- Email: [email protected]
Optimization of high-strength self-consolidating concrete mix design using an improved Taguchi optimization method
Construction and Building Materials 236 (2020) 117547
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Optimization of high-strength self-consolidating concrete mix design using an improved Taguchi optimization method Ebrahim Sharifi a, Seyed Jafar Sadjadi a, M.R.M. Aliha b,⇑, Ali Moniri c a
Department of Industrial Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran Welding and Joining Research Center, School of Industrial Engineering, Iran University of Science and Technology, Narmak, 16846-13114 Tehran, Iran, c School of Civil Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran b
h i g h l i g h t s BWM-Taguchi optimization developed by integrating BWM and Taguchi methods. Ten quality characteristics and six factor affecting these criteria were selected. The proposed approach simplifies the calculations. The proposed method is efficient for optimization of concrete mix design.
a r t i c l e
i n f o
Article history: Received 3 August 2019 Received in revised form 15 October 2019 Accepted 7 November 2019
Keywords: Mix design optimization High-strength self-consolidating concrete Taguchi optimization The BWM optimization Concrete mix design
a b s t r a c t Since many parameters are involved in the concrete mix design, finding the optimal mixing design has always been a problem for concrete engineers. In this research, the Taguchi optimization method is improved to model to optimum mix design of the high strength self-consolidating concrete (HSSCC). For this purpose, at first different quality criteria and the parameters influencing them were defined based on the available literature. The Taguchi approach was then utilized to generate an the orthogonal array of the parameters. The experimental tests were then conducted according to the suggested design array in order to obtain the experimental data for each and every single scenario. The Best-Worst method is then adopted for pairwise comparisons of the quality criteria and experiments as such to obtain the overall weights of experiments with respect to each quality characteristics. Analysis of variance was also utilized to appraise the effective factors and the optimal mixture design. It was found that the proposed method was efficient in obtaining the optimal mixture design of the manufacturing process according to decision makers’ preferences. The experimental results indicated a significant improvement in the total quality of concrete compared to the decision maker’s estimated mixture design. The cement amount, water to cementitious ratio and mixing time are the most significant parameters affecting the concrete mix design. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction The producing high strength self-consolidating concrete (HSSCC) which satisfy manufacturers’ preferences depends on the evaluation of all of the vital components at the same time indeed. These components influence the performance of the concrete and are often contradicted each other [1–3], hence by considering all these quality criteria it can be considered as a multi-objective optimization for the sake of determining the best mixture. The researchers have always been looking for a promising model to ⇑ Corresponding author. E-mail address: [email protected] (M.R.M. Aliha). https://doi.org/10.1016/j.conbuildmat.2019.117547 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.
avoid time and cost consuming laboratory tests [4–7]. The decision-makers are of the methods to model the mix design of cementitious and bitumenious material. In order to reach the optimized mixture, the decision-makers usually select an appropriate proportion of each component based on their judgments, which makes the process vulnerable to risk. Under these circumstances, the estimated mixture levels will be inaccurate. To help overcoming this gap, a promising optimization method is needed to determine the best concrete mixture with the advantage of performing the minimum experiments in a more efficient process [1]. One of the most popular optimization methods is Taguchi design of an experiment. Taguchi method seeks to find the optimal
2
E. Sharifi et al. / Construction and Building Materials 236 (2020) 117547
levels for control factors by minimizing the response variance close to the optimal response. Tanyildizi and Sßahin examined the effects of control factors of silica fume percentage, temperature and type of polymerization on the polymer strengthened concrete. They used a L32 orthogonal array to implement the experiments. Using analysis of variance (ANOVA), silica fume selected as the most effective factor [8–10]. Celik et al. [11] applied the Taguchi experimental design method to optimize factor levels of the heat exchanger. They also investigated the effect of friction factor on the heat transfer using grey relational analysis. Ji et al. Determined the optimal level for five design factors that affect the thermoelectric generator based on Taguchi method. They used L27 (35) orthogonal array for experiment design [12]. Teimortashlu et al. examined Taguchi method application for compressive strength optimization of tertiary blended self-consolidating mortar. Three factors at four levels were identified. Therefore, Experiments on samples were conducted using L16 design. Optimal factor levels were determined through the ANOVA [13]. Taguchi experimental method was used to optimize essential garlic oil by selecting a L9 orthogonal array design to investigate four factors having three levels [14]. Surfactant type, surfactant concentration, speed of string and blending ratio were the identified control factors. Results showed applying Taguchi method results in a slight difference in response values. Several researchers implemented the Taguchi method for optimizing products and improving processes in various fields. Many used Taguchi technique for optimization of plastic injection processes [15–18]. Another application of the Taguchi method was improving the machining process of hard steel [19]. Mehta et al. [20] studied factors affecting the compressive strength of geopolymer using Taguchi method. ANOVA used to examine the effects of factors on the compressive strength while the optimal design was obtained using S/N ratio plots. Jafari and Toufigh, optimized the properties of polymer concrete using Taguchi method. Their results indicated that polymer concrete is suitable for repair and renovations [21]. Taguchi method and ANOVA were used to optimize the polymer mixture in terms of compressive splitting tensile and flexural strengths. Results showed an increase in the temperature had an unfavorable effect on the mechanical properties of polymer concrete [22]. Moreover, the Taguchi approach is incapable of solving multi-objective problems and cannot optimize all of the quality characteristics concurrently and can only optimize a single quality criterion regardless of other criteria [23]. Since Rezaei introduced a new Multi-criteria decision-making method called Best-Worst method (BWM) in 2015, it has been widely appreciated by many researchers around the world due to its simplicity [24]. Less pairwise comparisons and higher consistency rate due to eliminating redundant comparisons are the advantages of BWM over other MCDM methods such as the analytic hierarchy process (AHP). Rezaei et al. proposed a novel approach to evaluate and segregate suppliers from capabilities and willingness perspective using Best-Worst method [25]. Badri Ahmadi et al. applied the best worst method to prioritize supply chain social sustainability criteria using 38 experts as decisionmakers [26]. Rezaei et al. used the Best-Worst method to select the best suppliers according to environmental and traditional criteria [27]. Also, he used the Best-Worst method to determine the best configuration of freights transportation from outstations to the airport [28]. Gupta identified Indian airline companies’ quality characteristics and prioritized them using a combined best worst method and VIKOR technique [29]. Shojaei et al. developed a method to assess and prioritize airports by integrating Taguchi loss function, Best-Worst method and VIKOR (VIseKriterijumska Optimizacija I Kompromisno Resenje). Best worst method enhanced
ranking process since only reference comparisons were needed [30]. The Best-Worst method was applied to rank forces impacting oil and gas supply chain sustainability. Results show that economic and political stability had the most impact and energy transition had the least impact on the oil and gas supply chain sustainability [31]. Gupta et al. identified and Ranked factors that inhibit energy efficiency using the Best-Worst method [32]. Aboutorab et al. introduced a novel approach by integrating z numbers and BestWorst method (ZBWM) to address the uncertain conditions in real-world problems. They realized ZBWM had higher consistency compared to traditional BWM [33]. Anvari et al. evaluated and ranked decision-making factors which have an impact on the problem of searching for lost and hidden items using a combination of Best-Worst method and SAW [34]. Sadjadi and Karimi developed an extension of Best-Worst multi-criteria decision-making by integrating robust optimization technique application into BWM [35]. Guo et al. presented a fuzzy best worst method to address the issue of vagueness when the decision maker’s preference has been expressed using qualitative judgments. They used triangular fuzzy numbers to describe pairwise comparisons. The results revealed that the fuzzy Best-Worst method gives higher consistency [36]. Mou et al. developed an intuitionistic fuzzy multiplicative best worst method in order to rank criteria under uncertainty. They validated their method by assessing the severity of pulmonary emphysema [37]. A novel approach was developed using fuzzy Best-Worst method based on group decision making in order to integrate the main decision maker and the experts them [38]. They demonstrated that group decision making gives higher consistency rate when there are contradictions among decision makers. The proposed BWM-based Taguchi optimization method preferences over other multicriteria decision-making are simplicity in calculations, adaptability and accurate results due to considering and integrating decision maker’s judgment and experimental data. It can be seen that the previous decision-making methods did not utilize expert judgment to generate the weights of experiments in accordance with the defined criteria, which can lead to inaccurate decision regarding the optimal mixture. This study proposes an integrated method by unifying the Taguchi method and BestWorst multi-criteria decision-making in order to convert a multiobjective problem into a single-objective problem to prepare the preliminaries of Taguchi procedure and also giving weights of importance for the objectives and experiments relative to the objective. This approach is also compared with the pre-existing methods and validated by reasonable results, which indicates that the proposed approach significantly reduces the calculations of previous approaches by proposing a soft computing process. The statistical significance of the experiments in terms of the overall objectives was also carried out using the ANOVA process. The main contributions of this study is highlighted as follows: Six different factors of concrete mix design were optimized using a novel approach based on the Taguchi and MCDM methods, which resulted in an overall improvement on the quality characteristics of high strength self-consolidating concrete. The Taguchi approach and MCDM methods was improved by encapsulating a proposal and applications of a new as BWMbased Taguchi method. The proposed BWM-based Taguchi approach significantly simplifies the calculation process comparing to previous approaches, which is an important issue in the design of the experimental models. This model also eliminates the limitations of traditional Taguchi approach in solving multiobjective problems.
3
E. Sharifi et al. / Construction and Building Materials 236 (2020) 117547
2. Materials and methods This research study is divided into three main phases. 1: At first a BWM—based taguchi method was proposed and developed based on the data included in Sßimsßek et al. [1]. Finally, the model was validated by the experimental results of the tests conducted in this study. 2.1. Experimental plan In this research, an experimental program was carried out on 18 different concrete mixtures in order to validate the proposed BWM-Taguchi approach. The details of the concrete samples tested in this research are presented in Table 1. 2.1.1. Materials The aggregates used in this research were crushed limestone, which were provided from quarries around Tehran. The gradation of this aggregate was chosen based on ASTM C33, which are depicted in Fig. 1. Standard Type III Portland cement was used for the laboratory production of the specimens. The physical properties of cement are given in Table 3, which are satisfying based on IS: 81121989. Fly ash, which is an efficient pozzolanic material, was used in this study to enhance the workability and durability of the concrete. Moreover, using fly ash results in lower permeability and, consequently, the higher resistance against carbonatassino. The chemical composition of the fly ash and cement material used in this study are listed in Table 2. Super plasticizer, which is a fundamental component of the high strength SCC concrete and substantially decreases the water to cement ratio was used in this research at rate of 1.1 kg/lit. 2.1.2. Testing plan In this research, concrete specimens was manufactured to conduct the required tests of Table 1 in order to validate the proposed model of optimizing the mix design of the HSSCC concrete. 2.1.2.1. Sample preparation. In this research 18 cylindrical and cubic speciens were made in order to conduct the splitting tensile strength and the compressive strength tests on the concrete specimens with 2, 7 and 28 days curing. For this purpose, at first, the coarse aggregate, some of the mixing water, and other admixture were added in a machine mixer, the mixer was started and then
the fine aggregate, cement and the remained water were added. The produced concrete were then poured in the molds using a shovel in two layers. The consolidation was carried out using a standard vibrator. The specimens were then cured for 2, 7 and 28 days based on ASTM C192. The diameter and height of the cylindrical specimens were 15 cm and 30 cm, respectively. The size of the cubic specimens were 15 15 15 cm. 2.1.2.2. Slump flow test. The slump flow of the fresh concrete and the time elapsed for the concrete to spread from the cone until the diameter of 500 mm (T50) was measured using the method described in EN 12350-2. According to previous researches, the appropriate slump flow for the HSSCC concrete is 600 mm. The T50 value should be between 3 and 6 s. The lower T50 value results in a faster compaction of the HSSCC concete [39]. 2.1.2.3. Compressive strength. The compressive strength is one of the most common performance tests of concrete [40]. This test is usually conducted by breaking cubic concrete specimens in a compression testing machin based on ASTM C39 as shown in Fig. 2. The test was carried out on the specimens at 2th, 7th and 28th day from the day of casting. 2.1.2.4. Splitting tensile strength. The splitting tensile strength were conducted on three replicates of each concrete mixture at at 2th, 7th and 28th day from the day of casting according to ASTM C496. For this purpose, a compressive force was applied along with the diameter of a cylindrical concrete specimen. The tensile strength of the specimes is then calculated using the folloing equation.
T¼
2p Pld
ð1Þ
where: T is the splitting tensile strength (MPa), P is the maximum applied load indicated by the testing machine (N), l and d are the lengthand diameter of the specimens respectively (mm). 2.1.2.5. Heat transfer coeficient. Currently, There is not any specific standard method for calculating the heat transfer coefficient [41]. However, there are many models and innovative methods to do this. In this research, the heat transfer coefficient was also measured using the method described in [1].
Table 1 Details of the concrete mixtures tested in this experiment. Exp. No.
Cement amount (kg)
Water to cementitious ratio (%) (%)
Coarse aggregate to fine aggregate ratio (%)
Super plasticizer amount (kg/m3)
Mixing time (s) (s)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
400 400 400 400 400 400 400 400 400 425 425 425 425 425 425 425 425 425
0.35 0.35 0.35 0.37 0.37 0.37 0.39 0.39 0.39 0.35 0.35 0.35 0.37 0.37 0.37 0.39 0.39 0.39
0.60 0.65 0.70 0.60 0.65 0.70 0.60 0.65 0.70 0.60 0.65 0.70 0.60 0.65 0.70 0.60 0.65 0.70
1 1.25 1.50 1.25 1.50 1 1 1.25 1.50 1.50 1 1.25 1.50 1 1.25 1.25 1.50 1
100 110 120 110 120 100 120 100 110 110 120 100 100 110 120 120 100 110
4
E. Sharifi et al. / Construction and Building Materials 236 (2020) 117547
Fig. 1. The aggregate garadation.
Table 2 Chemical compostion of the cmenet anf fly ash used in this study. Chemical composition
Cement (%)
Fly ash (%)
Cao SiO2 Al2O3 Fe2O3 SO3 MgO K2O Na1O Cl Heat loss
66.25 21.79 5.98 2.51 1.54 1.15 0.61 0.15 0.0071 3.71
4.76 56.21 23.1 6.51 0.73 2.11 2.53 0.27 0.0018 2.24
the aim is achieving the optimal combination of factor levels using a minimum number of experiments to decrease the time and the cost of the optimization process. In Taguchi method there is a special group of standard orthogonal arrays to design, conduct and analyze the experiments more easily and efficiently. These orthogonal arrays are selected based on the number of factors and their levels for each problem. Rows and columns in a Taguchi orthogonal array represent the number of factors and experiments respectively. In this method, the effect of factors on the response is determined by symmetrical change in factor levels. In order to analyze the results, a signal to noise ratio is utilized. The value of S/N expresses the variance around a certain value, or in other words how the responses have changed over a certain number of experiments. Based on the nature of the response different S/N ratio formula can be used:
" # n S 1X 2 ¼ 10log10 y N n i¼1 i
Smaller the better
ð2Þ
" # n S 1X 1 ¼ 10log10 N n i¼1 y2i
Larger the better
ð3Þ
S ¼ 10log10 r2 N
Nominal the better
ð4Þ
where yi is ith obtained value the response and nis the number of trial repetition. The signal to noise ratio indicates the effect of control factors on the response, therefore higher S/N value means better response value. So the optimal control levels are derived from the setting of control factor level with the highest S/N ratio value. 2.3. Best-Worst multi-criteria decision-making method
Fig. 2. The compressive strength test of concrete.
2.2. Taguchi design of experiment Taguchi method was first presented by Professor Genichi Taguchi as a design of experiment method [42]. In the Taguchi method,
In BWM Weight of each criterion is computed by showing the preference of the most important criterion (best) over all criteria and all the criteria over least important criteria (worst) using a scale number of 1–9. The steps BWM are elaborated in the following [43]: Step 1. Specifying the criteria (C1, C2, . . ., Cn) that should be considered in the decision-making process. Step 2. Identifying the best (most important) and the worst (least important) criterion by the decision maker.
E. Sharifi et al. / Construction and Building Materials 236 (2020) 117547
Step 3. Determining the performance of the best criterion against other criteria using numbers 1–9. Step 4. Specifying the performance of other criteria against the worst criterion, similar to Step 3. Step 5. Finding the optimal weights: ðw1 ; w2 ; :; wn Þ The values obtained for the criteria are unique, in other words, only one criterion is considered to be the best and only one criterion is considered to be the worst. For each pair of W B =W J and W J =W w we have:
W B =W j ¼ aBj
J ¼ 1; :; n
W j =W w ¼ aj w
5
each experiment with respect to that quality characteristic step 4 (Single response optimization problem). Fig. 3 illustrates the proposed BWM model. Step 6. Using the larger the better Eq. (3) for the S/N ratio method, the S/N ratio for the total weight of experiments in relation to all quality characteristics will be calculated. The combination with the highest S/N ratio will be selected as an optimal design. Also, the analysis of variance (ANOVA) will be used to determine the significant factors. Fig. 4 illustrates the proposed integrated approach.
ð5Þ
J ¼ 1; :; n
ð6Þ
In the above equation W B denotes the best criterion weight, W w denotes the worst criterion weight, and W j denotes the weight of other criteria. aBj and ajw represent the value derived from comparing the best criterion with other criteria and other criteria against the worst criterion, respectively. The optimal weights should be gained by minimizing the absolute value of the maximum differences with solving the linear model below:
min nL subject to wB aBj wj 6 nL for all j wj ajW wW 6 nL for all j P wj ¼ 1
ð7Þ
j
wj P 0; for all j
ðw1 ; w2 ; :; wn Þ are optimal weights and (nL ) is consistency ratio. 2.4. The proposed methodology In general, optimization problems contain more than one response, which often contradicts each other. In effect, the Taguchi design of experiment method is unable to address multi-response problems when the responses are in conflict with each other. This study presents a multi-response optimization approach to determine the optimal mixture design of high strength self-consolidating concrete (HSSCC), which is undoubtedly a multi-response if the multi quality characteristics of the concrete are taken into consideration. Hence, this study proposes an integrated approach to overcome this crucial gap by linking the involving HSSCC optimization objectives and the parameters. The steps of the proposed approach are as follows: Step 1. Identifying the control factors, their feasible range and quality characteristics (Multi-response optimization problem). Step 2. Calculating the weight of quality characteristic based on preferences of decision maker using Best-Worst method (BWM). Step 3. Selecting adequate Taguchi orthogonal array considering the number of control factors and their levels. There are 18 main orthogonal arrays presented by Taguchi. If proper array are not found among these 18 arrays, the next proper array will be selected. Step 4. Obtaining the values of responses for each quality characteristic by adopting experiments. Then use BWM to calculate the relative weight of each individual experiment with respect to each individual quality characteristic. Step 5. The total weight for each experiment with respect to all quality characteristics will be calculated by multiplying the weight of each quality characteristic step 2 to the weight of
2.5. Optimization of high self-consolidating concrete Evaluation of the optimal mixture design of concrete is a vital issue for achieving an optimal quality [44]. The production of concrete with high quality according to preferences of the manufacturer and with the least cost and use of materials is the goal of using optimization methods. High strength Self-consolidating concrete (HSSCC) is a type of concrete capable of consolidating under its own weight, completely and without separation of aggregates. Self-compacting concrete is also known as self-consolidating concrete due to its ability to exhaust air without vibration. The objectives of optimizing the HSSCC mixture design are as follows: Optimization of the criteria that determine the total quality of the concrete using the decision maker preferences in order to achieve the optimal mixing scheme for high strength selfconsolidating concrete. Optimization of the concrete production cost, which is an important preference of the decision maker.Researchers have been used several quality criteria for concrete in their studies. In this paper, the proposed criteria in the work of Sß imsßek et al. have been selected for optimization using BWM-based Taguchi optimization method [1]. They studied on optimization of high strength selfconsolidating concrete using a TOPSIS-based Taguchi method considering ten quality criteria for high strength self-consolidating concrete performance. The first criterion of concrete performance is the average heat transfer coefficient, which provides information on energy losses and heat damages caused by heat transfer in structures that are located in coastal areas or areas affected by strong winds [45]. The second criterion is the air content, which gives the amount of air in concrete. The third and fourth criteria are the slump flow and T50 time, respectively. The elapsed time from the moment concrete begins to spread from slump cone until its diameter reaches 50 cm is considered as T50 time. T50 is a measure for the filling ability of the concrete. The slump flow is a measure to assess the horizontal free flow of self-consolidating concrete in the absence of obstructions.
Fig. 3. The proposed BWM model.
6
E. Sharifi et al. / Construction and Building Materials 236 (2020) 117547 Table 4 Identified factors and their levels [1]. Factor
A B C D E F
Description
Levels
Cement amount (kg) Water to cementitious ratio (%) Coarse aggregate to fine aggregate ratio (%) Super plasticizer amount (kg/m3) Fly ash (kg) Mixing time (s)
1
2
3
400 0.35 0.60* 1 80 100*
425* 0.37* 0.65 1.25* 100 110
– 0.39 0.70 1.50 120* 120
plasticizer amount, and fly ash having three levels and mixing time having two levels. For sake of simplicity, these factors are indicated by letters A, B, C, D, E and F according to Table 4. Approximated mixture levels before conducting experiments are underlined (*) [1]. 3. Results and discussion In this section, the proposed methodology will be used for optimizing the mixture design of high strength self-consolidating concrete using the following steps: Step 1. Identifying performance optimization objectives, factors and their levels. Ten quality characteristics are selected as performance optimization objectives, moreover, six factors affecting these quality characteristics have been identified, one having two and five having three levels [1]. Step 2. Calculating the weight of quality characteristics using BWM. In this step, by taking into account the decision maker’s preferences weight of each quality characteristics will be calculated using Best-Worst method. The selected best and worst criteria are determined as compressive strength in 28 days (Q 8) and heat transfer coefficient (Q 1). Table 5 and 6 indicate the reference comparison of best to others (BO) and others to worst (OW). Finally, by solving the linear model (7) optimal weights of
Fig. 4. The steps of the proposed methodology.
Table 3 Selected quality characteristics [1]. No. Symbol Quality characteristic 1 2 3 4 5 6 7 8 9 10
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q 10
Target value
Heat transfer coefficient (W/m2K) Air percentage (%) Slump flow (mm) Time (s) T50 Absorbed water percentage (%) Compressive strength 2 days (N/mm2) Compressive strength 7 days (N/mm2) Compressive strength 28 days (N/mm2) Splitting tensile strength 28 days (N/mm2) cost ($$/mm2)
lower the better lower the better Higher the better lower the better lower the better Higher the better Higher the better Higher the better Higher the better lower the better
ðw1 ; w2 ; :; w10 Þ for each criterion and consistency ratio ðnL Þ
will be obtained. Consistency ratio ðnL Þ must be less than 0:1 for pair-wise comparisons to be consistent. Table 7 shows the quality characteristics weights considering the decision maker’s preferences (w101 Þ. Step 3. Selecting adequate Taguchi experimental array. Taguchi experimental array will be selected considering the number of factors and their levels. Since there are five factors having three levels and one factor having two levels a L27 (21 37) orthogonal is used to conduct the experiments. In the first step of experiment procedure, coarse aggregates are mixed with water, then Portland cement and additional water are added to the mix. For the last step, a mixture of water and superplasticizer will be added to the mixture. Mixing time will be started at this point. For each experiment, a 150 mm3 sample will be prepared according to ‘‘TS EN 12390/9” [1]. The Taguchi orthogonal array and the results of the experiment are indicated in Tables 8 and 9 respectively.
Another performance criterion is the percentage of water absorbed by concrete. This criterion shows the strength of concrete against water and the porosity of concrete. Other criteria are splitting tensile strength of concrete on day 28 and compressive strength on days 2, 7 and 28. These criteria give insight into concrete resistance. The last criterion is the cost of production. For more details see [1]. The ten selected criteria are shown in Table 3. For the sake of simplicity, we the ten chosen criteria are represented as Q1–Q10. Sßimsßek et al. considered six factors that affect identified quality characteristics. These factors are the Cement amount, water to cementitious ratio, coarse aggregate to fine aggregate ratio, Super
Table 5 The reference comparison of best to others. Quality criteria
Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
Q10
Best criteria (Q8)
9
7
3
5
7
4
7
1
9
5
7
E. Sharifi et al. / Construction and Building Materials 236 (2020) 117547
Finally, by solving linear model (7) optimal weights of
Table 6 The reference comparison of others to worst. Quality criteria
Worst criteria (Q1)
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10
1 3 7 5 3 6 3 9 1 5
¿1 a
¿1 a
¿1 a
ðw1 2 ; w2 2 ; :; w182 Þ and consistency ratio ðnL Þ for each experiment will be obtained. Consistency ratio of each experiment
ðnL Þ must be less than 0:1 for pair-wise comparisons to be consistent. Table 12 indicates the relative weight of each experiment with respect to each individual quality characteristics ¿1 a
2 ðw1810 Þ. Step 5. Calculating the total weight for each experiment with respect to all quality characteristics. In order to convert a multi-objective problem into a singleobjective problem, the total weight for each experiment with respect to all quality characteristics will be calculated by multi-
¿1 a
Table 7 Quality characteristics weights. No.
Symbol
Quality characteristic
Criteria weight
1 2 3 4 5 6 7 8 9 10
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10
Heat transfer coefficient (W/m2K) Air percentage (%) Slump flow (mm) Time (s) T50 Absorbed water percentage (%) Compressive strength 2 days (N/mm2) Compressive strength 7 days (N/mm2) Compressive strength 28 days (N/mm2) Splitting tensile strength 28 days (N/mm2) cost ($$/mm2)
0.03176 0.059992 0.179976 0.07199 0.059992 0.089988 0.059992 0.322898 0.051422 0.07199 0:037053842
Consistency ratio ðnL Þ
Additionally, using MINITAB software and by analyzing the S/N ratios given in Table 14 the optimal levels for control factors will be obtained. The mixture with the highest S/N ratio will be considered as the optimal design for optimization of high strength selfconsolidating concrete. Fig. 5 illustrates the optimal levels for factors. Results show that the highest S/N ratio is for A2B1C1D1E3F3 combination.
Step 4. Calculating the weight of experiments with respect to each individual quality characteristics. Similar to step 2, the relative weight of each experiment with respect to each individual quality characteristics can be calculated using the BWM method. The best and the worst experiments with respect to each quality characteristics can be determined easily by examining the experiment results. For example, the best and the worst experiments for Q8 are experiment number 11 and 8 respectively. The same process can be applied to the remaining quality characteristics. Tables 10 and 11 indicate the reference comparison of best to others (BO) and others to worst (OW).
Table 8 The proposed Taguchi experimental array. Exp. No.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
2 plying the weights obtained in step 4 and 2 ðw1810 w101 Þ. Table 13 gives the total weight for each experiments considering the decision maker’s preferences. Step 6. Calculating S/N ratio, determining optimal control factors and significance factors. Since the objective is maximizing the total quality, Eq. (3) for larger the better is used to calculate the signal to noise ratio for the total weight for each experiment with respect to all quality characteristics. The S/N ratios are given in Table 14.
Experimental array L18 A
B
C
D
E
F
1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2
1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
1 2 3 1 2 3 2 3 1 3 1 2 2 3 1 3 1 2
1 2 3 2 3 1 1 2 3 3 1 2 3 1 2 2 3 1
1 2 3 2 3 1 3 1 2 2 3 1 1 2 3 3 1 2
3.1. The analysis of variance (ANOVA) In order to determine the significant factors affecting the total quality of HSSCC, ANOVA is required. Table gives the results for ANOVA, p-values less than 0.05 indicate model terms are significant [46]. In this case, cement amount (A), water to the cementitious ratio (B) and mixing time (F) are significant model terms (Table 16). In order to demonstrate the importance of the proposed methodology a case of optimizing a single criterion using traditional Taguchi method will be considered. Assume optimizing the 28 days compressive strength (Q8) is required. Using experimental values in Table 9 and by implanting Taguchi method the optimal levels for control factor would be as A2B1C1D1E1F3 shown in Fig. 6. Comparison of the experimental results for the traditional Taguchi optimization with BWM-based Taguchi optimization are given in Table 17. As it can be seen although implementing traditional Taguchi method slightly improved the value Q8 but other quality characteristics were worsened. For example slump flow (Q3) of 570 was obtained using traditional Taguchi while by using BWM-based Taguchi method slump flow of 790 was achieved (Table 17). Therefore, the proposed BWMbased Taguchi method gave the highest importance weight to the 28 days compressive strength without ignoring other quality criteria. In summary, as mentioned before, Taguchi is incapable of solving multi-objective problems and cannot simultaneously optimize all of the quality characteristics. It can only optimize a single quality criterion regardless of other criteria. Since some of these criteria are conflicting with each other, with improvement in one criterion other criteria might get worst. It is obvious that optimizing a criterion without considering other criteria does not necessarily give us the optimal response. That is why it is essential to implement the proposed methodology for optimization of multi-objective
8
E. Sharifi et al. / Construction and Building Materials 236 (2020) 117547
Table 9 Experiment results based on Taguchi experimental array [1]. Exp. No.
Results
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Q1 (W/m2K)
Q2 %
Q3 mm
Q4 s
Q5 %
Q6 (N/mm2)
Q7 (N/mm2)
Q8 (N/mm2)
Q9 (N/mm2)
Q10 $/mm2
14.568 14.561 14.567 14.565 14.566 14.572 14.57 14.57 14.571 14.559 14.559 14.562 14.562 14.561 14.561 14.556 14.555 14.556
1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0
560 610 710 600 740 690 660 730 730 780 750 760 770 740 770 760 740 750
7 5 4 4 3 3 3 3 3 3 4 4 4 3 3 3 5 5
2.05 2.17 1.79 2.03 2.22 2.14 2.58 2.73 2.46 1.59 2.2 2.01 1.7 2.39 1.91 3.28 2.95 3.46
39.8 30.1 40.1 41.8 40.2 34.2 30.7 30.6 30.2 27.2 37.2 33.1 28.7 30.7 31.7 2.1 25.2 23.5
63.4 58.4 66 62.9 68.2 58.1 59.6 58.1 57 59.4 61.5 55.5 54.5 53.4 56 42.3 55 48.4
77.44 67.66 69.85 65.53 72.19 69.69 70.4 59.51 60.51 71.09 74.52 68.52 69.97 66.77 74.39 64.2 68.26 61.64
4.73 4.6 4.65 4.55 4.7 4.65 4.66 4.41 4.28 4.68 4.5 4.62 4.65 4.58 4.75 4.52 4.62 4.46
45.635 49.03 52.11 46.12 49.612 51.019 48.232 51.676 46.895 53.61 47.536 50.721 53.638 50.227 48.079 53.11 48.73 50.167
Table 10 The reference comparison of best to others. Quality criteria
Best Exp.
Experiments Exp. 1
Exp. 2
Exp. 3
Exp. 4
Exp. 5
Exp. 6
Exp. 7
Exp. 8
Exp. 9
Exp. 10
Exp. 11
Exp. 12
Exp. 13
Exp. 14
Exp. 15
Exp. 16
Exp. 17
Exp. 18
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10
18 10 10 10 10 4 5 11 11 1
5 9 9 9 4 2 4 3 2 1
3 9 7 5 5 6 5 6 5 4
5 9 4 3 2 2 2 5 4 8
5 9 7 3 4 1 4 6 6 2
5 9 3 1 5 2 1 3 2 4
9 9 4 1 5 4 5 5 4 7
8 9 5 1 6 6 5 4 4 3
8 9 3 1 7 6 5 9 7 7
8 9 3 1 6 6 5 7 9 2
2 1 2 1 1 7 5 4 3 8
2 1 2 3 5 3 4 1 1 3
3 1 2 3 4 4 6 5 5 7
3 1 2 3 2 7 6 4 4 9
3 1 3 1 6 6 6 6 6 6
3 1 2 1 3 6 6 2 1 3
1 1 2 1 8 7 9 6 6 8
1 1 3 5 7 8 6 5 5 4
1 1 3 5 9 9 8 7 7 6
Table 11 The reference comparison of others to worst. Quality criteria
Worst Exp.
Experiments Exp. 1
Exp. 2
Exp. 3
Exp. 4
Exp. 5
Exp. 6
Exp. 7
Exp. 8
Exp. 9
Exp. 10
Exp. 11
Exp. 12
Exp. 13
Exp. 14
Exp. 15
Exp. 16
Exp. 17
Exp. 18
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10
6 1 1 1 18 18 16 8 9 13
5 1 1 1 6 8 6 7 8 9
7 1 3 5 5 4 5 4 5 6
5 1 6 7 8 8 8 5 6 2
5 1 3 7 6 9 6 4 4 2
5 1 7 9 5 8 9 7 8 6
1 1 6 9 5 6 5 5 6 3
2 1 5 9 4 4 5 6 6 7
2 1 7 9 3 4 5 1 3 3
2 1 7 9 4 4 5 3 1 2
8 9 9 9 9 3 5 6 7 2
8 9 7 7 5 7 6 9 9 7
7 9 8 7 6 6 4 5 5 3
7 9 8 7 8 3 4 6 6 1
7 9 7 9 4 4 4 4 4 4
7 9 8 9 7 4 4 8 9 7
9 9 8 9 2 3 1 4 4 2
9 9 7 5 3 2 4 5 5 6
9 9 7 5 1 1 2 3 3 4
Table 12 The relative weight of each experiment with respect to each individual quality characteristics. Experiments
Exp.1 Exp.2 Exp.3 Exp.4 Exp.5 Exp.6
Quality characteristics Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
Q 10
0.0313 0.0521 0.0313 0.0313 0.0313 0.0113
0.0111 0.0111 0.0111 0.0111 0.0111 0.0111
0.0112 0.0224 0.0392 0.0224 0.0523 0.0392
0.0074 0.0205 0.0341 0.0341 0.0845 0.0845
0.0533 0.0427 0.1067 0.0533 0.0427 0.0427
0.1046 0.0349 0.1046 0.1719 0.1046 0.0523
0.0581 0.0465 0.1162 0.0581 0.1910 0.0465
0.0731 0.0365 0.0438 0.0365 0.0731 0.0438
0.0920 0.0368 0.0460 0.0307 0.0920 0.0460
0.1857 0.0565 0.0283 0.0727 0.0565 0.0323
9
E. Sharifi et al. / Construction and Building Materials 236 (2020) 117547 Table 12 (continued) Experiments
Exp.7 Exp.8 Exp.9 Exp.10 Exp.11 Exp.12 Exp.13 Exp.14 Exp.15 Exp.16 Exp.17 Exp.18
nL
Quality characteristics Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
Q 10
0.0196 0.0196 0.0196 0.0782 0.0782 0.0521 0.0521 0.0521 0.0521 0.1292 0.1292 0.1292 0.0272
0.0111 0.0111 0.0111 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.0000
0.0314 0.0523 0.0523 0.1288 0.0784 0.0784 0.0784 0.0523 0.0784 0.0784 0.0523 0.0523 0.0280
0.0845 0.0845 0.0845 0.0845 0.0341 0.0341 0.0341 0.0845 0.0845 0.0845 0.0205 0.0205 0.0178
0.0356 0.0305 0.0356 0.1753 0.0427 0.0533 0.1067 0.0356 0.0711 0.0267 0.0305 0.0152 0.0381
0.0349 0.0349 0.0349 0.0299 0.0697 0.0523 0.0299 0.0349 0.0349 0.0299 0.0262 0.0149 0.0374
0.0465 0.0465 0.0465 0.0465 0.0581 0.0387 0.0387 0.0387 0.0387 0.0166 0.0387 0.0291 0.0415
0.0548 0.0157 0.0313 0.0548 0.1801 0.0438 0.0548 0.0365 0.1096 0.0365 0.0438 0.0313 0.0391
0.0460 0.0263 0.0131 0.0613 0.1512 0.0368 0.0460 0.0307 0.1512 0.0307 0.0368 0.0263 0.0329
0.0754 0.0323 0.0727 0.0283 0.0754 0.0323 0.0162 0.0377 0.0754 0.0283 0.0565 0.0377 0.0404
Table 13 The total weight for each experiments considering the decision maker’s preferences. Exp. No.
Total weight
Exp.1 Exp.2 Exp.3 Exp.4 Exp.5 Exp.6 Exp.7 Exp.8 Exp.9 Exp.10 Exp.11 Exp.12 Exp.13 Exp.14 Exp.15 Exp.16 Exp.17 Exp.18 Total
0.0620066 0.0340732 0.0525137 0.0489045 0.0729759 0.0430691 0.0465633 0.0332666 0.0408579 0.0766233 0.1087108 0.0528242 0.0568566 0.0468281 0.0861675 0.0509908 0.0476067 0.0391610 1.00
Table 14 S/N ratios for the total weight. Experiment
S/N ratio
Exp.1 Exp.2 Exp.3 Exp.4 Exp.5 Exp.6 Exp.7 Exp.8 Exp.9 Exp.10 Exp.11 Exp.12 Exp.13 Exp.14 Exp.15 Exp.16 Exp.17 Exp.18
24.1512 29.3517 25.5945 26.213 22.7364 27.3167 26.6391 29.5598 27.7745 22.3128 19.2745 25.5433 24.9044 26.5899 21.2931 25.8502 26.4466 28.1429
Fig. 5. The optimal level for each factor using BWM-based Taguchi.
10
E. Sharifi et al. / Construction and Building Materials 236 (2020) 117547
Table 15 ANOVA for BWM-based Taguchi S/N ratio. Analysis of variance for S/N ratios Source
DF
Seq SS
Adj SS
Adj MS
F-value
P-value
Contribution (%)
A B C D E F Residua l Error Total
1 2 2 2 2 2 6 17
20.012 31.922 2.740 16.317 5.702 35.574 14.931 127.197
20.012 31.922 2.740 16.317 5.702 35.574 14.931
20.012 15.961 1.370 8.158 2.851 17.787 2.489
8.04 6.41 0.55 3.28 1.15 7.15
0.030 0.032 0.603 0.109 0.379 0.026
16% 25% 2% 13% 4% 28% 12%
Table 16 Quality characteristics improvement in optimal mixture design. Symbol
Quality characteristic
Estimated mixture design
Optimal mixture design using BWM-based Taguchi
Improvement (%)
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10
Heat transfer coefficient (W/m2K) Air percentage (%) Slump flow (mm) Time (s) T50 Absorbed water percentage (%) Compressive strength 2 days (N/mm2) Compressive strength 7 days (N/mm2) Compressive strength 28 days (N/mm2) Splitting tensile strength 28 days (N/mm2) cost ($$/mm2)
14.56 0.1 770 3.85 1.7 29.34 56.3 72.21 4.75 52.76
14.55 0.1 790 3 1.5 34.96 61.25 78 5.1 49.1
0.07% 0.00% 2.53% 28.33% 13.33% 16.08% 8.08% 7.42% 6.86% 7.45%
Fig. 6. The optimal level for each factor using traditional Taguchi.
11
E. Sharifi et al. / Construction and Building Materials 236 (2020) 117547 Table 17 Result comparison for the traditional Taguchi method and BWM-based Taguchi optimization. Symbol
Quality characteristic
Optimal mixture design using BWM-based Taguchi
Optimal mixture design for Q8 using traditional Taguchi method
Improvement (%)
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10
Heat transfer coefficient (W/m2K) Air percentage (%) Slump flow (mm) Time (s) T50 Absorbed water percentage (%) Compressive strength 2 days (N/mm2) Compressive strength 7 days (N/mm2) Compressive strength 28 days (N/mm2) Splitting tensile strength 28 days (N/mm2) cost ($$/mm2)
14.55 0.1 790 3 1.5 34.96 61.25 78 5.1 49.1
14.56 0.1 570 4.94 0.02 36.32 59.1 78.95 4.71 51.3
0.07% 0.00% 38.60% 39.27% 25.00% 3.89% 3.51% 1.20% 8.28% 4.29%
problems since BWM-based Taguchi provides the opportunity to optimize all quality criteria based on their importance weight. 4. Conclusion Several quality characteristics of high strength selfconsolidating concrete are contradicting each other, therefore, consequently, it is considered as a multi-response problem. Taguchi optimization method is incapable of solving multi-objective problems and cannot simultaneously optimize all of the quality characteristics. In order to address this issue, in this study, a Taguchi optimization method is developed using Best-Worst MultiCriteria Decision-Making technique to determine the optimal mixture design and significant factors affecting these quality criteria. Using Best-Worst method weights of quality characteristics are obtained according to the decision maker’s preferences. Then, by implementing Taguchi method results are obtained for each experiment. Afterwards, each experiment is weighted with respect to each quality characteristic using BWM. After computing overall weights, optimal mixture design is determined as A2B1C1D1E3F3. Values for control factors according to this combination are 425 kg cement (A), 0.35% water to cementitious (B), 0.60% coarse aggregate to fine aggregate (C), 1 kg/m3 super plasticizer (D), 120 kg fly ash (E) and mixing time (F) of 120 s. Finally, using analysis of variance (ANOVA) the significant factors with the most influences on the total quality of concrete were determined as mixing time, cement amount and water to cementitious, respectively. Using a case study, the preferences of optimal mixture design overestimated mixture design were illustrated. Significant improvement in properties of high strength self-consolidating concrete satisfied the decision maker’s preferences. Optimization of various manufacturing procedures and chemical compounds can be investigated using BWM-based Taguchi method as a future study for this research. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References [1] B. Sß imsßek, Y.T. Iç, E.H. Sßimsßek, A TOPSIS-based Taguchi optimization to determine optimal mixture proportions of the high strength self-compacting concrete, Chemom. Intell. Lab. Syst. (2013), https://doi.org/10.1016/j. chemolab.2013.03.012. [2] M.R.M. Aliha, A. Razmi, A. Mousavi, Fracture study of concrete composites with synthetic fibers additive under modes I and III using ENDB specimen, Constr. Build. Mater. 190 (2018) 612–622.
[3] M. Fakhri, E. Amoosoltani, M.R.M. Aliha, Crack behavior analysis of roller compacted concrete mixtures containing reclaimed asphalt pavement and crumb rubber, Eng. Fract. Mech. 180 (2017) 43–59. [4] H.R. Fattahi Amirdehi, M.R.M. Aliha, A. Moniri, A.R. Torabi, Using the generalized maximum tangential stress criterion to predict mode II fracture of hot mix asphalt in terms of mode I results – a statistical analysis, Constr. Build. Mater. 213 (2019), https://doi.org/10.1016/ j.conbuildmat.2019.04.067. [5] H. Ziari, M.R.M. Aliha, A. Moniri, Y. Saghafi, Crack resistance of hot mix asphalt containing different percentages of reclaimed asphalt pavement and glass fiber, Constr. Build. Mater. 230 (2020), https://doi.org/10.1016/J. CONBUILDMAT.2019.117015 117015. [6] M.R.M. Aliha, M. Ayatollahi, Mixed mode I/II brittle fracture evaluation of marble using SCB specimen, Procedia Engineer. 10 (2011) 311–318. [7] M.R.M. Aliha, M. Ayatollahi, Rock fracture toughness study using cracked chevron notched Brazilian disc specimen under pure modes I and II loading–A statistical approach, Theor. Appl. Fract. Mec. 69 (2014) 17–25. [8] H. Tanyildizi, M. Sßahin, Application of Taguchi method for optimization of concrete strengthened with polymer after high temperature, Constr. Build. Mater. (2015), https://doi.org/10.1016/j.conbuildmat.2015.01.039. [9] H. Ziari, A. Moniri, Laboratory evaluation of the effect of synthetic Polyolefin-glass fibers on performance properties of hot mix asphalt, Constr. Build. Mater. 213 (2019) 459–468, https://doi.org/10.1016/j.conbuildmat. 2019.04.084. [10] H. Ziari, A. Moniri, P. Bahri, Y. Saghafi, The effect of rejuvenators on the aging resistance of recycled asphalt mixtures, Constr. Build. Mater. 224 (2019) 89– 98, https://doi.org/10.1016/j.conbuildmat.2019.06.181. [11] N. Celik, G. Pusat, E. Turgut, Application of Taguchi method and grey relational analysis on a turbulated heat exchanger, Int. J. Therm. Sci. (2018), https://doi. org/10.1016/j.ijthermalsci.2017.10.007. [12] D. Ji, Z. Wei, S. Mazzoni, M. Mengarelli, S. Rajoo, J. Zhao, J. Pou, A. Romagnoli, Thermoelectric generation for waste heat recovery: application of a system level design optimization approach via Taguchi method, Energy Convers. Manage. (2018), https://doi.org/10.1016/j.enconman.2018.06.016. [13] E. Teimortashlu, M. Dehestani, M. Jalal, Application of Taguchi method for compressive strength optimization of tertiary blended self-compacting mortar, Constr. Build. Mater. (2018), https://doi.org/10.1016/ j.conbuildmat.2018.09.165. [14] L. Katata-Seru, T.C. Lebepe, O.S. Aremu, I. Bahadur, Application of Taguchi method to optimize garlic essential oil nanoemulsions, J. Mol. Liq. (2017), https://doi.org/10.1016/j.molliq.2017.09.007. [15] W.C. Chen, D. Kurniawan, Process parameters optimization for multiple quality characteristics in plastic injection molding using Taguchi method, BPNN, GA, and hybrid PSO-GA, Int. J. Precis. Eng. Manuf. (2014), https://doi. org/10.1007/s12541-014-0507-6. [16] W.C. Chen, M.H. Nguyen, W.H. Chiu, T.N. Chen, P.H. Tai, Optimization of the plastic injection molding process using the Taguchi method, RSM, and hybrid GA-PSO, Int. J. Adv. Manuf. Technol. (2016), https://doi.org/10.1007/s00170015-7683-0. [17] R. Pareek, J. Bhamniya, Optimization of injection moulding process using Taguchi and ANOVA, Int. J. Sci. Eng. Res. (2013). [18] N.C. Fei, N.M. Mehat, S. Kamaruddin, Practical applications of Taguchi method for optimization of processing parameters for plastic injection moulding: a retrospective review, ISRN Ind. Eng. (2013), https://doi.org/10.1155/2013/ 462174. [19] B.M. Gopalsamy, B. Mondal, S. Ghosh, Taguchi method and anova: an approach for process parameters optimization of hard machining while machining hardened steel, J. Sci. Ind. Res. (India) (2009). [20] A. Mehta, R. Siddique, B.P. Singh, S. Aggoun, G. Łagód, D. Barnat-Hunek, Influence of various parameters on strength and absorption properties of fly ash based geopolymer concrete designed by Taguchi method, Constr. Build. Mater. (2017), https://doi.org/10.1016/j.conbuildmat.2017.06.066. [21] K. Jafari, V. Toufigh, Experimental and analytical evaluation of rubberized polymer concrete, Constr. Build. Mater. (2017), https://doi.org/10.1016/ j.conbuildmat.2017.08.097.
12
E. Sharifi et al. / Construction and Building Materials 236 (2020) 117547
[22] K. Jafari, M. Tabatabaeian, A. Joshaghani, T. Ozbakkaloglu, Optimizing the mixture design of polymer concrete: An experimental investigation, Constr. Build. Mater. (2018), https://doi.org/10.1016/j.conbuildmat.2018.01.191. [23] F.A. Alkaabneh, M. Barghash, I. Mishael, A combined analytical hierarchical process (AHP) and Taguchi experimental design (TED) for plastic injection molding process settings, Int. J. Adv. Manuf. Technol. 66 (2013) 679–694, https://doi.org/10.1007/s00170-012-4357-z. [24] J. Rezaei, Best-worst multi-criteria decision-making method, Omega (United Kingdom). (2015), https://doi.org/10.1016/j.omega.2014.11.009. [25] J. Rezaei, J. Wang, L. Tavasszy, Linking supplier development to supplier segmentation using Best Worst Method, Expert Syst. Appl. (2015), https://doi. org/10.1016/j.eswa.2015.07.073. [26] H. Badri Ahmadi, S. Kusi-Sarpong, J. Rezaei, Assessing the social sustainability of supply chains using Best Worst Method, Resour. Conserv. Recycl. (2017), https://doi.org/10.1016/j.resconrec.2017.07.020. [27] J. Rezaei, T. Nispeling, J. Sarkis, L. Tavasszy, A supplier selection life cycle approach integrating traditional and environmental criteria using the best worst method, J. Clean. Prod. (2016), https://doi.org/10.1016/j. jclepro.2016.06.125. [28] J. Rezaei, A. Hemmes, L. Tavasszy, Multi-criteria decision-making for complex bundling configurations in surface transportation of air freight, J. Air Transp. Manage. (2017), https://doi.org/10.1016/j.jairtraman.2016.02.006. [29] H. Gupta, Evaluating service quality of airline industry using hybrid best worst method and VIKOR, J. Air Transp. Manage. (2018), https://doi.org/10.1016/ j.jairtraman.2017.06.001. [30] P. Shojaei, S.A. Seyed Haeri, S. Mohammadi, Airports evaluation and ranking model using Taguchi loss function, best-worst method and VIKOR technique, J. Air Transp. Manage. (2018), https://doi.org/10.1016/j.jairtraman.2017.05.006. [31] W.N.K. Wan Ahmad, J. Rezaei, S. Sadaghiani, L.A. Tavasszy, Evaluation of the external forces affecting the sustainability of oil and gas supply chain using Best Worst Method, J. Clean. Prod. (2017), https://doi.org/10.1016/j. jclepro.2017.03.166. [32] P. Gupta, S. Anand, H. Gupta, Developing a roadmap to overcome barriers to energy efficiency in buildings using best worst method, Sustain. Cities Soc. (2017), https://doi.org/10.1016/j.scs.2017.02.005. [33] H. Aboutorab, M. Saberi, M.R. Asadabadi, O. Hussain, E. Chang, ZBWM: the Znumber extension of Best Worst Method and its application for supplier development, Expert Syst. Appl. (2018), https://doi.org/10.1016/j. eswa.2018.04.015.
[34] A. Sotoudeh-Anvari, S.J. Sadjadi, S.M. Hadji Molana, S. Sadi-Nezhad, A new MCDM-based approach using BWM and SAW for optimal search model, Decis. Sci. Lett. (2018) 395–404, https://doi.org/10.5267/j.dsl.2018.2.001. [35] S.J. Sadjadi, M. Karimi, Best-worst multi-criteria decision-making method: a robust approach, Decis. Sci. Lett. (2018) 323–340, https://doi.org/10.5267/j. dsl.2018.3.003. [36] S. Guo, H. Zhao, Fuzzy best-worst multi-criteria decision-making method and its applications, Knowledge-Based Syst. (2017), https://doi.org/10.1016/ j.knosys.2017.01.010. [37] Q. Mou, Z. Xu, H. Liao, An intuitionistic fuzzy multiplicative best-worst method for multi-criteria group decision making, Inf. Sci. (Ny). (2016), https://doi.org/ 10.1016/j.ins.2016.08.074. [38] A. Hafezalkotob, A. Hafezalkotob, A novel approach for combination of individual and group decisions based on fuzzy best-worst method, Appl. Soft Comput. J. (2017), https://doi.org/10.1016/j.asoc.2017.05.036. [39] M.P.B.C.A. Arbeláez Jaramillo, J.W. Rigueira Victor, J.R. Martí Vargas, P. Serna Ros, Reduced models test for the characterization of the rheologic properties of self-compacting concrete (SCC), RILEM Publications SARL, 2003. [40] H. Ziari, A.T. Barakoohi, A. Moniri, Laboratory investigation of the effect of temperature on frictional properties of concrete pavements containing crushed glass, Int. J. Pavement Res. Technol. 10 (2017) 297–303, https://doi. org/10.1016/j.ijprt.2017.04.006. [41] J. Li, W. Cao, The heat transfer coefficient of recycled concrete bricks combination with EPS insulation board wall, Math. Probl. Eng. 2015 (2015), https://doi.org/10.1155/2015/695962. [42] G. Taguchi, Introduction to Taguchi methods, Eng. (1988). [43] J. Rezaei, Best-worst multi-criteria decision-making method: Some properties and a linear model, Omega (United Kingdom). (2016), https://doi.org/10.1016/ j.omega.2015.12.001. [44] S. Yan, H.C. Lin, Y.C. Liu, Optimal schedule adjustments for supplying ready mixed concrete following incidents, Autom. Constr. (2011), https://doi.org/ 10.1016/j.autcon.2011.04.005. [45] Y. Lee, M.S. Choi, S.T. Yi, J.K. Kim, Experimental study on the convective heat transfer coefficient of early-age concrete, Cem. Concr. Compos. (2009), https:// doi.org/10.1016/j.cemconcomp.2008.09.009. [46] M.J. Ayazi, A. Moniri, P. Barghabany, Moisture susceptibility of warm mixedreclaimed asphalt pavement containing Sasobit and Zycotherm additives, Pet. Sci. Technol. 35 (2017), https://doi.org/10.1080/10916466.2017.1290655.
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Optimization of high-strength self-consolidating concrete mix design using an improved Taguchi optimization method Ebrahim Sharifi a, Seyed Jafar Sadjadi a, M.R.M. Aliha b,⇑, Ali Moniri c a
Department of Industrial Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran Welding and Joining Research Center, School of Industrial Engineering, Iran University of Science and Technology, Narmak, 16846-13114 Tehran, Iran, c School of Civil Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran b
h i g h l i g h t s BWM-Taguchi optimization developed by integrating BWM and Taguchi methods. Ten quality characteristics and six factor affecting these criteria were selected. The proposed approach simplifies the calculations. The proposed method is efficient for optimization of concrete mix design.
a r t i c l e
i n f o
Article history: Received 3 August 2019 Received in revised form 15 October 2019 Accepted 7 November 2019
Keywords: Mix design optimization High-strength self-consolidating concrete Taguchi optimization The BWM optimization Concrete mix design
a b s t r a c t Since many parameters are involved in the concrete mix design, finding the optimal mixing design has always been a problem for concrete engineers. In this research, the Taguchi optimization method is improved to model to optimum mix design of the high strength self-consolidating concrete (HSSCC). For this purpose, at first different quality criteria and the parameters influencing them were defined based on the available literature. The Taguchi approach was then utilized to generate an the orthogonal array of the parameters. The experimental tests were then conducted according to the suggested design array in order to obtain the experimental data for each and every single scenario. The Best-Worst method is then adopted for pairwise comparisons of the quality criteria and experiments as such to obtain the overall weights of experiments with respect to each quality characteristics. Analysis of variance was also utilized to appraise the effective factors and the optimal mixture design. It was found that the proposed method was efficient in obtaining the optimal mixture design of the manufacturing process according to decision makers’ preferences. The experimental results indicated a significant improvement in the total quality of concrete compared to the decision maker’s estimated mixture design. The cement amount, water to cementitious ratio and mixing time are the most significant parameters affecting the concrete mix design. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction The producing high strength self-consolidating concrete (HSSCC) which satisfy manufacturers’ preferences depends on the evaluation of all of the vital components at the same time indeed. These components influence the performance of the concrete and are often contradicted each other [1–3], hence by considering all these quality criteria it can be considered as a multi-objective optimization for the sake of determining the best mixture. The researchers have always been looking for a promising model to ⇑ Corresponding author. E-mail address: [email protected] (M.R.M. Aliha). https://doi.org/10.1016/j.conbuildmat.2019.117547 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.
avoid time and cost consuming laboratory tests [4–7]. The decision-makers are of the methods to model the mix design of cementitious and bitumenious material. In order to reach the optimized mixture, the decision-makers usually select an appropriate proportion of each component based on their judgments, which makes the process vulnerable to risk. Under these circumstances, the estimated mixture levels will be inaccurate. To help overcoming this gap, a promising optimization method is needed to determine the best concrete mixture with the advantage of performing the minimum experiments in a more efficient process [1]. One of the most popular optimization methods is Taguchi design of an experiment. Taguchi method seeks to find the optimal
2
E. Sharifi et al. / Construction and Building Materials 236 (2020) 117547
levels for control factors by minimizing the response variance close to the optimal response. Tanyildizi and Sßahin examined the effects of control factors of silica fume percentage, temperature and type of polymerization on the polymer strengthened concrete. They used a L32 orthogonal array to implement the experiments. Using analysis of variance (ANOVA), silica fume selected as the most effective factor [8–10]. Celik et al. [11] applied the Taguchi experimental design method to optimize factor levels of the heat exchanger. They also investigated the effect of friction factor on the heat transfer using grey relational analysis. Ji et al. Determined the optimal level for five design factors that affect the thermoelectric generator based on Taguchi method. They used L27 (35) orthogonal array for experiment design [12]. Teimortashlu et al. examined Taguchi method application for compressive strength optimization of tertiary blended self-consolidating mortar. Three factors at four levels were identified. Therefore, Experiments on samples were conducted using L16 design. Optimal factor levels were determined through the ANOVA [13]. Taguchi experimental method was used to optimize essential garlic oil by selecting a L9 orthogonal array design to investigate four factors having three levels [14]. Surfactant type, surfactant concentration, speed of string and blending ratio were the identified control factors. Results showed applying Taguchi method results in a slight difference in response values. Several researchers implemented the Taguchi method for optimizing products and improving processes in various fields. Many used Taguchi technique for optimization of plastic injection processes [15–18]. Another application of the Taguchi method was improving the machining process of hard steel [19]. Mehta et al. [20] studied factors affecting the compressive strength of geopolymer using Taguchi method. ANOVA used to examine the effects of factors on the compressive strength while the optimal design was obtained using S/N ratio plots. Jafari and Toufigh, optimized the properties of polymer concrete using Taguchi method. Their results indicated that polymer concrete is suitable for repair and renovations [21]. Taguchi method and ANOVA were used to optimize the polymer mixture in terms of compressive splitting tensile and flexural strengths. Results showed an increase in the temperature had an unfavorable effect on the mechanical properties of polymer concrete [22]. Moreover, the Taguchi approach is incapable of solving multi-objective problems and cannot optimize all of the quality characteristics concurrently and can only optimize a single quality criterion regardless of other criteria [23]. Since Rezaei introduced a new Multi-criteria decision-making method called Best-Worst method (BWM) in 2015, it has been widely appreciated by many researchers around the world due to its simplicity [24]. Less pairwise comparisons and higher consistency rate due to eliminating redundant comparisons are the advantages of BWM over other MCDM methods such as the analytic hierarchy process (AHP). Rezaei et al. proposed a novel approach to evaluate and segregate suppliers from capabilities and willingness perspective using Best-Worst method [25]. Badri Ahmadi et al. applied the best worst method to prioritize supply chain social sustainability criteria using 38 experts as decisionmakers [26]. Rezaei et al. used the Best-Worst method to select the best suppliers according to environmental and traditional criteria [27]. Also, he used the Best-Worst method to determine the best configuration of freights transportation from outstations to the airport [28]. Gupta identified Indian airline companies’ quality characteristics and prioritized them using a combined best worst method and VIKOR technique [29]. Shojaei et al. developed a method to assess and prioritize airports by integrating Taguchi loss function, Best-Worst method and VIKOR (VIseKriterijumska Optimizacija I Kompromisno Resenje). Best worst method enhanced
ranking process since only reference comparisons were needed [30]. The Best-Worst method was applied to rank forces impacting oil and gas supply chain sustainability. Results show that economic and political stability had the most impact and energy transition had the least impact on the oil and gas supply chain sustainability [31]. Gupta et al. identified and Ranked factors that inhibit energy efficiency using the Best-Worst method [32]. Aboutorab et al. introduced a novel approach by integrating z numbers and BestWorst method (ZBWM) to address the uncertain conditions in real-world problems. They realized ZBWM had higher consistency compared to traditional BWM [33]. Anvari et al. evaluated and ranked decision-making factors which have an impact on the problem of searching for lost and hidden items using a combination of Best-Worst method and SAW [34]. Sadjadi and Karimi developed an extension of Best-Worst multi-criteria decision-making by integrating robust optimization technique application into BWM [35]. Guo et al. presented a fuzzy best worst method to address the issue of vagueness when the decision maker’s preference has been expressed using qualitative judgments. They used triangular fuzzy numbers to describe pairwise comparisons. The results revealed that the fuzzy Best-Worst method gives higher consistency [36]. Mou et al. developed an intuitionistic fuzzy multiplicative best worst method in order to rank criteria under uncertainty. They validated their method by assessing the severity of pulmonary emphysema [37]. A novel approach was developed using fuzzy Best-Worst method based on group decision making in order to integrate the main decision maker and the experts them [38]. They demonstrated that group decision making gives higher consistency rate when there are contradictions among decision makers. The proposed BWM-based Taguchi optimization method preferences over other multicriteria decision-making are simplicity in calculations, adaptability and accurate results due to considering and integrating decision maker’s judgment and experimental data. It can be seen that the previous decision-making methods did not utilize expert judgment to generate the weights of experiments in accordance with the defined criteria, which can lead to inaccurate decision regarding the optimal mixture. This study proposes an integrated method by unifying the Taguchi method and BestWorst multi-criteria decision-making in order to convert a multiobjective problem into a single-objective problem to prepare the preliminaries of Taguchi procedure and also giving weights of importance for the objectives and experiments relative to the objective. This approach is also compared with the pre-existing methods and validated by reasonable results, which indicates that the proposed approach significantly reduces the calculations of previous approaches by proposing a soft computing process. The statistical significance of the experiments in terms of the overall objectives was also carried out using the ANOVA process. The main contributions of this study is highlighted as follows: Six different factors of concrete mix design were optimized using a novel approach based on the Taguchi and MCDM methods, which resulted in an overall improvement on the quality characteristics of high strength self-consolidating concrete. The Taguchi approach and MCDM methods was improved by encapsulating a proposal and applications of a new as BWMbased Taguchi method. The proposed BWM-based Taguchi approach significantly simplifies the calculation process comparing to previous approaches, which is an important issue in the design of the experimental models. This model also eliminates the limitations of traditional Taguchi approach in solving multiobjective problems.
3
E. Sharifi et al. / Construction and Building Materials 236 (2020) 117547
2. Materials and methods This research study is divided into three main phases. 1: At first a BWM—based taguchi method was proposed and developed based on the data included in Sßimsßek et al. [1]. Finally, the model was validated by the experimental results of the tests conducted in this study. 2.1. Experimental plan In this research, an experimental program was carried out on 18 different concrete mixtures in order to validate the proposed BWM-Taguchi approach. The details of the concrete samples tested in this research are presented in Table 1. 2.1.1. Materials The aggregates used in this research were crushed limestone, which were provided from quarries around Tehran. The gradation of this aggregate was chosen based on ASTM C33, which are depicted in Fig. 1. Standard Type III Portland cement was used for the laboratory production of the specimens. The physical properties of cement are given in Table 3, which are satisfying based on IS: 81121989. Fly ash, which is an efficient pozzolanic material, was used in this study to enhance the workability and durability of the concrete. Moreover, using fly ash results in lower permeability and, consequently, the higher resistance against carbonatassino. The chemical composition of the fly ash and cement material used in this study are listed in Table 2. Super plasticizer, which is a fundamental component of the high strength SCC concrete and substantially decreases the water to cement ratio was used in this research at rate of 1.1 kg/lit. 2.1.2. Testing plan In this research, concrete specimens was manufactured to conduct the required tests of Table 1 in order to validate the proposed model of optimizing the mix design of the HSSCC concrete. 2.1.2.1. Sample preparation. In this research 18 cylindrical and cubic speciens were made in order to conduct the splitting tensile strength and the compressive strength tests on the concrete specimens with 2, 7 and 28 days curing. For this purpose, at first, the coarse aggregate, some of the mixing water, and other admixture were added in a machine mixer, the mixer was started and then
the fine aggregate, cement and the remained water were added. The produced concrete were then poured in the molds using a shovel in two layers. The consolidation was carried out using a standard vibrator. The specimens were then cured for 2, 7 and 28 days based on ASTM C192. The diameter and height of the cylindrical specimens were 15 cm and 30 cm, respectively. The size of the cubic specimens were 15 15 15 cm. 2.1.2.2. Slump flow test. The slump flow of the fresh concrete and the time elapsed for the concrete to spread from the cone until the diameter of 500 mm (T50) was measured using the method described in EN 12350-2. According to previous researches, the appropriate slump flow for the HSSCC concrete is 600 mm. The T50 value should be between 3 and 6 s. The lower T50 value results in a faster compaction of the HSSCC concete [39]. 2.1.2.3. Compressive strength. The compressive strength is one of the most common performance tests of concrete [40]. This test is usually conducted by breaking cubic concrete specimens in a compression testing machin based on ASTM C39 as shown in Fig. 2. The test was carried out on the specimens at 2th, 7th and 28th day from the day of casting. 2.1.2.4. Splitting tensile strength. The splitting tensile strength were conducted on three replicates of each concrete mixture at at 2th, 7th and 28th day from the day of casting according to ASTM C496. For this purpose, a compressive force was applied along with the diameter of a cylindrical concrete specimen. The tensile strength of the specimes is then calculated using the folloing equation.
T¼
2p Pld
ð1Þ
where: T is the splitting tensile strength (MPa), P is the maximum applied load indicated by the testing machine (N), l and d are the lengthand diameter of the specimens respectively (mm). 2.1.2.5. Heat transfer coeficient. Currently, There is not any specific standard method for calculating the heat transfer coefficient [41]. However, there are many models and innovative methods to do this. In this research, the heat transfer coefficient was also measured using the method described in [1].
Table 1 Details of the concrete mixtures tested in this experiment. Exp. No.
Cement amount (kg)
Water to cementitious ratio (%) (%)
Coarse aggregate to fine aggregate ratio (%)
Super plasticizer amount (kg/m3)
Mixing time (s) (s)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
400 400 400 400 400 400 400 400 400 425 425 425 425 425 425 425 425 425
0.35 0.35 0.35 0.37 0.37 0.37 0.39 0.39 0.39 0.35 0.35 0.35 0.37 0.37 0.37 0.39 0.39 0.39
0.60 0.65 0.70 0.60 0.65 0.70 0.60 0.65 0.70 0.60 0.65 0.70 0.60 0.65 0.70 0.60 0.65 0.70
1 1.25 1.50 1.25 1.50 1 1 1.25 1.50 1.50 1 1.25 1.50 1 1.25 1.25 1.50 1
100 110 120 110 120 100 120 100 110 110 120 100 100 110 120 120 100 110
4
E. Sharifi et al. / Construction and Building Materials 236 (2020) 117547
Fig. 1. The aggregate garadation.
Table 2 Chemical compostion of the cmenet anf fly ash used in this study. Chemical composition
Cement (%)
Fly ash (%)
Cao SiO2 Al2O3 Fe2O3 SO3 MgO K2O Na1O Cl Heat loss
66.25 21.79 5.98 2.51 1.54 1.15 0.61 0.15 0.0071 3.71
4.76 56.21 23.1 6.51 0.73 2.11 2.53 0.27 0.0018 2.24
the aim is achieving the optimal combination of factor levels using a minimum number of experiments to decrease the time and the cost of the optimization process. In Taguchi method there is a special group of standard orthogonal arrays to design, conduct and analyze the experiments more easily and efficiently. These orthogonal arrays are selected based on the number of factors and their levels for each problem. Rows and columns in a Taguchi orthogonal array represent the number of factors and experiments respectively. In this method, the effect of factors on the response is determined by symmetrical change in factor levels. In order to analyze the results, a signal to noise ratio is utilized. The value of S/N expresses the variance around a certain value, or in other words how the responses have changed over a certain number of experiments. Based on the nature of the response different S/N ratio formula can be used:
" # n S 1X 2 ¼ 10log10 y N n i¼1 i
Smaller the better
ð2Þ
" # n S 1X 1 ¼ 10log10 N n i¼1 y2i
Larger the better
ð3Þ
S ¼ 10log10 r2 N
Nominal the better
ð4Þ
where yi is ith obtained value the response and nis the number of trial repetition. The signal to noise ratio indicates the effect of control factors on the response, therefore higher S/N value means better response value. So the optimal control levels are derived from the setting of control factor level with the highest S/N ratio value. 2.3. Best-Worst multi-criteria decision-making method
Fig. 2. The compressive strength test of concrete.
2.2. Taguchi design of experiment Taguchi method was first presented by Professor Genichi Taguchi as a design of experiment method [42]. In the Taguchi method,
In BWM Weight of each criterion is computed by showing the preference of the most important criterion (best) over all criteria and all the criteria over least important criteria (worst) using a scale number of 1–9. The steps BWM are elaborated in the following [43]: Step 1. Specifying the criteria (C1, C2, . . ., Cn) that should be considered in the decision-making process. Step 2. Identifying the best (most important) and the worst (least important) criterion by the decision maker.
E. Sharifi et al. / Construction and Building Materials 236 (2020) 117547
Step 3. Determining the performance of the best criterion against other criteria using numbers 1–9. Step 4. Specifying the performance of other criteria against the worst criterion, similar to Step 3. Step 5. Finding the optimal weights: ðw1 ; w2 ; :; wn Þ The values obtained for the criteria are unique, in other words, only one criterion is considered to be the best and only one criterion is considered to be the worst. For each pair of W B =W J and W J =W w we have:
W B =W j ¼ aBj
J ¼ 1; :; n
W j =W w ¼ aj w
5
each experiment with respect to that quality characteristic step 4 (Single response optimization problem). Fig. 3 illustrates the proposed BWM model. Step 6. Using the larger the better Eq. (3) for the S/N ratio method, the S/N ratio for the total weight of experiments in relation to all quality characteristics will be calculated. The combination with the highest S/N ratio will be selected as an optimal design. Also, the analysis of variance (ANOVA) will be used to determine the significant factors. Fig. 4 illustrates the proposed integrated approach.
ð5Þ
J ¼ 1; :; n
ð6Þ
In the above equation W B denotes the best criterion weight, W w denotes the worst criterion weight, and W j denotes the weight of other criteria. aBj and ajw represent the value derived from comparing the best criterion with other criteria and other criteria against the worst criterion, respectively. The optimal weights should be gained by minimizing the absolute value of the maximum differences with solving the linear model below:
min nL subject to wB aBj wj 6 nL for all j wj ajW wW 6 nL for all j P wj ¼ 1
ð7Þ
j
wj P 0; for all j
ðw1 ; w2 ; :; wn Þ are optimal weights and (nL ) is consistency ratio. 2.4. The proposed methodology In general, optimization problems contain more than one response, which often contradicts each other. In effect, the Taguchi design of experiment method is unable to address multi-response problems when the responses are in conflict with each other. This study presents a multi-response optimization approach to determine the optimal mixture design of high strength self-consolidating concrete (HSSCC), which is undoubtedly a multi-response if the multi quality characteristics of the concrete are taken into consideration. Hence, this study proposes an integrated approach to overcome this crucial gap by linking the involving HSSCC optimization objectives and the parameters. The steps of the proposed approach are as follows: Step 1. Identifying the control factors, their feasible range and quality characteristics (Multi-response optimization problem). Step 2. Calculating the weight of quality characteristic based on preferences of decision maker using Best-Worst method (BWM). Step 3. Selecting adequate Taguchi orthogonal array considering the number of control factors and their levels. There are 18 main orthogonal arrays presented by Taguchi. If proper array are not found among these 18 arrays, the next proper array will be selected. Step 4. Obtaining the values of responses for each quality characteristic by adopting experiments. Then use BWM to calculate the relative weight of each individual experiment with respect to each individual quality characteristic. Step 5. The total weight for each experiment with respect to all quality characteristics will be calculated by multiplying the weight of each quality characteristic step 2 to the weight of
2.5. Optimization of high self-consolidating concrete Evaluation of the optimal mixture design of concrete is a vital issue for achieving an optimal quality [44]. The production of concrete with high quality according to preferences of the manufacturer and with the least cost and use of materials is the goal of using optimization methods. High strength Self-consolidating concrete (HSSCC) is a type of concrete capable of consolidating under its own weight, completely and without separation of aggregates. Self-compacting concrete is also known as self-consolidating concrete due to its ability to exhaust air without vibration. The objectives of optimizing the HSSCC mixture design are as follows: Optimization of the criteria that determine the total quality of the concrete using the decision maker preferences in order to achieve the optimal mixing scheme for high strength selfconsolidating concrete. Optimization of the concrete production cost, which is an important preference of the decision maker.Researchers have been used several quality criteria for concrete in their studies. In this paper, the proposed criteria in the work of Sß imsßek et al. have been selected for optimization using BWM-based Taguchi optimization method [1]. They studied on optimization of high strength selfconsolidating concrete using a TOPSIS-based Taguchi method considering ten quality criteria for high strength self-consolidating concrete performance. The first criterion of concrete performance is the average heat transfer coefficient, which provides information on energy losses and heat damages caused by heat transfer in structures that are located in coastal areas or areas affected by strong winds [45]. The second criterion is the air content, which gives the amount of air in concrete. The third and fourth criteria are the slump flow and T50 time, respectively. The elapsed time from the moment concrete begins to spread from slump cone until its diameter reaches 50 cm is considered as T50 time. T50 is a measure for the filling ability of the concrete. The slump flow is a measure to assess the horizontal free flow of self-consolidating concrete in the absence of obstructions.
Fig. 3. The proposed BWM model.
6
E. Sharifi et al. / Construction and Building Materials 236 (2020) 117547 Table 4 Identified factors and their levels [1]. Factor
A B C D E F
Description
Levels
Cement amount (kg) Water to cementitious ratio (%) Coarse aggregate to fine aggregate ratio (%) Super plasticizer amount (kg/m3) Fly ash (kg) Mixing time (s)
1
2
3
400 0.35 0.60* 1 80 100*
425* 0.37* 0.65 1.25* 100 110
– 0.39 0.70 1.50 120* 120
plasticizer amount, and fly ash having three levels and mixing time having two levels. For sake of simplicity, these factors are indicated by letters A, B, C, D, E and F according to Table 4. Approximated mixture levels before conducting experiments are underlined (*) [1]. 3. Results and discussion In this section, the proposed methodology will be used for optimizing the mixture design of high strength self-consolidating concrete using the following steps: Step 1. Identifying performance optimization objectives, factors and their levels. Ten quality characteristics are selected as performance optimization objectives, moreover, six factors affecting these quality characteristics have been identified, one having two and five having three levels [1]. Step 2. Calculating the weight of quality characteristics using BWM. In this step, by taking into account the decision maker’s preferences weight of each quality characteristics will be calculated using Best-Worst method. The selected best and worst criteria are determined as compressive strength in 28 days (Q 8) and heat transfer coefficient (Q 1). Table 5 and 6 indicate the reference comparison of best to others (BO) and others to worst (OW). Finally, by solving the linear model (7) optimal weights of
Fig. 4. The steps of the proposed methodology.
Table 3 Selected quality characteristics [1]. No. Symbol Quality characteristic 1 2 3 4 5 6 7 8 9 10
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q 10
Target value
Heat transfer coefficient (W/m2K) Air percentage (%) Slump flow (mm) Time (s) T50 Absorbed water percentage (%) Compressive strength 2 days (N/mm2) Compressive strength 7 days (N/mm2) Compressive strength 28 days (N/mm2) Splitting tensile strength 28 days (N/mm2) cost ($$/mm2)
lower the better lower the better Higher the better lower the better lower the better Higher the better Higher the better Higher the better Higher the better lower the better
ðw1 ; w2 ; :; w10 Þ for each criterion and consistency ratio ðnL Þ
will be obtained. Consistency ratio ðnL Þ must be less than 0:1 for pair-wise comparisons to be consistent. Table 7 shows the quality characteristics weights considering the decision maker’s preferences (w101 Þ. Step 3. Selecting adequate Taguchi experimental array. Taguchi experimental array will be selected considering the number of factors and their levels. Since there are five factors having three levels and one factor having two levels a L27 (21 37) orthogonal is used to conduct the experiments. In the first step of experiment procedure, coarse aggregates are mixed with water, then Portland cement and additional water are added to the mix. For the last step, a mixture of water and superplasticizer will be added to the mixture. Mixing time will be started at this point. For each experiment, a 150 mm3 sample will be prepared according to ‘‘TS EN 12390/9” [1]. The Taguchi orthogonal array and the results of the experiment are indicated in Tables 8 and 9 respectively.
Another performance criterion is the percentage of water absorbed by concrete. This criterion shows the strength of concrete against water and the porosity of concrete. Other criteria are splitting tensile strength of concrete on day 28 and compressive strength on days 2, 7 and 28. These criteria give insight into concrete resistance. The last criterion is the cost of production. For more details see [1]. The ten selected criteria are shown in Table 3. For the sake of simplicity, we the ten chosen criteria are represented as Q1–Q10. Sßimsßek et al. considered six factors that affect identified quality characteristics. These factors are the Cement amount, water to cementitious ratio, coarse aggregate to fine aggregate ratio, Super
Table 5 The reference comparison of best to others. Quality criteria
Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
Q10
Best criteria (Q8)
9
7
3
5
7
4
7
1
9
5
7
E. Sharifi et al. / Construction and Building Materials 236 (2020) 117547
Finally, by solving linear model (7) optimal weights of
Table 6 The reference comparison of others to worst. Quality criteria
Worst criteria (Q1)
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10
1 3 7 5 3 6 3 9 1 5
¿1 a
¿1 a
¿1 a
ðw1 2 ; w2 2 ; :; w182 Þ and consistency ratio ðnL Þ for each experiment will be obtained. Consistency ratio of each experiment
ðnL Þ must be less than 0:1 for pair-wise comparisons to be consistent. Table 12 indicates the relative weight of each experiment with respect to each individual quality characteristics ¿1 a
2 ðw1810 Þ. Step 5. Calculating the total weight for each experiment with respect to all quality characteristics. In order to convert a multi-objective problem into a singleobjective problem, the total weight for each experiment with respect to all quality characteristics will be calculated by multi-
¿1 a
Table 7 Quality characteristics weights. No.
Symbol
Quality characteristic
Criteria weight
1 2 3 4 5 6 7 8 9 10
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10
Heat transfer coefficient (W/m2K) Air percentage (%) Slump flow (mm) Time (s) T50 Absorbed water percentage (%) Compressive strength 2 days (N/mm2) Compressive strength 7 days (N/mm2) Compressive strength 28 days (N/mm2) Splitting tensile strength 28 days (N/mm2) cost ($$/mm2)
0.03176 0.059992 0.179976 0.07199 0.059992 0.089988 0.059992 0.322898 0.051422 0.07199 0:037053842
Consistency ratio ðnL Þ
Additionally, using MINITAB software and by analyzing the S/N ratios given in Table 14 the optimal levels for control factors will be obtained. The mixture with the highest S/N ratio will be considered as the optimal design for optimization of high strength selfconsolidating concrete. Fig. 5 illustrates the optimal levels for factors. Results show that the highest S/N ratio is for A2B1C1D1E3F3 combination.
Step 4. Calculating the weight of experiments with respect to each individual quality characteristics. Similar to step 2, the relative weight of each experiment with respect to each individual quality characteristics can be calculated using the BWM method. The best and the worst experiments with respect to each quality characteristics can be determined easily by examining the experiment results. For example, the best and the worst experiments for Q8 are experiment number 11 and 8 respectively. The same process can be applied to the remaining quality characteristics. Tables 10 and 11 indicate the reference comparison of best to others (BO) and others to worst (OW).
Table 8 The proposed Taguchi experimental array. Exp. No.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
2 plying the weights obtained in step 4 and 2 ðw1810 w101 Þ. Table 13 gives the total weight for each experiments considering the decision maker’s preferences. Step 6. Calculating S/N ratio, determining optimal control factors and significance factors. Since the objective is maximizing the total quality, Eq. (3) for larger the better is used to calculate the signal to noise ratio for the total weight for each experiment with respect to all quality characteristics. The S/N ratios are given in Table 14.
Experimental array L18 A
B
C
D
E
F
1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2
1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
1 2 3 1 2 3 2 3 1 3 1 2 2 3 1 3 1 2
1 2 3 2 3 1 1 2 3 3 1 2 3 1 2 2 3 1
1 2 3 2 3 1 3 1 2 2 3 1 1 2 3 3 1 2
3.1. The analysis of variance (ANOVA) In order to determine the significant factors affecting the total quality of HSSCC, ANOVA is required. Table gives the results for ANOVA, p-values less than 0.05 indicate model terms are significant [46]. In this case, cement amount (A), water to the cementitious ratio (B) and mixing time (F) are significant model terms (Table 16). In order to demonstrate the importance of the proposed methodology a case of optimizing a single criterion using traditional Taguchi method will be considered. Assume optimizing the 28 days compressive strength (Q8) is required. Using experimental values in Table 9 and by implanting Taguchi method the optimal levels for control factor would be as A2B1C1D1E1F3 shown in Fig. 6. Comparison of the experimental results for the traditional Taguchi optimization with BWM-based Taguchi optimization are given in Table 17. As it can be seen although implementing traditional Taguchi method slightly improved the value Q8 but other quality characteristics were worsened. For example slump flow (Q3) of 570 was obtained using traditional Taguchi while by using BWM-based Taguchi method slump flow of 790 was achieved (Table 17). Therefore, the proposed BWMbased Taguchi method gave the highest importance weight to the 28 days compressive strength without ignoring other quality criteria. In summary, as mentioned before, Taguchi is incapable of solving multi-objective problems and cannot simultaneously optimize all of the quality characteristics. It can only optimize a single quality criterion regardless of other criteria. Since some of these criteria are conflicting with each other, with improvement in one criterion other criteria might get worst. It is obvious that optimizing a criterion without considering other criteria does not necessarily give us the optimal response. That is why it is essential to implement the proposed methodology for optimization of multi-objective
8
E. Sharifi et al. / Construction and Building Materials 236 (2020) 117547
Table 9 Experiment results based on Taguchi experimental array [1]. Exp. No.
Results
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Q1 (W/m2K)
Q2 %
Q3 mm
Q4 s
Q5 %
Q6 (N/mm2)
Q7 (N/mm2)
Q8 (N/mm2)
Q9 (N/mm2)
Q10 $/mm2
14.568 14.561 14.567 14.565 14.566 14.572 14.57 14.57 14.571 14.559 14.559 14.562 14.562 14.561 14.561 14.556 14.555 14.556
1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0
560 610 710 600 740 690 660 730 730 780 750 760 770 740 770 760 740 750
7 5 4 4 3 3 3 3 3 3 4 4 4 3 3 3 5 5
2.05 2.17 1.79 2.03 2.22 2.14 2.58 2.73 2.46 1.59 2.2 2.01 1.7 2.39 1.91 3.28 2.95 3.46
39.8 30.1 40.1 41.8 40.2 34.2 30.7 30.6 30.2 27.2 37.2 33.1 28.7 30.7 31.7 2.1 25.2 23.5
63.4 58.4 66 62.9 68.2 58.1 59.6 58.1 57 59.4 61.5 55.5 54.5 53.4 56 42.3 55 48.4
77.44 67.66 69.85 65.53 72.19 69.69 70.4 59.51 60.51 71.09 74.52 68.52 69.97 66.77 74.39 64.2 68.26 61.64
4.73 4.6 4.65 4.55 4.7 4.65 4.66 4.41 4.28 4.68 4.5 4.62 4.65 4.58 4.75 4.52 4.62 4.46
45.635 49.03 52.11 46.12 49.612 51.019 48.232 51.676 46.895 53.61 47.536 50.721 53.638 50.227 48.079 53.11 48.73 50.167
Table 10 The reference comparison of best to others. Quality criteria
Best Exp.
Experiments Exp. 1
Exp. 2
Exp. 3
Exp. 4
Exp. 5
Exp. 6
Exp. 7
Exp. 8
Exp. 9
Exp. 10
Exp. 11
Exp. 12
Exp. 13
Exp. 14
Exp. 15
Exp. 16
Exp. 17
Exp. 18
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10
18 10 10 10 10 4 5 11 11 1
5 9 9 9 4 2 4 3 2 1
3 9 7 5 5 6 5 6 5 4
5 9 4 3 2 2 2 5 4 8
5 9 7 3 4 1 4 6 6 2
5 9 3 1 5 2 1 3 2 4
9 9 4 1 5 4 5 5 4 7
8 9 5 1 6 6 5 4 4 3
8 9 3 1 7 6 5 9 7 7
8 9 3 1 6 6 5 7 9 2
2 1 2 1 1 7 5 4 3 8
2 1 2 3 5 3 4 1 1 3
3 1 2 3 4 4 6 5 5 7
3 1 2 3 2 7 6 4 4 9
3 1 3 1 6 6 6 6 6 6
3 1 2 1 3 6 6 2 1 3
1 1 2 1 8 7 9 6 6 8
1 1 3 5 7 8 6 5 5 4
1 1 3 5 9 9 8 7 7 6
Table 11 The reference comparison of others to worst. Quality criteria
Worst Exp.
Experiments Exp. 1
Exp. 2
Exp. 3
Exp. 4
Exp. 5
Exp. 6
Exp. 7
Exp. 8
Exp. 9
Exp. 10
Exp. 11
Exp. 12
Exp. 13
Exp. 14
Exp. 15
Exp. 16
Exp. 17
Exp. 18
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10
6 1 1 1 18 18 16 8 9 13
5 1 1 1 6 8 6 7 8 9
7 1 3 5 5 4 5 4 5 6
5 1 6 7 8 8 8 5 6 2
5 1 3 7 6 9 6 4 4 2
5 1 7 9 5 8 9 7 8 6
1 1 6 9 5 6 5 5 6 3
2 1 5 9 4 4 5 6 6 7
2 1 7 9 3 4 5 1 3 3
2 1 7 9 4 4 5 3 1 2
8 9 9 9 9 3 5 6 7 2
8 9 7 7 5 7 6 9 9 7
7 9 8 7 6 6 4 5 5 3
7 9 8 7 8 3 4 6 6 1
7 9 7 9 4 4 4 4 4 4
7 9 8 9 7 4 4 8 9 7
9 9 8 9 2 3 1 4 4 2
9 9 7 5 3 2 4 5 5 6
9 9 7 5 1 1 2 3 3 4
Table 12 The relative weight of each experiment with respect to each individual quality characteristics. Experiments
Exp.1 Exp.2 Exp.3 Exp.4 Exp.5 Exp.6
Quality characteristics Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
Q 10
0.0313 0.0521 0.0313 0.0313 0.0313 0.0113
0.0111 0.0111 0.0111 0.0111 0.0111 0.0111
0.0112 0.0224 0.0392 0.0224 0.0523 0.0392
0.0074 0.0205 0.0341 0.0341 0.0845 0.0845
0.0533 0.0427 0.1067 0.0533 0.0427 0.0427
0.1046 0.0349 0.1046 0.1719 0.1046 0.0523
0.0581 0.0465 0.1162 0.0581 0.1910 0.0465
0.0731 0.0365 0.0438 0.0365 0.0731 0.0438
0.0920 0.0368 0.0460 0.0307 0.0920 0.0460
0.1857 0.0565 0.0283 0.0727 0.0565 0.0323
9
E. Sharifi et al. / Construction and Building Materials 236 (2020) 117547 Table 12 (continued) Experiments
Exp.7 Exp.8 Exp.9 Exp.10 Exp.11 Exp.12 Exp.13 Exp.14 Exp.15 Exp.16 Exp.17 Exp.18
nL
Quality characteristics Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
Q 10
0.0196 0.0196 0.0196 0.0782 0.0782 0.0521 0.0521 0.0521 0.0521 0.1292 0.1292 0.1292 0.0272
0.0111 0.0111 0.0111 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.0000
0.0314 0.0523 0.0523 0.1288 0.0784 0.0784 0.0784 0.0523 0.0784 0.0784 0.0523 0.0523 0.0280
0.0845 0.0845 0.0845 0.0845 0.0341 0.0341 0.0341 0.0845 0.0845 0.0845 0.0205 0.0205 0.0178
0.0356 0.0305 0.0356 0.1753 0.0427 0.0533 0.1067 0.0356 0.0711 0.0267 0.0305 0.0152 0.0381
0.0349 0.0349 0.0349 0.0299 0.0697 0.0523 0.0299 0.0349 0.0349 0.0299 0.0262 0.0149 0.0374
0.0465 0.0465 0.0465 0.0465 0.0581 0.0387 0.0387 0.0387 0.0387 0.0166 0.0387 0.0291 0.0415
0.0548 0.0157 0.0313 0.0548 0.1801 0.0438 0.0548 0.0365 0.1096 0.0365 0.0438 0.0313 0.0391
0.0460 0.0263 0.0131 0.0613 0.1512 0.0368 0.0460 0.0307 0.1512 0.0307 0.0368 0.0263 0.0329
0.0754 0.0323 0.0727 0.0283 0.0754 0.0323 0.0162 0.0377 0.0754 0.0283 0.0565 0.0377 0.0404
Table 13 The total weight for each experiments considering the decision maker’s preferences. Exp. No.
Total weight
Exp.1 Exp.2 Exp.3 Exp.4 Exp.5 Exp.6 Exp.7 Exp.8 Exp.9 Exp.10 Exp.11 Exp.12 Exp.13 Exp.14 Exp.15 Exp.16 Exp.17 Exp.18 Total
0.0620066 0.0340732 0.0525137 0.0489045 0.0729759 0.0430691 0.0465633 0.0332666 0.0408579 0.0766233 0.1087108 0.0528242 0.0568566 0.0468281 0.0861675 0.0509908 0.0476067 0.0391610 1.00
Table 14 S/N ratios for the total weight. Experiment
S/N ratio
Exp.1 Exp.2 Exp.3 Exp.4 Exp.5 Exp.6 Exp.7 Exp.8 Exp.9 Exp.10 Exp.11 Exp.12 Exp.13 Exp.14 Exp.15 Exp.16 Exp.17 Exp.18
24.1512 29.3517 25.5945 26.213 22.7364 27.3167 26.6391 29.5598 27.7745 22.3128 19.2745 25.5433 24.9044 26.5899 21.2931 25.8502 26.4466 28.1429
Fig. 5. The optimal level for each factor using BWM-based Taguchi.
10
E. Sharifi et al. / Construction and Building Materials 236 (2020) 117547
Table 15 ANOVA for BWM-based Taguchi S/N ratio. Analysis of variance for S/N ratios Source
DF
Seq SS
Adj SS
Adj MS
F-value
P-value
Contribution (%)
A B C D E F Residua l Error Total
1 2 2 2 2 2 6 17
20.012 31.922 2.740 16.317 5.702 35.574 14.931 127.197
20.012 31.922 2.740 16.317 5.702 35.574 14.931
20.012 15.961 1.370 8.158 2.851 17.787 2.489
8.04 6.41 0.55 3.28 1.15 7.15
0.030 0.032 0.603 0.109 0.379 0.026
16% 25% 2% 13% 4% 28% 12%
Table 16 Quality characteristics improvement in optimal mixture design. Symbol
Quality characteristic
Estimated mixture design
Optimal mixture design using BWM-based Taguchi
Improvement (%)
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10
Heat transfer coefficient (W/m2K) Air percentage (%) Slump flow (mm) Time (s) T50 Absorbed water percentage (%) Compressive strength 2 days (N/mm2) Compressive strength 7 days (N/mm2) Compressive strength 28 days (N/mm2) Splitting tensile strength 28 days (N/mm2) cost ($$/mm2)
14.56 0.1 770 3.85 1.7 29.34 56.3 72.21 4.75 52.76
14.55 0.1 790 3 1.5 34.96 61.25 78 5.1 49.1
0.07% 0.00% 2.53% 28.33% 13.33% 16.08% 8.08% 7.42% 6.86% 7.45%
Fig. 6. The optimal level for each factor using traditional Taguchi.
11
E. Sharifi et al. / Construction and Building Materials 236 (2020) 117547 Table 17 Result comparison for the traditional Taguchi method and BWM-based Taguchi optimization. Symbol
Quality characteristic
Optimal mixture design using BWM-based Taguchi
Optimal mixture design for Q8 using traditional Taguchi method
Improvement (%)
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10
Heat transfer coefficient (W/m2K) Air percentage (%) Slump flow (mm) Time (s) T50 Absorbed water percentage (%) Compressive strength 2 days (N/mm2) Compressive strength 7 days (N/mm2) Compressive strength 28 days (N/mm2) Splitting tensile strength 28 days (N/mm2) cost ($$/mm2)
14.55 0.1 790 3 1.5 34.96 61.25 78 5.1 49.1
14.56 0.1 570 4.94 0.02 36.32 59.1 78.95 4.71 51.3
0.07% 0.00% 38.60% 39.27% 25.00% 3.89% 3.51% 1.20% 8.28% 4.29%
problems since BWM-based Taguchi provides the opportunity to optimize all quality criteria based on their importance weight. 4. Conclusion Several quality characteristics of high strength selfconsolidating concrete are contradicting each other, therefore, consequently, it is considered as a multi-response problem. Taguchi optimization method is incapable of solving multi-objective problems and cannot simultaneously optimize all of the quality characteristics. In order to address this issue, in this study, a Taguchi optimization method is developed using Best-Worst MultiCriteria Decision-Making technique to determine the optimal mixture design and significant factors affecting these quality criteria. Using Best-Worst method weights of quality characteristics are obtained according to the decision maker’s preferences. Then, by implementing Taguchi method results are obtained for each experiment. Afterwards, each experiment is weighted with respect to each quality characteristic using BWM. After computing overall weights, optimal mixture design is determined as A2B1C1D1E3F3. Values for control factors according to this combination are 425 kg cement (A), 0.35% water to cementitious (B), 0.60% coarse aggregate to fine aggregate (C), 1 kg/m3 super plasticizer (D), 120 kg fly ash (E) and mixing time (F) of 120 s. Finally, using analysis of variance (ANOVA) the significant factors with the most influences on the total quality of concrete were determined as mixing time, cement amount and water to cementitious, respectively. Using a case study, the preferences of optimal mixture design overestimated mixture design were illustrated. Significant improvement in properties of high strength self-consolidating concrete satisfied the decision maker’s preferences. Optimization of various manufacturing procedures and chemical compounds can be investigated using BWM-based Taguchi method as a future study for this research. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References [1] B. Sß imsßek, Y.T. Iç, E.H. Sßimsßek, A TOPSIS-based Taguchi optimization to determine optimal mixture proportions of the high strength self-compacting concrete, Chemom. Intell. Lab. Syst. (2013), https://doi.org/10.1016/j. chemolab.2013.03.012. [2] M.R.M. Aliha, A. Razmi, A. Mousavi, Fracture study of concrete composites with synthetic fibers additive under modes I and III using ENDB specimen, Constr. Build. Mater. 190 (2018) 612–622.
[3] M. Fakhri, E. Amoosoltani, M.R.M. Aliha, Crack behavior analysis of roller compacted concrete mixtures containing reclaimed asphalt pavement and crumb rubber, Eng. Fract. Mech. 180 (2017) 43–59. [4] H.R. Fattahi Amirdehi, M.R.M. Aliha, A. Moniri, A.R. Torabi, Using the generalized maximum tangential stress criterion to predict mode II fracture of hot mix asphalt in terms of mode I results – a statistical analysis, Constr. Build. Mater. 213 (2019), https://doi.org/10.1016/ j.conbuildmat.2019.04.067. [5] H. Ziari, M.R.M. Aliha, A. Moniri, Y. Saghafi, Crack resistance of hot mix asphalt containing different percentages of reclaimed asphalt pavement and glass fiber, Constr. Build. Mater. 230 (2020), https://doi.org/10.1016/J. CONBUILDMAT.2019.117015 117015. [6] M.R.M. Aliha, M. Ayatollahi, Mixed mode I/II brittle fracture evaluation of marble using SCB specimen, Procedia Engineer. 10 (2011) 311–318. [7] M.R.M. Aliha, M. Ayatollahi, Rock fracture toughness study using cracked chevron notched Brazilian disc specimen under pure modes I and II loading–A statistical approach, Theor. Appl. Fract. Mec. 69 (2014) 17–25. [8] H. Tanyildizi, M. Sßahin, Application of Taguchi method for optimization of concrete strengthened with polymer after high temperature, Constr. Build. Mater. (2015), https://doi.org/10.1016/j.conbuildmat.2015.01.039. [9] H. Ziari, A. Moniri, Laboratory evaluation of the effect of synthetic Polyolefin-glass fibers on performance properties of hot mix asphalt, Constr. Build. Mater. 213 (2019) 459–468, https://doi.org/10.1016/j.conbuildmat. 2019.04.084. [10] H. Ziari, A. Moniri, P. Bahri, Y. Saghafi, The effect of rejuvenators on the aging resistance of recycled asphalt mixtures, Constr. Build. Mater. 224 (2019) 89– 98, https://doi.org/10.1016/j.conbuildmat.2019.06.181. [11] N. Celik, G. Pusat, E. Turgut, Application of Taguchi method and grey relational analysis on a turbulated heat exchanger, Int. J. Therm. Sci. (2018), https://doi. org/10.1016/j.ijthermalsci.2017.10.007. [12] D. Ji, Z. Wei, S. Mazzoni, M. Mengarelli, S. Rajoo, J. Zhao, J. Pou, A. Romagnoli, Thermoelectric generation for waste heat recovery: application of a system level design optimization approach via Taguchi method, Energy Convers. Manage. (2018), https://doi.org/10.1016/j.enconman.2018.06.016. [13] E. Teimortashlu, M. Dehestani, M. Jalal, Application of Taguchi method for compressive strength optimization of tertiary blended self-compacting mortar, Constr. Build. Mater. (2018), https://doi.org/10.1016/ j.conbuildmat.2018.09.165. [14] L. Katata-Seru, T.C. Lebepe, O.S. Aremu, I. Bahadur, Application of Taguchi method to optimize garlic essential oil nanoemulsions, J. Mol. Liq. (2017), https://doi.org/10.1016/j.molliq.2017.09.007. [15] W.C. Chen, D. Kurniawan, Process parameters optimization for multiple quality characteristics in plastic injection molding using Taguchi method, BPNN, GA, and hybrid PSO-GA, Int. J. Precis. Eng. Manuf. (2014), https://doi. org/10.1007/s12541-014-0507-6. [16] W.C. Chen, M.H. Nguyen, W.H. Chiu, T.N. Chen, P.H. Tai, Optimization of the plastic injection molding process using the Taguchi method, RSM, and hybrid GA-PSO, Int. J. Adv. Manuf. Technol. (2016), https://doi.org/10.1007/s00170015-7683-0. [17] R. Pareek, J. Bhamniya, Optimization of injection moulding process using Taguchi and ANOVA, Int. J. Sci. Eng. Res. (2013). [18] N.C. Fei, N.M. Mehat, S. Kamaruddin, Practical applications of Taguchi method for optimization of processing parameters for plastic injection moulding: a retrospective review, ISRN Ind. Eng. (2013), https://doi.org/10.1155/2013/ 462174. [19] B.M. Gopalsamy, B. Mondal, S. Ghosh, Taguchi method and anova: an approach for process parameters optimization of hard machining while machining hardened steel, J. Sci. Ind. Res. (India) (2009). [20] A. Mehta, R. Siddique, B.P. Singh, S. Aggoun, G. Łagód, D. Barnat-Hunek, Influence of various parameters on strength and absorption properties of fly ash based geopolymer concrete designed by Taguchi method, Constr. Build. Mater. (2017), https://doi.org/10.1016/j.conbuildmat.2017.06.066. [21] K. Jafari, V. Toufigh, Experimental and analytical evaluation of rubberized polymer concrete, Constr. Build. Mater. (2017), https://doi.org/10.1016/ j.conbuildmat.2017.08.097.
12
E. Sharifi et al. / Construction and Building Materials 236 (2020) 117547
[22] K. Jafari, M. Tabatabaeian, A. Joshaghani, T. Ozbakkaloglu, Optimizing the mixture design of polymer concrete: An experimental investigation, Constr. Build. Mater. (2018), https://doi.org/10.1016/j.conbuildmat.2018.01.191. [23] F.A. Alkaabneh, M. Barghash, I. Mishael, A combined analytical hierarchical process (AHP) and Taguchi experimental design (TED) for plastic injection molding process settings, Int. J. Adv. Manuf. Technol. 66 (2013) 679–694, https://doi.org/10.1007/s00170-012-4357-z. [24] J. Rezaei, Best-worst multi-criteria decision-making method, Omega (United Kingdom). (2015), https://doi.org/10.1016/j.omega.2014.11.009. [25] J. Rezaei, J. Wang, L. Tavasszy, Linking supplier development to supplier segmentation using Best Worst Method, Expert Syst. Appl. (2015), https://doi. org/10.1016/j.eswa.2015.07.073. [26] H. Badri Ahmadi, S. Kusi-Sarpong, J. Rezaei, Assessing the social sustainability of supply chains using Best Worst Method, Resour. Conserv. Recycl. (2017), https://doi.org/10.1016/j.resconrec.2017.07.020. [27] J. Rezaei, T. Nispeling, J. Sarkis, L. Tavasszy, A supplier selection life cycle approach integrating traditional and environmental criteria using the best worst method, J. Clean. Prod. (2016), https://doi.org/10.1016/j. jclepro.2016.06.125. [28] J. Rezaei, A. Hemmes, L. Tavasszy, Multi-criteria decision-making for complex bundling configurations in surface transportation of air freight, J. Air Transp. Manage. (2017), https://doi.org/10.1016/j.jairtraman.2016.02.006. [29] H. Gupta, Evaluating service quality of airline industry using hybrid best worst method and VIKOR, J. Air Transp. Manage. (2018), https://doi.org/10.1016/ j.jairtraman.2017.06.001. [30] P. Shojaei, S.A. Seyed Haeri, S. Mohammadi, Airports evaluation and ranking model using Taguchi loss function, best-worst method and VIKOR technique, J. Air Transp. Manage. (2018), https://doi.org/10.1016/j.jairtraman.2017.05.006. [31] W.N.K. Wan Ahmad, J. Rezaei, S. Sadaghiani, L.A. Tavasszy, Evaluation of the external forces affecting the sustainability of oil and gas supply chain using Best Worst Method, J. Clean. Prod. (2017), https://doi.org/10.1016/j. jclepro.2017.03.166. [32] P. Gupta, S. Anand, H. Gupta, Developing a roadmap to overcome barriers to energy efficiency in buildings using best worst method, Sustain. Cities Soc. (2017), https://doi.org/10.1016/j.scs.2017.02.005. [33] H. Aboutorab, M. Saberi, M.R. Asadabadi, O. Hussain, E. Chang, ZBWM: the Znumber extension of Best Worst Method and its application for supplier development, Expert Syst. Appl. (2018), https://doi.org/10.1016/j. eswa.2018.04.015.
[34] A. Sotoudeh-Anvari, S.J. Sadjadi, S.M. Hadji Molana, S. Sadi-Nezhad, A new MCDM-based approach using BWM and SAW for optimal search model, Decis. Sci. Lett. (2018) 395–404, https://doi.org/10.5267/j.dsl.2018.2.001. [35] S.J. Sadjadi, M. Karimi, Best-worst multi-criteria decision-making method: a robust approach, Decis. Sci. Lett. (2018) 323–340, https://doi.org/10.5267/j. dsl.2018.3.003. [36] S. Guo, H. Zhao, Fuzzy best-worst multi-criteria decision-making method and its applications, Knowledge-Based Syst. (2017), https://doi.org/10.1016/ j.knosys.2017.01.010. [37] Q. Mou, Z. Xu, H. Liao, An intuitionistic fuzzy multiplicative best-worst method for multi-criteria group decision making, Inf. Sci. (Ny). (2016), https://doi.org/ 10.1016/j.ins.2016.08.074. [38] A. Hafezalkotob, A. Hafezalkotob, A novel approach for combination of individual and group decisions based on fuzzy best-worst method, Appl. Soft Comput. J. (2017), https://doi.org/10.1016/j.asoc.2017.05.036. [39] M.P.B.C.A. Arbeláez Jaramillo, J.W. Rigueira Victor, J.R. Martí Vargas, P. Serna Ros, Reduced models test for the characterization of the rheologic properties of self-compacting concrete (SCC), RILEM Publications SARL, 2003. [40] H. Ziari, A.T. Barakoohi, A. Moniri, Laboratory investigation of the effect of temperature on frictional properties of concrete pavements containing crushed glass, Int. J. Pavement Res. Technol. 10 (2017) 297–303, https://doi. org/10.1016/j.ijprt.2017.04.006. [41] J. Li, W. Cao, The heat transfer coefficient of recycled concrete bricks combination with EPS insulation board wall, Math. Probl. Eng. 2015 (2015), https://doi.org/10.1155/2015/695962. [42] G. Taguchi, Introduction to Taguchi methods, Eng. (1988). [43] J. Rezaei, Best-worst multi-criteria decision-making method: Some properties and a linear model, Omega (United Kingdom). (2016), https://doi.org/10.1016/ j.omega.2015.12.001. [44] S. Yan, H.C. Lin, Y.C. Liu, Optimal schedule adjustments for supplying ready mixed concrete following incidents, Autom. Constr. (2011), https://doi.org/ 10.1016/j.autcon.2011.04.005. [45] Y. Lee, M.S. Choi, S.T. Yi, J.K. Kim, Experimental study on the convective heat transfer coefficient of early-age concrete, Cem. Concr. Compos. (2009), https:// doi.org/10.1016/j.cemconcomp.2008.09.009. [46] M.J. Ayazi, A. Moniri, P. Barghabany, Moisture susceptibility of warm mixedreclaimed asphalt pavement containing Sasobit and Zycotherm additives, Pet. Sci. Technol. 35 (2017), https://doi.org/10.1080/10916466.2017.1290655.