Prediction of scour depth at bridge abutments in cohesive bed using gene expression programming

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online), Volume 5, Issue 11, November (2014), pp. 25-32 © IAEME
25
PREDICTION OF SCOUR DEPTH AT BRIDGE ABUTMENTS
IN COHESIVE BED USING GENE EXPRESSION
PROGRAMMING
Mohd Danish
(Assistant Professor, Dept. of Civil Engineering, IFTM University, Moradabad, India)
ABSTRACT
The scour modelling in cohesive beds is relatively more complex than that in sandy beds and
thus there is limited number of studies available on local scour at bridge abutments on cohesive
sediment. Recently, a good progress has been made in the development of data-driven techniques
based on artificial intelligence (AI). It has been reported that AI-based inductive modelling
techniques are frequently used to model complex process due to their powerful and non-linear model
structures and their increased capabilities to capture the cause and effect relationship of such
complex processes. Gene Expression Programming (GEP) is one of the AI techniques that have
emerged as a powerful tool in modelling complex phenomenon into simpler chromosomal
architecture. This technique has been proved to be more accurate and much simpler than other AI
tools. In the present study, an attempt has been made to implement GEP for the development of
scour depth prediction model at bridge abutments in cohesive sediments using laboratory data
available in literature. The present study reveals that the performance of GEP is better than nonlinear
regression model for the prediction of scour depth at abutments in cohesive beds.
Keywords: Abutments, Artificial Intelligence, Cohesive soil, Gene Expression Programming, Scour.
I. INTRODUCTION
Scour is the removal of sediment in a stream due to action of flowing water. In connection
with bridges, scour could be defined as the result of erosive action of flowing water excavating and
carrying away sediment from the bed and banks of a stream due to interference of structures such as
abutments and bridge piers on the flowing water. In an alluvial stream there will be continuous
transport of sediment in the stream as a geomorphological process. If however there is additional
natural or man induced causes to upset the sediment supply and removal in a reach, such as
construction of a barrage or a dam, the stream will have long term changes in the stream bed
elevation. Abutment scour is caused by vortex action that forms near the abutment when flood-plain
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flow converges with main channel flow as shown in Fig.1. The vortices cause scouring action near
the toe of the abutment, which can lead to undermining of abutment footings. Hence, abutments are
essentially erodible short contractions.
Fig.1: Typical vortex action causing abutment scour[1]
Higher flow velocities and large-scale turbulence around an abutment may erode the
abutment boundary. As noted, the bed of the main channel is more erodible than the floodplain,
because the bed is formed of loose sediment while the floodplain is formed of more cohesive soil
often protected by a cover of vegetation. Field observations indicate that, typically, two prime scour
regions develop; (i) one region iswhere the boundary is least resistant to hydraulic erosion, this could
be the main bed if flow velocities (and unit discharges) are sufficiently large; (ii) the other region is
where the flow velocities (and unit discharges) and turbulence are greatest, this is usually near the
abutment [2].
Several researches have been done in past both in laboratory and on field to predict the scour
depth at piers and abutments in non-cohesive soils since 1950s. Several investigators have proposed
various relationships for scour depth, pier width and correction factors based on laboratory and field
experiments [Laursen and Toch(1956); Tison(1961); Garde et al. (1961); Larras(1963); Laurson
(1963); Jain and Fischer (1980); Raudkivi(1986); Melville and Sutherland (1988); Froehlich (1989);
Melville (1997);Gijs et al. (1995); Richardson et al. (1995),Richardson et al. (2001); Sheppard et al.
(2014); 15].Yakoub[17] conducted series of tests on abutment scour in cohesive material by varying
initial water content, clay content, the degree of compaction related to the optimum compaction and
clay type. He proposed different scour depth equations for different clay mineral and concluded that
for30% of Kaolinite clay, the degree of compaction and initial water content has no effect on the
scour depth.Seung[18] used laboratory data to predict abutment scour using Scour Rate In Cohesive
Soil (SRICOS) method and proposed equation for maximum abutment scour depth in cohesive soil
considering three correction factors to account for the shape of abutment, the attack angle of the flow
and the abutment location. Since, then various researches have been conducted experiments on field
and in laboratory for the prediction of scour depth [19, 20, 21].
Past researchers have developed the scour depth equation by dimensional analysis followed
by nonlinear regression analysis but this approach is less precise and involves tedious calculations
and hence, become less trendy in the new advance world where soft computational skills have
emerged with the artificial intelligence techniques where modelling can be easily done with precision
by applying less effort. Guven et al. (2008) and Azamathulla et al. (2010)[22, 23] have applied GEP
for the scour depth prediction around bridge pier and compared their results with that of other
regression techniques and found that the GEP is the best modelling technique for scour depth
prediction among other tools.

27
It is evident from the literature survey that the computational analysis of scour depth based on
AI techniques in general and GEP in particular has not been extensively done and there is an
immediate need to carry out work in this regard and therefore, in the present study, GEP has been
used to predict scour depth at bridge abutments in cohesive soil using experimental data obtained
from literature.
II. DATASET FOR SCOUR PARAMETERS AND CONVENTIONAL SCOUR
PREDICTION MODELS
The experimental data collected by Debnath[21] has been used in the present study. The
range of various parameters and their statistics are given in Table 1.Debnath[21]performed nonlinear
regression for the given dataset and obtained three different scour depth equations for different
ranges of clay content and water content, due to the complexity and non-linearity in the behaviour of
scouring in cohesive sediments (equations 1 to 3):
For WC = 0.197-0.233 and 0.35 ≤ C ≤ 1:
‫ݕ‬ො௦ = 3.02ሺ‫ܨ‬௔ሻ଴.଺଺ሺ‫ܥ‬ሻି଴.ଶ଻ሺܹ஼ሻ଴.଴ଷሺ߬̂௦ሻି଴.ଶ଺
(1)
For WC = 0.245-0.442 and 0.35 ≤ C ≤ 0.5:
‫ݕ‬ො௦ = 2.37ሺ‫ܨ‬௔ሻ଴.଺଼ሺ‫ܥ‬ሻିଵ.ଶସሺܹ஼ሻ଴.ଶହሺ߬̂௦ሻି଴.ସଵ
(2)
For WC = 0.245-0.442 and 0.5 ≤ C ≤ 1:
‫ݕ‬ො௦ = 4.31ሺ‫ܨ‬௔ሻ଴.଼଻ሺ‫ܥ‬ሻ଴.଻ଽሺܹ஼ሻ଴.ସଵሺ߬̂௦ሻି଴.଴଻
(3)
Table. 1: Range and statistics of the various parameters
Parameters
Data range Data statistics
Minimum Maximum Mean COV
C 0.3500 1.0000 0.6690 0.3456
Wc 0.1970 0.4430 0.3074 0.1913
ŷs 0.4920 1.9830 1.1344 0.2773
Fa 4.5005 9.3326 6.1568 0.1990
߬̂௦ 0.0001 0.0005 0.0003 0.3304
A nonlinear regression method in the MATLAB environment for the same dataset in the
present study was also implemented to get the scour depth prediction equation. It leads to the
following equation for the estimation of scour depth at the bridge abutment embedded in the bed of
the clay-sand mixture:
‫ݕ‬ො௦ = 0.01ሺ‫ܨ‬௔ሻ଴.ସ଼ଶଷሺ‫ܥ‬ሻ଴.଴଴ଶ଼ሺܹ஼ሻ଴.ଵସଽ଼ሺ߬̂௦ሻି଴.ସ଼ଷ଻
(4)
where, ‫ݕ‬ො௦ =
௬భ
௅′ , non-dimensional maximum equilibrium scour depth; ߬̂௦ =
ఛೞ
ఘ௎మ , non-dimensional
bed shear strength; ‫ܨ‬௔ =
௎
ඥ௚௅′
, abutment Froude number; C, is the clay content and WC, is the water

28
content.There is a slight change in the exponents in the input parameters, but the significance of this
equation is that it is valid for the entire range of dataset. The nonlinear regression equation obtained
in the present analysis (i.e. equation 4) is used to compare it with the GEP model.
III. GENE EXPRESSION PROGRAMMING (GEP)
Gene-Expression Programming (GEP) is a new evolutionary Artificial Intelligence (AI)
technique developed by Ferreira [24, 25]. This technique is an extension of genetic programming
(GP). The genome is encoded as linear chromosomes of fixed length, as in Genetic Algorithm (GA);
however, in GEP the genes are then expressed as a phenotype in the form of expression trees. GEP
combines the advantages of both its predecessors, i.e., genetic algorithm and genetic programming,
and thus removes their limitations. GEP is a full-fledged genotype/phenotype system in which both
are dealt with separately, whereas GP is a simple replicator system. As a consequence of this
difference, the complete genotype/phenotype GEP system surpasses the older GP system by a factor
of 100.In GEP, just like in other evolutionary methods, the process starts with the random generation
of an initial population consisting of individual chromosomes of fixed length. The chromosomes
may contain one or more than one genes. Each individual chromosome in the initial population is
then expressed, and its fitness is evaluated using one of the fitness function equations available in the
literature. These chromosomes are then selected based on their fitness values using a roulette wheel
selection process. Fitter chromosomes have greater chances of selection for passage to the next
generation. After selection, these are reproduced with some modifications performed by the genetic
operators. In gene expression programming, genetic operators such as mutation, inversion,
transposition and recombination are used for these modifications. Mutation is the most efficient
genetic operator, and it is sometime used as the only means of modification. The new individuals are
then subjected to the same process of modification, and the process continues until the maximum
number of generations is reached or the required accuracy is achieved. Because a random numerical
constant (RNC) is a crucial part of any mathematical model, it must be taken into account; however,
gene expression programming has the ability to handle RNCs efficiently. In GEP, an extra terminal
‘?’ and an extra domain ‘Dc’ after tail of the each gene is introduced to handle RNCs [23].
IV. GEP MODELLING FOR SCOUR DEPTH PREDICTION AT THE BRIDGE
ABUTMENT
In the present study, a new approach has been adopted for scour depth prediction model using
Gene Expression Programming (GEP), that was developed by Candida Ferreira in 1999 [24, 25]. In
GEP, the individuals are encoded as linear strings of fixed length (the genome or chromosomes)
which are afterwards expressed as nonlinear entities of different sizes and shapes (i.e. simple
diagram representations or expression trees). The great insight of GEP consisted in the invention of
chromosomes capable of representing any expression tree. For that Ferreira [24, 25] created a new
language (which she named as Karva language) to read and express the information of GEP
chromosomes. Furthermore, the structure of chromosomes was designed to allow the creation of
multiple genes, each encoding a sub-expression tree. The genes are structurally organized in a head
and a tail, and it is this structural and functional organization of GEP genes that always guarantees
the production of valid programs, no matter how much or how profoundly we modify the
chromosomes. There are five major steps to use gene expression programming [24, 25].
The first major step is to select the fitness function and initial population. For the present
problem, the fitness fi of an individual program i is measured by the following expression:
݂௜ = ∑ ൫‫ܯ‬ − ห‫ܥ‬ሺ௜,௝ሻ − ܶ௝ห൯
஼೟
௜ୀଵ (5)

29
where M is the range of selection, C(i,j) is the value returned by the individual chromosome i
for fitness case j (out of Ct fitness cases) and Tj is the target value for fitness case j. Now, if ห‫ܥ‬ሺ௜,௝ሻ −
ܶ௝| (the precision) less or equal to 0.01, then the precision is equal to zero, and fi= fmax = Ct.M. In this
case, M = 100 is used and, therefore, fmax = 1000. The advantage of this kind of fitness function is
that the system can find the optimal solution for itself [24, 25].
The second major step consists in choosing the set of terminals T and the set of functions F to
create the chromosomes. In this, the terminal set consists obviously of the independent variable(s),
(see table 2) but the choice of the appropriate function set is not so obvious, but a good guess can
always be done in order to include all the necessary functions[24, 25].
The third major step is to choose the chromosomal architecture, i.e., the length of the head
and the number of genes. A single gene and two head lengths were used initially and then, the
number of genes and heads were increased by one at a time during each run until the most
appropriate fit was obtained. It was observed that more than 7 genes and a head length greater than
twelve did not significantly improve the performance of GEP model. Thus, the head length, h = 12,
and 7 genes per chromosome were employed for the GEP model in the present study.
The fourth major step is to choose the linking function. In this study, addition was used as a
linking function and the final step is to choose the set of genetic operators that cause variation and
their rates. A combination of all genetic operators (mutation, transposition and crossover) is used for
this purpose (Table 2).
The explicit formulation of the GEP for the scour depth prediction at the bridge abutments in
the cohesive sediments has been obtained as:
yොୱ = ቂቄ
଴.଴଴଴ଵଵଶ
τ̂౩
+ logሺFୟሻ + ሺlogሺCଶሻଵ଺
ሻ + ൫0.162ሺCሻ൯ቅ − 0.548ቃ + ሾ0.884ሺWcሻሿ (6)
The expression trees for the above GEP formulation are shown in Figs.2(a) and 2(b). In these
figures, D0 = -0.548, D1 = 0.000112, D2 = 0.162, D3 = 16, D4 = 2 and D5 = 0.884.
Table. 2: Summary of GEP parameters
S. No. GEP Parameters Description
1. Population Size 36
2. Genes per chromosome 7
3. Gene head length 12
4. Functions + - × ÷ √ and log
5. Gene tail length 13
6. Mutation rate 0.044
7. Inversion rate 0.1
8. Gene transposition rate 0.1
9. One point recombination rate 0.3
10. Two point recombination rate 0.3
11. Gene recombination rate 0.1
12. Fitness function Root relative squared error

30
(a) (b)
Fig.2: Expression trees for the GEP model
V. PERFORMANCE OF SCOUR DEPTH PREDICTION MODELS AT BRIDGE
ABUTMENTS IN COHESIVE SEDIMENTS
In order to assess the performance of the various scour depth prediction models at bridge
abutments in cohesive sediments under considerations, the commonly used performance parameters
such as Root Mean Squared Error (RMSE), Mean Percentage Error (MPE), coefficient of correlation
(R) and Mean Absolute Deviation (MAD) are adopted in the present study.
Table. 3: Performance evaluation of models
Performance parameters Nonlinear regression (present study) GEP
R 0.82 0.87
MPE -3.04 -3.08
MAD 14.11 12.15
RMSE 0.19 0.17
The performance parameters for the GEP and the regression models for the same set of
scour data are shown in Table 3. It may be observed from this table that the correlation coefficient of
nonlinear regression of the present study is 0.82 and that of GEP is 0.87 whereas Debnath et al.[21]
equations 1, 2 and 3 are 0.98, 0.98 and 0.94 respectively. The MAD and RMSE of present regression
equation are more than that of GEP model. Since, the correlation coefficients of the Debnath’s
equations are better than the correlation coefficient of the equations obtained in this study, but it
should be noticed here that in the present analysis, the whole range of data have been used to obtain
scour prediction equation in order to obtain a single equation and so that to minimise the complexity
of the problem identified. Hence, it may be concluded that the performance of GEP is best among all
scour depth prediction equations in the present study. The scatter diagram between observed and

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976
ISSN 0976 – 6316(Online), Volume 5, Issue 11, November (2014), pp.
predicted relative scour depth has been shown in Fig.3. This figure also indicates that the gene
expression programming is least s
nonlinear regression equation.
Fig.
VI. CONCLUSION
The aim of the present study is to address the complexity of the scour phenomena and to
formulate it into a simple model. The prediction model for scour depth available in the literature
were based on nonlinear regression and were discrete, thus further accounting to complexity.
Gene expression programming (GEP) was implemented as an alternative tool for m
depth prediction at bridge abutment
performance over that of the conventional regression prediction model
that the performance of GEP is more encouraging an
model for the prediction of scour depth at bridge abutment in cohesive beds.It is observed that the
equation obtained by GEP (R=0.87 and RMSE=0.17) is much simpler and far better than the
regression equations proposed by Debnath’s equations
that not only GEP can suitably accounts for complexity and nonlinearity
cohesive sediments but also it can reduce the complex model into a simple equ
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International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976
6316(Online), Volume 5, Issue 11, November (2014), pp. 25-32 © IAEME
31
expression programming is least scattered from the line of perfect agreement than that of the
Fig.3: Plot of observed v/s predicted
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that the performance of GEP is more encouraging and better than that of the conventional regression
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Gene expression programming (GEP) was implemented as an alternative tool for modelling of scour
embedded in cohesive sediments and comparison of its
has been made. It was found
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0.87 and RMSE=0.17) is much simpler and far better than the
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Prediction of scour depth at bridge abutments in cohesive bed using gene expression programming