Rubbercrete mixture optimization using response surface methodology

Rubbercrete mixture optimization using response surface methodology

Accepted Manuscript Rubbercrete Mixture Optimization Using Response Surface Methodology Bashar S. Mohammed, Veerendrakumar C. Khed, Muhd Fadhil Nurud...

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Accepted Manuscript Rubbercrete Mixture Optimization Using Response Surface Methodology

Bashar S. Mohammed, Veerendrakumar C. Khed, Muhd Fadhil Nuruddin PII:

S0959-6526(17)32396-X

DOI:

10.1016/j.jclepro.2017.10.102

Reference:

JCLP 10894

To appear in:

Journal of Cleaner Production

Received Date:

15 February 2017

Revised Date:

22 August 2017

Accepted Date:

09 October 2017

Please cite this article as: Bashar S. Mohammed, Veerendrakumar C. Khed, Muhd Fadhil Nuruddin, Rubbercrete Mixture Optimization Using Response Surface Methodology, Journal of Cleaner Production (2017), doi: 10.1016/j.jclepro.2017.10.102

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Rubbercrete Mixture Optimization Using Response Surface Methodology Bashar S. Mohammed, Veerendrakumar C Khed and Muhd Fadhil Nuruddin Department of Civil and Environmental Engineering, Universiti Teknologi PETRONAS, 32610 Bandar Seri Iskandar, Perak Darul Ridzuan, Malaysia Email: [email protected] Abstract Rubbercrete is made of partially replacing fine aggregate, in normal concrete, with crumb rubber (CR) from scrap tires. Despite several advantages of rubbercrete, one of the most hindering factors on using it in the construction industry is the absence of specific mix design to optimize the mix ingredients. Response surface methodology (RSM) optimization has been incorporated using the design expert to eliminate the difficulty in obtaining the anticipated results. Experimental data of 45 rubbercrete mixtures (from the previous study) have been utilized to develop ANOVA models. These models have also been validated to predict the properties of rubbercrete based on different percentages of CR content and w/c. All models are significant with Prob > F is less than 0.05, and the difference between predicted R-squared and adjustable R-squared is less than 0.2. Also, an experimental validation has been performed for three of the optimized mixtures, and the results have been compared, and the variation in the results have found to be less than 5%. It has been concluded that the optimization can be performed for any target strength with desirability as approximately one by improving the performance, reliability for the product and processes. Keywords: Crumb Rubber, Rubbercrete, RSM, CCD, Optimization, Desirability

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1. Introduction Every day, new ideas and developments in the construction industries are being created with the economy and environmental sustainability as the main factors. Several of these ideas have been materialized in various construction domains. The disposals of scrap tires have become a serious issue in most countries due to its non-biodegradable nature (Raffoul et al., 2016). Other problems associated with scrap tires such as causing spatial depletion of landfills, high risk of fire, a breeding ground for harmful insects and rodents. Utilization of crumb rubber from scrap tires in the production of construction building materials leads to improving some properties of these materials and provide an economical solution and as well as helps in controlling the environmental pollution (Youssf et al., 2016). Crumb rubber particles are being used as a partial replacement by volume to fine aggregate in making concrete containing crumb rubber also refer to as rubbercrete (Mohammed et al., 2016). As it has been reported in the literature, many fresh and hardened properties of rubbercrete have been improved in comparison to normal concrete. The fresh rubbercrete mixture contains a higher percentage of air entrained which enable it to have a good freeze and thaw protection (Richardson et al., 2016) besides lighter unit weight and more workability (Kardos and Durham, 2015). While hardened rubbercrete exhibits more ductility (Mohammed, 2010), better seismic resistivity in terms of damping ratio and energy dissipation capacity (Youssf et al., 2015), higher impact resistance (Al-Tayeb et al., 2013), better impact capacity for replacement with fine aggregate than the coarse aggregate (Vadivel et al., 2014), lower thermal conductivity (Hall et al., 2012), better sound absorption were observed by replacing the fine aggregate with the styrene butadiene rubber (Ghizdăveț et al., 2016), cladding panels made with the

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rubbercrete had absorbed sound better than conventional concrete (Holmes et al., 2014a) ,higher electrical resistivity (Mohammed et al., 2012b), and better fatigue performances (Liu et al., 2015), great resistance to acid attack and chloride ion penetration (Thomas and Gupta, 2016). In spite of these advantages, rubbercrete has the drawback in the form of strength reduction due to the physical properties of crumb rubber particles and its compatibility with fine aggregate. Due to the hydrophobic nature, crumb rubber particles repel water and entrap air on its surface. This leads to increase the volume of air content in the fresh rubbercrete mixture, which in turn increases the voids ratio in the hardened state and subsequently reducing strength as observed for the hollow blocks by replacing the fine aggregate up to 50% (Mohammed et al., 2012b), by varying the particle size of crumb rubber (Yilmaz and Degirmenci, 2009), by pre-coating the crumb rubber with limestone (Onuaguluchi and Panesar, 2014), by pre-treating the crumb rubber with sodium hydroxide (Youssf et al., 2014). The static modulus of elasticity and the bond strength were decreased with the increase of crumb rubber size (Hilal, 2017). The mechanical properties of rubbercrete were improved by modifying the crumb rubber surface with KMnO4 and NaHSO3 (He et al., 2016). Crumb rubber inclusion in cement and uncemented clayey soil decreases the reinforcement cost (Yadav and Tiwari, 2017). By capitalizing on the advantages of rubbercrete, researchers have developed many construction building materials such as: composite slab with rubbercrete topping to investigate the ductile capacity (Mohammed, 2010) shear resisting capacity (Holmes et al., 2014b), reinforced column for earthquake application (Youssf et al., 2015), rubbercrete beams with high impact resistance (Al-Tayeb et al., 2013), hollow rubbercrete block with improved thermal conductivity and acoustic property (Mohammed et al., 2012b)

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, self-compacted concrete pavement for a sustainable approach in terms of economy and environment (Hesami et al., 2016), permeable concrete pavers with increased porosity (Murray et al., 2014),railway ballast with high energy dissipation factor and less degradation (Sol-Sánchez et al., 2015),ductile composite steel tubes filled with rubbercrete (Abendeh et al., 2016), masonry walls with improved failure mode (Sadek and El-Attar, 2015) , pavers with improved abrasion resistance (da Silva et al., 2015), bridge deck concrete pavement with better interfacial shear deformation (Lan et al., 2013), and wall panels with greater sound absorption and better thermal resistivity (Sukontasukkul, 2009). Although the usage of rubbercrete has been increasing, yet there is no appropriate design mix procedure as that of conventional concrete. The reduction factors (RFs) method was introduced for the mix design of rubbercrete. The reduction factor is the ratio of rubbercrete to conventional concrete property in which the correlation between RFs and crumb rubber replacement percentage have been made via regression analysis (Khatib and Bayomy, 1999). In another word, the rubbercrete mixture is to be proportioned and prepared according to ordinary concrete mix design but the target strength to be multiplied by a specific RF. RFs method has been expanded for different levels of slumps (low, medium and high). However, the outcome of the study indicated that the functional parameters are quite high and sensitive to the water-cement ratio. Therefore, there is an urgent need for appropriate design method for rubbercrete (Mohammed and Azmi, 2014). The design of experiment (DOE) allows multiple input factors manipulation to determine their effects on the desired output (response). By manipulating multiple inputs at the same time, DOE can identify important interactions that may be neglected when experimenting

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with one factor at a time. All possible combinations can be investigated (full factorial) or only a portion of the possible combinations (fractional factorial) (Achara et al.). The aspect DOE can be achieved by response surface methodology (RSM). RSM is the process of collecting the statistical and mathematical techniques which are useful for analysis and modeling in the applications where the concerned response is influenced by some variables (Mohammed et al., 2012a). Several studies have been carried out utilizing RSM technique in optimizing the mix design of concrete in which numerous variables are interacted to influence the response (Montgomery, 2017). The amount of hybrid fiber in the self-compacting concrete mixture has been optimized to maximize the flexural strength (Ghafari et al., 2014). For obtaining better performance of concrete containing paper mill fibers, the relationship between the slump and compressive strength has been optimized through RSM models using Minitab software (Mohammed et al., 2012a). Flow and compressive strength of geopolymer concrete mixtures have been established and predicted accurately using the experimental design method CCD (central composite design) of RSM (Jo et al., 2015). To reduce the number of trails, fresh properties of self-compacting concrete (SCC) using the statistical RSM model have been improved (Khayat et al., 2000). Metakaolin based concrete mixtures have been developed using RSM regression analysis, and the best mixture proportions have been established to improve the performance of hardened mixture concerning chloride permeability and compressive strength (Al-alaily and Hassan, 2016). Rubbercrete mixtures utilizing metakaolin have been modeled by employing the optimum predictor and interaction of variables by analysis of variance (ANOVA) for the finest correlation between water absorption and compressive strength (Rezaifar et al., 2016).

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Pervious concrete paste has been optimized using the Box-Behnken method of RSM for developing the most appropriate dosage of admixtures for particular applications (Jimma and Rangaraju, 2015). Fracture energy of steel fiber concrete has been predicted for high tensile strength using regression analysis and validated with the experimental results (Köksal et al., 2013). Normal concrete mixtures have been optimized by developing the graphical user interface MATLAB programs for effective, functional and flexible solutions (Şimşek et al., 2014). RSM was successful in optimizing lower thermal conductivity for the lightweight hollow concrete bricks (del Coz Diaz et al., 2014). Therefore, the main objective of research work reported in this paper is to utilize RSM optimization technique in modeling the fresh and hardened properties of rubbercrete to develop appropriate mix proportion. 2. Experimental program The experimental program including materials, methods, and results has been reported in the past research work (Mohammed and Azmi, 2014). Forty-five mixtures with different slump levels (low, medium and high) and five levels of crumb rubber replacement (0%, 10%, 15%, 20% and 30%) to fine aggregate were considered as shown in Table 1.

Table 1: Mixture constituents per m3 of rubbercrete (Mohammed and Azmi, 2014) Mix number

w/c

crumb rubber % kg/m³

Mix _1 Mix _2 Mix _3 Mix _4 Mix _5

0.41 0.41 0.41 0.41 0.41

0 10 15 20 30

0 17 25.5 34 46.36

Cement kg/m³

fine aggregate kg/m³

coarse aggregate kg/m³

water kg/m³

556.1 556.1 556.1 556.1 556.1

803.58 723.22 683.05 642.87 562.51

697.32 697.32 697.32 697.32 697.32

228 228 228 228 228

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Mix _6 Mix _7 Mix _8 Mix _9 Mix _10 Mix _11 Mix _12 Mix _13 Mix _14 Mix _15 Mix _16 Mix _17 Mix _18 Mix _19 Mix _20 Mix _21 Mix _22 Mix _23 Mix _24 Mix _25 Mix _26 Mix _27 Mix _28 Mix _29 Mix _30 Mix _31 Mix _32 Mix _33 Mix _34 Mix _35 Mix _36 Mix _37 Mix _38 Mix _39 Mix _40 Mix _41 Mix _42 Mix _43 Mix _44 Mix _45

0.57 0.57 0.57 0.57 0.57 0.68 0.68 0.68 0.68 0.68 0.41 0.41 0.41 0.41 0.41 0.57 0.57 0.57 0.57 0.57 0.68 0.68 0.68 0.68 0.68 0.41 0.41 0.41 0.41 0.41 0.57 0.57 0.57 0.57 0.57 0.68 0.68 0.68 0.68 0.68

0 10 15 20 30 0 10 15 20 30 0 10 15 20 30 0 10 15 20 30 0 10 15 20 30 0 10 15 20 30 0 10 15 20 30 0 10 15 20 30

0 18.77 28.15 37.53 51.18 0 19.5 29.25 39 53.18 0 16.41 24.62 32.83 49.24 0 18.3 27.45 36.6 54.9 0 19.08 28.62 38.16 57.24 0 15.83 23.75 31.66 47.49 0 17.83 26.75 35.66 53.49 0 18.66 27.99 37.32 55.98

400 400 400 400 400 335.29 335.29 335.29 335.29 335.29 592.68 592.68 592.68 592.68 592.68 426.32 426.32 426.32 426.32 426.32 357.35 357.35 357.35 357.35 357.35 629.27 629.27 629.27 629.27 629.27 452.63 452.63 452.63 452.63 452.63 379.41 379.41 379.41 379.41 379.41

887.16 798.44 754.08 709.73 621.01 921.8 829.26 783.53 737.44 645.26 775.96 698.37 659.57 620.77 543.18 750.65 778.53 735.28 692.03 605.53 901.96 811.76 766.67 721.57 631.37 748.35 673.51 636.09 598.68 523.84 842.92 758.63 716.48 674.33 590.04 882.12 793.31 749.8 705.69 617.48

769.84 769.84 769.84 769.84 769.84 799.9 799.9 799.9 799.9 799.9 673.35 673.35 673.35 673.35 673.35 750.65 750.65 750.65 750.65 750.65 782.69 782.69 782.69 782.69 782.69 649.39 649.39 649.39 649.39 649.39 731.45 731.45 731.45 731.45 731.45 765.47 765.47 765.47 765.47 765.47

228 228 228 228 228 228 228 228 228 228 243 243 243 243 243 243 243 243 243 243 243 243 243 243 243 258 258 258 258 258 258 258 258 258 258 258 258 258 258 258

3. Development and selection of RSM models Response surface methodology (RSM) is a technique which consists of statistical analysis where each response is interconnected with the number of variables to determine the effects, relationship and the interaction between the variables and

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responses. RSM analysis includes designing the series of experiments and collecting the experimental results as responses, then by constructing the response surface numerical models to validate the accuracy and optimizing the variables in satisfying the desired responses (Ghafari et al., 2014). The most commonly used design method in finding the functional relationship between the response and the factors using CCD (del Coz Diaz et al., 2014) , which is an effective experimental design method used in RSM. CCD involves the factorial design, where central points are enlarged by the star points and thereby increasing the variable space then the quadratic terms are estimated. In the current study, the Design-Expert_10 software has been used for the design, mathematical modeling, statistical analysis, and optimization of the process variables. The interaction and relationship between the process factors, water to cement ratio (w/c) and crumb rubber (CR) and the response (fresh and hardened properties) can be obtained using ANOVA (Rezaifar et al., 2016). In this case, the CCD consists of 45 experimental runs for the two variables, which are water to cement ratio ranging from 0.41 to 0.68 and CR replacement with fine aggregate ranging from zero to 30%. Hence, as shown in Figure 1, the classic CCD for the two factors can be represented as follows: 

Four corners of the square represent the factorial (+/- 1) design points.



Four central points represent the axial (+/- alpha) design points.



+/-1 to define the limits of the area of interest where the optimum is believed to exist, axial points will typically be outside this limit.



Alphas to define the area of operability, the area of interest will be within the area of operability (Mohammed et al., 2017b) .

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a) Four corners points

b) four central points

c) CCD design

Figure 1. CCD design module In this research, the response models were selected for the fresh and hardened properties of rubbercrete with the factors as w/c ratio and crumb rubber in partial replacement with the fine aggregate. The optimal conditions were determined by selecting an appropriate model which explains the response surface (Mohammed et al., 2017a) [51]. Thus in this case the quadratic equation selected for the model, which is as shown in the equation (1).

𝑘

𝑘

𝑘

𝑗=1

𝑦 = 𝛽0 + ∑𝑖 = 1𝛽𝑖𝑥𝑖 + ∑𝑖 = 1𝛽𝑖𝑖 𝑥2𝑖 + ∑𝑗 = 2.∑𝑖 = 1 𝛽𝑖𝑗𝑥𝑖𝑥𝑗 + 𝜀 .. ………………………………. (1) Where, 𝑦 is the response which are fresh and hardened properties, 𝑥𝑖𝑥𝑗 are the coded values for the variables w/c ratio and crumb rubber, 𝑖 is the linear co-efficient, 𝑗 is the quadratic co-efficient, 𝛽 represents

regression co-efficient, 𝑘 represents number of

factors and 𝜀 indicates random error. A suitable model has been selected, so that the response surface can be well described. The individual responses were analysed thus, a fitting model (linear, quadratic or cubic) was selected.

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3.1 Fresh properties Fresh properties such as slump test for workability, unit weight, and air content were tested for all mixtures and results have been reported in the previous studies. (Mohammed and Azmi, 2014). 3.1.1. Slump test The ease of flow, handling, placing and compaction are referred as workability of rubbercrete, and it is quantified by slump test. Three slump levels which are low (25 to 50 mm) for mixes 1 to 15, medium (75 to 100 mm) for mixes 16 to 30 and high (150 to 175mm) for mixes 31 to 45 were considered as shown in Table 1. The slump tests were conducted according to ASTM C143-90a for all mixes, and the results are represented in Figure 2. Due to the water repulsive action of crumb rubber (CR) particles and traps air on its surface, which is against the absorbent characteristics of sand had led to the participation of more water into the mixture, so the rubbercrete turn out to be more workable than the normal concrete. Thus, the results revealed the increase in CR replacement in the mixtures increased the slump. In previous literature (Kardos and Durham, 2015), reiterated that an increase in the slump with rubber addition, and they concluded that an acceptable workability could be achieved with crumb rubber up to 50% replacement of sand. The RSM delivers the models for response surface to replicate the outcome of factors. The model of second-order is more accurate than the first order model due to the ability to find the optimum number of each factor precisely (Ghafari et al., 2014). Therefore, second-order models representing slumps were established to correlate between the CR replacement and w/c ratio using ANOVA, and it is found the best fit

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according to the results of the slump. The slump (mm) of rubbercrete can be predicted using ANOVA equations 2, 3 and 4 for the low, medium and high slump, respectively.

Design-Expert® Software Factor Coding: Actual Slump (mm) Design points above predicted value Design points below predicted value 70

Design-Expert® Software Factor Coding: Actual Slump (mm) Design points above predicted value Design points below predicted value 130

30

80

80

X1 = A: CR X2 = B: w/c

X1 = A: CR X2 = B: w/c

70

140 130 120

Slump (mm)

50 40 30 20

110 100 90 80 70

0.41

0.41 30

0.48

0.48 23

A: CR (%)

30.00 18.00

B: w/c

0.61

8 0

0.55

24.00

0.55

15

0.61

12.00 6.00

0.68

A: CR (%)

a) Low slump

0.00

0.68

b) Medium slump

Design-Expert® Software Factor Coding: Actual Slump (mm) Design points above predicted value Design points below predicted value 172 150

175

X1 = A: CR X2 = B: w/c

170 165

Slump (mm)

Slump (mm)

60

160 155 150 145

30

0.41 24

0.48 18

0.55

12

A: CR (%)

0.61

6 0

0.68

B: w/c

B: w/c

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c) High slump Figure 2. 3D response surface diagram for slump

(Slump)Low = -24.7489 + 0.29772 ∗ CR + 172.704 ∗ w/c – 0.07505 ∗ CR ∗ w/c + 0.01302 ∗ CR2 – 92.1717 ∗ w/c2

(2)

(Slump)Medium = +1.3181 + 0.1813 ∗ CR + 250.7782 ∗ w/c + 3.0045 ∗ CR ∗ w/c - 0.03302 ∗ CR2 – 165.404 ∗ w/c2 (3) (Slump)High = +81.37766 + 0.12313 ∗ CR + 241.841 ∗ w/c + 0.31103 ∗ CR ∗ w/c + 0.00127 ∗ CR2 – 182.66 ∗ w/c2

(4)

3.1.2. Unit weight Unit weight of rubbercrete is to identify the density of wet or fresh rubbercrete so that the weight of ingredients required per volume for each set of the mixture can be calculated. The unit weight tests were performed according to the requirements of ASTM C29-91a. The phenomenon of reduction in the unit weight in rubbercrete can be explained by the flocculation of the crumb rubber particles during the mixing of concrete where higher rubber content creates large voids and lead to higher porosity. CR particles are hydrophobic and non-polar, which made it an air entraining agent, i.e. increasing the air in rubbercrete and turn it to more porous and consequently leading to reduction in the unit weight (Li et al., 2014). The results show that the unit weight of concrete diminished

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linearly with the increase of the CR content for all mixtures as shown in Figure 3. Also, it can be observed that unit weight decreased with the increased level of the slump. The unit weight can be anticipated using the ANOVA equations 5, 6 and 7 for low, medium and high slump by varying the CR replacement to fine aggregate (%) and w/c.

Design-Expert® Software Factor Coding: Actual Unit weight (kg/m2) Design points above predicted value Design points below predicted value 2400

Design-Expert® Software Factor Coding: Actual Unit weight (kg/m2) Design points above predicted value Design points below predicted value 2600

1250

1350

2400

X1 = A: CR X2 = B: w/c

X1 = A: CR X2 = B: w/c

2200

Unit weight (kg/m2)

2800 2600

2200 2000 1800 1600 1400 1200 0.61 0

2000 1800 1600 1400 1200

0.68

6

0.55 12

A: CR (%)

18

0.48 24

30

0

B: w/c

0.68 6

0.61 12

A: CR (%)

0.41

a) Low slump

18

0.55 0.48

24 30

0.41

b) Medium slump

Design-Expert® Software Factor Coding: Actual Unit weight (kg/m2) Design points above predicted value Design points below predicted value 2250 1200 X1 = A: CR X2 = B: w/c

2400 2200

Unit weight (kg/m2)

Unit weight (kg/m2)

2400

2000 1800 1600 1400 1200 0.68 0.61 0 6

0.55 12 18

0.48 24

A: CR (%)

c) High slump

30

0.41

B: w/c

B: w/c

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Figure 3. 3D response surface diagram for unit weight (Unit weight)Low = +2903.31018 – 15.81736 ∗ CR – 270.91210 ∗ w/c – 15.77758 ∗ CR ∗ w/c -0.30952 ∗ CR2 -757.57576 ∗ w/c2 (5) (Unit weight)Medium = + 1780.768 – 13.1784 ∗ CR + 2917.2242 ∗ w/c – 21.8806 ∗ CR ∗ w/c + 0.031746 ∗ CR2 - 3598.4849 ∗ w/c2 (6) (Unit weight)High = +2189.19585–14.57987 ∗ CR+899.985 ∗ w/c-13.96926 ∗ CR ∗ w/c0.039683 ∗ CR2 - 1788.72054 ∗ w/c2 (7) 3.1.3. Air content The presence of air in the rubbercrete creates voids that incite density reduction and also adversely affecting strengths. The percentage of air content was calculated according to ASTM C138-81. The hydrophobic nature of CR particles made the air entrap on its surface. Thus the percentage of air voids increased with the rise of CR replacement. Figure 4 illustrates the 3D surface diagram for air content against the variables CR replacement and w/c. The results demonstrate that the air content of concrete increased linearly with the increase of the crumb rubber content for all mixtures. The air content is inversely proportional to unit weight. Also, it can be observed that air content increased with the increased level of the slump. The air content can be estimated using ANOVA equations 8, 9 and 10 for the low, medium and high slump, respectively.

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Design-Expert® Software Factor Coding: Actual Air content (%) Design points above predicted value Design points below predicted value 12

Design-Expert® Software Factor Coding: Actual Air content (%) Design points above predicted value Design points below predicted value 11

3

3 X1 = A: CR X2 = B: w/c

12

X1 = A: CR X2 = B: w/c

12

10 8

Air content (%)

8 6 4

6 4 2

2 0.68 0

6

12

0.55 18

A: CR (%)

24

0.48 30

0.68

0

0.61

0.61

6 12

B: w/c

a) Low slump

4

14 12 10 8 6 4 2 0.68 0

0.61 6

0.48

24 30

0.41

b) Medium slump

Design-Expert® Software Factor Coding: Actual Air content (%) Design points above predicted value Design points below predicted value 12

X1 = A: CR X2 = B: w/c

0.55

18

A: CR (%)

0.41

Air content (%)

Air content (%)

10

12

A: CR (%)

0.55 18

24

0.48 30

B: w/c

0.41

c) High slump Figure 4. 3D response surface diagram for Air content

B: w/c

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(Air content)

Low

= +10.31959 – 0.0978 ∗ CR – 39.85487 ∗ w/c + 0.43178 ∗ CR ∗ w/c – 0.0012 ∗ CR2 + 49.68434 ∗ w/c2

(Air content)

Medium

(8)

= +2.1959 – 0.03258 ∗ CR – 5.6981 ∗ w/c + 0.3913 ∗ CR ∗ w/c – 0.00192 ∗ CR2 + 17.17172 ∗ w/c2

(9)

(Air content) High = +6.8424 – 0.1447 ∗ CR – 19.4429 ∗ w/c + 0.2538 ∗ CR ∗ w/c – 0.00413 ∗ CR2 + 28.0724 ∗ w/c2 (10) 3.2 Hardened properties Hardened properties such as compressive strength, flexural strength, and modulus elasticity were tested for all mixtures and results have been reported in the previous literature (Mohammed and Azmi, 2014). 3.2.1 Effects of w/c and crumb rubber content on the compressive strength Primarily, most of the structural applications are depending on the value of compressive strength. The compressive strength is mostly influenced by w/c and percentage of air content. The compressive strength test has been carried out by the requirements of BS 1881: Part 116:1983. The inclusion of CR particles has led to the presence of voids in the rubbercrete microstructure due to its hydrophobicity and thus CR replacement adversely affecting the compressive strength. From the response surface diagrams, as shown in Figures 5, 6, and 7, high slump rubercrete mixtures produces higher strength as compared with low and medium slump mixtures. The CR content has more impact in denouncing the compressive strength than the water-cement ratio. The 3D surface shows a steep reduction and has its minimum point at maximum CR content and maximum w/c

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and vice versa for the maximum point. In their study (Gao et al., 2016) it was determined that the optimal mixtures by adjusting the mix design parameters and the strength performance of alkali-activated slag (AAS), this verified that RSM was efficient in the preparation of AAS and it can control the compressive strength accurately, thus it was confirmed that the predictions coincided with the obtained test results and thus it was validated the RSM. However, the compressive strength of rubbercrete can be predicted using ANOVA equations 11, 12 and 13 for the low, medium and high slump, respectively.

a) 3D response surface

b) contour diagram

Figure 5. Compressive strength versus CR content and W/C for low slump

Design-Expert® Software Factor Coding: Actual compressive strength (MPa) Design points above predicted value Design points below predicted value 44.3

Design-Expert® Software Factor Coding: Actual compressive strength (MPa) Design Points 44.3

11.1

compressive strength (MPa)

50

11.1 24

40

X1 = A: w/c ratio X2 = B: crumb rubber

30 20 10 0

0

6

12

18

B: crumb rubber (%)

24

30

0.41 0.44 0.47 0.5 0.53 0.56 A: w/c 0.59 0.62 0.65 0.68

B: crumb rubber (%)

X1 = A: w/c ratio X2 = B: crumb rubber

compressive strength (MPa)

30

20

18

12

30 6

ratio 40 0 0.41

0.44

0.47

0.5

0.53

0.56

0.59

0.62

0.65

0.68

A: w/c ratio

a) 3D response surface

b) contour diagrams

Figure 6. Compressive strength versus CR content and W/C for medium slump

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Design-Expert® Software Factor Coding: Actual compressive strength (MPa) Design points above predicted value Design points below predicted value 48.1 13.4

Design-Expert® Software Factor Coding: Actual compressive strength (MPa) Design Points 48.1

60 50

compressive strength (MPa)

30

13.4 24

40

X1 = A: w/c ratio X2 = B: crumb rubber

30 20 10

0

6

12

18

B: crumb rubber (%)

24

30

0.41 0.46 0.52 0.57 A: w/c 0.63 0.68

20

B: crumb rubber (%)

compressive strength (MPa)

X1 = A: w/c ratio X2 = B: crumb rubber

18

12

30 6

40

ratio 0 0.41

0.44

0.47

0.5

0.53

0.56

0.59

0.62

A: w/c ratio

a) 3D response surface

b) contour diagrams

Figure 7. Compressive strength versus CR content and W/C for high slump

(Comp.str)Low = 56.29113 - 57.45064 ∗ w/c - 1.48692 ∗ CR + 0.96061 ∗ w/c ∗ CR + 15.85859 ∗ w/c2 + 0.012227 ∗ CR2

(11)

(Comp.str)Medium = 62.00275 - 36.73626 ∗ w/c - 1.81625 ∗ CR + 1.01218 ∗ w/c ∗ CR 14.52441 ∗ w/c2 + 0.016257 ∗ CR2

(12)

(Comp.str)High = 72.59396 - 62.11092 ∗ w/c - 1.98652 ∗ CR + 1.04087 ∗ w/c ∗ CR + 8.54377 ∗ w/c2 + 0.019175 ∗ CR2

3.2.2 Effects of w/c and crumb rubber content on the flexural strength

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The tensile strength and the bending resistance of concrete are quantified in terms of flexural strength. So the flexural strength tests have been carried out by the requirements of the ASTM C293-79. The flexural strength is influenced by the bond between cement paste and aggregate (Neville, 1995). The water’s repulsive action of crumb rubber leads to entrapping air on its surface and consequently increasing air content into the rubbercrete mixture. This lead to increasing the thickness of the interfacial transition zone (ITZ) between aggregate and hardened cement paste; in another word, it is weakening the bond between cement paste and aggregate (Mohammed et al., 2016). Figures 8, 9 and 10 show the 3D response surface diagrams for the low, medium and high slump, respectively. Low slump rubbercrete shows higher flexural strength in comparison to medium and high slump mixtures. The CR content has more impact in adversely affecting the flexural strength than the water-cement ratio. The 3D surface has decreased gently and has its minimum point at maximum CR content and maximum w/c and vice versa for the maximum point. A statistical model has been developed for optimization using RSM the performance of self-compacting mixtures and obtained maximum flexural strength for minimum content of steel fiber (Ghafari et al., 2014). RSM was used to optimize the effect of w/c, steel fiber tensile strength and volume fraction of fiber on mechanical properties and it has been concluded that RSM is a favorable approach for optimization (Köksal et al., 2013). However, the flexural strength of rubbercrete can be predicted using ANOVA equations 14, 15 and 16 for the low, medium and high slump, respectively.

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Design-Expert® Software Factor Coding: Actual Flexural strength (MPa) Design points above predicted value Design points below predicted value 9.8 3

Design-Expert® Software Factor Coding: Actual Flexural strength (MPa) Design Points 9.8

10

X1 = A: wc ratio X2 = B: CR

Flexural strength (MPa)

9

Flexural strength (MPa)

30

3

8

24

7

4

X1 = A: wc ratio X2 = B: CR

6 5

B: CR (%)

4 3

5

18

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0.68 0.63

7

0

0.57

A: wc ratio

6

6

0.52

12 18

0.46 0.41

8

24

9

30

B: CR (%)

0 0.41

0.46

0.52

0.57

0.63

0.68

A: wc ratio

a) 3D response surface

b) contour diagrams

Figure 8. Flexural strength versus CR content and W/C for low slump

Design-Expert® Software Factor Coding: Actual flexural strength (MPa) Design points above predicted value Design points below predicted value 9

Design-Expert® Software Factor Coding: Actual flexural strength (MPa) Design Points 9

9

flexural strength (MPa)

X1 = A: w/c ratio X2 = B: crumb rubber

3

2.5

8

24

X1 = A: w/c ratio X2 = B: crumb rubber

7 6 5 4 3 2

B: crumb rubber (%)

2.5

flexural strength (MPa)

30

4

18

5 12

6 6

A:

0.68 0.65 0.62 0.59 0.56 0.53 0.5 w/c ratio 0.47 0.44 0.41

7 8

30

24

18

12

6

0

B: crumb rubber (%)

a) 3D response surface

0 0.41

0.44

0.47

0.5

0.53

0.56

0.59

0.62

A: w/c ratio

b) contour diagrams

Figure 9. Flexural strength versus CR content and W/C for medium slump

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Design-Expert® Software Factor Coding: Actual flexural strength (MPa) Design points above predicted value Design points below predicted value 6.8

Design-Expert® Software Factor Coding: Actual flexural strength (MPa) Design Points 6.8

7

X1 = A: w/c ratio X2 = B: crumb rubber

flexural strength (MPa)

6

2

1.8 24

5

X1 = A: w/c ratio X2 = B: crumb rubber

4 3 2 1

A:

flexural strength (MPa)

30

0.68 0.65 0.62 0.59 0.56 0.53 0.5 w/c ratio 0.47 0.44 0.41

B: crumb rubber (%)

1.8

18

3

12

4 6

0

5

6 12

6

18 24 30

B: crumb rubber (%)

0 0.41

0.44

0.47

0.5

0.53

0.56

0.59

0.62

A: w/c ratio

a) 3D response surface

b) contour diagrams

Figure 10. Flexural strength versus CR content and W/C for high slump

(Flexural)Low

= 9.95771 + 4.48673 ∗ w/c – 0.33360 ∗ CR + 0.13680 ∗ w/c ∗ CR – 12.79461 ∗ w/c2 + 0.003619 ∗ CR2

(14)

(Flexural)Medium = 8.90735 + 5.47083 ∗ w/c – 0.31067 ∗ CR + 0.13752 ∗ w/c ∗ CR – 13.29966 ∗ w/c2 + 0.00295238 ∗ CR2 (Flexural)High

(15)

= 8.97006 – 5.25011 ∗ w/c – 0.2899 ∗ CR + 0.12125 ∗ w/c ∗ CR – 1.47306 ∗ w/c2 + 0.00379365 ∗ CR2

(16)

3.2.3 Effects of w/c and crumb rubber content on the modulus of elasticity Modulus of elasticity is the measure of resistance to deformation and is defined as the ratio of stress to strain within elastic limit. Generally, the modulus of elasticity depends on aggregate modulus. The test has been conducted in accordance to BS1881: Part121: 1983. Figures 11, 12 and 13 show the 3D surface diagram response for modulus of

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elasticity versus CR content and w/c for low, medium and high slumps, respectively. For rubbercrete with the low slump, 20 to 30 GPa can be predicted for about 4 to 12% of CR replacement. If the CR content is increased to 25%, 10 GPa modulus of elasticity can be obtained. Similarly, for the medium and high slump, the results can be expected from the contour diagrams. Low slump rubbercrete achieved higher modulus of elasticity when compared with the medium and high slump rubbercrete though it has lower compressive strength; it indicates that strain capacity was more for the low slump than the medium and high slump rubbercrete. The modulus of elasticity can be predicted using ANOVA equations 17, 18 and 19 for the low, medium and high slump, respectively.

Design-Expert® Software Factor Coding: Actual Modulus of Elasticity (GPa) Design points above predicted value Design points below predicted value 36

Design-Expert® Software Factor Coding: Actual Modulus of Elasticity (GPa) Design Points 36

7

40

10

7

24 X1 = A: wc ratio X2 = B: CR

30

20

B: CR (%)

Modulus of Elasticity (GPa)

X1 = A: wc ratio X2 = B: CR

Modulus of Elasticity (GPa)

30

10

18

12

20

0

0 0.68

6

6 0.63 18

0.52

A: wc ratio

a) 3D

30

12

0.57 24

0.46 0.41

30

B: CR (%)

response surface diagrams

0 0.41

0.46

0.52

0.57

A: wc ratio

0.63

0.68

b) contour

Figure 11. Modulus elasticity versus CR content and W/C for low slump

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Design-Expert® Software Factor Coding: Actual Modulus of Elasticity (GPa) Design points above predicted value Design points below predicted value 30

Design-Expert® Software Factor Coding: Actual Modulus of Elasticity (GPa) Design Points 30

6

35

6

30

24

X1 = A: w/c ratio X2 = B: crumb rubber

25

B: crumb rubber (%)

Modulus of Elasticity (GPa)

X1 = A: w/c ratio X2 = B: crumb rubber

Modulus of Elasticity (GPa)

30

20 15 10 5

18

15

12

20

0

0.68

10

6

25

6

0.63

12

0.57

A: w/c ratio

30

18

0.52 24

0.46 0.41

0

B: crumb rubber (%)

0.41

0.46

0.52

0.57

0.63

30

A: w/c ratio

a) 3D response surface

b) contour diagrams

Figure 12. Modulus elasticity versus CR content and W/C for medium slump Design-Expert® Software Factor Coding: Actual Modulus of Elasticity (GPa) Design points above predicted value Design points below predicted value 23

Modulus of Elasticity (GPa)

25

X1 = A: w/c ratio X2 = B: crumb rubber

Modulus of Elasticity (GPa)

30

4

5 24

20

X1 = A: w/c ratio X2 = B: crumb rubber

15 10 5 0

0.68 0.65 0.62 0.59 0.56 0.53

A: w/c ratio

0 6

B: crumb rubber (%)

4

Design-Expert® Software Factor Coding: Actual Modulus of Elasticity (GPa) Design Points 23

18

10 12

15 6

12 0.5 0.47 0.44 0.41

18 24

20

B: crumb rubber (%)

30

0 0.41

0.44

0.47

0.5

0.53

0.56

0.59

0.62

0.65

0.68

A: w/c ratio

a) 3D response surface

b) contour diagrams

Figure 13. Modulus elasticity versus CR content and W/C for high slump

(Mod. E)

Low

= 25.67864 + 61.77029 ∗ w/c – 2.01033 ∗ CR + 1.20886ӿw/c ∗ CR – 93.01347 ∗ w/c2 + 0.020159 ∗ CR2

(17)

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2

(Mod. E) Medium = 63.08384 - 0.69869ӿCR -97.47526 ∗ w/c+0.00749206 ∗ CR +51.38889 ∗ 2

w/c -0.050723 ∗ CR ∗ w/c (18) (Mod. E)

High

= 10.98365 – 58.46298 ∗ w/c – 1.23746 ∗ CR + 0.38698 ∗ w/c ∗ CR – 73.23232 ∗ w/c2 + 0.018889 ∗ CR2

(19)

3.3. ANOVA models validation

All models above have been statistically validated. However, to avoid repetition in this paper, only validation results for compressive strength (high slump) are shown as an example of model validation. From Table 2 and 3, it can be observed that ANOVA model terms were significant and valid since the values of Prob > F is less than 0.05 (i.e. α=0.05, 1-α=0.95 or 95% of confidence interval) (Subasi et al., 2016) , thus it indicates a more than 95% of confidence level. The predicted R-squared is in reasonable agreement with adjustable R-squared due to the difference of less than 0.2. Normal probability plot (Figure 14) is a graphical method for evaluating the normal distribution of the data. As shown in Figure 14, the points are approximately on a straight line, and thus it indicates the set of data is approximately normally distributed. Figure 15 is depicting the perturbation plot which helps to compare the effects of all the factors at a particular point. Factors A (w/c) and B (CR content) show steep slope and curvature, respectively. Therefore, this indicates that the response is sensitive to both factors (A and B). Figure 16, shows the predicted versus actual values, indicates that the predicted response by the model is accurate as the points are evenly split by the 45-degree line. "Run order” plots of the residuals are used to test the drift in the method. It is the special kind of scatter

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plot in which all residual is plotted versus an index which indicates the order in which the data were composed. This plot is helpful, however, only if data have been collected in a randomized run order, or some other order that is not increasing or decreasing in any of the predictor variables used in the model. In this case, as shown in figure 17, the even spread of the residual across the range of the data indicates that there is no apparent drift in this process.

Table 2. ANOVA for response surface quadratic model Analysis of variance table [Partial sum of squares - Type III] Sum of

Mean

F

p-value

Source

Squares

df

Square

Value

Prob > F

Model

1380.44

5

276.09

152.62

< 0.0001

252.00

1

252.00

139.30

< 0.0001

1062.52

1

1062.52

587.34

< 0.0001

AB

19.97

1

19.97

11.04

0.0089

A2

0.075

1

0.075

0.041

0.8437

A-w/c ratio B-crumb rubber

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B2

57.91

1

57.91

Residual

16.28

9

1.81

Cor Total

1396.72

14

Table 3 Model properties Model properties

Value

Std. Dev.

1.35

Mean

26.02

C.V. %

5.17

PRESS

45.40

-2 Log Likelihood

43.80

R-Squared

0.9883

Adj R-Squared

0.9819

Pred R-Squared

0.9675

Adeq Precision

41.568

BIC

60.05

32.01

0.0003

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AICc

66.30

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Design-Expert® Software compressive strength

Normal Plot of Residuals

Color points by value of compressive strength: 48.1

99

13.4

Normal % Probability

95 90 80 70 50 30 20 10 5 1

-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

Internally Studentized Residuals

Figure 14. Normal probability plot

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Design-Expert® Software Factor Coding: Actual compressive strength (MPa)

Perturbation 60

compressive strength (MPa)

Actual Factors A: w/c ratio = 0.545 B: crumb rubber = 15

50

B 40

30

A

A B

20

10

-1.000

-0.500

0.000

0.500

1.000

Deviation from Reference Point (Coded Units)

Figure 15. Perturbation curve

Design-Expert® Software compressive strength

Predicted vs. Actual

Color points by value of compressive strength: 48.1

50

13.4

Predicted

40

30

20

10

10

20

30

40

50

Actual

Figure 16. Predicted v/s Actual

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Design-Expert® Software compressive strength

Residuals vs. Run

Color points by value of compressive strength: 48.1

Internally Studentized Residuals

13.4

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Run Number

Figure 17. Run order residual plot

3.4. Optimization After analyzing the variables, a multi-objective simultaneous optimization technique incorporating RSM as the basis for finding the best solution has been used in this study. A common response surface experimental plan which can be used to find optimal settings for a two variable (CR = 0, 10, 15, 20 and 30%; w/c = 0.41, 0.57 and 0.68) is a central composite design method. If the optimal values for each response are localized in different regions, it will be more difficult to find the conditions that simultaneously satisfy all responses. The level of difficulty increases as these optimum regions become more

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distant from each other and do not intersect. It is not rare to encounter cases, where all surfaces found, do not present its optimum under the same set of experimental conditions. Thus, changes in the level of a factor can improve one specific response and have a very negative effect on another. An approach to solving the problem of the optimization of several responses is the use of a multi-criteria methodology. In this study, the multiple response optimization method is needed to optimize rubbercrete. The desirability function is one of the most important multi-criteria methodologies in mathematics. This methodology is based on constructing a desirability function for each response. In brief, the removal efficiencies related to each response are transformed into a dimensionless individual desirability (di) scale. The scale of the individual desirability function ranges between 0 for a completely undesirable response and 1 for a fully desired response. This transformation makes it possible to combine the results obtained from different responses (Azharul Islam et al., 2010) .

The multi-response optimization process has been done by selecting target strength for the desired ranges of variables. The thorough description of desirability functions has been discussed in other literature (Islam et al., 2009). Three responses of rubbercrete: compressive strength, flexural strength, and modulus of elasticity have been optimized simultaneously to obtain the desirability function as approximately 1. The finest optimized circumstances have been found and presented in Table 4 for different w/c ratio and CR replacement to fine aggregate by volume. Desirability variation for the low slump rubbercrete has been shown in figure 18 for all the two variables and three responses. Graphical ramp views for optimized low slump rubbercrete are shown in figure 19. After

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optimization process of each mixture level and with its agreeing response value, a validation study has been implemented with the optimized constraints. The compressive strength, flexural strength, and modulus of elasticity values obtained from validation study have been narrowly related to the results obtained from optimization desirability by using CCD. Table 4: Optimization desirability function for high slump concrete Crumb

Compressive

w/c, Type

Flexural

Modulus

strength, MPa

Elasticity, GPa

rubber, strength, ratio %

of Desirability

MPa

Low slump

0.53 0.12

30.00

8.67

31.95

1.00

Low slump

0.50 1.62

30.00

8.60

31.13

1.00

0.45 10.35

30.00

6.39

23.58

1.00

slump

0.44 11.02

30.00

6.35

23.99

1.00

High slump

0.42 14.21

30.00

3.89

11.15

1.00

High slump

0.41 14.32

30.00

3.89

11.08

1.00

Medium slump Medium

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Design-Expert® Software Factor Coding: Actual All Responses Actual Factors A: wc ratio = 0.533843 B: CR = 0.14509 Desirability = 1 Comp.str (MPa) = 30 Flex. str (MPa) = 8.66888 Mod. of E (GPa) = 31.9489

Figure 18 Actual Desirability for low slump rubbercrete

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0.41

0.68

0

A:wc ratio = 0.533843

30 B:CR = 0.14509

30 10 10.5

35.5 Compressive strength = 30

3

9.8 Flexural strength = 8.66888

Desirability = 1.000

7

36 Modulus of Elasticity = 31.9489

Figure 19 Graphical ramp views for optimized low slump rubbercrete

3.4.1 Experimental validation study for optimization A number of possible solution for desirability 1, are obtained from the optimized results and are shown in Table 5 for high, medium and low slump rubbercretes. The experimental justification was conducted for some of the above-optimized mixtures, and the results were obtained with lesser than 5% of the variation.

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Table 5. Experimental validation Type of Rubbercrete

High slump

Medium slump

Low slump

Validation Optimization Experimental Variation % Optimization Experimental Variation % Optimization Experimental Variation % Optimization Experimental Variation % Optimization Experimental Variation % Optimization Experimental Variation %

w/c ratio

Crumb rubber %

0.42

14.21

0.37

7.35

0.5

8.57

0.44

6.3

0.55

11.49

0.48

7.913

Compressive strength MPa 30 30.5 1.67% 40 38.59 3.65% 30 30.85 2.83% 35 36.2 3.43% 20 20.9 4.50% 25 26.2 4.80%

Flexural strength MPa 3.89 3.94 1.28% 5.25 5.05 3.96% 6.47 6.74 4.17% 7.28 7.63 4.81% 6.04 6.33 4.80% 7.27 7.61 4.68%

Modulus of Elasticity GPa 11.15 11.33 1.61% 15.4 14.85 3.70% 21.57 22.1 2.46% 25.86 26.65 3.05% 18.64 19.51 4.61% 23.84 24.93 4.57%

4. Conclusion In conclusion, RSM technique proved to be a useful tool in establishing optimum mix proportions for rubbercrete for the desired properties as responses. The optimum conditions obtained from RSM can be used for any given functional properties separately. The 3D surface diagram can be effectively used to observe the interaction of two variables

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with the responses. Contour diagrams are given away the intervals of different responses, from that it can be predicted that ranges of variables for the desired results and also the responses can be predicted by ANOVA equations. RSM 3D surface models for compressive strength, flexural strength and modulus elasticity for rubbercrete (CR replacement to fine aggregate by volume and w/c ratio) have been developed and statistically tested. The High content of crumb rubber in the concrete are more susceptible to the strength loss.

The RSM can be used to design the experiment for rubbercrete mixtures based on the variables experimental outcome. For example; the proportion of rubbercrete for the compressive strength of 30 MPa can be estimated for the various percentage of CR replacement to fine aggregate and w/c ratio with desirability 1. RSM optimization technique reduces the time of design, improves the performance of existing process and product, improves reliability, and achieves product and process robustness. Acknowledgment The authors would like to thank the Ministry of Education (MOE) of Malaysia for granting the project under code PRGS/1/13/TK03/UTP/02/02.

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