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 highperformance concrete depends on resulting mix factors, namely, water, cement, fine aggregate, and coarse aggregate ratios. This paper implements the multicriteria decisionmaking techniques (MCDM) for ranking concrete mix factors and representative mix design methods. The study presents a framework to identify critical mix factors found from the concrete mix design methods for highperformance concrete using the twophase AHP and TOPSIS approach. Three 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 ranking mix design methods and the resulting mix factors. Three hierarchy levels, having three criteria and seven subcriteria, and three alternatives are considered. The 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 performancebased concrete mix design techniques. Sensitivity and validation analysis is also provided to demonstrate the effectiveness of the proposed approach.
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. The various design guidelines that include the mix parameters such as properties of cement, minimum and maximum cement quantity, watertocement ratio, mixing water requirements, aggregatestocement 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. The mix factors significantly affecting the suitability of mix proportion for highperformance concrete are taken into consideration for ranking decision model. The concrete workability, strength and durability affecting mix factor, watercement (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 highperformance 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. MultiCriteria Decision Making (MCDM) techniques may be employed to ascertain the criticality of mix factors and grading of mix design techniques. The research work related to the implementation of MCDM techniques in civil engineering is mainly devoted to construction technology. The 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. [
The 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. The present study is the maiden attempt to apply MCDM techniques to select the mix design technique in concrete technology for highperformance 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 highperformance concrete.
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. The number of MCDM methods has been developed for value measurement, goal, preference level, and outranking selection. The 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 decisionmaking and puts forward sufficient confidence to translate their decisions into actions [
Comparison of proposed with individual AHP and TOPSIS methods [
Criteria  AHP  TOPSIS  Twophase AHPTOPSIS (proposed) 

Use hierarchical structure  √  √  
To provide objective criteria’s weight  √  √  
Comparison of ideal solution  √  √  
Ranking method  √  √  √ 
Be easy to understand  √  √  √ 
The selection of the preferential mix design method for achieving particular performance is an MCDM process. The 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. The problem criteria are identified based on experts’ opinion [
The main steps of the proposed approach to select the preferential mix design method are as follows.
Develop the problem criteria hierarchy and normalize the decision matrix and calculate the weights of matrix by AHP following the procedure outlines by Saaty [
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. The concrete mix parameters for extreme environment (level 2 subcriteria) are identified as watercement (w/c) ratio, density, coarse aggregatecement (CA/c) ratio, total aggregatecement (T/c) ratio, fine aggregatecement (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. The hierarchical structure of the preferential mix design method for an extreme environment is depicted in Figure
Hierarchical structure of the preferential mix design method and mix factors for high performance concrete.
Consistency check of each pairwise comparison matrix using AHP [
The consistency of the assessment process is checked by calculating the CI and CR value of each pairwise comparison matrix and the aggregate matrix [
Estimate the relative weights of the alternatives with respect to each weight of subcriterion.
The 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 [
Conduct TOPSIS by normalizing the decision matrix using AHP [
Calculate the normalized decision matrix and calculate the weighted normalized decision matrix, following the methodology is given by Hwang and Yoon [
Determine the ideal and negative ideal solutions and calculate the separation measures.
The ideal solution (
Calculate the relative closeness to the ideal solution and rank the preference order.
The relative closeness of each alternative (
Final score obtained by TOPSIS.
Criteria 



Ranking 

ACI  0.117  0.233  0.502  2 
DOE  0.130  0.246  0.530  1 
FM  0.096  0.219  0.439  3 
The sensitivity analysis demonstrates the influence and stability of criterion’s weight (mix factors weights) on alternative (mix design method) selection. Thus, the concrete method selection robustness may be verified 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. The weight of three main criteria, i.e., (workability, strength, and aggregate size) considered as
Sensitivity analysis output.
Conditions  Criteria weight 
 




ACI  DOE  FM  
1  0.297  0.539  0.164  0.502  0.530  0.439 
2  0.164  0.539  0.297  0.514  0.541  0.447 
3  0.297  0.164  0.539  0.509  0.509  0.456 
4  0.539  0.297  0.164  0.559  0.472  0.542 
Sensitivity analysis with respect to mix objective criteria.
The quantitative optimum values of concrete mix factors found in the literature (Table
Quantitative optimum values of mix factors from published literature.
Mix factors for extreme environment  Ahmed et al. [ 
Ahmed et al. [ 
Mix design guidelines for optimum value with lowest cost  

Ahmad [ 
Simon [ 
Soudki et al. [ 
Yurdakul, [  
w/c ratio  0.5  0.5  0.4–0.43  
CA/c ratio  2.43  2.51  
T/c ratio  4.31  4.26  4.88  4.3–5.1  3–3.6  
FA/c ratio  1.88  1.75  
FA/T ratio  0.43  0.41  0.38  0.39  0.45–0.4  0.42 
The results of the twophase AHP and TOPSIS approach implemented to preferential mix design technique to develop highperformance concrete suggested that the Department of Energy (DOE) method of mix design is the best choice for highperformance 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. The ranking of the mix design method predicted by the twophase AHP and TOPSIS approach is also compared with a predicted ranking of the mix design method when only the AHP approach is applied. The two MCDM techniques, AHPbased and integrated AHPTOPSISbased approach, suggest that the DOE method is the preferred design mix method for performance in an extreme environment as depicted in Figure
Ranking of mix design method for extreme environment using AHP and twophase AHPTOPSIS approach.
The sensitivity analysis also shows the stability of the priority of the DOE method. The 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. The fineness modulus method, which is a relatively older mix design method, has also all capabilities of developing into an advanced mix design technique for highperformance concrete as the closeness coefficients are found to be in close proximity.
There 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. The weight ranking of the subcriteria with respect to objective criteria obtained by the AHP approach is represented in Figure
Weights of subcriteria with respect to objective criteria.
The watercement ratio is a very important and critical factor for the mix design technique. The workability, strength, and durability of fresh and hardened concrete are strongly dependent on this factor. The watercement ratio has the highest weight for workability and strength criteria as evident from Figure
Sensitivity analysis of mix design methods with respect to w/c ratio weights.
The density and fine aggregate to total aggregate (FA/T) ratio factors is the indicator of the denseness of the concrete. These two factors are important for the mix design in an extreme environment. The density is the second in weight rank and rank is more or less same for all the objective criteria as presented in Figure
Sensitivity analysis of mix design methods with respect to density weights.
Sensitivity analysis of mix design methods with respect to FA/T weight.
The coarse aggregate to cement (CA/c) ratio is an important parameter for the design mix technique in an extreme environment performance and factor need to be of optimum value for concrete mix. The 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. The sensitivity of the mix design technique with respect to density and CA/c ratio is shown in Figure
Sensitivity analysis of mix design methods with respect to CA/c ratio weight.
The fine aggregate to cement (FA/c) ratio and total aggregate to cement (T/c) ratio are the indicators of the concrete quality. These factors are also significant 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
Sensitivity analysis of mix design methods with respect to FA/c weight.
Sensitivity analysis of mix design methods with respect to T/c weight.
The 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. The weighted rank of cost is the last for workability and strength criteria, and it is the first weight rank for durability criteria as given in Figure
Sensitivity analysis of mix methods with respect to cost weight.
Concrete mix design, i.e., the proportioning of the ingredients of concrete to get the specific performance of concrete, depends on various mix factors related to ingredients of concrete and their combinations. The present research attempts to provide an integrated AHPTOPSISbased 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 threelevel 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. The 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 AHPTOPSIS approach, that the DOE method is the preferred design mix method to design the mix for an extreme environment performance. The 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. The 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. The sensitivity analysis with respect to subcriteria weights also indicates the stability of the priority of the DOE method to the variation in weight of watercement ratio, fine aggregatecement ratio, and total aggregatecement ratio. The preference of the DOE method changes to the FM method with increase in the weights of density, cost, and fine aggregatetotal aggregate ratio. The preference of the DOE method changes to the ACI method with increase in the weights of coarse aggregatecement ratio. The proposed twophase AHPTOPSIS approach model may become a promising tool for evolving the performancebased concrete mix technique.
American concrete institute
Analytic hierarchy process
Department of energy
Technique for order of preference by similarity to ideal solution
Visekriterijumska optimizacija kompromisno resenje
Positive ideal solution
Negative ideal solution
Closeness coefficient
The relative closeness to ideal solution
Consistency Index
Consistency ratio
Separation distance from ideal solution
Separation distance from negative ideal solution.
The datasets generated and/or analysed during the current study are available from the corresponding author on reasonable request.
The authors declare that they have no conflicts of interest.
The authors acknowledge the Deanship of Scientific Research for proving administrative and financial supports. Funding for this work has been provided by the Deanship of Scientific Research, King Khalid University, and Ministry of Education, Kingdom of Saudi Arabia under research grant award number R.G.P.1/82/40 (1440).
The supplementary file contains Appendix A consists of seven (7) tables as given below. Table A1: pairwise comparison of three criteria for highperformance 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: ideal solution (