Fuzzy set based crack diagnosis system for reinforced concrete structures

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Computers and Structures 85 (2007) 1828–1844

Fuzzy set based crack diagnosis system for reinforcedconcrete structures

Yeong Min Kim a, Chee Kyeong Kim b,*, Geon Ho Hong c

a MIDAS IT Co., Ltd., SKn Technopark Tech Center 15th fl. 190-1 Sangdaewon1-dong, Jungwon-gu, Seongnam, Gyeonggi-do, 462-721, Republic of Koreab Department of Architectural Engineering, Sunmoon University, Kalsan-ri, Tangjeong-myeon, Asan-si, Chungnam 336-708, Republic of Korea

c Department of Architectural Engineering, Hoseo University, Baebang-myun, Asan-si, Chungnam 336-795, Republic of Korea

Received 27 October 2006; accepted 30 March 2007Available online 23 May 2007

Abstract

This paper presents a computer assisted crack diagnosis system for reinforced concrete structures which aids the non-expert to diag-nose the cause of cracks at the level of an expert in the general inspection of structures. The system presented adapts fuzzy set theory toreflect fuzzy conditions, both for crack symptoms and characteristics which are difficult to treat using crisp sets. The inputs to the systemare mostly linguistic variables concerning the crack symptoms and some numeric data about concrete and environmental conditions.Using these input data and based on built-in rules, the proposed system executes fuzzy inference to evaluate the crack causes under con-sideration. The built-in rules were constructed by extracting expert knowledge, primarily from technical books about concrete and con-crete cracks. We implemented the proposed system in a computer program with a graphic user interface for actual utilization in practicalbusiness fields. When applied to cracks actually diagnosed by experts, the proposed system provided results similar to those obtained byexperts, and we expect that this system can be used as an effective crack diagnosis tool for both experts and non-experts in the regularinspection of RC structures.� 2007 Elsevier Ltd. All rights reserved.

Keywords: Fuzzy set; Crack diagnosis; Reinforced concrete; General inspection; Safety diagnosis; Structural Assessment

1. Introduction

Structures deteriorate and are damaged by variouscauses, in particular, the lowering of the structural capac-ity, durability and water resistance of concrete structuresare primarily caused by cracks. Thus, the need for regularinspection and proper repair and rehabilitation schemes toprevent the permeation of deterioration into sound areas,and hence to maintain and enhance structural capacityand serviceability throughout the life cycle of structures.

There have been many specifications and guidebooks forthe maintenance and management of concrete structures[1–8]. Most of them treat cracks with special interest and

0045-7949/$ - see front matter � 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.compstruc.2007.04.001

* Corresponding author. Tel.: +82 41 530 2321; fax: +82 41 530 2839.E-mail address: [email protected] (C.K. Kim).

explain the importance of cracks to concrete structures.Therefore, it is very important to make it possible fornon-experts to perform the early diagnosis of cracks inthe regular inspection stages of concrete structures, and,based on the inspection results, to judge the need for morethorough inspection or special safety diagnosis, and henceto establish prompt repair and rehabilitation schemes tolengthen the life expectancy of structures [9].

The features of concrete cracks gathered from visualinspection are inherently subject to uncertainty and ambi-guity, and fuzzy based data manipulation has shown goodapplicability in these areas [10,11]. In this study, we presenta computer assisted crack diagnosis system which adaptsfuzzy set theory to reflect fuzzy conditions both for cracksymptoms and characteristics which are difficult to treatusing crisp sets. The inputs to the system are mostly linguis-tic variables concerning the crack symptoms and some

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Table 1Classification of causes of cracks

Category of crackcause

Crackno.

Causes of cracks

Concrete material A1 Abnormal setting of cement pasteA2 Heat of hydration of cementA3 Abnormal expansion of cementA4 Clay in aggregateA5 Low quality aggregateA6 Reactive aggregateA7 Chloride in concreteA8 Settlement and bleeding of concreteA9 Shrinkage of concrete

Construction work B1 Unequal dispersion of admixtureB2 Overtime mixingB3 Segregation during pumpingB4 Improper placement sequenceB5 Rapid placementB6 Insufficient compactionB7 Vibration or loading before

hardeningB8 Rapid shrinkage during initial curingB9 Initial frost damageB10 Improper treatment of work jointB11 Movement of reinforcing barB12 Insufficient protective coveringB13 Deformation of formsB14 Leakage (from form or ground)B15 Early removal of formsB16 Settlement of form support

Service andenvironmentalfactors

C1 Change in external temperature orhumidity

C2 Temperature/humidity gap betweenmember surfaces

C3 Repetition of freezing and thawingC4 FireC5 Surface heatingC6 Chemical reaction of acid and

chlorideC7 Corrosion of reinforcing bar

(neutralization)C8 Corrosion of reinforcing bar

(penetrated chloride)

Structure and appliedloads

D1 Eternal long time loading withindesign load

D2 Eternal long time loading over designload

D3 Dynamic short time loading withindesign load

D4 Dynamic short time loading overdesign load

D5 Lack of section size and reinforcingbars

D6 Differential settlement of structureD7 Freezing of ground

Y.M. Kim et al. / Computers and Structures 85 (2007) 1828–1844 1829

numeric data about concrete and environmental condi-tions. Using these input data and based on built-in rules,the proposed system executes fuzzy inference to estimatethe causes of cracks. The built-in rules were constructedby extracting expert knowledge from technical books aboutconcrete and concrete cracks, primarily books published bythe Japanese Concrete Institute and the Architectural Insti-tute of Korea [12,13].

2. Summary of previous research on crack diagnosis

Research on diagnosing cracks in concrete structureshas been carried out by various researchers and organiza-tions [10,12,13], and the results have shown good applica-bility in practical business fields. The systems or methodsdeveloped for diagnosis are, however, generally not appro-priate for use by non-experts performing regular inspec-tions, so the need for an easy-to-use diagnosis system fornon-experts has arisen. In this section, we consider two typ-ical studies of crack diagnosis and investigate their meritsand limits.

2.1. Fuzzy pattern recognition model for crack diagnosis

Chao et al. presented a crack diagnosis model for RCstructures based on fuzzy pattern recognition and cause-and-effect diagramming [10]. Causes and effects in theircause-and-effect diagram mean causes and symptoms ofcracks, respectively, and are related by fuzzy concepts.Causes are divided into two classes: primary and second-ary-level cause parameters. Primary-level cause parametersinclude four categories of crack causes – materials used,fabrication of structural elements, environmental condi-tions, and loading – and secondary-level cause parametersinclude detailed crack causes for each category of crackcauses. Effects are also divided into two classes: primaryand secondary-level characteristics. Primary-level charac-teristics include the time of crack formation, depth, regu-larity, and range of cracks, and secondary-levelcharacteristics include the type of the member, crack pat-tern, and crack location.

Linguistic variables are used to describe the degree ofrelationship between a cause and a characteristic. The diag-nosis proceeds on two levels. The first is to determine themost likely cause of the crack(s) on the primary level,and the second is to determine the most likely cause ofthe crack(s) on the secondary level. At each stage, crackcauses are obtained by performing pattern comparisonsfor each pair of fuzzy patterns among the cause parametersusing the weighted Hamming distance. The degree of con-firmation for the selected fuzzy pattern is also computed.

The proposed method produced good results by adapt-ing fuzzy linguistic variables and well defined diagnosticlevels to better represent realistic circumstances, but thediagnosis process is somewhat cumbersome and difficultfor the non-expert, because it requires professionalknowledge.

2.2. Checklist based crack diagnosis

JCI gave in detail a diagnosis method for concrete cracksfrom standard inspection [12]. Here, the causes of cracks aredivided into 40 classes as shown in Table 1, and are relatedto the crack symptoms as shown in Table 2. The diagnosisproceeds using both crack symptoms and construction

Table 2Definition of crack symptoms

Criterion of crack symptom Crack symptom Symptomno.

Time of formation Several hours–1 day S1Several days S2More than severaltens of days

S3

Shape Turtle S4Surface S5Penetrate S6

Regularity Regular S7Irregular S8

Cause of concrete deformation Contraction S9Expansion S10Settlement bendingshear

S11

Range Material S12Member S13Structure S14

Weather conditions during concreteplacement

High temperature S15Low temperature S16Dryness S17

Condition of concrete mixing Rich mix S18Lean mix S19

1830 Y.M. Kim et al. / Computers and Structures 85 (2007) 1828–1844

records and follows four independent stages, that is (1)decide the category of the crack cause, (2) perform crackpattern based diagnosis, (3) perform diagnosis based ondesign documents and construction records, and (4) per-form diagnosis based on the conditions of concrete mixingand weather conditions during concrete placement. If com-mon crack causes which appear in all four stages exist theyare evaluated as the primary causes, otherwise, the most fre-quent crack causes are regarded as the next best crackcauses. There may be more than one selected crack cause.The fourth stage is not essential and can be omitted if thecorresponding data are not obtainable.

The method proposed by JCI is mostly appropriate formiddle level engineers or for those who have special knowl-edge about cracks, for it is difficult for non-experts or pri-mary level engineers to decide the category of crack causesas required in the first stage. In addition, when consideringsuch items as are essential to the diagnosis, but for which itis difficult to determine the attribute values, there is nochoice but to consider all cases, which results in decreasedexactness of the diagnosis. Diagnosed crack causes of thesame appearance, that is, primary causes or the next bestcauses, etc. are treated equally, and it is therefore impossi-ble to distinguish the importance differences between evi-dent symptoms and weak symptoms. For such items astime of crack formation, condition of concrete mixing,and temperature and humidity during concrete placement,the attribute values of which can be acquired numericallyand whose contribution to the diagnosis must be treatedon a continual basis, there is the problem of treating themin a binary fashion.

3. Design of crack diagnosis system

3.1. Outline of crack diagnosis system

In this study we designed a crack diagnosis system refer-encing the method presented by JCI, added graphical cracktypes extracted from technical books, and adapted fuzzyinference to better reflect realistic circumstances and toimprove the performance of the diagnosis. The proposedsystem considers all the crack characteristics generally usedin crack diagnosis: the crack symptoms as presented inTable 2. Generally, the condition of concrete mixing andweather conditions during concrete placement are not con-sidered as direct crack symptoms, but are considered asindirect circumstances for crack causes, so these data arenot essentially required, but are used to complement andreinforce the diagnosis results worked out by othersymptoms.

The proposed system diagnoses causes of cracks by fol-lowing four steps as shown in Fig. 1. The steps are com-posed of estimation of crack causes based on (1) primarycrack type (PCT), (2) primary symptom combination(PSC), (3) reinforcing data (RFD), and (4) final determina-tion of crack causes.

The first two steps perform fuzzy operation and fuzzyinference on the input values of the linguistic variablesand numeric data concerning the crack symptoms, and cal-culate the possible values of each crack cause. The thirdstep performs fuzzy operation and fuzzy inference on theinput values of the numeric data and produces reinforcingvalues for each crack cause. The fourth step calculates thefinal possibility values by integrating the results of the pre-vious three steps and ranks the crack causes. The possibil-ity values are in the range of 0–1 and can be considered asthe reliability value of each crack cause: the higher the cal-culated value or rank, the more reliable is the determina-tion of the crack causes for the given cracks.

The primary crack type (PCT) is the typical crack typepeculiar to each structural member or the whole structure.The primary symptom combination (PSC) is the combina-tion of several related crack symptoms, which we classify asprimary symptom combination I (PSC I), and primarysymptom combination II (PSC II), where PSC I is the com-bination of crack symptoms in respect to crack patterns,and PSC II is the combination of crack symptoms inrespect to the cause of concrete deformation and the rangeof cracks. The reinforcing data (RFD) are used as indirectcomplementary data for the estimation of crack causes andis composed of concrete mixing conditions and weatherconditions during concrete placement.

3.2. Composition of primary crack type (PCT) and fuzzy

operation

The primary crack type (PCT) is the graphical represen-tation of typical crack types peculiar to each structuralmember or to the whole structure. For evident and typical

Fig. 1. Diagnostic process of proposed system.


cracks, approximate estimation of their causes is possibleonly by primary crack type. Primary crack type is definedas the union of the sub primary crack types, that is, pri-mary crack types of girder, column, wall, slab and structureexpressed as PCTGL, PCTCL, PCTWL, PCTSL and PCTTL,respectively, as in Eq. (1). And each sub primary crack typeis defined as the union of the typical crack types of its owntype as in Eq. (2):

PCT ¼ fPCTGL;PCTCL;PCTWL;PCTSL;PCTTLg ð1ÞPCTGL ¼ fGL1;GL2;GL3; . . . ;GL15gPCTCL ¼ fCL1;CL2;CL3; . . . ;CL12g

PCTWL ¼ fWL1;WL2;WL3; . . . ;WL14g ð2Þ

PCTSL ¼ fSL1;SL2;SL3; . . . ;SL13g

PCTTL ¼ fTL1;TL2;TL3; . . . ;TL5g

The causes of cracks according to the crack types of thestructural member or the whole structure are representedin Table 3. These typical crack types and their causes weredefined by referencing technical manuals dealing with con-crete and concrete cracks [1–4,12,13].

For the given crack, diagnosis from the PCT isperformed first by selecting the crack types most similar

Table 3Causes of cracks according to the crack types of member or structure

Member type Crack typeno.

Feature of cracks Estimated crack causes

Girder GL1 Vertical cracks on middle lower region B7, B15, B16, D1, D2, D5GL2 Inverted V-shaped diagonal cracks on telocentric region B15, B16, D1, D2, D5GL3 X-shaped diagonal cracks on telocentric region D3, D4GL4 Asymmetric diagonal cracks on telocentric region D6GL5 Vertical cracks along stirrup A7, B4, B11, B12, C6, C7, C8GL6 Cracks along main reinforcing bar and stirrup A7, B4, B11, B12, C6, C7, C8GL7 Cracks perpendicular to member axis A2, A9, B3, B15GL8 Horizontal cracks on boundary surface A8, B3, B5, B10GL9 Irregular turtle cracks A3, A4, B2, B8, B9, C3, C4,

C5GL10 Irregular turtle cracks and equally spaced large crack A3, A4, C4, C5GL11 Radiative cracks along member axis A6GL12 Irregular short cracks on overall region A1, B2, B6GL13 Irregular cracks on specific regions B1GL14 Popped cracks A5GL15 Vertical cracks on supporting region of cantilever B7, B13, B15, B16, D1, D2, D5

Column CL1 Horizontal cracks on the whole upper region B7, B15, D1, D2, D5CL2 Horizontal cracks on one side of upper region B16, D6CL3 Cracks consistent with neighboring walls A8, B3, B5, B10, D6CL4 X-shaped diagonal cracks on middle region B7, B15, B16, D3, D4, D5CL5 Popped cracks A5CL6 Radiative cracks along member axis A6CL7 Horizontal cracks on the edges A9, B3, B15CL8 Equally spaced horizontal cracks A7, B11, B12, C6, C7, C8CL9 Cracks along reinforcing bars A7, B4, B11, B12, C6, C7, C8CL10 Irregular turtle cracks A3, A4, B2, B8, B9, C3, C4,

C5CL11 Irregular cracks on specific regions B1CL12 Irregular short cracks on overall region A1, B2, B6

Wall WL1 X-shaped diagonal cracks on the corner of opening A9, B3, D1, D2, D3, D4, D5WL2 X-shaped diagonal cracks D3, D4WL3 Unidirectional diagonal cracks D3, D4, D6WL4 Cracks along with neighboring columns A2, B7, B15, B16, D1, D2WL5 Vertical cracks on the middle region C1, C2, D6WL6 Horizontal cracks along work joint A8, B3, B5, B10WL7 Diagonal cracks on the corner and vertical cracks on the middle region A9, B3, C1WL8 Cracks spaced along horizontal bar A7, B4, B11, B12, C6, C7, C8WL9 Grid like equally spaced cracks A7, B4, B11, B12, C6, C7, C8WL10 Irregular turtle cracks A3, A4, A6, B2, B8, B9, C3,

C4, C5WL11 Radiative cracks on the overall region A6WL12 Irregular short cracks on overall region A1, B2, B6WL13 Popped cracks A5WL14 Irregular cracks on specific regions B1

Slab SL1 Cracks along beam or girder (top side) B6, B7, B11, B12, B15, B16,D1, D2, D5

SL2 Bidirectional diagonal cracks on the middle region (bottom side) B7, B15, B16, D1, D2, D5SL3 Cracks along beam or girder (spaced constant distance) B7, B15, B16, D1, D2, D3, D4,

D5SL4 Horizontal crack on the middle region and diagonal crack on the corner A9, B3SL5 Horizontal crack on the middle region A8, A9, B3SL6 Diagonal crack on the corner A9, B3, B16, D3, D4, D6SL7 Cracks on the upper side of cantilever slab B11, B12, B13, B15, B16, D1,

D2, D5SL8 Grid like cracks along reinforcing bars and subsidence in specific parts A7, A8, B3, B4, B5, B11, B12,

C6, C7, C8SL9 Irregular turtle cracks A3, A4, A6, B2, B8, B9, C3,

C4, C5SL10 Radiative cracks on the overall region A6, B6SL11 Irregular short cracks on overall region A1, B2, B6SL12 Popped cracks A5SL13 Irregular cracks on specific region B1

(continued on next page)


Table 3 (contiuned)

Member type Crack typeno.

Feature of cracks Estimated crackcauses

Structure TL1 V-shaped diagonal cracks on telocentric of building D6TL2 Inverted V-shaped diagonal cracks on telocentric of building D6TL3 Unidirectional diagonal cracks on the overall structure D6TL4 V-shaped diagonal cracks on the lower telocentric of building C1TL5 Inverted V-shaped diagonal cracks on upper telocentric of building and vertical

cracks on middle region of buildingC1


to the types of a set of illustrated cracks, and second bydeciding the degree of feasibility that the given crackresembles the selected crack types using the linguistic vari-ables defined as the set V = {never, very low, low, slightlylow, unspecific, slightly high, high, very high, always},where the elements of the set V are related to those of setV={0.0, 0.1, 0.2, 0.3, 0.5, 0.7, 0.8, 0.9, 1.0}. If more thanone crack type is related to the given crack, one may selectall the related crack types and continue by using the aboveprocedure for each simultaneously. From this diagnosticprocess, the feasibility values relating the given crack toeach primary crack type, denoted by uPCT(x), are cal-culated and the reliability value of crack cause A byprimary crack type, uA,PCT(x), is determined directlyusing the feasibility value of the primary crack type on itsown, as

uA;PCTðxÞ ¼ uPCTðxÞ ð3Þ

Table 4Composition of primary symptom combination I (PSC I) according to crack

Crack patterns Estimated crac

Time of formation Regularity Shape

Several hours–1 day (S1) Regular(S7)

Turtle (S4) B2, B3Surface (S5) A8, B2, B3, B5Penetrate(S6)

B2, B3, B4, B1

Irregular(S8)

Turtle (S4) B8Surface (S5) A1, B5, B7, B8Penetrate(S6)

B4, B10

Several days (S2) Regular(S7)

Turtle (S4) –Surface (S5) A2, B15, D5Penetrate(S6)

A2, B16

Irregular(S8)

Turtle (S4) A4, B9Surface (S5) B7, B9Penetrate(S6)

–

More than several tens of days(S3)

Regular(S7)

Turtle (S4) A9, B2, B3

Surface (S5) A7, A9, B2, BD3, D5

Penetrate(S6)

A9, B2, B3, B4

Irregular(S8)

Turtle (S4) A3, A4, A6, B

Surface (S5) A3, A4, A5, APenetrate(S6)

B4, B10

Then, the final reliability values of each crack cause accord-ing to PCT are determined by performing the maximumoperation on the reliability values of the same crack causes.For example, let us consider the reliability value of crackcause A1 due to crack types generated in a girder,uA1;PCTGL

ðxÞ. The final reliability value of crack cause A1according to the primary crack type is calculated by select-ing the maximum value among the reliability values ofcrack cause A1 according to all the selected primary cracktypes, for example GL1, GL2, and GL3, as

uA1;PCTGLðxÞ ¼ maxðuA1;PCTGL1

ðxÞ;uA1;PCTGL2ðxÞ;uA1;PCTGL3

ðxÞÞ ð4Þ

3.3. Composition of primary symptom combination I

(PSC I) and fuzzy inference

Primary symptom combination I (PSC I) is the combi-nation of crack symptoms connected with time of forma-

pattern

k causes Primary symptom combination I(PSC I)

PSC1 = S1 ^ S4 ^ S7, B14, B16 PSC2 = S1 ^ S5 ^ S70, B16 PSC3 = S1 ^ S6 ^ S7

PSC4 = S1 ^ S4 ^ S8, B13 PSC5 = S1 ^ S5 ^ S8

PSC6 = S1 ^ S6 ^ S8

PSC7 = S2 ^ S4 ^ S7PSC8 = S2 ^ S5 ^ S7PSC9 = S2 ^ S6 ^ S7

PSC10 = S2 ^ S4 ^ S8PSC11 = S2 ^ S5 ^ S8PSC12 = S2 ^ S6 ^ S8

PSC13 = S3 ^ S4 ^ S7

3, B11, B12, C1, C2, C7, C8, D1, PSC14 = S3 ^ S5 ^ S7

, B10, C1, D2, D4, D5, D6 PSC15 = S3 ^ S6 ^ S7

1, B9, C3, C4, C5, C6 PSC16 = S3 ^ S4 ^ S8

6, B6, B9, C3, C4, C5, C6, D7 PSC17 = S3 ^ S5 ^ S8PSC18 = S3 ^ S6 ^ S8


tion (several hours–1 day, several days, more than severaltens of days), regularity (regular, irregular) and shape (tur-tle, surface, penetrate). PSC I is expressed as Eq. (5) andthe elements of PSC I are defined in Table 4:

PSCI ¼ fPSC1;PSC2; . . . ;PSC18g ð5Þ

For example, PSC9 is the combination of crack symptomswith time of formation as several days (S2), shape aspenetrate (S6) and regularity as regular (S7), and expressedas

PSC9 ¼ S2 ^ S6 ^ S7 ð6Þ

The reliability values of each element of PSC I, uPSCk (x)(k = 1–18), are calculated by performing the minimumoperation on the three reliability values of time of forma-tion, shape and regularity which compose the combination,as

uPSCkðxÞ ¼ minðuSiðxÞ;uSjðxÞ;uSlðxÞÞ¼ uSiðxÞ ^ uSjðxÞ ^ uSlðxÞ ði ¼ 1; 2; 3; j ¼ 4; 5; 6; l ¼ 7; 8Þ

ð7Þ

Here, the reliability values of the given crack to each cracksymptom, uSi(x), uSj(x) and uSk(x) are calculated by thefollowing procedure. The crack symptoms related to the

Table 5Definition of crack related rules for fuzzy inference

Category of rule Rule No. Description of rule

Time of formation Rule 1 If time of crack formation is ‘‘verof S1 is ‘‘very high,’’ of S2 is ‘‘lo

. . . . . .

Rule 7 If time of crack formation is ‘‘veof S1 is ‘‘very low,’’ of S2 is ‘‘ver

PSC I Rule 8 If the possibility of PSC1 is ‘‘very. . . . . .Rule 133 If the possibility of PSC18 is ‘‘ve

PSC II Rule 134 If the possibility of PSC19 is ‘‘vercrack causes is ‘‘very high’’

. . . . . .

Rule 196 If the possibility of PSC27 is ‘‘vecauses is ‘‘very low’’

Condition of concretemixing

Rule 197 If condition of concrete mixing is(Positive large) and the possibilit

. . . . . .Rule 203 If condition of concrete mixing is

(Negative large) and the possibili

Temperature duringconcrete placement

Rule 204 If temperature during concrete plcauses is PL (Positive large) and

. . . . . .

Rule 210 If temperature during concrete plcauses is NL (Negative large) and

Humidity on concreteplacement

Rule 211 If humidity during concrete placePL (Positive large)

. . . . . .

Rule 217 If humidity during concrete placemNL (Negative large)

time of formation S1, S2 and S3 are determined by calcu-lating the degree to which the time of crack formation gi-ven by numeric data belongs to the set of linguisticvariables defined as {very fast, fast, slightly fast, medium,slightly late, late, very late}, and obtaining the reliabilityprofiles of S1, S2 and S3 from the built-in rules concerningtime of crack formation as represented in Table 5 and themembership function of the linguistic variables expressedin Fig. 2b, and carrying out defuzzification. Here, weadapted the center of gravity method [14,15] as the defuzz-ification scheme.

The bold lines in Fig. 2 represent the process of calculat-ing the reliability value of crack symptom S1 when the timeof crack formation is 30 days. Here, the related rules con-cerning time of formation are as follows:

[Rule] If time of crack formation is ‘‘late’’, then the pos-sibility of time of crack formation being a member of S1 is‘‘very low’’.

[Rule] If time of crack formation is ‘‘slightly late’’, thenthe possibility of time of crack formation being a memberof S1 is ‘‘low’’.

The reliability values for the regularity and shapeof cracks are determined by selecting the degree of feasibil-ity of crack symptoms regarding regularity, classified as‘‘regular’’ or ‘‘irregular,’’ and crack symptoms regardingshape, classified as ‘‘turtle,’’ ‘‘surface’’ or ‘‘penetrate’’ from

y fast’’ then the likelihood of time of crack formation being a membershipw,’’ and of S3 is ‘‘very low’’

ry late’’ then the likelihood of time of crack formation being a membery low,’’ and of S3 is ‘‘very high’’

high’’ then the possibility of B2, B3 being crack causes is ‘‘very high’’

ry low’’ then the possibility of B4, B10 being crack causes is ‘‘very low’’

y high’’ then the possibility of A1, A2, A4, A9, B1, C1, C3, C4, C5 being

ry low’’ then the possibility of B6, C1, D1, D2, D3, D4, D6 being crack

‘‘very rich’’ then the possibility of A2, A6, A9 being crack causes is PLy of A8, C3, C6, C7, C8 being crack causes is NL (Negative large)

‘‘very lean’’ then the possibility of A2, A6, A9 being crack causes is NLty of A8, C3, C6, C7, C8 being crack causes is PL (Positive large)

acement is ‘‘very high’’ then the possibility of A2, B2, B8, B10 being crackthe possibility of B9 being a crack cause is NL (Negative large)

acement is ‘‘very low’’ then the possibility of A2, B2, B8, B10 being crackthe possibility of B9 being a crack cause is PL (Positive large)

ment is ‘‘very low’’ then the possibility of A4, A9, B8 being crack causes is

ent is ‘‘very high’’ then the possibility of A4, A9, B8 being crack causes is


the linguistic variables defined as a set V = {never, verylow, low, slightly low, unspecific, slightly high, high, veryhigh, always}, where the elements of set V are related tothe set V = {0.0, 0.1, 0.2, 0.3, 0.5, 0.7, 0.8, 0.9, 1.0}. By thismethod we can obtain the reliability values of S7 (regular),S8 (irregular), S4 (turtle), S5 (surface) and S6 (penetrate).Here, the elements of regularity, that is, ‘‘regular’’ or‘‘irregular’’ are in the relation of a complementary set, soby defining the reliability value of one element the reliabil-ity value of the remaining element is acquired.

After calculating the reliability values of the eighteenprimary symptom combinations of PSC I, the reliabilityprofiles of the estimated crack causes of PSC I are calcu-lated using fuzzy inference based on the built-in rulesregarding PSC I as represented in Table 5 and the member-ship function for linguistic variables as shown in Fig. 2b.Then defuzzification is carried out, which leads to the reli-ability values of each crack cause of PSC I as

uAi;PSCkðxÞ ði ¼ 1–9; k ¼ 1–18ÞuBj;PSCkðxÞ ðj ¼ 1–16; k ¼ 1–18ÞuCl;PSCkðxÞ ðl ¼ 1–8; k ¼ 1–18ÞuDm;PSCkðxÞ ðm ¼ 1–7; k ¼ 1–18Þ

ð8Þ

Fig. 2. Membership function of linguistic variables and example of calculatlinguistic variables to the time of crack formation. (b) Reliability profile after apgravity method.

The final reliability values of each crack cause according toPSC I are derived by performing the maximum operationon the same crack cause of PSC I as

uA;PSC IðxÞ ¼ maxðuA;PSC1ðxÞ;uA;PSC2ðxÞ; . . . ;uA;PSC18ðxÞÞð9Þ

3.4. Composition of primary symptom combination II

(PSC II) and fuzzy inference

The primary symptom combination II (PSC II) is thecombination of crack symptoms concerning cause of con-crete deformation (contraction, expansion, settlementbending shear) and range of crack (material, member,structure). PSC II is expressed as Eq. (10) and the elementsof PSC II are defined in Table 6.

PSC II ¼ fPSC19;PSC20; . . . ;PSC27g ð10Þ

The reliability values of each element of PSC II, uPSCk

(x)(k = 19–27), are calculated by performing the minimumoperation on the reliability values of cause of concretedeformation and range of crack, as

ing reliability value for crack symptom S1. (a) Membership function ofplying rules about time of crack formation. (c) Defuzzification by center of


uPSCkðxÞ ¼ minðuSiðxÞ;uSjðxÞÞ ¼ uSiðxÞ ^ uSjðxÞði ¼ 9; 10; 11; j ¼ 12; 13; 14Þ ð11Þ

The method for calculating the reliability values of the gi-ven crack regarding each crack symptom uSi(x), uSj(x) isidentical to that of PSC I. That is, the reliability valuesfor cause of concrete deformation and range of crack arecalculated by selecting the degree of feasibility of the cracksymptoms regarding cause of concrete deformation, classi-fied as ‘‘contraction’’, ‘‘expansion’’ and ‘‘settlement bend-ing shear’’, and crack symptoms regarding range ofcrack, classified as ‘‘material’’, ‘‘member’’ and ‘‘structure’’from the linguistic variables defined as a set V = {never,very low, low, slightly low, unspecific, slightly high, high,very high, always}, where the elements of set V are relatedto the set V = {0.0, 0.1, 0.2, 0.3, 0.5, 0.7, 0.8, 0.9, 1.0}. Bythis method the reliability values of S9 (contraction), S10(expansion), S11 (settlement bending shear), S12 (mate-rial), S13 (member) and S14 (structure) are obtained.

After calculating the reliability values of the nine pri-mary symptom combinations of PSC II, the reliability pro-files of the estimated crack causes of PSC II are calculatedusing fuzzy inference based on the built-in rules concerningPSC II as represented in Table 5 and the membershipfunction for linguistic variables as shown in Fig. 2b. Thendefuzzification is carried out which leads to the reliabilityvalues of each crack cause of PSC II as

uAi;PSCkðxÞ ði ¼ 1–9; k ¼ 19–27Þ

uBj;PSCkðxÞ ðj ¼ 1–16; k ¼ 19–27Þ

uCl;PSCkðxÞ ðl ¼ 1–8; k ¼ 19–27Þ

uDm;PSCkðxÞ ðm ¼ 1–7; k ¼ 19–27Þ

ð12Þ

The final reliability values of each crack cause according toPSC II are derived by performing the maximum operationon the same crack cause of PSC II as

uA;PSC IIðxÞ ¼ maxðuA;PSC19ðxÞ;uA;PSC20ðxÞ; . . . ;uA;PSC27ðxÞÞð13Þ

Table 6Composition of primary symptom combination II (PSC II) according to caus

Cause of concrete deformation Range Estimated cra

Contraction (S9) Material (S12) A1, A2, A4, AMember (S13) A2, A9, B2, BStructure (S14) A9, B2, B3, B

Expansion (S10) Material (S12) A3, A5, A6, BMember (S13) A7, B1, C1, CStructure (S14) A7, C1, C4, C

Settlement bending shear (S11) Material (S12) A5, A6, C1Member (S13) A8, B4, B5, B

C2, D1, D2, DStructure (S14) B6, C1, D1, D

The final reliability values of each crack cause according toPSC are derived by performing the minimum operation onthe reliability values calculated both from Eqs. (9) and (13)as

uA;PSCðxÞ ¼ minðuA;PSC IðxÞ;uA;PSC IIðxÞÞ ð14Þ

3.5. Composition of reinforcing data (RFD) and fuzzy

inference

Reinforcing data are composed of condition of concretemixing and weather conditions during concrete placementas shown in Table 7. These data are not direct causes ofcracks but indirect and complementary data, so they areused to reinforce the crack causes derived from the primarysymptom combination. The reinforcing values derivedfrom the reinforcing data are in the range of [�1, 1] andused to update the previously derived crack causes by add-ing the reinforcing values of each crack cause to each causederived from PSC. The reinforcing values may be scaleddown in the range of 0–100% according to the ambiguityand incorrectness of the input data. Further, if specific datais not obtainable, the corresponding participation ratio canbe set as zero to eliminate its participation. Reinforcingvalue may take both positive and negative values, and thismeans that, reinforcing data acts both to reinforce or toweaken specific crack causes.

3.5.1. Reinforcing of crack causes according to the condition

of concrete mixingThe condition of concrete mixing is mainly governed by

cement content. Reinforcing values for crack causesaccording to the condition of concrete mixing is calculatedas follows. First, obtain cement content in numeric data,second, calculate the degree of feasibility of the cementcontent to the linguistic variables defined as a set {very richmix, rich mix, slightly rich mix, medium mix, slightly leanmix, lean mix, very lean mix} as shown in Fig. 3a, andthird, calculate the reinforcing values of the crack causes,uA,Mix,RFD(x), using fuzzy inference based on built-in rules

e of concrete deformation and range of crack

ck causes Primary symptomcombination II (PSC II)

9, B1, C1, C3, C4, C5 PSC19 = S9 ^ S123, B8, B14, B15, C1, C2, C3, C4, C5 PSC20 = S9 ^ S138, B15, C1, C4, C5 PSC21 = S9 ^ S14

1, C1, C3, C4, C5, C6 PSC22 = S10 ^ S122, C3, C4, C5, C7, C8 PSC23 = S10 ^ S135 PSC24 = S10 ^ S14

PSC25 = S11 ^ S126, B7, B9, B10, B11, B12, B13, B16, C1,3, D4, D5, D7

PSC26 = S11 ^ S13

2, D3, D4, D6 PSC27 = S11 ^ S14

Table 7Causes of cracks according to reinforcing data (RFD)

Reinforcing data Crack symptom Estimated crackcauses

Condition of concrete mixing Rich mix (S18) A2, A6, A9Lean (S19) A8, C3, C6, C7,

C8

Weather conditions duringconcrete placement

Hightemperature(S15)

A2, B2, B8, B10

Low temperature(S16)

B9

Dryness (S17) A4, A9, B8


concerning concrete mixing as shown in Table 5 and themembership function for linguistic variables as shown inFig. 4.

3.5.2. Reinforcing of crack causes according to the weatherconditions during concrete placement

Weather conditions during concrete placement com-prise two sorts of data, that is, the temperature condition

Fig. 3. Membership function of linguistic variables for reinforcing data. (a) M(b) Membership function of linguistic variables for temperature condition onhumidity condition on concrete placement.

and the humidity condition, and the reinforcing valuesfor crack causes are calculated for each of them, respec-tively. The procedure is similar to that for the conditionof concrete mixing. That is, first, obtain the temperatureand humidity during concrete placement in numeric data,second, calculate the degree of feasibility of the tempera-ture and humidity to the linguistic variables defined as aset {very high, high, slightly high, medium, slightly low,low, very low} as shown in Fig. 3b and c, respectively,and third, calculate the reinforcing values of the crackcauses, uA,Tmp,RFD(x), uA,Hum,RFD(x) using fuzzy infer-ence based on built-in rules concerning temperature andhumidity conditions as shown in Table 5 and the mem-bership functions for linguistic variables as shown inFig. 4.

3.5.3. Derivation of final reinforcing values according to

reinforcing dataAfter calculating the reinforcing values of crack causes

for each of the three conditions, that is, condition of con-crete mixing, temperature condition and humidity condi-

embership function of linguistic variables for condition of concrete mixingconcrete placement (c) Membership function of linguistic variables for

Fig. 4. Membership function of linguistic variables for reinforcing crack causes.


tion, the final reinforcing values are derived by adding eachreinforcing value of each crack cause, as

uA;RFDðxÞ ¼ uA;Mix;RFDðxÞ þ uA;Tmp;RFDðxÞ þ uA;Hum;RFDðxÞð15Þ

The reason for adding the reinforcing values is that thethree types of reinforcing value are acting more or lessindependently and accordingly have additive charac-teristics.

3.6. Final determination of crack causes

Crack causes, both by primary symptom combination(PSC) and by reinforcing data (RFD), are aggregated usinga bounded-sum operation in the range of [0, 1], and theresulting crack causes are produced as

uA;PSCRFDðxÞ ¼ ðuA;PSCðxÞ þ uA;RFDðxÞÞ½0;1� ð16Þ

The final reliability values of crack causes, uA(x), are de-rived by integrating the reliability values, both from theprimary crack type, uA,PCT(x), as in Eq. (3), and fromthe aggregated primary symptom combination and rein-forcing data uA,PSCRFD(x) as in Eq. (16). As an integrationscheme, we adopted the Choquet fuzzy integral which hasshown excellent applicability in subjective decision makingproblems [9,16]. To execute the Choquet fuzzy integral, theimportance of each assessment criterion to the overallassessment must be determined. In this paper, we estab-lished the importance of assessment criteria by representingthem as linguistic variables and relating them to discretenumeric values. The linguistic variables are defined as aset of nine graded elements, that is, {never, very low, low,slightly low, unspecific, slightly high, high, very high,always} and the corresponding representative numericvalues are defined as a set {0, 0.1, 0.2, 0.3, 0.5, 0.7, 0.8,0.9, 1.0}.

In diagnosing the cause of cracks by crack symptoms, ifthe crack shape is evident, that is, the primary crack type isevident, then PCT has the dominant effect in crack diagno-

sis. On the other hand, if crack shape is not evident, thenthe primary symptom combination may have a more dom-inant effect in diagnosis. Therefore, in this paper we set thedefault importance of PCT as ‘‘very high’’, and aggregatedPSC and RFD as ‘‘high’’. However, in actual diagnosis, byassigning a higher grade to the assessment criterion havingrelatively more evident input, more reliable results can beacquired.

The Choquet fuzzy integral is defined as Eq. (17). Here,h( ) is the evaluated value of the assessment criterion, andg( ) is the importance of the assessment criterion, whereg({x1}) and g({x2}) are the importance of each assessmentcriterion, x1 and x2, respectively, and g({x1, x2}) is theimportance of both assessment criteria, x1 and x2, consid-ered simultaneously, and which is calculated by derivingthe interaction relationship between them and for whichthere are three kinds of relation, that is, super-additivity,additive and sub-additivity:

uAðxÞ ¼Z

AhðxÞ � gð�Þ

¼ hðx1Þgðfx1; x2gÞ þ ½hðx2Þ � hðx1Þ�gðfx2gÞ ðwhen hðx1Þ 6 hðx2ÞÞhðx2Þgðfx1; x2gÞ þ ½hðx1Þ � hðx2Þ�gðfx1gÞ ðwhen hðx1Þ > hðx2ÞÞ

�

ð17Þ

The finally calculated reliability values of each crack causemeans the feasibility of each crack cause to the given crack,and the higher the value the more reliable the crack cause.For crack causes whose reliability value is greater than 0.5,can be regarded as a possible candidate of the set of crackcauses.

4. Implementation of the crack diagnosis system and

evaluation of its applicability

4.1. Implementation of the crack diagnosis system

The proposed crack diagnosis system was implementedwith a GUI computer program using MS Visual Basic6.0. Figs. 5–10 show selected screens from the implementedsystem.


Fig. 5 shows screens from the diagnosis processaccording to primary crack type (PCT), where primarycrack types are selected and the given crack’s fitness tothe selected items are represented by linguistic variables.Fig. 6 shows screens from the diagnosis process accord-ing to primary symptom combination I (PSC I), wheretime of crack formation is input by numeric value,

Fig. 5. Selection of primary crack types and rep

Fig. 6. Diagnostic p

shape and regularity are represented by linguistic vari-ables, diagnosis by fuzzy inference is carried out accord-ing to the input data, and the diagnostic results aregenerated.

Fig. 7 shows the final diagnostic process, where the Cho-quet fuzzy integral is performed on the diagnosis resultsboth from PCT and from PSC and RFD.

resenting their fitness by linguistic variable.

rocess of PSC I.

Fig. 7. Final diagnostic results.

Fig. 8. Application examples for crack diagnosis. (a) Case 1 (cracks on upper and lower side of slab of elevated bridge). (b) Case 2 (cracks on wall) (c) Case3 (cracks on exterior wall of 1st and 2nd floor, dotted lines are cracks on inner side) (d) Case 4 (cracks on floor slab) (e) Case 5 (cracks on exterior wall of1st floor, girder, column and lower side of balcony).



4.2. Evaluation of the applicability of the proposed crack

diagnosis system

Evaluation of the applicability of the proposed systemwas carried out by comparing the diagnostic resultsextracted from technical manuals of cracks actually diag-

Table 8Data from application examples input into the crack diagnostic system (Cases

PCT Typical crack types Case 1

Upper side of slab SL4(very high), SL5 (veryhigh)

Loweslab Shigh)

PSCI

Time of formation 1 day 60 daShape Turtle Low Low

Surface High Unspe

Penetrate Slightly low HighRegularity Slightly high High

PSCII

Cause of concretedeformation

Contraction Slightly high SlightExpansion Low LowSettlementbendingshear

Slightly high Slight

Range Material High HighMember High HighStructure Low Low

RFD Condition ofconcrete mixing

Cementcontent(kgf/m3)

325 325

Weather conditionsduring concreteplacement

Temperature(�C)

9 9

Humidity(%)

60 60

Table 9Data from application examples input into the crack diagnostic system (Cases

PCT Typical crack types Case 4 Case 5

Floor slab SL4(very high)

ExteriWL10

PSCI

Time of formation 21 days 4 yearShape Turtle Low High

Surface Slightly high SlightlPenetrate Very high Slightl

Regularity High Low

PSCII

Cause of concretedeformation

Contraction High LowExpansion Low HighSettlementbending shear

Low Low

Range Material Unspecific HighMember High SlightlStructure Low Low

RFD Condition of concretemixing

Cementcontent(kgf/m3)

– 370

Weather conditions duringconcrete placement

Temperature(�C)

18 –

Humidity (%) 68 –

nosed by experts [12], to the diagnostic results generatedby the proposed system. Ten cracks, that is, four wallcracks, three slab cracks, one column crack, one girdercrack, and one balcony crack, generated in five structureswere chosen as application examples. The cracks with theirfeatures illustrated are shown in Fig. 8, and the inputs to

1–3)

Case 2 Case 3

r side ofL2 (very

Wall WL6(veryhigh)

Exterior wall of 1stfloorWL1 (very high), WL5(very high)

Exterior wall of2nd floor TL5(very high)

ys 30 days 1 year 1 yearLow Very low Very low

cific Slightlylow

High Slightly low

High Slightly low Very highSlightlyhigh

High Very high

ly high Low Slightly high Slightly highLow High High

ly high High Low Low

Unspecific Slightly low Slightly lowHigh High UnspecificLow Unspecific High

– – –

32 30 30

80 – –

4–5)

or wall of 1st floor(very high)

Girder GL11(very high)

Column CL6(very high)

Lower side ofbalcony SL8 (high)

s 4 years 4 years 4 yearsLow Low Low

y low High High Highy low Slightly low Slightly low Slightly low

Slightly low Slightly low Slightly high

Low Low LowHigh High Slightly highLow Low Slightly high

Slightly high Slightly high Slightly highy low Slightly high Slightly high High

Low Low Low

370 370 370

– – –

– – –


the proposed system are listed in Tables 8 and 9. The diag-nostic results both by experts and by the proposed systemare summarized in Tables 10 and 11.

The proposed system provided results similar to those ofthe experts, where eight cases out of ten are exactly the

Table 10Comparison of diagnostic results both by experts and proposed system (Case

Case Crack position Diagnosis by proposed system

Rank Crackno.

Cause of crack

Case 1 Upper side of slab 1 A8 Settlement and bleedinof concrete2 B3

3 A94 B5

B14B16

Lower side of slab 1 D2 Eternal long time loadover design load

D5 Lack of section size anreinforcing bars

2 D1 Eternal long time loadwithin design load

3 B15 Early removal of formB16 Settlement of form sup

4 B7 Vibration or loading bhardening

5 B3 Segregation during puB4 Improper placing sequC1 Change of external tem

and humidityD4 Dynamic short time lo

over design load6 A9 Shrinkage of concrete

Case 2 Wall 1 B10 Improper treatment of2 B3 Segregation during pu3 A8 Settlement and bleedin

concreteB5 Rapid placing

Case 3 Exterior wall of1st floor

1 C1 Change of external temand humidity

C2 Temperature/humiditybetween member surfa

2 D6 Differential settlementstructure

3 A9 Shrinkage of concreteB3 Segregation during pu

Exterior wall of 2ndfloor

1 C1 Change of external temhumidity

2 B2 Overtime mixing3 A9 Shrinkage of concrete

B3 Segregation during pu

same and the remaining two cases were only slightly differ-ent and turned out to be secondary and tertiary crackcauses. The proposed system was able to elevate the exact-ness of the diagnosis by using linguistic variables and fuzzyinference for crack symptoms which have ambiguous and

s 1–3)

Diagnosis by experts

Reliability Diagnostic opinion

g 0.882 It is estimated that cracks on the middle ofslab were generated onrebar positions due to ‘‘settlement andbleeding of concrete (A8)’’and cracks on the perimeters of slab weregenerated due to latehardening in cold weather by ‘‘settlement ofform support or early removal of formsupport (B16)’’

0.8810.8180.565

ing 0.881 It is estimated that penetrating cracks onlower side of slab were generated due to theconcrete hardening late in cold weather by‘‘settlement of form support or early removalof form support(B16).’’ ‘‘shrinkage of concrete (A9) may notbe the main reason,but it is estimated that it may have promotedthe occurrence and expansion of the cracks

d

ing 0.860

s 0.849portefore 0.831

mping 0.565enceperature

ading

0.540

work joint 0.889 It is estimated that ‘‘improper treatment ofwork joint (B10)’’ is themain cause of crack

mping 0.831g of 0.828

perature 0.889 It is estimated that cracks on the extremeedges of wall were generated more or less bythe ‘‘expansion of roof slab due to hightemperature in summer (C1)’’ but main crackswere generated on the inner side of the walldue to ‘‘differences in temperature andhumidity between member surfaces (C2)’’ dueto the heating of the exterior wall by sunlightfromthe south-west direction and low temperatureof the interior due to machine cooling

gapcesof 0.831

0.705mping

perature and 0.889 From the tendency of the inclined cracks it isestimated that ‘‘changeof external temperature and humidity (C1)’’ isa more likely reasonthan ‘‘shrinkage of concrete (A9).’’ That is, itis estimated that cracks were generated on thewall by the expansion of the roof slab and thewhole structure due to the high temperatureof the summer weather

0.6200.565

mping

Table 11Comparison of diagnostic results both by experts and proposed system (Cases 4–5)

Case Crack Diagnosis by proposed system Diagnosis by experts

Rank Crackno.

Cause of crack Reliability Diagnostic opinion

Case 4 Floor slab 1 B3 Segregation duringpumping

0.880 If there are no prominent construction faults, it is estimatedthat ‘‘shrinkage of concrete (A9)’’ is the significant primarycause of the cracks, and that it is necessary to scrutinizeconstruction records, because B2 and B3 are dominant causes ofpromoting A9

2 A9 Shrinkage of concrete 0.8753 B2 Overtime mixing 0.568

Case 5 Exteriorwall of 1stfloor

1 A6 Reactive aggregate 0.892 From the fact that crushed stones were used, lean mixing, aneasy condition for penetration of alkali from the exterior, cracksoccurred several years after building completion, and the similartypes of cracks were concentrated on the limited area, it isestimated that ‘‘reactive aggregate (A6)’’ is the main cause ofthe cracks. A3 was excluded based on the time of crackformation, and C3, C4 and C5 based on building history

2 A3 Abnormal expansionof cement

0.889

C4 FireC5 Surface heating

3 C3 Repetition of freezingand thawing

0.886

4 A4 Clay in aggregate 0.831B2 Overtime mixingB9 Initial frost damage

5 B8 Rapid shrinkageduring initial curing

0.821

Girder andcolumn

1 A6 Reactive aggregate 0.884 From the fact that crushed stones were used, lean mixing,an easy condition for penetration of alkali from exterior,cracks occurred several years after building completion,and similar types of cracks were concentrated on the limitedarea, it is estimated that ‘‘reactive aggregate (A6)’’ is the maincause of the cracks. A5 was excluded based on the aggregateactually used; A3 was excluded based on the time of crackformation, and C3, C4 and C5 based on building history

2 A3 Abnormal expansionof cement

0.565

A5 Low quality aggregateC4 FireC5 Surface heating

3 C3 Repetition of freezingand thawing

0.541

C6 Chemical reaction ofacid and chloride

Lower sideof balcony

1 A7 Chloride in concrete 0.791 It is estimated that ‘‘insufficient protective covering (B12)’’and ‘‘corrosion of reinforcing bar by penetrated chloride (C8)’’are the main causes of the cracks. ‘‘Movement of reinforcingbars (B11)’’ should be considered simultaneously, for it maypromote insufficient protective covering and may be the reasonfor the lowered structural capacity. A7 was excluded based onthe construction record, and C7 based on the neutralizationdepth of the concrete

B11 Movement ofreinforcing bar

B12 Insufficient protectivecovering

2 C7 Corrosion ofreinforcing bar(neutralization)

0.788

C8 Corrosion ofreinforcing bar(penetrated chloride)

3 B4 Improper placingsequence

4 C6 Chemical reaction ofacid and chloride

0.746

5 B3 Segregation duringpumping

0.741

6 B5 Rapid placing 0.7317 A8 Settlement and

bleeding of concrete0.728


uncertain characteristics and which are difficult to treat ona binary basis.

5. Summary and conclusions

In this paper, we constructed a crack diagnosis systembased on fuzzy set theory and fuzzy inference and imple-

mented the proposed system with a graphic user interfacecomputer program.

The proposed system diagnoses causes of cracks accord-ing to the following four steps, that is, estimation of crackcauses based on (1) primary crack type (PCT), (2) primarysymptom combination (PSC), (3) reinforcing data (RFD),and (4) integration of previously calculated diagnosticresults. The primary crack type (PCT) is the graphical rep-


resentation of typical crack types peculiar to each structuralmember or to the whole structure. The primary symptomcombination (PSC) is the combination of crack symptoms,classified into primary symptom combination I (PSC I) andprimary symptom combination II (PSC II), where PSC I isthe combination of crack symptoms concerning time ofcrack formation, regularity and shape, and PSC II is thecombination of crack symptoms concerning cause of con-crete deformation and range of crack. The reinforcing data(RFD) are composed of condition of concrete mixing andweather conditions during concrete placement.

The proposed system performs fuzzy operations andfuzzy inference based on built-in rules on the crack symp-toms expressed as linguistic variables and some numericdata, and calculates reliability values and reinforcingvalues for each crack cause. Finally, the system integratesthe previous diagnostic results using the Choquet fuzzyintegral, calculates final reliability values and ranks thecrack causes. The reliability values are in the range of0–1 and the higher the value or rank, the more likely it isthat that crack cause is responsible for the given cracks.

When the proposed system was applied to cracks diag-nosed by experts, it provided results similar to those fromthe experts, and we expect that this system can be usedas an effective crack diagnosis tool for RC structures byboth non-experts and experts. Further, by allowing cracksymptoms to be represented in linguistic variables, the pro-posed system should cope with the problems of ambiguityand uncertainty latent in symptoms and hence increase theperformance of the diagnosis.

The proposed system may be used independently indiagnosing causes of cracks or used as part of an overallstate assessment system for RC structures in judgingwhether given cracks are structural cracks with a dominantinfluence in determining structural capacity of the structureor are merely non-structural cracks generated only bydeterioration.

The concept and methodology of the proposed systemcan useful in diagnosing cracks generated in RC structures,but it has limits in the following two areas: first, the systemproduces reliability values and ranks each crack cause, butnot the relationship among related crack causes, which isvery important for cracks generated by complex causes,therefore with only the diagnostic results of this system,it would be difficult for non-experts to decide whether thegiven cracks were generated by a single cause or by multi-ple causes. Second, although we tried our best to employ allthe typical crack types and cover as many crack types aspossible along with crack symptoms which are easy to

handle for non-experts, there is room for them to be sup-plemented or replaced to improve the performance of thediagnosis and to be more easily handled by non-experts.

Acknowledgements

This research (05HaksimC03) was financially supportedby the Ministry of Construction & Transportation ofSouth Korea, Korea Institute of Construction and Trans-portation Technology Evaluation and Planning, and theRegional Research Centers Program (Bio-housing Re-search Institute) granted by the Korean Ministry of Educa-tion & Human Resources Development, and the authorsare grateful to the authorities for their support.

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Fuzzy set based crack diagnosis system for reinforced concrete structures

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