Stiffness and permanent deformation characteristics of open-graded unbound granular materials

1. 151
Bearing Capacity of Roads, Railways and Airfields – Loizos et al. (Eds)
© 2017 Taylor & Francis Group, London, ISBN 978-1-138-29595-7
Stiffness and permanent deformation characteristics of open-graded
unbound granular materials
M.S. Rahman, S. Erlingsson & F. Hellman
Pavement Technology, VTI, Linköping, Sweden
ABSTRACT: This paper presents the investigation of the deformation characteristics of two Open-
Graded (OG) Unbound Granular Materials (UGMs) that are generally used in permeable pavement
structures. Based on multistage Repeated-Load Triaxial (RLT) tests, the stiffness and resistance against
Permanent Deformation (PD) of these materials were compared to their well graded (standard) counter-
parts. The OG UGMs showed similar stiffness characteristics as standard UGMs. On the other hand, the
resistance against PD was slightly worse than the standard UGMs in a relatively dry state. However, the
OG UGMs showed less sensitivity to moisture variation, yielding similar performance to that of standard
materials at higher moisture content. The parameters of a stiffness model and a PD model were evaluated
for these materials which may be used for prediction of rutting, estimating bearing capacity and for layer
thickness design, using any suitable pavement design software.
types are built where the OG base and sub base lay-
ers allow for the movement of water, act as a water
reservoir for the trees and vegetation, and allow
their roots to grow and penetrate (Pratt, 1990; Lar-
son, 1990). Permeable pavements are usually built
with interlocking paving blocks or porous asphalt
with OG UGM layers underneath and are mostly
utilized in parking lots or low trafficked areas. For
the base and sub base layers several permeable and
structural or skeletal soils have been proposed or
utilized to meet the drainage requirements while
maintaining the load bearing capacity of the struc-
ture. The OG UGMs generally refer to the parti-
cle size gradation where the fine particles up to a
certain size have been removed to create voids to
allow for the passage of water. Since the fine parti-
cles are absent from the material, its density is less
than that of the well graded material. As a result,
it is presumed that these kinds of materials may
perform worse than the well graded counterparts
due to lack of skeletal support from the fine par-
ticles. The existing design guidelines for standard
materials therefore need to be revised when using
OG materials. Since practical experience regarding
the field performance of OG materials is relatively
limited, it is necessary to carry out studies on the
mechanical properties of these materials. Today’s
demand for increased traffic load and load bearing
capacity necessitates the development of a robust
analytic design approach. For this it is necessary to
formulate reliable predictive models to character-
ize the deformation behavior of OG UGMs that
can be used for the design of pavements.
1 INTRODUCTION
Pavements are generally composed of several lay-
ers. The functional performance of a pavement
structure greatly relies on the selection of materials
and thicknesses of the different layers. Structural
design of pavements involves selection of materi-
als and thicknesses of the different layers based
on load carrying requirements, topography and
climatic conditions, bearing capacity of the exist-
ing sub grade, availability of the materials and eco-
nomic considerations. The base and subbase layers
of pavements are most commonly constructed of
Unbound Granular Materials (UGMs) of well
graded rock aggregates with dense configuration to
provide the desired stiffness and resistance against
permanent deformation. However, these layers of
well graded aggregates are relatively impermeable
to water and therefore excess water may get trapped
inside the structure, which can accelerate damage
and premature failure of the pavement (Hajek,
et al., 1992). Another issue is that, due to increased
urbanization and construction of pavements, the
proportion of impervious land surface is increas-
ing, which poses a challenge for storm water
management as well as hampering the growth of
urban trees and vegetation (Ahmed et al., 2016).
One possible approach to solve the issue with
water trapping is to build pavements with Open-
Graded (OG) drainage layers so that the pavement
cannot retain any water (Hajek, et al., 1992). To
address the storm water management and vegeta-
tion growth issues permeable pavements of various

2. 152
This paper presents a comparative study of
the stiffness properties and Permanent Deforma-
tion (PD) behavior of some OG UGMs against
well graded UGMs of similar origin (referred to
here as standard or reference material), based on
MultiStage (MS) Repeated-Load Triaxial (RLT)
tests. The aim was to implement the findings and
enhanced understanding of the material behavior
to improve or modify the existing design guidelines
in future. Furthermore, two existing simple models
were implemented to characterize the stiffness and
PD behavior of these materials and thus a set of
material parameters was generated. The objective
was to come up with a simple analytical design tool
which may be used for the layer thickness design and
performance prediction of the pavement structure.
2 PROPERTIES OF OG UGMS
OG UMGs are UGMs where the fine portions up
to a certain size are absent from the grading. The
objective is to create voids in the aggregate assem-
bly so that water can easily penetrate and flow
through. Selection of the Particle Size Distribution
(PSD) of the materials is governed by the desired
use of the materials and infiltration capacity
requirements. Figure 1 shows a typical distribution
of hydraulic conductivities for a UGM with differ-
ent PSDs as determined by the Swedish Cement
and Concrete Institute (CBI). In the figure, for
example, 2/32 refers to the minimum particle size/
maximum particle size in millimeters.
For UGMs, it is generally accepted that the PSD
with a Fuller curve having n = 0.45 yields the dens-
est aggregate assembly. Since for the OG UGMs the
fine portion of the particles is absent, the density
of the aggregate assembly is comparatively lower.
It is therefore likely that the mechanical resistance
of OG materials will be inferior. However, accord-
ing to the Dominant Aggregate Size range (DASR)
concept, the load bearing skeleton of a UGM
assembly is comprised of particles of a certain size
range. Particles smaller than that size simply fill the
voids with no significant contribution to the load
bearing capacity. In that regard, OG UGMs may
possess similar mechanical strength as standard
ones if fines are removed up to a certain size in
compliance with the DASR concept.
The deformation characteristics of OG UGMs
are similar to those of well graded UGMs. The
total deformation due to compressive cyclic stresses
in a UGM consists of two parts: (a) elastic or recov-
erable or Resilient Deformation (RD) and (b) irre-
versible or plastic or Permanent Deformation (PD).
For a single load pulse, this can be expressed as:
ε ε εtot r p= + (1)
where, εtot is the total axial strain, εr is the axial
resilient strain and εp is the axial permanent strain.
Usually, the resilient strain is much larger than the
permanent strain (Erlingsson and Magnusdottir
2002, El Abd et al., 2005). Both kinds of defor-
mation in UGMs are non-linear stress depend-
ent (Kolisoja 1997, Lekarp 1999, Englund 2011).
Deformations occurring in a UGM assembly have
been attributed to the elastic deformation, bend-
ing, breaking, crushing, sliding and rolling of the
individual particles (Lekarp et al., 2000).
2.1 RD characteristics
The resistance of a UGM against the RD is
defined using the resilient modulus (or the resilient
stiffness), MR, which is an estimate of the stiffness
modulus of the specimen for rapidly applied loads,
expressed as (Huang 2004):
MR
d
r
=
σ
ε
(2)
where σd (or q) is the cyclic deviator stress. The
resilient strain, εr, is taken after several load rep-
etitions when the deformations are stabilized. The
MR is dependent on the state of stress, measured
as the sum of the principal stresses, called the bulk
stress, θ = σ1 + σ2 + σ3 or the mean normal stress
or the hydrostatic stress, p = θ/3. Other factors
that affect the MR are density, grading, moisture
content, stress history, aggregate type and shape
(Lekarp et al., 2000).
The variation of the MR with θ can be expressed
with the well-known k-θ model (Seed et al., 1962,
Hicks and Monismith 1971, Uzan 1985) in its
dimensionless form:
M k p
p
R a
a
k
=



1
2
θ
(3)Figure 1. Hydraulic conductivities of UGMs with dif-
ferent PSDs.

3. 153
where k1 and k2 are material parameters and pa
is a reference pressure usually taken equal to the
atmospheric pressure as 100 kPa.
The MR is an important parameter for pave-
ment design. A higher MR is desirable for better
resistance against fatigue cracking of the asphalt
concrete layer. Furthermore, a higher MR provides
better downward spreading of the load and thus
reduces stresses in the lower layers.
2.2 PD characteristics
The PD in UGMs accumulates with the number
of load applications and contributes to the rut-
ting in pavements. The PD is dependent on stress
levels, stress history, number of load cycles, degree
of compaction, particle size distribution, moisture
content (w) and aggregate type (Lekarp, 1999).
Based on the shakedown theory, Dawson and Well-
ner (1999) and Werkmeister et al., (2001) have iden-
tified that the accumulation of the PD in UGMs
falls within the three shakedown ranges, depend-
ing on stress levels (Figure 2). Range A occurs for
relatively low stress levels when permanent strain
accumulates up to a finite number of load appli-
cations, after which the response becomes entirely
resilient with no further permanent strain. For
stress levels higher than this, Range B occurs where
the accumulation of permanent strain continues at
a constant rate (per cycle). When stress levels are
even higher, Range C behavior is observed where
the permanent strain accumulates at an increasing
rate that may eventually lead to failure.
Several models are available in the literature to
characterize the PD behavior of UGMs. The fol-
lowing model proposed by Rahman and Erlings-
son (2015) was used for this study:
( )ˆ fbS
p fN aN Sε = (4)
where ( )ˆp Nε is the accumulated permanent strain,
Nisthetotalnumberof loadcycles,aandbareregres-
sion parameters associated with the material and the
term Sf takes into account the effect of stress state on
permanent deformation accumulation given as:
S
q
p
p
p
f
a
a
=








α
(5)
where α is a parameter obtained from regression
analysis. The advantages of this model are that a) it
contains only three material parameters, b) unlike
some other models, it does not require the shear
strength parameters, and c) it directly utilizes the
applied stress level as a predicting variable. These
simplify its application and it is convenient to use
for tests with a series of moisture contents. In this
study, this model was used for MS RLT tests by
applying the time hardening formulation proposed
by Erlingsson and Rahman (2013).
3 LABORATORY TESTING
This study was based on RLT tests in the labora-
tory. The advantages of the RLT tests are that it is
a widely used and convenient approach that reveals
a great deal of information regarding the material
behavior. The RLT tests were conducted in accord-
ance with the European standard EN-13286-7
(CEN, 2004a). The MS loading approach was pre-
ferred because (a) it allows for a more comprehen-
sive study of the PD behavior for a large number
of stress conditions, (b) it includes the effect of
stress history, and (c) all of these can be attained
using a single specimen with reduced effort.
The size of the cylindrical specimens was
150 mm in diameter and 300 mm in height. The
tests were carried out applying a set of different
stress paths according to the standard referred
to as ‘Low Stress Level’ (LSL) as presented in
Table 1. Each of the stress paths was applied for
10,000 cycles with a frequency of 10 Hz (Havers-
ine pulse) with no rest period. The total number of
load cycles applied during the tests were 300,000
(30 stress paths). The tests were performed under a
free drainage condition.
4 MATERIALS TESTED
The UGMs used for this study were assorted
from three different origins. Material 1 was a
Figure 2. Different types of PD behaviour, depending
on stress level.

4. 154
crushed rock aggregate commonly employed in
Swedish road construction. Two different PSDs
of this material were studied. The first one was a
standard PSD referred to here as ‘Material 1’ and
the second one a OG variant referred to here as
‘Material 1 OG’ where the fine particles below
2 mm were essentially absent from the sample. The
tests on these materials were conducted at identi-
cal moisture content regardless of their optimum
moisture contents (wopt). The second UGM was a
recycled material referred to here as ‘Material 2’
and ‘Material 2 OG’ where, for the OG variant,
fines below 1 mm were removed from the sample.
These materials were tested and compared at their
individual wopt. The third material, ‘Material 3’,
was also a crushed rock aggregate used in Swedish
road construction. This was tested at two different
moisture contents identical to those of Material 1
and was included in this study to serve as a ref-
erence. The properties of these materials are pre-
sented in Table 2. The PSDs are shown in Figure 3.
Figure 3. Particle size distributions.
Table 2. Material properties.
Material wopt [%]
Specific
Gravity
Test condition
Maximum
dry density
[Mg/m3
] w [%]
Degree of
saturation [%]
Dry
density
[Mg/m3
]
Void
ratio
Material 1
(crushed rock)
5.5 2.64 2.11 1 9.1 2.00 0.29
3.5 31.9 2.00 0.29
Material 1 OG
(crushed rock)
3.5 2.64 1.96 1 5.9 1.84 0.45
3.5 21.3 1.84 0.45
Material 2
(recycled)
11.9 2.22 1.74 11.9 95.8 1.74 0.30
Material 2 OG
(recycled)
4.1 2.22 1.52 4.1 19.8 1.52 0.47
Material 3
(crushed rock)
6.9 2.68 2.35 2 26.7 1.44 0.23
4 53.5 2.23 0.23
Table 1. Stress levels used for the MS RLT tests (LSL from the European standard).
Sequence 1 Sequence 2 Sequence 3 Sequence 4 Sequence 5
Confining
stress, σ3
kPa
Deviator
stress, σd
kPa
Confining
stress, σ3
kPa
Deviator
stress, σd
kPa
Confining
stress, σ3
kPa
Deviator
stress, σd
kPa
Confining
stress, σ3
kPa
Deviator
stress, σd
kPa
Confining
stress, σ3
kPa
Deviator
stress, σd
kPa
constant min max constant min max constant min max constant min max constant min max
20 0 20 45 0 60 70 0 80 100 0 100 150 0 100
20 0 40 45 0 90 70 0 120 100 0 150 150 0 200
20 0 60 45 0 120 70 0 160 100 0 200 150 0 300
20 0 80 45 0 150 70 0 200 100 0 250 150 0 400
20 0 100 45 0 180 70 0 240 100 0 300 150 0 500
20 0 120 45 0 210 70 0 280 100 0 350 150 0 600

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The modified Proctor method in accordance with
the European standard EN 13286-2 (CEN, 2004b)
was used to determine the maximum dry density
and wopt of the materials. The specimens were pre-
pared using a vibrocompactor. Some of these tests
were replicated to take into account any experi-
mental dispersion.
5 RESULTS AND DISCUSSION
From the RLT tests, the MR and the accumulated
permanent strain for each specimen were calcu-
lated. Figure 4(a) presents the measured MR val-
ues as a function of θ for all the tests. Figure 4(b)
shows the modelled results using the k-θ model
calibrated from the RLT test data. From this fig-
ure, it is observed that the OG variant of Mate-
rial 1 demonstrates slightly higher stiffness values.
Furthermore, when w was increased from 1% to
3.5%, the MR values of the material with stand-
ard PSD decreased slightly, whereas the MR val-
ues of the OG variant were essentially unaffected.
For Material 2, the MR values of the two variants
were identical; however, it should be noted that the
specimen with standard PSD had a much higher
w (11.9% compared to 4.2% for the OG variant).
Although Material 3 at w = 1% showed the high-
est MR values, it was reduced more significantly
compared to Material 1 when w was increased to
3.5%. The probable reason was that Material 3 had
more fine fractions which contributed to the lubri-
cation effect of water, thus decreasing the MR of
the material.
The accumulated permanent strain as a function
of N is plotted in Figure 5 for the individual tests.
This also includes the fitted model presented in Figure 4. Resilient moduli: (a) measured, (b) modelled.
Figure 5. Accumulated permanent strain.
Equation 4, calibrated using the test data. Analyses
of these plots show that at w = 1%, Material 1 dem-
onstrated a lower PD compared to Material 1 OG.
On the other hand, at w = 3.5%, Material 1 showed
an identical PD to that of Material 1 OG. In fact,
similar to the stiffness behavior, the PD perform-
ance of the OG variant was essentially unaffected
by moisture. At their individual wopt, Material 2
OG showed better resistance against PD compared

6. 156
to Material 2, while it should be noted that the wopt
of Material 2 OG was also much lower. Material
3, again in terms of PD, showed the similar high
sensitivity to moisture as in the case of MR val-
ues. It showed the highest resistance against PD at
w = 1% while its resistance against PD was the low-
est when w was 4%. Again, in this case the prob-
able explanation for this behavior was the relatively
higher amount of fines present in Material 3 which
enhanced the lubrication effect of moisture.
In general, it appears that the OG UGMs did
not perform any worse than the well graded mate-
rials. It also seems that the OG materials were
less sensitive to moisture and as a result they per-
formed relatively better than the reference materi-
als at higher moisture content. For the well graded
materials, the fines might have contributed to the
lubrication effect of water which increased the PD.
The k-θ model and the PD model used in this
study worked quite well for both kinds of mate-
rials, as can be realized from Figures 4 and 5.
The calibrated parameters of these models for
the materials used in this study are presented in
Table 3. The material parameter data obtained
here may be used as a guideline for future studies.
Furthermore, by establishing the relation of these
parameters to moisture, it can be used for predict-
ing the stiffness and PD behavior of the materials
with the seasonal variation of moisture.
6 CONCLUSIONS
The stiffness and PD characteristics of some OG
UGMs were studied by means of MS RLT tests in
the laboratory. This study was limited to 2/32 mm
(minimum/maximum particle size) UGMs where
the fine fraction up to 2 mm was removed from the
samples (Figure 3). Results showed that the stiff-
ness and PD characteristics of these materials were
still comparable to the well graded reference materi-
als. Because of the lack of fines, the OG materials
appeared to be less sensitive to moisture variation
for which they may exhibit more stable behavior
with seasonal variation of moisture and better pro-
tection against frost heaving. This result suggests
the suitability of the 2/32 mm UGMs for use in
drainage layers and in permeable pavements. The
models used for this study were quite well suited to
describe the MR and PD behavior of these materi-
als. Thus the model parameters obtained here may
be used for prediction of rutting, estimating bear-
ing capacity and for layer thickness design using
any suitable pavement design software. Since the
study was limited to RLT tests in the laboratory,
the results obtained here should be further vali-
dated with field studies and large scale tests such
as using a Heavy Vehicle Simulator (HVS). The
RLT test database should be further extended with
tests on more materials and replicate testing. The
study should also be extended to other OG UGMs
with different PSDs, for instance, using 4/32 mm
materials.
ACKNOWLEDGEMENTS
This work was sponsored by the Swedish Trans-
port Administration (Trafikverket). Part of the
tested materials was supplied by NCC (Sweden).
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