Evaluation of Rutting Potential of Asphalt Mixtures Using Linear Genetic Programming

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Evaluation of Rutting Potential of Asphalt Mixtures Using Linear Genetic
Programming
M.R. Mirzahosseini, A.H. Alavi
College of Civil Engineering, Iran University of Science & Technology, Tehran, Iran
F. Moghadas Nejad
Department of Civil and Environmental Engineering, Amirkabir University of Technology, Tehran, Iran
A.H. Gandomi
The Highest Prestige Scientific and Professional National Foundation, National Elites Foundation, Tehran, Iran
M. Ameri
College of Civil Engineering, Iran University of Science & Technology, Tehran, Iran
ABSTRACT: Rutting has been considered as the most serious distresses in flexible pavement for
many years. Flow number obtained from uniaxial dynamic creep test is an explanatory index for the
evaluation of rutting potential of asphalt mixtures. This is a pioneer study that presents a promising
variant of genetic programming, namely linear genetic programming (LGP) to predict the flow number
of dense asphalt-aggregate mixtures. Generalized LGP-based models were constructed to relate the
flow number of Marshall specimens to the coarse and fine aggregate contents, percentage of air voids,
percentage of voids in mineral aggregate, Marshall stability and flow. The comprehensive
experimental database used for the development of the models was established upon a series of
uniaxial dynamic creep tests conducted in this study. The contributions of the parameters affecting the
flow number were determined through a sensitivity analysis. A multiple least squares regression
(MLSR) analysis was performed using the same variables and same data sets to benchmark the LGP
models. For more verification, a subsequent parametric study was conducted and the trends of the
results were confirmed with the results of previous studies. The results indicate that the proposed LGP
models are capable of effectively evaluating the flow number of asphalt mixtures. The LGP models
are found to be significantly more accurate than the MLSR model.
KEY WORDS: Rutting, Flow number, Linear genetic programming, Regression Analysis, Marshall
mix design.
1 INTRODUCTION
Permanent deformation is one of the considerable load-associated distress types affecting the
performance of asphalt concrete pavements. The repetitive action of traffic loads results in
accumulation of permanent deformations in asphalt pavements (Kalosh 2001). Permanent deformation
is one of the major causes of pavement rutting. Rutting in asphalt pavement develops progressively
with increasing numbers of load application. It usually appears as longitudinal depression in the wheel
paths accompanied by small upheavals to the side (Pardhan 1995). Evaluation of rutting potential of
asphalt mix has been the focus of much research in pavement engineering over the last decades. The
available rutting evaluation procedures are generally categorized into three main groups: (1)

mechanistic-empirical modeling approaches, (2) advanced constitutive modeling approaches, and (3)
development of a simple performance test to identify the rutting potential of mixtures during design
based on measured fundamental engineering properties and response (Kim 2008). A comprehensive
description of these procedures can be found in Kim (2008). Majority of the available permanent
deformation models in the literature are empirical or semi-mechanistic with limited fundamental
material characterization. Unsatisfactory correlations with actual field performance are the common
result. Some of the empirical models are derived from limited sets of materials and environmental
conditions. Thus, they lack robustness and are not transferable to other conditions.
The time to tertiary flow failure is thought to be a good indicator of the rutting resistance of a given
mixture (Kim 2008). This can be quantified via the flow number as measured in a repeated load
permanent deformation test. Dynamic creep test is found to be one of the best methods among
different methods of assessing permanent deformation potential of asphalt mixtures (Kaloush and
Witczak 2002). The curve of accumulated strain against number of load cycles is the most important
output of the dynamic creep test. Witczak et al. (2002) defined the flow number as loading cycle
number where tertiary deformation starts. Flow number is more analogous to field conditions since
loading of pavement is not continuous. The dynamic creep test is a sensitive and costly test and it is
not always possible to conduct the test. Therefore, developing a relationship between the flow
numbers obtained from the dynamic creep test and parameters from Marshall mix design leads to
considerable savings in construction cost and time.
By extending developments in computational software and hardware, several alternative computer-
aided data mining approaches have been developed. Artificial neural networks (ANNs) are the most
widely used pattern recognition procedures. There has been some research with the specific objective
of applying ANNs to the evaluation of asphalt pavements performance characteristics (e.g., Tarefder et
al. 2005). Despite the acceptable performance of ANNs, they usually do not provide a better
understanding of the nature of the derived relationship between the different interrelated input and
output data. Another alternative approach, which is based on the data alone to determine the structure
and parameters of the model, is known as genetic programming (GP) (Koza 1992). GP may generally
be defined as a supervised machine learning technique that searches a program space instead of a data
space (Banzhaf et al. 1998). In recent years, a particular subset of GP with a linear structure similar to
the DNA molecule in biological genomes namely, linear genetic programming (LGP) (Brameier and
Banzhaf, 2007) has emerged. LGP is a machine learning approach that evolves the programs of an
imperative language or machine language instead of the traditional tree-based GP (Koza, 1992)
expressions of a functional programming language. There have been some scientific efforts directed at
applying LGP to the civil engineering tasks (e.g., Gandomi et al. 2009a,b). LGP can substantially be
useful in deriving empirical models for characterizing the rutting behavior by directly extracting the
knowledge contained in the experimental data.
In this study, the LGP approach was utilized to evaluate the rutting potential of dense asphalt
mixtures in the form of the flow number. The proposed correlations were developed based on several
uniaxial dynamic creep tests on standard Marshall specimens conducted at Iran University of Science
and Technology civil engineering laboratories. The experimental database covers a wide range of
aggregate gradation. A linear regression analysis was performed to benchmark the LGP-based
correlations.
2 GENETIC PROGRAMMING
GP is a symbolic optimization technique that creates computer programs to solve a problem using the
principle of Darwinian natural selection (Koza 1992).GP was introduced by Koza as an extension of
the genetic algorithms (GAs), in which programs are represented as tree structures and expressed in
the functional programming language LISP (Koza 1992).In GP, a random population of individuals
(trees) is created to achieve high diversity. The symbolic optimization algorithms present the potential

solutions by structural ordering of several symbols. A comprehensive description of GP can be found
in Koza (1992). LGP is a linear variant of GP. The linear variants of GP make a clear distinction
between the genotype and the phenotype of an individual. Thus, the individuals are represented as
linear strings that are decoded and expressed like nonlinear entities (trees).
2.1 Linear Genetic Programming
LGP is a subset of GP that has been emerged recently. LGP has some main differences with the
traditional tree-based GP, there are. Linear genetic programs (LGPs) have graph-based functional
structures and evolve in an imperative programming language C/C ++ and machine code ather than in
expressions of a functional programming language like LISP (Brameier and Banzhaf, 2007). Unlike
the tree-based GP, structurally noneffective codes coexist with effective codes in LGPs. Noneffective
code in genetic programs which is referred to as “intron”, represents instructions without any influence
on the program behavior. Structural introns act as a protection that reduces the effect of variation on
the effective code. The introns allow variations to remain neutral in terms of fitness change (Brameier
and Banzhaf, 2007). Because of the imperative program structure in LGP, these noneffective
instructions can be identified efficiently. This allows the corresponding effective instructions to be
extracted from a program during runtime. Since, only effective programs are executed, evaluation can
be accelerated significantly (see Figure 1).
Figure 1: Elimination of noneffective code in LGP. Only effective programs are executed (Brameier
and Banzhaf, 2007).
The instructions from imperative languages are restricted to operations that accept a minimum number
of constants or memory variables, called registers (r), and assign the result to a destination register,
e.g., r0 := r1 + 1. Automatic Induction of Machine code by Genetic Programming (AIMGP) is a
particular form of LGP. In AIMGP evolved programs are stored as linear strings of native binary
machine code, which are directly executed by the processor. The absence of an interpreter and
complex memory handling results in a significant speedup in AIMGP execution compared to tree-
based GP. This machine-code-based LGP approach searches for the computer program and the
constants at the same time. Descriptions of basic parameters and steps used to direct the search for a
linear genetic program can be found in Brameier and Banzhaf (2007).
3 EVALUATION OF RUTTING POTENTIAL AND ANALYSIS
Evaluation of field rutting potential of asphalt mix has traditionally been a complicated task. In order
to provide accurate assessment of the rutting potential of asphalt mix, the effects of several influencing
factors should be incorporated into the model development. In the following subsections, first, the
factors governing rutting potential are analyzed. Next, the details of developing the models including
the database description, and comparison of the performance of the LGP and regression-based models
are presented.
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3.1 Analysis of Internal Factors Affecting Rutting
The internal factors affecting rutting can be divided into three basic categories of aggregate, bitumen
and asphalt mixture characteristics (Sousa et al. 1991). Mineral aggregates constitute the rate of 90-
95% of mixture weight and 75-85% of mixture volume of asphalt mixtures and perform as skeleton
and bearing member in it (Topal and Sengoz 2004). Therefore, the physical and mineralogical
properties of mineral aggregate have noticeable effects on quality and characteristics of asphalt
mixtures (Sousa et al. 1991).
Binder is one of the fundamental components of asphalt mixtures and is used as a cohesive material
to bond the aggregates. Rutting propensity of the asphalt mixture is significantly affected by the
stiffness of the binder. Many researchers have recognized the importance of the binder in contribution
to the permanent deformation behavior of an asphalt aggregate mixture (Pardhan 1995, Pirabarooban
et al. 2003). With increase in binder stiffness, mixture stiffens, and therefore, resistance to rutting
increases (Sousa et al. 1991).
Optimum amount of bitumen obtained from mix design methods may have an appreciable influence
on the capability of asphalt mixture to resist permanent deformation (Sousa et al. 1991). The mixture
air voids are negatively correlated with the asphalt binder content. The higher the asphalt binder
content is in the mixture, the lower the air voids content is (Lavin 2003). VMA is important in the
sense that it allows room for enough asphalt binder to make a durable mixture plus enough room for
air voids to ensure a stable mixture (Lavin 2003). It is widely known that the rutting resistance of
mixture increases as the air void and VMA decrease (Sousa et al. 1991, Pardhan 1995). Stability of an
asphalt pavement is the most important property of the asphalt-aggregate mixtures in the wearing
course design. The Marshall quotient is calculated as the ratio of stability to flow. This ratio is an
indicator of the mix stiffness, resistance to shear stress, permanent deformation and hence rutting of
the bitumen concrete (Hinislioglu and Agar 2004).
3.2 Experimental Study and Data Preprocessing
On the basis of the results of the previous research (Kaloush and Witczak 2002), the dynamic creep
test was chosen as an appropriate laboratory method to investigate the rutting potential of dense
bituminous mixtures. Results of this experimental study were used in the development of the LGP-
based models. Uniaxial dynamic creep test has been used to determine the rutting potential of asphalt
mixtures for many years. Universal Testing Machine (UTM-5) was utilized to conduct the tests. The
aggregates employed in the construction of asphalt samples were crushed aggregates and prepared
from the gravel and sand mines of Rigzar Asphalt Factory located in the Shahryar road, Karaj, Iran.
The used fillers were river materials and obtained from Makadam-e Shargh Asphalt Factory, Semnan
road, Iran. Also, bitumen with the penetration of 60/70 was supplied by Tehran Refinery and
Pasarghad Oil Company, Tehran, Iran. In this research, the rutting behavior of asphalt mixtures
constructed by 9 grading has been investigated. Among different grading systems presented by Code
234 of Iran Management and Planning Organization (IAHC 2000), upper, middle and lower limits of
grading no. 3, 4 and 5, which cover a wide range of grading, were selected in this research. In order to
control the quality of aggregates, a number of tests such as Los Angeles abrasion, crushed percentage
and determination of specific weight of coarse aggregate, fine aggregate and filler were conducted.
Some tests such as penetration test, ductility test, and determination of softening point and unit weight
of bitumen were performed. The samples were constructed based on the Marshall method (ASTM
D1559 1993). The percentage of used bitumen was selected in a way that the optimal amount of
bitumen to be in the mean range of percentage. A total of 270 samples were constructed and tested in
this research. After conducting the Marshall stability test on half of the samples, Rice test was

performed to determine the percentage of air void of the samples. Voids in mineral aggregate (VMA)
was determined and eventually final VMA was obtained by taking the average of three samples. After
conducting dynamic creep test on the samples, the flow numbers were determined. The final flow
numbers were obtained by taking the average of three samples.
The database includes the measurements of coarse aggregate (C), fine aggregate (S), filler, air voids
(Va), VMA, bitumen, Marshall stability (M), Marshall flow (F) and flow number (Fn). The descriptive
statistics of the data used in this study are given in Table 1. It is noteworthy that some of the above
variables are fundamentally interdependent. This interdependency can cause problems in analysis as it
will tend to exaggerate the strength of relationships between the variables. Filler is calculated by
subtracting the sum of coarse and fine aggregate from 100. Hence, it has been excluded from the
models. Coarse and fine aggregate could potentially have been excluded rather than filler. They were
retained as traditionally they have been more frequently used indicators of rutting and also have more
favorable distributions of values. Out of the 270 samples constructed and tested herein, the final 118
flow number values were extracted by taking the average of three samples.
Table 1: Descriptive Statistics of variables used in the model development.
Parameter Influencing Variables Output
C (%) S (%) Va (%) VMA (%) M (KN) F (mm) Fn
Mean 57.31 37.15 4.54 16.55 10.16 3.50 227
Standard Error 1.32 1.04 0.14 0.13 0.19 0.06 13.25
Range 48 39 7.06 5.84 12.57 2.65 488
Minimum 33 18 1.71 13.20 2.73 2.10 22
Maximum 81 57 8.77 19.04 15.30 4.75 510
3.3 LGP-Based Models for Flow Number of Asphalt Mix
In this study, the LGP technique was employed to obtain meaningful relationships between the flow
number of asphalt mixes and the factors affect mixture resistance to permanent deformation. The most
important factors representing the rutting behavior were selected based on an extensive trial study and
literature review. Consequently, the flow number (Fn) predictive models were considered to be as
follows:
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C/S represents grain size distribution, and Va, VMA and M/F are asphalt mixture characteristics. Va
has highly negative correlation with the asphalt binder content. Hence, it can also be considered as a
representative of the binder content. VMA is actually a property of aggregates in the mixture. Changes
in the aggregates gradation or shape provide significant changes in VMA (Lavin 2003). For the LGP
modeling, a computer software called Discipulus (Conrads et al. 2004) was used. This software works
on the basis of the AIMGP approach. After completing a project, the single solutions are combined
into team solutions (Brameier and Banzhaf, 2007) to produce better results and the evolved programs
are written in Java, C, or Intel assembler code, automatically. The resulting code may be linked to the
optimizer and compiled or it may be compiled into a DLL or COM object and called from the
optimization routines. Discipulus interactive evaluator mode was employed to run the resulting C

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a
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otential o
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g of Measured F
l
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vation. So
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ow Number
R
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M
SE = 0.004
M
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Validation
M
A (%)
M
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w number
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1
1
2
3
1
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Log of Predicted Flow Number
Lo
g
M
/F
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s
same input
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l
ow Number
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i
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the influential mixture properties, aggregate characteristics are particularly important contributors to
permanent deformation resistance. Elliott (1991) showed that the fine-coarse and coarse-fine gradation
variations had the greatest impact on mix properties. Also, the amount and stiffness of the asphalt or
modified asphalt binder, which is directly correlated with VMA, are important. With lower asphalt
contents and stiffer binders improved resistance to permanent deformation is provided (Sousa et al.
1991).

Figure 5: A comparison of the ratio between the predicted and experimental flow number values using
different models.
5 PARAMETRIC ANALYSIS
For further verification of the proposed models, a parametric study was performed using the LGP
evolved solutions. Figures 6(a)–(d) present the predicted values of the flow number (Fn) obtained by
the LGP-based models as a function of each parameter. The tendency of the Fn prediction to C/S, Va
(%), VMA (%), and M/F can be determined according to these figures.
Figure 6: Flow number parametric analysis in the LGP-based models.
As can be seen in Figure 6, Fn continuously decreases due to increasing C/S. This is an expected case
from the pavement engineering viewpoint. It is well known that increase in the fine aggregate and
filler content will stiffen the total asphalt mixture, leading to higher Marshall stability values and
better resistance to permanent deformation. The results of parametric analysis state that increases in Va
significantly decrease Fn. This is also an expected case since the specimens with higher Va become
less dense. In other words, increases in Va leads to less aggregate particles interlock and internal
friction in the mixture. These result in less shear resistance for the asphalt mixture which increases the
deformation of the mix caused by loading (Lavin 2003). As VMA values increase, the specimens
become less resistant to applied loads. This can be attributed to the increase of bitumen percent in the
sample. In general, increase in the bitumen percent corresponds to increase in the rutting potential and
softening of the sample. This is verified completely by Figure 6(c). The results of several studies
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
1 11 21 31 41 51 61 71 81 91 101 111
Measured / Predicted
Sam
p
le Number
LGP (Single Solution)
(R = 0.970, MSE = 0.009, MAE = 0.075)
(a)
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
1 11 21 31 41 51 61 71 81 91 101 111
Measured / Predicted
Sam
p
le Number
(b)
LGP (Team Solution)
(R = 0.982, MSE = 0.005, MAE = 0.060)
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
1 11 21 31 41 51 61 71 81 91 101 111
Measured / Predicted
Sam
p
le Number
(c)
MLSR
(R = 0.920, MSE = 0.023, MAE = 0.117)
0
200
400
600
800
1000
012345
Fn
(a) LGP (Single Solution)
LGP (Team Solution)
C/S
0
50
100
150
200
250
300
1357911
Fn
(b) LGP (Single Solution)
LGP (Team Solution)
Va(%)
0
200
400
600
800
12 14 16 18 20
Fn
(c) LGP (Single Solution)
LGP (Team Solution)
VMA
(
%
)
0
100
200
300
400
500
0246
Fn
(d) LGP (Single Solution)
LGP (Team Solution)
M/F

indicate that resistance against permanent deformation increases as Va and VMA decrease (e.g., Sousa
et al. 1991, Pardhan 1995, Lavin 2003).
As can be seen in Figure 6(d), increases in M/F increase Fn. The results of parametric analysis for
M/F are also in acceptable agreement with the results presented by previous researchers. Based on the
previous studies, a higher M/F value indicates a high stiffness mix with a greater ability to spread the
applied load. Therefore, the pavements being more resistant to permanent deformation are obtained
(Nicholls 1998, Hinislioglu and Agar 2004, Lavin 2003). The above considerations confirm that the
developed LGP models are robust and can be used with confidence.
6 CONCLUSIONS
In this study, a new variant of GP, namely LGP is utilized to assess the rutting resistance of asphalt-
aggregate mixtures. On the basis of an extensive trial study and literature review, the coarse aggregate
to fine aggregate ratio (C/S), air voids (Va), voids in mineral aggregate (VMA) and Marshall quotient
(M/F) were identified to be used as the predictor parameters. Several uniaxial dynamic creep tests on
standard Marshall specimens carried out in the laboratory environment to develop a comprehensive
database. The LGP-based models were benchmarked against the developed multivariable linear
regression model. The following conclusions can be derived from the results presented in this
research:
• It was observed that the LGP models are capable of predicting the flow number of asphalt mixtures
with high accuracy. The LGP team solution provides superior performance compared with the
single solution. Due to nonlinearity in rutting behavior, the proposed nonlinear LGP single and
team solutions produce considerably better outcomes over the linear regression-based model
developed with the same variables as inputs.
• Unlike majority of the previous studies on constitutive modeling of rutting, the proposed models
simultaneously take into account the role of several important factors representing the rutting
behavior.
• In addition to the acceptable accuracy, LGPs are white-box models, that is, they provide the
transparent programs of an imperative language or machine language. LGP evolved solutions in C,
Java and assembler codes for flow number prediction are available from the authors. These models
can be used for routine design practice in that they were derived from tests on mixtures with a wide
range of aggregate gradation and properties.
• A major advantage of LGP for determining the flow number lies in its powerful ability to model the
mechanical behavior without any prior assumptions whatsoever regarding material behavior.
• The contribution of each input parameter in the LGP models was evaluated through a sensitivity
analysis. C/S and VMA were found to be more effective to explain the variations of the flow
number compared with the other mixture properties.
• The sensitivity of the proposed correlations to the variation of influencing parameters was evaluated
through a parametric study. The results were supported by the results presented by other
researchers.
• A major distinction of the LGP approach is that for a specific type of asphalt mixture and for
predetermined testing conditions, the flow number can accurately be estimated without carrying out
destructive, sophisticated and time-consuming laboratory tests with UTM or any similar testing
equipment. Thus, the rutting potential can be explored by this means in a perfect manner.
• As more data become available, including those for other types of asphalt mixtures and test
conditions, the proposed models can be improved to make more accurate predictions for a wider
range.

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