Open Journal of Civil Engineering, 2011, 1, 1-6
doi:10.4236/ojce.2011.11001 Published Online September 2011 (http://www.SciRP.org/journal/ojce)
Copyright © 2011 SciRes. OJCE
Resilient Modulus of Unbound Aggregate Base Courses
from Senegal (West Africa)
Makhaly Ba, Meissa Fall, Fatou Samb, Déthié Sarr, Mapathé Ndiaye
Department of Geotechnical Engineering, University of Thiès, Thiès, Senegal
E-mail: makhaly.ba@univ-thies.sn
Received August 13, 2011; revised September 13, 2011; accepted September 20, 2011
Abstract
This paper presents the results of research conducted to investigate the Resilient Modulus (Mr) of unbound
aggregates used as pavement layer in Senegal (West Africa) as well as the effect of water content and density
on the Resilient Modulus of the materials tested. Four different aggregates was collected from different sites
within Senegal and then subjected to repeated load triaxial tests. Test results showed that the Bandia lime-
stone is around 44% stiffer than the basalt, and 71% to 104% stiffer that the Black and the Red quartzites
(GNB and GRB). The basalt is 21% to 43% stiffer than the GNB and the GRB. Basalt specimens compacted
at Wopt– 2% were 30% stiffer than basalt specimens compacted at Wopt and 40% stiffer than those com-
pacted at Wopt+ 2%. The Summary Resilient Modulus (SRM) at Wopt– 2% is 22% higher than SRM at
Wopt and 35% higher than SRM at Wopt+ 2% for the GRB and the GNB. The SRM at Wopt– 2% is 30%
higher than SRM at Wopt and 40% higher than SRM at Wopt+ 2%, for the Basalt. For the Bandia limestone,
the SRM at Wopt– 2% is 81% higher than SRM at Wopt and 126% higher than SRM at Wopt+ 2%. Results
show also that the Resilient Modulus increases around 25% when relative density increases from 77% to
119% and the variation is more significant at high stress states than at low stress state. Results of statistical
analysis and coefficients of determination (R2) showed that the Uzan and NCHRP models are more suitable
to predict the Resilient Modulus of the aggregates tested.
Keywords: Resilient Modulus, Summary Resilient Modulus, Quartzite, Basalt, Bandia Limestone, Unbound
Aggregates
1. Introduction
Achieving a proper modulus for an unbound base course
is important for pavement performance [1]. One com-
monly used parameter to define material stiffness is the
Resilient Modulus (Mr), which is similar to Young’s
modulus based on the recoverable axial strain under an
imposed axial (deviator) stress. In Senegal as in a lot of
developing countries, road specifications are primarily
based on the material characterization but rarely on the
real mechanical behavior of materials [2]. Indeed, crack-
ing and rutting are the main modes of flexible pavement
failures. These are mainly due to tensile stresses and ac-
cumulation of permanent strains over the d iff er en t laye r s.
Therefore, a rational design of flexible pavements passes
necessarily by a good modeling of the mechanical be-
havior of these materials. Unfortunately, this mechanical
behavior is poorly taken into account and, the design
methods do not reflect well the rheological behavior of
these materials. In the current method of pavement de-
sign in Senegal, determining the mechanical behavior of
materials is usually done by a calculation in linear elas-
ticity and the behavior is described by two constant pa-
rameters that are the Young modulus (E) and the Poisson
ratio (v). However, under traffic loading, the behavior of
unbound granular materials is rather nonlin ear. This calls
into question the inputs of these different methods, which
use a linear elasticity theory to describe a nonlinear elas-
toplastic phenomenon. These shortcomings are led to the
development of Resilient Modulus for measuring non-
linear elastic properties of unbound granular materials.
This underlines the interest of the repeated load triaxial
test that can characterize the behavior of materials re-
lated to the granular mixture, more representative of the
M. BA ET AL.
Copyright © 2011 SciRes. OJCE
2
state of the material in the pavement, but not only from
characteristics of its aggregates. However, no studies on
the mechanical behavior of crushed granular materials
under cyclic loading has been conducted in Senegal
where the interest of this work wh ich will investigate the
Resilient Modulus of granular materials to have input
parameters for a mechanistic design approach in Senegal.
These results will be the first obtained on unbound gra-
nular material from Senegal.
2. Background
The Resilient Modulus (Mr) is an elastic modulus based
on the recoverable strain under repeated loads. It is de-
fined as Equation (1) where σd is the applied deviatoric
stress (σ1 - σ3) and εr is the recoverable strain.
d
r
Mr (1)
A number of factors affect the Mr of unbound granular
materials, some of which are stress history, moisture
content, density, aggregate type, gradation, percent fines
[3]. A number of researchers have developed models to
predict the Mr of granular materials [4]. However, for
this research study, a Summary Resilient Modulus was
calculated using the bulk stress model [5] and calculated
with
= 208 kPa. This model can be expressed as fol-
lows:
2
1
k
a
Mrk P



(2)
where 13
2

 is the bulk stress; k1 and k2 are the
material properties determined from regression analyses.
3. Materials Characterization and Testing
Procedure
3.1. Materials
Resilient Modulus tests were conducted on four (04)
types of crushed aggregates collected from different
locations corresponding to the main sources of aggre-
gate within Senegal: Red quartzite from Bakel (GRB),
Black quartzite from Bakel (GNB), Basalt from Diack
(BAS), and Limestone from Bandia (BAN). Each speci-
men was labeled “letter_number1_number2,” where the
letter represented the sample identification, number1
indicated the moisture content, and number2 indicated
the dry unit weight. Grain size distributions for the ma-
terials tested are shown in Figure 1. Maximum and
minimum dry unit weight and compaction characteriza-
tion are presented in Table 1. Moreover, the repeated
load triaxial test was used to determine the Resilient
Modulus of these aggregates.
0
20
40
60
80
100
0,010,1110100
GRB
GNB
Basalt
Bandia Limestone
Percent fi n er (%)
Particle size (mm)
Figure 1. Particles sizes distribution for the 4 materials.
Table 1. Relative density vs. relative compaction for the
four materials.
Relative Density Compaction test
Materials
dmin (kg/m3)
dmax (kg/m3)
dmax
(kg/m3)
Wopt
(%)
GRB 1656 2002 2140 5.5
GNB 1644 2000 2150 4.5
BAS 1890 2240 2420 4.2
BAN - - 2065 7.6
3.2. Resilient Modulus Test Procedure
The cyclic loading triaxial tests were performed using a
MTS closed-loop servo-electrohydraulic testing system
which is capable of applying repeated load in haversine
waveform with a wide range of load duration. The axial
deformations were measured by LVDTs mounted inside
the triaxial cell. The specimens were submitted to cyclic
loading triaxial tests according to the NCHRP 1-28A [6]
test protocol, which was used to establish the 30 loading
sequences. The loading involves conditioning, which
attempts to establish steady-state or resilient behavior,
through the application of 1000 cycles of 207 kPa devia-
tor stress at 103.5 kPa confining pressure. The cycles are
then repeated 100 times for 30 loading sequences with
different combinations of deviator stress and confining
pressure. The Mr is calculated as the mean of the last
five cycles of each sequence from the recoverable axial
strain and cyclic axial stress.
4. Test Results and Analyses
Mr versus confining pressure plots for the four different
M. BA ET AL.
Copyright © 2011 SciRes. OJCE
3
materials compacted at their optimum moisture contents
and at 98% of the maximum dry unit weight for the GRB,
GNB and the basalt, 95% of the maximum dry unit
weight for the limestone are shown in Figure 2. The
spread in the data at a constant confining pressure repre-
sents the Mr at various deviator stresses. The curve fit is
based on power dependence on confinement. Typical of
granular materials, the Mr increased consistently with
increase of confining pressure. Bandia limestone is
around 44% stiffer than the basalt, and 71% to 104%
stiffer that the GNB and the GRB. The basalt is 21% to
43% stiffer than the GNB and the GRB. The difference
of Resilient Modulus between the GRB and the GNB
doesn’t exceed 10%.
A summary of the Mr results is presented in Figure 3,
for Basalt sample, compacted at three moisture contents
(Wopt– 2%, Wopt and Wopt+ 2%). The results show that
specimens compacted at Wopt– 2% exhibited the highest
Mr, followed by the specimen compacted at Wopt, and
specimen compacted at Wopt+ 2% exhibited the lowest
Mr. Specimens compacted at Wopt– 2 was 30% stiffer
than those compacted at Wopt and 40% stiffer than those
compacted at Wopt+ 2%.
Figure 4 shows the variation of the Summary Resil-
ient Moduli (SRM) with compaction water content for
the four materials tested. The SRM at Wopt– 2% is 22%
higher than SRM at Wopt and 35% higher than SRM at
Wopt+ 2% for the GRB and the GNB. The SRM at
Wopt– 2% is 30% higher than SRM at Wopt and 40%
higher than SRM at Wopt+ 2%, for the Basalt. The SRM
at Wopt– 2% is 81% higher than SRM at Wopt and
126% higher than SRM at Wopt+ 2% for the Bandia
limestone. Then, The Bandia limestone is much more
sensitive to water content than the GRB, GNB and Ba-
salt.
Variation of Resilient Modulus values as a function of
dry density was also determined for the GRB and the
GNB. Resilient Modulus values obtained from the bulk
model are shown in Figures 5 and 6 for three selected
stress states representing lower, intermediate and higher
states of stress. At the intermediate stress state, Resilient
Modulus of the GRB increases from 147 MPa to 186
MPa, and from 181 MPa to 222 MPa for the GNB for
relative density ranging from 83% to 119% and 77% to
119%, respectively. At higher stress level, Resilient
Modulus of the GRB increases from 235 MPa to 297
MPa, while the Resilient Modulus of the GNB increases
from 287 MPa to 331 MPa for the GNB and for relative
density ranging from 83% to 119% and 77% to 119%,
respectively. These results show that the Resilient
Modulus increases around 25% for relative density
ranging from 77% to 119% and the variation is more
significant at high stress state than at low stress state.
100
1000
20304050607080 90100200
GRB 0/31.5
GNB 0/31.5
Basalte
Bandia Limestone
y = 20,148 * x^(0,57453) R2= 0,84657
y = 18,915 * x^(0,55711) R2= 0,83708
y = 20,453 * x^(0,64926) R2= 0,86148
y = 49,8 8 * x ^(0,50 487) R2= 0,80112
Resilient Modulus, Mr (MPa)
Confining Pressure, 3 (kPa)
Figure 2. Comparison between Mr of different materials
tested at their optimum water content.
100
200
300
400
500
600
700
2030405060708090100200
Wopt + 2
Wopt
Wopt - 2
y = 20,417 * x^(0,63751) R2= 0,79015
y = 20,453 * x^(0,64926) R2= 0,86148
y = 38,05 * x^(0,54401) R2= 0,84414
Resilient Modulus, Mr (MPa)
Confining Pressure, 3 (kPa)
Figure 3. Effect of water content on the Resilient Modulus
for the Basalt.
5. Regression Analysis of the Resilient
Modulus Test Results
There are several models that were developed for the
estimation of Resilient Modulus of unbound granular
materials [5] and [7]. The Seed model is specified as
bulk model (equation 1) and the Uzan model is known as
universal model (Equation 2)
23
1
 
 
 
kk
d
a
aa
Mrk PPP
(3)
where Mr is the Resilient Modulus,
d is the deviator
stress,
is the bulk stress, Pa is the atmospheric pressure
(used to normalize Mr units), and k1, k2 and k3 are mate-
rial constants.
M. BA ET AL.
Copyright © 2011 SciRes. OJCE
4
0
50
100
150
200
250
300
350
400
GRBGNBBas a l tBan dia li m estone
Wopt - 2
Wopt
Wopt + 2
Internal Summary Resilient Modulus (MPa)
Materials
Figure 4. Variation of the summary resilient modulus with
water content for GRB, GNB, Basalt and Bandia Limestone.
0
50
100
150
200
250
300
350
80859095100105 110 115 120
3=20,7 kPa, d=20,7 kPa
3=69 kPa, d=138 kPa
3=138 kPa, d=414 kPa
Resilient Modulus, Mr (MPa)
Relative D en sity, D r (%)
Figure 5. Effect of relative density on the resilient Modulus
calculated from the power model (GRB).
A new “harmonized” Resilient Modulus test protocol
was developed through the NCHRP project 1-28A [6].
This model called either NCHRP model or MEPDG
model is implemented in the new “Mechanistic-Empiri-
cal Pavement Design Guide” (MEPDG). The new pro-
tocol uses the universal nonlinear model that is applica-
ble for unbound base or su bbase materials Equation (3):
23
11




kk
oct
a
aa
Mrk PPP (4)
where Mr is the Res ili ent Modu lus,
d is the deviator stre ss,
is the bulk stress (=
1 +
2 +
3),
oct is the octahedral
shear stress, Pa is the atmospheric pressure (used to nor-
malize Mr units), and k1, k2 and k3 are mat erial constants.
0
50
100
150
200
250
300
350
8090100 110 120
3=21,7 kPa, d=21,7 kPa
3=69 kPa, d=138 kPa
3=138 kPa, d=414 kPa
Resilient Modulus, Mr (MPa)
Rel ati ve De ns i ty, Dr (%)
Figure 6. Effect of relative density on the resilient modulus
calculated from the power model (GNB).
In this paper, these three models were used to charac-
terize the Resilient Modulus of the investigated aggre-
gate base courses. Regression analysis was conducted to
evaluate the material constants k1, k2 and k3. The GRB,
GNB and the Basalt are compacted at Wopt– 2% and
98% of the maximum dry unit weight, while the Bandia
limestone is compacted à Wopt– 2% and 95% of the
maximum dry unit weight. Results of the statistical
analysis are summarized in Table 2. The coefficient of
determination (R2) was calculated for each sample tested
to provide information about the regression analysis.
Figures 7-10 represent the variation of measured Re-
silient Moduli with the predicted Resilient Moduli from
Seed, Uzan and NCHRP models for BAN_5.80_1956,
GNB0/31.5_2.08_1921, BAS_3.90_2417 and GRB
0/31.5_00_2042 samples. These results show that the
Uzan and NCHRP models are more suitable to predict
the Resilient Modulus of the aggregates tested.
6. Conclusions
Repeated load triaxial test was conducted on four differ-
ent aggregates collected from different sites within
Senegal (West Africa) in order to determine the Resilient
Moduli of these aggregates. Aggregate specimens were
subjected to Resilient Modulus test in accordance with
the NCHRP project 1-28A [6]. Tests results showed that
the Bandia limestone exhib it the higher Resilien t Modu li,
followed by the Basalt and the GNB and GRB. Test re-
sults showed also that the Resilient Modulus is signifi-
cantly affected by the water content for the limestone and
less affected by water content for the GNB, the GRB and
the basalt tested. Specimens compacted with different
density showed that the Resilient Modulus increases
M. BA ET AL.
Copyright © 2011 SciRes. OJCE
5
Table 2. Results of the statistical analysis from Seed, Uzan and NCHRP models.
Seed model Uzan model NCHRP model
Specimen ID k1 k2 R
2 k1 k2 k3 R
2 k1 k2 k3 R
2
GRB_3.00_2100
GRB_5,28_2136
GRB_2,57_2070
GRB_2,62_2008
GRB_6,33_2039
GRB_00.0_2083
GRB_00.0_2042
143
116
105
92
100
97
93
0.47
0.50
0.51
0.55
0.58
0.53
0.52
0.90
0.96
0.91
0.94
0.97
0.94
0.95
87,486
80,695
68,734
63,488
71,706
62,794
62,002
0.93
0.84
0.95
0.92
0.90
0.96
0.91
–0.36
–0.23
–0.35
–0.28
–0.23
–0.33
–0.27
0.98
0.99
0.99
0.98
0.99
0.99
0.98
1270
1029
918
832
881
841
785
0.86
0.72
0.91
0.84
0.81
0.88
0.85
–0.67
–0.30
–0.64
–0.47
–0.31
–0.52
–0.46
0.99
0.97
0.99
0.98
0.98
0.98
0.97
GNB_2.55_2106
GNB_3,95_2129
GNB_3,81_2088
GNB_2,63_2141
GNB_1,55_2100
GNB_00.0_2087
GNB_00.0_1979
143
99
95
157
125
127
113
0.44
0.51
0.55
0.45
0.47
0.46
0.42
0.90
0.95
0.96
0.96
0.90
0.90
0.83
90,572
67,885
70,862
91,545
72,615
74,979
58,214
0.90
0.89
0.85
0.95
1.00
0.98
1.07
–0.36
–0.28
–0.22
–0.41
–0.41
–0.42
–0.48
0.98
0.99
0.98
0.95
0.98
0.98
0.97
1283
871
848
1258
1033
1113
926
0.79
0.81
0.79
0.89
0.95
0.91
0.93
–0.57
–0.44
–0.34
–0.75
–0.74
–0.79
–0.78
0.96
0.99
0.97
0.95
0.98
0.98
0.93
BAS_2.15_2352
BAS_5,55_2254
BAS_3,90_2417
BAS_3,20_2364
BAS_3,14_2198
BAS_1,99_2294
BAS_3,32_2261
216
134
149
143
135
146
148
0.37
0.58
0.53
0.46
0.56
0.46
0.51
0.93
0.97
0.94
0.90
0.95
0.93
0.95
122,310
83,682
93,717
90,802
85,768
94,089
97,762
1.00
1.09
1.00
0.92
1.03
0.97
0.97
–0.46
–0.38
–0.32
–0.38
–0.34
–0.37
–0.35
0.97
0.98
0.96
0.98
0.98
0.96
0.96
2079
1102
1224
1294
1183
1339
1347
0.78
1.04
0.93
0.86
0.92
0.89
0.80
–0.75
–0.64
–0.52
–0.71
–0.54
–0.64
–0.42
0.94
0.97
0.95
0.98
0.96
0.95
0.94
BAN_5.80_1956
BAN_7,80_2070
BAN_7,53_1963
BAN_8,86_1973
309
229
143
100
0.25
0.49
0.49
0.68
0.38
0.72
0.81
0.95
109,852
133,017
70,485
63,570
1.29
1.05
1.20
1.13
–0.81
–0.53
–0.55
–0.36
0.97
0.98
0.98
0.99
2390
2097
1131
842
1.13
0.98
1.10
1.08
–1.45
–0.96
–0.95
–0.62
0.91
0.96
0.96
0.99
100
200
300
400
500
600
700
800
900
100 200 300 400 500 600 700 800 900
BAN_5,80_1956
Seed
Uzan
NCHRP
Predicted Resilient Moduli, Mrp (MPa)
Mesured Resilient Moduli, Mrm (MPa)
Figure 7. Measured vs. predicted Resilient Moduli from
Seed, Uzan and NCHRP models (BAN_5.80_1956 sample).
50
100
150
200
250
300
350
400
50100 150 200 250 300350 400
GNB 0/31.5_2.08_1921
Dunlap
Seed
Uzan
NCHRP
Predicted Rfesilient Moduli, Mrp (MPa)
Measured Resilient Moduli, Mrm (MPa)
Figure 8. Measured vs. predicted Resilient Moduli from
Seed, Uzan and NCHRP models (GNB 0/31.5_2.08_1921
sample).
M. BA ET AL.
Copyright © 2011 SciRes. OJCE
6
100
200
300
400
500
600
700
100200 300 400 500 600 700
BAS_3.90_2417
Seed
Uzan
NCHRP
Predicted Resilient Moduli, Mrp (MPa)
Measured Resilient Moduli, Mrm (MPa)
Figure 9. Measured vs. predicted Resilient Moduli from
Seed, Uzan and NCHRP models (BAS_3.90_2417 sample).
50
100
150
200
250
300
350
400
50100 150 200 250 300 350 400
GRB 0/31.5_00_2042
Seed
Uzan
NCHRP
Predict ed Resi l ie nt Modul i, Mrp (M Pa)
Measured Resilient Moduli, Mrm (MPa)
Figure 10. Measured vs. predicted Resilient Moduli from
Seed, Uzan and NCHRP models (GRB 0/31.5_00_2042
sample).
around 25% for relative density ranging from 77% to
119% and the variation was more significant at high
stress states than at low stress states.
7. Acknowledgements
The authors would like to acknowledge the Geo-Eng-
neering research group of the University of Wiscon-
sin-Madison for their guid ance and valuable input in this
research project; and the “Entreprise Mapathé NDI-
OUCK” for supporting the high price shipping of aggre-
gates from Senegal to United States of America.
8. References
[1] E. J. Yoder and M. W. Witczak, “Principles of Pavement
Design,” 2nd Edition, Wiley, New York, 1975.
[2] M. Fall, A. Sawangsuriya, C. H. Benson, T. B. Edil and P.
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(West Africa),” Geotechnical and Geological Engineer-
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[3] R. G. Hicks and C. L. Monismith, “Factors Influencing
the Resilient Properties of Granular Materials,” Ph.D.
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[4] F. Lekarp, U. Isacsson and A. Dawson, “State of the Art. I:
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[5] H. B. Seed, F. G. Mitry, C. L. Monismith and C. K. Chan,
“Prediction of Flexible Pavement Deflections from Labo-
ratory Repeated Load Tests,” National Academy of Sci-
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[6] NCHRP, “Laboratory Determination of Resilient Modu-
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Highway Research Program (NCHRP), Transportation
Research Board of National Academies, Washington,
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[7] J. Uzan, “Characterization of Granular Material,” Trans-
portation Research Board, Washington, 1985, pp. 52-59.