Decision Support Model for Design of High-Performance Concrete Mixtures Using Two-Phase AHP-TOPSIS Approach

Concrete mix design is the science to obtain concrete proportions of cement, water, and aggregate, based on the particular concrete design method and their mix design parameters. However, the suitability of concrete proportion for high-performance concrete depends on resulting mix factors, namely, water, cement, fine aggregate, and coarse aggregate ratios. )is paper implements the multicriteria decision-making techniques (MCDM) for ranking concrete mix factors and representative mix design methods. )e study presents a framework to identify critical mix factors found from the concrete mix design methods for high-performance concrete using the two-phase AHP and TOPSIS approach. )ree methods of concrete mix design, namely, American Concrete Institute (ACI) mix design method, Department of Energy (DOE) method, and Fineness Modulus (FM) method, are considered for rankingmix designmethods and the resultingmix factors.)ree hierarchy levels, having three criteria and seven subcriteria, and three alternatives are considered. )e present research is attempted to provide MCDM framework to rank the concrete mix guidelines for any given environment such as concrete under sulphate and chloride attack and for evolving the performance-based concrete mix design techniques. Sensitivity and validation analysis is also provided to demonstrate the effectiveness of the proposed approach.


Introduction
Concrete mix design is the process of deciding the proportioning of the ingredients of concrete using wellexperimented design guidelines to get the specific performance of concrete. e various design guidelines that include the mix parameters such as properties of cement, minimum and maximum cement quantity, water-to-cement ratio, mixing water requirements, aggregates-to-cement ratio, properties of aggregates, aggregates grading, and proportions of aggregate may change with different concrete exposure conditions, with required properties of concrete in green or hardened state, and with performance requirement. e mix factors significantly affecting the suitability of mix proportion for high-performance concrete are taken into consideration for ranking decision model. e concrete workability, strength and durability affecting mix factor, water-cement (w/c) ratio, concrete denseness indicators, density and fine aggregate to total aggregate (FA/T) ratio, concrete quality indicators, fine aggregate to cement (FA/c) ratio, and total aggregate to cement (T/c) ratio are considered. Other factors that may affect the suitability of mix proportion for high-performance concrete are coarse aggregate to cement (CA/c) and cost of concrete. Due to interdependency among the concrete mix factors, it is not an easy task to select the concrete mix factors and mix design methods guidelines for particular environment and for highperformance concrete. Multi-Criteria Decision Making (MCDM) techniques may be employed to ascertain the criticality of mix factors and grading of mix design techniques. e research work related to the implementation of MCDM techniques in civil engineering is mainly devoted to construction technology. e application of MCDM approaches in the civil engineering theoretical concepts and methods are very scarce. An integrated model of median ranked sample set (MRSS) and an analytic network process (ANP) has been proposed by Younes et al.
[1] to select a suitable landfill site. Kabir et al. [2] present a review of the application of MCDM procedures and their taxonomy in the field of infrastructure management. Caterino et al. [3] studied the applicability and performance of most widely adopted MCDM methods for the seismic retrofitting technologies of structures. ey have concluded that the technique for order of preference by similarity to ideal solution (TOPSIS) and VIKOR methodologies are more suitable for the retrofit technology selection because of potentiality to deal with each kind of judgment criteria, parameters, and involving choices. Zavadskas et al. [4] studied the accuracy of ranking in a particular situation obtained in the TOPSIS methods. AHP is implemented by Do and Kim [5] to select an optimal patching material for concrete repair satisfying chemical performance and physical performance. Cheng and Kang [6] have proposed a fuzzy preference relationbased Multi-Criteria Prospect Model (MCPM) for the construction contractor selection. A multiattribute fuzzy weighted average approach-assisted MCDM process is used by Alhumaidi [7] for the selection of construction contractors having a set of attributes. AHP model-based MCDM methodology has successfully been applied for the sustainability assessment in civil engineering [8,9]. Antucheviciene et al. [10] have presented a review of decisionmaking methods and applications in civil engineering. Monghasemi et al. [11] have developed a new MCDM model to optimize the time-cost-quality in construction projects. Do and Kim [5] applied AHP to select an optimal repair material for a chloride-deteriorated concrete member by focusing on the chemical and physical performance quantitatively. Ozbay et al. [12] use Taguchi's experiment design methodology for optimal design for analysis of mix proportion parameters of high-strength self-compacting concrete. e optimal levels for mix proportions are determined for maximization of ultrasonic pulse velocity (UPV), compressive strength, and splitting tensile strength, and for the minimization of air content, water permeability, and water absorption values. De Angelis et al. [13] propose Multi-Criteria Decision Making (MCDM) analysis based on the TOPSIS method for comparing four building components with conflicting structural and environmental performance criteria. Hamdia et al. [14] present fuzzy Analytic Hierarchy Process-(FAHP-) based assessment model to estimate the importance of structural assessment criteria of damages and deteriorations for concrete buildings. e applications of MCDM to civil engineering are limited to the general problems, and they are not illustrative enough to evaluate the specific problems such as design methods, guidelines, and theoretical concept. e present study is the maiden attempt to apply MCDM techniques to select the mix design technique in concrete technology for high-performance concrete. Two popular MCDM techniques, namely, AHP and TOPSIS approach, which have demonstrated their applicability in different fields, are implemented for the problem of preferential mix design method applicable to high-performance concrete.

AHP and TOPSIS
While designing a concrete mix for achieving particular performance, the designer chooses the mix design method from the available methods and considers the mix parameters as per the requirement of the method. e number of MCDM methods has been developed for value measurement, goal, preference level, and outranking selection. e different MCDM method depends on the distinct types of inputs and results in equally distinct outputs but the most suitable method is which best satisfies decision-making and puts forward sufficient confidence to translate their decisions into actions [15]. Among the available MCDM techniques, the integrated AHP [16] and TOPSIS [17] approach has been chosen for the present study. e selected approach exploits the advantages of both the AHP and TOPSIS method. e advantage of using the integrated two-phase AHP-TOPSIS approach over the individual MCDM methods [18] is presented in Table 1.

Methodology
e selection of the preferential mix design method for achieving particular performance is an MCDM process. e proposed model decomposes the process into three levels, concrete mix objective criteria, resulting mix factors as subcriteria, and mix design methods as alternatives. Problem formulation determines the problem aims, assessment criteria, and experts. e problem criteria are identified based on experts' opinion [19][20][21][22][23]. e study adopted an integrated and more realistic MCDM methodology, two-phase AHP and TOPSIS approach, to select the priority concrete mix for high performance. For this purpose, the weights that are obtained from AHP calculations are used in TOPSIS calculations. e selection steps determine the weights (importance) of the mix factors and the prioritization of the mix design method.

Proposed Approach.
e main steps of the proposed approach to select the preferential mix design method are as follows.
Step 1. Develop the problem criteria hierarchy and normalize the decision matrix and calculate the weights of matrix by AHP following the procedure outlines by Saaty [16].
In this step, the criteria of the problem (preferential mix design method for extreme environment) are identified as per the methodology, and the problem is decomposed into three levels as per experts' opinion, authors' experience, and literature review. In level 1, the most important factors of mix design, namely, workability, strength, and durability are considered as a criterion of the problem. e concrete mix parameters for extreme environment (level 2 subcriteria) are identified as water-cement (w/c) ratio, density, coarse aggregate-cement (CA/c) ratio, total aggregate-cement (T/c) ratio, fine aggregate-cement (FA/c) ratio, fine aggregatetotal aggregate (FA/T) ratio, and cost. In level 3, three mix design methods, namely, the ACI mix design method, DOE mix design method, and FM mix design method, are considered as alternatives. e hierarchical structure of the preferential mix design method for an extreme environment is depicted in Figure 1. e pairwise comparisons of various criteria and subcriteria are done as shown in Tables A1-A3 (Appendix-A). e pairwise comparison matrix of the main criteria of Table A1 is then used to normalize the decision matrix, and the weights of the matrix are calculated.
Step 2. Consistency check of each pairwise comparison matrix using AHP [16]. e consistency of the assessment process is checked by calculating the CI and CR value of each pairwise comparison matrix and the aggregate matrix [16] and [24]. e calculated values of CI and CR are below 0.10 (maximum permissible value), indicating a satisfactory degree of consistency.
Step 3. Estimate the relative weights of the alternatives with respect to each weight of subcriterion. e relative weights of the objective criteria, namely, workability, strength and durability, and design mix parameters are obtained from the aggregated values using the eigenvector method [16], and afterward, the design mix methods weight for each mix factors are calculated. e relative weights of three design methods with respect to weight of each design mix factor are given in Table A4 (Appendix-A).
Calculate the normalized decision matrix and calculate the weighted normalized decision matrix, following the methodology is given by Hwang and Yoon [17]. e obtained normalized decision matrix and weighted normalized decision matrix are shown in Tables A5 and A6 (Appendix-I).
Step 5. Determine the ideal and negative ideal solutions and calculate the separation measures. e ideal solution (A * ) and negative ideal solution (A − ) is determined from weighted normalized decision matrix and separation distances of each alternative are calculated from the positive (D * j ) and from a negative ideal solution (D j ) [17]. e separation distances from an ideal solution (D * j ) and negative ideal solution (D − j ) are given in Table A7.
Step 6. Calculate the relative closeness to the ideal solution and rank the preference order.
e relative closeness of each alternative (C * j ) determination to the ideal solution is the nal step of the TOPSIS methodology [17]. e two-phase AHP and TOPSIS approach results including the ranking of alternative as per values of the relative closeness to the ideal solution are shown in Table 2.
e ranking of the alternatives in descending order is the DOE method, ACI method, and FM method of concrete mix design for an extreme environment.

Sensitivity Analysis.
e sensitivity analysis demonstrates the in uence and stability of criterion's weight (mix factors weights) on alternative (mix design method) selection. us, the concrete method selection robustness may be veri ed by exchanging criterion weight. Each criterionʼs weight has been exchanged with another criterion's weights which gives various combinations resulting from the three main criteria. e weight of three main criteria, i.e., (workability, strength, and aggregate size) considered as w1, w2, and w3 are obtained as 0.297, 0.539, and 0.164. On using these weights, the model gives the C * j , for ACI, DOE, and FM as 0.502,0530, and 0.439. Similarly, by exchanging weight, w1, w2, and w3 may further be used in sensitivity analysis. e sensitivity analysis output is summarized in Table 3 and Figure 2. e rst condition of Table 3 expresses the original results of the two-phase AHP and TOPSIS methodology. e DOE method has the highest C * j value of 0.541 from 0.530 when the rst and third criteria weights are exchanged in condition 2. Also, the DOE method has the lowest value of 0.472 when the rst and second criteria weights are exchanged in condition 4. e ACI method will have the highest C * j value of 0.559 from 0.502 when the rst and second criteria weights are exchanged in condition 4. e ACI method is having the lowest value of 0.502 in the rst condition. e FM method will have the highest C * j value of 0.542 from 0.439 when the rst and second criteria weights are exchanged in condition 4. e FM method will have the lowest value of 0.439 when the rst condition is met.

Validation.
e quantitative optimum values of concrete mix factors found in the literature (Table 4). Helmy [28] may play a signi cant role while comparing various subcriteria of workability, strength, and durability, i.e., w/c density, CA/c, T/c, FA/c, FA/T, and cost for identifying a preferential mix design method for high-performance concrete. us, the various mix design guidelines for optimum values giving dense concrete with the lowest cost could be realized. e study reveals that the DOE mix design method produces a mix with the lowest cement content and gives the best workability in comparison to the other mix design method of ACI and FM. Moreover, from the published literature, it has been found that the performance of the DOE mix design method is better than the other mix design technique which is in line with the obtained result in the present study. us, the ranking obtained in the present research matches with the literature results.

Discussion
e results of the two-phase AHP and TOPSIS approach implemented to preferential mix design technique to develop high-performance concrete suggested that the Department of Energy (DOE) method of mix design is the best choice for high-performance concrete having objective factors as workability, strength, and durability, and mix design parameters as w/c ratio, density, CA/c ratio, T/c ratio, FA/c ratio, FA/T ratio, and cost. e ranking of the mix design method predicted by the two-phase AHP and TOPSIS approach is also compared with a predicted ranking of the mix design method when only the AHP approach is applied. e two MCDM techniques, AHP-based and integrated AHP-TOPSIS-based approach, suggest that the DOE method is the preferred design mix method for performance in an extreme environment as depicted in Figure 3. However, the preference level of the mix design method is not the same in two MCDM techniques. e AHP approach suggests that the preference level of the DOE method is double than the preference level of the ACI method and the FM method. e two-phase AHP-TOPSIS approach predicts a more or less similar level of preference for the three mix design technique. e preference level given by the AHP approach is 57%, 24%, and 19%, respectively, for DOE method, ACI method, and FM method. e closeness coe cients to rank priority level obtained in the two-phase AHP-TOPSIS approach are 0.53, 0.50, and 0.44, respectively, for the DOE method, ACI method, and FM method. e sensitivity analysis also shows the stability of the priority of the DOE method. e DOE method prioritization will change to the American Concrete Institute (ACI) method when the workability criterion given more weight than the strength criteria weight. When the durability criterion has more weights as compared to workability and strength criterion, the DOE method and the ACI method have equal preference. e neness modulus method, which is a relatively older mix design method, has also all capabilities of developing into an advanced mix design technique

Advances in Civil Engineering
for high-performance concrete as the closeness coe cients are found to be in close proximity.

Ranking of Design Mix Parameters (Subcriteria).
ere are seven subcriteria, namely, w/c ratio, density, CA/ c ratio, T/c ratio, FA/c ratio, FA/T ratio, and cost, under each main criterion. e weight ranking of the subcriteria with respect to objective criteria obtained by the AHP approach is represented in Figure 4. e weight of the seven subcriteria is varying with respect to objective criteria. e sensitivity of design methods with interchanging the weight of subcriteria is presented and discussed in the following section.

Water-Cement Ratio.
e water-cement ratio is a very important and critical factor for the mix design technique. e workability, strength, and durability of fresh and hardened concrete are strongly dependent on this factor. e water-cement ratio has the highest weight for workability and strength criteria as evident from Figure 4. Figure 5 shows the sensitivity of the mix design method with respect to w/c ratio calculated using the TOPSIS approach. e sensitivity for the DOE method with respect to the watercement ratio is stable as the closeness coe cient increases with increase of w/c ratio weight.

Density and Fine Aggregate to Total Aggregate Ratio.
e density and ne aggregate to total aggregate (FA/T) ratio factors is the indicator of the denseness of the concrete. ese two factors are important for the mix design in an extreme environment. e density is the second in weight rank and rank is more or less same for all the objective criteria as presented in Figure 4. e weighted rank of the ne aggregate to total aggregate (FA/ T) ratio is second last in the list. Figures 6 and 7 show the sensitivity of the mix design method with respect to density and FA/T ratio factors calculated using the TOPSIS approach. e two factors are sensitive to change the preference of the mix design technique for an extreme environment performance when the weight of density and FA/T changes. When the weight of FA/T is higher, preference of method is changed from the DOE method to FM method.

Coarse Aggregate to Cement Ratio.
e coarse aggregate to cement (CA/c) ratio is an important parameter for  Advances in Civil Engineering 5 the design mix technique in an extreme environment performance and factor need to be of optimum value for concrete mix. e factor is sensitive enough to change the preference of the mix design method for an extreme environment when the weight of CA/c changes. When the weight of CA/c is more, the mix method preference is changed from the DOE method to the ACI method. e sensitivity of the mix design technique with respect to density and CA/c ratio is shown in Figure 8.

Fine Aggregate to Cement Ratio and Total Aggregate to Cement
Ratio. e ne aggregate to cement (FA/c) ratio and total aggregate to cement (T/c) ratio are the indicators of the concrete quality. ese factors are also signi cant for the design mix technique in an extreme environment performance. FA/c ratio and T/c ratio are of intermediate weights as shown in Figure 4. e sensitivity for the ACI method with respect to FA/c ratio and T/c ratio is stable as closeness coe cient increases with an increase of factor ratios weights. Figures 9 and 10 depict the sensitivity of mix design technique with respect to FA/ c and TA/c ratio.

Cost.
e cost is the important factor of the mix design technique for an extreme environment performance as the additional cost is incurred to increase concrete durability in an adverse environment and to improve the concrete workability and strength. e weighted rank of cost is the last for workability and strength criteria, and it is the rst weight rank for durability criteria as given in Figure 4. It is clear from Figure 11 that portrays the sensitivity of mix design technique with respect to cost that the sensitivity for the DOE method with respect to cost ratio is stable when there is a minor change in the cost of weight. However, mix technique preference changes with the major increase in weight (importance) of cost.

Conclusions
Concrete mix design, i.e., the proportioning of the ingredients of concrete to get the speci c performance of concrete, depends on various mix factors related to ingredients of concrete and their combinations. e present research attempts to provide an integrated AHP-TOPSISbased MCDM model to rank the concrete mix guidelines for performance of concrete under water, sulphate, and chloride attack and performance of concrete for underground conditions and for evolving the performancebased concrete mix design techniques based on the required mix factors.
In the present study, a three-level hierarchical structure to rank the mix design methods for an extreme environment, namely, concrete mix objective criteria, mix factors as subcriteria, and mix design methods as alternatives, is formulated. e sensitivity analysis for the mix design methods and resulting mix factor has also been carried out. It is concluded from the outcomes of the MCDM techniques, AHP and integrated AHP-TOPSIS approach, that the DOE method is the preferred design mix method to design the mix for an extreme environment performance. e sensitivity analysis with respect to the variation of criteria weights, i.e., workability, strength, and durability importance, indicates the stability of the priority of the DOE method. e sensitivity analysis also suggests that when the durability criterion has more weights as compared to workability and strength criterion, the DOE method and ACI method have equal preference. e sensitivity analysis with respect to subcriteria weights also indicates the stability of the priority of the DOE method to the variation in weight of water-cement ratio, ne aggregate-cement ratio, and total aggregate-cement ratio. e preference of the DOE method changes to the FM method with increase in the weights of density, cost, and ne aggregate-total aggregate ratio. e preference of the DOE method changes to the ACI method with increase in the weights of coarse aggregate-cement ratio. e proposed two-phase AHP-TOPSIS approach model may become a promising tool for evolving the performance-based concrete mix technique.

ACI:
American concrete institute AHP: Analytic hierarchy process DOE: Department of energy TOPSIS: Technique for order of preference by similarity to ideal solution VIKOR: Visekriterijumska optimizacija kompromisno resenje A * : Positive ideal solution A − : Negative ideal solution CC: Closeness coe cient C * j : e relative closeness to ideal solution CI: Consistency Index CR: Consistency ratio D * j : Separation distance from ideal solution D − j : Separation distance from negative ideal solution.
Data Availability e datasets generated and/or analysed during the current study are available from the corresponding author on reasonable request.

Conflicts of Interest
e authors declare that they have no con icts of interest.
Supplementary Materials e supplementary le contains Appendix A consists of seven (7) tables as given below. Table A1: pairwise comparison of three criteria for high-performance concrete. Table A2: pairwise comparison of subcriteria (mix factors) with workability criteria (performance). Table A3: pairwise comparison of alternatives with respect to water/cement (w/ c) ratio. Table A4: priority weights of three alternatives obtained by AHP with respect to each weights of subcriterion. Table A5: priority weights of three alternatives obtained by AHP with respect to each weights of subcriterion (normalized decision matrix). Table A6: priority weights of three alternatives obtained by AHP with respect to each weights of subcriterion (weighted normalized decision matrix). Table A7: