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66
CHAPTER FIVE
Correlations and Matrix Tables
Resilient Moduli Correlations
practice sometimes results in correlations with attributes
that do not follow physical or practical expected trends. For
Different types of correlations are used to estimate the resil- example, in MRDS 7, the stiffness of a soil decreases with
ient properties of subgrades and bases. Several literature an increase in dry unit weight. Users should evaluate the use
sources were collected that provided comprehensive details of any select correlations with the local soil test database
of these models and correlations. The following sections are before routine use.
prepared based on the information available in these reports.
Currently, two approaches are followed to analyze resilient MRDS 1
moduli test data. One of them is to develop relationships
between resilient moduli values and various soil properties The following model defining resilient modulus as a func-
or different in situ test-related parameters. Statistical regres- tion of degree of saturation and compaction moisture content
sion tools are usually adopted for this exercise. was developed by Jones and Witczak (1972):
The other one is to analyze the resilient moduli data with Log MR (ksi) = -0.111w + 0.0217S + 1.179 (16)
a formulation that accounts for confining or deviatoric or
both stress forms. This formulation usually contains several where w is the compaction moisture content in percent
model constant parameters. Once these parameters are deter- and S is degree of saturation in percent. The R2 value of
mined, they are correlated with different sets of soil proper- this equation is 0.44. This equation is valid for clays (A-7-6
ties. These correlations are termed here as semi-empirical or type), because the model correlation was developed primar-
indirect correlations. The next few sections cover some of the ily using the same types of clayey samples from California.
correlations currently used in the resilient moduli modeling. The MR of clays used in this correlation was determined
from RLT tests on clay samples under a maximum cyclic
deviator stress of 6 psi and a confining pressure of 2 psi.
Direct Resilient Moduli Correlations
MRDS 2
In the direct correlations, two types of correlations were
reported in the literature. The first correlates resilient mod- Thompson and Robnett (1979) studied the resilient char-
uli directly with the soil properties. The second correlates acteristics of several Illinois fine-grained subgrade soils
the moduli with in situ test parameters. Both types are fre- described in the earlier sections. Resilient modulus test
quently used by pavement design engineers. Because there results at a deviatoric stress of 6 psi and zero confining pres-
are several models, this section associates these models with sure are then correlated with soil characteristics. The fol-
simple terminology for quick identification. lowing correlation has a coefficient of determination, R² of
0.80, suggesting a good correlation obtained for the Illinois
In the case of direct correlation of resilient modulus with subgrades. The equation follows:
soil properties, the abbreviation MRDS (MR stands for
Resilient Modulus and DS stands for Direct Correlations MR (ksi) = 6.37 + 0.034×%CLAY + 0.45×PI
and Soil Properties–Based Relationship) is used. For in situ- (17)
based correlations, the abbreviation MRDI (MR stands for − 0.0038×%SILT − 0.244×CLASS
Resilient Modulus and DI stands for Direct and In Situ Test–
Based Relationship) is used. where MR is resilient modulus measured at σd = 6 psi for
soils with a relative compaction of 95% as per AASHTO
Direct and Soil Property–Based Models T99; %CLAY is clay content in percent; PI is plasticity index
in percent; %SILT is silt content in percent; and CLASS is
In the following section, several direct models from the lit- AASHTO classification (for A7-6 soils, use 7.6 in the expres-
erature are presented. The development of these correlations sion). This model is valid for cohesive soils and does not
was based primarily on multiple linear regression tools. Such address stress effects.

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Thompson and LaGrow (1988) developed the following (Asphalt Institute 1982) (24)
correlation for the compacted subgrades of Illinois:
(Lee et al. 1997) (25)
(18)
where qu is unconfined compression strength. Equation
where C is percent clay and PI is the plasticity index. 25 was developed based on the resilient modulus test data-
They proposed the following correction factors for mois- base compiled from testing the subgrades from Indiana.
ture susceptibility, which need to be applied to the estimated Su,1% is undrained shear strength at 1% axial strain and a is
resilient moduli. For clay, silty clay, and silty clay loam, the the constant determined from Figure 80.
correction factor is 0.7; for clay loam, the correction factor
is 1.5. Several state DOTs formulated their own procedures for
determining the resilient modulus of compacted subgrades.
MRDS 3 The following procedure describes the steps followed by the
Ohio DOT for predicting the resilient properties of their sub-
Several models based on CBR, R value, were introduced grades. It uses the following MR –CBR relationship, where
in the mid-1980s and a list of these including a few recom- CBR is estimated in two steps. The first step is to estimate
mended by the AASHTO design guide are presented here. the group index (GI) from basic soil properties (Figure 81a)
The Asphalt Institute (1982) recommended the following and the second step is to correlate CBR with the GI param-
relationship (Equation 19) between resilient modulus and R eter determined in step 1 (Figure 81b):
value:
(26)
(19)
where A is constant and varies from 772 to 1,155; B is con- MRDS 5
stant and varies from 369 to 555; and R is R value (AASHTO
T190). For fine-grained soils whose R values are less than The following model was developed by Carmichael and
or equal to 20, the 1993 AASHTO guide recommends A is Stewart (1985), which is based on a large database of resil-
1,000 and B is 555. ient moduli test results. The formulation of this expression
follows:
Buu (1980) reported the following relationship for fine-
grained Idaho soils with R values greater than 20. This cor-
relation is valid for σd = 6 psi and σ3 = 2 psi. (27)
(20)
where CH is 1 for CH soil, 0 otherwise; MH is 1 for MH
MRDS 4 soil, 0 otherwise; S200 is percent passing #200 sieve (%).
The coefficient of determination R² value is 0.80, suggesting
Both CBR and unconfined compression strength–based that this is a good correlation. This correlation is valid for
correlations are presented in the following. One of the ear- subgrade soils containing clays and silts.
lier equations, developed by Heukelom and Klomp (1962),
provided a relationship between resilient modulus and CBR
value and has been recommended by several AASHTO
design guides. This relationship follows:
(21)
The lower and upper bound values of the constant of pro-
portionality ranged between 750 and 3,000, respectively.
This equation provides reasonable estimates of resilient
modulus for fine-grained soils with a CBR value of 10 or
less. Other MR correlations are given here:
(22)
(Thompson and Robnett 1979)
(Powell et al. 1984) (23) FIGURE 80 ‘a’ parameter for MR prediction (Lee et al. 1997).

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FIGURE 81 Correlations to predict resilient modulus using CBR and soil support values (Ohio DOT 1999).

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Carmichael and Stewart (1985) also proposed a separate
correlation for granular soils and base aggregates:
(28)
where %W is compaction moisture content; θ is bulk
stress in psi; SM is 1 for SM soil and 0 for other soils; and
GR is 1 for gravelly soils (GM, GW, GC, and GP) and is 0
for other soils.
MRDS 6
Elliott et al. (1988) tested several Arkansas soils and devel- FIGURE 82 Hyperbolic model and definitions of model
constants (Drumm et al. 1990).
oped the following two resilient modulus models at two dif-
ferent deviator stresses of 4 and 8 psi:
stants used in this correlation are defined as functions of
At sd = 4 psi: various soil properties:
MR (ksi) = 11.21 + 0.17%CLAY + 0.20PI − 0.73wopt (29)
(32)
At sd = 8 psi:
where
MR (ksi) = 9.81 + 0.13%CLAY + 0.16PI – 0.60wopt (30)
The coefficients of determination for Equations 29 and
30 were 0.80 and 0.77, respectively. The resilient moduli
determined from these relationships are valid for the above
stresses. This relationship is valid for cohesive subgrades.
%CLAY is percent finer than 0.002 mm; and LL is liquid
MRDS 7 limit (%). The coefficient of determination of this expres-
sion is 0.80.
Drumm et al. (1990) tested several fine-grained soils from
different parts of Tennessee and test data were used to This model adequately predicts resilient moduli for Ten-
develop the following direct relationships for resilient modu- nessee subgrades containing predominantly cohesive soils
lus. The first of these two relationships presents breakpoint and subjected to a wider range of deviator stresses applied
resilient modulus: to them. The above resilient moduli models yield resilient
modulus at zero confining stress only.
(31) MRDS 8
The Farrar and Turner (1991) correlation was developed
where Mri is the breakpoint resilient modulus, which based on the resilient properties measured on 13 subgrade
assumes that the resilient modulus versus deviator stress materials from Wyoming.
relationship is bilinear, and Mri represents the intersection
of the bilinear plot; a is initial tangent modulus (psi) of a
stress–strain curve from unconfined compression tests; qu is (33)
unconfined compressive strength (psi); PI is plasticity index
(%); γ is dry unit weight (pcf); S is degree of saturation (%);
d The coefficient of determination (R²) for this correlation
and S200 is percent passing the #200 sieve. The coefficient of was 0.663, and this expression is recommended for fine-
determination (R²) for the breakpoint resilient modulus cor- grained subgrades.
relation was 0.83. Figure 82 presents the definitions of moduli
parameters; a and b are determined from this relationship. MRDS 9
The second correlation introduces a hyperbolic relation- Several resilient modulus tests were performed on eight
ship for the determination of resilient modulus, and the con- Tennessee subgrade soils composed of A4 through A7-6

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types (Hudson et al. 1994). Based on the tests, the following Table 11
model was proposed for the estimation of resilient modulus: Correction factors for the resilient modulus
model (Pezo and Hudson 1994)
Moisture Content F γ /γ F
1 d d max 2
(%) (%)
(34) 10 4.0 100 1.00
15 2.0 95 0.90
20 1.0 90 0.80
25 0.5 85 0.70
where Δγd (pcf) is deviation from the Standard Proctor
maximum dry density, which is γd − γdmax; LI is liquid- Plasticity Index F Sample Age F
ity index (%); and Δw (%) is deviation from the optimum (%)
3
(days)
4
water content, wopt, based on the Standard Proctor compac-
10 1.00 2 1.00
tion tests. The coefficient of determination (R²) was 0.70, and
this expression is valid for cohesive subgrades. 20 1.50 10 1.10
30 2.00 20 1.15
MRDS 10 ≥40 2.50 ≥30 1.20
Li and Selig (1994) proposed the following expression for σ F σ F
predicting the resilient modulus of fine-grained soils. To use c 5 d 6
(kPa/psi) (kPa/psi)
this model, the modulus value at optimum moisture content
should be known to users. Once it is known, the moduli at 13.8/2 1.00 13.8/2 1.00
other moisture contents can be estimated using the following 27.6/4 1.05 27.6/4 0.98
equation, which was developed based on a review of resil- 41.4/6 1.10 41.4/6 0.96
ient modulus data obtained from soils throughout the United
55.2/8 0.94
States. The equation for resilient modulus along paths of con-
stant dry density but at different compactive efforts follows: 69.0/10 0.92
(35) The properties of the soils tested have the following ranges:
moisture content from 10% to 35%; relative compaction from
80% to 100% based on AASHTO T99; plasticity index from
where Rm1 is MR /MR opt; MR opt is the resilient modulus at 4% to 52%; compacted specimen age from 2 to 188 days;
the optimum water content; and change in moisture content is confining stress from 13.8 to 41.4 kPa (2 to 6 psi); and devia-
the difference between moisture content at which moduli are tor stress from 11 to 102.8 kPa (1.6 to 14.9 psi). Factors such as
being estimated and optimum moisture content values. This AASHTO classification, seating pressures, and percent fines
equation is predominantly used for cohesive subgrades. were also analyzed for the above resilient modulus correla-
tion. However, these factors were not included in the correla-
MRDS 11 tion. The coefficient of determination for this model was 0.80
and the expression is valid for silty to clayey subgrades.
Resilient modulus tests were performed on several subgrade
samples from Texas by following SHRP Protocol P46 (Pezo MRDS 12
and Hudson 1994). Based on the test database, the following
resilient modulus prediction model was established, which Berg et al. (1996) conducted a study on one fine-grained and
requires six factors that gave the highest degree of correla- several coarse-grained Minnesota soils. The fine-grained
tion for these soils. The model is as follows: soil was prepared at several different moisture contents but
at a single dry density of about 110 pcf. The resilient modu-
MR = F0 × F1 × F2 × F3 × F4 × F5 × F6 (36) lus model developed from these test results is given in the
following equation:
where F0 is 9.80 ksi (English units) or 67.60 MPa (SI units);
F1 is the correction factor for moisture content; F2 is the cor- (37)
rection factor for relative compaction; F3 is the correction
factor for soil plasticity; F4 is the correction factor for age of
compacted specimen; F5 is the correction factor for confining where f(S) is saturation normalized by a unit saturation
pressure; and F6 is the correction factor for deviator stress. of 1.0%; f(σ) is octahedral shear stress, τ , normalized by
oct
Values for the correction factors are presented in Table 11. a unit stress of 1.0 psi; and τ is (√
oct 2/3) σd. The coefficient