Missouri University of Science and Technology Missouri University of Science and Technology

Scholars' Mine Scholars' Mine

Civil, Architectural and Environmental Engineering Faculty Research & Creative Works

Civil, Architectural and Environmental Engineering

01 Jan 1994

Determination of AASHTO Layer Coefficients for Granular Determination of AASHTO Layer Coefficients for Granular

Materials by Use of Resilient Modulus Materials by Use of Resilient Modulus

David Newton Richardson Missouri University of Science and Technology, richardd@mst.edu

Follow this and additional works at: https://scholarsmine.mst.edu/civarc_enveng_facwork

Part of the Civil Engineering Commons

Recommended Citation Recommended Citation D. N. Richardson, "Determination of AASHTO Layer Coefficients for Granular Materials by Use of Resilient Modulus," Proceedings of the 37th Annual Asphalt Conference (1994, Rolla, MO), University of Missouri--Rolla, Jan 1994.

This Article - Conference proceedings is brought to you for free and open access by Scholars' Mine. It has been accepted for inclusion in Civil, Architectural and Environmental Engineering Faculty Research & Creative Works by an authorized administrator of Scholars' Mine. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact scholarsmine@mst.edu.

DETERMINATION OF AASHTO LAYER COEFFICIENTS for

GRANULAR MATERIALS

Presented at the 37th Annual UMR Asphalt Conference November 9-10, 1994

University of Missouri-Rolla

David Richardson, PE Area Coordinator for Construction Materials,

Construction Engineering, and Transportation

DETERMINATION OF AASHTO LAYER COEFFICIENTS FOR GRANULAR MATERIALS BY USE OF RESILIENT MODULUS

INTRODUCTION The layer coefficients a2 or a3 for an unbound granular base or subbase material

are found from a relationship with resilient modulus, Eb. The resilient modulus for a

given material can be found by test using the "theta model" or by use of an estimation

regression equation. Eb is a function of several factors, as discussed below.

FACTORS AFFECTING RESILIENT MODULUS The factors that most significantly affect unbound granular base resilient modulus

are stress state, relative density, degree of saturation, gradation, and particle shape. Of

these variables, stress state is the dominant factor in material stiffness (modulus). The

higher the confining pressure, the higher the modulus. The significance of the other

parameters seems less well defined. Higher relative density, or compactive effort,

increases modulus, but to varying degrees (1-5). The significance may be influenced by

gradation. A higher degree of saturation has been shown to significantly decrease

modulus (1-9). For some aggregates, this effect is of a minor significance (1, 8). It

appears that as fines content increases, resilient modulus decreases (2, 3, 10, 11).

Perhaps with higher fines content, the influence of a high degree of saturation is more

pronounced, possibly due to the generation of pore pressures (2). Thus there may be

an interaction between amount and moisture content of fines. This may be the reason

that several studies have shown that open-graded mixtures have higher modulus values

than their dense-graded counterparts. However, several studies have shown the

reverse (2, 12), or at least that gradation is of negligible significance (7), and others

have shown that there is an optimum fines content for maximum modulus (5, 10). In

regard to particle shape/texture, a more angular/rough aggregate generally exhibits a

higher modulus (3, 12), although in some cases the reverse seems to be true (12, 13).

The effect has been shown to be of variable significance (2), of minor significance (3,

12) and of major significance (3). Thus the influence and significance of particle shape

is not well-defined.

Eb FROM THETA MODEL

It has been shown that the resilient modulus of a granular material is a function of

stress-state:

k2b 1E k= θ (1)

where

θ = bulk stress

= σ1 + σ2 + σ3

= σx + σy + σz + geostatic stresses

σ1 = σz + γ1z1 + γ2z2 in pavement under centerline of load

(σ1 is vertical total major principal stress; γ1 and γ2 are unit weights of each

overlying material; z’s are thicknesses of each layer overlying the point of

stress computation; γnzn = geostatic stresses)

σz = normal stress in vertical direction from wheel load as computed by elastic

layer analysis

= σd + σc in triaxial cell test (σd = deviator stress; σc = confining pressure)

σ2 = intermediate principal stress in y-horizontal direction

= σy + k0 (γ1z1 + γ2z2)

σ3 = minor principal stress in x-horizontal direction

= σx + k0 (γ1z1 + γ2z2)

σx = normal horizontal stress in x-direction induced by wheel load

σy = normal horizontal stress in y-direction induced by wheel load

k0 = coefficient of each pressure at rest

= (1 – sinΦ) for granular materials (Φ = angle of internal friction)

k1, k2 = regression coefficients as determined from laboratory cyclic triaxial

testing thus, in a pavement structure:

( ) ( ) ( )

( )( )z 1 1 2 2 x 0 1 1 2 2 y 0 1 1 2 2

z x y 1 1 2 2 0

z z k z z k z z

z z 1 2k

θ = σ + γ + γ + σ + γ + γ + σ + γ + γ = σ + σ + σ + γ + γ +

(2)

In order for Eb to be calculated by use of Eq. 1, values for k1, k2, and θ are

necessary. The following discussion shows the methods by which these three

parameters can be determined.

k1 and k2

The constants k1 and k2 can be determined for a given material by cyclic triaxial

testing (CTX) as shown in Fig. 1. Alternately, in order to be able to estimate k1 (and

hence Eb) without performing a CTX test, values may be approximated as shown in

Table 1. It must be emphasized that k1 values vary considerably within an aggregate

source class, and it is quite possible for a given gravel to have a k1 value greater than a

given crushed stone.

Fig. 1: Typical Resilient Modulus Test Results

Table 1: Estimated Values of k1

Material

SCE (100%)

MCE

(100%) Gravel

4300

5000

Crushed stone

4800

6100

NOTE: at ≤ 60% saturation; minus #200 ≤ 10%

SCE = standard compactive effort

MCE = modified compactive effort

The parameter k1 represents the granular material condition and characteristics:

gradation, particle shape and texture, degree of saturation, and relative density. A

larger k1 indicates a superior material/condition. k2 has been shown (5) to correlate with

k1 as follows:

12

4.657 log kk1.807

−= (3)

This relationship is shown in Fig. 2. Thus, k1 can be estimated from physical properties

of the aggregate, and k2 can be estimated from a relationship with k1.

Bulk Stress (θ)

Bulk stress in an unbound granular base layer is a function of applied load (P)

and contact pressure (p), stiffness (E1) and thickness (D1) of the overlying asphalt-

bound layer, stiffness (Esg) of the subgrade underlying the base layer, stiffness (Eb) and

thickness (D2) of the base layer, and unit weight of the overlying layers. Because Eb is

a function of θ, and θ is a function of Eb, an iterative procedure is necessary in order to

reconcile the Eb and θ. This can be done by such computer programs as KENLAYER.

Fig. 2: Relationship between experimentally derived factors (k1 and k2) for Theta Model

Eb FROM REGRESSION EQUATION Bulk stress can be determined for a specific combination of load condition and

pavement cross section by use of KENLAYER. If the use of KENLAYER is not

possible, the following regression equation can be used:

( )( ) ( ) ( ) ( ) ( )0.458 0.426 0.107 0.207 0.067R 1 1 1 sg 2M 510.505 D k E E D− −= (4)

where k1 can be obtained by test or by estimation as previously discussed. The other

variables in Eq. 4 are necessary to compute bulk stress conditions. As E1 and D1

increase, less stress is transmitted to the base layer, hence Eb decreases. As Esg

decreases, the base layer is less confined under loading, hence Eb decreases. Note

that Eq. 4 can only be used for a single granular layer sandwiched between an asphalt

layer and the subgrade.

Eq. 4 was developed by calculation of base Eb by use of Eq. 1 (Eb = k1θk2). In

the regression equation development, resilient modulus was varied by use of 237

combinations of k1, k2, and θ in the program KENLAYER. These combinations

represented three levels of the following variables: layer thicknesses (D1 and D2),

subgrade modulus (Esg), asphalt layer modulus (E1), and granular material constants k1

and k2:

Stress state: D1 = 2,8,15 in

D2 = 4,12,18 in

E1 = 130,000; 500,000; 2,100,000 psi

Esg = very soft, medium, stiff

K1 = 1800; 3000; 11,000 psi

K2 = 0.776, 0.653, 0.341

For each combination, KENLAYER calculated the bulk stress θ in the granular base and

the deviator stress σd in the subgrade soil from an applied load.

USAGE Eq. 4 can be used by the designer to approximate Eb of granular material which

is functioning either as a base under an asphalt layer or as a subbase under an asphalt

surface layer and a bituminous base layer. If the latter is the case, E1 should represent

a combination of the two asphalt bound layers as follows:

( ) ( )30.333 0.333

1a 1a 1b 1beq

1a 1b

D E D EE

D D

+=

+ (5)

where: Eeq = combined modulus of both asphalt bound layers

E1a = modulus of the asphalt surface layer

D1a = thickness of the asphalt surface layer

E1b = modulus of the asphalt base layer

D1b = thickness of the asphalt base layer

So, to use Eq. 4, the designer should:

1. Assume a D1 and D2 for a particular trial.

2. Determine E1 by either test or by the approximation technique detailed in the

handout on "Determination of AASHTO Layer Coefficients for Asphalt Mixtures"

knowing mixture design characteristics and approximate pavement temperature.

3. Calculate Esg from the procedure given in the handout "Estimation of Fine-

Grained Subgrade Resilient Modulus".

4. Determine k1 of the granular material by test or by assumption (see Table 1).

Other trials of cross-section would only entail further assumptions of D1 and D2.

Once Eb is determined, it can be converted to a layer coefficient a2 or a3 as

shown in the next section.

SEASONAL EFFECTS ON GRANULAR BASE MODULUS Seasonal effects on Ebase can be found by using KENLAYER. Input to use:

1. Vary k1:

k1(max) = (3) (k1(normal))

k1(thaw) = (0.2)(k1(normal))

k1(wet) = (0.75)(k1(normal))

2. k2 should vary, but KENLAYER does not allow this. It is suggested that k2 be

calculated from k1, avg. If the output is to be used in the AASHTO method to find

layer coefficient a3, then the effects of moisture are taken care of with the m-

coefficient. Thus, a single value of k1 that should be used is the “normal” value.

Esg - for use with the AASHTO method, for the same reason stated above, a

single value (normal, or dry, Esg) should be used.

3. Emax - use 30,000 for base, 20,000 for subbase

4. Emin - use 1000 psi

5. E1 - vary E1 as affected by temperature

RECOMMENDATIONS

Layer coefficients for unbound granular base or subbase materials can be

determined in the following manner:

1. Determine a2 or a3 from the 1986 AASHTO Guide nomographs, or more

accurately:

( )2 ba 0.249 log E 0.977= − (6)

( )3 ba 0.227 log E 0.839= − (7)

2. Eb (resilient modulus of granular material) can be determined by use of an elastic

layer analysis program such as KENLAYER or by the following equation (Eq. 4):

( )( ) ( ) ( ) ( ) ( )0.458 0.426 0.107 0.207 0.067R 1 1 1 sg 2M 510.505 D k E E D− −=

3. D1 and D2 (D1 = asphalt bound layer, D2 = granular base or subbase layer

thickness) are assumed for a particular design trial. (Note, D1 is the combined

thickness of all asphalt-bound layers).

4. E1 (asphalt material resilient modulus), is determined at a given design

temperature as developed in Ref. 14 knowing either resilient modulus or mix

design characteristics. If more than one asphalt layer is involved, the weighted

average can be obtained by the following equation (Eq. 5):

( ) ( )30.333 0.333

1a 1a 1b 1beq

1a 1b

D E D EE

D D

+=

+

5. Esg (subgrade soil modulus) can be calculated in accordance with the subgrade

resilient modulus handout.

6. k1 can be determined by resilient modulus testing of the granular material, or by

estimation. See Table 1 for guidance.

REFERENCES

1. Rada, G. and M. M. Witczak, "Material Layer Coefficients of Unbound Granular

Materials from Resilient Modulus", Trans. Res. Rec. 852, 1982, pp. 15-21.

2. Barksdale, R. D., "Laboratory Evaluation of Rutting in Base Course Materials",

Proc. 3rd Int'l. Conf. on the Structural Design of Asphalt Pavements, London,

England, 1972, pp. 161-174.

3. Barksdale, R.D., S.Y. Itani, and T.E. Swor, "Evaluation of Recycled Concrete,

Open-Graded Aggregate", Trans. Res. Bd. 71st Annual Meeting, Trans. Res.

Bd., Washington, D.C., 1992, 25 p.

4. Jin, M., K.W. Lee, and W.D. Kovacs, "Field Instrumentation and Laboratory Study

to Investigate Seasonal Variation of Resilient Modulus of Granular Soils",

Trans. Res. Bd. 71st Annual Meeting, Trans. Res. Bd., Washington, D.C.,

1992, 30 p.

5. Rada, G. and M.W. Witczak, "Comprehensive Evaluation of Laboratory Resilient

Moduli Results for Granular Material", Trans. Res. Rec. 810, Trans. Res. Bd.,

1981, pp. 23-33.

6. Kallas, B.F. and J.C. Riley, "Mechanical Properties of Asphalt Pavement

Materials", Proc. 2nd Int'l. Conf. on the Structural Design of Asphalt

Pavements, Univ. of Michigan, 1967, pp. 931-952.

7. Thom, N.H. and S.F. Brown, "The Effect of Moisture on the Structural

Performance of a Crushed Limestone Road Base", Trans. Res. Bd. Annual

Meeting, Trans. Res. Bd., Washington, D.C., 1987, 24 p.

8. Hicks, R.G. and C.L. Monismith, "Prediction of the Resilient Response of

Pavements Containing Granular Layers Using Non-Linear Elastic Theory",

Proc. 3rd Int'l. Conf. on the Structural Design of Asphalt Pavements, London,

Vol I, 1972, pp. 410-427.

9. Finn, F.N., C.L. Saraf, R. Kulkarni, K. Nair, W. Smith, and A. Abdullah,

"Development of Pavement Structural Subsystems", NCHRP Rpt. 291, Hwy.

Res. Bd., Washington, D.C., 1986, 59 p.

10. Jorenby, B.N. and R.G. Hicks, "Base Course Contamination Limits", Trans. Res.

Rec. 1095, Trans. Res. Bd., 1986, pp. 86-101.

11. Barker, W.R. and R.C. Gunkel, "Structural Evaluation of Open-Graded Bases for

Highway Pavements", Misc. Paper GL-79-18, U.S. Corps of Engrs., WES,

1979, 82 p.

12. Thompson, M.R. and K.L. Smith, "Repeated Triaxial Characterization of Granular

Bases", Trans. Res. Rec. 1278, Trans. Res. Bd., Washington, D.C., 1990, pp.

7-17.

13. Haynes, J.H. and E.J. Yoder, "Effects of Repeated Loading on Gravel and

Crushed Stone Base Course Materials Used in the AASHTO Road Test", Hwy.

Res. Rec. 39, Hwy. Res. Bd., Washington, D.C., 19 , pp. 82-96.

14. Richardson, D.N., J.K. Lambert, and P.A. Kremer, "Determination of AASHTO

Layer Coefficients, Vol I: Bituminous Materials", MCHRP Final Rpt. Study 90-

5, Univ. of Missouri-Rolla, Rolla, Missouri, 1993, 237 p.