1250
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
Load = 80 kN
Rutting = 0.075 m
Rutting = 0.15 m
(a)
(b)
(c)
h (m)
C
u
(kPa)
Figure 2. (a) Base layer thickness as a function of subgrade undrained shear strength, number of load application (80 kN) and rut depth (Giroud and
Noiray 1981); (b) cyclic load used for finite element modelling; (c) geometry of finite element model.
Figure 2a shows a chart proposed by Giroud and Noiray
(1981) to select the required thickness of un-reinforced granular
layer, which provides an allowable rut depth on unpaved roads.
This chart shows that even for low trafficked road it is required
a ganular thickness larger than 1 m when subgrade soil presents
undrained shear strenght less than C
u
= 20 kPa, and number of
load application N is greater than 10000. With more greater N
and less values of Cu, base layers tend to be too large. In these
cases the settlements after construction stage and the
consolidation periods may be unacceptable.
3 MODELLING OF SOFT SUBGRADE
3.1 Introduction
A theoretical procedure to estimate the structural response of a
pavement founded over a deep soft subgrade is presented,
focusing on vertical stresses and strains within the subgrade.
For this purpose a mechanistic finite element model has been
performed with the program Plaxis v8.2, considering the
pavement structure depicted in Figure 2c. The analysis is
separately presented according to static and cyclic load
conditions, and basically is focused on the influence of subgrade
behavior. Accordingly only stresses and strains regarding
subgrade layers will be analyzed.
3.2 Geometry and general inputs
The pavement modelling is carried out with axisymmetric
conditions for a multi-layered system composed by an asphalt
surface layer, followed by two unbound granular layers as base
and subbase. A subgrade composed by natural soil is adopted
below pavement structure considering the water table at 1 m
depth. Vertical boundaries are restrained for lateral
displacements, while the bottom horizontal boundary is full
restrained for both lateral and vertical displacements. It was
adopted an extra-fine mesh of 15-noded elements close to upper
part of the model axis, where loading is applied. All of materials
constituting the pavement superstructure are modeled as linear
elastic, so that the required parameters are only the young
modulus E and Poisson’s ratio
. In Table 1 are outlined the
parameters of pavement superstructure.
Table 1. Parameters of asphalt layer and unbound granular layers
Thickness
E
Layer
m
kPa
Asphalt
0.1
1.3·10
6
0.2
Base
0.25
1.5·10
5
0.33
Subbase
0.5
1·10
5
0.33
On the other hand, isotropic hardening soil behavior is
considered for the subgrade, which is governed by a stress-
dependent stiffness that is different for both virgin loading and
unloading-reloading process (Schanz 1998). The hardening soil
model may be considered as an extension of the well known
hyperbolic model (Duncan and Chang 1970), owing to the use
of plasticity theory and yield cap surface to account for the
hardening effect produced by isotropic compression strains. The
parameters adopted for the soft subgrade soil are presented in
Table 2., and its characterization is in accordance with the
stiffness increase due to the typical small strains that affects
pavement performance.
Table 2. Parameters of subgrade soil
Parameter
Symbol Values
Unit
Unit weight
16.5
kN/m
3
Small Strain stiffness
G
0
ref
45000
kN/m
2
Shear strain at 0.7G
0
0.7
ref
1.75·10
-4
-
Poisson's ratio
ur
0.3
-
Triaxial compression stiffness
E
50
ref
10000
kN/m
2
Primary oedometer stiffness
E
oed
ref
10000
kN/m
2
Unloading - reloading stiffness
E
ur
ref
20000
kN/m
2
Rate of stress-dependency
m
0.85
Cohesion
c’
5
kN/m
2
Friction angle
'
10
o
Failure ratio (q
f
/q
asymptote
)
R
f
0.9
-
Stress ratio in primary compression K
0
nc
0.83
-
The parameter G
0
and
0.7
are used in order to consider the
variation of moduli at small strains, as describe below.
The load condition has been evaluated by means of a static
surcharge, which represents the application of a single axle load
of 13 t, with a contact area of 0.15 m radius, so that maximum
pressure on the surface reaches up to 900 kPa. The cyclic
loading conditions have been performed considering a
waveform pattern in order to simulate the accumulation of
permanent deformation. Thereby, it is assumed a stress pulse
over the pavement surface in the form of a haversine function,
which may be defined by the use of an equivalent pulse time of
0.1 second, associated to a vehicle speed of 30 km/h (Barksdale
1971). Figure 2b shows the cyclic load pulse adopted.
3.3 Modelling procedure
The calculation consists of one stage that is related to the
pavement construction, where unbound granular and asphalt
layers are laid out over the subgrade soil. Following stage
consist of cyclic load application, in order to simulate the action
of traffic. Initially, no drained condition is assumed for two
stage considered. After the load application a consolidation
phase is included to take account of the final stress state and to
evaluate the time of the pore-pressure dissipation.
The effects of cyclic loading on the pavement behavior are
analyzed in several steps in order to consider the influence of
strain level and the soil damping on the pavement response.
Thus, it is adopted an iterative procedure to consider the
updating of the soil stiffness according to the strain level during
the cyclic loading. This procedure was performed through the
stoppage of the loading process once 10 cyclic of load repetition
completed, determining the average values of shear strains
related to the subgrade layers. In order to update the actual
