than ever, mixture design must lead to materials that are stable enough to resist rulting under severe loading and heat in summer months, yet

BlIlllar, Al-Khaleeb, and Bozkurt

durable enough to resist fatigue, thermal, and block cracking during cooler months. The responsibility for the proper design of tomorrow's mixtures will fall largely on the shoulders of the contracting industry. The Supt'rpave mixture design SYStem offers the contractor a volumetric mix design system plus advanced performance tests and modds to help meet this challenge. The tests originally selected to suppon. the performance based. prediction modds were the Superpave Shear Tester (SST) and Superpave Indirect Tension Tester {101l The SST collects mechanical properties at high and intermediate service temperatures for use in rutting and fatigue prediction models, while the JOT collects low-temperature mechanical propenies for thermal cracking performance prediction. These testS have proven to be excellent research tools, and in some instances, have been employed to enhance Superpave volumetric mix designs for recent paving projttt.s in the United States. To meet the needs of the paving industry, every e(fon mUSt be made to obtain the required properties in the simplest manner, and using compact, portable equipment whenever poisible.

Because of the modularity of the Superpave performance prediction system, it may be possible to develop surrogate tests, which will yidd the required properties for the Superpave prediction models using simpler, more portable devices. Care must be taken; however, to ensure that the surrogate device produces suitably acrurate and repeatable measures of the desired property, for the 1e-.'eJ of design reliability sought. A Hollow Cylinder Tensile Tester is presented in this paper, which appears to have promise as a surrogate test for the lOT in asphalt mixture design . The device also appears to have other useful measurement capabilities related to asphalt mixture design and analysis.

ObjectiVes

The objectives of this paper m :

1. To describe potential benefits of the hollow cylinder tensile teSt arrangement 2. To describe theoretical analyses conducted (0 evaluate the feasibility of a thick­

walled Hollow Cylindtr Tensi le Tester (Her) to obtain tensile propenies of asphaltiC paving mixtures

3. To describe initial design concepts for a hollow cylinder tensile test device, critical design issues, and the need for three-dimtnsional finite element analysis when test conditions depan from assumed conditions for closed·form solutions

-l . To present results of fin ite element Msed sensitivity analyses, including Stress, strain. and defleclion fi elds when closed·form solutions are not applicable

5. To describe the developmem of a suaightforward procedure for converting teSt measurements into accurate, fundamental material propenies, which utiliu finite element results

6 To briefl~' summarizt ongoing developments on a prototype HCT, to present prdiminary leSI results, and to outline plannffi testing and validation effons

Buttlar, AI-Khateeb, and Bozkurt

S<ope

This study is focussed on the development of a thick-walled hollow cylinder device to

obtain tensile propenies of brittle materials, such as asphalt concrete. The loading arrangement considered is that of internal (cavity) pressure only, with uncapped, unrestrained cylinder ends.

Hollow Cylinder Testi ng

Previous Studies A review of the literature revealed that the hollow-cvlinder test mode has never been

specifically used to dmrmine the tensile properties of asphalt concrete. The literature is replete with applications involving the hollow-cylinder testing of granular materials. mostly to

delermine compressive, shear and torsional properties (Saada {1988J, Hight et al. [1983]). The hollow cylinder test mode is viewed favorably by geotechnical researchers because of its ability to produce fundamental material properties, while giving the versatility to manipulate principle stress orientation by controlling axial and torsional loads. along with inner and outer pressure.

The application most closely related to the proposed research was reported by Alavi and Monismith (1994 ). In their study. hollow cylinders having 114.3 mm (4.5-inch) and 88.9 mm (3.5-inch) outer and inner radii, respectively, were tested in compression along the axis of symmetry. The scope of their research, however, was aimed at determining shear and compressive properties of asphalt concrete at moderate and high in-service temperatures (4. 25, and 40 C) . Crockford (1983). also used hollow cylindrical specimens to determine shear and compressive properties of asphalt mixtures.

Proposed Application: Hollow Cylinder Tensile Tester (HCT) Modulus, creep compliance, and smngth under tension are key fundamental

propenies used in bituminous pavement design and in mixture design . This paper describes the use of a thick-walled pressure cylinder arrangement (figure I) for measuring these propenies on asphaltic concrete sp«imens. Constitutive equations aTe available for both thin-walled and thick-walled cylinders (Timosh~nko and Woinowsky-Krieger [1959 J), where Lhin·walled cylinders are generally regarded as those having inner and outcr radii differing by no more than ten percent. In the case of asphaltic paving mixtures. the use of thick-walled cylinders is necessary, since aggregate-size-to-wall-thickness ratio can affect test results. For the purposes of obtaining tensile propenies. the only applied stress that will be considered hereafter is internal (cavity) pressure. Cylinders with uncapped ends were studied. since capping ends complicates test procedures and requires larger pressures to induce desired tensile stresses.

Advantages of Hollow Cylinder Test Mode fo r Obtaining Tensile Properties

There are several methods for inducing and measuring tensile propenies of materials in the laboratory, including: direct tension, indirect tension (figure 2), beam testing, and

Applied Pressure 10 Hollow Cavity

a

Circumferential (Hoop) Stress

• • • ,"":-f--;'" " " -.. · I -' : '-..: .. --~- : • • • • ~ ~

Vertical Stress

Radial Stress

Figure 1. Schematic and Stress Defin itions for Hollow Cylinder Tensile Test Specimen

Burtlar, Al-Khateeb, and Bozkurt

Figure 2. The SUPERPAVE Indirect Tensile Test (l OT)

hollow cylinder test ing (figure I). In ~am testing. it is difficult to derive a fundamental measure of tensile suength because of neutral axis shifting and stress redistribution after the initiation of tensile fractu~. Also. for compatibility with Superpave. it is most desirablt to utilize 150-mm diameter by 115-mm tall cylindrical specimens as obtained from the gyratory compactor, which limits maximum possible specimen dimensions for direct tension testing. A similar restriction occurs for di rect tension testing.

Figure 3 compares the relative advantages and disadvantages of dirtct tension, indi rw tension, and hollow cylinder tensile testing. Oirtct ttnsion has the advantage of ~ing the only mode with a pure tensile stress state, but has several disadvantages. One dassic probltm is the difficulty in gripping and testing brittle materials in ttnsion, as suess concentrations often result in failures near damping points (grips). End platens are sometimes used; how~r, specimen preparation then involves gluing tht platens to the specimen with careful alignment, which is time-ronsuming. Indirect tension has many advantages, induding; direct utilization of cylindrical specimtns, simple application of compressive loads through loading strips. and good accuracy if surface-mounted transducm and three-dimensional correction factors art used, as in the Superpave lOT (Buular and Roque [1994]) . Potential disadvantages of the IDT include the size and lack of portability of the test device.

One of the advantages of the HCf is the long gage length in the direction of tensile response, which is along the inner diameter of the C)~indrical hoop (e.g., tangential). Tension is induced uniformly around the entire circumference of the cylinder (figure 1), giving a -gage length" of approximately 3DO-mm around the inner wall for a standard 150·mm diameter specim«l with a lDO-mm diameter cavity. Another advantagt of the Her is the mechanical advantage afforded by applying load through pressurizing the inner cavity. By -pushing from the inside" and by utilizing a simple pressure intensifier. there is no need for load (rame

Test Direct Tension Test Indirect Tensile Hollow Cylinder

IOn Te.t lion Ten.it, Test IHen

a l J- /l~ Schematic /' " diagram ~y

• • t ... t A': t (possible m m

"y r-..... ,.~m location of /" ~ "-~-i" maximum

tensile stress '- .... :./ is donoted bV Applied Stress, 01 l oad , P

Internal pre~sure, p point "m1

, , , Stless state a,n 4'1~ t8 p at point Mm" ( 1,\ I( '\ ( I 1\ a (plotted on a -

Mohr's circle) a IE1 ~

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a, 0.8 p

-2'IIP) , Can use cylindrical

, Pure tensHe state specimens • Can use cylindrical • Accurate • Accurate, it test Can test

specimens Potential performed carefully • Simple, portable specimens from •

Advantages thin paving lifts device is possible

• large measurement • Identifies first failure of specimen 'ffi' during strength les\

• Requifes beam or bar .... m." • Effects of usng only

Potential • Dlfficu~ 10 gnp Equipment not outer portion of • Dis· specimen &1d ensure

"""'" gyrato.'y spectmen

advantages aligned loads • Silort gage leflgth needs study

• Specimefl • Wall thickness effects preparatKlfl\ime fleeds study consumil'lg

Figure 3. Comparison of Tensile Test Modes

Buttlar, Al·Khateeb, and Bozkurt

apparatus. Based upon developments with a current prototype (described in detail later) . it appears HCf apparatus can be assembled that weighs less than 1.33 kN (300 Ibn ·

Another advantage of the HCf is the lack of stress concentration at the point of load application. Unlike direct and indirect tensile tesling. which results in stress concentrations at load platens, the HCf involves the application of a uniform internal pressure to induce tension. This may have advantages in obtaining properties at test temperatures abovt' 0 C. and for testing of ct'rtain polymer.modified mixtures. For instance, soft or highly ductile mixtures can fail in compression and sht'ar in the IDT rather than in tension, denott'd by y. shaped shear failure regions near load strips.

Finally, specimen preparation for HCf testing is uncomplicated , involving only coring of the central cavity in the case of cylindrical specimens, or l' .... O coring operations in the case of laboratory compacted slabs or field specimens. Hence, the HCf is envisioned to be a small, portable, and operationally simple test device, capable of measuring fundamental mixture properties. Some potential disadvantages related to the hollow cylinder tensile test arrangement are also listed in figure 3, which include wall-thick.ness·to·partic!e ratio and tfft'cts of non-homogeneity of gyratory-compacted specimens. These issues will be discussed at length in a later section.

Theoretical Analysis of the HCT

Theoretical analyses were performed to assess the feasibility of a thick·walled cylinder test for the determination of cretp, modulus, and strength properties of asphalt concrete. The following issues were investigated, all of which are interrelated:

I. The optimum wall thickness for hollow cylinder specimens 2. The resulting stress distribution across the waH 3. The amount of internal pressure required to rupture asphalt concrete specimens

Assuming all specimens have ouler diameters of 150-mm and 3450 kPa (500 psi ) tensile strength, the required inlernally applied breaking pressure was estimated to be no greater than 2070 kPa (300 psi). depending on wall thickness (lable I ). This pressure can easily be achieved through compressed gasses or by using a small piston to compress a volume of fluid .

Table i . Breaking Pressure VI. Wall Thickness for 150-mm Diameter Specimen

Wall Thickness, Required Internal mm Pressure, kPa (psi) 38.1 2070 (300) 31.8 1697 (246) 25.4 1325 (192) 19.1 966(140) 12.7 621 (90)

Note. Based Upoo Tangential BreaklTlg Strengl/l 01 Asphall Concrete of 3450 kPa (500 psi)

Buttlar, Al-Khateeb, and Bozkurt

Breaking pressures and stress distributions were computed using constitutive equations for thick-walled cylinders (Timosnenko and WOinowsky-Krieger [1959j), givt'n by equations I and 2:

Where: p = Internally-applied pressure

cr, = Tangential (hoop) stress, which is tensile cr, = Radial suess, which is compressive

All other quantities are as defined in figure 1.

(I )

(2)

A second concern was that me change in tangential (hoop) stress across the thick wall should be minimized to the extent possible. Figure 4 shows the tangential (hoop) stress distribution across the specimen wall as a function of wall thicknt'ss. Note that tensilt' sut'sse. are highest at the inner wal!. Based upon this analYSiS, a 25.4-mm (I-inch) wall thickness would give an outer walVinner wall tangential stress ratio of 0.63. This wall thickness st'ems to strike a reasonable balance between the relative advantages and disadvantages of using thin- or thick-walled specimens. Thick. walls are advantageous for increasing the wall thickness-to-maximum aggregate size ratio. Thin walls favor unifonn stress distributions, accurate tensile strength determination, higher deformations (and thus improved signal-to-noise ratiOS), and lower required pressum to fail spC(imens.

Development of a Prototype HoUow Cylinder Tensile Tester

Two possible test configurations for the Hollow Cylinder Tensile Tester (HCf) art' shown in figures 5 and 6. A spool-shaped metal "intensifier" is the hean of the HCf apparatus and serves three main purposes: I) to reduce the amount of fluid that will undergo bulk compression; 2) to house the loading pistOn, and; 3) to intensity (amplify) pressure. The arrangement in figure 6 appem to be superior to that of figure 5, sinet' pressurization along the entire height of {he inner wall leads to more uniform stress Slates. However, the preliminary teSI results reponed herein were collected using the first prototype HCT developed, which is described by figure S. In any case, since available closed-form solutions require both full-height loading and concentric coring of the inner cavity, finite element analYSis were conducted to obtain accurate measures of stress, strain, and deflection when these conditions are not met..1S described in the next section.

Pressure is t'asi ly monitored using a pressure transducer located anywhere in the fluid on Ihe specimen ·sidt'· of the piston. as shown in figures 5 and 6. In this way, applied pressure and rhus tensile Stress are monitored independent of friction in the loading piston. A fl exible membrane is used to keep the pressurizing fluid from penetrating voids in and

11500

10000 • ~ ~ 8500 • • g

7000 ~

;;

" 5500 • • Q • • 4000 >-

2500

1000

Inner wall for specimen with 11 .5 mm walilhicl\ness Outer wall for all cases

Axis of symmetry Applied cavily pressure = 2070 kPa

lR".tiD":f":""~"~f;:'f:'f:":"~' ~'"~'~'~"~ff;fi;"~",,~w;'ff1~~~~~~~~;;;~ 35 45 55 65

Radial Distance from Axis of Symmetry (mm)

Figure 4: Tangential (Hoop) Stresses Distribution Across Wall of Hollow Cylinder Specimens of Various Wall Thickness

75

150 mm

n . Pressure

Intensifter ~--J ..

Flexible Membrane -4---- Piston

100mm

Section A·A'

Possible LVDl

Arrangement for Poission's

Ratio Determination

Figure 5. Cross-Sectional View of Original Her Prototype Arrangement: Partially . Loaded Inner Cavity Wall

T

Rigid Cylindrical

Intensifier

Pressure Transducer

Flexible Membrane

Cylindrical Specimen

Possible LVDT

Arrangement for Poission's

Ratio Determination

'Dimensions X and Y can be varied to allow range of possible cylinder heights

Figure 6. Cross-Sectional View of Proposed Modified HCT Prototype Arrangement:

Fully-Loaded Inner Cavity Wall

ButtJar, Al·Khaleeb. and Bozkurt

around the specimen. and to contain the fluid after specimen rupture occurs in a strength le~1

To measure propeTlies such as creep compliance. dynamic modulus. and resilient modulus of asphalt concrete sperimen. it is necessary to measure specimen deformations in response to the applied pressure. Originally. it was assumed that an externally mounted chain tyPf: extensometer would be the most con\.'enient measure of circumferential expansion. Ho\\"~·t'r. since tensile suesses are largest on the inner wall, a method to measure inner curcumfercnlial expansion was sought This was eventually accomplished by measuring the change in cavit}' expansion . which was quantified by monitoring fluid movement in the inner ca,·ily A flu id was selw.ed as the pressurizing medium to reduCt' volume changes associated \Iith bulk compression under ten pressures.

A piston is driven inside the intensifier to compress the fluid and induce pressure loading. Since the area of the piston is known. the movement of the piston can be monitored to measure the extension of the hollow cylinder under pressure loading. Of course, one must be able to subtract out any pinon movement due to bulk fluid compression and compression of the membrane. fittings. etc .. to arrive at an accurate result. This can be accomplished by first measuring the piston movement as a function of cavity pressure for a very rigid cylinder. such as a steel cylinder with very thick walls.

Based upon these considerations. a protot)~ Hollow Cylinder Tensile Tester was constructed. as displayed in figu re 7. A detailed description of the prototype device is beyond the scope of this paper. However, some of the key features of the HCT prototype afe:

• It is much simpler to induce tension by ~pushing from the inside.- For example, faili ng a specimen with 3450 kPa (500 psi) tensile strength in the HCT requires that about 1.50 kN (337 Ibf) be applied to the piston in the intensifier. [n the lOT, applying the same tensile stress takes over 4 1.8 kN (9400 lb£).

• The HCf only requires a standard pressure transducer and a Single. standard linear voltage differential transducer (LVDT) to take all necessary measurements to determine creep compliance. tensile strength, resilient modulus. etc.

• The final HCf device is expeae:d to weigh less than 1.33 kN (300 Ibf).

The hollow cylinder asphalt mixture specimen shown in figure 7 was produced by coring a standard gyratory compacted specimen using a portable coring rig (figure 8) with a I01.6·mm (4'inch) outer diammr core barrel. A description of preliminary test resulLS is presented in a later 5e{:tion.

PltJnned Equipment FetJtuns A servo·hydraulic system will be used to drive: the piston, with a control system

capable of dosed loop control on either piston movtment or fluid pressure. A post failure restraint cylinder will sunound the outer diameter of the asphalt specimen, to prevent large 0IXnings in the ~sph.all cylindef after loading .to failure. ~ heating/cooling ~stem ~Il also be employed to malntam consunt temperature In the speomen and test deVIce dunng testing. A f1uid·based bath system is being considered, due to the good temperature stability and accuracy offered by these systems.

The HCT devil"t' (like the JOT device) will be capable of running creep and strength tesls on asphalt mixtures to determine the material properties needed for the SUPERPAVE

Figure 7a : Intensifier Unit on HCT

Figure 7c: HCT With Specimen In Place, Before Strength Test

Attached

Figure 7d: HCT With Specimen In Place, After Strength Test

Figure 7: Prototype Hollow Cylinder Tensile Tester

Figure B. Coring Rig With Two-Dimensional Centering Capabilities for Producing HCT Specimens

Bunlar. AI-Khaleeb. and Bozkurt

thermal cracking model. A creep test involves the sudden application of a constant pressure in the cavity of a hollow cylinder specimen for a specified period of time and the measurement of resulting specimen deformation. Material properties such as creep complianct, which is required by SU PERPAVE, can De: obtained from this test. A strength test involves the application of a uniformly increasing piston displacement on the specimen until rupture occurs. Because of the excellent dynamiC control characteristics of fluid-based loading S)'Slems, it will also be possible to measure dynamic modulus and resilient modulus with the Her. These tests will involve dosed·loop pressure control of the desired stress pulse, and recording the resuhing piston displactment so that specimen main response can be obuined, and the approprim modulus be determined.

Three-Dimensional Finite Element Modeling

Three·dimenSional finite element modeling was condumd to evaluate deflection, mm, and strain fields for instances where specimen and test configurations deviated from dosed-form solution assumptions. These deviations include:

• Wall thicknm: Assumed to be uniform around cylinder, but in practice some eccentricity will occur due pranicallimitations in coring equipment

• Pressure on inner cavity Assumed to be applied (l\Ier full height of specimen, but if a panial-loading arrangement such as described by figure 5 is used, finite element analysis will be needed

Description of Modtl Gyratory-sized hollow cylinder specimens were modeled, with outer diameters of

150 mm, and specimen heights of 112 , II S, and 118 mm. Three different load cases were used, where pressure was applied across the region representing the middle 90, 95, and 100 !'trcent of total specimen height. Cavitr !!ccenuicities were modeled using O-mm, S.08·mm (0.2·inch). and 10.1 6-mm (OA-inch) differences betw!!en maximum and minimum wall thidn!!sses. Finite element modeling was conducted using ABAQUSl"looI . For modeling concentrically-cored speci mens, axisymmetric modeling was conducted. However, for the Casl! of eccentrically cored specimens, three-dim!!nsional models were necessary, as shown in figure 9. In this case, symmetry was taken advantage of in the y- and z-rlirections. Thus, t.he half-circle, half·height model uses onlr IHth as many elements as would be necessary to

model the entire ~ .. .,.lind(r. For thrl'c.'·dimensionaJ modeling, 20·noded quadratiC brick elements were employed.

Originally, 8·noded isoparametric brick elements were used; however, inadequate acrurae), was achieved wllh Ihe element Illesh used. Rath!!r than regenerate the original mesh, the more complic31c.'d 20·noded quadratic bri.:k elements were substituted and satisfactory results were al:htewd. Element aspect ratios (largest to smallest dimensionsl were predommantly less than 2: 1; e.~cqJl in areas where suess gradients were low, where maximum as!'tct ratios of about -1 .1 were pemlined Two-degree·of.frcedom rollt'r supportS were supplied al ea(h nodt' along plants of symmetry In addition. nodes at the center of the inner cavity wall were fi~cd mil'll.' x-Jirwion 10 pr!.'\'ent rigid bod~' mo\'ement. Poi sson's rat io was taken as 0.30 for the model runs reponed herein.

20·Noded Isoparametric Brick Elements

Figure 9. Finite Element Mesh and Typical Stress Contour, 100~/. Loading, Zero Cavity Eccentricity

Buttlar, Al-Khateeb, and Bozkurt

!mults qJ Finiu Eltmtnl Ana[ysis Figure 10 illustrates the effect of eccentric cavity location on hoop stresses in the

hollow tylinder. Obviously, a 10.1 6-mm (0.4 inch) wall thick.ness differential (between maximum and minimum thickness) is not acceptable, as a maximum to minimum hdbp stress ratio of about 2: I results. Fortunate.ly, with a simple centering attachmwt as shown in figure 8, one should be able to core specimens routinely with under 5.08-mm (0.2 inch) wall thickness diffmntial. which will yield maximum to minimum hoop stress ratios no larger than 1.24 to 1. Although correction factors based upon finite element results will be presented, careful coring will reduce the magnitude of the correction factor to be applied.

Figures I I through 14 illustrate the effects of partially loaded inner walls, which OCctJr when using test conditions such as those described by figure 5. For this analysis, concentric coring was assumed and axisymmetriC fi nite element modeling was employed. Axisymmetric modeling is much more efficient than three-dimensional (solid) modding and allo .... 'td more mesh refinement to be utilized. Three load cases, which are <kscribed by fi gure I I, are presented. Complete inner wall loading (100% loaded) and partial loading (90% loaded) were considered. For the part ially loaded cylinder, the unloaded region was assumed to be identical at the top and bottom of the test specimen, as in the arrangement shown in figure 5. Two analysis cases are presented for partially·loaded cylinders: sudden and gradual transition from full to zero pressure, as illustrated in figure II .

As ex~ed, figure 12 illustrates that partial loading results in a cuMd inner wall afler deformation, due to the restraint caused by the unloaded tylinder ends. However, the suess discontinuity associated with partial loading has a more pronounced effect on tensile and shear messes, as sho ..... n in figu res 13 .and 14. By examining shear messes in figure 14, it is apparent that the sudden transition from full 10 zero pressure results in a stress condition indicatl\'e of double·shear in the materi al near the transition. This shear response resembles that of material being extruded through an orifice. In the case of the partially loaded hollow cylinder, however, the double shear is being caused by the sharp stress gradient on one side, and by the constraint of the material in the unloaded, ring-shaped portion of the cylinder on the other side.

Shear and hoop stress magnitudes are lower in the more realistic case of gradual pressure reduction, as shown in figures 13 and 14. In summary, this analysis illustrates that although deflections are lower near cylinder ends for partiaJl)'·loaded cylinders, suess conctntrations result m less reduction in hoop suess than would be expected. This analySIS also shows the advantage of the load system shown in figure 6, which pro\1des for 100· percent loadmg of the lOner 9'hndcr wal!. and thus. no Stress lQnCentrallon

Fin ite Element-Based Suess and Strain Correction FaCtors

The followmg relationships were derived so thai measurements of volume change and applied pressure could be accumely com'erted into maximum hoop sum and strain. based upon 3·0 finile element stress and stram fields. These resul ts, in rum , can be used 10 obtam fundamental propertH.'S such as creep l:omphance, tensile strength, etc. The fol!olling procedure and relationships were developed.

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50 100 150 200 250 300

Pressure Ipsi)

- 100% loaded

-+- 90% loaded. Sudden Pressure Removal

-+- 90% loaded, Gradual Pressure Removal

Figure 11. Applied Cavity Pressures for Axisvmmetric Finite Element Modeling, Three Cases

350

575

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Radial Denection (mm)

- 100% loaded

-+- 90% l oaded, Sudden Pressure Removal

-+-90% loaded, Gradual Pressure Removal

Figure 12. Radial Deneclion for Axisymmetric Finite Element Modeling, Three Cases

57.5,-------------.1

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o 1000 2000 3000 4000 5000 6000

Tangentlal Stress (kPa)

- 100% loaded

-+- 90% Loaded, Sudden Pressure Removal

......... 90% loaded, Gradual Pressure Removal

Figure 13. Hoop Stress

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" ~-<L-"~

oL-----____________________ ~------~

.. " ·300 .,,, o ,so Shu ' SlrHl (kP'1

100% l oaded

-+- 90% loaded, Sudden Pressure Removal

-+- 90% loaded, Gradual Pressure Removal

Figure 14. Shear Stress

BunJar, AI·Khaleeb, and Bozkun

Ta nKlntial (Hoop) Stress ConvlTSioll Fat1.ors

The conversion faclOrs for tangential st ressts are dttermined based on the maximum (critical) tangential stress results obtained from the finite element analysis (FEA) at the mid· height of the hollow cylinder inner wall, and the internal pressure used for analysis 2070 kPa (300 psi). Where ttcentricity exists. the critical hoop stress occurs at the thinner side of the hollow cylinder. The conversion factors for hoop stress, based upon finite element load cases with various combinations specimen heights. cavity eccentrici ties, and percent inner wall loading are determined by:

F = (J', •• __

• P (3)

Where:

F., Hoop stress conversion factor for given FEA load case Ow " ... 1 Critical {maximum) tangential {hoop) mess for given FEA load case

p '" Applied cavity pressure

The dosed form solution for hoop Stress conversion factor for the cavity wall can be applied in case of no eccentricily and for 100 % loading. By seuing r=a in Equation I and combining with Equation 3. we obtain:

Where:

b! +a ! F"":-b' , -,

F.... '" Conversion factor for hoop stresses. based upon doscd·form solution (100 perctnt loading of cavity wall, no coring eccentricit~')

a '" Inner radius of hollow (ylinder b Outer radius of hollow ("\'Jinder

TanGential (Hoop) Strains

(4)

The com'erslon factors of tangenlial mains are determined based upon the strains obtained from the F£:\. again at the nllJdle of the hollow cylinder. and the change in ca\'It~·

volume und~r pressure as shown in equation \3).

(S)

Wher~ ,

Where:

8Ulllar, AI-Khateeb, and Bozkurt

F" = Conversion factor for tangential strains for gi\"en FEA load case t, ""'Kal ::: Critical tangential strain for given FEA load case

:.\ V = Change in volume calculated ba~ on FfA nodal deflection re5ulLS and equation 6

V(; •• I = Volume of the inner cavin' after deformation V,...".. ::: Volume of the inner ca\'itv lx-fore deformation

(6)

Volumes were found by determining crms-sectional areas at each row of elements throughout the height of the cylinder. based upon nodal coordinates before and after loading. The cros.s sections were then used to detennine volume using the equation for a frustum cone for each pair of adfacent cross-sectional areas.

The coll\'ersion factor for tangential strain based upon the dosed fonn solution, f"". lI'as obtained by manipulating dasticity equations for thick-walled cylinders (Timoshenko and Woinowsky'Krieger [1959J:

Where:

2 F .. :: I

ITH,D,

Fete ::: Conversion factor for hoop strain. based upon dosed-form solUlion (100 percent loading of cavity, no coring eccentricity)

(7)

Equation 7 can also be applied in the case of zero mentricity and 100 % loading of inner wall.

Table 2 summarizes the HO' conversion factors for ungential stress, while table 3 summarizes HCT conversion factors for tangential strain. A comparison betwetn the convers ion factors from FEA and those from the closed-form solutions. for the case of 100% loading of inner wall and zero eccentricity is summarized in table 4. The convmion factors based upon FEA and dosed-form solution are nearly identical. ali should be expected. One can gain an appreciation for the magnitude of correction factors for cases of partially loaded inner walls. and eccentrically cored cavities. by comparing the factors of tables 2 and 3. to the corresponding dosed-form conversion factors in table 4.

Table 2: HCT Convers ion Factors for Hoop Stresses, F ot (kPalkPa)

Eccentri- Height (mm) D, ci~ 112 115 116

(mml ~t (mm)lll % loaded % loaded % loaded 100 95 90 100 95 90 100 95 90

0.00 2.658 2.608 2.548 2.658 2.616 2.5&\ 2.658 2.6201 2.578 102.6 5.08 3.1 43 3.108 3057 3.143 3.118 3.076 3.143 3.127 3 094

10.16 3990 3.987 3.957 3.990 4.000 3.980 3.993 4.010 4.003

~'olfference between maximum and minimum wall thickness for eccenlncally-cored speCJmens

Table 3: HCT Conversion Factors for Tangential Strains , F u (1'10·/ lImml)

Eccentri- Hei hi (mm) D, ,,~ 112 115 116

(mml ~1 (mm)I'1 % loaded % loaded % loaded 100 95 90 100 95 90 100 95 90

0.00 5.396 5995 5578 5.255 5.848 5.424 5.122 5.708 6276 102.6 5.08 5.127 6.833 7.523 5.968 6.664 7.342 5.815 6.503 7169

10.16 7064 7.899 8.714 6.882 7.701 8.498 6.708 7.512 8.291

"' Difference between maximum and minimum walllhtekness for eccenlncally-cored s~mens

Table 4: Comparison of HCT Conversion Factors: Finite Element Analysis Versus Closed·Form Solution, ~I = 0.0 mm (no eccentrici ty), 100% loaded

t.1 = 0 0 mml11 Hei hi (mm)

D, (no eccentricity) 112 115 118 (mml arid 100% Closed- Closed· Closed· l oaded FEA Form FEA Form FEA Foon

ConverSIOn Faclor For 5.396 5398 5255 5257 5 122 5124 Tangential

1025 Strains (1"10.1)

ConversIOn Faclor For 2658 2659 2658 2659 2658 2659 Tangential Stresses

" ( Difference between maximum and minimum walllhickness for eccentncally-cored spectmens

ButtJar, AJ-Khaleeb. and Bozkurt

Use of Convers ion Factors

Obtililring Crup Cornpliana

Now (hal the conversion factors for hoop (tangential) stresses and tangemial strains have been delermined, accurale measures of creep compliance, correctw for actual test conditions, can ea5i1v be determined, This approach assumes test ml:3surements were obtained in the linear viscoe:laSlic range of mamial response. In mep testing of asphalt mixtures, this c~n generally Ix accomplished by testing at 0 C and below, and by keeping tensile strains in the 5p«imen below 500 microStTains (conservati\'ely) at all times, Thl: correspondencl: principle allows one to convl:rt elasticity solutions, including finite element results, to viscoelastic solulion, if malerial response is ml:asured in the linear range.

Based upon measurw pressure and volume change from the Her, one can determine the stms at the center of the cylinder's inner wall, a" as:

(J , '" F,. • p_ (8)

{; = F " oV , . - (9)

Where:

P ..... , :: Measured pressure in fluid inside intensifier (kPa) 6. V..... :: Measured volume change in specimen due to cavity expansion (mml)

Fa, and F&, arl: determined from tables 2 and 3. respectively.

Creep complianct can then ~ determined using the follov.ing equation. based upon Hook's Law:

D( &, ----'&~, -:-,) = = (J , - p(J, (J, +J1 " P

(10)

Where:

O(t) Creep compliance (kPa") I.l '" Poisson's ra tio = 0.30 (assumed) a, '" Radial stress = -p (kPa)

Bunlar, AI·Kha!eeb, and 80zkurt

Tensile Strength

Tensil~ sHength can also bt: dmrmined using the conversion factors developed as follows:

S, ::p~ 'F .. (I I)

Where:

Pi ........ :: lnu:rnal pressure recorded at lime of specimen failure

Sensitivity to Poisson 'f Ratio

For the HCf, deflection, and hence modulus or compliance measurements are affected by Poisson's ralio, while tensile strength is independent Poisson's ratio. Sensitivity analyses revealed that a maximum error in me.1sured modulus or compliance of about 5% \\;11 occur by simply assuming a v.1lue of 0.3 for Poisson's T.1tio in the HCT. Alternativel),. additional transducm can be added to the HCf to enable direct measurement of Poisson's ratio (ligure 5), The principle is that since Poisson's dfect causes the height of the cylinder to decrease when pressure is applied to the inner cavity, measurements of chang~ in specimen height could be used to determine the Poisson's ratio of the material being tested. The measured Poisson's rat io could then be used in equation 10 in lieu of an assumed I'alue, although correction fa ctors F~ and F" would be needed for values of Poisson's ra tio other than 0.3.

Preliminary Test Result s

PreliminalY tes ts have been performed using the prOtOtype HCT del'ice to determine the accurac)' of the device in measuring the strains and deflections, and to inveStIgate the feasibility of the HCf mode for determini ng the tenSl[e properties of asphalt concrete mixtures at low temperatures. Calibration spelimens of Aluminum and Delrin plastiC were fabricated to lest Ihe prolOt)'pt: uni t using specimens of varied rigIdity, or 20.7 and 2. i ) CPa (3,000,000 psi and 400,000 psi), respectil'ely (figure 15). t\ re sistance·t~'Pe strain gage was mounted on the outside of the aluminum C\'linder \0 check measured \'ersus theoretical st ra in. The results of lhe firsl testS run on th~ prOtOI ~'pt HCf were quile good, as summarized in labl~ 5. The predlftion of strain on an aluminum l.yhnder, and the prediction of the modulus ot' el a sll~'lty of a l)e[rin plastiC ~-:-'1inder wer~ bolh \\;thin 1% of the t:xpt(led n:sult.

Material

Bunlar, AI-Khatetb_ and BozkuJt

Figure 15. Hollow Cylinder Tensile Tester Prototype Along With Aluminum and Oelrin Plastic Calibration Cylinders

Table 5. Preliminary Test Results

Test Description Expected Resull Measured Result Delrin Plastic Estimate Modulus E = 2.76 GPa E - 2.75 GPa

of Delrin Hollow (Manufacturer Cylinder Reported Value)

Aluminum Estimate Strain on , = 379.6 I: - 380 Outer Wall of microslrains microstrains Aluminum Hollow (closed-form Cylinder solulion)

Prtliminary Tat 0" Asphall Mixtun Spedmm

A preliminary low-temperature test has now been performed on a dense-graded Ill inois surface mixture with an AC-20 binder. The results of creep testing al -25 C are presented in figure 16. Under an applied pressure of 379 kPa (55 psi), which corresponds to a tensile stress of 993 kPa (144 psi) (equation 8). approximately 4.06 microns (160 microinches) of deOroion were obtained in the 45·second test (using measured volume change due to cylinder expansion during testing). At 10 seconds loading time, about 5.16 microns (13 1

160 r-=====:::~::1 Appned T.nslle Stress '" 993 kPa (144 psi)

]; f .. 120

e .!! E o f ;; ! • o ~

80

40 --

o~------------------------------~ o 10 20 30 40

Time (sec)

Figure 16. Preliminary Creep Test Result with the Prototype HeT for Dense-Graded Surface Course Mixture at -25 C

Buttlar. Al·Khateeb. and Bozkun

microinches) of denection occurred , which corresponds to a creep compliance (equation 9) of 019 GPa ] (8.16 . 10 1 psi]). or 8.4 GPa (1.23"100 psi) stiffness modulus. which is very rtasonablt for this material at this temperature. Despite the rather crude naturt of the prototype HCT at the time of this testing. the crtep curvt obtained was extrtmely dean and stable Tht L \'OT signal stability and resolution is a direct result of the advantage of measuring cavity expansion to obtain ci rcumferential strain. Even with thtse very small st ra ins 4.06 microns (160 microinches). the cavity expansion was about 0.26 mml

{O.016in'1. which corrt sponds \0 a piston movement of 0.28 mm (0.011 inches). A movement of this magnitude can be measured with ease \\;th a slandard lVoT.

Due \0 the crudt temperature control system used in this early prototype (endosed chamber cooled with dr;.' ice). a testing delay caused the system to warm up. such that strength tests were performed when temperature equillibrium was restored at -16 C. The internal cavity pressure was ramped until the specimen ruptured at 938 kPa (1 36 psi), which corresponds to a tensile strtngth of 2442 kPa (354 psi) using equation 10. Again. th is value is very reasonable for this material at this tI:mperature Tensile strengths usually vary from about 1725 to 3450 kPa (250 to 500 psi). in the range of -10 to -20 C.

Al though the test results to date on reference materials and asphalt mixtures look very promising, obviously much more testing is needed to validate the accuracy and repeatability of the HCT.

Key Issues to Resolve through Additional Testing

Panicle Siu·to·WaIlThickntJs Ratio

The wall thickness of HCT specimens in the prototype arrangement is 25.4 mm. It could be argued that the wall thickness to maximum aggregate (stone) diameter ra tio is too small , and could l~ad to inaccuracies. For unbound aggregate masses, a specimen size to maximum particle diameter ratio of approximately fiv~ is desired. as a rule of thumb (Height et al. [1 983)). Obviously. there is no way to sat isfy this criterion if tensile properties are to be obtained from a gyratory·sized specimen, regardless of the test method ustd. However, the extent to which this rule of thumb appHu to bound aggregate materials. such as asphalt concrete is not well understood. ~ mentioned earlier. the HCT has an excellent gage length. to· maximum particle size ratio in the dirtttion of measurement (around the hoop on the inner cavity wall). since the inner ci rcumference of the sptcimen is over 300·mm in length.

One way to resolve this issue is through testing of mixtures with varying maximum aggregate size in the HCT. [n addi tion, sptcimens of varying wall thiclrness could be tested in the HCT to ~ dentify minimum wall thiclrness requirements for various types of mixtures. Properties measured on identical mixtures using the lOT and direct tension ttsting mode could be used as an additional basis of comparison.

Effects of Density Gradients and Broken Particles in Gyratory Compacted Spttimens

Since the HCT specimens represent th~ outer 25-mm ring of a gyratory specimen, significant density gradients in the specimen could affect the measured properties, depending

Buttlar, Al-Khatccb, and Bolkun

upon mixture composition and compactive effon . Harvey et al. (! 994) and Shashidhar (! 998) have shown that density gradients in gyratory-compacted specimens can be significant. The effects of aggregate orientation and aggregate crushing, particularly near the outer portion of the specimen, where aggregates are in contact with the steel gyratory mold, should also be investigated. It is envisioned that mixtures with larger andlOT weaker aggregates, including fl at and elongated aggregates, will show the most pronounced effects.

Testing should be conducted on cylinders obtained from gyratory specimens and those cored from slabs to assess the magnitude of theSt effects. ill a control case, !DT tests should be performed on a similar set of specimens. Conlrol tests are necessary to quantify the magnitude of differences that exist simply becauSt slab and gyratory compaction do not yield identical specimens, regardless of the physical test they will be used in. Also deserving investigation is the feaSibility of *double coring" gyratory specimens, to discard the oUlermost ring of material , if deemed necessary. A slightly smaller inner diameter could then be used to maintain adequate wall thickness.

It should be recognized, however, that maximum hoop mess occurs at the inner wall of the HCT specimen, which is gradually reduced to sixty-three percent of this value on the outer wall (figure 4) . Thus, material closer to the inner wall of the cylinder, which is less likely to have been altered by edge effects in gyratory compaction, governs a larger portion of the material response.

Tensile Strength Determination

One advantage of the four deflection transducers required in the !DT is the ability to identify "first failure" of the specimen, which is in turn uStd to determine the true tensile strength of the mixture (Bultlar et al. [1996]). The peak value of vertical minus horizontal deflection was found 10 be a good indicalOr of fi rst failure in the lOT, and occurs, on average, at about eighty percen! of the ult imate load 10 complmly fail the specimen. It is unknOlITI whether or not the onStt of failure will be dearly evident from the deflection measurement (piston movement and hence change in cavity volume ) obtained in the proposed HCf arrangement (figures 5 through 7). However, it is suspected that the difference in load at fi rst failure and ultimale load \\~11 be fairly small in the HCT, since tensile suesses are fairly uniform across the wall of the C\'Hnder. Future studies should include the use of crack detection gages al various locations on the inner and OUlcT walls of HCT speci mens \0 stud~' this issue in more detail.

Other Potential Modes and Appl ications of the HCT

In addition \0 creep compliance an..! tensile strength. the HCT should be capable of obtaining other usdul asphah concrete propmies, including POisson's ratio, resilient modulus, and dynamiC modulus. Funhermore, use of the HCf 10 obtain measures of fatigue resistance, fracture toughness, and moisture sensitil'it~' of asphalt mixtures will be investigated. Olher materials that (oulJ potentially be tested in the HCT mode include: Portland cement concrete, mortal>, ceramics, polymers, asphalt binders, asphalt mastics, and cohesive soils. For heterogeneous materials or nl.llaial s lI"ith small particks, smaller test specimens could be used.

Buttlar, AI·Khatecb, and B07.kUrt

The simplicity, versatility, and portability of the HCT suggests that the device has merit for use in quality controVquality assurance of hm·mix asphalt construction. Tensile strength, modulus. andlor compliance could be measured on as·produced or as·constructed materials at periodic intervals. This would ensure that any changes that occur in production, induding changes in properties of malerials, proportioning, etc., would not Significantly alter these important fundamental mixture properties. Tests could be performed on cylinders from gvratory·compacted spe<:imens, which are normally produced for control of volumetric plOperties. or from cores obtained from the compacted pavement In the case of field cores. it would be necessary to use the HCf arrangement shown in figure 6. This arrangement allows the tesung of shorter cylinciers, such as would be needed to characteriu a single p.m ng li ft.

Summary and Conclusions

A new hollow cylinder tensile test (HCT) device was developed, which can be used to obtain fundamental tensile properties of brittle materials such as asphaltic paving mixtures. These propmies include creep compliance, tensile strength, and dynamic modulus, at low and intermediate temperatures. The theoretical and experimental results obtained can be summarized as follows:

I. The hollow cylinder test mode provides a favorable method for imparting tensile stresses to brittle materials, such as asphalt concrete, with minimum stress concentrations.

2. The HCf takes average properties over the entire inner wall of the specimen, which is over 4()() mm long in circumference and 115 mm high for standard gyratory-siztd specimens (about 460 square centimeters) . This offers excdlent resolutio!! and gage length-to-partide size ratio in tht direction of measurement (along the inner wall of tht cylinder).

3. Finite elemtnt·based conversion factors were presented, which allow stresses and maim to be accurately determined from test mtasurements. Test arrangements with partially loaded cavity walls andlor tests performed on eccentric.ally-cored. specimens require tht use of the finite elemtnt formulas presented.

4. A second LVOT can be added to the HCT to directly measure Poisson's ratio: however, the added complexity does not appear to be justified for most applications. On the other hand. hoop stress, and hence, tensile strength is independent of Poisson's ratio.

5. Preliminary teslS have verified the accuracy of the HCf modt using calibration cylinders of known properties. Tests on asphalt concrete spedmens have given promising results, but much more experimentation is needed to validate accuracy and precision of the HCf device.

Based upon tht rtsults of this study, the following conclusions can be drawn:

Bunlar, Al-Khateeb, and Bozkurt

I. The HCf has many potential advantages for obtaining fundamental proptrties of bnuie matenals, such as asphalt concrete, and funher development and validation of test results should be pursued.

2. The Her appears to have the Simplicity, versatility, and portability to be used for routine measurements of modulus and strength. Thus, the Her has potential application as a supplement to volumetric mixture design, such as Superpave level I mix design.

3. The simplicity, versatility, and portability of the HCf suggests that the device has ment for use in quality controVquality assurance of hot·mix asphalt construction.

Acknowledgements

The authors would like 10 acknowledge the Significant contributions of Mr. Tom 8rovold and Mr. Jim Adams ill the design, asstmbly, and preliminary testing of the protOtype hollow cylinder tensile tester. Without their expertise and dedication, this work would nOl have been possible.

References

Alavi , S. H., and C. L Monismith, "orne and Temptrature Dependent Propenies of Asphalt Concrete Mixes Tested as Hollow Cylinders and Subjected to Dynamic Axial and Shear wads", Journal of Iht Assodatlilll oj Asphalt Pavmg T echllDWgists, Vol. 63, pp. 152-181 , 199-1 .

Buttlar, W. G. and R. Roque, "Experimental Development and Evaluation of the New SHRl) Measurement and Analysis System for Indirect Tensile Testing of Asphalt MiX"tures at Low Temperatures·, TrallSportation Rtsearrh Rtcord, No. 1454, National Research Council. National Academy Press, Washington, D. c., pp. 163-171 , 1994.

Bunlal, W. G. and R. Roque, "Evaluation of Empirical and Theoretical Mooels to Determine Asphalt Mixture Suffnesses at Low Temperatures·, JouJ7UII oj thr AUO(IatlO1I of Asplralt Ptll'lIlg T echlWlogiJtS , Vol. 65 , 1996.

Buular, W.G., Roque, R., and N. Kim, "A.'curate Asphalt Mixture Tensile Strength: PfI}aedillgs oj -I" Mmtrillis EIl!llUtnllg Gm/mlla, Maunals for til( Nffl' A1J/Irl/lum , American Society of Civil Engineers, Washington D.c.. pp. 163·172. 1996

Crockford , W. W., "Roll' of Principll'·Plane Rotat ion in Flexible Pavement Deformation", Journal oJ Trtlll5ptlrtlll /<JU EU!lIZmillg , the Amw.:an Soci(t~' of Ci\'il Enginl'crs, \VashinglOn, 0 C, Vol. 119, No. I , 1993.

Harvey, J.. K. Erikst-n. I. Sousa . and C. L Monismith, "EffectS of Laboratory Sptlimen Preparation on Aggregate·Asphalt Struaure, Air·Vold Content Measurement, and Repetitive Simple Shear Test Results: TnllZS/lllrtntroll Rrstardl Rmmi, No. 145-1 National Research Council , National Academy Press, Washington. D C , pp. 113·122, 1994.

Buttlar, AI·l(hateeb, and Bozkurt

Hight. O. W. A. Gens. and M. I. S~'mes . ~The Ot'velopment of a New Hollow Cylinder Apparatus fot [m'estigating the Effects of Principal Stress Rotation in Soils·, Gtoftchlliqul Vol. 33. pp 355·383. [983.

L~1ton . R. L.. R. Roque. I. Uzan. O. R. Hiltunen. E Fernando and S. M. Stoffels, MPerformance Models and Validation of Test Results·, FIIlIII Ripon Iil Strategic Highway Rtlt~r{h Progrll/lr. Asphalt Proiect A·OO5. Repon SHRP·t\·357. National Academy of Sciences. \\"a ~hi nglOn . 0 c.. 1993.

Roque. R. and W. G. Butdar. -The Oe\'elopment of a Measurement and Anal ~'sis System to r\ccurately Determine Asphalt Concrete Properties Using the Indirect Tensile Mode"./aunutl af tIlt AssocintU!lI af mphalf PavIng Ttchnologists. Vol. 61. pp 304·332. 1992 .

Roque. R. . O. R. Hiltunen. and W. G BUlllar. "Thermal Cracking Performanct and Design of ~lixtures Using SUPERPAVE". SympoSium for SUPERPAVE Implementation. Ponland Oregon . Journal of Ihr AssowlIlon of Asphnlt Pflvmg Ttchllolcgists , Vol. 64 , pp. i 18·735. 1995.

Roque. R .. O. R. Hiltunen . and W. G Buttlar. and T. A Farwana. "Del'elopment of the SHRP SU PERPAVE Mixture Specification Test Method to Control Thermal Cracking Performanct of Pavements", Amrricall Sodr~ for TminK IlIld Malm·als. ASTM STP 1265, G. A Huber and O. S. Decker. edilOrs. Philadelphia, PA, 1995.

Saada . A S., "Hollow Cylinder Torsional Devim: Their Advantages and limitations". ASTM STP 977. American Society for Testi ng and Materials, Philadelphia. pp. 766· 795. 1988.

Shashidhar, N. M X.Ray Tomgraphy of Asphalt Concrm: Acctpttd for Publication in Transparrario/l Rtstllrrh Rtcord. National Rtseareh Council. National Academy Press. Washington . O. c.. 1998.

Timoshinko. S. and S. Woinowsky.Krieger. -Theory of Plates and She!1s-, Me Craw·HilI, New York, NY. pp. 236·241 . 1959.