Determination of AASHTO Layer Coefficients for Granular Materials by Use of Resilient Modulus

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by  David Newton Richardson

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Civil, Architectural and Environmental Civil, Architectural and Environmental
Engineering Faculty Research & Creative Works Engineering
01 Jan 1994
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David Newton Richardson
Missouri University of Science and Technology, [email protected]
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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.
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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 a or a for an unbound granular base or subbase material
2 3
are found from a relationship with resilient modulus, E . The resilient modulus for a
b
given material can be found by test using the "theta model" or by use of an estimation
regression equation. E is a function of several factors, as discussed below.
b

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.
E FROM THETA MODEL
b
It has been shown that the resilient modulus of a granular material is a function of
stress-state:

E =k θk2 (1)
b 1
where
θ = bulk stress
= σ + σ + σ
1 2 3
= σ + σ + σ + geostatic stresses
x y z
σ = σ + γ z + γ z in pavement under centerline of load
1 z 1 1 2 2
(σ is vertical total major principal stress; γ and γ are unit weights of each
1 1 2
overlying material; z’s are thicknesses of each layer overlying the point of
stress computation; γ z = geostatic stresses)
n n
σ = normal stress in vertical direction from wheel load as computed by elastic
z
layer analysis
= σ + σ in triaxial cell test (σ = deviator stress; σ = confining pressure)
d c d c
σ = intermediate principal stress in y-horizontal direction
2
= σ + k (γ z + γ z )
y 0 1 1 2 2
σ = minor principal stress in x-horizontal direction
3
= σ + k (γ z + γ z )
x 0 1 1 2 2
σ = normal horizontal stress in x-direction induced by wheel load
x
σ = normal horizontal stress in y-direction induced by wheel load
y
k = coefficient of each pressure at rest
0
= (1 – sinΦ) for granular materials (Φ = angle of internal friction)
k , k = regression coefficients as determined from laboratory cyclic triaxial
1 2
testing thus, in a pavement structure:

θ= σ +(γ z +γ z )+σ +k (γ z +γ z )+σ +k (γ z +γ z )
 z 1 1 2 2   x 0 1 1 2 2   y 0 1 1 2 2 
(2)
=σ +σ +σ +(γ z +γ z )(1+2k )
z x y 1 1 2 2 0
In order for Eb to be calculated by use of Eq. 1, values for k , k , and θ are
1 2
necessary. The following discussion shows the methods by which these three
parameters can be determined.

k and k
1 2
The constants k and k can be determined for a given material by cyclic triaxial
1 2
testing (CTX) as shown in Fig. 1. Alternately, in order to be able to estimate k (and
1
hence E ) without performing a CTX test, values may be approximated as shown in
b
Table 1. It must be emphasized that k values vary considerably within an aggregate
1
source class, and it is quite possible for a given gravel to have a k value greater than a
1
given crushed stone.

Fig. 1: Typical Resilient Modulus Test Results
Table 1: Estimated Values of k
1

Material SCE MCE
(100%) (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 k represents the granular material condition and characteristics:
1
gradation, particle shape and texture, degree of saturation, and relative density. A
larger k indicates a superior material/condition. k has been shown (5) to correlate with
1 2
k as follows:
1
4.657−logk
k = 1 (3)
2
1.807

This relationship is shown in Fig. 2. Thus, k can be estimated from physical properties
1
of the aggregate, and k can be estimated from a relationship with k .
2 1

Bulk Stress (θ)
Bulk stress in an unbound granular base layer is a function of applied load (P)
and contact pressure (p), stiffness (E ) and thickness (D ) of the overlying asphalt-
1 1
bound layer, stiffness (E ) of the subgrade underlying the base layer, stiffness (E ) and
sg b
thickness (D ) of the base layer, and unit weight of the overlying layers. Because E is
2 b
a function of θ, and θ is a function of E , an iterative procedure is necessary in order to
b
reconcile the E and θ. This can be done by such computer programs as KENLAYER.
b
Fig. 2: Relationship between experimentally derived factors (k and k ) for Theta Model
1 2

E FROM REGRESSION EQUATION
b
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:

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

where k can be obtained by test or by estimation as previously discussed. The other
1
variables in Eq. 4 are necessary to compute bulk stress conditions. As E and D
1 1
increase, less stress is transmitted to the base layer, hence E decreases. As E
b sg
decreases, the base layer is less confined under loading, hence E decreases. Note
b
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 E by use of Eq. 1 (E = k θk2). In
b b 1
the regression equation development, resilient modulus was varied by use of 237
combinations of k , k , and θ in the program KENLAYER. These combinations
1 2
represented three levels of the following variables: layer thicknesses (D and D ),
1 2
subgrade modulus (E ), asphalt layer modulus (E ), and granular material constants k
sg 1 1
and k :
2
Stress state: D = 2,8,15 in
1
D = 4,12,18 in
2
E = 130,000; 500,000; 2,100,000 psi
1
E = very soft, medium, stiff
sg
K = 1800; 3000; 11,000 psi
1
K = 0.776, 0.653, 0.341
2

For each combination, KENLAYER calculated the bulk stress θ in the granular base and
the deviator stress σ in the subgrade soil from an applied load.
d

USAGE
Eq. 4 can be used by the designer to approximate E of granular material which
b
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, E should represent
1
a combination of the two asphalt bound layers as follows:

3
D (E )0.333 +D (E )0.333
1a 1a 1b 1b
E =   (5)
eq
 D1a+D1b 
where: E = combined modulus of both asphalt bound layers
eq
E = modulus of the asphalt surface layer
1a
D = thickness of the asphalt surface layer
1a
E = modulus of the asphalt base layer
1b
D = thickness of the asphalt base layer
1b
So, to use Eq. 4, the designer should:
1. Assume a D and D for a particular trial.
1 2
2. Determine E by either test or by the approximation technique detailed in the
1
handout on "Determination of AASHTO Layer Coefficients for Asphalt Mixtures"
knowing mixture design characteristics and approximate pavement temperature.
3. Calculate E from the procedure given in the handout "Estimation of Fine-
sg
Grained Subgrade Resilient Modulus".
4. Determine k of the granular material by test or by assumption (see Table 1).
1
Other trials of cross-section would only entail further assumptions of D and D .
1 2
Once E is determined, it can be converted to a layer coefficient a or a as
b 2 3
shown in the next section.

SEASONAL EFFECTS ON GRANULAR BASE MODULUS
Seasonal effects on E can be found by using KENLAYER. Input to use:
base
1. Vary k :
1
k = (3) (k )
1(max) 1(normal)
k = (0.2)(k )
1(thaw) 1(normal)
k = (0.75)(k )
1(wet) 1(normal)
2. k should vary, but KENLAYER does not allow this. It is suggested that k be
2 2
calculated from k , avg. If the output is to be used in the AASHTO method to find
1
layer coefficient a , then the effects of moisture are taken care of with the m-
3
coefficient. Thus, a single value of k that should be used is the “normal” value.
1
E - for use with the AASHTO method, for the same reason stated above, a
sg
single value (normal, or dry, E ) should be used.
sg
3. E - use 30,000 for base, 20,000 for subbase
max
4. E - use 1000 psi
min
5. E - vary E as affected by temperature
1 1
RECOMMENDATIONS
Layer coefficients for unbound granular base or subbase materials can be
determined in the following manner:
1. Determine a or a from the 1986 AASHTO Guide nomographs, or more
2 3
accurately:
a =0.249log(E )−0.977 (6)
2 b
a =0.227log(E )−0.839 (7)
3 b

2. E (resilient modulus of granular material) can be determined by use of an elastic
b
layer analysis program such as KENLAYER or by the following equation (Eq. 4):

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

3. D and D (D = asphalt bound layer, D = granular base or subbase layer
1 2 1 2
thickness) are assumed for a particular design trial. (Note, D is the combined
1
thickness of all asphalt-bound layers).
4. E (asphalt material resilient modulus), is determined at a given design
1
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):

3
D (E )0.333 +D (E )0.333
1a 1a 1b 1b
E =  
eq
 D1a+D1b 

5. E (subgrade soil modulus) can be calculated in accordance with the subgrade
sg
resilient modulus handout.
6. k can be determined by resilient modulus testing of the granular material, or by
1
estimation. See Table 1 for guidance.