Farhad Salour Doctoral Thesis

5.3.
 
Permanent deformation of unbound materials 
The plastic response and consecutive accumulation of permanent deformation of 
unbound materials under repetitive traffic loading is also a complex phenomenon and 
depends on many factors with different degrees of significance. The main influential 
factors are: stress state, number of load cycles, reorientation of principal stresses, 
loading history, moisture content, grain size distribution, degree of compaction and 
fines content (Lekarp et al., 2000). 
The permanent deformation development in fine-grained materials under repeated 
traffic loads can be mainly associated with three different mechanisms. These 
mechanisms are the cumulative compaction, cumulative plastic shear strain (distortion 
of material fabric) and cumulative consolidation (Li and Selig, 1996; Werkmeister et al. 
2004). The development of permanent strains of unbound materials under repeated 
cyclic loads can be described using the shakedown concept (Sharp and Brooker, 1984). 
According to Werkmeister et al. (2001 and 2004) the permanent strain accumulation of 
unbound materials under repeated cyclic loads can be classified into three categories, 
namely; Range A: the plastic shakedown, Range B: the intermediate response or plastic 
creep and Range C: the intermediate collapse (Figure 14). 
Figure 14.
Theoretical behaviour of unbound materials under repeated cyclic load 
(modified after Werkmeister et al., 2001). 
From a pavement engineering perspective, unbound layers should preferably not 
undergo stress levels higher than the plastic shakedown limit. Under this condition, the 
permanent strains would cease after a sufficient number of load applications and only 

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29 
minor accumulation of permanent deformation would take place. The exposure of 
unbound materials to stress levels higher than the plastic shakedown limit (Range B) 
should be restricted to only occasional cases and stress level higher than the plastic 
creep (Range C) should never occur as it can cause severe rutting and structural failure 
in the pavement system (Erlingsson and Rahman, 2013). 
Modelling permanent deformation of pavement unbound materials 
In practice, the permanent deformation characterization of pavement unbound 
materials is generally studied by conducting RLT tests. However, due to the time 
consuming nature of permanent deformation tests, it has been less studied compared to 
the resilient behaviour of the material. 
In spite of this, over the past few years several research has been conducted to develop 
test procedures and outline prediction models for permanent strain characterization of 
pavement unbound materials through RLT tests. The permanent deformation models 
can be generally divided into two different categories: empirical relationships describing 
the influence of the number of load applications or level of stress (or a combination of 
them), and elastoplastic models (Lekarp et al., 2000; Hornych and El Abd, 2004). Most 
of the established models were originally developed based on tests from single stage 
RLT test procedures. These models can be generally described as follows: 
 
)
,
,
(
)
(
ˆ
2
1
r
p
q
p
f
N
f
N



[6] 
where 
N
is the total number of load cycles, 
p
is the hydrostatic stress, 
q
is the deviator 
stress. 
In the single stage RLT based models a certain number of load applications are applied 
only under a constant cyclic stress condition. However, the material in the field 
generally experiences traffic load pulses with different magnitudes. Thus, a more 
realistic and practical simulation approach would be to conduct a series of different 
stress paths on a single specimen (multistage RLT tests). Modelling the permanent 
deformation behaviour of the material to cover the entire range of the stress paths 
therefore requires certain modification of the discussed models to accommodate the 
time-hardening concept (Lytton et al., 1993; Erlingsson and Rahman, 2013). 
In the time-hardening concept (Figure 15), the accumulated permanent strain from the 
preceding loading history is used to calculate the number of load cycles required so that 
the same amount of accumulated permanent strain in the current stress path (stress path 
i
) is obtained. This is called the equivalent load cycle (
eq
i
N
). The 
eq
i
N
for a certain stress 
path 
i
is used to transform the total number of load cycles (
N
) from the beginning of 
the test so the stress path 
i
alone attain the equal deformation that is accumulated from 
all the preceding stress paths. The 
eq
i
N
is then used to adjust the total number of load 

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30 
cycles,
N
, applied from the beginning the test to calculate the effective number of load 
cycles (
eq
i
i
N
N
N



1
). 
1

i
N
is the total number of load cycles at the end of the (
1

i
)
stress path. The subscript 
i
refer to the 
th
i
stress path. Thus, using this concept, it is 
possible to model the whole range stress paths from the multistage RLT tests (Figure 
15).