86 Transportation Research Record 930

Abridg111e111

Possible Effect of Relative Plastic Behavior of Pavement Layers on Pavement Life

W.O. YANDELL

The effect of the relative plastic behavior of the layers of three flexible pave­ments on the accuracy of their predicted pavement life (10 million standard ~~!~ p!!!!!d d~~'M!'! Qn !! Sh~~~ d~!!g~ cl!!!rt !! inY'!!~i~1'ld 1h.,orati~.ally . Tha layers are treated by mechano~attice stress analysis as elastoplastic materials. The analyses suggest that (al when the asphaltic surface acts more plastically than the base and subgrade, lower-surface fatigue life becomes infinite but upper-surface fatigue life is reduced to less than that predicted by the Shell chart and (bl whan the base and subgrade act more plastically than the as· phaltic concrete surface, lower-surface fatigue life is drastically reduced. The rutting lives of pavements with upper layers that behave more plastically are shorter than those with upper layers that behave less plastically.

A number of flexible pavement design systems use the theory of linearized elasticity to determine those critical repeated stresses and strains that control rutting life and fatigue life. A question arises: What are the consequences of subjecting a pavement whose layers have different plastic behavior to the usual elastic analysis? The mechano-lattice stress­strain analysis is used in this paper to suggest some answers to this question.

The mechano-lattice, which is a type of mecha­nized finite-element analysis applied to multilay­ered elastoplastic flexible pavements, has been de­scribed fully elsewhere (1-4). It has also been used successfully to predict-measured pavement per­formance (5,6) and to assess fahric reinforcement 12l • Thl'.ee -points on a curve from Shell design

Figure 1. Assembly of mechano·lattice units to simulate three-layered pavements.

/ ~ ~ PAVEMENT SIMULA!~~~

BY 3300 CUBE· SHAPED ,

chart HNB4 (BJ, modified to a weighted mean air tem­perature (WMAAT) of 23°C (74°FJ, are examined to de­te!"mine the theoretically possi hl P r.hanges in fa­tigue life and rutting life caused by variations in the plastic behavior of the pavement materials.

The elastoplastic mechano-lattice units are as­sembled as shown in Figure 1. The loaded wheel is assumed to move in one direction only so that one or more simulace<i passes l~av~ u~i1iucJ

and stresses that accumulate with s imulated pass.

_ .! _ .. _ __ , -- -J.-"-~--

L~b.1.UUQ~ LU'-'-..1.ll':f

each additional

To illustrate the possible effects of variations in relative plastic behavior between layers, three hypothetical pavements with different relative plas­tic behavior were analyzed (see Figure 2) for each of the thickness designs represented hy points A, B, and C on the Shell design chart shown in Figure 3. Thus, nine pavements were analyzed.

REPRESENTATION OF PLASTIC BEHAVIOR

The definition of relative plastic behavior is given in Figure 2, where the means of achieving the three relative plastic behavior values used in this inves­tigation are illustrated by load-unload hysteresis loops . Thus, whe n th" relative plastic behavior is positive (+0.000086), the asphaltic concret0 · ~r\ in a triaxial test has a residual compr,.ssive st(a~n ~ t

ELASTO ·PLASTIC MECHANO· '-..._

SU B GR~DE SIMULATED BY 660 MECHANO ·LATTI C E UNITS MODIFIED BY INFLUENCE FACTORS

--_)

LATTIC E UNI T S . \ -.........,

'

I '

Transportation Research Record 930

Figuer 2. Hysteresis loops that characterize plastic behavior of each of three layers in pavements for different relative plastic behavior values.

RELATIVE PLASTIC BEHAVIOR VALUE

+ O·OOOOB6

~ t "'

--­b=O·O

--C "'O·O

STRAIN a - STRAIN b OR C n (number Of load cycles )

- 0·000086 zero

_J b-0·000006

C= 0·000086 ~ 1c=

uJ u

Lt Q'.

:::J

"' u '.:; .. J: a.

"' ..

w

"' rr :::J 0 u w

"' <I

"' 0 z :::J 0 til

w 0 .. rr

"' til :::J

"' 0 z :::J

lil

87

0 . 000086 because the unloading modulus is greater than the loading modulus and the bound base and bound subgrade are assumed to be elastic (elastic moduli are taken from the particular Shell design chart). When the base and subgrade act more plas­tically than the elastic asphaltic concrete surface, the relative plastic behavior is negative (-0.000086 column in Figure 2). When all three layers have the same plastic behavior, the relative plastic behavior is zero, as in the third column in Figure 2.

The unloading moduli shown in Figure 2 are cal­culation expedients and only affect the relation be­tween calculation passes and standard axle passes, as will be seen later.

COMPUTATION RESULTS

The two outputs from the computations studied here are (a) a 1.22-m (4-ft) straight-edge rutting ratio, defined as the rut depth under a 1. 22-m straight edge, and (b) the transient and residual lateral stress (to determine fatigue behavior).

Rutting

Figure 4 shows the cumulative rutting ratio extrapo­lated over a range from one or two calculation passes to past the life of the pavement expected by the Shell chart. The extrapolations were assumed to be circular curves. Zero plastic behavior (PP) gave straight lines, positive relative plastic behavior (PE) gave a common large radius, and negative rela­tive plastic behavior (EP) gave smaller radii •

The relation between calculation passes and stan­dard axle passes is fixed by making the following assumptions:

1. The relative plastic behavior represented by the Shell design chart (last column of figure 2) is zero (see plot 0 in Figure 4).

Figure 3. Part of Shell design chart HN84 (modified forWMMATof 23°C and one base modulus of 0.4 millio11 MPa) with calculated variations in rutting and fatigue life due to variations in relative plastic behavior values. ·

SHELL CRITICAL RUTTING -- -

0 10- l

d -loo>--- EP 0·75

a: QI c

+ ·--·-·- EP 1· 5 .... .... " a:

.. >

/ _ ...

+ +-~ +......... -- - EP no bose

.... d

" E :J u

10-•

10° 10' 102 ml 104 10'

Number Of Calculation Passes ( log 10 scale

10° 10• 10 ' 1010

Number of Standard Axle Posses for the 3 layer pavements

BB

2. According to the Shell chart, Shell critical rutting is achieved at 10 million standard axle passes, which i n Figure 4 is equivalent to about BOO calculation passes for points B and C in the Shell chart in Figure 3.

3. The first calculation pass is assumed to sim­ulate the first standard axle pass.

The predicted rutting lives for the nine pavements are summarized in the lower plot in Figure 3.

Fatigue

Figure 5 shows how the transient lateral tensile stress at the bottom of the AC layer decreases with each calculation pass for pavement B with positive relative plastic behavior (PE). Thus, lower-surface fatigue life is likely to increase although upper­surface life may decrease. On the other hand, Fig­ure 6 shows that the transient lateral stress at the bottom of the AC layer increases with each pass when the relative plastic behavior is negative (EP). This should reduce fatigue life in the lower sur­f ace. The rise, fall, and steady state of these fatigue stresses were converted to stra i ns and ex-

Transportation Research Record 930

trapolated on a linear strain v ersus log1 o (num­ber of standard axle passes) plot. The fatigue lives were then determined on plots of log (tensile strain) versus log (number of standard axle passes) • The Shell f at i gue enve l o p e and the same equivalency bet ween calcul ation pass es and standard axle passes as were determined from rutting were used (Figure 4) •

CONCLUSIONS

Figure 3 summarizes the results of this study. Part of the Shell design chart, modified to a WMAAT of 23,,C, is shown abcva the variations in fatigue anl1 rutting life suggested as being the effects of vary­ing relative plastic behavior. Thus, when the rela­tive plastic behavior is positive--i.e., the as­phaltic surface acts more plastically than the base and subgrade--then

1. Calculations indicate that fatigue life could be controlled by cracking in the upper surface and that it is shorter tpan that indicated by the Shell method. But the fatigue life of the lower AC sur­f ace is extended.

Figure 4. Cumulative rutting versus number of calculation passes extrapolated to Shell critical rutting on log-log plot, including some pavements with linearly elastic layers.

kP<l 500 400

70 60

d,

1'i.5 mm

( 9 in )

dz 150 mm

( 6 in . )

300 200

ASPHALTIC

BASE

COMPRESSIVE

100

10

0 TENSILE

- 100

- 10 - 20

transient latera.l stress

- 30 '

COMPRESSIVE

100

10

' I '

TENSILE

- 100

residua.l stress

Figure 5. Stress results for three-layered pavement (B in Figure 3) for first three calculation passes: positive relative plastic behavior value and consequent reduction in transient tensile stresses in bottom of AC layer.

kPa. 500 400

psi. 70 60

d, 225 mm ( 9 in . )

dz

150 mm ( 6 in. J

300 200

50 30

COMPRESSIVE TENSILE

100 0 -100

20 10 -10 -20 -30

2

transient lateral stress

20

C~PRESSIVE

100

10

f/ I I

I

TENSILE

-100

-10

residual stress

- 20

Transportation Research Record 930

Figure 6. Stress results for three-layered pavement (B in Figure 3) for first three calculation passes: negative relative plastic behavior value and consequent increase in transient tensile stresses in bottom of AC layer. - I A- -- --

BASE E = 4 • 106

kPa

! 300~ IQ" -----~ ~ I ~ a d,lct,~1·5 r----...._ t FATIGUE

l:; ~ LIFE ..._ I If) 20 0 --If)

1oc- - c ~ I~ ~ I x .....

100-+.------.----,-----"'-....---'----..,...:.-----..... 100 I 0

I THICKNE SS

200

OF 300 400

BASE ( mm

"'{x-x-x-x- )(-x- ~ 1o"' 10 +-+-+-+-++--t--f- 1 PE fatigue lower surface

I EP rutting

w a:: ::l ...J

1010 -+--.-..,._ 1010

+-.......

I "-....." ~ q ' 10 -1---------4-- ---+- lO~PE rutting 0 .....

~ 8 I ~ 10 ....,.. ____ _ _ ______ _._10 6

: X-- I ...J -->< - --x ,_,,,,-< 7 x---- ............,............ 1

. 10 - - -=- ---+- - >< 10 a . -*'...._ ~ -

~PP fat i g u e SHELL

PP rutting SHELL

LL "';('-PE 0

a: 10"-+--------~----4,... w CD ;[ ::l z

- JI: -.-. --x-""- -x '-t 5 '~

10 -+-- --------1-----''""'"l- EP fatigue lower surface of A(C

89

2. Rutting life is longer than Shell rutting life due to the fact that in this study the base and subgrade are nonplastic.

This work has been supported since June 1981 by the Australian Research Grants Committee.

When the relative plastic behavior is negative-­i. e., the base and subgrade act more plastically than the asphaltic concrete--then

1. The fatigue life of the lower AC surface can decrease, in one case, to one-hundredth of the Shell fatigue life.

2. Rutting life is again longer than Shell rut­ting life because the AC is assumed. to be elastic. The significant observation is that rutting is also less than it is when positive relative plastic be­havior obtains. The absolute plasticity of all lay­ers has the greatest effect on rutting.

ACKNOWLEDGMENT

I wish to thank I.K. Lee of the University of New South Wales and R.L. Lytton of the Texas Transporta­tion Institute for their support and encouragement.

REFERENCES

1. w.o. Yandell. Prediction of the Behavior of Elastoplastic Roads During Repeated Rolling Us­ing the Mechano-Lattice Analogy and the Results of Cyclic Load Material Tests. HRB, Highway Re­search Record 374, 1971, pp. 29-41.

2. W.O. Yandell and R.L. Lytton. The Effect of Residual Stress and Strain Buildup in a Flexible Pavement by Repeated Rolling of a Tire. Texas Transportation Institute, A&.M Univ., College Station, Rept; RF 4087-1, Oct. 1979.

3. W.O. Yandell. Residual Stresses and Strains a~d Fatigue Cracking. Transportation Engineering Journal, ASCE, Vol. 108, No. TEl, Jan. 1982, pp. 103-116.

4. W.O. Yandell. The Use of the Mechano-Lattice Analysis to Investigate Relative Plastic Behav­ior. International Conference on Constitutive Laws for Engineering Materials, Tucson, Ariz., Jan. 8, 1983.

90

s. w.o. Yandell. Measurement and Prediction . of Forward Movement and Rutting in Pavements Under Repetitive Wheel Loads. TRB, Transportation Re­search Record BBB, 19B2, pp'. 77-B4.

6. W .o. Yandell. Rutting and Cracking Prediction at P.s.u. Test Track Using Mechano-Lattice Analysis. Univ. of New South Wales, Kensington, Australia, Rept. UNICIV R-207, Nov. 19B2.

7. w.o. Yandell and J.I. Curiskis. Fabric Rein­forcement to Extend Pavement Life. Annual meet-

Transportation Research Record 930

ing, Assn. of Asphalt Paving Technologists, At­lanta, March 19B3.

B. Shell Pavement Design Manual: Asphalt Pavements and Overlays for Road Traffic. Shell Interna­tional Petroleum Co., Ltd., London, 197B.

Publication of this paper sponsored by Committee on Strength and Deforma­tion Characteristics of Pavement Sections.