Farhad Salour Doctoral Thesis

5.2.
 
Resilient modulus of unbound materials 
The stiffness property of unbound granular materials and subgrade soils is widely 
characterized using the resilient modulus parameter (
R
M
). This parameter is generally 
defined using Repeated Load Triaxial (RLT) tests. In conventional resilient modulus test 
using RLT testing, the material is compacted into cylindrical specimens at the degree of 
compaction and moisture contents occurring in the field. The specimen that is 

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enwrapped in a latex membrane is then confined by pressurising the test chamber using 
air, water or oil and exposed to cyclic axial deviator stresses. Usually, series of 
computer-controlled cyclic axial deviator stresses are applied to the specimen using the 
piston attached to the top loading platen, and the axial deformation is recorded. Axial 
deformations are either measured using fixed gauges on the loading piston and out of 
the pressurised chamber or using gauges that are directly mounted on the specimen. 
Figure 12 shows the principles of the resilient modulus test suing RLT test. 
Figure 12
. Principles of the RLT test. 
Using the cyclic deviator stress (
d

or 
q
) and the measured axial recoverable strain (
r

), 
the resilient modulus is then defined as: 
r
d
R
M



[2] 
In a constant confined RLT test, the deviator stress (
d

) is the cyclic axial stress applied 
on the specimen in addition to the constant confinement pressure of the triaxial 
chamber (
3
2





c
) that is applied to the specimen in all the directions. 
Above all the other influential factors (discussed later), the resilient modulus is highly 
dependent on the state of stress of the material. The state of stress of the material is 
usually expressed by the bulk stress (

), where 
)
(
3
2
1







or the mean normal 
stress (
p
) where 
3


p
. The 
1

, 
2

and 
3

are the principal stresses. 
Stress dependent behaviour of pavement unbound material from laboratory measurements
 
There are many factors that influence the mechanical properties of pavement unbound 
materials and subgrade soils. Lekarp et al. (2000) conducted an extensive literature 
review on the resilient modulus of unbound materials and the different factors that can 
affect the resilient modulus. According to this survey the resilient modulus of unbound 
materials may to different degrees be affected by the stress state, material density, grain 

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22 
size distribution and particle shape, stress history and moisture content. From the 
literature it is known that the material stress state is certainly the most significant factor 
that can affect the resilient modulus property of unbound materials (Hicks and 
Monismith, 1971; Rada and Witczak, 1981; Uzan, 1985; Kolisoja, 1997). Many studies 
on the mechanical response of unbound materials have shown that the resilient 
modulus property is highly dependent on the confinement pressure and sum of the 
principal stresses. An increase in confining pressure and the sum of the principal 
stresses result in a considerable increase in the resilient modulus. However, the deviator 
or the shear stress has a much less significant influence on the material stiffness. In 
coarse-grained granular materials, change in deviator stress had no or insignificant 
influence on the stiffness of the material (Lekarp et al., 2000). The effect of the deviator 
stress on the resilient modulus seemed to be very much dependent on the material type, 
compaction and the deviator stress level itself. In a study conducted by Hicks and 
Monismith (1971) minor softening behaviour of the material was observed at low stress 
levels while minor hardening behaviour was observed at higher stress levels. Hicks 
(1970) stated that the resilient modulus is in practice independent of the deviator stress 
level if no plastic deformation is experienced. This implies that the resilient modulus 
stress-dependent behaviour of coarse-grained granular materials can sufficiently be 
captured by only using the first stress invariant. 
In fine-grained materials and subgrade soils, the resilient modulus usually decreases with 
increase in the deviator stress. The softening behaviour in the material due to increase 
in the deviator stress level is assumed to be related to increase in the shear stress, which 
softens the material and thus yields to a lower resilient modulus (Drumm et al., 1990; Li 
and Selig, 1994; Muhanna et al., 1999). 
The significant impact of the stress state on the resilient modulus of unbound materials 
has resulted in the development of a number of constitutive models that mathematically 
describe the material stress-strain relationship. Most of these models describe the 
resilient modulus stress dependency using different stress state variables (Lekarp et al., 
2000) and are mainly developed through curve fitting and nonlinear least square 
regression methods using RLT test data. A comprehensive analysis and evaluation of 
the resilient modulus models can be found in Andrei (2003), Lekarp et al. (2000), Rada 
and Witczak (1981) and Kolisoja (1997). 
Among all the available stress dependent resilient modulus models, the generalized 
constitutive model proposed in the