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Parameter sensitive analysis of flexible pavement
Article in International Journal of Pavement Research and Technology · November 2016
DOI: 10.1016/j.ijprt.2016.12.001
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Mahadeo Sambhaji Ranadive
Anand B. Tapase
College of Engineering, Pune
Rayat Shikshan Santha's Karmaveer Bhaurao Patil College of Engineering, Satara
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International Journal of Pavement Research and Technology 9 (2016) 466–472
www.elsevier.com/locate/IJPRT
Parameter sensitive analysis of flexible pavement
M.S. Ranadive, Anand B. Tapase ⇑
Department of Civil Engineering, College of Engineering, Pune, Maharashtra, India
Received 21 March 2016; received in revised form 17 October 2016; accepted 2 December 2016
Available online 18 December 2016
Abstract
This paper describes the usefulness of FEM for exploring the parameter sensitive analysis. Using 2D axisymmetric analysis, the critical performance parameters are examined by varying the thickness and material properties of different layers of flexible pavement.
Hypothetical pavement sections are also analyzed with a view to check the sensitivity of horizontal axisymmetric extent and refinement
of mesh. The developed computer program after validation is used to calculate the horizontal tensile strain at the bottom of the bituminous layer (BL) and the vertical compressive strain at the top of the subgrade. These computed strains are incorporated in the fatigue
and rutting criteria recommended in Indian Road Congress (IRC: 37-2012) to estimate the pavement life for various hypothetical conditions. Tensile strain at the bottom of BL and compressive strain on top of the subgrade decreases with an increase in the thickness of
BL, which results in increase of fatigue and rutting lives. An increase in thickness of the base layer and the increase in its elastic modulus
reduces the damage due to rutting, while it has less effect on damage due to fatigue. Such type of analysis proves beneficial for designing a
pavement, keeping equilibrium between fatigue and rutting lives.
Ó 2016 Chinese Society of Pavement Engineering. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND
license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Flexible pavement; Parametric study; Finite element method
1. Introduction
The application of direct or indirect empirical approach
in the current design procedures, results either in premature
failure of the pavement or building up of uneconomical
pavement sections. The relationship between design inputs
and pavement failure is applied through experience, experimentation or a combination of both, which is limited to a
certain set of environmental and material conditions [1,2].
A good pavement design is one that provides the expected
performance with appropriate economic consideration, so,
here the need arises to find an economical alternative in the
⇑ Corresponding author.
E-mail
addresses:
msrtunnel@yahoo.co.in
(M.S. Ranadive),
tapaseanand@gmail.com (A.B. Tapase).
Peer review under responsibility of Chinese Society of Pavement
Engineering.
form of analytical tool which can accommodate the details
of the complex pavement system [3].
Application of such enhanced analytical tool can prove
to be beneficial to predict the performance of pavement
without actual construction or even by surpassing the
expensive and time consuming laboratory or in situ tests,
for various thicknesses and material properties of different
component layers instead of relying on CBR values. In this
connection, the application of the versatile finite element
method (FEM) towards the design of flexible pavement
holds a perfect assurance. As FEM is not constrained to
two dimensional axisymmetric conditions, if required
FEA can be easily used for two-dimensional plane stress/
strain as well as more rigorous three dimensional finite
element analysis for further extension of work [4]. Axisymmetric modeling predicts pavement behavior using a 2D
mesh revolving around a symmetric axis by assuming identical stress states exist in every radial direction; therefore,
loading is circular [5].
http://dx.doi.org/10.1016/j.ijprt.2016.12.001
1996-6814/Ó 2016 Chinese Society of Pavement Engineering. Production and hosting by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
M.S. Ranadive, A.B. Tapase / International Journal of Pavement Research and Technology 9 (2016) 466–472
Figs. 1 and 2 summarizes many of the finite element
parameters and should be referenced throughout the paper.
Fatigue and rutting are generally assumed as two independent modes of distresses which can be analytically evaluated [6]. If the horizontal tensile strain at the bottom of
the bituminous layer (Point P as shown in Fig. 1) is excessive, cracking of the surface layer will occur, and the pavement distresses due to fatigue. If the vertical compressive
Fig. 1. Flexible pavement composition showing critical line and its
material properties.
467
strain on top of the subgrade (Point Q as shown in
Fig. 1) is excessive, permanent deformation occurs on the
surface in the pavement structure, and the pavement distresses due to rutting.
Present analysis is performed considering the tyre pavement interaction as an axisymmetric solid to mechanistically solve the layered pavement response to variation in
material properties of different component layers, variation
in thickness, considering any point on the critical line as a
center[7]. The obtained results are then incorporated as
input to estimate the pavement life in terms of rutting
and fatigue lives in number of standard axles.
The major objective of the paper is to illustrate the usefulness of finite element analysis for examining the effect of
variation in thickness and material properties of critical
parameters, especially on rutting and fatigue lives, with a
view to develop a design chart for particular condition
which correlates with actual field condition. If such type
of analysis is validated, it will prove to be beneficial to
derive useful design charts for any combinations of thicknesses, material properties and field conditions without
relying on theoretical/empirical design procedures. The
hypothetical thicknesses and material properties which
are considered for analysis are generally used in practice
as per IRC: 37-2012 [8]; hence it is an attempt to correlate
the present study with actual field conditions. An equilibrium between fatigue and rutting lives can be achieved
from such type of analysis.
Fig. 2. Pavement section showing critical line and hypothetical idealization.
468
M.S. Ranadive, A.B. Tapase / International Journal of Pavement Research and Technology 9 (2016) 466–472
2. Literature review
Number of literatures have reported the use of an
axisymmetric configuration like Abdhesh et al. [9], Issac
et al. [5], Helwany et al. [10], Tutumluer et al. [11], Ranadive et al. [12]. Cho et al. [13] favored axisymmetric analysis
for simulating pavement from a comparative study of 3
dimensional, plane-strain, and axisymmetric modeling
structure and traffic loading interaction.
Immanuel and Timm (2006) [14] used layered elastic
analysis to compare predicted vertical stress in the base
and subgrade layers to field measured vertical pressures
obtained from the National Center for Asphalt Technology
(NCAT) Test Track. The authors found that the predicted
pressure was only a reasonable approximation up to vertical pressures of 82 kPa in the base and 48 kPa in the
subgrade.
The IRC: 37-2012 [8] Guidelines for the design of flexible pavement recommends using the IITPAVE, which is a
modified version of FPAVE developed under the research
scheme R-56 for layered system analysis.
Sam Helwany et al. [10], illustrates the usefulness of
finite element method by discretising a three layer pavement system with the right boundary at a distance of about
8 times the loaded radius subjected to different types of
loading. The author carried out two dimensional and three
dimensional analyses. In this analysis three layers were
assigned the same elastic moduli, transforming the three
systems into a simpler one layer system.
Ranadive et al. [15] illustrates that axisymmetric analysis
of flexible pavement is carried out by a computer program
(ANSYS), and different performance parameters of pavement were studied for varying conditions of thickness.
Increase in thickness of the base course and sub-base
course layer does not help to reduce stress and deflection
as compared to asphalt concrete layer in which it is
observed that there is a substantial reduction in stress as
there is an increase in thickness of asphalt concrete.
Abdhesh K. Sinha et al. [9] Illustrates the usefulness of
finite element method to study the performance of a flexible
pavement with different types of local materials in its subbase. Three types of naturally occurring materials, namely;
coarse sand, conventional subbase material, stone dust and
four types of industrial waste materials; Blast furnace slag,
granulated blast furnace slag, Linz-Donawitz slag and fly
ash were used. In this work multilinear elasto-plastic hardening model in Ansys was used and the effect of the type of
subbase on life of the pavement is evaluated. In the study,
right boundary was placed at 1100 mm from the outer edge
of loaded area, which is more than 7 times the radius
150 mm of the applied load. A uniform pressure of
0.575 MPa (575 kPa) was applied to a circular contact area
having a radius of 150 mm causing a single axle load of
40.80 KN.
Tapase and Ranadive [16], reported the usefulness of
two dimensional finite element analysis to study the effect
of variation in thickness of different component layers on
the critical parameters. They noted that the tensile strain
at the bottom of the bituminous layer (BL) and compressive strain on top of the subgrade decreases with an
increase in the thickness of BL, which ultimately results
in increase of fatigue and rutting lives. In continuation with
the investigation related to varying the thickness and material properties of different layers reported in Tapase and
Ranadive [16], this paper reports the usefulness of finite element analysis for exploring the parameter sensitive analysis
of flexible pavement. A part of the analysis is to check the
sensitivity of horizontal axisymmetric extent for the hypothetical trials. Also, the mesh refinement study of the
selected thicknesses and material properties of different layers is conducted.
3. Model geometry and material characteristics
Depending on different material constituents of individual layers, the layers posses varied strength characteristics,
and this information is used as the input for analysis. The
function of granular base and sub base (many times considered as a single granular layer for analysis) is to reduce traffic induced stresses in the pavement structure and to
minimize the intensities of rutting. In the present study, a
conventional pavement section as per IRC:37-2012 consisting of bituminous layer and single granular layer which
together are constructed over the subgrade soil as shown
in Fig. 1 are considered for analysis. To study the effect
of varying thickness of the bituminous layer (h1) and the
base layer (h2) on critical parameters, in all four trial thicknesses of the bituminous layer as explained in Fig. 1 and
three trials of granular base layer thicknesses starting from
300 mm with an increment of 150 mm for each trial is considered for analysis.
Similarly, to study the effect of variation in material
property of base layer on the rutting and fatigue lives, three
naturally occurring materials like natural gravel,
E2 = 100 MPa, 300 MPa and high quality graded crushed
rock, E2 = 450 MPa are considered in base layer for analysis keeping Poisson’s ratio l2 = 0.35 constant for each
trial. In the present study, a uniform pressure of
0.575 MPa (575 kPa) caused by a single axle wheel load
of 40.80 KN [8,9] is applied on a circular contact area having a radius of 150 mm as shown in Figs. 1 and 2.
All the above trials are checked for their suitability in
the pavement section for selected bituminous layer material
(modulus of bituminous mix is taken as E1 = 1700 MPa
and Poisson’s ratio (l1 = 0.35) and subgrade condition
E3 = 80 MPa [17].
4. Finite element modeling
In general the finite element solution technique is
adopted through three basic stages of the analysis; those
are idealization of the system being investigated, formulation and solution of equations governing the phenomenon
and evaluation of the structural response required for
M.S. Ranadive, A.B. Tapase / International Journal of Pavement Research and Technology 9 (2016) 466–472
undertaking the design process as reported by Tapase and
Ranadive [16].
Basically, constitutive laws in the present development
are confined towards consideration to only modulus of
elasticity and the Poisson’s ratio of the materials used in
the pavement system being analyzed is presented in Fig. 1.
5. Finite element idealization
Wherever examination is necessary about soil structure
interaction problem, the required structure in modeled. It
is well known fact that the area away from the load intensity is not affected much. However, the question arises
about exactly upto what extent the parameters are sensitive
to the intensity of loading. Sam Helwany et al. [10], discretized a three layer pavement system with the right
boundary at a distance of about 8 times the loaded radius.
Abdhesh K. Sinha et al. [9] located the right boundary of
which is more than 7 times the radius 150 mm of the
applied load.
One way of evaluating the effect of loading is, to start
with certain assumed extent and determine the critical
parameters. Then increase or decrease the extent, analyse
and compare the obtained results with an earlier one. This
type of preliminary sensitive study helps in identifying the
more accurate area for analysis. In respect to this, a trial
horizontal axisymmetric extent of finite element idealization is considered for analysis from 5 times the radius to
8 times the radius.
On the other hand, accuracy of calculation increases if
higher order elements or more number of elements is used
during analysis. There was a time when limitation on the
use of a number of elements comes from the total degrees
of freedom the computer can handle and the cost of computation time required. However, the cost of the calculation is coming down so much that such limitations are
not relevant today. Accuracy is the only criteria left due
to the modern high speed techniques used today. In the
present study, the finite element idealization for the pave-
469
ment system being analyzed is developed by means of the
four noded quadrilateral elements.
A very fine mesh near the load that becomes progressively coarser with distance from the load is commonly
observed in the literature, the same phenomenon is used
during the analysis also the aspect ratio is maintained as
close as possible to the specified limits. In order to study
the effect of refinement of mesh, few hypothetical separate
meshes are developed and analyzed for a typical pavement
structure as shown in Figs. 1 and 2, consisting of 200 mm
of the bituminous layer (E = 1700 MPa, l = 0.35) over
450 mm of granular base (E = 3000 MPa, l = 0.35) over
a subgrade (E = 1000 MPa, l = 0.3). A single wheel load
was modeled as a uniform pressure of 0.575 MPa
(575 kPa) over a circular area of 150 mm radius.
A very coarse refinement mesh consisting of 12 elements,
with a smallest element size of 150 mm by 200 mm. Four
elements spanned the thickness of the bituminous layer,
four elements spanned the thickness of the base layer and
four elements spanned the thickness of the sub grade layer.
A medium refinement mesh consisting of a 96 elements,
with a smallest element size of 75 mm by 50 mm. A very
fine refinement mesh consisting of 210 elements, with a
smallest element size of 50 mm by 25 mm (Fig. 3). Intermediately numbers of hypothetical meshes are studied during
analysis. In the present work, the total thickness of the
pavement is taken as 1300 mm to 1750 mm as per the trials
described in Figs. 1 and 2 with constant thickness of
900 mm for the subgrade.
6. Boundary conditions
The nodes over the base of the subgrade i.e., at depth of
more than eight times the radius of circular contact area
are restrained in both radial (r) and axial (z) directions.
The nodes over the axis of symmetry are restrained in
radial direction. Considering preliminary sensitive study
to identify how much horizontal axisymmetric extent
should be used for analysis, four trial extents of finite
element idealization are considered starting from assuming
Fig. 3. Comparison of vertical stresses of finite element analysis with Ansys results.
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M.S. Ranadive, A.B. Tapase / International Journal of Pavement Research and Technology 9 (2016) 466–472
5 times the radius to 8 times the radius. Also, it is assumed
that, due to the indefinite lateral extent of the pavement
section, the nodes over the extreme vertical face of the
pavement from the centerline of the wheel loading [2,9];
do not suffer radial displacements. Hence those nodes are
treated as restrained in the radial (r) direction for each trail
[18]. By employing the interpolation characteristics of the
elements, the modulus of elasticity and the Poisson’s ratio
at the element nodes are extrapolated by using their respective values at the Gauss integration points. Finally after
employing direct averaging technique, the strains and stresses at the nodes of the idealized system are established.
The nodal displacements provide information regarding
the deflection suffered, which in turn helps in analyzing
the phenomenon of rutting.
the allowable limit 178 10 06 and the computed vertical
compressive strain on subgrade is 127 10 06 which is also
found well within the allowable limits which is 370 10 06.
From the obtained results, it is observed that the pavement
composition is safe for the selected trial ultimately validating the current analytical process. A sensitivity analysis
conducted to find the influence of the horizontal extent
on the model geometry suggests that a length of seven
times the radius (Fig. 6) is appropriate and hence is
adopted in present study. Also, the surface displacements
(Fig. 4) and stress (Fig. 5) for the fine and very fine refinement meshes appears to be coinciding and seems to be virtually identical, so fine mesh is selected for analysis.
Effect of variation in thickness of the base layer, BL and
use of different materials in base layer on conventionally
critical parameters like the horizontal tensile strains at
7. Results and discussion
A preliminary analysis is conducted to verify the correctness of the FEA. For the same, the three layers are
assigned the same elastic moduli, transforming the three
layer system into simpler one layer system. The obtained
results of the FEA are checked against the Boussinesq close
form solution which is readily available for uniform circular pressure and also compared with the results obtained
through the general purpose software Ansys as presented
in Fig. 3. The obtained results are coinciding with the
results of Boussinesq’s close form solution, which is validating the developed program. Secondly, validation of present finite element analysis is done against IRC: 37-2012
pavement design plate/chart. Available data from IRC:
37-2012 for plate 8 (CBR 15%) with 150 msa is analysed
with the program used in present analysis and results are
compared with the allowable limits set by the guidelines
for the design charts. The computed horizontal tensile
strain in bituminous layer is 161 10 06 which is less than
Fig. 4. Surface displacements computed at different mesh refinement.
Fig. 5. Horizontal stresses along centreline at different mesh refinement.
Fig. 6. Surface displacements computed for different hypothetical horizontal extent.
M.S. Ranadive, A.B. Tapase / International Journal of Pavement Research and Technology 9 (2016) 466–472
the bottom of BL and the vertical compressive strain at the
top of the subgrade is observed and interpreted.
For the selected subgrade condition, the values of horizontal tensile strain at the bottom of BL for E2 = 100 MPa,
l = 0.35 as a hypothetical base material, is exceeding the
allowable limit at all trial thicknesses. At every base thickness, it is observed that E2 = 300 MPa, l = 0.35 and
E2 = 450 MPa, l = 0.35 as a trial base material, show values of all critical parameters well within the allowable limit
as per IRC: 37-2012. When a material property of base
course varies from E2 = 100 MPa, l = 0.35 to
E2 = 300 MPa, l = 0.35 more than 20 percent reduction
in vertical displacement is noticed, wherein from
E2 = 300 MPa, l = 0.35 to E2 = 450 MPa, l = 0.35 not
even a 2 percent reduction in vertical displacement is
observed. At every trial increase in the thickness of the base
layer and its elastic modulus, a gradual decrease in vertical
compressive strain is noticed at the top of selected
subgrade.
For the selected subgrade condition and constant base
thickness (450 mm), variation in thickness of BL for three
trial base layer material properties is analyzed. From
Fig. 6, it is observed that the value of horizontal tensile
strain for E2 = 300 MPa, l = 0.35 and for E2 = 450 MPa,
0.35 is safe at 200 mm and 250 mm thickness of bituminous
layer. Also, it is obvious from the Fig. 7, that 100 mm and
150 mm thickness of BL are not safe for the selected trials.
At every base thickness, it is observed that E2 = 450 MPa,
l = 0.35 shows the values of horizontal tensile strain within
the allowable limit, also vertical compressive strain is
within the safe limit for all trials except at base
E2 = 100 MPa and 100 mm BL thickness.
The computed strains are taken as input and are incorporated in the fatigue and rutting criteria recommended in
Indian Road Congress (IRC: 37-2012) to estimate the
pavement life for various hypothetical conditions.
Fig. 7. Effect of BL thickness on horizontal tensile strain at bottom of BL.
471
7.1. Fatigue criterion
As per the guidelines for the design of flexible pavements
(IRC: 37-2012), Fatigue criterion for 80 percent reliability
level is considered for analysis. The obtained results for
horizontal tensile strain at bottom of bituminous layer is
incorporated in fatigue criteria to calculate the fatigue life
in terms of number of standard axles.
The fatigue cracking of flexible pavements is based on
the horizontal tensile strain at the bottom of BL. On this
criterion, the allowable number of load repetitions that
causes fatigue cracking is related to the tensile strain at
the bottom of BL. Fig. 8 gives a graphical presentation
of fatigue life in a number of standard axles on y-axis versus the thickness of the bituminous layer on x-axis for all
trail base material.
7.2. Rutting criterion
As per the guidelines for the design of flexible pavements
(IRC: 37-2012), rutting criterion for controlling rutting in
the subgrade and granular layers is considered for analysis.
The obtained results for vertical compressive strain at top
of subgrade is incorporated in rutting criteria as inputs to
calculate the ruttin life in terms of number of cumulative
standard axles. Fig. 9 gives a graphical presentation of a
number of cumulative standard axles on y-axis versus the
thickness of the bituminous layer on x-axis for all trail base
material.
8. Conclusions and recommendations
It is observed that number of rutting cycles increase by
4.48% with change in thickness of base layer from
300 mm to 450 mm. However, the same increase is only
2.47% when the change in thickness is from 450 mm to
Fig. 8. Fatigue life in number of standard axles Vs thickness of
bituminous layer.
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M.S. Ranadive, A.B. Tapase / International Journal of Pavement Research and Technology 9 (2016) 466–472
References
Fig. 9. Number of cumulative standard axles Vs thickness of bituminous
layer.
600 mm. From the observations, it is concluded that the
increase in thickness of the base layer and increase in its
elastic modulus reduces the damage due to rutting, while
it has less effect on damage due to fatigue. Also, the number of fatigue cycles increase by 5.13% due to variation of
elastic modulus of base layer from 100 MPa to 300 MPa.
However, beyond 300 MPa, its effect is least. Hence, the
increase in the elastic modulus of base layer reduces damage due to fatigue. From the selected trials for base materials and base thicknesses, use of 300 MPa material and
450 mm thickness of the base layer is suitable at the
selected subgrade condition.
Here it is clear that 100 mm and 150 mm thickness of
bituminous layer is not safe for the selected trials. The
value of tensile strain at the bottom of BL for
E2 = 300 MPa, l = 0.35 and E2 = 450 MPa, l = 0.35 is
under the allowable limit at 200 mm and 250 mm thickness
of bituminous layer for the selected subgrade condition. At
every base thickness, it is noticed that high quality graded
crushed rock (E2 = 450 MPa, l = 0.35) shows the values of
tensile strain at the bottom of BL within the allowable
limit, also the value of vertical compressive strain is within
the safe limit for all trials except at base E2 = 100 MPa and
100 mm bituminous layer thickness. Horizontal tensile
strain at bottom of bituminous layer and vertical compressive strain at top of subgrade is decreased with increase in
the thickness of bituminous layer. Increase in bituminous
layer thickness reduces the damage due to both rutting
and fatigue.
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