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SYSTEMS SCIENCE & CONTROL ENGINEERING: AN OPEN ACCESS JOURNAL
2021, VOL. 9, NO. 1, 430–439
https://doi.org/10.1080/21642583.2021.1919936
Vulnerability evaluation method of inland waterway revetment project subjected
to wave and current
Meili Wanga,b, Shengfa Yangb, Jie Zhangband Xiaoling Lic
aCollege of Architecture and Urban Planning, Chongqing Jiaotong University, Chongqing, People’s Republic of China; bCollege of Hehai,
Chongqing Jiaotong University, Chongqing, People’s Republic of China; cSouthwest Water Transportation Engineering Research Institute,
Chongqing Jiaotong University, Chongqing, People’s Republic of China
ABSTRACT
The flood damage of inland waterway revetment project has become one of the most serious dis-
asters that affect the water transportation, municipal environment, human life and property safety.
Scientific and reasonable evaluation of the vulnerability of waterway revetment eProject subjected
to wave and current can effectively prevent and reduce disaster losses. According to the character-
istics of multi factors and fuzziness in the vulnerability evaluation of waterway revetment project
subjected to wave and current, a two-level fuzzy comprehensive evaluation mathematical model for
vulnerability assessment is established by using fuzzy mathematics method. Based on the field inves-
tigation and observation data of the waterway revetment project in the middle and upper reaches
of the Yangtze River and the relevant measurement of laboratory experiments, four main factors
affecting the stability of the waterway revetment project, including design and construction, pro-
tective measures, wave-current characteristics and river waterway factors, are selected based on the
establishment of vulnerability evaluation index system. Analytic hierarchy process (AHP) is used to
determine the weight of evaluation factors and their sub factors, which improves the objectivity
and scientificity of vulnerability assessment of waterway revetment project subjected to wave and
current.
ARTICLE HISTORY
Received 24 February 2021
Accepted 17 April 2021
KEYWORDS
Wave and current; revetment
project; vulnerability
evaluation; fuzzy
mathematics; membership
degree
1. Preface
The damage degree of inland waterway revetment
project is closely related to climate, geology, hydrology,
hydraulic, river environmental conditions, engineering
design and construction, and improvement of protective
measures. The disaster-bearing body of different bank
protection projects suffers from the same intensity of
water damage, and the loss degree may be different. The
same disaster-bearing body suffers from different inten-
sity of water damage to the same extent, that is, the
vulnerability is different. The so-called vulnerability of the
disaster-bearing body refers to the degree of difficulty of
the disaster-bearing body suffering from different inten-
sities of water damage. The vulnerability evaluation of
inland waterway revetment project and its water damage
protection facilities is to find out the advantages and dis-
advantages of the waterway revetment project’s ability
to resist the wave-current loading, so as to take effec-
tive preventive and remedial measures in time, which
is of great significance to ensure the safety of human
economic activities and reduce disaster losses.
CONTACT Meili Wang wml9106@163.com
At present, there are many researches on the hazard
or risk assessment of geological disasters such as land-
slides, collapses, and mudslides (Ali et al., 2014; Erener
&Düzgün,2013; Liu et al., 2012). There are also lots of
investigations on risk analysis and evaluation of flood
disaster, especially on flood resistance capacity of high-
way and waterway and flood damage assessment (Chen,
2012; Wang, Yang & Wang, 2015;Wangetal.,2018). How-
ever, the research on vulnerability evaluation of water-
way revetment project subjected to wave and current is
relatively less. Among all kinds of disaster risk and vul-
nerability assessment, the commonly used and mature
evaluation methods mainly include comprehensive index
method, fuzzy comprehensive evaluation method and
chromatography analysis method. As one of the compre-
hensive evaluation methods, fuzzy mathematics method
has the advantages of simple mathematical model, easy
operation, and good evaluation effect for complex prob-
lems with multi factors and multi-level. Therefore, when
the evaluation factors or levels of some specific problems
are fuzzy, the comprehensive evaluation is called fuzzy
© 2021 The Author(s). Published by Informa UK Limited, trading as Taylor& Francis Group.
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distribution, and reproduction in any medium, provided the original work is properly cited.
SYSTEMS SCIENCE & CONTROL ENGINEERING: AN OPEN ACCESS JOURNAL 431
comprehensive evaluation, also known as fuzzy compre-
hensive evaluation (Li, 2004). Fuzzy comprehensive evalu-
ation is a kind of evaluation based on the principle of fuzzy
transformation and the principle of maximum subordina-
tion. Fuzzy comprehensive evaluation has the advantages
of simple calculation and strong practicability. It is an
effective mathematical method to deal with fuzzy eval-
uation problems. It is widely used in the risk assessment
of geological disasters such as debris flow in various engi-
neering construction, landslide stability evaluation, water
conservancy engineering stability evaluation and high-
way engineering risk assessment (He et al., 2011; Liao
et al., 2013,2015;Ma,2008; Slingerland & VoightPaolo,
1982;Wangetal.,2004;Yang,2014;Zhao&Tan,2017;Zou
et al., 2019). According to the characteristics of multi fac-
tors and fuzziness in the vulnerability evaluation of water-
way revetment project subjected to wave and current,
a two-level fuzzy comprehensive evaluation mathemat-
ical model for vulnerability evaluation is established by
using fuzzy mathematics method. The evaluation factor
set, comment set and weight set are determined by com-
bining with engineering examples, and the vulnerability
of waterway revetment project under wave and current is
evaluated.
2. Overview of fuzzy comprehensive evaluation
method
Fuzziness is a kind of uncertainty, that is, it is difficult to
determine whether an object conforms to the concept
of something. Fuzzy comprehensive evaluation method
is a comprehensive evaluation method based on fuzzy
mathematics. According to the membership degree the-
ory of fuzzy mathematics, the comprehensive evaluation
method transforms qualitative evaluation into quantita-
tive evaluation. Thus, fuzzy mathematics is used to make
an overall evaluation of things or objects restricted by
many factors. It has the advantages of clear results and
strong systematicness, and can solve the fuzzy and diffi-
cult to quantify problems, which is suitable for solving all
kinds of non deterministic problems. The disadvantage is
that the calculation is relatively complex and the deter-
mination of index weight vector is subjective. In 1965,
Zadeh, an expert in automatic control theory, put forward
the concept of fuzzy set and used membership function
to describe the fuzziness of the object. This approximates
accuracy to fuzziness. Therefore, it is necessary to intro-
duce the fuzzy theory to study the vulnerability of river
revetment.
2.1. Fuzzy sets and membership functions
Let the total objects under discussion be called the field,
denoted by U. Objects in the domain are called elements
and are represented by U. A part of the elements in uni-
verse Uis called a set on universe U, which is called A.
According to general set theory, there are only two rela-
tions between element uand set Ain universe U, either
u∈A,oru/∈A. Both must occupy one and only one of
them. However, the attribution of many things is ‘one
or the other’, that is, there are not only two relations
between the element uand set Ain the field U, and some
of them belong to this relation, that is fuzziness. This kind
of set which contains some elements or whose boundary
is not clear is called fuzzy set, which is usually represented
by A
∼.
Then, a given universe U,A
∼is a fuzzy set over U,iffor
any u∈U, it can be determined a number μA(u)∈[0, 1],
which indicates the degree to which ubelongs to A
∼,which
means that a mapping is made:
μA(u):U→[0, 1]
u→μA(u)
The mapping μAis called the membership function
of A
∼, and the number μA(u)is called the membership
degree of element uin Uto Fuzzy Set A
∼. The degree of
membership can also be recorded as A
∼(u).
It can be seen from this definition that fuzzy sets are
completely characterized by membership functions. The
determination of membership function is the basis of
fuzzy theory, but so far there is no unified method to
determine membership function. The determination of
membership function is based on subjective factors of
human beings, but can never be arbitrary, and must be
based on objective laws. Usually, the rough membership
function is initially determined, and then, through con-
stant practical tests, it is gradually revised and improved
to achieve the final agreement between the subject and
the objective. There are many methods available for the
determination of membership function, such as subjec-
tive determination method (expert experience method),
typical function method, fuzzy statistics method, example
method, multidimensional scale method, etc.
2.2. Steps of fuzzy comprehensive evaluation
(1) Establish the factor set
The factors that affect the main indexes of the water-
way revetment to resist the damage caused by wave-
current are composed of factor set U, and the factors in
Uare divided into mcategories according to their prop-
erties, namely, msubsets:
u={u1,u2...,um}(1)
432 M. WANG ET AL.
where ui(i=1, 2, ...,m)is the ith factor subset. Let each
factor subset include nfactors:
u1={ui1,ui2...,uim }(2)
Among them, uij(i=1, 2, ...,m;j=1, 2, ...,n)is the
jth factor of the ith factor subset, and different imay have
different n. Each factoruij(i=1, 2, ...,m;j=1, 2, ...,n)is
divided into plevels according to its degree. If the design
level is divided into five grades: high, relatively high,
general, relatively low, low, it can be expressed as the
following factor level set:
uij ={uij1,uij2...,uijp}(3)
Among them, uijk(k=1, 2, ...p)is the kth rank of fac-
tor uij. The factor hierarchy set should be regarded as a
fuzzy subset on the hierarchy universe:
uij =μij1
uij1
+μij2
uij2
+...+μijp
uijp
(4)
Among them, uijk is the membership degree of uij’s kth
grade to the factor.
(2) Set up a collection of comments
Before the vulnerability evaluation of waterway revet-
ment, the evaluation set should be established. Evalua-
tion set is given by the review of each level evaluation
index set of comments (language), is all kinds of possible
results in various evaluation factors for the elements of a
collection of Vl(l=1, 2, ...,q), that is, V=v1,v2,...,vqas
the comment set, where vqis the qth possible evaluation
result.
(3) First-level fuzzy comprehensive evaluation
The fuzzy comprehensive evaluation was carried out
according to the grade of each factor, μijk could be
evaluated according to the standard designated by
K-level, which is subordinated to j-factor in i-category, the
membership degree of the first factor in the evaluation
setisasfollows:rijkl (i=1, 2, ...,m;j=1, 2, ...,n;k=
1, 2, ...p;l=1, 2, ...,q), then the evaluation matrix of
factor uij is as follows:
Rij =⎡
⎢
⎢
⎣
rij11 rij11 ... rij1q
rij21 rij22 ... rij1q
... ... ... ...
rijp1rijp2... rijpq
⎤
⎥
⎥
⎦(5)
In order to make each factor have a common evalu-
ation matrix Rij to simplify the calculation, the grade of
each factor should be arranged according to the consis-
tency of the evaluation objects.
In order to reflect the influence of a factor on the value
of the evaluation object, the weight assigned to each level
of the factor is called the weight set of the factor level.
If the weight of factor grade uijk is aijk, the weight set of
factor uij is as follows:
Aij
∼
=(aij1,aij2,...,aijp)(6)
Among them, aijk =μijk/p
k=1μijk(i=1, 2, ...,m;
j=1, 2, ...,n)
The first level fuzzy comprehensive evaluation set is as
follows:
Bij
∼
=Aij
∼
·Rij
∼
=(bij1,bij2,...,bijl)(7)
Among them, bijl =p
k=1aijkl ·rijkl(i=1, 2, ...m;
j=1, 2, ...n;l=1, 2, ...,q),bijl is a general fuzzy com-
prehensive evaluation index, which represents the mem-
bership degree of the evaluation object to the lth element
in the comment set when fuzzy comprehensive evalua-
tion is carried out according to all levels of factors.
(4) Multi-level fuzzy comprehensive evaluation
According to all factors uij(i=1, 2, ...,m;j=1, 2, ...,
n)of the prime subset ui, fuzzy comprehensive evalua-
tion is carried out. The single factor evaluation set Bij of
uij should be the first level fuzzy comprehensive evalua-
tion set Bij, so the single factor evaluation matrix of uiis as
follows:
Ri
∼
=
⎡
⎢
⎢
⎢
⎢
⎢
⎣
Bi1
∼
Bi2
∼
...
Bin
∼
⎤
⎥
⎥
⎥
⎥
⎥
⎦
(8)
If aij is the weight of factor uij, the weight set of subset
uiis as follows:
Ai
∼
=(ai1,ai2,...,ain)i=(1, 2, ...,n)(9)
The primary fuzzy comprehensive evaluation set is as
follows:
Bi
∼
=Ai
∼
·Ri
∼
=(bi1,bi2,...,biq)(10)
Among them, bil =n
j=1aijbijl (i=1, 2, ...m;l=1,
2, ...,q),bil is the primary fuzzy comprehensive evalua-
tion index, which represents the membership degree of
the first element in the alternative set when the evalua-
tion object is comprehensively evaluated according to all
the sub factors of the uiof the factor subset.
SYSTEMS SCIENCE & CONTROL ENGINEERING: AN OPEN ACCESS JOURNAL 433
The single factor evaluation set Riof type ishould be
the primary fuzzy comprehensive evaluation set Bi,sothe
single factor evaluation matrix of Vis as follows:
R
∼=
⎡
⎢
⎢
⎢
⎢
⎢
⎣
B1
∼
B2
∼
...
Bn
∼
⎤
⎥
⎥
⎥
⎥
⎥
⎦
=[bil]m×q(11)
If the weight of the ifactor of class uiis ai, the weight
set of the factor set Uis:
A
∼=(a1,a2,...,ap)(12)
The second-level fuzzy comprehensive evaluation
set is:
B
∼=A
∼·R
∼=(b1,b2,...,bq)(13)
Among them, bl=ai·ril(l=1, 2, ...,q).blis the
total fuzzy comprehensive evaluation index, which repre-
sents the membership degree of the lth element in the
comment set when the evaluation object is evaluated
according to all factors.
After getting the evaluation index bl, when deter-
mining which comment the comprehensive evaluation
result belongs to, the principle of maximum member-
ship degree is adopted. In other words, the value of the
comment set corresponding to max blis taken, and then
the evaluation result is determined as a certain comment
according to the evaluation set.
3. Fuzzy comprehensive evaluation method for
vulnerability of river revetment project
subjected to wave and current
3.1. Determination of evaluation factor set and
comment set
In view of the complex system of flood damage of water-
way revetment subjected to wave and current, there are
a lot of uncertainties in the evaluation factors due to the
diversity, variability and complexity of the natural envi-
ronmental conditions in which it is located. This kind of
uncertainty has randomness and fuzziness, and the fac-
tors are often divided into different levels. If the first level
evaluation is adopted, it is difficult to compare the good
and bad order of the things in the system, and no mean-
ingful evaluation results can be obtained. Therefore, the
fuzzy comprehensive evaluation method is used to eval-
uate the vulnerability of waterway revetment project to
water damage. In the process of fuzzy evaluation, the
selection of evaluation factors and the construction of
subjection function should be carried out in combination
with the characteristics of river revetment.
(1) Determination of evaluation factor set
According to the principles of objectivity, scientificity,
rationality and integrity, the vulnerability evaluation
index of waterway revetment project subjected to wave
and current should be selected. It is required that the
assessment factor set should include the main factors
which have significant impact on the vulnerability of
revetment works to water damage as comprehensively
as possible, and the influence factors are independent
of each other, without inclusion relationship, so as to
avoid repetition. In addition, the vulnerability assessment
of bank revetment project needs to distinguish the pri-
mary and secondary factors while considering all the
influencing factors systematically and comprehensively.
In order to avoid complicated evaluation and analysis,
some minor factors which have no obvious influence can
be ignored.
In the selection of the evaluation index of the flood
damage vulnerability of the waterway revetment sub-
jected to wave and current, not only the factors of the
project itself, but also the protection and maintenance
measures, flood, wave and other factors that have impor-
tant influence on the project vulnerability should be con-
sidered, which makes the selection of evaluation fac-
tors involve many factors. The strength of vulnerability
is determined by the function of each influencing fac-
tor, and each influencing factor is determined by the
action characteristics of its sub factors. Therefore, the
comprehensive evaluation of vulnerability is a multi-
factor and multi-level comprehensive evaluation prob-
lem. However, subjective factors often account for a large
proportion in the comparison and selection of evaluation
factors, most of which are fuzzy and difficult to describe
with quantitative data.
Under the wave-current loading, the water damage of
waterway revetment project is the result of interaction
and interaction among revetment project, wave-current
dynamics and sediment erosion and deposition. The ero-
sion damage of bank protection engineering is the main
type of water damage, and the scouring intensity and
depth will directly affect the safety of bank protection
engineering. In practice, it is generally not allowed to
have a large degree of scouring to affect the integrity and
stability of the revetment project. Therefore, riprap, soft
mattress, permeable frame, hydraulic plug-in board and
spur dike are usually used to resist the scour and ero-
sion induced by wave and current (Ma, 2008;Wangetal.,
2018).
In this study, the appropriate evaluation factors are
selected from the angle of bank protection damage
caused by lash and collision. The selection of evalua-
tion index is based on the data of field investigation
434 M. WANG ET AL.
and indoor experiment observation, and widely absorb-
ing the research results of relevant experts. According
to the fuzzy mathematics theory, after comprehensive
induction, analysis and research comparison, the evalu-
ation index is established. Then, many factors are divided
into four categories. The factor set Uthat affects the vul-
nerability of waterway revetment works is divided into
four sub-factors, specifically:
(1) Design and construction (u1): the anti-impact capac-
ity of revetment project largely depends on its own
strength and stability, and the design and construc-
tion factors play a key role in the strength and stability
of the project itself.
It can be analysed from four aspects:
(a) Geological composition of bank slope (u11): The nat-
ural geological composition of bank slope or the
quality of artificial fillings affect the stability of bank
revetment project. For revetment project, the bear-
ing capacity as well as the permeability of natural
geological composition or human engineering filler
should be considered. Therefore, the slope geologi-
cal type often determines the anti-erosion character-
istics and stability of the slope surface.
(b) Design rationality (u12): the ability of the waterway
revetment to resist the wave-current impact dam-
age is related to the flood control standard and
waterway grade, and the ability to resist the dam-
age is also different when the flood control standard
and waterway grade are different. In addition, the
design of cross-section and vertical section, drainage
design, filling water content and treatment of slope
toe of revetment all have influence on the stability
of the project. The optimization of design scheme
can effectively reduce the occurrence of water
damage.
(c) The slope of the upstream surface of bank slope
(u13): the slope of the upstream surface of protec-
tive structures such as river revetment and retaining
wall (slope coefficient m), which is also an important
parameter affecting the maximum scouring depth
of the river bank. The increase of slope coefficient
can largely reduce the impact capacity of current
and wave, and reduce the depth and scope of
scour pit. When m=0 and other conditions remain
unchanged, the maximum scouring depth reaches
its maximum, and the maximum scouring depth
decreases with an increase of M. Generally, under the
vertical condition of the side wall (m=0), the maxi-
mum erosion depth of the river bank is multiplied by
the erosion reduction coefficient Kmof the previous
slope to reflect the influence of slope coefficient m
on the erosion depth.
(d) Construction quality (u14): mainly including foun-
dation treatment, groundwater, treatment of filling
and excavation joint, treatment of adverse geolog-
ical conditions, compaction and levelling of filling
materials, construction technology, etc. The higher
the construction quality, the better the stability of the
project.
(2) Protective measures (u2): the common anti-scour
structures of slope toe and foundation of revetment
project mainly include riprap and soft rock body row,
permeable frame, hydraulic plug plate, spur dike and
their combination forms. Due to the long-term lash-
ing, dashing, scouring and erosion induced by cur-
rent and wave, the irrational selection of protection
form and plane layout are also important reasons for
water damage. Therefore, the setting and use of pro-
tective structures are very important to evaluate the
vulnerability of revetment and the ability to resist
wave and current.
(a) Layout perfection (u21): including the type, size,
masonry materials, strength, quantity (scale), lay-
out location, foundation buried depth and ratio-
nality of its own protection. These factors affect
the impact resistance, erosion resistance and
wear resistance of protective structures.
(b) Maintenance and maintenance (u22): it refers to
whether the engineering stability is inspected
regularly, whether the maintenance are timely
and reasonable, the intensity of the implementa-
tion of the disaster control project, maintenance
and maintenance technology and the establish-
ment of archives, etc. This is related to the effec-
tiveness and durability of the protection project.
(3) Wave-current characteristics (u3): mainly considered
from two aspects of local velocity and wave height.
(a) Local flow velocity (u31): the shape of river
section (Canyon / open reach) has significant
influence on the cross-section distribution of
velocity. Water conservancy facilities, river reg-
ulation and development and utilization activi-
ties (river dredging, sand excavation and earth
rock piling) change the local topography of the
riverbed, disturb the flow, and increase the cross-
section heterogeneity of flow velocity. When the
velocity is small, the bank slope is gentle and
the revetment building blocks are large, which
can resist the scour and impact of the current
and maintain the stability of the project. How-
ever, in the case of high flow velocity, the struc-
tures on the bank slope are easy to be impacted
SYSTEMS SCIENCE & CONTROL ENGINEERING: AN OPEN ACCESS JOURNAL 435
and scoured and become unstable. At the same
time, the greater the local flow velocity, the
stronger the ability to carry sand and gravel in
the riverbed, and the more likely to cause ero-
sion damage to the bank slope and its protective
structures. Therefore, in practice, the local flow
velocity and the threshold velocity of revetment
block stone and surrounding riverbed sediment
can be determined, while the ratio was calcu-
lated and judged.
(b) Wave height (u32): the wind-induced wave, ship
travelling wave, flood discharge wave of dam
and surge wave formed by landslide will have
significant impacts and scouring effect on revet-
ment project, leading to instability and damage
of the project. The higher the wave height, the
greater the impact force on the bank slope, and
the more likely to cause damage to the bank
slope and its protective structures. According to
the requirements of discharge wave height in
‘emergency plan for storm surge, wave, tsunami
and sea ice disaster’ issued by the State Oceanic
Administration (State Oceanic Administration,
2012) and the general design code for ship lock
(Industry standards of the People’s Republic of
China, 2001), considering that the inland river is
a non-open narrow water area, the early warning
division of wave risk for inland waterway project
safety is carried out. When the wave height
is greater than 2 m, it is extremely dangerous.
When the wave height is between 1.5 and 2 m, it
is a high dangerous area. When the wave height
is between 1 and 1.5 m, it is a medium dangerous
area. When the wave height is between 0.5 and
1 m, it is a low risk area. When the wave height is
less than 0.5 m, it is a low risk area.
(4) Waterway factors (u4): it is mainly evaluated from
two aspects of waterway morphology and riverbed
composition.
(a) Waterway morphology (u41): The curved and
straight plane shape of the river makes the flow
pattern different. The flow in curved waterway
is related to the change of geometric bound-
ary conditions. The main parts of bank revet-
ment project are as follows: concave bank of
river bend and straight section of concave bank
near the outlet of river bend; Canyon reach
and its upstream and downstream; oblique and
top scour points of wave and current caused
by topography and nearby downstream, which
indicates that river morphology has significant
influence on the location of water damage. The
influence of waterway shape on revetment can
Tab le 1 . Vulnerability evaluation index system of revetment
project.
Indicator System Influence Factor Factor Subset
Vulnerability
index system
of revetment
project U
u1Design and
construction
u11 Geological composition
of bank slope
u12 Rationality of design
u13 Bank slope
u14 Construction quality
u2Protective measures u21 Layout integrity
u22 Maintenance and repair
u3Wave-current
characteristics
u31 Local flow velocity
u32 Wave he ight
u4Water way factors u41 River configuration
u42 Riverbed composition
be comprehensively evaluated according to the
bending degree of river waterway, compression
ratio of cross section and local terrain change.
(b) Riverbed composition (u4): the riverbed com-
position can be generally divided into clay and
non-clay, leading to different scour resistance.
For non-clay riverbed (sandy river bed, sandy
pebble bed), the main parameters affecting
riverbed deformation and scouring depth are
sediment particle size and sediment gradation.
Due to the non-uniformity of sediment in natu-
ral rivers, the influence of sediment heterogene-
ity on local scour depth of revetment works or
protective structures should be considered. For
clay riverbed, it is related to the type and con-
tent of cohesive soil, clay characteristics and clay
compression and consolidation state. The size
and classification of sediment particles adopt the
classification method of China’s Hydrologic Engi-
neering field (Qian & Wan, 1983).Combined with
the above analysis, the vulnerability assessment
factors of river revetment project subjected to
wave and current are listed in Table 1.
(2) Determination of comment set
Before the vulnerability assessment of waterway revet-
ment project, a set of comments should be established.
The evaluation set is a collection of comments (language
description) given by the reviewers for each level of eval-
uation indicators, and it is also a set composed of various
possible results of each evaluation element.
In order to better describe the nature and degree of
advantages and disadvantages of each factor or sub-
factor in the evaluation, this study divides the evalua-
tion of the vulnerability evaluation model into five levels,
which can be expressed as:
That is, V={v1,v2,v3,v4,v5}={extremely high vul-
nerability, high vulnerability, medium vulnerability, low
vulnerability, very low vulnerability}.
436 M. WANG ET AL.
Tab le 2 . Grading standards for each evaluation factor.
Rating scale
Score
Factor set 10 8 6 4 2
Design and
construction u1
Geological
Composition of
bank slope u11
Other weak Banks Clayey soil or silty soil Gravel soil with
good water
permeability
Drift (block) stone soil,
pebble soil, gravel
soil or gravel soil,
etc.
Hard rock that is not
easily weathered
Rationality of
design u12
Extremely poor: the
cross-section and
drainage design
of the project
is extremely
unreasonable
Poor: poor design of
cross-section and
drainage of the
project
General: the
horizontal and
vertical sections
and drainage
design of the
project are
basically feasible
Good: the cross-section
and drainage design
is reasonable
Excellent: the
cross-section and
drainage design
schemes have
been compared
and selected
Superior scheme
Bank slope u13 m=00<m≤0.75 0.75 <m≤1.25 1.25 <m≤2.0 m>2.0
Construction
quality u14
Extremely poor:
improper
foundation
treatment
measures and
poor construction
technology
Poor: unreasonable
base treatment
and poor
construction
technology
General: the
foundation
treatment of the
project is basically
reasonable, and
the construction
technology is
general
Good: good foundation
treatment and
good construction
technology
Excellent: the
foundation
treatment
measures are
reasonable and
the construction
technology is
good
Anti-erosion
measures u2
Layout perfection
u21
Extremely poor:
no anti-scour
prevention
measures
Poor: the anti-scour
type and structural
strength are
unreasonable
General: the anti-
scour type and
structural strength
are reasonable
Good: the anti-scour
type and structural
strength are
generally good
Excellent: good
anti-scour type
and structural
strength
Maintenance u22 Extremely poor: no
maintenance and
disaster control
measures
Poor: the main-
tenance is not
timely, and
the treatment
measures are
unreasonable
General: temporary
subgrade
maintenance
and treatment
measures
Good: the maintenance
and repair is timely,
and the treatment
measures are
feasible
Excellent: timely
maintenance and
repair, reasonable
treatment
measures
Wave-current
characteristics u3
Local flow velocity
u31
It is higher than the
threshold velocity
of revetment
block stone and
surrounding
riverbed sediment
It is slightly higher
than the threshold
velocity of
revetment
block stone and
surrounding
riverbed pebble
It is equal to the
starting velocity
of revetment
block stone and
surrounding
riverbed pebble
It is smaller than the
starting velocity
of the larger block
stones and the
pebbles in the
riverbed around the
revetment
It is far less than the
threshold velocity
of revetment
block stone and
surrounding
riverbed pebble
Wave he ight u32 H>2m 1.5m <H≤2m 1m <H≤1.5 m 0.5m <H≤1m H ≤0.5 m
Riverway factor u4Riverway
morphology u41
Sharp bend reach
(θ≥90°);
The local topography
of the river waterway
causes the obvious
top or oblique
scour of water flow;
Section compression
ratio ≥45%
Highly curved reach
(60° <90°);
The results show that
the local topography
of the river causes
obvious top or
oblique scour, and
the compression
ratio of river section
is 30–45%
The results show that
the river section is
moderately curved
(30° <θ≤60°);
the local
topography of the
river waterway
causes obvious
water crest or
oblique scour; the
compression ratio
of river section is
15–30%
The results show
that there is a
slight bend section
(θ≤300); the local
topography of the
river waterway does
not cause the water
toprushoroblique
scour; the section
compression ratio of
the reach is ≤15%
There is no
local abrupt
topography in the
waterway
Riverbed com-
position
u42
Mainly boulders
(particle size
greater than
200 mm)
Mainly pebbles
(20–200 mm)
Mainly gravels
(2–20 mm)
Mainly sandy soil
(0.05–2 mm)
Mainly fine grained
soil (particle size
less than 0.05 mm)
In order to facilitate the evaluation, score values are
assigned to each impact factor respectively, and it is pro-
posed to establish the evaluation grade comment set
V={v1,v2,v3,v4,v5}={10,8,6,4,2}in the form of a 10-
point scale. The upper limit of each grade is used in the
evaluation.
Through investigation and analysis, combined with
expert consultation and evaluation, the basis and
standards for determining the different rating levels of
each evaluation factor are shown in Table 2.
3.2. Determination of membership function
Membership degree refers to the degree of member-
ship of the factor set to the comment set, and is the
contribution of various evaluation factors to vulnerability.
SYSTEMS SCIENCE & CONTROL ENGINEERING: AN OPEN ACCESS JOURNAL 437
The factor membership function is constructed by the
method of half trapezoid.
(1) Determination of membership function of quantita-
tive element evaluation index set
According to the optimal value and the worst value of
the scoring results, vj(j=1, 2, 3, 4) is discretized as the
comment set according to the equal step size. The results
show that vjand vj+1 are the two adjacent classification
criteria. If vj>vj+1
, the membership function of factor to
vjis:
r(x)=0, x>vj,x<vj+1
(x−vJ+1)/(vj−vJ+1),vj+1≤x≤vj
(14)
If vj<vj+1
, then the membership function of the fac-
tor to vjlevel is:
r(x)=0, x>vj+1,x<vj
(vJ+1−x)/(vj+1−vJ),vj≤x≤vj+1
(15)
In the equation: r(x)is the membership function; X is
the score of the index.
(2) Determination of membership function of qualitative
factor evaluation index set
The qualitative factor evaluation index is based on
the same evaluation grade standard after comprehensive
comparison and analysis of the same element in each
scheme by experts. The score of a certain element is set as
X, and the calculation method of its membership function
is the same as Equations (14) and (15).
3.3. Determination of weight set
In fuzzy comprehensive evaluation, the determination of
weight will have a great impact on the final evaluation
results. There are many methods which can be used to
determine the weight, such as expert estimation method,
analytic hierarchy process (AHP), etc. No matter which
method is used, whether the weight is reasonable or
not mainly depends on the detailed understanding of
the disaster investigation of river revetment project and
the experience of experts. In this study, based on the
field investigation, the weight of the evaluation factor
set and the factor subset in the evaluation index sys-
tem is determined by the conventional AHP, which is
a multi-objective decision analysis method combining
quantitative and qualitative methods (Wang, 2016;Xu,
1988). Finally, the factor weight sets of sub elements cor-
responding to various elements are calculated by using
AHP:
(5) The weight set of each kind of factor
A1
∼
=(0.2, 0.5, 0.1, 0.2),A2
∼
=(0.667, 0.333)
A3
∼
=(0.333, 0.667),A4
∼
=(0.667, 0.333)
(6) Factor class weight set
A
∼=(0.275, 0.513, 0.138, 0.074)
According to the above method, the vulnerability
assessment can be carried out for specific river revet-
ment. In practice, the evaluation index can be increased
or decreased flexibly, and the weight set can also be
adjusted appropriately.
4. Application examples of evaluation methods
In this study, the vulnerability of the waterway revetment
project in Nanxi urban section of Yibin City is evaluated.
Nanxi urban area of Yibin City is located on the left bank of
the Yangtze River, which is 42 km downstream of the con-
fluence of Jinsha River and Minjiang River. The Yangtze
River is 55 km long in Nanxi area, and the river course is
distributed in ‘S’ shape. The river section of the revetment
project is located on the left bank of the upper section of
the Dananmen bend. The river surface is narrowed, with
an average width of 855 m. The left bank is a terrace of
the Yangtze River, and the right bank is a steep moun-
tain. The total length of the revetment project is 5603 m,
and the waterway revetment project is constructed with
local gravel. The natural slope angle of the engineering
area is 15°–25°, and the surface layer is mainly silty soil,
with a thickness of 1–5 m. The lower part is sand and
gravel layer. The riverbed in this reach is composed of
pebbles and bedrock. The flow velocity is high and the
flood season high water level lasts for a short period.
Affected by the flood discharge wave from the upstream
to Xiangjiaba Water Conservancy project, a wave about
2.1 m high is formed in this reach. The embankment body
of the project is filled with rolled sand and gravel, and the
upstream slope ratio is 1:1.8. The cast-in-place concrete
slope protection is adopted, and the diameter of drainage
hole is 3 cm. The slope protection surface is added with
concrete lattice green plants, and the upstream water toe
protection adopts the steel wire cage with the gravel par-
ticle size of no less than 10 cm. The riverbed evolution
analysis and model test are used to study the engineer-
ing design scheme. The engineering construction tech-
nology and construction technology are good, and the
maintenance is timely. The comprehensive ability of the
project to resist wave and current disasters is improved,
and the ecological landscape effect is good (Lu et al.,
2017), as shown in Figure 1.
438 M. WANG ET AL.
Figure 1. Bank revetment of Nanxi City section of Yibin upper reaches of the Yangtze River.
Tab le 3 . Evaluation Form for the vulnerability of the revetment
works in Nanxi urban section.
U
u1u2u3u4
Factor u11 u12 u13 u14 u21 u22 u31 u32 u41 u42
Score 5.5 3.5 4.0 3.5 3.0 2.5 8.0 10.0 6.5 7.5
According to the criteria for the grading of each evalu-
ation factor in Table 2, the ratings are shown in Table 3.
According to the score value of each factor, the fuzzy
mapping from uito Vis established by the reduced half
trapezoid method of constructing membership function,
and the fuzzy relation matrix Riis determined. According
to the factor weight set of various elements and their cor-
responding sub-elements calculated above. The results
of the first level fuzzy comprehensive evaluation can be
obtained:
B1
∼
=A1
∼
·R1
∼
=(0 0 0.15 0.75 0.1);
B2
∼
=A2
∼
·R2
∼
=(0 0 0 0.42 0.58);
B3
∼
=A3
∼
·R3
∼
=(0.667 0.333 0 0 0);
B4
∼
=A4
∼
·R4
∼
=(0 0.42 0.58 0 0);
The results of second level fuzzy comprehensive eval-
uation are as follows
B
∼=A
∼·R
∼=(b1,b2,b3,b4,b5)=(0.1 0.08 0.08 0.42 0.32)
According to the maximum membership method,
b4=max bl=0.42(1≤l≤5)can be obtained. There-
fore, the fourth evaluation result is determined as ‘low
vulnerability’. The current actual operation situation (no
water damage) is basically consistent with the comple-
tion of the main construction of the project in April 2009.
5. Conclusions
(1) The vulnerability evaluation of inland waterway
revetment project should adopt the combination of
qualitative and quantitative methods, and the main
influencing factors should be selected for objective
and scientific comprehensive evaluation. In order to
meet the needs of vulnerability analysis, through the
comprehensive comparison of a large number of pro-
totype observation data and research results, the
design and construction (geological composition of
bank slope, rationality of design, slope of upstream
surface of bank slope, construction quality), protec-
tive measures (layout perfection, maintenance and
repair), wave-current characteristics (local flow veloc-
ity, wave height) these four main factors that affect
the stability of waterway revetment project, includ-
ing 10 sub factors.
(2) According to the characteristics of multi factors and
fuzziness in the vulnerability evaluation of waterway
revetment project subjected to wave and current,
a two-level fuzzy comprehensive evaluation mathe-
matical model for vulnerability evaluation of water-
way revetment project under wave-current loading
is established by using fuzzy mathematics method,
and the steps of fuzzy comprehensive evaluation are
given. Based on the establishment of vulnerability
evaluation index system, AHP is used to determine
the weight of evaluation factors and their sub factors.
(3) The relevant evaluation methods are used to evalu-
ate the vulnerability of the bank revetment project
SYSTEMS SCIENCE & CONTROL ENGINEERING: AN OPEN ACCESS JOURNAL 439
of Nanxi urban section of Yibin City in the upper
reaches of the Yangtze River, the weight of the eval-
uation index and the vulnerability evaluation results
are given. The vulnerability evaluation result of the
project is ‘low vulnerability’, which is consistent with
the actual project operation. The fuzzy mathemat-
ics method is feasible to evaluate the vulnerability
of waterway revetment projects under the action of
waves and currents, which provides a reference for
the vulnerability assessment and disaster prevention
of other similar river revetment projects.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Funding
The authors would like to acknowledge the financial sup-
port from the Science and Technology Research Program
of Chongqing Municipal Education Commission [Geomorphic
changes of the upper reaches of the Yangtze River under new
water and sediment conditions and their impacts on habitat
conditions, No. KJQN-201900745]; National Key R&D Program
of China [Technology for online monitoring, early warning and
functional recovery intelligent decision making on Service sta-
tus of inland waterway facilities, 2018YFB1600403].
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