Use Of Marshall Stability Test In Asphalt Paving Mix Design

Use of Marshall Stability Test inAsphalt Paving Mix DesignC . T . METCALF, Research Laboratory, Shell Oil Co., Wood River, E l .A continuing problem in the design of bituminous pavementsis the specification of the properties of the mix so that it willhave sufficient stability to resist displacement under traffic.This problem has been made more acute by the demands ofheavier wheel loads which are anticipated for modern highwaysand airfields. Thus, to aid mix formulation there is a pressingneed for specifications in terms of the results of laboratorytests.An analysis of the Marshall Stability test shows that thebearing capacity of a paving mix can be related to MarshallStability and flow by the following equation:Bearing Capacity (psi) 1/5 x (2 K) Fin which1 sin 1 - sin j F (1-0.055 K)Derivation of this equation is based on two important assumptions:1. Allowable design stress corresponds to the stress calculated at 1 percent strain in the Marshall test.2. Confining pressure in the pavement is equal to 50 percentof unconfined compressive strength (confinement is proportionalto lateral strain; this is 50 percent of vertical strain for materials that do not change volume).A convenient approximation of the above equation is given by:Bearing capacity (psi)l O The design curves representing the above relationships emphasizethat the load-carrying ability of an asphaltic mix is a fimction of theflow value as well as the stability and reveal the inadequacy of theusual specifications which call for only a minimum stability and maximum flow value. A single bearing capacity for any mix can be calculated from the combination of stability and flow. Marshall Stabilityalone, however, is not an absolute measure of strength.It is believed that the results of this analysis will be veryuseful in highway and airfield design.# THERE ARE several tests commonly employed at the present time to measure theresistance to deformation of asphalt-aggregate mixtures (JL). These tests include:1.2.3.4.5.Marshall StabilityHveem StabilometerHubbard-FieldUnconfined CompressionTriaxialAll of these are used to measure plastic stability or the ability of a mix to resistbeing squeezed out from under a load. All except the triaxial and possibly the uncon12

13fined compression tests are empirical and are not considered to measure any fundamental material property. They are extensively used, however, in design and controlwork.Popularity of these tests can be divided somewhat according to geographical location, but the most widely used at present is the Marshall Stability test ( 2 ) , originallydeveloped by the U. S. Army, Corps of Engineers (J). Because of its wide usage itis the basis of many specifications and is a familiar and accepted measure of stability.Quite often design problems must be solved by this test alone. Thus, it is essentialto obtain a better understanding of its significance.During the study of a number of small-scale pavement test sections, however, itbecame especially evident that neither Marshall Stability nor flow value alone satisfactorily predicted resistance to plastic displacement. It appeared that sections havingequal stabilities did not have the same supporting power when their flow values differed.Similarly, sections having equal flow values often performed quite differently as a result of differences in stability. Examples are shown in the foUowii table.MIXES OF EQUAL Flow Value(0.01 in.)612131616Performance(Resistanceto PlasticDisplacement)MIXES OF EQUAL FLOW 111Satisfactory11Plastic11Because of these problems and of the need to make a satisfactory appraisal of theproperties of the field test sections, it was decided to make a closer investigation ofthe Marshall test which could serve as a basis for interpretation. To make better useof the test it appeared necessary to answer two fundamental questions: (a) What material properties are being measured in the Marshall test? (b) What is the relation ofthese properties to the bearing capacity of a paving mix?INTERPRETATION OF MARSHALL STABILITY RESULTSA review of the literature shows that only a limited amount of work has been doneto define the properties measured in the Marshall test. A previous investigation byFink and Lettier (4) has shown the influence of asphalt viscosity on stability valuesand Endersby and Vallerga ( 5) have demonstrated the effects of different compactionmethods on test results. Van Iterson (6) interpreted the loading of a cylindrical shapesuch as used in the Marshall test as being similar to an unconfined compression test.Goetz and McLaughlin ( 7,J) have made some of the few studies that attempted to examine the results of Marshall testing in the light of triaxial and unconfined compressiontests. A conclusion from their work is that the Marshall test is a type of confined testin which the confinement is attributed to the curved shape of the testing heads. Theirwork is significant because identical materials were tested in both the Marshall testand the unconfined compression test. The method of specimen preparation was not avariable in the comparison.Use of the test for design purposes has indicated that a type of shear failure occurs

14in the test (Figure 1) that is similar to failures in direct compression tests.Analysis of the forces involved in the Marshall test shows that the measured vertical force is the sum of the stresses acting on the curved surface of the testir head atthe interface with the specimen. These stresses consist of normal (S ) and tangential(Sg) components as shown in Figure 2. For any small elemental area dA on the testing head, the vertical stress Sy is given by:Sy cos a dA Sn cos a dA Sg sin a dA(1)substitutingdA rt dawherer radius of curved surfacet width of area (normal to plane surface of specimen)producesrt Sy cosa da rt Sjj cos a da rt Sg sin a da(2)Then, since a ranges from 0 to 70 in the Marshall apparatus, the sum of all thevertical forces acting on the head"becomes/ a 70 /.a 70 ra 70 21rtSyCosa da 2lrt S„ cos a da 21r t S g S i n a d a (3)Ja 0Ja 0Ja 0Deformation of the specimen normal to the testing head is approximately equal toy cos a where Yq is the vertical deformation of the specimen at the center. If stressis taken to be proportional to deformation, then the normal stress at any point on thetesting head is S SQ cos a , in which SQ is the vertical stress at the center of thetest head. Substituting this in Eq. 3, the total vertical reaction force R in theMarshall test is given by the value of the integral./ a 70 f a 70 ra 70 21rt Sy cos a d a R 2\rtSo cos a d a 21rt Sg sinada (4)Ja 03a 0J a 0If the tangential or shearing stresses are developed by friction alone,Sg f SQ f SocosaThe expression for vertical reaction then becomes70 R 2 rtl( SQ COS a SQ sin a cos a) daJo 0(5)Evaluation of the integral producesR (1.54 0.88 f) rtSjj(6)For values of the coefficient of friction in the range of 0.4 to 0.6, Eq. 6 isapproximately equal to: R 2 rt S For the Marshall test, r 2 in., t 2.5 in., so using English units,R 10So(7)Coefficients of static friction of 0.4 to 0.5 have been measured in the laboratoryand thus Eq. 7 seems a fair representation of stress conditions in the Marshalltest.K, then, the Marshall test is a type of unconfined compression test, MarshallStability should be approximately ten times the unconfined compressive stress. TheInvestigations of McLaughlin and Goetz (J), however, have demonstrated that MarshallStabilities are much greater than this amount. Thus, the Marshall test resembles acompression test performed on a specimen of low height to diameter ratio in which the

15F i g u r e 1.Shear planesdevelopedM a r s h a l l T e s t specimen.infailure planes intersect the testing head.Such an arrangement is represented bythe drawing in Figure 3. This shows themiddle portion of a specimen with aheight-diameter ratio of approximatelytwo to one being confined by the excessmaterial around it. Such material wouldhave the effect of exerting a lateral confining pressure on the center section.The strength of a confined specimenaccording to the Mohr theory is given by:SQ F i g u r e 2.Stress relations inStability test.2c 1 LKMarshall(8)' -iin which(1 sin 4 )(1 - sin (j))j angle of internal frictionc cohesionL confining pressureK.,'jThus, strength is composed of elements involving the unconfined compressive strength( 2c - KT plus a confining effect ( LK) that depends upon the angle of internal friction ofthe material. Confining pressure " L " in the above equation must be considered to bean "effective" pressure rather than a uniformly applied pressure as employed in arational triaxial test. McLeod (8) has asserted that the effective lateral support whichbecomes active in the Marshall test is not constant but depends upon:1. Coefficient of friction between specimen and test head.2. Maximum vertical load applied.3. Angle of internal friction of the mix.I; 4. Shearirg resistance of the material.1He has made use of these premises in a theory of pavement design (10) in which the]importance of friction in the development of pavement stability is pointed out.A review of the work by McLaughlin and Goetz reveals that the effective confiningpressures as calculated on the basis of their Marshall Stability values are directly re- \lated to the applied vertical load in the test. Confinement behaves as if developed bythe friction between the testing head and specimen. A reasonable approximation ofthis confinement can be obtained by taking 5. 5 percent of the Marshall Stability/10.Thus, a stability of 1, 000 lb tends to produce a confining pressure of 5. 5 psi and 2, 000lb corresponds to 11 psi. While these figures are approximate, and frictional forcesare probably not constant, this method provides a reasonable approach to the establishment of a relationship between Marshall Stability and unconfined compressive stress.

16Substituting L 0.055 j' y in Eq. 8 and remembering that 10 'equation becomes:Stability 2 c V i r . 0.05510Stability10( yty) (9)2c V K "1 - 0.055 KBy providing a reasonable measure of K which is a function of the angle of internalfriction, it is possible to calculate the unconfined compressive stress from MarshallStability results. The Purdue investigations (8) also showed that reasonably good correlation existed between the "flow" value in the Marshall test and actual measuredvalues of the angle of internal friction. Although flow cannot be considered a directmeasure of friction, the properties that affect friction appear to affect flow in a similar manner and thus the flow value offers a convenient, if inexact, means of estimating the friction angle. A rough estimate of internal friction can be obtained from:Angle of internal friction (degrees) 60 - Flow(10)Evaluation of K on this basis permitsthe unconfined compressive stress to beestimated from Marshall results. A convenient expression for estimating K directly from the flow value is given by:„ „ . (30 - Flow)"the quantity(1-0.055 K) inEq.Similarly,9 can be estimatedfrom(30 - Flow)'(1-0.055 K) 0.ir8— TUnconfined Compressive Stress MarahnllpmmitY ( i - o 055 K)//V/,//VCorrelation Ratio 0 96Estimated Unconfined Compressive Stress (psijFigure 3. Confinement provided by specimenof low height-diameter ratio.Figure U. Correlation of measured unconfined compressive stress with unconfinedcompressivestress estimatedfromMarshall Stability test.