Optimization of the Mixture Design of Low-CO2 High-Strength Concrete Containing Silica Fume

As abundant CO2 is released by high-strength concrete due to its high binder content, the reduction of CO2 emissions has become increasingly important. .is study proposed a general procedure to optimize the mixture design of low-CO2 high-strength concrete containing silica fume. First, the equations for evaluating strength and slump were regressed based on available experimental results. CO2 emissions were calculated based on the concrete mixtures and the unit CO2 emissions of the concrete components. By using the genetic algorithm, the concrete mixtures with the lowest CO2 emissions were determined by considering various constraints. Second, the cost of concrete was calculated based on the concrete mixtures and the unit cost of the concrete components. Similarly, the concrete mixtures with the lowest cost were determined based on the genetic algorithm. We found that, in some cases, the mixtures with the lowest CO2 emissions were different from those with the lowest cost. .ird, through adding the constraint equation of cost, Pareto optimal mixtures with relatively lower CO2 emissions and lower cost were determined. In summary, the proposed technique is valuable for designing high-strength concrete considering both CO2 emissions and cost.


Introduction
High-strength concrete is increasingly used in the modern construction industry. Many advantages can be achieved by using high-strength concrete such as reducing the quantity of sections needed in structural elements, increasing the occupancy rate of buildings, and extending the service life of the building [1]. However, high-strength concrete generally has a lower water-to-binder ratio than normal strength concrete. As abundant binder is used and lots of CO 2 is released when producing high-strength concrete, the reduction of CO 2 emissions has become more and more important [2].
Fundamental studies have been conducted regarding the evaluation of CO 2 emissions of high-strength concrete. Larsen et al. [3] found that ultra-high-performance concrete could offer increased benefits over traditional concrete design. Voo and Foster [4] and Yu et al. [5] proposed that using slag in producing ultra-high-performance concrete could reduce CO 2 emissions and embodied energy and save total life cycle cost. Park et al. [6] assessed the life cycle CO 2 emissions of concrete with different strength levels and found that life cycle CO 2 increased linearly as the compressive strength increased. Kim et al. [7] proposed a method for evaluating CO 2 emissions from the production process of concrete and found that the application of highstrength concrete and the standardization of the mixing process could reduce CO 2 emissions in the construction stage. Latawiec et al. [8] proposed an index for concrete desirability where the effects of compressive strength, durability, CO 2 emissions, and cost on concrete desirability were considered.
On the other hand, some methods have been proposed for the material design of low-CO 2 or low-cost concrete. Based on neural networks and the genetic algorithm, Yeh [9] proposed software for designing concrete mixtures with the lowest possible cost. Mosaberpanah and Eren [10] proposed a full factorial method to maximize the strength and minimize the carbon dioxide emissions. e effects of cement content, silica fume content, fiber content, water-to-binder ratio, and superplasticizer are considered for determining strength and CO 2 emissions. Yang et al. [11] proposed an approach for designing low-CO 2 concrete containing various supplementary cementitious materials such as fly ash, slag, and silica fume. Tapali et al. [12] proposed an iteration approach to design concrete with a low environmental cost, considering strength and service life. Khan et al. [13] designed low-cost high-strength self-compacting concrete using a response surface methodology. e optimal combinations of cement, water-to-binder ratio, fine aggregate, fly ash, and superplasticizer were determined using a desirability function. Ji et al. [14] combined neural networks and a harmony search algorithm to find the optimal design of reactive powder concrete with the lowest cost. Although many studies [9][10][11][12][13][14] have been carried out on the design of low-CO 2 or low-cost concrete, some questions need to be further clarified: first, what are the differences between the mixture designs of low-CO 2 concrete and low-cost concrete? Second, how can we design concrete with both low CO 2 emissions and low cost? ird, how can we create a general design procedure of low-CO 2 concrete for different countries whose design codes may be different?
In this study, we proposed a general procedure to optimize the mixture design of low-CO 2 high-strength concrete containing silica fume. By using the genetic algorithm, concrete mixtures with the lowest CO 2 emissions and lowest cost were individually determined. We found that, for some cases, the mixtures with the lowest CO 2 emissions were different from those with the lowest cost. Furthermore, through adding the constraint equation of cost, Pareto optimal mixtures with relatively lower CO 2 emissions and lower cost were determined. e innovations of this study are summarized as follows: first, we propose a general method for designing low-CO 2 concrete; second, we consider the difference between low-CO 2 concrete and low-cost concrete; third, we propose a Pareto optimal method to determine mixtures with lower CO 2 and lower cost.

Optimization Design of Concrete Mix Proportions
To optimize the mixing proportions of high-strength concrete containing silica fume, the object function and constraint conditions need to be established. In this study, the CO 2 emissions were placed as the object function. e constraint conditions were the desired concrete strength, workability, component contents, component ratios, and absolute volume [9].

Object Function.
e total CO 2 emissions of silica fumeblended concrete include CO 2 emissions from the concrete materials and transport and from the mixing of the concrete [15]. e total CO 2 emissions can be calculated from the following equation [15]: where CO 2−e , CO 2−eM , CO 2−eT , and CO 2−eP represent the total CO 2 emissions, CO 2 emissions from concrete materials, CO 2 emissions from transport, and CO 2 emissions from the mixing operation of concrete, respectively. CO 2−eM can be calculated according to the concrete mixture and unit CO 2 emissions of the concrete components as follows: where CO 2−C , CO 2−SF , CO 2−W , CO 2−CA , CO 2−S , and CO 2−SP are the unit CO 2 emissions of cement, silica fume, water, coarse aggregate, sand, and superplasticizer, respectively, and C, SF, W, CA, S, and SP are the masses of cement, silica fume, water, coarse aggregate, sand, and superplasticizer in the concrete mixtures, respectively. Table 1 shows the CO 2 emissions of the concrete components [11]. In this study, the object function was placed as CO 2−eM .

Constraint
Conditions. e object function (the minimum CO 2 emission, CO 2−eM ) is exposed to various constraints, for example, concrete strength, workability, component contents, component ratios, and absolute volume [9]. e strength constraint means that the design strength should be higher than the required strength. e formula for the strength constraint is shown as follows [9]: where f c (t) is the concrete strength at age t and f cr (t) is the required strength at age t. e workability constraint of fresh concrete is shown in the following equation [9]: where Slump r is the required slump of concrete. e range of component contents is shown as follows: where the components are the cement, silica fume, binder, water, fine aggregate, coarse aggregate, and superplasticizer. Table 2 shows the lower and upper limits of the contents of concrete components [16]. e component ratio constraint is shown as follows: where R i is the component ratio (for example, the water-tobinder ratio, water-to-cement ratio, sand ratio, silica fumeto-binder ratio, and superplasticizer-to-binder ratio). R l and R u are the lower and upper limits of the component ratio, respectively. Table 3 shows the component ratio constraints [16]. Because the aim of this study is to design silica fumeblended concrete with high strength, the range of binder content is higher and the range of water-to-binder ratio is lower than those of ordinary strength concrete [9]. e absolute volume constraint is shown as follows: where ρ W , ρ C , ρ SF , ρ S , ρ CA , and ρ SP are the densities of water, cement, silica fume, sand, coarse aggregate, and superplasticizer, respectively, and V air is the volume of air in the concrete. e densities of water, cement, silica fume, sand, coarse aggregate, and superplasticizer are 1000, 3150, 2260, 2610, 2700, and 1220 kg/m 3 , respectively. Equation (7) implies that the sum of each concrete component should equal 1 m 3 [9].

Property Evaluation of the Silica Fume-Blended Concrete.
Lim et al. [16] conducted experimental studies on the strength and slump of silica fume-blended high-strength concrete where a total of 77 mixing proportions of concrete were studied. e effects of the water-to-binder ratio, water content, sand ratio, silica fume replacement ratio, and superplasticizer content on the mechanical workability of concrete were considered [16]. e compressive strength of highstrength concrete at 28 days ranged from 90 to 120 MPa. e slump of concrete ranged between 180 and 235 mm. e upper and lower limits of contents of concrete components are shown in Table 2. e upper and lower limits of the ratios of concrete components are shown in Table 3. Based on the experimental results of compressive strength [16], the strength of concrete at 28 days can be regressed as a function of the water-to-binder ratio, water content, sand ratio, and silica fume replacement ratio. e regression equation of compressive strength is shown as follows: First, equation (8) shows that as the water content and water-to-binder ratio increases, concrete strength decreases.
is is due to the increase in the porosity of the concrete. Next, as the sand ratio increases, the strength of the concrete increases. is is because when compared with coarse aggregate, the range of the interfacial transition zone of fine aggregate is not obvious [17]. ird, as the silica fume replacement ratio increases, the concrete strength increases.
is is because the pozzolanic reaction of silica fume can produce secondary calcium silicate hydrate and improve the concrete strength.
e correlation index between the experimental results and the regression results of compressive strength was 0.954. e high correlation index proves the validity of equation (8).
Based on the experimental results of slump [16], the slump of concrete can be regressed as a function of the water-to-binder ratio, water content, sand ratio, silica fume replacement ratio, and superplasticizer content. e regression equation of slump is shown as follows: As shown in this equation, as the water content, superplasticizer content, and water-to-binder ratio increase, the concrete slump increases. As the sand ratio and silica fume replacement ratio increase, the concrete slump decreases.
Based on the mixtures of concrete, the superplasticizer content is determined as a function of the water-to-binder ratio and the silica fume replacement ratio [16]. e regression equation of superplasticizer content is shown as follows:

Advances in Civil Engineering
As shown in this equation, as the water-to-binder ratio decreases or the silica fume replacement ratio increases, the superplasticizer content increases [18].
Summarily, within this section, we determined the object function and constraints of the concrete mixing proportions. e object function was the minimum CO 2 emissions, CO 2−eM . e constraints included various mechanical and constructability performance measures, for example, the compressive strength, workability of fresh concrete, component contents, component ratios, and absolute volume of the concrete mixture. Once the object's function and constraints are solved, concrete mixtures that meet various performance requirements can be acquired.
On the other hand, it should be noticed that the equations for evaluating strength, slump, and superplasticizer content are obtained from materials mixed by Lim et al. [16]. For other countries, because the compositions of binders and the varieties of superplasticizer may be different from Lim et al. [16], the calculation equations of strength, slump, and superplasticizer may also be different from those proposed in this study. e technique for solving the object's function with constraints is the genetic algorithm. e genetic algorithm is an adaptive global optimization probability search algorithm that simulates the genetic and evolutionary processes of living things in the natural environment [19]. e process of the genetic algorithm is summarized as follows: Step 1: generate the initial population; Step 2: calculate the fitness; Step 3: select cross mutation operations, and compute fitness function; Step 4: check convergence criteria; and Step 5: repeat Step 3 until the convergence criteria are met.
In this study, we used the MATLAB global optimization toolbox for solving objective optimization with constraints [19]. e object function and constraints equation can be set in the MATLAB global optimization toolbox. According to the genetic algorithm, the optimal mixture which has the minimum CO 2 emission and can meet various constraints can be found.

Design of Low-CO 2 High-Strength Concrete.
In this section, examples are shown for the mixture design of low-CO 2 high-strength concrete with different strength levels such as 95, 100, 105, 110, and 115 MPa. e required slump was assumed to be 180 mm. e air content was assumed to be 2%. e object function of the genetic algorithm was the minimum CO 2 emission. e strength of concrete can be evaluated using equation (8), the slump of concrete can be evaluated using equation (9), and CO 2 emissions can be evaluated using the unit CO 2 emission (Table 1) and concrete mixtures. e constraints included the range of the concrete components, range of the component ratios, and absolute volume. Based on the genetic algorithm that considers the various constraints, the mixtures were calculated and are shown in Table 4. e strengths of Mix1, Mix2, Mix3, Mix4, and Mix5 were 95, 100, 105, 110, and 115 MPa, respectively. e following results were obtained based on the contents of Table 4. First, as the required strength of concrete increased, the silica fume contents in the mixtures also increased.
is shows the significance of silica fume in producing high-strength concrete. Second, the water contents for concrete with higher strengths, such as Mix3 (105 MPa), Mix4 (110 MPa), and Mix5 (115 MPa), were equal to the lower limit of water (Table 2). is means that a lower water content is helpful for producing high-strength concrete. e performances of Mixes 1-5 are shown in Table 5. e following results were obtained based on the contents of Table 5. First, as the compressive strength of concrete increased from 95 MPa to 115 MPa, the water-to-binder ratio decreased from 0.26 to 0.23 and the silica fume replacement ratio increased from 0.05 to 0.25. is means that a lower water-to-binder ratio and a higher silica fume replacement ratio can improve the strength of concrete. Second, the sand ratio for each mixture was equal to the upper limit of the sand ratio (Table 3). is is because the concrete strength increases as the sand ratio increases (equation (8)). ird, the slumps for each mixture were all higher than the required slump of 180 mm. As the strength of the concrete increased, the superplasticizer content also increased. Fourth, as shown in Figure 1(a), as the strength of concrete increased, the CO 2 emissions also increased. Furthermore, based on the unit cost of concrete components (Table 6 [9]) and concrete mixtures, the cost for each mixture was calculated and they are shown in Figure 1(b). As the strength of concrete increased, the cost for each mixture also increased.

Design of Low-Cost High-Strength Concrete.
In Section 3.1, the objective function of the genetic optimization was set as the minimum CO 2 emissions. However, in the concrete industry, concrete producers and construction companies are interested not only in CO 2 emissions but also in the cost of concrete. Like CO 2 emissions, the cost of concrete can also be calculated from the contents and unit prices of the concrete components (Table 6 [9]).
Based on similar methods in Section 3.1, the concrete mixture with the lowest price, considering various constraint equations, can be determined. e mixtures were calculated and are shown in Table 7. e strengths of Mix6, Mix7, Mix8, Mix9, and Mix10 were 95, 100, 105, 110, and 115 MPa, respectively. e following results were obtained based on the contents of Tables 7 and 8. First, for concrete with strengths of 95 and 100 MPa, the mixtures of the lowest cost were the same as that of the lowest CO 2 emissions (Mix1 was the same as Mix6 and Mix2 was the same as Mix7). For the concrete with strengths of 95 MPa and 100 MPa, the silica fume replacement ratio was 0.05, which equaled the lower limit of the silica fume replacement ratio (Table 3). Second, for concrete with strengths of 105, 110, and 115 MPa, the silica fume replacement ratio of the lowest cost mixtures (Mix8, Mix9, and Mix10) was lower than that of the lowest CO 2 emission mixtures (Mix3, Mix4, and Mix5). For example, the compressive strengths of Mix3 and Mix8 were both 105 MPa, but the silica fume replacement ratio of Mix8 was lower than that of Mix3. is is because the unit price of silica fume is much higher than that of cement (the unit price     Advances in Civil Engineering of silica fume is five times that of cement (Table 6)). When the object function is the lowest price, the content of silica fume will be as low as possible. ird, for concrete with strengths of 105 MPa, 110 MPa, and 115 MPa, the water-tobinder ratio of the lowest cost mixtures (Mix8, Mix9, and Mix10) was lower than that of the lowest CO 2 emission mixtures (Mix3, Mix4, and Mix5). is means that a lower water-to-binder ratio can compensate for the impairment of strength due to the lower silica fume content. Fourth, the slumps for each mixture were all higher than the required slump of 180 mm. As the strength of concrete increased, the superplasticizer content also increased. Fifth, as shown in Figure 2(a), as the strength of concrete increased, the cost of concrete also increased. As shown in Figure 2(b), as the strength of concrete increased, the CO 2 emissions for each mixture also increased.

Pareto Optimal Mixtures for Lower CO 2 Emissions and
Lower Cost. As shown in Sections 3.1 and 3.2, for concrete with higher strengths such as 105, 110, and 115 MPa, the mixtures with the lowest cost were different from those with the lowest CO 2 emissions. Although the aims of the lowest CO 2 emissions and lowest price cannot be achieved simultaneously, some compromises can be made between low CO 2 emissions and low price. In other words, we can design concrete with relatively lower CO 2 emissions at a relatively lower price. To design concrete with both lower cost and lower CO 2 emissions, we set an additional constraint regarding the cost of concrete. For example, when the required strength of concrete is given as 110 MPa (the strengths of Mix4 and Mix9 were both 110 MPa), the constraint equation of cost can be set as follows: COST � (2800, 2900, 3000, 3100).
e values of cost (2800, 2900, 3000, and 3100) were between the cost of Mix4 and Mix9 (the cost of Mix4 and Mix9 was 3169.04 and 2740.48, respectively). e design requirements can be summarized as follows: the object function was the lowest CO 2 emission; the cost of each mixture was equal to 2800 or 2900 or 3000 or 3100, respectively; the design value of compressive strength was 110 MPa; the design value of the slump was 180 mm; and the air content was 2%. In this section, the additional equality constraint was the cost of concrete (equation (11)), while in Section 3.1, there was no constraint for cost.
Based on the genetic algorithm, the mixtures were calculated and named as Mix11, Mix12, Mix13, and Mix14, respectively (shown in Table 9). e performances of Mix11 to Mix14 are shown in Table 10. e following results were obtained based on the contents of Table 10. First, the compressive strengths of Mix11, Mix12, Mix13, and Mix14 were the same, i.e., 110 MPa, and the slumps of Mix11, Mix12, Mix13, and Mix14 were higher than the required slump of 180 mm. Second, the cost of Mix11, Mix12, Mix13, and Mix14 was 2800, 2900, 3000, and 3100, respectively, and the CO 2 emissions of Mix11, Mix12, Mix13, and Mix14 were 640.46, 619.25, 597.92, and 576.43, respectively. e cost and CO 2 emissions of Mix11, Mix12, Mix13, and Mix14 were generally between Mix4 and Mix9. In other words, Mix11, Mix12, Mix13, and Mix14 had both lower cost and lower CO 2 emissions. Figure 3(a) shows the CO 2 emissions versus the concrete cost. As CO 2 emissions increased, concrete cost decreased.
e Pareto optimality is an ideal state of resource allocation. Given an inherent group of people and assignable resources, if there is a change from one state of assignment to another, at least one person's situation becomes better without making anyone's situation worse; this is the Pareto improved state. Pareto's optimal state is the idea that it is impossible to have more Pareto's improved state; in other words, it is impossible to improve the situation of some people without damaging anyone else [20]. Figure 3(b) shows an illustration of the Pareto optimal solutions [21,22]. e x-axis and y-axis represent that of function f2 and performance f1, correspondingly. Point A and point B are a pair of points on the Pareto optimal solutions graph. At point A, the value of f1 is greater, while at point B, the value of f2 is greater.
Based on the comparison between Figures 3(a) and 3(b), we found that Mix11, Mix12, Mix13, and Mix14 were the Pareto optimal solutions for designing lower CO 2 emissions and lower concrete cost.

Generalization of the Proposed Method.
In this study, the calculation equations of strength and slump were obtained based on the regression of experimental results in [16]. For different design specifications, the calculation equations of strength and slump may be different from those used in this study [23][24][25]. In addition, the unit CO 2 emission, unit price, constraints of component range, and component ratio used in this study cannot cover all cases presented in different countries and regions [26]. In Sections 3.1-3.3, the air content of concrete is assumed as 2%. e additional mixture designs are performed for different-strength concrete with 1% air content. e analysis results show that when air content changes from 2% to 1%, the contents of cement, silica fume, water, and sand ratio of optimized mixtures do     Advances in Civil Engineering not change, while the contents of fine aggregate and coarse aggregate increase.
To adapt the proposed design method, other researchers can use their own equations to replace the corresponding equations such as the equations for strength, slump, and various constraints. Although the calculation equations may be different, the basic calculation procedure is very similar. Hence, to some extent the proposed method can be regarded as a general method for the design of low-CO 2 high-strength concrete. On the other hand, as this study focused on the mixture design of high-strength concrete, durability aspects such as carbonation or chloride ingress were not considered. ese durability aspects can be considered as additional inequality constraints of the concrete mixture [27].

Conclusions
is study proposed a general procedure to optimize the mixture design of low-CO 2 high-strength concrete containing silica fume.
First, CO 2 emissions were calculated based on the concrete mixtures and the unit CO 2 emissions of the concrete components. By using the genetic algorithm, concrete mixtures with the lowest CO 2 emissions were determined considering the various constraints. Similarly, concrete mixtures with the lowest cost were determined based on the genetic algorithm. We found that for concrete with design strengths higher than 105 MPa, the mixtures with the lowest CO 2 emissions were different from those with the lowest cost. As the strength of concrete increased, the CO 2 emissions and cost of concrete also increased.
Second, for concrete with design strength higher than 105 MPa, the objects of the lowest CO 2 emissions and lowest cost cannot be achieved simultaneously. By adding a constraint equation of cost, Pareto optimal mixtures were determined. e Pareto optimal mixtures had relatively lower CO 2 emissions and lower cost. Regarding the Pareto optimal mixtures, as CO 2 emissions increased, the concrete cost decreased. e cost and CO 2 emissions of the Pareto optimal mixtures were between the lowest cost mixture and lowest CO 2 emissions mixture.
In conclusion, the proposed technique is valuable for designing high-strength concrete that considers both CO 2 emissions and cost. To adapt the proposed design method, other researchers can use their own equations to replace the corresponding equations in this study.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.