/1,

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j J

DEVELOPMENT OF BASE LAYER THICKNESS EQUIVALENCY

DEVELOPMENT OF BASE LAYER THICKNESS EQUIVALENCY

s. s. Kuo

Research Laboratory Section Testing and Research Division

Research Project 68 E-42 Research Report No. R-1119

Michigan Department of Transportation Hannes Meyers, Jr., Chairman; Carl v. Pellonpa.a., Vice-Chairman; Weston E. Vivian, Rodger Young,

Lawrence C. Patrick, Jr. , William C. Marshall John P. woodford, Director

Lansing, June 1979

The information contained in this report was compiled exclusively for the use of the Michigan Department of Transportation. Recommendations contained herein are based upon the research data. obtained and the expertise of the· re­searchers, and are not necessarily to be construed as Department policy. No materia.! contained herein is to be reproduced-wholly or in part-without the expressed permission of the Engineer of Testing and Research.

SUMMARY

Two current projects in the Research Laboratory's Soils Research Unit, "Comparative Study on Performance of Bituminous Stabilized Bases (M 66 and M 20)" and "Comparison of Cracked and Uncracked Flexible Pavements in Michigan, 11 deal with performance of flexible pavement sec­tions built with 'black bases. 1 It has been felt that a better knowledge of the interaction of black bases with the rest of the pavement system would be a valuable tool in assessing and designing a flexible pavement.

The purpose of this study is to establish a 'thickness equivalency' of the base layer on the basis of: a) elastic layer theory; and, b) limiting strains at critical locations in the pavement. The elastic layer theory con­siders the pavement to be a system of homogeneous layers of infinite hori­zontal extent spread over a semi-infinite depth subgradeand is, therefore, a static linear-elastic boundary-values problem. The limiting strains are the horizontal tensile strain at the bottom of any asphaltic layer and the compressive strain at the top of the subgrade. Control of these strain values provides control over the a.bility of the pavement to resist fatigue cracking and subgrade failure.

The Chevron CHEV 5L computer program, whose algorithm is based on the elastic layer theory, was used to calculate all critical strains in this study. The allowable values for tensile strain are based on fatigue data. established by Santucci @) and modified to be compatible with Michigan's mix design by equations developed by Pelland Cooper @i) and Epps (25). The subgra.de compressive strain criteria. developed by Monismith a.nd McLean (~ a.re used in this study.

The determination of appropriate modulus values for computer input parameters in bituminous concrete, black base, and subgra.de soils is dis­cussed. The moduli of granular base and subbase materials are determined from subgrade modulus by stress-dependent concepts, which consider the modulus of a base or subbase layer to be a function of the modulus of the layer below it. All granular base and subbase materials are assumed to have adequate drainage characteristics so that variations in moisture con­ditions do not affect the strength and stiffness of these materials.

With the use of computer data obtained from models of two standard Michigan flexible pavement sections subjected to 5 x 105, 1 x 106, and 2 x 1 o6 18-kip equivalent axle load repetitions , thickness equivalency curves were developed; each curve definingthe relationship between the base thick­ness h2 and the base modulus E2 for given pavement and loading systems.

With these equivalency curves, highway engineers should be able to design the thickness of a granular or a.spha.It-treated base which will satisfy the strain restrictions in a flexible pavement section with known bituminous concrete and sub grade moduli. Procedures for designingtheoretical thick­ness combinations of granular base and black base pavements are also pre­sented as design alternatives in this report. An example problem is pro­vided to illustrate the procedures for using the thickness equivalency charts and the procedures for development of design alternatives.

One of the other uses of the thickness equivalency charts developed in this study is in determiningwhether or not a black base is needed in a pave­ment section, or whether a black base may be substituted for a granular base, as results of the study indicate that black bases ha.ve an economic advantage only when the subgra.de is weak. Another use is for predicting the remaining years of performance life in an existing flexible pavement.

This investigation considers only load-related failures, i.e., those failures associated with fatigue cracking and surface rutting. Other failures caused by frost heave, thermal cracking, etc., are not taken into account here but will be considered in another study.

This study has yielded considerable groundwork which is readily ap­plicable to future investigations in the design and performance of black base for pavement sections in which the subgrade is weak, or in which the sub­base layer is omitted.

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INTRODUCTION

Purpose and Scope

The purpose of this study is to establish a. thickness equivalency of the base layer of a. flexible pavement on the basis of: a.) elastic layer theory; and, b) limiting strains at critical locations in the pavement.

Thickness equivalency curves for the base layer define the relationship between the thickness and the resilient modulus of a. base layer necessary for optimum pavement performance. By their use, not only can the thick­ness of a. base la.yerof a material with known modulus, E2 , be determined, but decisions can also be made regarding the use of granular or asphalt­treated bases or combinations of both for a given set of loading conditions.

An 18-kip equivalent axle load (EAL) was used for this study. On the basis of results obtained in fatigue studies by numerous investigators, it was assumed that a. 2. 5-in. thick bituminous concrete layer would be ex­pected to carry from one-half toone million 18-kip EAL repetitions before failing and a 4. 5-in. thick bituminous concrete layer would carry from one to two million 18-kip EAL repetitions before failure.

The study is limited to two typical Michigan flexible pavement designs with the loading condition and layer characteristics shown in Figure 1. Only load-related failures-fatigue cracking and surface rutting-are con­sidered in the calculations for pavement damage.

Furthermore, all granular base and subbase materials are assumed to have adequate drainage characteristics so that variations in moisture· conditions do not have a significant effect on the strength and stiffness of these materials. However, moisture conditions which influence the stiff­ness and strength characteristics of the sub grade soils need to be taken into consideration.

Background of the Study

Research Laboratory interest in base layer equivalencies dates back to 1971 when I. AlNouri, of the Soils Research Unit, proposed a. 'qua.si~ela.stic' modulus 'E*' for 'black bases' (!). In 1976, F. Hsia, also of the Soils Re­search Unit presented charts of thickness equivalencies between asphalt­treated and untreated base layers (~. Two current projects in the Unit, "Comparative Study on Performance of Bituminous Stabilized Bases (M 66 and M 20)," (Research Project 75 E-59), and "Comparison of Cracked and Uncra.cked Flexible Pavements in Michigan" (Research Project 78 D-36),

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~ DUAL TIRES

I 4500 LBI4500 LB

~ TIRE

I 4500 LB 4500 LB

Ev SUBBASE Ev

SUBGRADE

STRAINS MIDWAY BETWEEN DUAL TIRES

> ? STRAINS DIRECTLY

BENEATH ONE TIRE

Figure 1. Schematic representation of location of maximum horizontal tensile and vertical compressive strains in flexible pavement structures.

also deal with performance of flexible pavement sections built with black bases. It has been felt that a. better knowledge of the interaction of black bases with the rest of the pavement system would be a. valuable tool in as­sessing and designing flexible pavements.

Theoretical Basis of the Study

An essential step in the design of pavements is the evaluation of stress­es and strains that are induced in a road structure by traffic loads. One of the methods used today to determine a pavement's response to load is by elastic layer theory which assumes that the pavement is a. system of hori­zontally-infinite homogeneous la.yers of uniform thickness, resting on a. semi -infinite sub grade. If the pavement layers and sub grade respond to traffic loa.dinga.s linearly elastic solids, the multilayer system of analysis can be used to analyze stresses and strains. Kingham @) made a. study which verified that deflections, vertical strains, and radial strains can be reasonably computed from elastic layer theory. Hicks and Finn (!) have shown that the measured deflections and strains in the San Diego test road

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are reasonably close to those computed by the elastic layer system. More recently, investigators have shown that past pavement design experience correla,tes reasonably well with multilayer, elastic theory computations.

In 1963, Dormonand Metcalf@) rationalized that the horizontal stress and strain at the bottom of an asphalt layer and the vertical strain at the top of the subgrade layer are critically related to pavement performance. Today, there is general agreement that the horizontal tensile strain at the bottom of the asphalt layer is the controlling criterion for fatigue cracking and that the vertical compressive strain at the surface of the subgrade is the controlling criterion for permanent surface deformation. Control of these strains provides control over pavement performance factors that are related to traffic loading.

In this report, the critical strains under a 9, 000-lb equivalent wheel load on dual tires were calculated at two different locations in the wheel load area. One location is midway between the tires, the other directly under one of the tires. Figure 1 illustrates the modes of loading with the location of maximum strain in a typical pavement structure. The values of the strain under one of the dual tires and midway between the tires, are obtained by superimposing the separate strains induced under each of the two locations by one of the tires. The strain values obtained by superposi­tion at the two locations are compared and the greater value is used for analysis purposes.

COMPUTERIZATION OF ELASTIC MULTILAYER SYSTEMS

Characterization of the mechanical behavior of materials is compli­cated, and stress analysis of a pavement consisting of different types of materials is even more complicated. Without the use of computers, the solutions for stresses, strains, displacements, and other pavement res­ponse parameters are tedious and might even be impossible.

There are several elastic layer computer programs that will satis­factorily compute pavement response parameters. CHEV 5L @)and BISAR CD computer programs are currently available for use in the Department. Both programs have a similar mathematical development and give essen­tially the same results. The principal difference between the two programs is that CHEV 5L is restricted to a single normal load while BISAR is cap­able of analyzing multiple loads.

The CHEV 5L program, which was chosen for this study, was written with the following assumptions:

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i l !

I

"'

4500 LB 4500 LB 4500 LB 4500 LB

I BITUMINOUS I + <.. i BITUMINOUS I T .~ (CONCRETE . "' E,, VI h,= 2·5 \CONCRETE E,, v, h1=4.s/ ) s z "-t t > I · E. f 1

I I f 1 I .. ,. t I \ BLACK BASE OR E V ) I \ \ AGGREGATE BASE · 2 ' 2 hz = ) ) BLACK BASE OR E2, V2 h 2 = ( { TENSILE STRESS IN VARIABLE \ AGGREGATE BASE . VARIABLE

i SUBBASE

I - - B SE I TENSILE STRESS IN I .I I \ ..... - BLACK BASE

\ ( \

\ I I. ( ., E3,V3 h3=15")) I

~-~ j

) ) suBBASE .

1

E3 , v3 h3=2s") J E.v - \ \ \

I J Z 'E.v (

I. E4, v4 ( 1--------'-------+----1 00 \ I \

\ suBGRADE E4 , V4 ( I ex>

SUB GRADE

A. This design, with the thinner bituminous concrete surface was used in constructing the thickness equivalency curves shown in Figures 17-22.

B. This design, with the thicker bituminous concrete surface was used in constructing the thickness equivalency curves shown in Figures 23-28.

Figure 2. Schematic representation of two typical Michigan flexible pavement systems.

,,

1) The pavement is a. composite of horizonta.lla.yers of uniform finite thickness spread over a. subgra.de la.yer,

2) The layers a.re infinite in extent in a.ll horizontal directions, the subgra.de la.yer being infinite in extent in both the horizontal and vertical (downward) directions,

3) The layers a.re homogeneous a.nd isotropic with respect to their mechanical behavior,

4) The materials of the layers ha.ve a. linear stress-strain relationship,

5) The components of stress a.nd displacement a.t interfaces between layers a.re continuous, a.nd

6) Allloa.ds a.re circular and uniform over the contact a.rea..

These assumptions a.re, in fa.ct, necessary conditions for pavement design. CHEV 5L enables designers to ca.lcula.te stresses, strains, and displacements a.t a.ny position in a. multilayer system, with a.n arbitrary number of layers subjected to a singlenorma.lloa.d. In the ca.se of dual tire loadings, CHEV 5L is ru.n for ea.ch point loa.d and the effects of the a.dja.cent tire load accounted for by the principle of superposition. The input para­meters for the CHEV 5L program are traffic loading, tire pressure, num­ber and thickness of layers in the flexible pavement cross-section, the resilient modulus E, and Poisson's ratio, v, of each component layer. The determination of values to assume for the resilient modulus of ea.ch la.yer wa.s .a. major portion of this study.

CHARACTERIZATION OF MATERIALS USED IN MICHIGAN FLEXIBLE PAVEMENT SYSTEMS

An investigation was conducted to determine the elastic modulus and Poisson's ratio properties of ea.ch la.yerof two typical four-la.yer pavement systems used in Michigan (Fig. 2). The base course, of variable depth h2 in Figure 2, can be constructed of either asphalt-treated ma.teria.l (bla.ck ba.se) or unbound granular material. The parameters, h, E, and v shown in Figure 2 are, respectively, layer thickness, modulus of elasticity, a.nd Poisson's ratio, with the numerical subscript denoting the layer order of depth. Note that for the two typical systems used, a 2. 5-in. bituminous concrete surface layer, h1, isa.ssumed to havea.15-in. subbase layer, h3, (Fig. 2A) and a. 4. 5-in. bituminous concrete surface layer is assumed to have a. 25-in. subbase layer, h3, (Fig. 2B). The standard subbase la.yer thicknesses shown are known to provide for satisfactory drainage. Each layer is discussed in the following sections.

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u..

w' 0:: :;:)

~ 0:: w a. :::. w t-w t-w 0:: u z

00 0 I

u rJ) :;:) 0 z ~ :;:) t-iii

110 POISSON~-RATIO-,;-O.SO-u --- '( POISSON'S RATIO= 0.3SJ I

100

90

80

70

60

50

40

30

20

10

0

-10 1,000 10,000 100,000

I I I I I I I

1,000,000

STIFFNESS MODULUS OF BITUMINOUS CONCRETE, PSI

Figure 3. Effect of temperature on stiffness of 120-150 penetration bituminous concrete a.t various vehicle speeds (after Novak @) )·

·.·c·:.·

10,000,000

Bituminous Concrete

The modulus and the tensile strength of bituminous concrete depend not only on the mix properties such as air void content, aggregate gradation, and bitumen content, but also on pavement temperature and time of loading. On the basis of all these factors, the modulus of bituminous concrete can be determined using the bitumen-stiffness nomograph originally proposed by VanderPoel @)with later changes by Heukelom and Klomp (~)·

Novak (!Q), using the same stiffness nomograph, developed a series of charts for determining the stiffness modulus of bituminous concrete. Fig­ure 3 illustrates one of Novak's charts for bituminous concrete consisting of 120/150penetrationgrade bitumen. Claessen (11) used a similar nomo­graph for determining the stiffness moduli of bituminous mixes, but his nomograph did not include loading time, which is, essentially, a function of vehicle speed.

Other methods for determining the modulus of a bituminous mix include direct testing methods such as that outlined in ASTM's Annual Book of Standards, Part 15, and by rough estimates from tables such as Table 1 of Ref. @·

Unbound Granular Base and Subbase Materials

The materials used for highway construction must meet gradation and other requirements as specified in Michigan's "Standard Specifications for Highway Construction. "

The method used to determine the modulus values of unbound granular base and subbase materials is based on stress-dependent principles first reported by Izatt, Lettier, and Taylor @)· The modulus values in this report are calculated from mathematica.l expressions developed at the Wa­terway Experiment Station (g) from analysis of test track performance data. This method was developed in accordance with the concept that the modulus value of unbound granular materials is stress-dependent and that, since induced stresses decrease with depth, modulus values also decrease with depth. This implies that the modulus of the granular materia.! in each layer is a function of the layer thickness and of the modulus of the under­lying layer. Therefore, the modulus of the subbase layer directly over the subgrade is a function of the subgrade modulus and the modulus of the base layer is a function of subbase modulus.

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The Waterway Experiment Station equation, applicable to base course material, is:

En = En+1 (1 + 10.52 log t - 2.10 log En+1 log t) (1)

where the base course is layer n. For subbase materials,

En = En+l (1 + 7.18 log t - 1. 56 log En+llog t) (2)

where the subba.se course is layer n. For each equation, En+1 is the modu­lus value of the lower layer n+1, in psi, tis the thickness of the overlying layer, n, in in. , and En is the modulus value of layer, n, in psi.

For thick granular base and subbase layers, each layer should be di­vided into sublayers 6 to 8 in. thick and the modulus of each subla.yer as­sumed to be a. function of its thickness and the modulus of the sub layer be­low it@)·

Eqs. (1) and (2) plotted in Figures 4 and 5 show the relationship of modulus and depth for 2 in. to 10-in. unbound base and 3 in. to 10-in. un­bound subbase.

A series of road vibration measurements recorded by Heukelom and Klomp @) further support the concept that the effective modulus of a granu­lar base course is dependent on the modulus of the underlying subgrade soil. On the a.verage, the modulus of each granular layer is appro:ximately three times greater than that of the layer below it. Klomp and Dormon (!i) obtained field measurements that showed the modulus ratios between the overlying unbound layers and the subgrade to be in the range of 1. 5 to 2. 5. The relationship reflecting the effect of subbase thickness is presented by Klomp and Dormon as follows:

E3 = K3 E4

where: K3 = 0. 206 h3 °· 45; 2 < K3 < 4

h3 = thickness of unbound layers in millimeters, and E4 = known subgrade modulus.

(3)

(4)

In order to keep the value of K3 between 2 and 4, h3 can be assigned only values which are greater than 6.15 in. and less than 28.69 in.

In this study, the two values assigned to the subbase thickness are 15 in. and 25 in., both of which are within the requirement of Eqs. (3) and (4).

For these two subbase thicknesses, a comparison was made between the resulting subbase moduli obtained by using Eqs. (2) and (3) for three

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t !·

different subgra.de modulus values. The calculations were further extended to show how the division into sublayers affect the resulting modulus of a thick subbase. Table 1 shows the results of the comparison. The thickness equivalency charts presented later in this report are based on the average subbase modulus values as determined bydivision intosublayers and listed in Table 1.

rJ.l rJ.l Q)

.§ .: " ·~ ·~ LQ

~ .... <ll II

rJ.l "" '""" .D "§ IZl

. rJ.l rJ.l <ll .§ .: " -~ ·~ lQ ..:., E-< <ll II

rJ.l "" '""" .D "§ IZl

TABLE 1 COMPARISON OF SUBBASE MODULI AS

OBTAINED BY EQS. (2) AND (3)

Subgra.de Modulus, E4, psi Subbase Moduli

3, ooo 1 7. 500 1 15. ooo

Eq. (3), subbase modulus, E3 8,960 22,400 44,800

Eq. (2), subbase modulus, E3 9,180 17,500 26,700

· Eq. (2), subbase modulus (divided into subla.yers)

h31 ~ 7. 5 in. , E 31 7,590 14,900 23,700 h32 ~ 7. 5 in., E 32 15, 000 23,600 31,000

Average subbase modulus, E3 11,000 19,000 27,000

Eq. (3), subbase modulus, E3 11,280 28,200 56,400

Eq. (2), subbase modulus, E3 10,350 19,400 29,000

Eq. (2), subbase modulus (divided into sublayers)

h31 ~ 8 in., E31 7,740 15, 150 24,000 h32 ~ 8 in., E32 15,480 24,000 31,400 h33 ~ 9 in., E33 24,900 32,000 36,400

Average subbase modulus, E3 16,000 24,000 30,000

Asphalt-Treated Material (Black Base)

The term black ba.se is understood to refer to a well-compacted, high stone content hot bituminous mix, having a void content of less than 10 per­cent and a bitumen content of not less than 4 percent. It is assumed to be a part of the asphalt bond layer. Therefore, the properties of black base are assumed similar to those of bituminous concrete (15). The resilient modulus of the black base is determined on the basis of two concepts. The

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;;; a. " £ X c

"' I

..... t¢

6

~'

iL-----~--~--_L_L_L_L~J_ ____ ~L_--~_J~L_~~~

I 2 4 6 8 10 20 40 60 80 100

En+! X 103 PSI

Figure 4. Relationship between modulus of layer n and modulus of layer n+l for various thicknesses of unbound base course.

;;; a. " £ X c

"'

lOr---------------------------------------------------, 9 8 7 6

5

2

1 L,--------~2"----"---"4c--L-"6-"-"8-L~IOL_ _______ 2~0c----L---4~0c-"-~6LO-L~8~0~100

En+ 1XI03 PSI

Figure 5. Relationship between modulus of layer n and modulus of layer n+l for various thicknesses of unbound subbase course.

first concept assumes that the black base will withstand the applied load without development of tensile cracking at the bottom of the black base. Under this concept, the modulus value is determined using the principles described in the "Bituminous Concrete" section of this report. The second concept assumes that tensile cracking will develop, and a. reduced modulus value, termed 'black-base cracked section modulus, 1 is used which is de­termined by laboratory testing. Barker (13) utilized the unconfined com­pression test to determine an equivalent cracked section modulus of stabi­lized base material.

To design a pavement system with black base, an initial black base modulus value is used. The maximum tensile strain at the bottom of the black base la.yer is computed and compared with the permissible strain in­dicated by the black base fatigue criteria. (Explained in detail on page 27 and Fig. 15). If the black base strain value is smaller than the permissible strain, the black base will not crack before the design number of 18-kip EAL repetitions is applied by traffic. However, if the computed tensile strain is larger than the permissible strain, cracking will occur and a. black base cracked section modulus must be used to design the pavements.

In this report, the modulus values of black base used for the computer runs, can be assumed to range from a. minimum of 50,000 psi to a. maxi­mum of 1, 500,000 psi similar to that of bituminous concrete. The high modulus values are used to approximate more closely pa. vement conditions under moving traffic. The quasi-elastic modulus of black base reported in Ref. (!) is very low compared to values reported by other sources. Ref. Q) results were obtained using the conventional triaxial test equipment in which load cycles were repeated 20 times. The rate of loading is too slow compa.red with that of movingtra.ffic. Ref. (!) reports that the average black base modulus at a pavement temperature of 77 F is 41,000 psi, while the same mix at the sa.me temperature has, on the basis of Figure 3, a. modulus of 150, 000 psi for a. vehicle speed of 30 mph. The difference is attributed to the rate of loading. It has been reported ~) that long loading periods such as that used in Ref. (!) will change the internal structure of the bituminous mix which, in turn, causes the modulus to differ from that obtained with rapid load cycles. With the use of the MTS electro-hydraulic loading system recently acquired for the Research Laboratory, the deter­mination of black base modulus can be made at rates of loa.dingwhich better simulate actual traffic loading conditions.

Subgrade Soils

The term 'subgrade' refers to the natural, processed, or fill soils on which the pavement structure is placed. Most subgra.des show stress­dependent behavior, and both laboratory and full-scale pavement studies

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I

have demonstrated that linear-elastic theory can be used to describe the pavement response, provided the moduli of all pavement materials are de­termined under the appropriate loading conditions. Therefore, the sub­grade modulus is preferably determined in-situ from surface deflection measurements. There are several different methods of determining sub­grade modulus on the basis of surface deflection (!2, 18, 19).

Heukelom and Klomp @Q_) present a. relationship between dynamic modu­lus and California Bearing Ratio (CBR) values which can be used to estimate subgra.de modulus when pavement surface deflection or subgrade modulus data are not ava.ila.ble.

E = 1500 x CBR (5)

This empirical relationship is often used in practice to estimate subgrade modulus.

In this report, three values of subgrade modulus, 3, 000 psi, 7, 500 psi, and 15, 000 psi, are assumed to represent the full range of sub grade condi­tions found in Michigan. Interpolation procedures can be used to estimate results for other subgrade moduli.

Poisson's Ratio

Hills and Heukelom (1&) conducted an investigation to determine how much of an effect Poisson's ratio has on the computed tensile strain at the bottom of the bituminous concrete layer and on the compressive strain at the subgra.de surface. The value of Poisson's ratio can vary with stress, temperature, etc. Generally speaking, changes in Poisson's ratio have little effect on the maximum tensile and compressive strains, as shown in Figures 6 through 13. Figure 6 shows that changes in subgra.de modulus have little effect on tensile strains; whereas, changes in the modulus of either the bituminous concrete surface layer or the base layer have a signi­ficant effect on tensile strain.

Poisson's ratio for bituminous concrete is known to approach a value of 0. 5 as the modulus of bituminous concrete decreases. Kingham and Kallas@) used 0.45 when the modulus wa.s below 500,000 psi. Barker, et a.l, @) assigned values of 0. 5 a.nd 0. 3, respectively, for moduli less than and greater than 500, 000 psi while Santucci (~ uses a. value of 0. 4 rega.rdless of the modulus of the mix. In this study, a Poisson's ratio of 0. 5 is used for conditions when the bituminous modulus is less than 500,000 psi, and 0. 4 when the modulus is greater than 500, 000 psi.

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i ' i ... ' Q X ... w

7

6

Et=IOO,OOO; Ez= IS,OOOi EJ=I9,000i £ 4 :7,500

E1=tOO,OOOi Ez= 15,000; Ea=27,000; £4 = 15,000

Et=3oo,ooo; E2= ts,ooo; Ea=n,ooo; £ 4 = a,ooo £ 1=300,000; E2=15,000i Ea=l9,000i £ 4 =7,500

E1=aoo,ooo; E2=1s,ooo; Ea=27,ooo; E4=1s,ooo Et= IOO,OOOi £2=25,000; Ea=27,000i £4=15,000 Et=IOO,OOO; £2=25,000; Ea= 19,000; £4 ::7,500

z

~ 4 ~=============:::3~~ t­lf)

w ..J If) 3 z w t-

2

£ 1:300,000; £2=25,000; Ea= II,OOOi £4=3,000 E1=aoo,ooo; E2=2s,ooo; Ea= 19,ooo; E4=7,soo Et=Joo,ooo; E2=2s,ooo; Ea=27,ooo; E4=ts,ooo

Et=3001ooo; E2=so,ooo; Ea=u,ooo; £4= a,ooo Et=Joo,ooo; E2=so,ooo; Ea=tg,ooo; £ 4=7,soo

Et=too,ooo; E2=so,ooo; Ea=t9,ooo;£4 =7,soo Et=too,ooo; Ez=so,ooo; Ea=u,ooo; £4=a,ooo

0~-------L~----~~----~ 0.35 0.40 0.45 0.50

POISSON'S RATIO, V,

Figure 7. Effect of Poisson's ratio, V 2 , on tensile strain at the bottom of the bitu­minous concrete for various combinations of moduli in a four-la.yer system where h1 = 2. 5-in., h2 = 6-in., h3 = 15-in., h4 = semi -infinite, axle load = 18, 000 lb, tire pressure = 70 psi.

I~ Figure 6. Effect of Poisson's ratio, VI> on tensile strain at the bottom of the bitu­minous concrete for various combinations of moduli in a four-layer system where h1 = 2. 5-in. , hz = 6-in. , h3 = 15-in. , h4 = semi-infinite, axle load = 18, 000 lb, tire pressure = 70 psi.

9.----------------------.

8

7

EJ=3oo,ooo: E2=1s,ooo; E3::u,ooo; E4=a,ooo

z 5 <( 0::

lii w :! UJ 4 z w E 1 =300,000; £2=25,000; EJ=II,OOO; £4=3,000

f--

3

2

1 L _______ J_ ______ _L~----~

0.35 0.40 0.45 0.50 POISSON'S RATIO, V2

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z ' z .. I Q X ~ .., z <( 0::

tii w _J

(/) z w 1-

9

8 - Ei=IOO,OOO; E2=1!»,000; Ea= 11,000; £ 4 =3,000+

7 >-

6 1-

EJ=300,000; £2=15,000; Ea:=II,000;£4 =3,000,

5 Ei=loo,ooo; E2=·2s,ooo; Ea=u,ooo; r 4=a,ooo__}

4 I-Ei=300,000,; E2=25,000i Ea=II,OOO; £4 :3,000_)

3 1-E,=aoo,ooo; E2=so,ooo; Ea=n,ooo; r 4=a,ooo\

2 ~Ei=IOO,OOO; E2=50,000i Ea=II,OOO; £ 4:3,007

r,, E2,E3,E4 IN PSI

I 0.35

I I

0.40 0.45 0.50 POISSON'S RATIO, V3

Figure 9. Effect of Poisson's ratio, V4, on tensile strain at the bottom of the bitu­minous concrete for various combinations of moduli in a four-layer system where h1 = 2. 5-in. , h2 = 6-in. , h3 = 15-in. , h4 = semi-infinite, axle load = 18, 000 lb, tire pressure = 70 psi.

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~ ' z " I Q X ~ ..,

z ~ 0:: r-(/)

w _J

(/)

z w 1-

Figure 8. Effect of Poisson's ratio, V3, on tensile strain at the bottom of the bitu­minous concrete for various combinations of moduli in a four-layer system where h1 = 2. 5-in., h2 = 6-in., h3 = 15-in., h4 = semi-infinite, axle load = 18, 000 lb, tire pressure = 70 psi.

9

8 -Ei=IOO,OOOi E2=15,000i Ea=II,OOO; £4=3,000\

7 1-

6 1-

Ei=aoo,ooo; E2=1s,ooo; Ea= u,ooo: E4=3,ooo \

5 Ei=IOO,OOO; £2=25,000; Ea=II,OOO; £4=3,000_)

4 ~ Et=aoo,ooo; E2= 2s,ooo; Ea= n,ooo; E4=3,ooo _}

3 1-r, =aoo,ooo; E2=5o,ooo; Ea=n,ooo; r4=a,ooo \

2 1- Ei=IOO,OOO; E2=50,000; Ea=II,OOo; £4=3,~ _/

E1, E2,E3,E4 IN PSI

I 0.35

I

0.40 I

0.45 0.50 POISSON'S RATIO, V4

10

Et=IOO,OOO; E2=1~o000i E3=11,000; £4=3/lO;:J

9 ~

Et=300,000; E2=15,ooo; Ea= II,OOOi £4 =3,000\

Et=IOO,OOO; £2=25,000; Eg=II,000;£4 =3,0007 Et=300,000j E2=25,000i Ea=II,OOO; £4=3,000\ ~

Figure 10. Effect of Poisson's ratio, V1, on compressive strain at the bottom of the bituminous concrete for various combina­tions of moduli in a. four-layer system

8 -Et=too,ooo; Ez=so,ooo; Ea=u,ooo; E4=a,ooo7

Et=300,~; E.z=so,ooo; Ea = n,ooo; E4=a,ooo \ ~ ' ~

-.. 1 I Q

£ 1,£2 ,£3 ,£ 4 IN PSI X >

0)

~ t: <( 6

Et = IOO,OOOj E2=-l5,000i E3= 19,000i E4= 7,500 a: t-

Et = 300,000j E2= 15,000; Ea=l9,000i £4=7,500 t

(/)

w Et=too,ooo; Ez=25,ooo; E3=1o,ooo; E4=7,5oo\_ ?:

(/) 5 (/)

Et=3oo,ooo; E2=2s,ooo; Ea=te,ooo; E4==7,soo-...._ w a: Q_ :::; 0 EJ=IOO,OOOj E2=50,000i Ea=t9,000i £ 4 ::7,5007

~ , Et=aoo,ooo; Ez=so,ooo; Ea=ts,ooo; E4=7,soo-l

u4

Et=too,ooo; Ez=ts,ooo; Ea=27,ooo; E4=1s,oo~-\\ Et=3oo,ooo; E2=Js,ooo; Ea=27,ooo; E4=ts,ooo\'

' 3 Et=loo,ooo; Ez=25,ooo; Ea=27,ooo; E4= ts,ooCl7

J

Et:too,ooo;.Ez=_so,ooo; .Ea=~7,ooo: .E4= ts,oooj Et-300,000, E2~50,000, Ea-27,0~0, E4=15,000

2 0.35 0.40 0.45 0.50

POISSON'S RATIO, V1

Figure 11. Effect of Poisson 1 s ra.tio, V 2 , ~ on compressive strain a.t the bottom of the bituminous concrete for various combina­tions of moduli in a. four-la.yer system where h1 = 2. 5-in., h2 = 6-in., h3 = 15-in., h4 = semi-infinite, a.xle loa.d = 18, 000 lb, tire pressure = 70 psi.

where h1 = 2. 5-in., h2 = 6-in., h3 = 15-in., h4 =semi-infinite, a.xle loa.d = 18,000 lb, tire pressure = 70 psi.

I

10

9

z ' z 1 8 Q X >

0)

z <( 1 a: !n w ?: (/) (/) 6 w a: (1.

:::;

8 5

4

f.-

1-

f.-

1-

1-

3 0.35

Et=too,ooo; E2= ts,ooo; Ea=n,ooo; E4=a,ooo \_

Et =3oo,ooo; E2=1s,ooo; Ea=u,ooo; E4=3,ooo ~

E1=100,000; E2=25,000; E3=11,000; E4=3,000)

Et =3oo,ooo; E2=2s,ooo; £3 ;:: u,ooo; E4 ::: 3,ooo ......._

Et = too,ooo; E2=so.ooo: Ea::: u,ooo; E4:::3,ooo }

Et=3oo,ooo; E2:::so,ooo; Ea=n,ooo; E4=3,ooo"

Et, E2,E3,E4 IN PSI

I I

0.40 0.45 0.50 POISSON'S RATIO, V2

-17-

z ' z

I

10

9

.. 8 I Q X >

uJ

z ~ 7

t;; w ~

~ 6 w a: a. :::;:

8 5

4

1-

Ec=IOO,OOO; E2=1~,000; EJ=II,OOO; t 4 :,:J,OOO\

Ec=3oo,ooo; £2=15,000; E3=11,000; £4:3,000~

Ec= coo,ooo; E2=2s,ooo; Ea=n,ooo; E4=3,ooo Ec=JOO,OOO; E2=25,000; EJ=II,OOO; £ 4 =3,000\

F Ec =100,000; E2=50,000; EJ=II,Ooo; E4=J,O::J Ec =300,000; E2=S0,000; EJ=II,OOO; £4 =3,000 't

f-

f-

f-

1-

Ec~ E21 E3,E 4 IN PSI

I I l

Figure 12. Effect of Poisson's ratio, V3 ,

on compressive strain a.t the bottom of the bituminous concrete for various combina­tions of moduli in a. four-layer system where hl = 2. 5-in., h2 = 6-in., h3 = 15-in., h4 = semi-infinite, axle load = 18, 000 lb, tire pressure = 70 psi.

z ' z

> uJ

llr--------------------------,

10

9

z <i:7 a: 3

0.35 0.40 0.45 POISSON'S RATIO, V3

0.50 ' t;;

Figure 13. Effect of Poisson's ratio, V4, ~ on compressive strain a.t the bottom of the bituminous concrete for various combina­tions of moduli in a. four-layer system where h1 = 2. 5-in. , h2 = 6-in. , h3 = 15-in. , h4 = semi-infinite, axle load = 18, 000 lb, tire pressure = 70 psi.

-18-

w > Ul UlS w a: a. :::. 8

5

4

3L_ ______ ~------~------__J 0.35 0.40 0.45 0.50

POISSON'S RATIO, V4

Dormon and Edwards @ reported that Poisson's ratio for subgra.de soils and granular material lies in the range of 0.35 and 0.45. In this study, a value of 0.45 for subgrade soils and 0. 35 for base and subbase granular materials were chosen.

FATIGUE CRITEIDA FOR BITUMINOUS CONCRETE AND BLACK BASE

The literature on asphalt technology is filled with research evidence to show that bituminous concrete, when subjected to repeated or fluctuating stress, will fail under stresses lower than those that would cause failure under static conditions. This decrease in resistance is !mown as fatigue failure.

The fatigue criterion for bituminous concrete and black base is based on permissible strains which are a. function of the number of load repeti­tions and modulus values. Several direct laboratory test procedures exist for evaluating the permissible strain. These test procedures involve ap­plying a., repetitive load to a specimen, under controlled stress or strain conditions, until failure of the specimen occurs. With such test procedures, limiting horizontal tensile strains can be determined for the normal modu­lus range of a given bituminous mix.

The fatigue criteria used in this study are based on Santucci's @) re­sults. The fatigue curves shown in Santucci's report are based on data. derived from bituminous mixtures with air voids and bitumen contents by volume, of 5 and 11 percent, respectively. For Michigan's standard mix design, air wid and bitumen contents are 3and 13.8 percent, respectively, for bituminous concrete, and 6 and 10. 5 percent for black base. An equ­ation developed by Pell and cooper ~ and Epps @ was used to adapt Santucci's fatigue data to fatigue curves for Michigan's bituminous concrete and black base. This equation is:

(6)

where: Nc ~ corrected number of repetitions to failure, Nf ~ number of repetitions to failure at a. given strain level and

modulus from Santucci's fatigue curves.

(7)

and: V a ~ air void content in percent, Vb ~ bitumen content by volume in percent.

- 19-

1o,ooo c---------

i

' ~ •' ' ~ • ,;; w' >-w « u z 0 u 0 , 0 z ~ , !: m ~

~ « >-0

w J ;;; z w >-

1,000

100

E1 50,000 PSI, 100,000 ·~ 150,000---.: 300,000 ~ 600,000-.............. 900,000 ~

= 1,500,000---- --.::::::::::::::;:::::::==

AIR VOIDS VOLUME, Vv=3% ASPHALT VOLUME, V6 = 13_8,-0

Nc-NUMBER OF LOAD REPETITIONS TO FAILURE

Figure 14. Fatigue criteria. for a. Michigan bituminous mix.

IO,OOOc--------------------------------------------,

E2= 40,000 P~ = 75,000""\ = 100,000-= 150,000_... = 300,000-= 600,000-' = aoo,oooj =~500,000

AIR VOID VOLUME, Vv = 6'}'0

ASPHALT VOLUME, V8 = 10.5 '}'o

Nca- NUMBER OF LOAD REPETITIONS TO FAILURE

Figure 15. Fatigue criteria. for Michigan asphalt-treated black base.

-20-

Figures 14 and 15 represent the corrected fatigue curves for Michigan's bituminous concrete and black base, respectively, and may be used for Michigan's bituminous concrete and black base until actual fatigue proper­ties are established by direct laboratory tests. Table 2 summarizes the bituminous concrete fatigue data used to develop the thickness equivalency charts presented in this report.

TABLE 2 PERMISSIBLE TENSILE STRAINS (€t) AND COMPRESSIVE

STRAINS (€.v) FROM FIGURES 14 AND 16 FOR THREE DIFFERENT LOAD APPLICATIONS (Nc) AND VARIABLE E1

----------------------.--------------------------

Type of Strain

Pavement Thickness (hl) and Number of Load Applications (Nc)

h1 = 2. 5 in., ht = 2. 5 and 4. 5 in., h1 = 4. 5 in., Nc = 5 x 105 Nc = 1 X 106 NC = 2 X 106

{

E 1 = 50,000 psi E1 = 100, ooo psi

Tensile Strain f E 1 = 300,000 psi Et. x to-4 or E1 = 600,000 psi

E1 = 900,000 psi E

1 = 1, 000,000 psi

Compressive Strain, fv x to-4

5.77 4.64 5.10 4.15 4. 00 3.33 3.60 3.02 3.24 2.73 2.95 2.51

5.65 4.82

SUBGRADE STRAIN CRITERIA

3.75 3.38 2.77 2.53 2.30 2.13

4.12

The basic hypothesis rega.rding rutting of a pavement surface is that if the maximum compressive vertical strain at the top of the subgrade is less than a critical (permissible) value, then surface rutting will be within tol­erable limits for a specified number of 18-kip EAL applications. There­lationship between the number of load applications and permissible subgra.de compressive strain shown in Figure 16 was originally developed by Moni­smith and McLean @§_) and is in good agreement with other results (!£). Table 2 also summarizes the limiting vertical sub grade compressive strains used to develop the thickness equivalency charts presented in this report.

PROCEDURE USED FOR CONSTRUCTING TIDCKNESS EQUIVALENCY CHARTS

Step A - The CHEV 5L computer program was run with 720 different modulus and thickness data combinations to calculate tensile strains at the bottom of the bituminous concrete surface layer and compressive strains at the top of the subgrade for each of the two standard pavement designs shown inFigure 2. These pavements are assumed tohave layer properties as summarized in Table 1 and permissible tensile and compressive strains as listed in Table 2.

-21-

10,000~---

• ~-tii 1,000

~ ~ m • " u i; w >

Nv-NUt.!BER OF 18,000 LB. EAL APPLICATIONS

Figure 16. Sub grade strain criteria..

Step B - The results of the computer runs were summarized as strain­modulus curves which relate key permissible tensile and compressive strains to the full range of layer modulus values. Seventy-two sets of curves were drawn, two typical sets of which are presented in the Appendix; the others are available in the investigator's files. Of the 70 sets of curves, 31 sets showed the strain developed in the pavement system to be far below the permissible strains; these are being preserved for a. future study.

Step C - The permissible strain values presented in Table 2 are plotted on the strain-modulus curves (Appendix Figs. 1A and 2A are examples). The intersection of permissible strain with the desired base thickness, h2, willgivethe base modulus, E2, required to carry, without failure, the num­ber of 18-kip EAL indicated. As an example, Appendix Figure 1A shows that, for the pavement and loading system in the figure, a. 6-in. base would need to have a. modulus E 2 of 21,600 psi for 500,000 load repetitions or 26,000 psi for 1, 000,000 load repetitions to enable it to carry the loading shown without failure.

Step D- The base modulus E2 for each corresponding h2 obtained from the strain-modulus curves are replotted (Figs. 17 through 28) with the base modulus, E2, as the ordinate and the base thickness, h2 , as the abscissa. for each bituminous concrete modulus listed in Table 2 and for each of the two standard pavement cross-sections shown in Figure 2. The curves in Figures 17 through 28, also identified as the thickness equivalency curves, define the relationship between E2 and h2 necessary to obtain optimum pavement performance.

-22-

j Figure 17. Thickness equivalency chart, ~loading= 500,000, 18 kipEAL repetitions.

0:

"' > < -'

"' !:! "' "-0

Ul :> -' :> c 0

"

4,500 LB ---j .4,500 LB

lia ~II V1 = 0.50-0.40, E1=VAR.

V2 = 0.35, E2 = VAR.

V3= 0.35 E3= 11,000 PSI

v4 = o.45 E4= 3,000 PSI

VAR.

15"

I04!----_l------o-----L------' 0 3 6 9 12

THICKNESS OF BASE LAVER 1 hz, INCHES

Figure 18. Thickness equivalency chart, loading= 500,000, 18 kipEAL repetitions.

2 X 105',---------------------,

0:

"' li -'

"' !:! "' "-0

Ul

3 :> c 0

"

4,500 LB~ wr4,500 LB

v1 = 0.50-0.40, E1 ;:;VAR.

V2 = 0.35, E2 = VAR.

V3= 0.35 E3= 271 000 PSI

V4 :;::; 0.45 E4 = 15,000 PSI

E1 = 100,000 e, = so,ooo

e1 = 3oo,ooo e, = &oo,ooo

2.5"

VAR.

THICKNESS OF BASE LAVER, h2 1 1NCHES

Figure 20. Thickness equivalency chart, tt._ loading=1,000,000,18kipEAL repetitions.,

2 X 105 4,500 LB

2.5·

V2 = 0.35, Ez = VAR. VAR.

;;; 105 .. V3= 0.35 15"

N E3= 19,000 PSI

"' a:' v4 = o.45 = "' ~ ~= 7,500 PSI

-'

"' e1 = so,ooo Ul < e,= 100,000

"' e,= 300,000 "-0 e1 = eoo,ooo Ul :> -' :> c 0

"

lo4L ____ L_ ____ J_ ____ L_ ___ --o-' 0 3 6 9 12

THICKNESS OF BASE LAVER 1 hz ,INCHES

Figure 19. Thickness equivalency chart, loading= 500,000, 18 kipEAL repetitions.

N

"' 0:

~ -'

"' !:! "' "­c Ul

3 :> c 0

"

4,500 LB 4,500 LB

V1 = 0.50-0.40, E1 =VAR.

Vz = 0.35, E2 = VAR.

V3= 0.35 E3= 11 1 000 PSI

v4 = o.45 E4= 3,000 PSI

2.5"

VAR.

15"

104~-----o--------!,-----o--------;c 0 3 6 9 12

THICKNESS OF BASE LAYER, h 2 1 INCHES

-23-

Vz;:;. 0.35, Ez:;;: VAR. VAR.

N w

0: w ~ -' w

"' a\ "-0

"' 3 :>

8 "

v3;:;. 0.35 E3-::: 19,000 PSI

E1;:;. 600,000 Et;:;. 900,000

15"

104~------~--------~------~L-------~ 0 3 6 9 12

THICKNESS OF BASE LAYER, hz 1 INCHES

Figure 22. Thickness equivalency chart, loa.ding=l, 000,000, 18kipEAL repetitions.

2 X 105

;;; lo" .. ru

w

0: w ~ -' w ~ ID

i!;

"" 3 :> Q 0

"

-

-4,500 LB~ t-4,500 LB

Vt - 0.50-0.40, E1 ;:;.VAR. 4.5"

Vz;:;. 0.35, Ez;:;. VAR. VAR.

y3;:;. 0.35 25" E3= 16,000 PSI

v4;:;. 0.45 = ~;:;. 3,000 PSI

-E1 = 50,000 ;!_} E1:::: 100,000 E1;:;. 300,000\

3 6 9 THICKNESS OF BASE LAYER 1 h2 1 INCHES

Figure 24. Thickness equivalency chart, loading=l, 000,000, 18kipEAL repetitions.

12

0: w ~ -' w

"' < ID

i!;

"' 3 :> Q 0

"

f-

r

4pOOLB~-til~4,500 LB

V1 ;:;. 0.50- 0.40, E1;:;. VAR.

Vz:;;: 0.35, E2 ;:;. VAR.

V3;:;. 0.35 E3;:;. 27,000 PSI

v4 ;:;. 0.45 ~;:;. 15,000 PSI

II£1;:;. 100,000 E1;;: 300,000

E1;:;. 50,000 __j e 1 ~ 60o,ooo\

E,=902-:

3 6 9 THICKNESS OF BASE LAYER, hz 1 INCHES

2.5·

VAR.

15"

=

12

.4 Figure 23. Thickness equivalency chart, ~ loading=l,OOO,OOO, 18kipEAL repetitions.

2 X 10

u; 10 .. N

w

0: w s w

"' < ID

"-0

"' 3 :> Q 0

"

5

5

4 10 0

4,500 LB-j t-4,500 LB

Ill V1;:;. 0.50 0.401 E1 ;:;.VAR. 4.5·

Vz;:;. 0.35, E2 ;:;. VAR. VAR.

v3;:;. 0.35 25' E3;:;. 24,000 PSI

v4 ;:;. o.45 = E4;:;. 7,500 PSI

/;~1 ;:;. 50,000 E1;:;. 100,000

I

Et ~ 3001000\

~ 3 6 9 12

THICKNESS OF BASE LAYER, h2 ,INCHES

-24-

2XI05.------------------------------------, 4,500 LB -i f-4,500 LB

~"g 11'11 4.5"

V2 = 0.35, E2 = VAR. VAR.

~ 105 ~-----------------+ o.. V3= 0.35

N w

E3= 30,000 PSi

v4 = o.45 E4::; 15,000 PSI

I I

E1= 50,000 E1= 100,000 E1 = 300,000

I04!----------'c--------_,_ ________ ,_ ______ -;; 0 3 6 9 12

THICKNESS OF BASE LAYER, h 21 1NCHES

Figure 26. Thiclmess equivalency chart, loading=2, 000,000, 18 kipEALrepetitions.

2 x 1o5·~-------------------------------------,

- 105

"' .. N

w a.' w ~ .J

w "' < "' u. 0

"' 3 :> 0 0 :>

4,500 LB --j t-4,500 LB

~~ 1'10 V1 = 0.50-0.40, E1 =VAR. 4.5"

V2 = 0.35, E2 = VAR. VAR.

V3= 0.35 E3 = 24,000 PSI 25 11

v4 = o.45 ~ E4::; 7, 500 PSI

~

E1=so,ooo,V E1 = 100,000

E1 = 300,000_/

104!-------_,_ '-------!:--'-------!--------;: 0 3 6 9 12

THICKNESS OF BASE LAYER, h2 1 INCHES

Figure 28. Thiclmess equivalency chart, loading=2,000,000, 18 kipEALrepetitions.

,.&i Figure 25. Thiclmess equivalency chart, ~ loading=1,000,000, 18kipEAL repetitions.

2 X lo5

Ui 105 .. WN

a.'

~ w

"' ~ i';

"' :> .J

~~ 4

4,500 LB ~U .t-4,500 LB

V1 =0.50-0.40,E!=VAR. 4.5"

V2 = 0.35, E2 = VAR. VAR.

V3= o.35 25' E3= 16,000 PSI

v4 = 0.45 ~

E1 = 50,000 E4 = 3,000 PSI

E1 = 100,000~

.~ E1= 300,000

3 6 9 12

THICKNESS OF BASE LAYER 1 h2 ,INCHES

~ Figure 27. Thiclmess equivalency chart, ., loading=2,000,000, 18 kipEALrepetitions.

~

2XI~.---------------------------------,

N w

a. w ~ .J w

"' ~ u. 0

"' 3 :> 0 0

"

4,500 LB 4,500 LB

V3= 0.35 E3= 30,000 PSI

v4= o.45 E4 = 15,000 PSI

E1 = 100,000

E1 = .50,000

E1 = 300,000

VAR.

2511

-25-

INTERPRETING THE TIDCKNESS EQUIVALENCY CHARTS

The steep curves seen in Figures 17 and 20 indicate that base thickness equivalency is dependent on the subgrade compressive strain, i.e., base thickness is needed to prevent or minimize pavement surface rutting. The flat curves seen in Figures 19, 22, 23, 24, 25, 27, and 28 indicate that base thickness equivalency is dependent on the asphaltic tensile strain, i.e. , base thickness is needed to prevent or minimize pavement surface cracking. Other figures having a combination of steep and flat curves in­dicate that both compressive and tensile strains influence pavement per­formance.

As a specific example: Figures 19, and 22 to 28 indicate that when the pavement's subgrade modulus is over 15, 000 psi or the bituminous concrete thickness is over 4. 5 in., tensile strain controls, i.e., failure would be in the form of fatigue cracking. For the pavement systems in this study, a 3-in. granular base is adequate and a black base is not needed. Increas­ing base thickness over 3 in. has virtually no effect on improving perfor­mance. However, when the subgrade modulus value is less than15, 000 psi, increasing the base thickness to over 3 in. may be necessary to prevent subgrade failure. When the required base thickness is greater than 3 in., black bases may have economic benefits. In Michigan, where firm sub­grades predominate, pavement analysis using the procedures described here is necessary to determine where the use of black bases would result in improved performance.

Application of Thickness Equivalency Charts

The thickness equivalency curves (Figs. 17 through 28) developed in this study make possible the design of base layer thickness for any material whose modulus, E2, is known or can be reasonably estimated. The thick­ness equivalency curves can also be used to determine the thickness of asphalt-treated black base needed to replace standard thicknesses of granu­lar base material. A sample application is given below.

A standard Michigan flexible pavement consists of a 2. 5-in. bituminous concrete surface and a 15-in. subbase. If this pavement is constructed on a sandy subgrade, and is to be designed to carry a traffic loading of one million (1 x 106) 18-kip EAL applications over the life of the pavement, what is the required granular base thickness? Assume, on the basis of Figure 3, the bituminous concrete modulus to be 300, 000 psi for 72 F design temperature and the subgra.de modulus to be 7, 500 psi. If asphalt-treated black base is to be used in place of standard granular base, what is its re­quired thickness? Assume the elastic modulus of black base to be 100, 000 psi at 72 F design temperature.

-26-

The solution to the first part of the problem is a.s follows:

Step A - Dividing the subbase into subla.yers and using Eq. (2) or Fig­ure 5, the average subbase modulus, E3, is 19, 000 psi when the subgra.de modulus, E4, is 7, 500 psi.

Step B - Select the thickness of the base layer from Figure 21 using the curve for E1 ~ 300, 000 psi. If h2 ~ 4 in. is selected, a. stiffness E 2 of 49, 000 psi is required.

Step C - Using Figure 4, with E3 ~ 19,000 psi, E2 can only reach 36,500 psi which is well below the required 49,000 psi forh2 ~ 4 in. Thus, an h2 of 4 in. will not be thick enough to carry the one million 18-kip axle load. Try h2 ~ 4.4 in. and use Figure 21 again; now the required E 2, from Figure 21, is 36,500 psi. Going back to Figure 4, still using E3 ~ 19,000 psi but with h2 ~ 4. 4 in., Ez ~ 36,500 psi, meeting the required modulus value. Therefore, h2 ~ 4. 4 in. is an adequate thickness of granular base for this pavement system. The granular base thickness of 4. 4 in. in this example is controlled by subgra.de compressive strain, i.e., pavement surface rutting.

The solution to the second part of the problem is obtained by following the concepts described in the section on "Asphalt-Treated Material (Black Base)."

Step D -Assume the black base will not crack. Then, from Figure 21, with black base modulus = 100,000 psi, a 3. 3-in. black base is adequate. However, the horizontal tensile strain, Em at the bottom of a 3. 3-in. black base layer with the given loading and pavement conditions, is computed by CHEV 5L to be 3. 97 x 10-4 in. /in.

From Figure 15 (black base fatigue curves), for etB = 3. 97 x 10-4 in. I in., the number of load repetitions, NcB, to failure is 1. 5 x 10

5. This

means that 150, 000 repetitions of 18-kip EAL will crack the black base. Also, at the end of 150,000 load repetitions, a. cumulative damage, DF, to the top of the subgra.de is

DF = 1.5 x6105 = 0.15, 10

on the basis of Miner's hypothesis of damage fatigue.

Once the black base has cracked, it is necessary to determine how many more load repetitions will be needed to either crack the bituminous concrete surface or fail the subgra.de.

-27-

Step E - Determine the black base cracked section modulus, E2c, from laboratory tests. In this example, the cracked section modulus is assumed to be 60,000 psi. The maximum compressive strain, E.v, a.t the top of the subgra.de is then computed by CHEV 5L a.s 5. 05 x 1o-4 in. /in.

From Figure 16, for E.v ~ 5. 05 x lo-4 in. /in. Nv is 8. 2 x 105 repeti­tions. However, the cumulative da.ma.ge to the subgra.de is DF ~ 0.15 or 1. 5 x 105 repetitions. Thus, the a.ctua.lloa.d repetitions the pavement can withstand after the black ba.se cracks is 820,000 x (1 - DF) ~ 697,000.

The total of load repetitions to failure for this pavement system is the sum of the load repetitions before and after cracking of black base, i.e., 1.5 x 105 + 6.97 x 105 ~ 8.47 x 105, failure occurring before the design load of one million (106) repetitions is reached. Therefore, a. thicker black base is needed.

Step F - Following the procedure outlined above a.nd increasing a. black base thickness to 3. 8 in. the following results are obtained:

E.tB ~ 3. 75 x 104 in. /in. . 5

NcB ~ 1.8 X 10

DF ~ 0.18

E.v ~ 4. 81 x 1o-4 in./in.

Nv ~ 106

106 loa.d repetitions are needed to cause subgra.de failure. Therefore, a. 3. 8-in. black ba.se is equivalent to a. 4. 4-in. unbound granular base.

Step G - A check of tensile cracking of the bituminous concrete layer is not necessary since, with the subgra.de modulus less than 15, 000 psi and the bituminous concrete thickness less than 4. 5 in., the pavement system is controlled by compressive strain, according to the criteria. on page 20. However, it is interesting to note how many load repetitions a.re needed to crack the bituminous concrete after the 3. 8-in. black ba.se cracks. The maximum tensile strain, E.t, a.t the bottom of the bituminous concrete is computed to be 2.43 x l0-4 in. /in. From Figure 14, for E1 ~ 300, 000 psi, N c is 3. 2 x 1 o6. Thus, the total number of loa.d repetitions needed to crack the bituminous concrete surface layer is 3. 2 x 106 + 1. 5 x 105 ~ 3. 35 x 106, which is considerably more than the repetitions of traffic loa.d needed to cause rutting failure.

One other method of increasing pavement life without increasing black base thickness is to improve black ba.se quality, i.e., to increase the as­phalt content and reduce the air void volume in the black ba.se so tha.t it will

- 28-

sustain a. greater number of loa.d repetitions without failing. The limits will need to be determined by laboratory and field testing.

PAVEMENT DESIGN ALTERNATIVES, SAMPLE APPLICATION

The method presented can a.lso be applied to the design of flexible pave­ments where a. portion of granular ba.se is replaced by black ba.se such that no loss in predicted performance occurs. The basic model becomes a. five­layer system instead of a. four-layer system. The pavement system and materia.! properties presented in this sample problem a.re similar to the previous problem except that subgra.de moduli of 3, 000 psi a.nd 7, 500 psi a.re used.

As in the previous problem, the maximum tensile strains at the bottom of the black ba.se and compressive strains at the top of the subgrade were calculated using the CHEV 5L computer program. From these strain data., Figures 29 through 32 were developed to show the relationship between granular ba.se and black ba.se thickness for a. given tensile or compressive strain. Note tha.t the compressive strains a.re computed in the first sample problem a.nd the information provided by Figures 29 through 32. The thick­ness relationship between granular ba.se and black ba.se wa.s developed and is summarized in Figure 33 (solid line). The dashed lines, also shown in Figure 33, are results obtained by assuming that the black ba.se will not cra.ck before failure by surface rutting.

The four hypothetical design alternatives summarized in Tables 3 and 4 show tha.t there is little reduction in total ba.se thickness a.s black ba.se is used to replace gra.nula.r base. For example, Table 3 shows that 3 in. of black ba.se replaces 3. 3 in. of gra.nula.r ba.se, and 5 in. of black ba.se re­places 5. 6 in. of granular ba.se. The 11.8 in. gra.nula.r ba.se can be re­placed by 9. 8 in. of black ba.se. For subgra.de modulus, E 5 = 7, 500 psi in Table 4, the equivalency of 3. 8 in. of black ba.seto 4.4 in. of granular ba.se has the sa.me solution a.s was illustrated in the previous example. Figure 33 ca.n be used to determine any combination of granular ba.se and black base thickness when the design load is one million 18-kip EAL and the pave­ment cross-section and material properties a.re a.s shown in the figure.

Development of a. series of figures similar to Figure 33 for pavement cross-sections normally encountered in Michigan is suggested. They should cover the full range of bituminous concrete and subgra.de moduli, layer thickness, and design range of 18-kip EAL repetitions normally considered for Michigan pavements.

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•.---------------------------.

7

2

4,!100 LB ~ t-4,~00 LS

~ u V1=0.S, E,-300,000 PSI 2.5"

Vz 0.5, Ez 100,000 PSI hz

VJ-0.35, E3- VAR. h3

V4= 0.35, E4= 11,000 15"

V!>-0.45, E.!i-3,000 PSI

12 ~~~--~2--~3~-4~~5--~6~~7~-L.--~.--~IOL--L--"_

THICKNESS OF BLACK BASE , hz IN.

Figure 30. ·Compressive strain at the top of the subgrade as a function of black base thickness, h2, and granular base thickness, h3.

7,------------------------------,

6

~ ' :?: 5

1 Q h3 =0" X

J hl=2"

:i4

~ t; w ~ 3 ~ z w r ~ s 2 x ~

4.!i00 LB ----i r-4/!>00LI:I

V,=O.S, E,=JOO,OOOPSI 2.5"

Vz=O.S, Ez=IOO,OOO PSI hz

VJ=0.35, E3=VAR, h3

Ys=0.45, Es=7,500 PSI

0o~-+--~2~~3~-4~~5---6~~7--~.--~,~~1Lo__j· THICKNESS OF BLACK BASE , h2 IN

Figure 32. Compressive strain at the top of the subgrade as a function of black base thickness, h2, and granular base thickness, h3.

~

~

~

Figure 29. Tensile strain at the bottom of black base as a function of black base thickness, h2 , and granular base thick­ness, h3•

14r-----------------------------------,

12

~ ' ~ -110 X > w

z < 8 ~ r • w > ~

6 • w ~

" , 0 u , 4 ~ , x < ~

2

01

4.!100 Lll.-i r-4.!i00 Lfl

UIJUIJ

Vo-0.5, E1-300,000PSI 2.5"

Vz-0.35, Ez-60,000PSI hz

V3 0.35, EJ- VAR. h3

V4=0.JS, E4=11,000 PSI 1.5"

Y!!>=0.45, E5= 3,000 PSI

2 3 4 5 6 7 8 9 10 II 12 THICKNESS OF BLACK BASE , hz IN.

Figure 31. Tensile strain at the bottom of black base as a function of black base thickness, h , and granular base thick­ness, h .

•r------------------------------,

7

~ ' ~ 1 6

Q X >

w

'ts < ~

t; w > ~ 4 ~ w ~

" ~ 8 ~ 3 ~ , x < ,

2

I I

4500 LB -i r-4$00LB

1111 IIIII

V1-0.S,E1 300,000PSI 2.5"

Vz=0.35, Ez=60,000 PSI hz

V3=0.JS, £.3-VAR. h3

V4='0.JS, E4= 19,000PSI 15"

V.s=0.45, E$-7,500 PSI

2 3 4 5 6 7 8 9 ~

THICKNESS OF BLACK BASE , h2 IN. 12

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12

II 4,500 LB -i r- 4,500 LB

Wm UIID

10 V1 = 0.5

1 E 1 = 300,000 PSI 2.5

11

E2 = 60,000 PSI

z Es = 3,000 PSI V2 = 0.5, E2 = 100,000 PSI hz

' 9

E2 = 100,000 PSI V2 = 0.35, E2 = 60,000 PSI

N .s::. Es = 3,000 PSI

' 8 V3 = 0.35, E3 = VAR h3

w Ill <( m :ls::: u <(

. ...I m 1.1.. 0

Ill Ill w z :ls::: u I 1-

E4 = 19,000 PSI 15"

v4 = 0.35, E4 = ll,ooo PSI 7

V _ 0 5 E5 = 7,500 PSI 5 - .4. ' E5 = 3,000

00

6 PSI

5 E2 = 60,000 PSI Es= 7,500 PSI

E2 = 100,000 PSI

3 Es = 7, 500 PSI

2

OL-__ L_ __ L_ __ ~--~L_~ __ _L __ _L __ _L __ _L __ ~--~--~

0 2 3 4 5 6 7 8 9 10 II

THICKNESS OF GRANULAR BASE, h3,1N.

Figure 33. Design alternative curves for combination of black base, h2, and granular base, h3.

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12

TABLE 3 DATA ILLUSTRATING USE OF DESIGN ALTERNATIVE CHART

(FIG. 33) FOR E 5 = 3, 000 psi, 18-kip EAL = 106

TABLE 4 DATA ILLUSTRATING USE OF DESIGN ALTERNATIVE CHART

(FIG. 33) FOR E 5 = 7, 500 psi, 18-kip EAL = 106

Material Design Alternatives

1 2 3 4

Thickness of bituminous concrete, in. 2.5 2.5 2.5 2.5 Thickness of black base, in. 1.0 2.1 3.8 Thickness of granular base, in. 4.4 3.4 2.1 Thickness of granular subbase, in. 15.0 15.0 15.0 15.0

Total Thickness, in. 21.9 21.9 21.7 21.3

- 32 -

i"

SUMMARY AND CONCLUSIONS

Summary

1) The elastic layer theory and two limiting strains, the horizontal tensile strain at the bottom of any asphaltic layer and the vertical compres­sive strain at the top of the subgrade, are used to establish 'thickness equi v­alency' charts and 'design alternatives.' Chevron's CHEV 5L computer program was used to calculate the critical strains.

2) Determination of a.ppropriate modulus values for bituminous con­crete and subgrade soils is discussed. Asphalt-treated black base and bitu­minous concrete are considered to have similar stiffness, although different fatigue properties. The modulus of base or subbase materials is deter­mined from subgrade modulus by means of stress-dependent principles first reported by Izatt, Lettier, and Taylor @).

3) Santucci @) established the fatigue characteristics of bituminous concrete, of a. given mix design, on the basis of controlled stress labora­tory tests. Santucci's fatigue data were modified to make them compatible with Michigan's mix designs, adapting the equations developed by Pell and Cooper @!) and Epps @).

4) The subgra.de compressive strain criterion (Fig. 15) origina.lly de­veloped by Monismith and McLean @)was chosen for this study, because it demonstrated good agreement with other results.

5) The thickness equivalency charts were developed on the basis of a. design load carrying ca.pa.cityof 5 x 105, 1 x 106, and 2 x 106 18-kip EAL.

6) Design alternative curves were also developed to illustrate the thickness interchanges possible between granular ba.se and black base for equivalent pavement performance.

7) The design a.lternati ve curves shown in Figure 33 are based on a. assumption of a. 60, 000 psi black base cracked section modulus. A limited number of black base samples could be tested in the laboratory to verify this value.

Conclusions

The following conclusions are restricted to the loading and the range of cross-sections, moduli, load repetitions and other materials charac­teristics assumed in this study. The effects of environmental factors such as frost heave, thermal cracking, etc. , are not taken into account.

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1) Thickness equivalency charts, Figures 17 through 28, developed in this study for two standard Michigan flexible pavement sections, can be used for thickness design of the base layer.

2) From the thickness equivalency charts developed in this study, it can be inferred that a. black base is not needed for the pavement sections where the subgra.de modulus is over 15, 000 psi or the bituminous concrete thickness is over 4. 5 in. and that a. granular base thickness of more than 3 in. will not significantly improve pavement performance.

3) The thickness equivalency charts presented, Figures 17 through 28, indicate that the base thickness used for Michigan standard designs are much thicker than needed for pavements expected to carry two million (2 x 106) 18-kip equivalent axle loads or less.

4) The principles used to develop the thickness equivalency charts can also be used to develop alternative design charts for determining the thick­ness relationship between granular base and black base for equivalent pave­ment performance. Any combina.tionof gra.nula.rba.seand black base thick­nesses can be selected from such design alternative charts.

5) For Michigan standard pavement sections, if the analysis shows that a. given black base has little or no thickness advantage over granular bases, it is possible to make an 'equivalent' but thinner black base by in­creasing the asphalt content and reducing the air void volume.

6) This study has yielded considerable groundwork which is readily applicable to future investigations in the design and performance of black base for pavement sections in which the subgra.de is weak, or in which the subbase layer is omitted.

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REFERENCES

1. AlNouri, I., "Effect of Temperature on the Elastic Response of Asphalt Treated Base Material, " Michigan Department of State Highways and Transportation, Research Report No. R-816, 1972.

2. Hsia, F. T., "Thickness Equivalencies for Asphalt-Treated and Un­treated Aggregate Base Course Layers, " Michigan Department of State Highways and Transportation, Research Report No. R-1025, Novem­ber 1976.

3. Kingham, R. I., "Failure Criteria. Developed from AASHO Road Test Da.ta.," Proceedings, Third International Conference on the Structural Design of Asphalt Pavements, 1972.

4. Hicks, R. G. and Finn, F. N., "Prediction of Pavement Performance from Calculated Stresses and Strains at the San Diego Test Road," Proceedings, Association of Asphalt Paving Technologists, 197 4.

5. Dormon, G. M. and Metcalf, C. T., "Design Curves for Flexible Pavements B a. sed on Layered System Theory, " Highway Research Board, Record No. 71, 1964.

6. Michelow, J. , "Analysis of Stresses and Displacements in an n-Layered Elastic System Under a. Load Uniformly Distributed on a. Circular Area," California Research Corporation, Richmond, California, 1963.

7. DeJong, D. L., Pentz, M. G. F., and Korswa.gen, A. R., "External Report Computer Program BISAR Layered System Under Normal and Tangential Surface Loads," Shell Research B. V., 1973.

8. Van der Poel, c., "A General System Describing the Viscoelastic Properties of Bitumens and Its Relation to Routine Test Data," Journal of Applied Chemistry, Vol. 4, 1954.

9. Heukelom, W. and Klomp, A. J. G., "Road Design and Dynamic Load­ing, " Proceedings, Association of Asphalt Paving Technologists, Vol. 33, 1964.

10. Novak, E. c., ''Procedures for Evaluation of the Overload Capacity of Flexible Pavements," Michigan Department of Transportation, Re­search Report in preparation.

- 35 -

11. Claassen, A. I. M., Edwards, J. M., Sommer, P., and Uge, P., "Asphalt Pavement Design, the Shell Method," Proceedings, Fourth International Conference Structural Design of Asphalt Pavements, Uni­varsity of Michigan, 1977.

12. Izatt, J. 0., Lettier, J. A., and Taylor, c. A., "The Shell Group Methods for Thickness Design of Asphalt Pavements," Paper presented at the Annual Meeting of the National Asphalt Paving Association, San Juan, Puerto Rico, January 1967.

13. Barker, w. R., Brabston, w. N., and Chou, Y. T., "AGeneralSy­stem for the Structural Design of Flexible Pavements," Proceedings, Fourth International Conference Structural Design of Asphalt Pave­ments, University of Michigan, 1977.

14. Klomp, A. J. G. and Dormon, G. M., "Stress Distribution and Dyna­mic Testing in Relation to Roa.d Design, " Proceedings of the Second Conference of the Australian Road Research Board, Melbourne, 1964.

15. Lettier, J. A. and Metcalf, c. T., "Application of Design Calculations to 'Black B as e 1 Pavements, " Proceedings, Association of Asphalt Paving Technologists, Vol. 33, 1964.

16. Hills, J. F. and Heukelom, w., ''The Modulus and Poisson's Ratio of Asphalt Mixes," Journal of the Institute of Petroleum, Vol. 55, Janu­ary 1969.

17. Jones, M. P. and Witczak, M. W., "Subgra.de Modulus on the San DiegoTest Road," TransportationResearch Board, Record 641, 1977.

18. Irwin, L. H., "Determination of Pavement Layer Moduli from Surface Deflection Data for Pavement Performance Evaluation, " Fourth Inter­national Conference on Structural Design of Asphalt Pavements, Uni­versity of Michigan, 1977.

19. Ullidtz, P., "Overlay and Stage by Stage Design," Fourth International Conference on Structural Design of Asphalt Pavements, University of Michigan, 1977.

20. Heukelom, W. and Klomp, A. J. G., "Dynamic Testing as a Means of Controlling Pavements During and After Construction," Proceedings, First International Conference on Structural Design of Asphalt Pave­ments, University of Michigan, 1962.

- 36-

21. Kingham, R. I. and Kallas, B. F., "Laboratory Fa.tigne and Its Re­lationship to Pavement Performance," The Asphalt Institute, Research Report 72-3, 1972.

22. Santucci, L. E., "Thickness Design Procedure for Asphalt and Emul­sified Asphalt Mixes," Proceedings, Fourth International Conference on Structural Design of Asphalt Pavements, University of Michigan, 1977.

23. Dorman, G. M. and Edwards, J. M., "Developments in the Applica­tion in Practice of a Fundamental Procedure for the Design of Flexible Pavements," Proceedings, Second International Conference on Struc­tural Design of Asphalt Pavements, University of Michigan, 1968.

24. Pell, P. S. and Cooper, K. E., "The Effect of Testing and Mix Vari­ables on the Fatigue Performance of Bituminous Materials, '' Proceed­ings, Association of Asphalt Paving Technologists, Vol. 44, 1975.

25. Epps, J. A., ''Influence of Mixture variables on the Flexural Fa.tigne and Tensile Properties of Asphalt Concrete," Ph. D. Dissertation, University of California., 1968.

26. Monismith, c. L. and McLean, D. B., ''Design Considerations for Asphalt Pavements," University of California., Report No. TE-71-8, 1972.

- 37-

APPENDIX

- 39-

' i:

7r------rr---------------~-----------------------------,

~

"' £4 < a: Iii ~ 3 iii G'i >­:::; ::> 2 ;;;;; X <( :::;

h2 = 3" 4,500 LBS i I 4,500 LBS

li!!J® V1 = 0.50, E1 = 50,000 PSI 2.5"

V2 = 0.35, E2 = VAR. VAR.

v3 = o.3s IS" E3 = 11,000 PSI

v. = 0.45 E4 = 3,000 PSI

FOR 1'.1 = 5.77 X 10-4 l Nc= 5 X 105 )

h2 = 3", E2 = 2.37 X 10 4 PSI h2 = 611

, E2 = 2.16 X 104 PSI h2 = 9", E2 = 2. 16 X 104 PSI h2 = 12", E2 = 2.17 X 104 PSI

FOR l'.t = 4.64 X 10-4 ( Nc = 106 )

h2 = 3", E2 = 2.85 X 104 PSI h2 = 6"

1 E2 = 2.60 X 104 PSI

h2 = 9", E2 = 2.60 X 104 PSI h2 = 12'; E2 = 2.65 X 104 PSI

~~0~.--~----~----~---L--L--L~~-LIJO~.--~~---L-----L--~---L~--L-~~106 MODULUS OF BASE LAYER, E2 , PSI

Figure lA. Tensile strain at the bottom of bituminous concrete as a function of E 2 and h2.

0~------~-----L--~~--L-~~~--------L---~--~--~-L-L~~

~ I~ I~ MODULUS OF BASE LAYER, E2 ,PSI

Figure 2A. Compressive strain at the top of the subgrade as a function of E2 and h2.

-41-