Application of response surface methodologyPredicting and optimizing the properties of concrete containing steel fibre extracted fromwaste tires with limestone powder as fillerAwolusi, T.F.; Oke, O.L.; Akinkurolere, O.O.; Sojobi, A.O.

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Publication details:Awolusi, T. F., Oke, O. L., Akinkurolere, O. O., & Sojobi, A. O. (2019). Application of response surfacemethodology: Predicting and optimizing the properties of concrete containing steel fibre extracted from wastetires with limestone powder as filler. Case Studies in Construction Materials, 10, [e00212].https://doi.org/10.1016/j.cscm.2018.e00212

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Case Studies in Construction Materials 10 (2019) xxx–xxx

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Case Studies in Construction Materials

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Case study

Application of response surface methodology: Predicting andoptimizing the properties of concrete containing steel fibreextracted from waste tires with limestone powder as filler

T.F. Awolusia,*, O.L. Okea, O.O. Akinkurolerea, A.O. Sojobib

aDepartment of Civil Engineering, Ekiti State University, NigeriabDepartment of Architecture and Civil Engineering, City University of Hong Kong, Kowloon, Hong Kong, China

A R T I C L E I N F O

Article history:

Received 22 July 2018Received in revised form 8 November 2018Accepted 13 November 2018

Keywords:Compressive strengthConcreteFibre reinforcementResponse surface methodologyWaste management

* Corresponding author.E-mail addresses: temitopeawolusi06@g

(O.O. Akinkurolere), aosojobi2-c@my.cityu

https://doi.org/10.1016/j.cscm.2018.e002122214-5095/© 2018 The Authors. Publishedlicenses/by-nc-nd/4.0/).

mail.com.edu.hk (

by Elsev

A B S T R A C T

This study showcases the predictive and optimization capabilities of response surfacemethodology with respect to the fresh and hardened properties of waste tyre steel fibrereinforced concrete containing limestone powder. Response surface methodology has theadvantage of simultaneously varying chosen independent variables to provide a usefulmodel for overall response variation. The study identifies aspect ratio (50–140), watercement ratio (0.2–0.4) and cement content (25%–40%) as independent variables whilelimestone powder was kept constant at 5% by weight of concrete. Predictive equations forthe water intake/absorption, compressive strength, flexural strength, split tensilestrength and slump of fibre reinforced concrete were obtained using the independentvariables. The analysis of variance (ANOVA) for all properties indicates that the modifiedquadratic model was able to effectively predict the fresh and hardened properties of fibrereinforced concrete with coefficient of determination ranging between 0.86 and 0.98. Inaddition, RSM model predictive efficiency was classified as very good for compressivestrength, splitting tensile strength, slump and water absorption and acceptable for FS interms of Nash & Sutcliffe coefficient of model efficiency. An optimum condition of 140 forthe aspect ratio, 0.26 for water cement ratio and 40% for cement content corresponding to0.94%, 42.69 N/mm2, 7.97 N/mm2 5.23 N/mm2 7.65 cm for water intake/absorption,compressive strength, flexural strength, split tensile strength and slump respectively wasachieved. These predictions were validated and a good correlation was observed betweenthe experimental and predicted values judging by the absolute relative percent error of0.842, 11.35, 3.6, 18.22 and 2.04 for water intake/absorption, compressive strength,flexural strength, split tensile strength and slump respectively. The proposedmathematical models are capable of predicting the required fresh and hardenedproperties of fibre-reinforced concrete as to inform early decision making when utilizedin construction.© 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC

BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

(T.F. Awolusi), seyioke@hotmail.com (O.L. Oke), funke_akinkurolere@yahoo.co.ukA.O. Sojobi).

ier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/

http://creativecommons.org/licenses/by-nc-nd/4.0/mailto:temitopeawolusi06@gmail.commailto:seyioke@hotmail.commailto:funke_akinkurolere@yahoo.co.ukmailto:aosojobi2-c@my.cityu.edu.hkhttps://doi.org/10.1016/j.cscm.2018.e00212http://creativecommons.org/licenses/by-nc-nd/4.0/http://creativecommons.org/licenses/by-nc-nd/4.0/https://doi.org/10.1016/j.cscm.2018.e00212http://www.sciencedirect.com/science/journal/22145095www.elsevier.com/locate/cscm

2 T.F. Awolusi et al. / Case Studies in Construction Materials 10 (2019) e00212

1. Introduction

The ever increasing population growth, urbanization and rising standards of living resulting from technologicalinnovations have contributed to the increasing quantity of solid wastes generated. The management of these disposedwastes becomes a major environmental problem in the long term. One of such solid wastes is tires. Owing to the rise in thenumber of vehicles being purchased, many tires end up as waste and if not properly disposed it results to environmentalpollution in major towns and cities globally [1].

It is estimated that about 1000 million tires are being discarded at the end of their useful life annually across the globe,and there is need for proper handling in order to prevent severe ecological hazard. It is also anticipated that this number willincrease by 20% by the year 2030, thereby increasing the estimated quantity to 5000 million (including stock piled).Therefore, the large volume of this waste has made it a material of research interest [2,1,5,52,3,50,51].

Their cheap availability, bulk and resilience have made the handling of waste tires problematic in a developing countrysuch as Nigeria. Although there is no estimated record for the quantity of waste tires generated in the country is faced withthe challenge of shortage landfill space to accommodate the huge volume of waste tires generated annually. These tires arestock piled at different locations in undeveloped lands and are in most cases set ablaze whenever such lands are to beutilized. Another common practice in the country is that these waste tires litter roadsides across the country and are oftenincinerated on the highways during unrest due to their proximity.

The unwholesome methods of disposal provide excellent breeding space for mosquitoes – the malaria parasite carrier,before being burnt and when burnt, they result in fire hazards as well as environmental pollution. Although there isfeasibility in the use of tires as fuel, it is impaired by high initial cost. The large amount of carbon dioxide emitted in theprocess is also a major source of concerns for the environment. The pyrolysis process which produces carbon black is costlyand substandard to the obtained products of petroleum [2–4]. One of the promising ways in which waste tires can be useful isin concrete. This can be done by incorporating the waste tire crumbs as aggregates in concrete and by using the extractedsteel fibre component of waste tires as reinforcements in concrete mix. This attempt could be environmental friendly. Thisstudy in particular focuses on the use of such extracted steel fibres in concrete.

Balaguru and Shah [5] identified steel as one of the fibres useful in concrete. Other fibres include ceramics, glass,polymers, ceramics, asbestos, carbon. Altun et al. [6] indicated that steel fibre volume fraction of concrete containing shouldrange between 1 and 2.5%, estimated by the absolute concrete volume. Bayramov et al. [7] and Yazıcı et al. [8] observed thatunreinforced cementitious materials are usually brittle and of low tensile strength and that the presence of fibrereinforcement decreases the brittleness of concrete. They identified aspect ratio (length/diameter), volumetric fraction andfibre distribution as factors that influence the performance of steel fibre reinforced concrete (SFRC).

Holschemacher et al. [9] also identified aspect ratio and volumetric fraction of steel fibres as factors which significantlyenhance the mechanical properties of concrete. The inclusion of steel fibres into concrete matrix has positive influence on themechanical properties of concrete such as tensile strength, impact strength and toughness while the aspect ratio and volumetricfraction were identified as important factors for successful design of SFRC. In addition Suhaendi & Horiguchi [10] also observedthat the mechanical properties of SFRC depend on fibre volume and length. The authors observed that the tensile strength ofSFRC was improved as a result of the bridging action of steel fibres. Likewise, some investigations reported that concretereinforced waste tire steel fibres exhibited improved mechanical performance similar to industrial steel fibres [11–12].

In addition, concrete as a porous material with discrete and interconnected pores of different sizes and shapes, requires thepresence of very finely grounded material of about the same fineness as portland cement for proper pore size refinement andreduced permeability [13]. One of such very finely grounded material is limestone powder. Nehdi et al. [14] observed improvedworkability and stability of fresh concrete containing limestone powder as fillers. Although it has been identified that theincorporation of limestone powder reduces certain properties of concrete such as compressive strength, flexural strength andsplit tensile strength as the percentage of limestone powder increases in the concrete [15]. However, according to EuropeanStandard [16], the addition of five percent calcareous filler material like limestone powder to concrete mix is acceptable.

Therefore, this study explores the aspect ratio of steel fibres alongside cement content and water cement ratio asindependent variables in predicting the compressive strength, flexural strength, split tensile strength, water absorption andslump of waste tire steel fibre reinforced concrete using response surface methodology (RSM). The RSM design identifiesboth linear interactions and quadratic contributions of the independent variables to the concrete properties. Furthermore,this study optimizes the combined effect of these factors to maximize or minimize desired outputs. The introduction of RSMin defining a suitable mix design for concrete containing steel can enhance the concrete performance in both fresh andhardened states. RSM has the predictive capability to determine properties such as slump, water absorption capacity,compressive strength, flexural strength and split tensile strength, thereby reducing the time and drudgery of repetitivelaboratory experiments. The accurate and speedy determination of these properties reduces construction time especiallywhen they are required for fast project execution. Such innovative application of RSM provides opportunity to make essentialadjustments in mix proportions of concrete ingredients to achieve design objectives. In addition, such approach preventscircumstances in which either the targeted design strength is not met or concrete with excessive strength is produced. Thisapproach invariably results in cost-effective utilization of raw-material, reduced construction failure and reducedconstruction cost [17].

RSM provides statistically validated predictive models that can be manipulated for finding optimal process configurations[18]. RSM typically is useful in situations where several factors influence one or more performance characteristics, or

T.F. Awolusi et al. / Case Studies in Construction Materials 10 (2019) e00212 3

responses. It can also be utilized to optimize one or more responses to meet a given set of specifications. More importantly,RSM, provides sufficient experimental interpretation of the non-linear responses surfaces of experimental results [19].

Response Surface Methodology (RSM) is an effective statistical tool for experimental design, model building, factorseffects evaluation and optimum condition search [20–23]. In RSM, several factors which vary simultaneously are fitted toquadratic function [24]. RSM offers several advantages for optimization over the one factor at a time approach which istedious and also does not take into account the interaction of factors [25]. RSM proportions the constituent material to obtainan optimum mix proportions used as a mathematical model for the prediction of the desired properties [26].

Even though RSM has been applied to numerous cement and concrete researches[27–30], its application to steel fibrereinforced concrete is very limited. Therefore, this study focuses on application of RSM in predicting and optimizing thecompressive strength, flexural strength, split tensile strength, water absorption and slump of waste tire steel fibre reinforcedconcrete. The objectives of this study are (i) to evaluate the interactive effects of water-cement ratio, aspect ratio of waste tiresteel fibres and cement content on the mechanical properties of waste-tire steel fibre reinforced concrete (ii) develop andassess predictive models for the mechanical properties (iii) Optimize the waste tire steel fibre reinforced concrete mixturesfor construction applications [49].

2. Experimental programme, material and procedure

2.1. Experimental programme and model efficiency assessment

A total of twenty experimental runs were generated using the Central composite rotatable design (CCRD) of responsesurface methodology. CCRD can be used in predicting dependent variables also known as response by means of a smallnumber of experimental data, with all parameters varied in preferred range. Each numerical factor is varied over five (5)levels. They are plus Alpha (+α), minus Alpha (-α), (axial/star points) +1(high level), -1(low level) (factorial points) and thecenter point (mid-level). Table 1 and Fig. 1 give a representation of the above explanation. The three parameters also knownas independent variables considered in the design are aspect ratio, water cement ratio and cement. They are represented asA, B and C in coded terms (independent variables) while R1- R5 represent the water absorption/intake and compressivestrength, flexural strength, split tensile strength and slump (dependent variables) respectively. The coding of variable wasdone using Eq. (1).

coded value ¼ r � ch � c ð1Þ

Table 1Independent parameter including coded levels.

Parameters Code Unit Coded parameter levels

�1 0 +1Aspect ratio A 50 95 140Water cement ratio B 0.25 0.33 0.4Cement C % 25 32.25 40

Fig. 1. A Pictorial representation of CCRD.

4 T.F. Awolusi et al. / Case Studies in Construction Materials 10 (2019) e00212

Where r is the runs number to be coded, c is the center point of the factor to be coded and h is the highest value of the factorbeing considered as given by the design of experiment.

The independent variables ranged between 50–140, 0.25–0.4 and 25%–40% for the aspect ratio of steel fibre extractedfrom waste tires (A), water cement ratio (B) and percentage of cement content (C) respectively.

The predictive efficiency of the RSM model in terms of output error/differences between observed (experimental) valuesand predicted values were measured using the following indices: mean prediction error (MPE), mean square error (MSE),root-mean-square error (RMSE), and Nash & Sutcliffe coefficient of efficiency (NSE) as given in Eqs. (2) to (6).

MPE ¼P

Yi � Oið Þn

ð2Þ

MSE ¼P

Yi � Oið Þ2n

ð3Þ

RMSE ¼ MSEð Þ1=2 ð4Þ

NSE ¼ 1 � 1ht þ 1

� �2ð5Þ

Where nt ¼ SDRMSE � 1 ð6Þ

(Source: [31]; Sojobi et al. [32])Where Yi is the predicted value, Oi is the observed (experimental) value, n is the number of data set, nt is the number of

times the standard deviation is greater than RMSE [31]. In terms of NSE values, a model is classified as very good, good,acceptable and unsatisfactory if the NSE values are in the range of � 0.90, 0.8–0.9, 0.65–0.8 and < 0.65 respectively [31].Model efficiency was also classified as very good, good, acceptable and unsatisfactory for SD � 3.2 RMSE, 2.2 RMSE < SD < 3.2RMSE, 1.2 RMSE < SD < 2.2 RMSE and SD < 1.7 RMSE [31].

2.2. Experimental material

Steel fibres with specific gravity of five (5) and diameter 0.25 mm were used in the study. These fibres were extractedfrom waste tires by shredding. The indention microscope was used to ensure a constant diameter was maintained. Thefibres were cut into different lengths depending on the required aspect ratio as presented in Fig. 2. The aspect ratio isusually defined as ratio of the length of fibre to diameter ðl d= ). The tensile strength of the fibre was determined at a crosshead speed of 20 mm/min. The test piece was properly griped and mounted before testing. The average tensile strength wasdetermined to be 700 N/mm2 with a strain at failure of 0.097. The volumetric fibre content was kept constant at 1% asrecommended by Chanh [33].

Ordinary Portland cement (OPC) of grade 42.5 was used in the study. The specific gravity, initial and final setting times inaccordance to BS 12, [34] were determined and presented in Table 2. A pictorial view of the cement and limestone powder ispresented in Fig. 3. Lime stone powder (LSP) with specific gravity of 2.48 was used as fillers. The percentage composition ofLSP was kept constant at 5% of the weight of concrete. The chemical composition of the cement and limestone powder ispresented in Table 3. River sand with specific gravity of 2.58 was used as fine aggregate. Granite passing through sieve size20 mm was used as coarse aggregate. The particle size gradations of the aforementioned materials are presented in Fig. 4. Thehigh range water reducing admixture (HRWRA) also known as superplasticizer conforming to ASTM C 494 [35] kindlyprovided by Advanced Chemical Technology, Ikeja was used to enhance the workability of the concrete, and lastly potablewater was used for mixing.

Fig. 2. Different length of steel fibre.

Table 3Chemical composition of OPC and LSP.

Composition (%) OPC LSP

Silicon dioxide (SiO2) 20.99 5.82Calcium oxide (CaO) 62.50 51.40Aluminium oxide (Al2O3) 4.18 0.58Ferric oxide (Fe2O3) 3.30 0.72Magnesium oxide (MgO) 1.87 0.50Sodium oxide (Na2O) 0.37 0.04Potassium oxide (K2O) 0.92 0.18Sulphur trioxide (SO3) 2.02 0.08pH 11.19 7.89Loss on Ignition (LOI) 1.53 0.18

Table 2Basic test carried out on OPC.

Characteristics Values obtained Standard Values BS 12

Normal consistency (%) 28 26-33Initial setting time (mm) 112 >45Final setting time (mm) 175

Table 4Details of Mix proportion.

Run A B C (%) FibreLength(mm)

Cement(kg/m3)

Water(kg/m3)

Fibre(kg/m3)

SP(kg/m3)

LSP(kg/m3)

Sand (FA)(kg/m3)

Granite (CA)(kg/m3)

1 95(0) 0.33(0) 32.5(0) 24 780 257.4 24 15.6 120 546.75 668.252 50(�1) 0.25(�1) 40.0(+1) 13 960 240.0 24 15.6 120 473.58 578.823 140(+1) 0.25(�1) 40.0(+1) 35 960 240.0 24 15.6 120 473.58 578.824 95(0) 0.33(0) 32.5(0) 24 780 257.4 24 15.6 120 546.75 668.255 140(+1) 0.25(�1) 25.0(�1) 35 600 150.0 24 15.6 120 676.08 826.326 95(0) 0.33(0) 32.5(0) 24 780 257.4 24 15.6 120 546.75 668.257 140(+1) 0.40(+1) 40.0(+1) 35 960 384.0 24 15.6 120 408.78 499.628 50(�1) 0.40(+1) 40.0(+1) 13 960 384.0 24 15.6 120 408.78 499.629 50(�1) 0.25(�1) 25.0(�1) 13 600 150.0 24 15.6 120 676.08 826.3210 140(+1) 0.40(+1) 25.0(�1) 35 600 240.0 24 15.6 120 635.58 776.8211 95(0) 0.33(0) 32.5(0) 24 780 257.4 24 15.6 120 546.75 668.2512 50(�1) 0.40(+1) 25.0(�1) 13 600 240.0 24 15.6 120 635.58 776.8213 95(0) 0.20(�1.68) 32.5(0) 24 780 156.0 24 15.6 120 592.38 724.0214 95(0) 0.45(+1.68) 32.5(0) 24 780 351.0 24 15.6 120 504.63 616.7715 95(0) 0.33(0) 19.0(�1.68) 24 456 150.5 24 15.6 120 740.66 905.2616 170(+1.68) 0.33(0) 32.5(0) 43 780 257.4 24 15.6 120 546.75 668.2517 95(0) 0.33(0) 45.1(+1.68) 24 1083 357.3 24 15.6 120 365.62 446.8718 19.32(�1.68) 0.33(0) 32.5(0) 5 780 257.4 24 15.6 120 546.75 668.2519 95(0) 0.33(0) 32.5(0) 24 780 257.4 24 15.6 120 546.75 668.2520 95(0) 0.33(0) 32.5(0) 24 780 257.4 24 15.6 120 546.75 668.25

A = Aspect ratio; B = Water cement ratio; C = Cement; SP = Super plasticizer; LSP = limestone powder; FA = Fine Aggregate; CA = Coarse Aggregate.

Fig. 5. Samples of test specimen.

6 T.F. Awolusi et al. / Case Studies in Construction Materials 10 (2019) e00212

stopped after proper blending of all constituent materials was achieved. The duration of concrete mixing for each batch (run)was approximately 5–7 minutes.

Thereafter, the fresh concrete mix was poured into already lubricated moulds. The moulds used for the compressionstrength, split tensile strength and water absorption tests were 100 mm x 100 mm x 100 mm. The moulds used for the four-point bending flexural test was 100 mm x 100 mm x 400 mm. Each mould was filled in three layers, with each layer receiving35 strokes of the tampering rod. This was done to ensure uniform compaction. The specimens were covered with damp sacksbefore demoulding after 24 h. All the specimens for compressive strength, flexural strength and split tensile strength testswere water-cured for 28 days after demoulding. Sample of specimens in slump, compressive, flexural and split tensilestrengths testing respectively are presented in Fig. 5.

2.3.1. Slump testThe test was done in accordance to [36] to know the consistency of freshly mixed concrete. The consistency of a

concrete mix is closely related to workability. A slump cone of bottom diameter 10 cm, top diameter 20 cm and height30 cm was used. The concrete was filled in three layers with each layer receiving approximately twenty five strokes (25) ofthe tampering rod (the tampering rod is a steel of 16 mm diameter and 600 mm long). On filling the third layer excessconcrete was removed using a hand trowel. The mould was immediately raised slowly in a vertical direction. The slumpmeasured in centimeter (cm) is the difference between the height of the mould and the height point of the highest point ofthe specimen being tested.

2.3.2. Water Absorption/ intakeThe test was done in accordance with ASTM C 642-06 [46]. Test specimens were immersed in water at temperature of

29 �C for twenty four (24) hours. Subsequently, samples were drained with towel for ten (10) minutes to remove excess

T.F. Awolusi et al. / Case Studies in Construction Materials 10 (2019) e00212 7

water. The water absorption/intake was determined using Eq. (7). Three samples were tested for each concrete mix to obtaina reliable average value.

W2 � W1W1

� 100 ð7Þ

W1= Weight of sample before immersion in waterW2= Weight of sample after immersion in water

2.3.3. Compressive strengthThe concrete specimens were prepared according to [47] and tested at twenty eight (28) days. Compressive strength

values obtained were determined by taking the average of three specimens. Testing was done using compression testingmachine. The bearing surface of the supporting and loading rollers was wiped clean before placing specimen.Positioning of specimen was done with load applied on the uppermost surface of specimen as cast in the mould. Carewas taken to ensure that specimen aligned with the loading device. Loading was done gradually and continuouslyincreased until the dial stopped moving and the maximum load was recorded. The compressive strength of thespecimen was expressed as the maximum crushing load in Newton (N) divided by the effective surface area of the testedspecimen in millimeter (mm).

2.3.4. Flexural strength testThe beams at 28 days were tested under four point loading until failure using flexural testing machine in line with [48]. A

constant loading configuration with shear span of 300 mm and shear span depth ratio of 3.0 was applied. Specimens wereplaced on the supporting bearing blocks with side in respect to its position when moulded. The upper surface of the testspecimen was brought in contact with the load-applying block at one quarter distance from the end of supports. Followingthis action, the load applying block is brought in full contact with the beam surface. The beam was checked to ensure it haduniform contact with both the bearing and the load applying blocks. Loading was done continuously until the specimenfailed and the dial stopped moving. The maximum applied load indicated by the testing machine was recorded. The Flexuralstrength is calculated using Eq. (8).

R ¼ 3Fl4bd2

ð8Þ

R = Flexural strength (N/mm2)F = Applied load at failurel = beam span measured in millimeterb = beam breadth measured in millimeterd = beam depth measured in millimeter

2.3.5. Split tensile strength testThe samples at twenty eight (28) days were tested using compression testing machine according to BS EN 12390-6 [37].

Samples were placed between the loading surfaces of a compression testing machine. The compressive line loads appliedalong a vertical symmetrical plane. This loading arrangement sets up normal tensile stress along the loading axis of twoequal and opposed loads. The splitting of the specimen at maximum load was recorded and Eq. (9) was used to determine thesplit tensile strength

Ft ¼ 2Pp DLð Þ ð9Þ

Ft = Tensile Strength (N/mm2)P = Load at failure (N)D = Diameter of cylinder or side of the cube (mm)L = Length of the cylinder/ cube (mm)

3. Result and discussion

3.1. Perturbation plots and predictive efficiency of the derived models

Perturbation plots in RSM design revealed significant parameters by displaying changes in response of each factor as eachfactor moves from the reference point, which is the zero coded level of each factor, with all other factors held constant at thereference value.

Perturbation plot for water intake presented in Fig. 6a revealed that all the three factors have significant influence on thewater intake. However water intake reduces with increased water-cement ratio (B), while it increases with increased cementcontent (C). For fibres, water intake was found to be lower with long fibres signifying high aspect ratio when compared to

Fig. 6. (a) Perturbation plot for water intake (b) Perturbation plot for compressive strength (c) Perturbation plot for flexural strength (d) Perturbation plotfor split tensile strength (e) Perturbation plot for slump.

8 T.F. Awolusi et al. / Case Studies in Construction Materials 10 (2019) e00212

short fibres signifying low aspect ratio. This corroborates earlier research finding that the presence of fibres prevent ingressof external substances [10].

Perturbation plot for compressive strength (CS) in Fig. 6b revealed that only water cement ratio has significant influenceon CS as higher CS was obtained in the region close to the reference point. This corroborates earlier research reports thatfibres do not contribute significantly to the static compressive strength of concrete and even concrete structures withconventional reinforcements [33].

T.F. Awolusi et al. / Case Studies in Construction Materials 10 (2019) e00212 9

Perturbation plot of flexural strength (FS) in Fig. 6c revealed that water-cement ratio had the most significant influence onflexural strength. The influence of factors such as aspect ratio and cement were less significant when compared to watercement ratio. It also revealed that flexural strength will slightly reduce with increasing aspect ratio. This implies that shortfibres with low aspect ratio have positive contribution on flexural strength.

Perturbation plot in Fig. 6d revealed that the highest split tensile strength (STS) can be achieved close to the referencepoint (middle region) of both aspect ratio (A) and w/c ratio (B) while the influence of cement on STS was observed to benegligible.

Perturbation plot for Fig. 6e revealed that all the factors have effect on slump. Slump was observed to reduce withincreased aspect ratio, increased with increasing w/c ratio and cement. It can be inferred that short fibres with low aspectratio provide high acceptable slump while long fibres contributes to slump reduction. This will enhance proper blendingand mixing with the aggregate in freshly prepared concrete mix and also translates to improved workability. This impliesshort fibres are applicable where high slump is required while long fibres are more effective where slump reduction isrequired.

3.2. Predictive efficiency of the derived models

In terms of predictive efficiency (Table 5), the RSM model can be classified as ‘very good’ for Compressive strength (CS),Split tensile strength (STS), Slump and water absorption/ Intake (WA) while it was classified as ‘acceptable’ for flexuralstrength (FS). The NSE values of 0.97, 0.96, 1.0 and 0.95 for CS, STS, slump and WA fell within � 0.9 NSE specification requiredfor very good model while NSE value of 0.70 for FS was within NSE specification for acceptable model.

Comparative evaluation of the model results with respect to SD and RMSE revealed that RSM model was very good for CS,STS, slump and WA but acceptable for FS. This is because the SD values of 7.42,1.30, 9.35 and 0.37 were found greater than 3.2times their respective RMSEs. On the other hand, the SD for FS fell within the range of 1.2–2.2 RMSE required for ‘acceptable’model classification [31].

3.3. ANOVA and regression models equations for investigated properties

The analysis of variance (ANOVA) for all properties investigated is presented in Tables 6A–6E . From the table, it wasobserved that the following linear terms were statistically insignificant according to the Student’s t-test (p-value < 0.05). Theterms A and B for water absorption, terms A and C for flexural strength and terms A, B and C for both compressive and splittensile strengths. However, all linear terms were significant for slump judging by the p-values obtained. The interaction andquadratic effect were also evaluated using same parameter.

Table 5SD, MPE, MSE, RMSE and NSE for CS, FS, STS, Slump and water absorption.

Test SD MPE MSE RMSE NSE Modelclassification

CS 7.42 �0.007 2.49 1.58 0.97 Very goodFS 1.16 �0.1317 0.41 0.64 0.70 AcceptableSTS 1.30 �0.0015 0.10 0.31 0.96 Very goodSlump 9.35 �0.18 0.0764 0.28 1.0 Very goodWA 0.37 0.0006 0.01 0.11 0.95 Very good

Table 6AANOVA for Water intake/absorption.

SoD SoS DoF MS F-value P-value Comment

Model 1.43 10 0.14 5.08 0.0152 SD = 0.17A 2.103E-003 1 2.103E-003 0.075 0.7915 Mean = 0.99B 0.077 1 0.077 2.73 0.1370 R2 = 0.8640C 0.34 1 0.34 12.18 0.0082 Adj. R2 = 0.70AB 0.084 1 0.084 2.97 0.1230 AP = 10.901AC 0.053 1 0.053 1.88 0.2075BC 1.125E-003 1 1.125E-003 0.040 0.8465A2 0.16 1 0.16 5.81 0.0425C2 0.25 1 0.25 9.05 0.0169ABC 0.22 1 0.22 7.86 0.0231A2 B 0.28 1 0.28 10.03 0.0133Residual 0.23 8 0.028Lack of Fit 0.19 4 0.049 6.36 0.0503Pure Error 0.031 4 7.640E-003

Table 6DANOVA for Split tensile strength.

Model 25.04 11 2.28 8.15 0.0052 SD = 0.53

A 0.13 1 0.13 0.45 0.5250 Mean = 5.84B 0.7 1 0.70 2.50 0.1578 R2 = 0.93C 0.080 1 0.080 0.29 0.6082 Adj. R2 = 0.81AB 0.39 1 0.39 1.40 0.2758 AP = 10.80AC 2.80 1 2.80 10.03 0.0158BC 0.40 1 0.40 1.42 0.2727A2 5.98 1 5.98 21.39 0.0024B2 6.51 1 6.51 23.31 0.0019C2 0.011 1 0.011 0.038 0.8508ABC 6.28 1 6.28 22.47 0.0021AB2 1.72 1 1.72 6.15 0.0422Residual 1.96 7 1.96Lack of Fit 1.93 3 1.93 92.45 0.0004Pure Error 0.028 4 6.950E-003

Table 6BANOVA for Compressive strength.

Model 942.03 13 72.46 7.32 0.0193 SD = 3.15

A 2.00 1 2.00 0.20 0.6720 Mean = 28.51B 21.13 1 21.13 3.13 0.2040 R2 = 0.95C 8 1 8 0.81 0.4100 Adj. R2 = 0.82AB 0.82 1 0.82 0.083 0.7851 AP = 12.11AC 6.64 1 6.64 0.67 0.4502BC 52.44 1 52.44 5.29 0.0697A2 9.22 1 9.22 0.3789 0.3789B2 287.77 1 287.77 0.0030 0.0030C2 2.71 1 2.71 0.27 0.6234ABC 7.38 1 7.38 0.74 0.4276A2 B 287.98 1 287.98 29.07 0.0030A2 C 73.47 1 73.47 7.42 0.0416A C2 2.47 1 2.47 0.25 0.6384Residual 49.53 5 9.91Lack of Fit 49.42 4 49.42 1838.92 < 0.0001Pure Error 0.11 4 0.027

Table 6CANOVA for Flexural strength.

Model 23.60 12 1.97 19.91 0.0008 SD = 0.31

A 0.57 1 0.57 5.76 0.0533 Mean = 6.76B 7.22 1 7.22 73.08 0.0001 R2 = 0..98C 5.000E–003 1 5.000E-003 0.051 0.8295 Adj. R2 = 0.93AB 0.36 1 0.36 3.63 0.1054 AP = 19.61AC 0.42 1 0.42 4.25 0.0849BC 2.26 1 2.26 22.91 0.0030A2 0.16 1 0.16 1.67 0.2440B2 7.92 1 7.92 80.17 0.0001C2 0.55 1 0.55 5.55 0.0566ABC 1.83 1 1.83 18.48 0.0051A2 B 9.12 1 9.12 92.34 < 0.0001A2 C 0.087 1 0.087 0.88 0.3851Residual 0.59 6 0.099Lack of Fit 0.46 2 0.23 6.71 0.0527Pure Error 0.14 4 0.034

10 T.F. Awolusi et al. / Case Studies in Construction Materials 10 (2019) e00212

Conversely, the interaction effects AB and AC for flexural strength and AC for split tensile strength were statisticallysignificant while for the other properties all interaction effects were insignificant. The significant quadratic terms are A2 andC2 for water absorption, terms A2 and B2 for split tensile strength and term B2 for slump, and compressive and flexuralstrengths while all other quadratic terms were insignificant. In order to improve the performance of the models, some cubicterms were introduced. The introduction of both significant and insignificant cubic terms for all properties investigated

Table 6EANOVA for Slump.

Model 1553.21 11 141.20 33.17 < 0.0001 SD = 2.06

A 24.50 1 24.50 5.75 0.0475 Mean = 12.20B 392.00 1 392.00 92.08 < 0.0001 R2 = 0.98C 239.66 1 239.66 56.29 0.0001 Adj. R2 = 0.95AB 2.66 1 2.66 0.62 0.4552 AP = 18.38AC 0.056 1 0.056 0.013 0.9116BC 13.33 1 13.33 3.13 0.1201A2 1.68 1 1.68 0.40 0.5492B2 76.34 1 76.34 17.93 0.0039C2 7.38 1 7.38 1.73 0.2295A2 B 8.54 1 8.54 2.01 0.1996AB2 9.98 1 9.98 2.34 0.1696Residual 29.80 7 29.80Lack of Fit 27.30 3 9.10 14.56 0.0128Pure Error 2.5 4 0.63

SoD: Source of data; SoS: Sum of squares; DoF: Degree of freedom; MS: mean square SD:standard deviation; R2: Coefficient of determination; Adj. R2: Adjusted coefficient ofdetermination; AP: Adequate precision. A = Aspect ratio, B = Water cement ratio andC = Cement.

T.F. Awolusi et al. / Case Studies in Construction Materials 10 (2019) e00212 11

improved the p- values of the models and the coefficient of determination (R2). The aim was to ensure that all R2 valuesobtained were greater than 0.8 since the closer this value is to one/unity the better the predictive efficiency of the models.

The significance of the models obtained from ANOVA (Tables 6A–6E was discussed in descending order; the model forslump was most significant at 95% confidence level, F-value of 33.17 and a p-value < 0.0001. Although the lack of fit (LOF) wassignificant, it did not invalidate the model for predictive purpose because R2was approximately 0.98. This high value for R2

shows that the regressors in the model did not explain only about 5% of the total variability. The flexural strength is next, at95% confidence level, F-value of 19.91, p-value of 0.0008 and an insignificant LOF of 0.0527 were obtained. This implies thatthe specified model fits the data satisfactorily [38].

With respect to compressive strength at same confidence level, F-value was 7.32, p-value was 0.0193 and a significant LOFwas obtained. It is worth noting that while LOF was significant, R2was approximately 0.95 which implies that approximately95% of total variation of outcomes was explained by the model. As regards the split tensile strength, and at the sameconfidence level of 95%, R2 of 0.93, F-value of 8.15 and a p-value 0.0052 were attained. With respect to water intake, at thesame confidence level of 95%, R2 of 0.86, F-value of 5.08, p-value of 0.0152 and an insignificant LOF of 0.0650 was obtained,signifying good fit of the derived model.

Adequate precision (AP) was also used in evaluating the performance of the model. It compares the range of valuespredicted at design point with the average prediction error. In this study, the AP values of the models were 10.90, 12.11, 19.61,10.8 and 18.38 for water intake/absorption, compressive strength, flexural strength, split tensile strength and slumprespectively. All values of AP obtained were greater than 4 which indicate that the model can be used to navigate the spacedefined by the CCRD [39]. By applying multiple regression analysis on the experimental data, the following regressionequations namely (Eqs. 10a–10e) were derived for all responses.

Water Absorption=intake ¼ þ0:16 þ 0:062A � 0:14B � 0:14C þ 0:098AB þ 0:1AC þ 0:17BC � 0:036A2þ 0:047B2 � 0:082C2 þ 0:14ABC þ 0:25 A2 B þ 0:25 A2 C ð10aÞ

Compressive strength ¼ þ32:99 � 1:15A � 4:46B þ 6:24C � 1:24AC � 5:04BC þ 0:19B2 � 5:11 C2 þ 0:67 B2 C� 1:93 BC2 ð10bÞ

Flexural strength ¼ þ6:82 þ 0:24A þ 1:23B þ 1:17C � 0:19AB � 0:38AC � 0:80BC � 1:01B2 � 0:37 C2� 0:69B2 C � 1:04BC2 ð10cÞ

Split tensile ¼ 4:65 þ 0:095A þ 1:22B þ 1:07C þ 0:21AB þ 0:016AC þ 0:16BC � 0:25A2 � 0:56B2 � 0:42 C2þ 0:75 ABC � 1:54 A2B � 0:71A2C ð10dÞ

Slump ¼ þ10:95 � 0:54A þ 8:62B þ 7:73C � 1:62AB þ 5:88AC þ 2:63BC � 4:04A2 þ 2:27B2 þ 1:74 C2� 4:88A BC � 6:25 A2B � 6:85 A2C ð10eÞ

12 T.F. Awolusi et al. / Case Studies in Construction Materials 10 (2019) e00212

3.4. Normal probability plot

Data were analyzed to check the normality of residuals as well as actual versus predicted plots for all propertiesinvestigated. Fig. 7a–e display the normal probability plot of both residuals and the actual versus predicted for allresponses. From these figures it was observed that for water intake, all the plotted points fell very close to the distributionfitted line while for flexural strength, split tensile strength and slump, majority of the plotted points fell very close to thedistribution fitted line. However for compressive strength, the plotted points fell at a far distance from the distributionfitted line [40]. In all, it was observed that the normal distribution plots generally was a better choice for analyzinginterested responses (properties) compared to predicted vs actual plots disparity between prediction values and actualexperimental values.

3.5. Contour and 3D plots for all responses

Assessment of the interactive relationship between the mix design parameters and the properties of steel fibre reinforcedconcrete was done and displayed using contours and 3D plots of RSM. These plots for all investigated responses werepresented in Fig. 8–e. Fig. 8a–e display the contour and 3D plots of dependent variables drawn as function of twoindependent variables while the third independent variable was held constant. From the contour and 3D plots of waterintake shown in Fig. 8a, it was observed that there is no clear interaction between the factor A and B with C held constant.Reduced water intake was observed with reduced B while A had reduced water intake for both low and high values of A.

The interaction between factors A and C shows elliptical contours and this is the pattern obtained when there are perfectinteractions between factors (independent variables) [41]. The observations from the contour and 3D plots imply that thewater intake will reduce with increase in factor A and reduction in factor C. For the interaction between C and B, reduction infactor C and increase in factor B will also reduce the water intake. From the contour and 3D plots of compressive strengthpresented in Fig. 8b, a clear relationship was observed for the interaction between A and B as increase in A and reduction in Bwill increase the compressive strength. For the interaction between A and C, increase in these factors increased thecompressive strength. For the interaction between B and C, it was observed that the compressive strength increased withincrease in C and at reduced value of B. This implies that an increase in factor C and a reduction in factor B will increase thecompressive strength.

The contour plots for Flexural strength presented in Fig. 8c show distorted contours which is the pattern obtained wheninteractions between independent variables are few [41]. From the contour plots of the interaction between the factors A andB with C held constant, no clear trend was observed, however from the 3D plot it was observed that an increase in flexuralstrength can be achieved with increased A and reduced B. From the interaction between A and C it could be observed for bothplots that changes in A and C have little effect on the Flexural strength. From the contour and 3D plots for the interactionbetween B and C, increase in both factors will enhance the Flexural strength.

From the contour and 3D plots presented in Fig. 8d, it was observed that an increase in A and reduction in B will increasethe split tensile strength. For the interaction between A and C, it was observed that increase in C and reasonable increase in Awill enhance split tensile strength. From the interaction between B and C it was observed that at B of 0.33 with a reasonableincrease in C, the split tensile strength can be enhanced. From the contour and 3D plots for flexural and split tensile strengthsit could be deduced that both the flexural and split tensile strengths do not really require as much cement for improvedstrength when compared to compressive strength. Reduced slump was observed for all interactions at reduced factors B andC, and increased factor A as presented in Fig. 8e.

Overall, it was observed that long fibre length obtained with higher aspect ratio will reduce the water absorption, slumpand compressive strength properties of steel fibre reinforced concrete which implies that longer fibre length has a positivefilling effect which increases the compactness of the concrete and hence reduces porosity. For concrete containing fibres,workability measured in terms of slump was not really affected by the presence of fibres which may be ascribed to the factthat the fibres generally had low surface area and are impermeable to water absorption. With respect to other responses,shorter fibre length obtained from lower aspect ratios will increase the flexural and split tensile strengths at reduced water/cement ratio.

3.6. Optimum conditions for the mix design components

The optimization process considered all responses simultaneously in order to achieve a concrete mix design that will befavorable for all investigated responses. According to Oehlert [42], when there is more than one response, then it isimportant to find the compromise optimum that does not optimize only one response. The process was carried out todetermine the optimum values for aspect ratio (A), water-cement ratio (B) and cement content (C) required to achievedesirable values for the dependent parameters coded R1-R5. Parameters R1, R2, R, R4 and R5 represent water intake,compressive strength (CS), flexural strength (FS), split-tensile strength (STS) and slump respectively.

The ‘maximum’ condition (goal) was selected for CS, FS and STS in order to achieve highest strength possible while‘minimum’ condition was selected for water absorption to ensure low penetration capacity of external substances. However,‘in range’ condition was selected to achieve desirable slump. The optimization process gave several solutions but the solutionwith the highest CS is presented in Table 7.

Fig. 7. (a) Normal probability distribution plot for water absorption/intake (b) Normal probability distribution plot for compressive strength (c) Normalprobability distribution plot for flexural strength (d) Normal probability distribution plot for split tensile strength (e) Normal probability distribution plotfor slump.

T.F. Awolusi et al. / Case Studies in Construction Materials 10 (2019) e00212 13

Fig. 7. (Continued)

14 T.F. Awolusi et al. / Case Studies in Construction Materials 10 (2019) e00212

Furthermore, an additional experiment was carried out to validate the optimum design proportions obtained by the RSMmodel and the result is also presented in Table 7. The standard deviation (SD) and absolute relative percent error (PE) of theRSM model with respect to the experimental results were observed to be low. Therefore, the model predicted the desiredresponses with good accuracy. The estimation of PE was done using Eq. (11).

Absolute relative percent error ðPEÞ ¼ 1 � Predicted valueExperimenta value

� �x 100 ð11Þ

(Source: [43])From the optimization process, it could be inferred that fibres with higher aspect ratio will withstand more split, flexural

and compressive loadings with acceptable slump and water absorption capacity than lower aspect ratio. This agrees withChanh [33] who observed that higher aspect ratio enhances the performance of hardened concrete. He also pointed out theadverse effect of higher aspect ratio on the workability of fresh mix concrete. However from this study, acceptableworkability measured in terms of slump has been achieved with higher aspect ratio.

It was also observed that the aforementioned properties are inversely proportional to water cement ratio. Cihan et al. [44]also observed that at certain water cement ratio during optimization, increase in workability does not significantly reducecohesion in the concrete due to the addition of superplasticizer. According to Neville [45], the presence of superplasticizers

Fig. 8. (a) Contour and 3D plots for water absorption/intake (b) Contour and 3D plots for compressive strength (c) Contour and 3D plots for Flexural strength(d) Contour and 3D plots for Split tensile strength (e) Contour and 3D plots for Slump.

T.F. Awolusi et al. / Case Studies in Construction Materials 10 (2019) e00212 15

could reduce the water content for a given workability by 25–35%. In addition, the presence of limestone powder used asfiller in this study was observed to absorb low quantity of water during concrete mixing. The advantage of having bothmaterials (superplasticizer and LSP) included in the concrete mix for this study at water cement ratio of 0.26 will provide aworkable concrete with improved fresh and hardened properties.

Fig. 8. (Continued)

16 T.F. Awolusi et al. / Case Studies in Construction Materials 10 (2019) e00212

Fig. 8. (Continued)

T.F. Awolusi et al. / Case Studies in Construction Materials 10 (2019) e00212 17

Fig. 8. (Continued)

18 T.F. Awolusi et al. / Case Studies in Construction Materials 10 (2019) e00212

Fig. 8. (Continued)

T.F. Awolusi et al. / Case Studies in Construction Materials 10 (2019) e00212 19

Table 7Optimum conditions for all variables.

Parameters Unit Goal Modelprediction

Laboratoryexperiment

SD PE

A In range 140 140B In range 0.26 0.26C % In range 40 40R1 % Minimum 0.9410 0.94899 �0.03 0.841948R2 N/mm2 Maximum 42.6855 38.333 �1.47 11.3544R3 N/mm2 Maximum 7.967 7.69 �0.42 3.60208R4 N/mm2 Maximum 5.234 6.4 �1.1 18.21875R5 Cm In range 7.653 7.5 �0.5 2.04

20 T.F. Awolusi et al. / Case Studies in Construction Materials 10 (2019) e00212

4. Conclusion

The following conclusions were derived from the study:

i

The statistical error analysis used for evaluating the RSM model shows the accuracy of the obtained models and as wellthe significant contributions made by the independent variables.

ii

RSM model predictive efficiency was classified as very good for CS, STS, slump and WA and acceptable for FS in terms ofNash & Sutcliffe coefficient of model efficiency.

iii

The practical approach described by the study for prediction provides a dependable tool for evaluating both the designstrength and performance of fibre reinforced concrete.

iv

Utilization of steel fibres from waste tires in concrete will encourage and help curb the menace arising from poordisposal and low recycling of waste tires in developing countries.

v

Waste tire fibres can be safely utilized to improve the fresh and hardened properties of concrete especially at optimumconditions.

vi

RSM models can be used to show the interactions of the investigated factors such as aspect ratio, water-cement ratio andcement content.

vii

RSM is useful in optimization of concrete mixtures to achieve desired experimental and project objectives. Owing to itshigh predictive efficiency, RSM is useful in predicting the fresh and hardened properties of steel fibre reinforced concrete,thereby eliminating the drudgery of repetitive laboratory tests and facilitates prompt decision making for constructionapplications.

viii

Appropriate collection and recycling schemes with incentives should be put in place in developed and developingcountries to discourage poor disposal and burning of waste tires in landfills and unapproved open dumps. (vii) Owing toits high predictive efficiency, RSM is useful in predicting the fresh and hardened properties of steel fibre reinforcedconcrete, thereby eliminating the drudgery of repetitive laboratory tests and facilitates prompt decision making forconstruction applications.

Conflict of interest

The authors declare no conflict of interest.

Acknowledgments

The authors would like to acknowledge Advanced Chemical Technology Ikeja Lagos the Manufacturer of the high rangewater reducing admixture used in the study. The authors also express their sincere gratitude to Engr. Tawio Abiola of theDepartment of Chemical Engineering, Cape Peninsula University of Technology, South Africa for his help and support.

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Application of response surface methodology: Predicting and optimizing the properties of concrete containing steel fibre e ...1 Introduction2 Experimental programme, material and procedure2.1 Experimental programme and model efficiency assessment2.2 Experimental material2.3 Experimental procedure2.3.1 Slump test2.3.2 Water Absorption/ intake2.3.3 Compressive strength2.3.4 Flexural strength test2.3.5 Split tensile strength test

3 Result and discussion3.1 Perturbation plots and predictive efficiency of the derived models3.2 Predictive efficiency of the derived models3.3 ANOVA and regression models equations for investigated properties3.4 Normal probability plot3.5 Contour and 3D plots for all responses3.6 Optimum conditions for the mix design components

4 ConclusionConflict of interestAcknowledgmentsReferences