© 2023 IIETA. This article is published by IIETA and is licensed under the CC BY 4.0 license (http://creativecommons.org/licenses/by/4.0/).
OPEN ACCESS
In recent times, the construction industry has been recognized as a critical sector in achieving the Sustainable Development Goals. However, construction activities and infrastructure have both beneficial and nonbeneficial impacts, making infrastructure design the focus of current research in finding the best way to meet society's demands for sustainability. Although methods for economic, environmental, and social life cycle assessments of infrastructures are wellknown, the challenge lies in combining these dimensions into a comprehensive indicator that aids decisionmaking. This study uses three decisionmaking techniques, namely TOPSIS, COPRAS, and VIKOR, to evaluate five different design alternatives for a concrete bridge exposed to a coastal environment. To enhance the consistency of the multicriteria decisionmaking process, a DEMATELbased approach is applied. The study's results demonstrate unanimously that concrete containing even small amounts of silica fume performs better over its life cycle than other solutions typically considered to increase durability, such as reducing the water/cement ratio or increasing concrete cover.
sustainable design, bridges, life cycle assessment, DEMATEL, TOPSIS, VIKOR, COPRAS, multicriteria decisionmaking
The pursuit of sustainable development has become a top priority for both the public and private sectors. Since the inception of the Sustainable Development Goals in 2015, our society has taken significant strides towards their implementation. An excellent example is the ambitious European Green Deal, which aims to achieve climate neutrality in Europe while promoting a circular economy. The construction industry is crucial in achieving this objective, as it is one of the sectors with the most substantial negative impact on the environment. As a result, numerous researchers are focusing on infrastructure design optimization to minimize economic and environmental impacts. Their work encompasses a wide range of infrastructures [15], making it a highly significant area of interest.
When it comes to addressing sustainability concerns, society often resorts to ecological reductionism, oversimplifying the complex and multidimensional nature of these issues. In reality, assessing sustainability requires a holistic approach that acknowledges the need to consider multiple perspectives and disciplines. Multicriteria decisionmaking (MCDM) techniques are highly effective tools for achieving a multidisciplinary approach to sustainability assessment [6]. Consequently, researchers have been working in recent years to develop various tools and methods for evaluating the sustainability of different infrastructures. A wide range of MCDM techniques has been employed to draw relevant conclusions, which can inform future design actions. However, there is no consensus on which MCDM method is best suited for sustainable infrastructure assessment. Some authors argue that using multiple MCDM techniques is necessary to achieve a comprehensive and reliable sustainability assessment [7].
The use of MCDM techniques typically depends on determining the relevance of each criterion in the final decision. This is often done through the Analytic Hierarchy Process (AHP), a widely used MCDM technique. However, there has been criticism of AHP's accuracy for complex problems since human judgment consistency is inversely proportional to problem complexity. Several approaches aim to reduce uncertainty in the results. One popular method is reducing the number of judgments requested from experts to increase the consistency of their judgments by simplifying the problem's complexity.
This study proposes using the DEMATEL technique to reduce the number of comparisons required of experts to determine criteria weights using the AHP technique. After determining the weights, the study assesses the life cycle sustainability of five design alternatives for a concrete bridge in a coastal area, using three MCDM techniques: TOPSIS, VIKOR, and COPRAS. The sustainability assessment considered a set of nine quantitative criteria that encompassed all three sustainability dimensions: economy, environment, and society.
2.1 AHP
The Analytic Hierarchy Process (AHP) is a MCDM technique first defined by Saaty back in 1980 [8]. This method is nowadays widely used to determine the weights to be assigned to each criterion involved in decisionmaking problems of any kind. This technique requires an expert to compare pairwise the relevance that each criterion shall have with respect to each other when taking the decision. By doing so, a square socalled comparison matrix A_{nxn} is constructed, where n is the number of criteria involved in the decisionmaking process. The comparison between two criteria is based on the Saaty’s fundamental scale, which is used to transform linguistic judgements into numerical values (Table 1).
Table 1. Saaty’s fundamental scale [8]
Semantic Comparison Term 
Numerical Equivalence 
Criteria A and B are equally relevant 
1 
Criterion A is slightly more relevant than B 
3 
Criterion A is more relevant than B 
5 
Criterion A is much more relevant than B 
7 
Criterion A is extremely more relevant than B 
9 
Intermediate values can be used if required 
2, 4, 6, 8 
The elements of the resulting comparison matrix A_{nxn} correspond to values of the Saaty’s fundamental scale. It shall be noted that if criterion A is considered, for example, extremely more relevant than criterion B, then criterion B is considered extremely less relevant than criterion A. This results in the comparison matrix A_{nxn} to be reciprocal by definition, i.e., a_{ij }= 1/a_{ji}. The AHP allows to extract the relevance of each criterion from a sobuilt comparison matrix as the values of the eigenvector associated to the greatest eigenvalue of the matrix (λ_{max}).
The resulting criteria weights are considered valid only of the comparison matrix A_{nxn} is consistent, i.e., the judgements of the decision maker should have been coherent. If a perfect consistency of a comparison matrix was achieved, that would result in a_{ij} × a_{jk }= a_{ik} ∀ i, j, k.
The consistency shall be evaluated by means of the socalled Consistency Index CI, of the comparison matrix A_{nxn}, as:
$C I=\left(\lambda_{\max }n\right) /(n1)$ (1)
where, n is the total number of criteria involved in the decisionmaking process. The resulting weights are then valid only if the Consistency Ratio CR = CI/RI falls below a limiting value CR_{lim} which depends on the number of criteria n (Table 2). In the above presented equation RI stands for the socalled Random Index, which indicates the consistency of a fully randomized nxn comparison matrix.
Table 2. Values for RI and CR_{lim} depending on the number of criteria involved
Number of Criteria n 
3 
5 
7 
9 
Random Index RI 
0.58 
1.12 
1.32 
1.45 
Allowable CR_{lim} 
0.05 
0.10 
0.10 
0.10 
2.2 DEMATELbased completion technique
The weights obtained through the application of the above presented AHP technique are widely used as a basis for many other decisionmaking techniques, such as TOPSIS, COPRAS or VIKOR. However, one of the most criticised aspects of the AHP technique is that the resulting criteria weights are highly subjective. In fact, the ability of the decision makers to adequately reflect their view on a problem diminishes as the complexity of the problem increases. There exist several approaches to attempt reducing the subjectivity of the decisions based on the application of MCDM techniques. Research has been conducted on the application of the fuzzy theory to mathematically model the diffusivity of human thinking and include it as a source of relevant information for the decisionmaking process [9, 10].
Another approach which is also in the spotlight of many researchers is to reduce the complexity of the problem by reducing the number of judgements to be made by the decision maker when filling the AHP comparison matrix [11, 12]. To do so, the DEMATEL method can be used.
2.2.1 DEMATEL method
The goal of the MCDM DEMATEL technique is to transform intricate causeandeffect connections among diverse elements into a wellstructured and easytounderstand visual model. This involves grouping factors into causeandeffect categories, as explained in reference [13]. The conventional approach involves four distinct stages:
Stage 1: To generate a Direct Influence Matrix (DIM), experts are requested to complete a comparison matrix using a process similar to the Analytic Hierarchy Process (AHP). In this process, each expert estimates the degree of influence that factor i has on factor j using a fourlevel scale of integers ranging from 0 to 3. The scores represent "no influence," "low influence," "medium influence," and "high influence," respectively. The nonnegative influence matrix DIM_{k }= {z_{ij}} is created for each expert k, where z_{ij} denotes the assigned influence score based on the aforementioned scale. The diagonal elements in the matrix are set to zero. Finally, the Direct Influence Matrix DIM is derived by averaging the matrices DIM_{k} obtained from all the experts.
Stage 2: The direct influence matrix shall now be normalized to the socalled NIM by dividing each element z_{ij} by p, where:
$\mathrm{p}=\max \left(\max _{1 \leq i \leq n} \sum_{j=1}^n z_{i j}, \max _{1 \leq i \leq n} \sum_{i=1}^n z_{i j}\right)$ (2)
Stage 3: A total relation matrix TRM is now constructed by aggregating both direct and indirect influential effects as:
$T R M=N I M+N I M^2+N I M^3+\cdots+N I M^{\infty}=N I M(IN I M)^{1}$ (3)
In the equation above, I stands for an identity n×n matrix.
Stage 4: To determine the influential factors R_{i} and C_{i}, the sum of each row and column of the TRM must be calculated. If R_{i}  C_{i} is positive, a particular factor i is classified as a cause, whereas if it is negative, it is considered an effect.
2.2.2 DEMATELbased AHP restoration
Zhou et al. [14] proposed a technique inspired by DEMATEL to restore incomplete AHP comparison matrices and ensure their initial state and consistency. This is relevant because DEMATEL is designed to uncover nonevident relationships among a group of factors, and both DEMATEL and AHP rely on the analysis of comparison matrices. This restoration technique can be used to reduce the number of pairwise comparisons to be made by the decisionmaker, this reducing the complexity of the assessment and increasing the accuracy of the resulting weights. The DEMATELbased completion technique consists in the following stages:
Stage 1: From an incomplete AHP comparison matrix A_{nxn}^{* }= {a_{ij}}, a DIM matrix can be derived. The elements of the DIM matrix {z_{ij}} are set equal to a_{ij}, but are set to zero, when the comparison element a_{ij} is unknown.
Stage 2: To generate the normalized influence matrix (NIM), each element z_{ij} of the matrix shall be divided by p as in the classical DEMATEL method.
Stage 3: The total relation matrix TRM = {g_{ij}} shall now be computed as in classical DEMATEL.
Stage 4: Based on the relationships between factors identified in the total relation matrix (TRM), a fully reciprocal pairwise comparison matrix A_{nxn}^{’} = {a^{’}_{ij}} as:
$g_{i j} / a_{i j}^{\prime}=g_{j i} / a_{j i}^{\prime}$ (4)
It is important to ensure that the synthetic comparison matrix A'_{nxn} includes reciprocal central elements. To achieve this and considering the equation above that describes the relationship between factors, any missing entry a_{ij} in the original incomplete comparison matrix A_{nxn}^{*} can be calculated.
2.3 Scoring MCDM techniques
2.3.1 TOPSIS
The TOPSIS method was introduced by Hwang and Yoon [15] and is recognised as the most popular MCDM method used in civil engineering [16]. TOPSIS has been used to analyse the sustainability performance of wide variety of infrastructures, from bridges [17, 18] to buildings [2]. TOPSIS technique is applied following several steps. The first step consists in constructing a decision matrix R = [r_{ij}] and obtaining the weight w_{i} of each criterion i considered in the problem. Weights are usually derived using the Analytical Hierarchy Process (AHP) [19]. The decision matrix R is then normalized as:
$r_{i j}^{\prime}=\frac{r_{i j}}{\sqrt{\sum_{j=1}^n r_{i j}^2}}$ (5)
In the equation above, n is the total number of criteria. Now, the normalized decision matrix is weighted as:
$v_{i j}=w_i \cdot r_{i j}^{\prime}$ (6)
The ideal positive and negative solutions (PIS or NIS) are derived for each criterion. These solutions are constructed by maximising the utility criteria and minimising the cost criteria in the PIS case and vice versa in the NIS case. After that, the distance of each alternative to the PIS and NIS is obtained as:
$d_j^{+}=\sqrt{\sum_{i=1}^n\left(v_{i j}v_i^{+}\right)^2}$ (7)
$d_j^{}=\sqrt{\sum_{i=1}^n\left(v_{i j}v_i^{}\right)^2}$ (8)
In the equations above, v_{i}^{+} and v_{i}^{} are the elements of the PIS and NIS respectively, d_{j}^{+} and d_{j}^{} are the distances of alternative j to the PIS and NIS, respectively. Finally, a score Q_{j} is obtained that evaluates the relative distance of each alternative j to the PIS as:
$Q_j=\frac{d_j}{d_j^{}+d_j^{+}}$ (9)
2.3.2 VIKOR
VIKOR is a MCDM method introduced by Opricovic [20] overcome the limitations of existing MCDM techniques where decision problems involve conflicting criteria. VIKOR is also a popular assessment tool, that has been used as well to solve the evaluation performance of a variety of infrastructures, such as bridges [2123], airport infrastructures [24] or logistic centers [25].
VIKOR shares the same first step as TOPSIS: a decision matrix must be constructed R = [r_{ij}] the criteria weights w_{i} must be determined. The second step consists in finding the best and worst criteria values, namely r_{i}^{+} and r_{i}^{}, so that the decision matrix R can be normalized as:
$r_{i j}^{\prime}=\frac{r_i^{+}r_{i j}}{r_i^{+}r_i^{}}$ (10)
The third step requires to determine two distance measures S_{j} and R_{j} for each alternative j as follows:
$S_j=\sum_{i=1}^n w_i \cdot r_{i i}^{\prime}$ (11)
$R_j=\max \left\{w_i \cdot r_{i j}^{\prime}\right\}$ (12)
At last, the VIKOR measure index Q_{j} for each alternative j is calculated as:
$Q_j=v \cdot \frac{S_j\min \left\{S_j\right\}}{\max \left\{S_j\right\}\min \left\{S_j\right\}}+(1v) \cdot \frac{R_j\min \left\{R_j\right\}}{\max \left\{R_j\right\}\min \left\{R_j\right\}}$ (13)
It is usual to compromise both distance metrics S_{j} and R_{j} by setting v = 0.5. The alternative that results in the greatest score Q_{j} will be the best performing one according to this decisionmaking technique.
2.3.3 COPRAS
COPRAS technique was defined by Zavadskas et al. [26] and has been also applied in a wide range related decisionmaking situations related with sustainability issues, such as the design of buildings [27, 28], the choice of construction materials [29] and others [30] due to its simplicity. As usual in other decisionmaking methods, COPRAS requires a decision matrix R = [r_{ij}] and the obtention of the criteria relevancies w_{i} as a starting point Then, the decision matrix must be normalized:
$r_{i j}^{\prime}=\frac{r_{i j}}{\sum_{i=1}^n \;r_{i j}}$ (14)
The second step consists in normalizing the decision matrix elements as:
$v_{i i}=w_i \cdot r_{i i}^{\prime}$ (15)
Then, the sum of the weighted normalized scores for both cost and benefit criteria for each alternative j are obtained as:
$S_{+j}=\sum_{i=1}^n w_i \cdot r_{i j,+}^{\prime}$ (16)
$S_{j}=\sum_{i=1}^n w_i \cdot r_{i j,}^{\prime}$ (17)
In the equations above, r’_{ij,+} and r’_{ij,} represent respectivelyfor the normalized scoring for the benefit and cost criteria. After doing so, the final score Q_{j} of each alternative j is calculated:
$Q_j=S_{+j}+\frac{\sum_{k=1}^m \;S_{k}}{S_{j} \cdot \sum_{k=1}^m \;S_{k}}$ (18)
The alternative that reaches the greatest value of the index Q_{j} results in the best performance according to COPRAS method.
The MCDM methods presented above are applied for the evaluation of the sustainability life cycle performance of different design alternatives to a particular concrete bridge near shore. In those environments, the aggressive chlorideladen atmosphere induces the corrosion of the reinforcing steel, thus leading to intensive maintenance demanding designs. Being the maintenance stage usually a great source of negative impacts in every dimension of sustainability (economy, environment and society), working on enhancing the durability of coastal structures results in an effective way to reduce the impacts that harm the sustainability of these structures. To prevent concrete to degrade and increase the durability of concrete structures exposed to marine environments, conventional concrete designs are usually modified. The present analysis considers five different alternatives intended to provide high durability and thus reducing maintenance. The first one consists in using a conventional concrete mix but considering a concrete cover of 50 mm, which is significantly greater than usual cover values. This design alternative will be called CC50 hereafter. The second alternative consists in using reduced water to cement ratios to reduce the porosity of the concrete cover and consequently reducing the capacity of chlorides to ingress and reach the rebars (alternative W/C35 hereafter). The third alternative consists in reducing the porosity of concrete through the addition of latexbased additives to the concrete mix (alternative PMC10). The fourth alternative is based on the addition of silica fume to the concrete mix, which also results in reduced concrete porosity. A similar effect is achieved by using flyash additions. These two design alternatives will be called SF5 and FA20 hereafter respectively. The characterization of each of the abovedescribed design alternatives is shown in Table 3.
The sustainability performance of these five design alternatives is evaluated on a functional unit consisting of a 1 m long portion of a concrete bridge deck built near shore. The considered bridge shows a conventional 2.3 m deep and 12 m wide boxgirder section. The analysis considers a 100 year long maintenance stage. To investigate the different maintenance needs of each design option, a reliability analysis is conducted. The required maintenance interval for each design alternative is set to the interval for which its reliability reaches 60% of a target reliability β_{lim} = 1.3, which corresponds to a probability of failure of 9.68% [31]. In the analysis, failure is assumed to occur when the chloride concentration at the rebar depth reaches the critical chloride threshold associated to each alternative. The advance of the chloride front is modelled following Fick’s second Law of diffusion, as recommended in Fib Bulletin 34 [32]. The reliability analysis has been performed for each alternative running 20,000 MonteCarlo simulations to ensure that results converge, resulting in a relative estimation error below 1%. The parameters used to characterize probabilistically each design option are presented in Table 4. Table 4 contains the mean value for each parameter and the standard deviation in parentheses. In Table 4, D_{0} stands for the chloride diffusivity of concrete, and C_{cr} for the critical chloride threshold, both parameters that affect the chloride ingress into concrete.
Table 3. Definition of each design alternative

CC50 
W/C35 
PMC10 
FA20 
SF5 
Cement (kg/m³) 
350 
350 
350 
329 
315 
Water (l/m³) 
140 
122 
140 
140 
140 
Gravel (kg/m³) 
1017 
1037 
1017 
1017 
1017 
Sand (kg/m³) 
1068 
1095 
1068 
1086 
1098 
Silica Fume (kg/m³) 
 
 
 
 
17.5 
Fly Ash (kg/m³) 
 
 
 
70 
 
Plasticiser (kg/m³) 
5.25 
7 
 
4.94 
 
Latex (kg/m³) 
 
 
35 
 
 
Concrete Cover (mm) 
50 
40 
40 
40 
40 
Table 4. Parameters for the reliability evaluation of each design option
Parameter 
CC50 
W/C35 
PMC10 
FA20 
SF5 
D_{0} (x10^{12} m²/s) 
8.90 (0.90) 
5.80 (0.47) 
6.51 (0.55) 
4.65 (0.35) 
2.94 (0.23) 
C_{cr} (%) 
0.60 (0.10) 
0.60 (0.10) 
0.60 (0.10) 
0.60 (0.10) 
0.60 (0.06) 
Cover (mm) 
50 (2.5) 
40 (2) 
40 (2) 
40 (2) 
40 (2) 
Mainten. Interval (β_{lim}/β(t) = 0.6) 
9 yrs. 
12 yrs. 
10 yrs. 
17 yrs. 
25 yrs. 
The sustainability performance of each design option is evaluated through a set of 9 criteria. The first two criteria deal with the economic impacts of the designs. The first criterion (C1) considers the costs associated to the construction of the functional unit defined for each of the alternatives under study. The second criterion (C2) includes the costs resulting from the maintenance along the life cycle of each of the designs. It shall be noted that a discount rate d = 2% has been considered to discount future expenses to the date of construction. The costs of materials, machinery and construction activities are taken from national databases for the construction industry.
Three criteria have been defined to capture the environmental performance of each design. In particular, these three criteria stand for the three endpoint indicators associated with the environmental life cycle assessment technique ReCiPe [33]. These indicators are the damage to human health (C3), the damage to ecosystems (C4) and the affection to the availability of natural resources (C5) resulting from the production of the construction materials and energy consumptions along the life cycle of each design option. The inventory data from which the relevant information for quantifying the three selected endpoint indicators was obtained came from the environmental database Ecoinvent [34].
At last, a set of four criteria are defined to assess the social impacts derived from the different design alternatives. These criteria are suggested in studys [35, 36] to evaluate the social impacts of bridges. The first of these criteria (C6) deals with the ability of each design to generate employment. The second social criteria (C7) considers the contribution of each alternative to the economic wealth of the regions affected by the different construction and maintenance activities associated to it. The third social criterion (C8) takes into account how the recurrent maintenance activities might affect the traffic safety and accessibility of the users of the bridge. The last social criterion (C9) accounts for the negative effect that maintenance activities can have on the public opinion of the local communities, which are affected by the noise, vibrations or dust generated by these. The inventory data to determine the values of the social impacts has been gathered from the Spanish National Statistics Institute [37] and the Spanish Tax Office [38].
4.1 Life cycle assessment of the design alternatives
Table 5 shows the life cycle performance of each of the design alternatives against the different economic, environmental and social impacts involved in the present decisionmaking problem. It shall be noted that impacts are referred to the functional unit described above and exclude the effect of every activity that might be equal between alternatives.
Table 5. Life cycle impact results for each alternative under study
Criterion ID 
Definition 
CC50 
W/C35 
PMC10 
SF5 
FA20 
C1 
Construction Costs 
1296.4 € 
1322.5 € 
2355.7 € 
1546.2 € 
1386.3 € 
C2 
Maintenance Costs 
4014.8 € 
2301.3 € 
3269.8 € 
1025.3 € 
1489.4 € 
C3 
Human Health 
207.8 
141.7 
203.5 
95.6 
110.3 
C4 
Ecosystems 
107.8 
73.1 
100.5 
47.6 
53.9 
C5 
Resources 
244 
180.1 
288.8 
145.6 
145 
C6 
Employment Generation 
67.5% 
57% 
73.2% 
53.5% 
54.4% 
C7 
Economic Wealth 
55.8% 
45.8% 
63.4% 
44.5% 
42.2% 
C8 
Users 
8.3% 
11.5% 
9.1% 
22.9% 
18.4% 
C9 
Externalities 
7.9% 
11.1% 
8.8% 
22.5% 
18% 
It can be observed the solution associated with the greatest life cycle costs is the solution based on the addition of latex to the baseline concrete mix, closely follower by the CC50 solution. Although close in total terms, it shall be highlighted that PMC incurs in lesser maintenance costs than CC50 solution. The reduced competitiveness of this alternative in comparison to the rest relies on its associated high construction costs (C1). The concrete mix solution with the lowest life cycle costs is the one that involves adding silica fume (SF5) to the mix. The alternative FA20 solution closely follows in terms of costeffectiveness. It is interesting to note that in almost every case, costs resulting from maintenance along the life cycle of the different alternatives under analysis are greater than the installation costs. An exception to that conclusion is the SF5 alternative.
When it comes to environmental aspects, it can be observed that, in general terms, the impact on the availability of natural resources is the most impacting effect of every alternative, followed by the impact on human health. Environmental results (criteria C3 to C5) are expressed in accordance with the ReCiPe scoring system. Regarding the life cycle performance of each alternative, similar results are obtained as for the economical assessment: PMC10 solution is again the worst environmentally performing alternative, closely followed by CC50.
However, in terms of social impacts, PMC10 is the most favourable solution, while W/C35 has the least impact. It's important to note that while economic and environmental criteria are costbased (i.e., the best solution is the one that scores less), social criteria are benefitbased, meaning that the greater the social impact, the better the solution. In this study, it is observed that for the maintenancedemanding alternatives, the impacts on users and public opinion are relatively insignificant if compared to the impacts on workers and on the regional development. For SF5 and FA20, even though the impacts on workers and regional development are more significant, the impacts on users and public opinion account for up to a third of their total social score.
4.2 Sustainability performance evaluation
In order to compare the various alternatives and make a decision based on sustainability performance, the results shown above must be converted into a single indicator. To achieve this, a variety of MCDM techniques are utilized, namely TOPSIS, VIKOR and COPRAS. Each of these methods uses as an input the criteria weighting resulting from the application of the AHP technique. However, in order to maximize the accuracy of the weighting calculation, the number of comparisons is reduced in order to reduce the complexity of the assessment problem and increase the reliability of the results. The above presented DEMATELbased completion technique is used to restore complete comparison matrices out of the incomplete ones.
4.2.1 Criteria weighting
To derive the relevance of the abovedescribed criteria, a conventional AHP technique is applied. The weights resulting after evaluating the maximum eigenvector are presented in Table 6. It can be observed that, according to the decision maker’s perception of the problem, environmental aspects should weight much more than economic and social impacts. In fact, the environmental criteria weights (C3 to C5) sum up to 61.7%, while the economic criteria (C1 and C2) sum up to 23.7% and the social ones (C6 to C9) sum 14.7%. The consistency of the comparison matrix is evaluated by means of the Consistency Ratio, which takes a value of CR = 9.6% for the present analysis. As This value is below the limiting CR_{lim} = 10% required for 9×9 comparison matrices, the obtained weights are consistent.
Table 6. Criteria weights resulting from the application of the AHP technique
Decision Criterion 
Weight of the Criterion 
C1  Construction Costs 
0.158 
C2  Maintenance Costs 
0.079 
C3  Human Health 
0.149 
C4  Ecosystem 
0.181 
C5  Resources 
0.287 
C6  Employment 
0.027 
C7  Wealth 
0.031 
C8  Users 
0.049 
C9  Externalities 
0.040 
4.2.2 Completion results
Three distinct incompleteness levels of the baseline matrix are considered to assess the effectiveness of the presented completion technique. For each scenario, a varying number of entries are randomly chosen and considered as missing. In particular, for scenario 1, 5 entries are removed, 8 for scenario 2 and 12 for scenario 3, which implies the elimination of 33% of the judgements required to the decision maker when completing a conventional 9×9 comparison matrix. 1000 simulations are run to generate in each of them a unique random incomplete comparison matrix based on the baseline one presented above.
Figure 1 shows the dispersion of the weights resulting for each criterion depending on the number of entries missing in the baseline comparison matrix. Although 3 scenarios have been evaluated, results are shown for scenarios 1 and 3, being scenario 2 enveloped by these. It can be observed that the maximum deviation from the baseline is obtained, as expected, in scenario 4, where 33% of the judgements are omitted. The average relative deviation between these weights and the baseline weight set is 4.9%. It can be noticed that as the number of missing entries increases, there is an increase in the dispersion of the results, even though the mean fits well. However, the maximum deviation with respect to the baseline is 7.6%.
Figure 1. Weights of the different criteria considering incompleteness scenarios 3 and 4
Considering the outcomes, the root mean square error (RMSE) is utilized to assess the overall effectiveness of the completion model. The RMSE measures the disparities between the forecasted estimations and the baseline weights. Figure 2 shows the normalized RMSE obtained for each criterion and incompleteness scenario. It can be observed that the greatest estimation errors are associated, as expected, for the incompleteness scenario with the greatest number of entries to be restored, namely scenario 3, for which the mean normalized RMSE reaches 24.2%.
Figure 2. Normalized root mean square error for each criterion
It can be concluded from the results presented that the weight estimation is robust even if 8 entries are missing (incompleteness scenario 2). Removing more than 8 would lead to greater error values and results dispersion, and a socalled rank reversal phenomenon could occur.
4.2.3 MCDM results
The TOPSIS, COPRAS and VIKOR methods have been adopted to calculate a relative score for each design alternative, providing insight into its sustainability performance during its life cycle. The results obtained assuming these weights are presented in Table 7. These have been obtained considering the baseline weighting set.
Table 7. Alternative scores for the different MCDM techniques considering the baseline weights set
Alternative 
TOPSIS 
VIKOR 
COPRAS 
CC50 
0.329 
0.521 
0.715 
W/C35 
0.665 
0.689 
0.260 
PMC10 
0.101 
0.485 
1.000 
SF5 
0.913 
0.906 
0.013 
FA20 
0.888 
0.854 
0.035 
It can be observed that the best solution in terms of its sustainability life cycle performance is the alternative based on the use of silica fume as an addition to a conventional concrete mix (SF5), closely followed by alternative SF20. The outstanding performance of these solutions when used in chlorideladen environments is explained by the fact that the use of such additions result in a drastic reduction of the chloride diffusivity of the concrete cover, thus hindering the advance of the chloride front into the reinforcing bars. The reduced maintenance of these solutions, together with the fact that it allows a reduction in the cement content, results in the best sustainability scores among the rest of the alternatives.
The sensitivity of the results is now checked against the different defined incompleteness scenarios. Results are presented in Tables 8, 9 and 10. Mean weights for each of these scenarios are considered as an input to get the alternative scoring.
Table 8. TOPSIS scores considering different incompleteness scenarios
Alternative 
CC50 
W/C35 
PMC10 
SF5 
FA20 
Baseline 
0.329 
0.665 
0.101 
0.913 
0.888 
Scenario 1 
0.321 
0.661 
0.101 
0.915 
0.887 
Scenario 2 
0.317 
0.659 
0.100 
0.916 
0.887 
Scenario 3 
0.314 
0.656 
0.100 
0.916 
0.884 
Table 9. VIKOR scores considering different incompleteness scenarios
Alternative 
CC50 
W/C35 
PMC10 
SF5 
FA20 
Baseline 
0.521 
0.689 
0.485 
0.906 
0.854 
Scenario 1 
0.519 
0.689 
0.485 
0.909 
0.855 
Scenario 2 
0.519 
0.689 
0.485 
0.911 
0.856 
Scenario 3 
0.519 
0.688 
0.487 
0.911 
0.855 
Table 10. VIKOR scores considering different incompleteness scenarios
Alternative 
CC50 
W/C35 
PMC10 
SF5 
FA20 
Baseline 
0.715 
0.260 
1.000 
0.013 
0.035 
Scenario 1 
0.720 
0.264 
1.000 
0.013 
0.036 
Scenario 2 
0.723 
0.265 
1.000 
0.012 
0.036 
Scenario 3 
0.724 
0.268 
1.000 
0.009 
0.038 
It can be concluded that, although slight differences can be observed depending on the incompleteness scenario considered, the results are on average robust and consistent.
This research aims to evaluate the life cycle sustainability of five design alternatives to a concrete bridge exposed to a chlorideladen, marine environment. The alternatives are based on usual approaches to overcome such aggressive environments. The analysis of their life cycle performance is conducted by means of a set of 9 criteria, including a variety of economic, environmental and social criteria. The evaluation is based on a multicriteria decisionmaking approach in order to derive a sustainability score for each solution that allows us to compare alternatives. As there is no consensus on the best MCDM technique, three scoring MCDM methods are used here, namely TOPSIS, VIKOR and COPRAS. All of them consider as an input the weights derived from the AHP technique. To reduce the subjectivity of the input weights, a DEMATELbased approach is applied to reduce the number of judgements required by the decision maker, thus reducing the complexity of the assessment and increasing the reliability of the obtained results.
From the results, it can be concluded that using silica fume and fly ash additions to conventional concrete mixes increases significantly the sustainability performance of concrete designs exposed to chlorides. The use of silica fume and fly ash increases the durability of concrete against chlorides, reducing enormously the maintenance requirements along their life cycle. On the other hand, such additions allow to reduce the cement content, reducing the environmental impacts associated to the production of cement. Moreover, these products result as byproducts of the industry. Its recycling also contributes significantly to the environment.
Grant PID2020117056RBI00 funded by MCIN/AEI/ 10.13039/501100011033 and by “ERDF A way of making Europe”.
[1] Peng, J., Yang, Y., Bian, H., Zhang, J., Wang, L. (2022). Optimisation of maintenance strategy of deteriorating bridges considering sustainability criteria. Structure and Infrastructure Engineering, 18(3): 395411. https://doi.org/10.1080/15732479.2020.1855215
[2] SánchezGarrido, A.J., Navarro, I.J., Yepes, V. (2022). Multicriteria decisionmaking applied to the sustainability of building structures based on Modern Methods of Construction. Journal of Cleaner Production, 330: 129724. https://doi.org/10.1016/j.jclepro.2021.129724
[3] Figueiredo, K., Pierott, R., Hammad, A.W.A., Haddad, A. (2021). Sustainable material choice for construction projects: A Life Cycle Sustainability Assessment framework based on BIM and FuzzyAHP. Building and Environment, 196: 107805. https://doi.org/10.1016/j.buildenv.2021.107805
[4] Pons, J.J., PenadésPlà, V., Yepes, V., Martí, J.V. (2018). Life cycle assessment of earthretaining walls: An environmental comparison. Journal of Cleaner Production, 192: 411420. https://doi.org/10.1016/j.jclepro.2018.04.268
[5] Navarro, I.J., Martí, J.V., Yepes, V. (2022). Group analytic network process for the sustainability assessment of bridges near shore. WIT Transactions on Ecology and the Environment, 209: 143154. https://doi.org/10.2495/HPSU220131
[6] Sousa, M., Almeida, M.F., Calili, R. (2021). Multiple criteria decision making for the achievement of the UN sustainable development goals: A systematic literature review and a research agenda. Sustainability, 13(8): 4129. https://doi.org/10.3390/su13084129
[7] Tučník, P., Bureš, V. (2016). Experimental evaluation of suitability of selected multicriteria decisionmaking methods for largescale agentbased simulations. PLOS ONE, 11(11): e0165171.
[8] Saaty, T.L. (1980). The Analytic Hierarchy Process. McGrawHill, New York, NY, USA.
[9] Prascevic, N., Prascevic, Z. (2017). Application of fuzzy AHP for ranking and selection of alternatives in construction project management. Journal of Civil Engineering and Management, 23(8): 11231135. https://doi.org/10.3846/13923730.2017.1388278
[10] Kahraman, C., Cebi, S., Onar, S.C., Oztaysi, B. (2018). A novel trapezoidal intuitionistic fuzzy information axiom approach: An application to multicriteria landfill site selection. Engineering Applications of Artificial Intelligence, 67: 157172. https://doi.org/10.1016/j.engappai.2017.09.009
[11] Chen, K., Kou, G., Tarn, J.M., Song, Y. (2015). Bridging the gap between missing and inconsistent values in eliciting preference from pairwise comparison matrices. Annals of Operations Research, 235: 155175. https://doi.org/10.1007/s104790151997z
[12] Navarro, I.J., Martí, J.V., Yepes, V. (2021). Neutrosophic completion technique for incomplete higherorder AHP comparison matrices. Mathematics, 9(5): 496. https://doi.org/10.3390/math9050496
[13] Gabus, A., Fontela, E. (1972). World Problems, an Invitation to Further Thought Within the Framework of Dematel; Battelle Geneva Research Centre: Geneva, Switzerland.
[14] Zhou, X., Hu, Y., Deng, Y., Deng, Y., Chan, F.T., Ishizaka, A. (2018). A DEMATELbased completion method for incomplete pairwise comparison matrix in AHP. Annals of Operations Research, 271: 10451066. https://doi.org/10.1007/s1047901827693
[15] Hwang, C.L., Yoon, K. (1981). Multiple Attribute Decision Making. SpringerVerlag, Berlin, 1981.
[16] Navarro, I.J., PenadésPlà, V., MartínezMuñoz, D., Rempling, R., Yepes, V. (2020). Life cycle sustainability assessment for multicriteria decision making in bridge design: A review. Journal of Civil Engineering & Management, 26(7): 690704. https://doi.org/10.3846/jcem.2020.13599
[17] Jia, J., Ibrahim, M., Hadi, M., Orabi, W., Xiao, Y. (2018). Multicriteria evaluation framework in selection of accelerated bridge construction (ABC) method. Sustainability, 10(11): 4059. https://doi.org/10.3390/su10114059
[18] Navarro, I.J., Yepes, V., Martí, J.V. (2020). Sustainability assessment of concrete bridge deck designs in coastal environments using neutrosophic criteria weights. Structure and Infrastructure Engineering, 16(7): 949967. https://doi.org/10.1080/15732479.2019.1676791
[19] Marzouk, M., Sabbah, M. (2021). AHPTOPSIS social sustainability approach for selecting supplier in construction supply chain. Cleaner Environmental Systems, 2: 100034. https://doi.org/10.1016/j.cesys.2021.100034
[20] Opricovic, S. (1998). Multicriteria optimization of civil engineering systems. Ph.D. dissertation. University of Belgrade, Belgrade, Serbia.
[21] Kripka, M., Yepes, V., Milani, C.J. (2019). Selection of sustainable shortspan bridge design in Brazil. Sustainability, 11(5): 1307. https://doi.org/10.3390/su11051307
[22] Bansal, S., Singh, A., Singh, S.K. (2017). Sustainability evaluation of two iconic bridge corridors under construction using Fuzzy Vikor technique: A case study. Revista ALCONPAT, 7(1): 114. http://dx.doi.org/10.21041/ra.v7i1.171
[23] GarcíaSegura, T., PenadésPlà, V., Yepes, V. (2018). Sustainable bridge design by metamodelassisted multiobjective optimization and decisionmaking under uncertainty. Journal of Cleaner Production, 202: 904915. https://doi.org/10.1016/j.jclepro.2018.08.177
[24] Kumar, A., Aswin., A., Gupta, H. (2020). Evaluating green performance of the airports using hybrid BWM and VIKOR methodology. Tourism Management, 76: 103941. https://doi.org/10.1016/j.tourman.2019.06.016
[25] Baki, R. (2022). Extended VIKOR method based on intervalvalued intuitionistic fuzzy numbers for selection of logistics centre location. Journal of the Human and Social Science Researches, 11(3): 18211837. https://doi.org/10.15869/itobiad.1084212
[26] Zavadskas, E.K., Kaklauskas, A., Sarka, V. (1994). The new method of multicriteria complex proportional assessment of projects. Technological and Economic Development of Economy, 1(3): 131139.
[27] Mulliner, E., Malys, N., Maliene, V. (2016). Comparative analysis of MCDM methods for the assessment of sustainable housing affordability. Omega, 59: 146156. https://doi.org/10.1016/j.omega.2015.05.013
[28] Nuuter, T., Lill, I., Tupenaite, L. (2015). Comparison of housing market sustainability in European countries based on multiple criteria assessment. Land Use Policy, 42: 642651. https://doi.org/10.1016/j.landusepol.2014.09.022
[29] Invidiata, A., Lavagna, M., Ghisi, E. (2018). Selecting design strategies using multicriteria decision making to improve the sustainability of buildings. Building and Environment, 139: 5868. https://doi.org/10.1016/j.buildenv.2018.04.041
[30] Zhan, Y., Tan, Y., Li, N., Liu, G., Luo, T. (2018). DecisionMaking in Green Building Investment Based on Integrating AHP and COPRASGray Approach. In International Conference on Construction and Real Estate Management, Charleston, SC, USA, August 910, 2018, pp.6571. https://doi.org/10.1061/9780784481738.008
[31] ISO 2394:2015. (2015). General principles on reliability for structures. Geneva, ISO.
[32] Schiessl, P., Bamforth, P., BaroghelBouny, V., et al. (2006). fib Bulletin 34. Model code for service life design. Fib, Lausanne, Switzerland. https://doi.org/10.35789/fib.BULL.0034
[33] Goedkoop, M., Heijungs, R., Huijbregts, M., De Schryver, A., Struijs, J., Van Zelm, R. (2009). ReCiPe 2008: A life cycle impact assessment method which comprises harmonised category indicators at the midpoint and the endpoint level. https://web.universiteitleiden.nl/cml/ssp/publications/recipe_characterisation.pdf, accessed on June 10, 2022.
[34] Ecoinvent. https://www.ecoinvent.org, accessed on June 10, 2022.
[35] Navarro, I.J., Yepes, V., Martí, J.V. (2018). Social life cycle assessment of concrete bridge decks exposed to aggressive environments. Environmental Impact Assessment Review, 72: 5063. https://doi.org/10.1016/j.eiar.2018.05.003
[36] Navarro, I.J., Yepes, V., Martí, J.V. (2021). Sustainability life cycle design of bridges in aggressive environments considering social impacts. International Journal of Computational Methods and Experimental Measurements, 9(2): 93107. https://doi.org/10.2495/CMEMV9N29310
[37] The INE. https://www.ine.es, accessed on June 12, 2022.
[38] Tax Agency. https://sede.agenciatributaria.gob.es, accessed on April 10, 2022.