Prediction of Mechanical Strength of Fiber Admixed ...downloads.hindawi.com/journals/amse/2019/4654070.pdfaspects, it was observed that the MRA gains its accurateness in predicting

Research ArticlePrediction of Mechanical Strength of Fiber Admixed ConcreteUsingMultiple Regression Analysis and Artificial Neural Network

S Karthiyaini 1 K Senthamaraikannan 2 J Priyadarshini3 Kamal Gupta1

and M Shanmugasundaram 1

1School of Mechanical and Building Sciences Vellore Institute of Technology-Chennai Campus Chennai-600127 TamilnaduIndia2Department of Civil and Architectural Engineering Al Musanna College of Technology Muladdah Musanna Oman3School of Computing Science and Engineering Vellore Institute of Technology-Chennai Campus Chennai-600127 TamilnaduIndia

Correspondence should be addressed to M Shanmugasundaram shanmugaresearchgmailcom

Received 28 September 2018 Accepted 21 March 2019 Published 7 May 2019

Guest Editor Kazunori Fujikake

Copyright copy 2019 S Karthiyaini et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

e present study is to compare the multiple regression analysis (MRA) model and artificial neural network (ANN) modeldesigned to predict the mechanical strength of fiber-reinforced concrete on 28 daysemodel uses the data from early literaturesthe data consist of tensile strength of fiber percentage of fiber watercement ratio cross-sectional area of test specimen Youngrsquosmodulus of fiber and mechanical strength of control specimen and these were used as the input parameters the respectivestrength attained was used as the target parameter e models are created and are used to predict compressive split tensile andflexural strength of fiber admixed concrete ese models are evaluated through the statistical test such as coefficient of de-termination (R2) and root mean squared error (RMSE) e results show that these parameters produce a valid model throughboth MRA and ANN and this model gives more precise prediction for the fiber admixed concrete

1 Introduction

Concrete is considered to be the fundamental and an im-portant material in construction industry Maintaining andtesting the quality and behavior of concrete is the challengefaced by the industries in recent times Also the modeling ofmaterials through regression tools and AI tools is recentlyincreasing due to its accurate prediction and evaluation econcrete as generally known for its good compressive be-havior is made to behave well under tension and flexurethrough addition of fiber additives e general tensile andflexural strength enhancements are made through additionof fibers made up of various materials with different physicaland chemical properties e addition of fibers made up ofvarious materials changes the behavior of cement-basedcomposites and enhances the toughness tension re-sistance and flexural resistance [1ndash9] ese fibers act atvarious levels in altering themechanical behavior of concreteand thus defy the rules framed for its tensile and flexural

performance making it hard to predict e major factorsthat act in enhancing the tensile and flexural strength arefiber distribution and its physical parameters In recentyears analyzing the concrete properties through predictionmodeling is gaining importance due to its accuracy andeffectiveness in real-time applicationese concrete modelswere presumed to predict the strength development throughcertain factors which are used as input parameters isprediction facilitates in making decision on concrete mixand material selection [10ndash15] But there is a challenge whencreating a model of concrete for predicting tensile strengthand flexural strength as an effective prediction model is notcreated through parameters which were used for predictingthe compressive strength [16ndash18] e challenge on accuracyin prediction increases in fiber admixed concrete whilepredicting tensile strength and flexural strength this is dueto the fiber properties and its distribution

In this study the predictive model was created throughmultiple regression analysis (MRA) and artificial neural

HindawiAdvances in Materials Science and EngineeringVolume 2019 Article ID 4654070 7 pageshttpsdoiorg10115520194654070

network (ANN) e fiber properties were used as param-eters along with basic concrete and fiber parameters withsingle target system and the model is tested through sta-tistical tools for its performance

2 Prediction Modeling and Testing

e model created here is for fiber-reinforced concrete thedata set was collected for steel fiber polypropylene fiberhybrid fiber glass fiber and basalt fiber from early studiese actual compressive strength split tensile strength andflexural strength are taken as the target values based on thefollowing parameters which are used as input parameters

(1) Tensile strength of fiber (F)(2) Percentage of fiber (P)(3) Watercement ratio (R)(4) Cross-sectional area of test specimen (A)(5) Youngrsquos modulus of fiber (Y)(6) Mechanical strength of control specimen (S)

Based on the input parameter and target values theoutput was generated through ANN and MRA and theseoutput values were compared with target (actual) values etypes of fibers and its respective literature source are pre-sented in Table 1e active compressive strength data set has5 columns and 252 rows (5times 252) of input data and 1 columnand 252 rows (1times 252) of target data e active split tensilestrength data set has 5 columns and 119 rows (5times119) ofinput data and 1 column and 119 rows (1times 119) of target datae active flexural strength data set has 5 columns and 150rows (5times150) of input data and 1 column and 150 rows(1times 150) of target data e target data for compressivestrength split tensile strength and flexural strength were usedin both the MRA and ANN model as separate target in thisstudy is single target system was used due to the usage ofcross-sectional area of test specimens as one of the param-eters and it was known that the shape of the specimens varieswith different mechanical strengths

21 Prediction Model and Its Statistical Test Two predictionmodels artificial neural network (ANN) and multiple re-gression analysis (MRA) are used in this study to predict thecompressive strength split tensile strength and flexuralstrength of fiber-reinforced concrete (FRC)

22 Artificial Neural Network (ANN) e ANN predictionmodel is programmed through MATLAB with two hiddenlayers 15 neurons in each hidden layer and one output layerwith dependent variable as compressive strength split ten-sile strength and flexural strength Among all the data ap-proximately 70 15 and 15 has been considered fortraining testing and validation respectively e LevenbergndashMarquardt (LM) algorithm is used for training due to itsrobustness and speed Layered feed-forward networks havebeen used in this algorithm in which the neurons are arrangedin layers Here signals are sent forward and errors arepropagated backwards

23 Multiple Regression Analysis (MRA) In this study thelinear-type multiple regression analysis modeling is carriedout using MS excel e coefficients of regression are cal-culated by considering 95 confidence level hence the errortolerance level is limited to maximum of 5 For a giveninput variable the calculated probability value (p value)is considered to be significant if and only if its value is lessthan 005 rough the regression analysis the followingcoefficients presented in Table 2 were found and substitutedin linear multiple regression equation (equation (1))

output I + C1F + C2P + C3R + C4A + C5Y + C6S (1)

24 Statistical Test e performance of the ANN and MRAprediction for the mechanical behavior was tested throughthe statistical methods e tests involved are coefficient ofdetermination (R2) and root mean squared error (RMSE)e coefficient of determination is presented in equation (2)is can be obtained from the comparative chart of pre-dicted compressive strength vs experimental compressivestrength e accuracy of the predictions of a network wasquantified by the root of the mean squared error difference(RMSE) between the experimented and the predictedvalues and the procedure of finding RMSE is presented inequation (3)

R2

1minussum of squares of residuals

sum of sqaures of predicted values (2)

RMSE

1n

1113944

n

i1(ACSTminus PCST)

2

11139741113972

(3)

3 Results and Discussion

e effectiveness and the acceptance of prediction modelsare based upon the ability of the model to predict the outputIn this study the models were designed to predict themechanical behavior (mechanical strength) of FRC based oninput parameters and two methods of predictions ANNand MRA are used e prediction models are validatedthrough coefficient of determination (R2) and root meansquared error (RMSE) and are consolidated in Table 3

e MRA and ANN prediction of the compressivestrength value is plotted with respect to the actual compressivestrength and presented in Figures 1 and 2 respectively eMRA prediction has the coefficient of determination R2 as093 which is almost an acceptable value whereas the ANNhas an R2 value of 1 which indicates that the ANN model isaccurate e RMSE of the MRA model is 723MPa and theANNmodel is 014MPa which demonstrates that error in theMRA model is large and cannot be relied upon for predictingthe compressive strength

e MRA and ANN prediction model plot for splittensile strength with respect to its actual value is presented inFigures 3 and 4 respectively e R2 value for the MRAmodel is 087 and ANN model is 094 e RMSE for the

2 Advances in Materials Science and Engineering

Tabl

e1

Rang

eof

parametersin

data

base

forpredictio

nmod

el

Datarang

eforpredictio

nmod

el

Type

offib

er

Tensile

streng

thof

fiber

inMPa

Percentage

additio

nof

fiber

Water

bind

erratio

Areaof

specim

entested

for

compressio

nin

mm

2

Areaof

specim

entested

for

tension

inmm

2

Areaof

specim

entested

for

flexu

rein

mm

2

Com

pressio

nstreng

thin

MPa

Split

tensile

streng

thin

MPa

Flexural

streng

thin

MPa

Elastic

mod

ulus

offib

erin

MPa

Steelfi

ber[19ndash

27]

1000ndash2

800

0025ndash

2000

015ndash0

51600ndash2

2500

22500ndash

62832

25200ndash

90000

382ndash1463

323ndash8

95

35ndash

202

22830ndash

6047726846

Polyprop

ylenefib

er[18

242

8ndash34]

320ndash1200

00001ndash2

000

030ndash0

64

1600ndash2

2500

22500ndash141372

40000ndash

79500

127ndash9

75

198ndash7

98

3ndash1202

1781853ndash4

937104

Hybridfib

er[35

36]

450ndash1200

0200ndash

2000

038ndash0

50

7850ndash17671

mdash25200ndash

40000

2701ndash

7322

mdash431ndash1

13

18460ndash

4278434

Glass

fiber

[1537ndash4

8]1500ndash3

750

0100ndash

0300

02ndash

071

380ndash141371

648ndash14137167

10000ndash

50000

14ndash7

582

107ndash7

1339ndash101

3680ndash4

353734

Basaltfib

er[2349ndash5

2]3400ndash4

600

0015ndash12450

04ndash

05

7850ndash14137

22500ndash

6283185

24000ndash

92720

2913ndash

8578

237ndash4

59

39ndash108

26986ndash

44415

Advances in Materials Science and Engineering 3

MRA model is 070MPa and ANN is 042MPA e sta-tistical validation of the split tensile strength model showsthat both the MRA model and ANNmodel are in acceptablelimit even though ANN shows more accuracy than MRAthe mathematical model is also predicting the split tensilestrength in par with the ANN model From Figure 3 it isobserved that the MRA model predicts to a high accuracyuntil actual split tensile strength is 4MPa after which the

scatter plots were deviating from the actual trend line FromFigure 4 it is observed that the ANN prediction is accurateuntil the actual strength is 75MPa after which the scatteredplot almost does not shyt the trend line

e MRA and ANN prediction model plot for exuralstrength with respect to its actual value is presented inFigures 5 and 6 respectively e R2 value for MRA andANN was 092 and 094 respectively which has similarvalidation value e RMSE value of the MRA model is099MPa and ANN model is 079MPa Both the MRA andANN were having similar model behavior in terms of sta-tistical validation and graphical representation throughFigures 5 and 6 e prediction is accurate in both MRA andANN models until the actual exural strength is 9MPa afterwhich the scattered plot is observed for both models Butthere were shytted plots for the MRA model at higher actualexural strength which lies between 13MPa and 14MPais higher-order exural strength shytness towards the trendline was not observed in the ANN model e observationindicates that exural strength prediction using MRA andANN model has eectiveness and more accurate predictionis rendered in both models rough the three strengthaspects it was observed that the MRA gains its accuratenessin predicting split tensile and exural strength e ANNpredicts compressive strength to the maximum possibleaccuracy and the prediction of split tensile strength and

Table 2 Multiple regression analysis coecients

MRAcoecients

Coecients forcompressivestrength

Coecients forsplit tensilestrength

Coecientsfor exuralstrength

I minus2083944795 2864487059 7214539466C1 0000669227 524726times10minus05 minus423499times10minus05C2 1097340646 081644571 0513456489C3 minus3143416778 minus6912788644 minus1336882713C4 minus556151times 10minus05 871841times 10minus06 19284times10minus05C5 0001154844 470901times 10minus05 260556times10minus05C6 0569536979 0475257898 0551752286

Table 3 Statistical test conducted on prediction models

Predicted parametersMRA ANN

R2 RMSE R2 RMSECompression strength 093 723 100 014Split tensile strength 087 070 094 042Flexural strength 092 099 094 079

R2 = 093

000

2000

4000

6000

8000

10000

12000

14000

16000

000 2000 4000 6000 8000 10000 12000 14000 16000

MRA

pre

dict

ed co

mpr

essiv

e str

engt

h in

MPa

Actual compressive strength in MPa

Figure 1 Actual vs MRA predicted value for compressivestrength

R2 = 1

0002000400060008000

10000120001400016000

000 2000 4000 6000 8000 10000 12000 14000 16000Actual compressive strength in MPa

AN

N p

redi

cted

com

pres

sive

stren

gth

in M

Pa

Figure 2 Actual vs ANN predicted value for compressivestrength

R2 = 087

000100200300400500600700800900

000 200 400 600 800 1000

MRA

pre

dict

ed sp

lit te

nsile

str

engt

h in

MPa

Actual split tensile strength in MPa

Figure 3 Actual vs MRA predicted value for split tensile strength

R2 = 094

000

100

200

300

400

500

600

700

800

900

1000

000 200 400 600 800 1000

AN

N p

redi

cted

split

tens

ile st

reng

th in

MPa


Figure 4 Actual vs ANN predicted value for split tensile strength


exural strength was also of higher accuracy ough theshybers have various factors on inuencing the strength de-velopment in concrete the prediction models MRA andANN are accurate by its output values e ANN eventhough has its advantage of higher accuracy over MRAmodel the performance of the MRA model is also eciente contribution of shyber properties in the prediction modelproved to be eective and also gives more preciseness to themodel Earlier models that uses other parameters such asquantity of cement admixtures coarse aggregate shyne ag-gregate and water were not able to perform well in pre-diction of tensile and exural properties [53] this limitationwas overcome by the current model where both the MRAand ANN model performs well with the given factors usboth current models can predict the complete mechanicalbehavior of shyber admixed concrete with high precision

4 Conclusion

is study investigated the feasibility of modeling a pre-dictive analysis through earlier study data converting theunstructured factors to possible structured parameters andusing those in creating the MRA model and ANN modelAlso the eectiveness of these models is tested using sta-tistical tools such as R2 and RMSEe compressive strengthmodel shows that ANN has ecient prediction model withR2 value in unity e MRA model has R2 value of 093 butthe error dierence is 723MPa which is very high for apredictive model e MRA model of split tensile strengthand exural strength shows high eciency even though theR2 values are lesser than the compressive model the per-formance of models is relatively strong e ANN model for

split tensile and exural strength has similar statisticalvaluation e MRA model shows more robustness whilepredicting the exural strength than the split tensilestrength Also it is noted that the MRAmodel performs wellin split tensile and exural strength prediction and is vali-dated through the R2 and RMSE values e MRA performswell similar to that of ANN and achieves half its eective-ness except in compressive strength prediction e studyconcludes that the shyber properties contribute high to theprediction model thus increasing the modelsrsquo performance

Data Availability

e data supporting this work are available from previouslyreported studies and datasets which have been cited eprocessed data used to support the shyndings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare no conicts of interest

References

[1] X Lu and C-T T Hsu ldquoBehavior of high strength concretewith and without steel shyber reinforcement in triaxial com-pressionrdquo Cement and Concrete Research vol 36 no 9pp 1679ndash1685 2006

[2] V F P Dutra S Maghous and A C Filho ldquoA homogeni-zation approach to macroscopic strength criterion of steelshyber reinforced concreterdquo Cement and Concrete Researchvol 44 pp 34ndash45 2013

[3] P S Song and S Hwang ldquoMechanical properties of high-strength steel shyber-reinforced concreterdquo Construction andBuilding Materials vol 18 no 9 pp 669ndash673 2004

[4] M L Allan and L E Kukacka ldquoStrength and durability ofpolypropylene shybre reinforced groutsrdquo Cement and ConcreteResearch vol 25 no 3 1995

[5] B Chen and J Liu ldquoResidual strength of hybrid-shyber-reinforced high-strength concrete after exposure to hightemperaturesrdquo Cement and Concrete Research vol 34 no 6pp 1065ndash1069 2004

[6] C S Poon Z H Shui and L Lam ldquoCompressive behavior ofshyber reinforced high-performance concrete subjected to el-evated temperaturesrdquo Cement and Concrete Research vol 34no 12 pp 2215ndash2222 2004

[7] Y Ding C Azevedo J B Aguiar and S Jalali ldquoStudy onresidual behaviour and exural toughness of shybre cocktailreinforced self compacting high performance concrete afterexposure to high temperaturerdquo Construction and BuildingMaterials vol 26 no 1 2011

[8] A Avci H Arikan and A Akdemir ldquoFracture behavior ofglass shyber reinforced polymer compositerdquo Cement andConcrete Research vol 34 no 3 pp 429ndash434 2004

[9] I Curosu V Mechtcherine and O Millon ldquoEect of shyberproperties and matrix composition on the tensile behavior ofstrain-hardening cement-based composites (SHCCs) subjectto impact loadingrdquo Cement and Concrete Research vol 82pp 23ndash35 2016

[10] I B Topccedilu and M Sarıdemir ldquoPrediction of compressivestrength of concrete containing y ash using artishycial neuralnetworks and fuzzy logicrdquo Computational Materials Sciencevol 41 no 3 pp 305ndash311 2008

R2 = 092

000

500

1000

1500

2000

2500

000 500 1000 1500 2000

MRA

pre

dict

ed fl

exur

al st

reng

thin

MPa

Actual flexural strength in MPa

Figure 5 Actual vs MRA predicted value for exural strength

R2 = 094

000

500

1000

1500

2000

2500

000 500 1000 1500 2000 2500

AN

N p

redi

cted

flex

ural

stre

ngth

in M

Pa


Figure 6 Actual vs ANN predicted value for exural strength


[11] N Al-Mutairi M Terro and A-L Al-Khaleefi ldquoEffect ofrecycling hospital ash on the compressive properties ofconcrete statistical assessment and predicting modelrdquoBuilding and Environment vol 39 no 5 pp 557ndash566 2004

[12] M A Kewalramani and R Gupta ldquoConcrete compressivestrength prediction using ultrasonic pulse velocity throughartificial neural networksrdquo Automation in Constructionvol 15 no 3 pp 374ndash379 2006

[13] R Siddique P Aggarwal and Y Aggarwal ldquoPrediction ofcompressive strength of self-compacting concrete containingbottom ash using artificial neural networksrdquo Advances inEngineering Software vol 42 no 10 pp 780ndash786 2011

[14] Z H Duan S C Kou and C S Poon ldquoPrediction ofcompressive strength of recycled aggregate concrete usingartificial neural networksrdquo Construction and Building Mate-rials vol 40 pp 1200ndash1206 2013

[15] H I Erdal O Karakurt and E Namli ldquoHigh performanceconcrete compressive strength forecasting using ensemblemodels based on discrete wavelet transformrdquo EngineeringApplications of Artificial Intelligence vol 26 no 4pp 1246ndash1254 2013

[16] A Nazari and S Riahi ldquoComputer-aided prediction of theZrO2 nanoparticlesrsquo effects on tensile strength and per-centage of water absorption of concrete specimensrdquo Journalof Materials Science amp Technology vol 28 no 1 pp 83ndash962012

[17] M Baena A Turon L Torres and C Mias ldquoExperimentalstudy and code predictions of fibre reinforced polymerreinforced concrete (FRP RC) tensile membersrdquo CompositeStructures vol 93 no 10 pp 2511ndash2520 2011

[18] H Fathi T Lameie M Maleki and R Yazdani ldquoSimulta-neous effects of fiber and glass on the mechanical properties ofself-compacting concreterdquo Construction and Building Mate-rials vol 133 pp 443ndash449 2017

[19] S Yehia A Douba O Abdullahi and S Farrag ldquoMechanicaland durability evaluation of fiber-reinforced self-compactingconcreterdquo Construction and Building Materials vol 121pp 120ndash133 2016

[20] MMastali and A Dalvand ldquoFresh and hardened properties ofself-compacting concrete reinforced with hybrid recycledsteelmdashpolypropylene fiberrdquo Journal of Materials in CivilEngineering vol 29 no 6 article 04017012 2017

[21] W-C Liao W Perceka and E-J Liu ldquoCompressive stress-strain relationship of high strength steel fiber reinforcedconcreterdquo Journal of Advanced Concrete Technology vol 13no 8 pp 379ndash392 2015

[22] C D Atis O Karahan K Ari O C Sola C Bilim and F AshldquoRelation between strength properties (flexural and com-pressive) and abrasion resistance of fiber (steel and poly-propylene) reinforced fly ash concreterdquo Journal of Materialsin Civil Engineering vol 21 no 8 pp 402ndash408 2009

[23] M Z N Khan Y Hao H Hao and F U A Shaikh ldquoMe-chanical properties of ambient cured high strength hybridsteel and synthetic fibers reinforced geopolymer compositesrdquoCement and Concrete Composites vol 85 pp 133ndash152 2018

[24] J J Li C J Wan J G Niu L F Wu and Y C Wu ldquoIn-vestigation on flexural toughness evaluation method of steelfiber reinforced lightweight aggregate concreterdquo Constructionand Building Materials vol 131 pp 449ndash458 2017

[25] A Caggiano S Gambarelli E Martinelli N Nistico andM Pepe ldquoExperimental characterization of the post-crackingresponse in hybrid steelpolypropylene fiber-reinforcedconcreterdquo Construction and Building Materials vol 125pp 1035ndash1043 2016

[26] M Hsie C Tu and P S Song ldquoMechanical properties ofpolypropylene hybrid fiber-reinforced concreterdquo MaterialsScience and Engineering A vol 494 no 1-2 pp 153ndash1572008

[27] L Shan and L Zhang ldquoExperimental study on mechanicalproperties of steel and polypropylene fiber-reinforced con-creterdquo Applied Mechanics and Materials vol 584ndash586pp 1355ndash1361 2014

[28] H Mohammadhosseini A S M Abdul Awal and J B MohdYatim ldquoe impact resistance and mechanical properties ofconcrete reinforced with waste polypropylene carpet fibresrdquoConstruction and Building Materials vol 143 pp 147ndash1572017

[29] M G Alberti A Enfedaque and J C Galvez ldquoFibre rein-forced concrete with a combination of polyolefin and steel-hooked fibresrdquo Composite Structures vol 171 pp 317ndash3252017

[30] S Fallah and M Nematzadeh ldquoMechanical properties anddurability of high-strength concrete containing macro-polymeric and polypropylene fibers with nano-silica andsilica fumerdquo Construction and Building Materials vol 132pp 170ndash187 2017

[31] M Hassani Niaki A Fereidoon and M GhorbanzadehAhangari ldquoExperimental study on the mechanical andthermal properties of basalt fiber and nanoclay reinforcedpolymer concreterdquo Composite Structures vol 191 pp 231ndash238 2018

[32] A M Alhozaimy P Soroushian and F Mirza ldquoMechanicalproperties of polypropylene fiber reinforced concrete and theeffects of pozzolanic materialsrdquo Cement and Concrete Com-posites vol 18 no 2 pp 85ndash92 1996

[33] V Afroughsabet and T Ozbakkaloglu ldquoMechanical anddurability properties of high-strength concrete containingsteel and polypropylene fibersrdquo Construction and BuildingMaterials vol 94 pp 73ndash82 2015

[34] S Iqbal A Ali K Holschemacher and T A Bier ldquoMe-chanical properties of steel fiber reinforced high strengthlightweight self-compacting concrete (SHLSCC)rdquo Construc-tion and Building Materials vol 98 pp 325ndash333 2015

[35] G M Ren H Wu Q Fang and J Z Liu ldquoEffects of steel fibercontent and type on static mechanical properties of UHPCCrdquoConstruction and Building Materials vol 163 pp 826ndash8392018

[36] P Iyer S Y Kenno and S Das ldquoMechanical properties offiber-reinforced concrete made with basalt filament fibersrdquoJournal of Materials in Civil Engineering vol 27 no 11 article04015015 2015

[37] V R Sivakumar O R Kavitha G Prince Arulraj andV G Srisanthi ldquoAn experimental study on combined effectsof glass fiber and Metakaolin on the rheological mechanicaland durability properties of self-compacting concreterdquo Ap-plied Clay Science vol 147 pp 123ndash127 2017

[38] S Ahmad A Umar and A Masood ldquoProperties of normalconcrete self-compacting concrete and glass fibre-reinforcedself-compacting concrete an experimental studyrdquo ProcediaEngineering vol 173 pp 807ndash813 2017

[39] S T Tassew and A S Lubell ldquoMechanical properties of glassfiber reinforced ceramic concreterdquo Construction and BuildingMaterials vol 51 pp 215ndash224 2014

[40] A B Kizilkanat N Kabay V Akyuncu S Chowdhury andA H Akccedila ldquoMechanical properties and fracture behavior ofbasalt and glass fiber reinforced concrete an experimentalstudyrdquo Construction and Building Materials vol 100pp 218ndash224 2015


[41] M Khan andM Ali ldquoUse of glass and nylon fibers in concretefor controlling early age micro cracking in bridge decksrdquoConstruction and Building Materials vol 125 pp 800ndash8082016

[42] A Hanif P Parthasarathy Z Lu M Sun and Z Li ldquoFiber-reinforced cementitious composites incorporating glasscenospheres - mechanical properties and microstructurerdquoConstruction and Building Materials vol 154 pp 529ndash5382017

[43] M E Arslan ldquoEffects of basalt and glass chopped fibersaddition on fracture energy and mechanical properties ofordinary concrete CMOD measurementrdquo Construction andBuilding Materials vol 114 pp 383ndash391 2016

[44] T A Soylev and T Ozturan ldquoDurability physical andmechanical properties of fiber-reinforced concretes at low-volume fractionrdquo Construction and Building Materialsvol 73 pp 67ndash75 2014

[45] R M Novais J Carvalheiras M P Seabra R C Pullar andJ A Labrincha ldquoEffective mechanical reinforcement of in-organic polymers using glass fibre wasterdquo Journal of CleanerProduction vol 166 pp 343ndash349 2017

[46] T Simotildees H Costa D Dias-da-Costa and E Julio ldquoInfluenceof fibres on the mechanical behaviour of fibre reinforcedconcrete matrixesrdquo Construction and Building Materialsvol 137 pp 548ndash556 2017

[47] G B Maranan A C Manalo B BenmokraneW Karunasena and P Mendis ldquoEvaluation of the flexuralstrength and serviceability of geopolymer concrete beamsreinforced with glass-fibre-reinforced polymer (GFRP) barsrdquoEngineering Structures vol 101 pp 529ndash541 2015

[48] W H Kwan M Ramli and C B Cheah ldquoFlexural strengthand impact resistance study of fibre reinforced concrete insimulated aggressive environmentrdquo Construction and Build-ing Materials vol 63 pp 62ndash71 2014

[49] J Branston S Das S Y Kenno and C Taylor ldquoMechanicalbehaviour of basalt fibre reinforced concreterdquo Constructionand Building Materials vol 124 pp 878ndash886 2016

[50] U Larisa L Solbon and B Sergei ldquoFiber-reinforced concretewith mineral fibers and nanosilicardquo Procedia Engineeringvol 195 pp 147ndash154 2017

[51] T Ayub N Shafiq and S U Khan ldquoCompressive stress-strainbehavior of HSFRC reinforced with basalt fibersrdquo Journal ofMaterials in Civil Engineering vol 28 article 06015014 2016

[52] M Abdulhadi and Liaoning University of Technology Jinz-hou ldquoA comparative study of basalt and polypropylene fibersreinforced concrete on compressive and tensile behaviorrdquoInternational Journal of Engineering Trends and Technologyvol 9 no 6 pp 295ndash300 2014

[53] M F M Zain H B Mahmud A Ilham and M FaizalldquoPrediction of splitting tensile strength of high-performanceconcreterdquo Cement and Concrete Research vol 32 no 8pp 1251ndash1258 2002


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Submit your manuscripts atwwwhindawicom

network (ANN) e fiber properties were used as param-eters along with basic concrete and fiber parameters withsingle target system and the model is tested through sta-tistical tools for its performance

2 Prediction Modeling and Testing

e model created here is for fiber-reinforced concrete thedata set was collected for steel fiber polypropylene fiberhybrid fiber glass fiber and basalt fiber from early studiese actual compressive strength split tensile strength andflexural strength are taken as the target values based on thefollowing parameters which are used as input parameters

(1) Tensile strength of fiber (F)(2) Percentage of fiber (P)(3) Watercement ratio (R)(4) Cross-sectional area of test specimen (A)(5) Youngrsquos modulus of fiber (Y)(6) Mechanical strength of control specimen (S)

Based on the input parameter and target values theoutput was generated through ANN and MRA and theseoutput values were compared with target (actual) values etypes of fibers and its respective literature source are pre-sented in Table 1e active compressive strength data set has5 columns and 252 rows (5times 252) of input data and 1 columnand 252 rows (1times 252) of target data e active split tensilestrength data set has 5 columns and 119 rows (5times119) ofinput data and 1 column and 119 rows (1times 119) of target datae active flexural strength data set has 5 columns and 150rows (5times150) of input data and 1 column and 150 rows(1times 150) of target data e target data for compressivestrength split tensile strength and flexural strength were usedin both the MRA and ANN model as separate target in thisstudy is single target system was used due to the usage ofcross-sectional area of test specimens as one of the param-eters and it was known that the shape of the specimens varieswith different mechanical strengths

21 Prediction Model and Its Statistical Test Two predictionmodels artificial neural network (ANN) and multiple re-gression analysis (MRA) are used in this study to predict thecompressive strength split tensile strength and flexuralstrength of fiber-reinforced concrete (FRC)

22 Artificial Neural Network (ANN) e ANN predictionmodel is programmed through MATLAB with two hiddenlayers 15 neurons in each hidden layer and one output layerwith dependent variable as compressive strength split ten-sile strength and flexural strength Among all the data ap-proximately 70 15 and 15 has been considered fortraining testing and validation respectively e LevenbergndashMarquardt (LM) algorithm is used for training due to itsrobustness and speed Layered feed-forward networks havebeen used in this algorithm in which the neurons are arrangedin layers Here signals are sent forward and errors arepropagated backwards

23 Multiple Regression Analysis (MRA) In this study thelinear-type multiple regression analysis modeling is carriedout using MS excel e coefficients of regression are cal-culated by considering 95 confidence level hence the errortolerance level is limited to maximum of 5 For a giveninput variable the calculated probability value (p value)is considered to be significant if and only if its value is lessthan 005 rough the regression analysis the followingcoefficients presented in Table 2 were found and substitutedin linear multiple regression equation (equation (1))

output I + C1F + C2P + C3R + C4A + C5Y + C6S (1)

24 Statistical Test e performance of the ANN and MRAprediction for the mechanical behavior was tested throughthe statistical methods e tests involved are coefficient ofdetermination (R2) and root mean squared error (RMSE)e coefficient of determination is presented in equation (2)is can be obtained from the comparative chart of pre-dicted compressive strength vs experimental compressivestrength e accuracy of the predictions of a network wasquantified by the root of the mean squared error difference(RMSE) between the experimented and the predictedvalues and the procedure of finding RMSE is presented inequation (3)

R2

1minussum of squares of residuals

sum of sqaures of predicted values (2)

RMSE

1n

1113944

n

i1(ACSTminus PCST)

2

11139741113972

(3)

3 Results and Discussion

e effectiveness and the acceptance of prediction modelsare based upon the ability of the model to predict the outputIn this study the models were designed to predict themechanical behavior (mechanical strength) of FRC based oninput parameters and two methods of predictions ANNand MRA are used e prediction models are validatedthrough coefficient of determination (R2) and root meansquared error (RMSE) and are consolidated in Table 3

e MRA and ANN prediction of the compressivestrength value is plotted with respect to the actual compressivestrength and presented in Figures 1 and 2 respectively eMRA prediction has the coefficient of determination R2 as093 which is almost an acceptable value whereas the ANNhas an R2 value of 1 which indicates that the ANN model isaccurate e RMSE of the MRA model is 723MPa and theANNmodel is 014MPa which demonstrates that error in theMRA model is large and cannot be relied upon for predictingthe compressive strength

e MRA and ANN prediction model plot for splittensile strength with respect to its actual value is presented inFigures 3 and 4 respectively e R2 value for the MRAmodel is 087 and ANN model is 094 e RMSE for the


Tabl

e1

Rang

eof

parametersin

data

base

forpredictio

nmod

el

Datarang

eforpredictio

nmod

el

Type

offib

er

Tensile

streng

thof

fiber

inMPa

Percentage

additio

nof

fiber

Water

bind

erratio

Areaof

specim

entested

for

compressio

nin

mm

2

Areaof

specim

entested

for

tension

inmm

2

Areaof

specim

entested

for

flexu

rein

mm

2

Com

pressio

nstreng

thin

MPa

Split

tensile

streng

thin

MPa

Flexural

streng

thin

MPa

Elastic

mod

ulus

offib

erin

MPa

Steelfi

ber[19ndash

27]

1000ndash2

800

0025ndash

2000

015ndash0

51600ndash2

2500

22500ndash

62832

25200ndash

90000

382ndash1463

323ndash8

95

35ndash

202

22830ndash

6047726846

Polyprop

ylenefib

er[18

242

8ndash34]

320ndash1200

00001ndash2

000

030ndash0

64

1600ndash2

2500

22500ndash141372

40000ndash

79500

127ndash9

75

198ndash7

98

3ndash1202

1781853ndash4

937104

Hybridfib

er[35

36]

450ndash1200

0200ndash

2000

038ndash0

50

7850ndash17671

mdash25200ndash

40000

2701ndash

7322

mdash431ndash1

13

18460ndash

4278434

Glass

fiber

[1537ndash4

8]1500ndash3

750

0100ndash

0300

02ndash

071

380ndash141371

648ndash14137167

10000ndash

50000

14ndash7

582

107ndash7

1339ndash101

3680ndash4

353734

Basaltfib

er[2349ndash5

2]3400ndash4

600

0015ndash12450

04ndash

05

7850ndash14137

22500ndash

6283185

24000ndash

92720

2913ndash

8578

237ndash4

59

39ndash108

26986ndash

44415






MRAcoecients








R2 = 093

000

2000

4000

6000

8000

10000

12000

14000

16000

000 2000 4000 6000 8000 10000 12000 14000 16000

MRA

pre

dict

ed co

mpr

essiv

e str

engt

h in

MPa



R2 = 1

0002000400060008000

10000120001400016000


AN

N p

redi

cted

com

pres

sive

stren

gth

in M

Pa


R2 = 087

000100200300400500600700800900

000 200 400 600 800 1000

MRA

pre

dict

ed sp

lit te

nsile

str

engt

h in

MPa



R2 = 094

000

100

200

300

400

500

600

700

800

900

1000

000 200 400 600 800 1000

AN

N p

redi

cted

split

tens

ile st

reng

th in

MPa





4 Conclusion



Data Availability




References











R2 = 092

000

500

1000

1500

2000

2500

000 500 1000 1500 2000

MRA

pre

dict

ed fl

exur

al st

reng

thin

MPa



R2 = 094

000

500

1000

1500

2000

2500

000 500 1000 1500 2000 2500

AN

N p

redi

cted

flex

ural

stre

ngth

in M

Pa



















































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




Tabl

e1

Rang

eof

parametersin

data

base

forpredictio

nmod

el

Datarang

eforpredictio

nmod

el

Type

offib

er

Tensile

streng

thof

fiber

inMPa

Percentage

additio

nof

fiber

Water

bind

erratio

Areaof

specim

entested

for

compressio

nin

mm

2

Areaof

specim

entested

for

tension

inmm

2

Areaof

specim

entested

for

flexu

rein

mm

2

Com

pressio

nstreng

thin

MPa

Split

tensile

streng

thin

MPa

Flexural

streng

thin

MPa

Elastic

mod

ulus

offib

erin

MPa

Steelfi

ber[19ndash

27]

1000ndash2

800

0025ndash

2000

015ndash0

51600ndash2

2500

22500ndash

62832

25200ndash

90000

382ndash1463

323ndash8

95

35ndash

202

22830ndash

6047726846

Polyprop

ylenefib

er[18

242

8ndash34]

320ndash1200

00001ndash2

000

030ndash0

64

1600ndash2

2500

22500ndash141372

40000ndash

79500

127ndash9

75

198ndash7

98

3ndash1202

1781853ndash4

937104

Hybridfib

er[35

36]

450ndash1200

0200ndash

2000

038ndash0

50

7850ndash17671

mdash25200ndash

40000

2701ndash

7322

mdash431ndash1

13

18460ndash

4278434

Glass

fiber

[1537ndash4

8]1500ndash3

750

0100ndash

0300

02ndash

071

380ndash141371

648ndash14137167

10000ndash

50000

14ndash7

582

107ndash7

1339ndash101

3680ndash4

353734

Basaltfib

er[2349ndash5

2]3400ndash4

600

0015ndash12450

04ndash

05

7850ndash14137

22500ndash

6283185

24000ndash

92720

2913ndash

8578

237ndash4

59

39ndash108

26986ndash

44415






MRAcoecients








R2 = 093

000

2000

4000

6000

8000

10000

12000

14000

16000

000 2000 4000 6000 8000 10000 12000 14000 16000

MRA

pre

dict

ed co

mpr

essiv

e str

engt

h in

MPa



R2 = 1

0002000400060008000

10000120001400016000


AN

N p

redi

cted

com

pres

sive

stren

gth

in M

Pa


R2 = 087

000100200300400500600700800900

000 200 400 600 800 1000

MRA

pre

dict

ed sp

lit te

nsile

str

engt

h in

MPa



R2 = 094

000

100

200

300

400

500

600

700

800

900

1000

000 200 400 600 800 1000

AN

N p

redi

cted

split

tens

ile st

reng

th in

MPa





4 Conclusion



Data Availability




References











R2 = 092

000

500

1000

1500

2000

2500

000 500 1000 1500 2000

MRA

pre

dict

ed fl

exur

al st

reng

thin

MPa



R2 = 094

000

500

1000

1500

2000

2500

000 500 1000 1500 2000 2500

AN

N p

redi

cted

flex

ural

stre

ngth

in M

Pa



















































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls








MRAcoecients








R2 = 093

000

2000

4000

6000

8000

10000

12000

14000

16000

000 2000 4000 6000 8000 10000 12000 14000 16000

MRA

pre

dict

ed co

mpr

essiv

e str

engt

h in

MPa



R2 = 1

0002000400060008000

10000120001400016000


AN

N p

redi

cted

com

pres

sive

stren

gth

in M

Pa


R2 = 087

000100200300400500600700800900

000 200 400 600 800 1000

MRA

pre

dict

ed sp

lit te

nsile

str

engt

h in

MPa



R2 = 094

000

100

200

300

400

500

600

700

800

900

1000

000 200 400 600 800 1000

AN

N p

redi

cted

split

tens

ile st

reng

th in

MPa





4 Conclusion



Data Availability




References











R2 = 092

000

500

1000

1500

2000

2500

000 500 1000 1500 2000

MRA

pre

dict

ed fl

exur

al st

reng

thin

MPa



R2 = 094

000

500

1000

1500

2000

2500

000 500 1000 1500 2000 2500

AN

N p

redi

cted

flex

ural

stre

ngth

in M

Pa



















































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





4 Conclusion



Data Availability




References











R2 = 092

000

500

1000

1500

2000

2500

000 500 1000 1500 2000

MRA

pre

dict

ed fl

exur

al st

reng

thin

MPa



R2 = 094

000

500

1000

1500

2000

2500

000 500 1000 1500 2000 2500

AN

N p

redi

cted

flex

ural

stre

ngth

in M

Pa



















































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls



















































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




















Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls






Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




Documents

Prediction of Mechanical Strength of Fiber Admixed ...downloads.hindawi.com/journals/amse/2019/4654070.pdfaspects, it was observed that the MRA gains its accurateness in predicting