* Author to whom all correspondence should be
addressed: e-mail: mostafa.yousefirad@yahoo.com
Analysis of Protection of Body Slope in the Rockfill Reservoir Dams
on the Basis of Fuzzy Logic
Mostafa Yousefi Rad
1*
, Sina Shaffiee Haghshenas
2
,
Payam Rajabzade Kanafi
2
and Sami Shaffiee Haghshenas
3
1*
Department of Geology, Faculty of Earth Sciences, Payam Noor University, Po BOX 38195-854, Arak, Iran
2
Department of Civil engineering, Islamic Azad University, Arak branch, Arak, Iran
3
Department of Civil engineering, Islamic Azad University, Astara branch, Astara, Iran
Keywords: Body Slope, Rockfill Reservoir Dam, Fuzzy Multiple Criteria Decision, Fuzzy Analytical Hierarchical.
Abstract: The objective of this study is to survey the most appropriate way to protect body slope of the rockfill
reservoir dams on the basis of fuzzy multiple criteria decision and analyze the Fuzzy Analytical Hierarchy
Process (FAHP). In the present study, the reservoir dam of Shahr-e-Bijar, situated in Guilan province of
Iran, has been studied. Also, for using the fuzzy analytical hierarchy process, eight important criteria in
order to select the fittest way to protect body slope of the dam as well as five methods, namely, Riprap,
Concrete facing, Asphalt concrete, Soil – Cement, and Geo-synthetic protection have been studied and
analyzed. The fuzzy numbers used in this study are triangle fuzzy numbers. Moreover, Visual Basic
Program has been used in calculations. Due to the result of the study, concrete protection is the best method
among all other methods used to protect the body slope of the dams.
1 INTRODUCTION
Iran is one of the arid and semiarid countries in the
world which has about fifty five dusty dams. So,
constructing control and storage dams are very
important. Storage dams consist of different parts.
Upstream and downstream slopes are among those
parts (Rahimi, 2003).
In a rockfill reservoir dam, slope protection
especially upstream slope protection is one of the
most important parts which should be designed and
chosen very carefully otherwise occurring lots of
damages will be unavoidable.
Therefore, to prevent the erosion and destruction
of upstream and downstream slopes of the rockfill
reservoir dams, a suitable protective method should
be considered. Making decision and choosing an
appropriate method in such cases are usually
complicated therefore quantitative and qualitative
criteria are very important. Hence, in this article
based on the Fuzzy Multi-Criteria Decision Making
(FMCDM) and Fuzzy Analytical Hierarchy Process,
it has been tried to consider most appropriate
method to protect body slope of the reservoir dams
in constructing Shahr-e-Bijar dam which is a rockfill
dam. The dam designers are going to use concrete
facing to cover the dam.
In this study eight effective criteria, including the
economic advantage, resistance to environmental
factors, cut-off, being a hard work, being time
consuming, plasticity, destructive environmental
impacts, and accessibility of materials for five
methods of body slope protection of rockfill
reservoir dams have been determined. Then, all
factors have been examined. Further, by using the
process of fuzzy analytical hierarchy, triangle fuzzy
numbers as well as fuzzy logic, the accuracy or
inaccuracy of the decision and the analysis of all
items have been analyzed.
2 THE CRITERIA OF THE
STUDY
Having collected and analyzed the data required for
the study, eight criteria which are effective in
choosing the best method for protecting upstream
slope of rockfill reservoir dams have been considered
as the following:
economic advantage, resistance to
367
Yousefi Rad M., Shaffiee Haghshenas S., Rajabzade Kanafi P. and Shaffiee Haghshenas S. (2012).
Analysis of Protection of Body Slope in the Rockfill Reservoir Dams on the Basis of Fuzzy Logic.
In Proceedings of the 4th International Joint Conference on Computational Intelligence, pages 367-373
DOI: 10.5220/0004153803670373
Copyright
c
SciTePress
Yousefi Rad M., Shaffiee Haghshenas S., Rajabzade Kanafi P. and Shaffiee Haghshenas S..
Analysis of Protection of Body Slope in the Rockfill Reservoir Dams on the Basis of Fuzzy Logic.
DOI: 10.5220/0004153803670373
In Proceedings of the 4th International Joint Conference on Computational Intelligence (FCTA-2012), pages 367-373
ISBN: 978-989-8565-33-4
Copyright
c
2012 SCITEPRESS (Science and Technology Publications, Lda.)
environmental factors, cut-off, hardship of doing
job, being time consuming, plasticity,
environmental destructive effects as well as
accessibility of materials. These criteria are
classified in two categories as quantitative and
qualitative criteria.
3 FIVE METHODS FOR
PROTECTING THE SLOPES
OF STORAGE DAMS
3.1 Riprap
One method of protecting the body of the dam's
slope is using riprap protection. This layer is usually
located on a filter made of sand and gravel with
proper granulation. The material which is used as
riprap should be made of sound stone so it can resist
against factors such as frequent drying and wetting
as well as weathering and erosion. Riprap protection
is carried out in two ways hand placed and dumped.
3.2 Concrete Facing
Using concrete protection is another commonly
used method in protecting dam’s body slope.
Supplying the required materials is one of the
requirements in this protection method. Generally
speaking, due to the fact that applying the recently
mentioned method costs more than riprap
protection, concrete protection would be thiner than
that of the riprap. Concrete protective layers are
either located next to each other as mosaic sheets or
noncoplanar and disordered layers. Concrete
protection is carried out in the shape of reinforced or
non reinforced concrete.
3.3 Asphalt Concrete
Another protective method is asphalt concrete
protection or more accurately, concrete asphalt
protection.
This protection is consisted of a mixture of sand
and or fine sand with tar which can be used as
protective layer in protecting of dam’s body slope
through a proper mix design.
3.4 Soil–cement Protection
Soil-cement protection is one of the construction
materials which has been used since 1920s and
enjoys competitive economic advantage and
simplicity. One of the most significant applications
of soil – cement protection is using this protection as
a protective coverage of a dam body slope. The
quality of soil – cement protection is affected by
factors such as the amount of applied cement
(Rahimi, 2003), the moisture content, granulation of
the soil and the density percentage.
3.5 Geo-synthetic Protection
Technological development in petrochemical
industries leads to the usage of geo synthetic
protection. This kind of materials belongs to the
family of polymers which are divided in two
categories including geo-textiles and geo-membrine
categories. These substances enjoy multiple
properties such as reinforcing the soil for increasing
the resistance of soil, filtration, cut-off, separating
different materials and drainage. Ultraviolet rays and
sun light lead to the decrease of the resistance of the
materials.
4 FUZZY ANALYTICAL
HIERARCHY PROCESS STEPS
ACCORDING TO CHANG’S
METHOD
The AHP method cannot straightforwardly be
applied to solving uncertain decision problems and
imprecisely defined ones. In this case, a natural way
to cope with such uncertain judgments is to the
comparison ratios as fuzzy judgments as fuzzy sets
or fuzzy numbers. The fuzzy set theory was proposed
by (Zadeh, 1965, pp.338-353), and Bellman and
Zadeh (1970), described the decision making method
in fuzzy environment. (Laarhoven and Pedrycz,
1983, pp.229-241).
Proposed the first studies that applied fuzzy logic
principle to AHP (Koorepazan, 2008). Buckley
(1985) initiated trapezoidal fuzzy numbers to express
the decision maker’s evaluation on alternatives with
respect to each criterion. Asgharpour (1997) while
Laarthoven and Pedrycz were using triangular fuzzy
numbers. Chang (1996) introduced a new approach
for handling fuzzy AHP, with the use of triangular
fuzzy numbers for pair-wise comparison scale of
fuzzy AHP, and with use the extent analysis method
for the synthetic extend values of the pair-wise
comparison.
One of the most important applications of this
logic is in multi-criteria decision making. Also, one
of the most common methods of fussy multi- criteria
IJCCI2012-InternationalJointConferenceonComputationalIntelligence
368
decision making is the Fuzzy Analytical Hierarchy
Process (FAHP) method.
Lee et al., (2008), Zare et al., (2009) and Tang
(2009) are among those researchers who use fuzzy
multi-criteria hierarchy process in their works for
energy conservation, choosing underground mining
method of Jajroom bauxite mine of Iran, and budget
appropriation for Space Company respectively.
Also, with this regard Yager et al., (1999), Leung et
al., (2000), Karhaman et al., (2003) and Atai et al.,
(2007) research can be mentioned. Chang (1996) is
a researcher who has done different researches and
presented different methods about Fuzzy Analytical
Hierarchy Process. In a fuzzy multi-criteria decision
making of Chang’s fuzzy analytical hierarchy
process with m items and n criteria, seven steps
have been defined.
4.1 Step One: Hierarchical Graph
Drawing
In this step, first the hierarchical graph of the
subject of the study is drawn in three levels: the first
level (the objective), the second level (criteria), and
the third level (the investigated items). Of course,
the criterion of decision making may have some
sub-criteria of decision making in the second level.
4.2 Step Two: Defining Fuzzy
Numbers for Pairwise
Comparisons
The fuzzy numbers which can be used are triangle
and trapezoid fuzzy numbers. The fuzzy scale of
numbers is obtained through considering each
selected fuzzy number as well as its membership
function.
4.3 Step Three: Forming Pairwise
Comparison (
A
) Matrix with
Fuzzy Numbers
Matrix of pairwise comparison (
A
) will be as
follows:
(1)
Fuzzy numbers of the matrix are as follows:
(2)
4.4 Step Four: Calculation of Each
Rows of Pairwise Comparison
Matrix
If I and j represent the numbers of rows and columns
and
j
g
i
M
show triangle fuzzy numbers of pairwise
comparison matrix, the amount of
1
m
j
g
i
j
M
11
nm
j
g
i
ij
M
,
1
11
nm
j
gi
ij
M
is calculated as following:
1111
,,
mmmm
j
gi j j j
jjjj
M
lmu
(3)
11 1 1 1
,,
nm n n n
j
gi i i i
ij i i i
M
lmu
(4)
1
11
11 1
111
,,
nm
j
gi
nm n
ij
iii
ii i
M
uml
(5)
4.5 Step Five: Calculation of Values
Magnitude
In this step the magnitude of each value is compared
to other values.
Consider
,, , S ,,
22221111
SLmu Lmu
as two
triangle fuzzy numbers. In order to determine their
magnitude degree, the following equation is used.
The degree of largeness has been shown in Figure 1.
21
22
112
12
22 11
2( )
)
2
()
1 ifm
( 0 ifl
otherwise
()()
d
Ss
VS S
m
hgt S u
lu
mu ml
(6)
Figure 1: The largeness degree of two triangle fuzzy
numbers S
1
, S
2
in relation to each other.
31111
1 i=j
1,3,5,7,9 or 1 ,3 ,5 ,7 ,9 i j
ij
a
AnalysisofProtectionofBodySlopeintheRockfillReservoirDamsontheBasisofFuzzyLogic
369
4.6 Step Six: Calculating the Priority
of Each Criterion and Item in
Pairwise Matrices
In this stage use from following equation:
( ) ( ) K=1,2,...,n , k i
iik
dA MinVS S
(7)
Through the following equation the vector of non
normalized priority can be obtained.
2
( ( ), ( ),..., ( ))
T
in
wdA dA dA
(8)
4.7 Step Seven: Determining and
Calculating the Overall Priority
Vector
In this stage, the vector of priority which was
calculated in the previous step is normalized so the
overall priority vector is obtained.
12
(( ),( ),...,( ))
T
n
WdAdA dA
(9)
5 EVALUATING THE MOST
APPROPRIATE COVERAGE
FOR PROTECTING BODY
SLOPE OF SHAHR-E-BIJAR
STORAGE DAM
Shahr-e-Bijar reservoir dam is located 8 kilometers
far from Shahr-e-Bijar village, 35 km from Rasht,
on Zilky River in Guilan province of Iran. Zilky
River enters Sepidrood River from the eastern of
Sepidrood Drainage basin (watershed). The storage
capacity of this dam reservoir is 105 million cubic
meters which can also store water up to 165 million
cubic meters،Figure 2. This reservoir dam is a
rockfill one،Figure 3, therefore the correct choice of
upstream slope protection type is of utmost
importance. In this article, the most appropriate type
of upstream slope protection for Shahr-e-Bijar
reservoir dam with the use of the Fuzzy Analytical
Hierarchy Process has been examined.
Figure 2: Location of the dam.
Figure 3: Upstream slope of dam.
5.1 Drawing of Hierarchical Graph for
Evaluating the Most Appropriate
Protection Coverage
The hierarchical structure of this decision for Shahr-
e-Bijar reservoir dam has been shown in figure 4.
Figure 4: Analytical Hierarchy Chart.
The best protection of upstream slope of reservoir dam of Shahr Bjar
Economic
interest
Resistance
against the
environment
factors
Cut-off
Long time
taking of the
project
Hardship of
doing the job
Getting
shape
Environment
al effects
Materials
access
(getting
access)
Riprap
Concrete
facinfg layer or
protections
Asphalt
concrete layer
protections
Soil – Cement
layer or
protections
Geo synthetic
layers or
protections
IJCCI2012-InternationalJointConferenceonComputationalIntelligence
370
5.2 Difining the Fuzzy Numbers
The fuzzy numbers used in this research are as
follows:
1
1
1
1
1
1(1.1.1)
11
2 (1, 2, 4) 2 ( , ,1)
42
11
3 (1, 3,5) 3 ( , ,1)
53
111
4 (2, 4, 6) 4 ( , , )
642
111
5 (3,5, 7) 5 ( , , )
753
111
6 (4, 6,8) 6 ( , , )
864
(10)
5.3 Making a Pairwise Comparison
Matrix and Doing All 7 Steps
Regarding all eight criteria, five choices, and
available statistical information or data, the pairwise
comparison matrix is established. Then, for each row
of pairwise comparison matrix, the required
calculations should be done and the greatness degree
of each compared to others is measured based on no.
5 and 6 formulas. Since calculations are to be carried
out accurately and its time consuming, all
calculations as well as the overall priority of each
item and criterion can be calculated with the use of
Visual Basic Software and then they should be
normalized. The amount calculated for each item is
examined based on each criterion and then the results
have been shown in figures 5 to 13.
F
igure 5: Normalized weight of choices in relation to the
criterion of economic interest.
Figure 6: Normalized weight of choices in relation to th
e
criterion of assistance environmental factors.
F
igure 7: Normalized weight of choices in relation to the
criterion of cut-off.
Figure 8: Normalized weight of choices in relation to th
e
criterion of hard ship of job.
F
igure 9: Normalized weight of choices in relation to the
criterion of project time taking.
Figure 10: Normalized weight of choices in relation to th
e
criterion of being formed.
AnalysisofProtectionofBodySlopeintheRockfillReservoirDamsontheBasisofFuzzyLogic
371
Table 1: Results and final score of each of the options.
Economic
interest
Assistance
environmental
factors
Cut-off
Hard ship of
job
Project time
taking
Being formed
Environmental
destructive
effects
Material access
Final score
0.167 0.184 0.169 0.079 0.035 0.105 0.14 0.121
Rip rap 0.145 0.181 0 0.006 0.116 0.26 0.063 0.102 0.11
Concrete
facing
0.26 0.308 0.368 0.162 0.19 0.114 0.175 0.291 0.253
Asphalt
concrete
0.218 0.231 0.305 0.23 0.193 0.182 0.259 0.236 0.24
soil-cement
protection
0.184 0.105 0.185 0.278 0.244 0.221 0.35 0.207 0.209
Geo synthetic
protection
0.192 0.175 0.123 0.324 0.275 0.221 0.154 0.163 0.184
F
igure 11: Normalized weight of choices in relation to
the criterion of environmental destructive effects.
Figure 12: Normalized weight of choices in relation to th
e
criterion of material access.
Figure 13: Normalized weight of each criteria.
Finally, results and final score of each of the options
as shown in Table 1.
6 CONCLUSIONS
Five methods which have been used in the
protection of the slope of the reservoir dam of
Shahr-e-Bijar and have been analyzed through
analytical Hierarchy are as the following:
Riprap, concrete facing protection, asphalt
concrete protection, soil – cement protection and geo
synthetic protection.
Shahr-e-Bijar reservoir dam is a rockfill dam
type with concrete facing protection. According to
the results, it can be concluded that the applying
concrete facing protection is the best method of
protection among all the other alternatives.
Moreover, applying concrete coverage was also
proved to be a proper method. However, according
to the results of the present investigation it can be
declared that if concrete facing protection is not
used, the most proper protection is asphalt concrete
protection which has the highest resemblence to the
concrete facing protection through which slope of
the aforementioned dam can be protected.
ACKNOWLEDGEMENTS
We would like to express our deepest thanks to
Professor Lashteneshaee for his excellent advice.
We would also like to thank all those who helped us
in conducting this research.
IJCCI2012-InternationalJointConferenceonComputationalIntelligence
372
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