Mixture Optimization of Sustainable Concrete with Silica Fume Considering CO2 Emissions and Cost

Abstract

This research presents a framework for the mixture design of sustainable SF-modified concrete. The design strength at 28 days was scaled to different values (e.g., 30, 40, 50, and 60 MPa). CO₂ emissions and cost were chosen as the design variables to optimize. Strength, slump, and carbonation durability with global warming were applied as constraints of optimal design. The analysis revealed that, for low-CO₂ concrete, when the design strength was 30 or 40 MPa, to fulfill the requirement of carbonation, the actual concrete strength ought to be 45.39 MPa, which was much greater than the design strength. Carbonation did not affect the mixtures scaled to a high design strength (50 and 60 MPa). The SF/binder ratio was maximum for low-CO₂ concrete. Furthermore, for low-total-cost concrete, when the design strength was 30 MPa, the actual strength was 31.28 MPa after considering carbonation. Moreover, when considering global warming, the actual strength should be 33.44 MPa. The SF/binder ratio was minimum for low-cost concrete. Lastly, for low-material-cost concrete, the design was equivalent to the low-total-cost concrete, along with much lower CO₂ emissions. In summary, the suggested technique is valuable for the design of sustainable SF-modified concrete with low CO₂ and low cost.

1. Introduction

Different waste materials can be used in the production of low-cost concrete with acceptable mechanical properties [1]. Silica fume (SF) is a byproduct of the silicon and ferrosilicon production industry. Silica fume is a highly reactive pozzolanic material which has been increasingly used in concrete production. Concrete containing silica fume shows various benefits, such as low bleeding, high strength, low drying shrinkage, and good resistance to chloride penetration [2].

Many experimental studies have investigated the workability, hydration, strength, and durability properties of SF-modified concrete. Ahmad et al. [3] found that, when the replacement level of silica fume was higher than 4%, as the silica fume content increased, the slump flow of concrete decreased, whereas the compressive strength, tensile strength, and modulus of rupture increased. Abdulkareem et al. [4] proposed that KOH can improve the early-age compressive strength of SF-modified high-strength concrete. Wang et al. [5] found that silica fume can improve the abrasion resistance and compressive strength of concrete due to the pozzolanic reaction of silica fume. Wang et al. [6] found that SF-modified low-heat cement was suitable for use in mass concrete because of its adequate strength and low hydration heat. Lu et al. [7] established a homogenized silica fume/concrete matrix and evaluated strength using the fractal dimension of concrete. Bajja et al. [8] proposed that silica fume can refine concrete pores and decrease the diffusion coefficient. Savija and Lukovic [9], and Papadakis [10] found that silica fume can increase the carbonation depth of concrete.

Mixture design is an important research topic for blended silica fume/concrete. Compared with fundamental experimental studies investigating the properties of SF-modified concrete, those focusing on mixture design are relatively limited. Akalin [11] established an optimal design of composite concrete using the statistical mixture design method considering the setting time, strength, and cost. Khaloo et al. [12] and Ghafari et al. [13] generated a mixture design of SF-modified ultrahigh-strength concrete considering strength and workability. Naseri et al. [14] developed a mixture design of sustainable concrete considering strength, cost, and environmental impacts. Golafshani and Behnood [15] evaluated the strength of blended silica fume/concrete using biogeography-based programming, and they determined the optimal mix design of concrete with varying strengths using constrained biogeography-based optimization. Zhang et al. [16] generated a mixture design of SF-modified concrete using machine learning and a metaheuristic algorithm considering mechanical, cost, and environmental aspects.

Despite the number of studies determining the optimal mixture of SF-modified concrete, some flaws can be identified. First, most previous studies focused on strength and workability. Because adding SF impairs the carbonation resistance of concrete, the carbonation service life may be the dominant constraint factor of SF-modified concrete [10,17,18]; yet, this was not previously considered. Second, these studies mainly evaluated the material cost or CO₂ emissions of SF-modified concrete. Whereas SF presents a much greater cost than cement, its CO₂ emissions are considerably lower [19]. Thus, in terms of SF-modified concrete, the compositions yielding low-CO₂ concrete and low-cost concrete might differ [20]. Previous studies did not distinguish between low-cost concrete and low-CO₂ concrete. Third, global warming is an urgent problem which can accelerate carbonation and affect concrete mixture design [21,22,23]; however, this was not considered in previous mixture design approaches.

To address the flaws in previous studies, the aim of this research was to present a framework for the mixture design of sustainable SF-modified concrete. The scope of this study was SF-modified concrete with low CO₂ emissions or low cost. The genetic algorithm was used to identify optimal mixtures. Concrete strength, concrete workability (slump), and carbonation service life with global warming were applied as constraints of the genetic algorithm. Five design cases were considered: low-CO₂ concrete without carbonation, low-CO₂ concrete with carbonation, low-material-cost concrete with carbonation, low-total-cost concrete with carbonation, and low-total-cost concrete with global warming. In line with the analysis of design cases, the significance of carbonation and global warming was highlighted, and the distinction between low-cost concrete and low-CO₂ concrete was clarified. Following the introduction, the remainder of this study is structured as follows: Section 2 and Section 3 present the materials and methods and the results and discussion, respectively, while conclusions are drawn in Section 4.

2. Materials and Methods

2.1. Aim of Mixture Design

The sustainability of concrete features many aspects, such as CO₂ emissions and material cost. The purpose of optimal mixture design depends upon the selected index of sustainability. The CO₂ emissions of SF-modified concrete can be calculated using the following formula:

$${\mathrm{M}}_{{\mathrm{CO}}_2}={\mathrm{CO}}_{2-\mathrm{C}}\ast \mathrm{C}+{\mathrm{CO}}_{2-\mathrm{SF}}\ast \mathrm{SF}+{\mathrm{CO}}_{2-\mathrm{W}}\ast \mathrm{W}+{\mathrm{CO}}_{2-\mathrm{S}}\ast \mathrm{S}+{\mathrm{CO}}_{2-\mathrm{CA}}\ast \mathrm{CA}+{\mathrm{CO}}_{2-\mathrm{SP}}\ast \mathrm{SP},$$

(1)

where ${\mathrm{M}}_{{\mathrm{CO}}_2}$ represents the CO₂ emissions of concrete, ${\mathrm{CO}}_{2-\mathrm{C}}$, ${\mathrm{CO}}_{2-\mathrm{SF}}$, ${\mathrm{CO}}_{2-\mathrm{W}}$, ${\mathrm{CO}}_{2-\mathrm{S}}$, ${\mathrm{CO}}_{2-\mathrm{CA}}$, and ${\mathrm{CO}}_{2-\mathrm{SP}}$ indicate the CO₂ emissions from 1 kg of cement, SF, water, sand, coarse aggregate, and superplasticizer, respectively (shown in

Table 1. CO₂ emissions, cost, and density of concrete components [19,24].

	Cement	Silica Fume	Water	Coarse Aggregate	Fine Aggregate	Superplasticizer
CO2 emissions (kg/kg)	0.83	0.00031	0.000196	0.0075	0.0026	0.25
Cost (TWD/kg)	2.25	22.5	0.01	0.30	0.25	25.1
Density (kg/m3)	3150	2200	1000	2540	2600	1200

) [24], and $\mathrm{C}$, $\mathrm{SF}$, $\mathrm{W}$, $\mathrm{S}$, $\mathrm{CA}$, and $\mathrm{SP}$ denote the masses of cement, SF, water, sand, coarse aggregate, and superplasticizer in concrete, respectively.

The CO₂ emission of concrete consists of different phases, such as material phase, production phase, and transportation phase. Compared with other two phases, the CO₂ emission from the material phase is much higher [25]. Hence, in this study, we only consider CO₂ emission from the material phase. In future work, the CO₂ emission from the production phase and transportation phase should be considered for improvement.

Similarly, the material cost of SF-modified concrete can be calculated using the following formula:

$${\mathrm{COS}\mathrm{T}}_{\mathrm{M}}={\mathrm{Pr}}_{\mathrm{C}}\ast \mathrm{C}+{\mathrm{Pr}}_{\mathrm{SF}}\ast \mathrm{SF}+{\mathrm{Pr}}_{\mathrm{W}}\ast \mathrm{W}+{\mathrm{Pr}}_{\mathrm{S}}\ast \mathrm{S}+{\mathrm{Pr}}_{\mathrm{CA}}\ast \mathrm{CA}+{\mathrm{Pr}}_{\mathrm{SP}}\ast \mathrm{SP},$$

(2)

where ${\mathrm{COS}\mathrm{T}}_{\mathrm{M}}$ is the material cost of concrete, and ${\mathrm{Pr}}_{\mathrm{C}}$, ${\mathrm{Pr}}_{\mathrm{SF}}$, ${\mathrm{Pr}}_{\mathrm{W}}$, ${\mathrm{Pr}}_{\mathrm{S}}$, ${\mathrm{Pr}}_{\mathrm{CA}}$, and ${\mathrm{Pr}}_{\mathrm{SP}}$ denote the prices of 1 kg of cement, SF, water, sand, coarse aggregate, and superplasticizer, respectively (shown in Table 1) [19,26].

CO₂ emission cost can be established as a function of the mass of CO₂ emissions multiplied by the unit cost of CO₂. In Table 1, the values of CO₂ emission are from [19,24]. The CO₂ emission of cement mainly comes from two sources: CO₂ emission from calcination of limestone, and CO₂ emission from heating of kiln. The CO₂ emission of water, silica fume, aggregate, and superplasticizer is from [19,24] considering life cycle assessments, such as extractions of resources, material productions, product manufacture, use, and end-of-life phase. Furthermore, the total cost can be established as the sum of the material cost and CO₂ emission cost. Thus, the total cost can be calculated using the following formula:

$$\mathrm{COS}\mathrm{T}={\mathrm{COS}\mathrm{T}}_{\mathrm{M}}+{\mathrm{COS}\mathrm{T}}_{\mathrm{CO}2}={\mathrm{COS}\mathrm{T}}_{\mathrm{M}}+{\mathrm{Pr}}_{\mathrm{CO}2}{\ast \mathrm{M}}_{\mathrm{CO}2},$$

(3)

where $\mathrm{COS}\mathrm{T}$ and ${\mathrm{COS}\mathrm{T}}_{\mathrm{CO}2}$ represent the total cost and CO₂ emission cost, respectively, and ${\mathrm{Pr}}_{\mathrm{CO}2}$ is the unit price of CO₂ (${\mathrm{Pr}}_{\mathrm{CO}2}$ = 862.897 TWD/ton) [20].

2.2. Constraints of Mixture Design

(1)

The mixture design of concrete is subject to numerous constraints, e.g., the component range of concrete, ratio among concrete components, strength, slump, absolute volume, and carbonation durability [27].

(2)

The component range of concrete positions the mass of concrete components within an upper mass boundary and lower mass boundary, expressed as follows [27]:

$$\mathrm{lower} \mathrm{mass}\le \mathrm{component} \mathrm{mass}\le \mathrm{upper} \mathrm{mass},$$

(4)

where the lower mass and upper mass represent the lower and upper mass boundaries of concrete components, respectively, as shown in

Table 2. Upper and lower mass boundaries of concrete components.

	Cement	Silica Fume	Water	Coarse Aggregate	Fine Aggregate
Lower mass boundary	50	0	120	780	600
Upper mass boundary	540	300	250	1150	1100

[27].

(3)

The ratio of concrete components, e.g., water/binder ratio, sand/aggregate ratio, SF/binder ratio, water/solid ratio, and aggregate/binder ratio should also be positioned within upper and lower boundaries, expressed as follows:

$$\mathrm{lower} \mathrm{ratio}\le \mathrm{component} \mathrm{ratio}\le \mathrm{upper} \mathrm{ratio},$$

(5)

where lower ratio and upper ratio represent the lower and upper ratio boundaries of concrete components, respectively, as shown in

Table 3. Upper and lower ratio boundaries of concrete components.

	Water/Binder	SF/Binder	Sand/Aggregate	Aggregate/Binder	Water/Solid
Low ratio boundary	0.25	0.05	0.40	2.7	0.08
Upper ratio boundary	0.85	0.15	0.52	8.4	0.12

[27].

(4)

The strength constraint ensures that the actual strength exceeds the projected strength, expressed as follows:

$${\mathrm{f}}_{\mathrm{c}}\left(\mathrm{t}\right)\ge {\mathrm{f}}_{\mathrm{cr}}\left(\mathrm{t}\right),$$

(6)

where ${\mathrm{f}}_{\mathrm{c}}$ is the actual strength, and ${\mathrm{f}}_{\mathrm{cr}}$ is the design strength. Furthermore, the 28-day strength of SF-modified concrete can be calculated using the following formula [2,18,28,29]:

$${\mathrm{f}}_{\mathrm{c}}=11.145\ast {(\mathrm{W}/\left(\mathrm{C}+3.0\ast \mathrm{SF}\right))}^{-1.528},$$

(7)

where 3.0 is the strength efficiency factor of SF [2,18,28,29]. Thus, the addition of SF can improve concrete strength. It should be noted that some other parameters such as chemical content, mineralogical composition, specific gravity, particle size, or surface area of silica fume, may be relevant in the design of the mixture of concrete. In future studies, these parameters should be considered to improve the performance evaluation model.

(5)

The slump constraint ensures that the actual slump exceeds the projected slump, expressed as follows for SF-modified concrete:

$$\mathrm{Slump}\ge {\mathrm{Slump}}^{\mathrm{r}},$$

(8)

where $\mathrm{Slump}$ and ${\mathrm{Slump}}^{\mathrm{r}}$ are the actual slump and design slump, respectively. Moreover, slump can be calculated using the following formula [29,30,31]:

$$\mathrm{slump}=209.27\ast \frac{\mathrm{W}}{\mathrm{C}+\mathrm{SF}}+1.34\ast \mathrm{W}-325.1\frac{\mathrm{S}}{\mathrm{S}+\mathrm{CA}}-69.28\ast \frac{\mathrm{SF}}{\mathrm{C}+\mathrm{SF}}+1.29\ast \mathrm{SP}+63.3$$

(9)

Equation (9) shows that an increase in water/binder ratio, water content, and superplasticizer content leads to an increase in slump, whereas an increase in SF/binder ratio and sand/aggregate ratio leads to a decrease in concrete slump.

The superplasticizer content can be calculated using the following formula [29,30,31]:

$$\mathrm{SP}=\left(9.20-7.74\ast \frac{\mathrm{W}}{\mathrm{C}+\mathrm{SF}}\right)\ast \left(1+6.3\ast \frac{\mathrm{SF}}{\mathrm{C}+\mathrm{SF}}\right).$$

(10)

Equation (10) shows that an increase in water/binder ratio or a decrease in SF/binder ratio leads to a decrease in superplasticizer content.

(6)

The absolute volume constraint denotes that the total volume of individual concrete components ought to be 1 m³, expressed as follows [26,27]:

$$\frac{\mathrm{W}}{{\mathsf{\rho }}_{\mathrm{W}}}+\frac{\mathrm{C}}{{\mathsf{\rho }}_{\mathrm{C}}}+\frac{\mathrm{SF}}{{\mathsf{\rho }}_{\mathrm{SF}}}+\frac{\mathrm{CA}}{{\mathsf{\rho }}_{\mathrm{CA}}}+\frac{\mathrm{S}}{{\mathsf{\rho }}_{\mathrm{S}}}+\frac{\mathrm{SP}}{{\mathsf{\rho }}_{\mathrm{SP}}}+{\mathrm{V}}_{\mathrm{air}}=1,$$

(11)

where ${\mathsf{\rho }}_{\mathrm{W}}$, ${\mathsf{\rho }}_{\mathrm{C}}$, ${\mathsf{\rho }}_{\mathrm{SF}}$, ${\mathsf{\rho }}_{\mathrm{CA}}$, ${\mathsf{\rho }}_{\mathrm{S}}$, and ${\mathsf{\rho }}_{\mathrm{SP}}$ are the densities of water, cement, SF, coarse aggregate, sand, and superplasticizer, respectively, and ${\mathrm{V}}_{\mathrm{air}}$ is the volume of entrapped air in concrete.

(7)

For SF-modified concrete, the carbonation depth increases with SF content. Hence, carbonation durability may limit the use of SF in the concrete industry. This can be expressed as follows:

$${\mathrm{x}}_{\mathrm{c}}\left(\mathrm{t}\right)\le \mathrm{CV},$$

(12)

where ${\mathrm{x}}_{\mathrm{c}}\left(\mathrm{t}\right)$ is the concrete carbonation depth, and $\mathrm{CV}$ is the cover depth of concrete.

The carbonation depth of SF-modified concrete can be established in line with the efficiency factor of carbonation, which can be calculated using the following formula [18]:

$${ \mathrm{x}}_{\mathrm{c}}=\sqrt{\frac{2\mathrm{D}{[{\mathrm{CO}}_2]}_0\mathrm{t}}{0.218\ast \left(\mathrm{C}+0.3\ast \mathrm{SF}\right){\ast \mathsf{\alpha }}_{\mathrm{H}}}},$$

(13)

$$\mathrm{D}=6.1\ast {10}^{-6}{\left(\frac{\left[\mathrm{W}-0.267\ast \left(\mathrm{C}+0.30\ast \mathrm{SF}\right){\ast \mathsf{\alpha }}_{\mathrm{H}}\right]/1000}{\frac{\mathrm{C}+0.30\ast \mathrm{SF}}{{\mathsf{\rho }}_{\mathrm{c}}}+\frac{\mathrm{W}}{{\mathsf{\rho }}_{\mathrm{w}}}}\right)}^3{\left(1-\frac{\mathrm{RH}}{100}\right)}^{2.2}\exp \left[\mathsf{\beta }\left(\frac{1}{{\mathrm{T}}_{\mathrm{ref}}}-\frac{1}{\mathrm{T}}\right)\right],$$

(14)

where ${[{\mathrm{CO}}_2]}_0$ is the CO₂ concentration, $\mathrm{t}$ is time, $\mathrm{D}$ is the CO₂ diffusivity, ${\mathsf{\alpha }}_{\mathrm{H}}$ is the degree of hydration (${\mathsf{\alpha }}_{\mathrm{H}}=\min \left(\frac{\left(\frac{\mathrm{W}}{\mathrm{C}+0.3\ast \mathrm{SF}}\right)}{0.4},1\right)$) [22,23], $\mathrm{RH}$ is the relative humidity of the environment, ${\mathrm{T}}_{\mathrm{ref}}$ is the reference temperature (${\mathrm{T}}_{\mathrm{ref}}$ = 293 K), $\mathrm{T}$ is the temperature of the environment, and $\mathsf{\beta }$ is the temperature sensitivity coefficient of CO₂ diffusion ($\mathsf{\beta }$ = 4300) [22,23]. In Equations (13) and (14), ${[{\mathrm{CO}}_2]}_0$, $\mathrm{RH}$, and $\mathrm{T}$ represent environmental factors. The denominator of Equation (13) ($0.218\ast \left(\mathrm{C}+0.3\ast \mathrm{SF}\right){\ast \mathsf{\alpha }}_{\mathrm{H}}$) denotes the content of carbonizable substances. $\left(\frac{\left[\mathrm{W}-0.267\ast \left(\mathrm{C}+0.30\ast \mathrm{SF}\right){\ast \mathsf{\alpha }}_{\mathrm{H}}\right]/1000}{\frac{\mathrm{C}+0.30\ast \mathrm{SF}}{{\mathsf{\rho }}_{\mathrm{c}}}+\frac{\mathrm{W}}{{\mathsf{\rho }}_{\mathrm{w}}}}\right)$ in Equation (14) is an expression of concrete porosity. Hence, the diffusivity $\mathrm{D}$ is related to both concrete material properties and the exposure environment. Additionally, Equations (13) and (14) show that increases in CO₂ concentration and temperature lead to an increase in the carbonation depth of concrete. It is worth noting that global warming leads to an increase in CO₂ concentration and temperature.

SF leads to a reduction in heat of hydration, while the compressive strength of concrete for 90 or 360 days will be even greater in comparison with ordinary concrete. The performance evaluation model for SF blended concrete does not consider hydration heat and long-term (90 or 360 days) strength. In future work, these points should be considered to expand the functions of proposed methods. Moreover, the tests of CO₂ emissions and concrete performance, such as CO₂ emissions of concrete components, strength test, and carbonation depth test, should be performed to validate the used equations.

2.3. Genetic Algorithm

Mixture design allows establishing the individual masses of concrete components (e.g., cement, SF, water, sand, stone, and superplasticizer) that can achieve the design goal while fulfilling the various constraints [32,33,34]. These individual component variables can be determined using numerical methods, e.g., the genetic algorithm. The genetic algorithm is a widely used global optimization method. Drawing on the theory of biological evolution, the problem to be solved by the genetic algorithm is simulated as a process of biological evolution. The next-generation solutions are generated through duplication, crossing, mutation, and other operations, whereby the solutions with a low fitness function are gradually eliminated and those with a high fitness function are selected. Accordingly, after N generations of evolution, it is very likely that only individuals with a high fitness function will evolve [30]. The global optimization toolbox in MATLAB (Mathworks, Natick, MA, USA) may be used to determine the optimal mixtures.

The flowchart of the genetic algorithm is presented in Figure 1. The goal was to optimize CO₂ emissions, material cost, or total cost. The constraints of optimization considered were compressive strength, slump, carbonation, component range, component ratio, and absolute volume. After inputting the goal and constraints, the optimal mixtures for the design cases were determined.

3. Results and Discussion

This section outlines illustrated design cases with various design strengths. The 28-day strengths were set as 30, 40, 50, and 60 MPa, whereby the first two can be considered ordinary-strength concrete, while the last two can be considered high-strength concrete. The required slump was set as 180 mm. According to the design code [35], the cover depth was set as 25 mm. The environmental temperature was set as 20 °C. The relative humidity of the atmosphere was set as 0.60. The CO₂ concentration was set as 0.036%, with exposure starting in the year 2000. The service life was assumed to be half a century. The proportion of entrapped air content was set as 2%.

As presented in

Table 4. Optimal design cases of SF-modified concrete.

Cases	Mixtures	Aim	Carbonation Constraint	Design Strength
Case 1	Mixes 1–4	Low CO2	No carbonation	30, 40, 50, 60 MPa
Case 2	Mixes 5–8	Low CO2	Carbonation	30, 40, 50, 60 MPa
Case 3	Mixes 9–12	Low material cost	Carbonation	30, 40, 50, 60 MPa
Case 4	Mixes 13–16	Low total cost	Carbonation	30, 40, 50, 60 MPa
Case 5	Mixes 17–20	Low total cost	Carbonation with global warming	30, 40, 50, 60 MPa

, five design cases were considered: low-CO₂ concrete without carbonation, low-CO₂ concrete with carbonation, low-material-cost concrete with carbonation, low-total-cost concrete with carbonation, and low-total-cost concrete with global warming and carbonation.

As outlined in

Table 5. Highlighted points of design cases.

Highlighted Point	Comparison
Carbonation	Case 1 to Case 2
Difference between low-CO2 and low-material-cost concrete	Case 2 to Case 3
Difference between low-material-cost and low-total-cost concrete	Case 3 to Case 4
Global warming	Case 4 to Case 5

, cases 1 and 2 allowed clarifying the effect of carbonation durability on mixture design, cases 2 and 3 allowed distinguishing between low-CO₂ concrete and low-material-cost concrete, cases 3 and 4 allowed distinguishing between low-material-cost concrete and low-total-cost concrete, and cases 4 and 5 allowed clarifying the effect of global warming on mixture design. Furthermore, the comparison of strength levels ranging from 30 to 60 MPa enabled us to determine the effect of design strength on optimal design.

3.1. Case 1: Low-CO₂ Concrete without Carbonation

The genetic algorithm enabled us to identify mixtures with low CO₂ emissions. The carbonation durability constraint was not considered in this case. The optimal mixtures for case 1 are given in

Table 6. Optimal design mixtures for Case 1: low-CO₂ concrete without carbonation (unit: kg/m³).

	Cement	SF	Water	Fine Aggregate	Coarse Aggregate	Superplasticizer
Mix 1	210.30	37.11	168.23	964.87	890.65	7.66
Mix 2	254.16	44.85	168.43	939.33	867.07	9.41
Mix 3	294.56	51.98	168.68	916.24	845.76	10.57
Mix 4	332.42	58.66	168.95	894.83	826.00	11.39

, while their performance is presented in

Table 7. Performance of optimal design mixtures for Case 1: low-CO₂ concrete without carbonation.

	Strength (MPa)	Slump (mm)	CO2 Emissions (kg/m3)	Carbonation Depth (mm)	Water/Binder Ratio	SF/Binder Ratio	Water/Solid Ratio
Mix 1	30.00	261.11	185.69	43.07	0.68	0.15	0.08
Mix 2	40.00	239.22	222.30	30.01	0.56	0.15	0.08
Mix 3	50.00	225.02	255.90	21.47	0.49	0.15	0.08
Mix 4	60.00	214.98	287.33	15.53	0.43	0.15	0.08

. The water content for Mixes 1–4 was similar due to the water/solid ratio constraint, which was toward the lower limit, whereas the SF/binder ratio was toward the upper limit. This is because the CO₂ emissions are greater for 1 kg of cement than 1 kg of SF. When the goal of optimization was low CO₂ emissions, the SF/binder ratio was pushed toward the upper limit. Additionally, as shown in Figure 2, as the strength of concrete increased, the CO₂ emissions of concrete increased (Figure 2a), whereas the water/binder ratio decreased (Figure 2b), in accordance with [30,33,34].

The carbonation depth over time of Mixes 1–4 is depicted in Figure 2c–f. Following a service life of half a century, the carbonation depths of Mixes 1 and 2 exceeded the cover depth limit of 25 mm (Figure 2c,d), whereas the carbonation depths of Mixes 3 and 4 were below this limit (Figure 2e,f). Thus, carbonation durability could be satisfied for high-strength concrete (Mixes 3 and 4 with 50 and 60 MPa, respectively), but not ordinary-strength concrete (Mixes 1 and 2 with 30 and 40 MPa, respectively).

3.2. Case 2: Low-CO₂ Concrete with Carbonation

Section 3.1 presents the importance of and demand for carbonation durability for mixture design. The constraints were identical to the previous section except for the addition of carbonation.

The optimal mixtures and their performance are presented in

Table 8. Optimal design mixtures for Case 2: low-CO₂ concrete with carbonation (unit: kg/m³).

	Cement	SF	Water	Fine Aggregate	Coarse Aggregate	Superplasticizer
Mix 5	276.31	48.76	168.56	926.63	855.35	10.09
Mix 6 (Mix 5)	276.31	48.76	168.56	926.63	855.35	10.09
Mix 7	294.56	51.98	168.68	916.24	845.76	10.57
Mix 8	332.42	58.66	168.95	894.83	826.00	11.39

and

Table 9. Performance of optimal design mixtures for Case 2: low-CO₂ concrete with carbonation.

	Strength (MPa)	Slump (mm)	CO2 Emissions (kg/m3)	Carbonation Depth (mm)	Water/Binder Ratio	SF/Binder Ratio
Mix 5	45.39	230.90	240.73	25.00	0.52	0.15
Mix 6	45.39	230.90	240.73	25.00	0.52	0.15
Mix 7	50.00	225.02	255.90	21.47	0.49	0.15
Mix 8	60.00	214.98	287.33	15.53	0.43	0.15

, respectively. Mixes 5 and 6 had design strengths of 30 MPa and 40 MPa, respectively; however, their actual strengths were identical at 45.39 MPa. This suggests that carbonation durability may be the dominant factor of mixture design for Mixes 5 and 6. To improve carbonation durability, a greater actual strength can be used. The SF/binder ratio for Mixes 5 and 6 was toward the upper limit, as SF presents much lower CO₂ emissions than cement. Furthermore, the actual strengths of Mixes 7 and 8 were as projected, suggesting that carbonation did not influence the strength properties of high-strength concrete (50 and 60 MPa). As shown in Figure 3, an increase in concrete strength led to an increase in CO₂ emissions (Figure 3a) and a decrease in water/binder ratio (Figure 3b), in accordance with [30,33]. For Mixes 5 and 6, the carbonation depth was equal to the cover depth (Figure 3c,d, respectively), whereas, for Mixes 7 and 8, the carbonation depth was lower than the cover depth (Figure 3e,f, respectively).

Moreover, we can find that Mix 3 in Table 4 is the same as Mix 7 in Table 8. Similarly, Mix 4 in Table 4 is the same as Mix 8 in Table 8. This is because Mix 3 and Mix 4 have higher design strengths (the design strengths of Mix 3 and Mix 4 are 50 MPa and 60 MPa, respectively). Concrete with higher design strengths show higher resistance of carbonation, and the requirement of carbonation durability can be satisfied for these high-strength concretes. In other words, the constraint of carbonation durability does not affect the optimal design results of high-strength concrete.

3.3. Case 3: Low-Material-Cost Concrete with Carbonation

In the previous two sections, the goal of optimal design was low CO₂. However, material cost is also a vital index of concrete sustainability. In this section, the material cost of concrete was taken as the goal of optimal design. Using the genetic algorithm, the optimal mixtures with a low material cost were calculated, as presented in

Table 10. Optimal design mixtures for Case 3: low-material-cost concrete with carbonation (unit: kg/m³).

	Cement	SF	Water	Fine Aggregate	Coarse Aggregate	Superplasticizer
Mix 9	287.79	15.15	169.60	944.90	872.21	6.40
Mix 10	338.99	17.84	170.08	919.96	849.19	7.25
Mix 11	393.54	20.71	170.62	893.61	824.87	7.91
Mix 12	444.78	23.41	171.15	868.99	802.14	8.38

. The performance of the optimal mixtures for Case 3 is outlined in

Table 11. Performance of optimal design mixtures for Case 3: low-material-cost concrete with carbonation.

	Strength (MPa)	Slump (mm)	Material Cost (TWD/m3)	Carbonation Depth (mm)	Water/Binder Ratio	SF/binder Ratio
Mix 9	31.28	243.11	1648.56	25.00	0.56	0.05
Mix 10	40.00	227.42	1832.50	16.55	0.48	0.05
Mix 11	50.00	215.44	2022.50	10.34	0.41	0.05
Mix 12	60.00	207.06	2197.35	7.73	0.37	0.05

. First, for Mixes 9–12, the SF/binder ratio was equal to the lower limit, as the material cost of SF is greater than that of cement. Second, for Mix 9, the design strength was 30 MPa but the actual strength was 31.28 MPa, suggesting that carbonation dominated the mix style of Mix 9. After 50 years of service life, the carbonation depth of Mix 9 was equal to the cover depth. Third, as shown in Figure 4, as the strength of concrete increased, the cost of material increased (proven in Figure 4a), whereas the water/binder ratio of concrete (Figure 4b) and the carbonation depth of concrete decreased (Figure 4c–f), in agreement with [32,33,34]. For Mixes 10–12, the carbonation depth after 50 years of service life was lower than the cover depth (Figure 4d–f, respectively).

3.4. Case 4: Low-Total-Cost Concrete with Carbonation

The previous two sections outlined the optimal design of low-CO₂ concrete and low-material-cost concrete. However, as CO₂ emissions cannot be directly compared to material cost, this study used the carbon price to convert CO₂ emissions into CO₂ emission cost; furthermore, the total cost was calculated as the sum of material and CO₂ emission cost. Using the genetic algorithm, the optimal design of low-total-cost concrete with carbonation (

Table 12. Optimal design mixtures for Case 4: low-total-cost concrete with carbonation (unit: kg/m³).

	Cement	SF	Water	Fine Aggregate	Coarse Aggregate	Superplasticizer
Mix 13 (Mix 9)	287.79	15.15	169.60	944.90	872.21	6.40
Mix 14 (Mix 10)	338.99	17.84	170.08	919.96	849.19	7.25
Mix 15 (Mix 11)	393.54	20.71	170.62	893.61	824.87	7.91
Mix 16 (Mix 12)	444.78	23.41	171.15	868.99	802.14	8.38

) was found to overlap with the results in the previous section. This is because the CO₂ emission cost, representing approximately 12% of the total cost (Figure 5a), was substantially lower than the material cost; thus, the optimal design was not substantially altered. Figure 5b also shows that an increase in concrete strength led to an increase in total cost.

3.5. Case 5: Low-Total-Cost Concrete with Global Warming

In the previous three sections, the effect of carbonation on optimal design was considered. Carbonation is a complex physicochemical process, whose rate varies as a function of the environmental conditions, e.g., CO₂ concentration and environmental temperature. Global warming is the unusually rapid increase in Earth’s average surface temperature over the past century primarily due to the greenhouse gases released by people burning fossil fuels. The increases in CO₂ concentration and temperature are vital indicators of global warming. Due to global warming, both CO₂ concentration and temperature are increasing, consequently affecting the carbonation service life. Thus, concrete mixture design might also be affected.

The Intergovernmental Panel on Climate Change (IPCC) has proposed several representative concentration pathways (RCPs), such as RCP2.6, RCP4.5, RCP6.0, and RCP8.5 [36], representing various global warming scenarios. Among these scenarios, RCP8.5 features the greatest increase in CO₂ concentration and temperature. This study considered the effect of RCP8.5 on optimal design, thereby introducing the effect of global warming.

The increases in CO₂ concentration and temperature under RCP8.5 are depicted in Figure 6a,b, respectively. To determine the carbonation depth under this global warming scenario, the time-averaged CO₂ concentration $\frac{{{\displaystyle \int }}_0^{\mathrm{t}}{\left[{\mathrm{CO}}_2\right]}_{\mathrm{t}}\mathrm{dt}}{\mathrm{t}}$ and time-averaged CO₂ diffusivity $\frac{{{\displaystyle \int }}_0^{\mathrm{t}}{\left[\mathrm{D}\right]}_{\mathrm{t}}\mathrm{dt}}{\mathrm{t}}$ were utilized [36].

According to the genetic algorithm, the optimal mixtures were determined, as presented in

Table 13. Optimal design mixtures for Case 5: low-total-cost concrete with global warming (unit: kg/m³).

	Cement	SF	Water	Fine Aggregate	Coarse Aggregate	Superplasticizer
Mix 17	300.83	15.83	169.72	938.52	866.33	6.64
Mix 18 (Mix 10)	338.99	17.84	170.08	919.96	849.19	7.25
Mix 19 (Mix 11)	393.54	20.71	170.62	893.61	824.87	7.91
Mix 20 (Mix 12)	444.78	23.41	171.15	868.99	802.14	8.38

. The performance of these optimal mixtures for Case 5 is shown in

Table 14. Performance of optimal design mixtures for Case 5: low-total-cost concrete with global warming.

	Strength (MPa)	Slump (mm)	Total Cost (TWD/m3)	Carbonation Depth (mm)	Water/Binder Ratio	SF/Binder Ratio
Mix 17	33.44	238.58	1920.72	25.00	0.54	0.05
Mix 18	40.00	227.42	2084.45	18.35	0.48	0.05
Mix 19	50.00	215.44	2313.43	11.47	0.41	0.05
Mix 20	60.00	207.06	2524.89	8.58	0.37	0.05

. The design strength of Mix 17 was 30 MPa; however, its actual strength was 33.44 MPa, as carbonation durability dominated the mixture design to a greater extent than Mix 13 due to global warming. To address carbonation with global warming, a greater binder content and greater strength ought to be used. The results for Mixes 18–20 overlapped with those for Mixes 14–16, respectively, suggesting no influence of global warming. The superior binder content of these mixes led to increased resistance to carbonation even in the face of global warming. Figure 7 shows that, as the strength of concrete increased, the total cost of concrete increased (Figure 7a), whereas the water/binder ratio (Figure 7b) and carbonation depth decreased (Figure 7c–f). Furthermore, the case study results show that the carbonation depth of concrete under global warming was substantially greater than that without global warming, especially toward the end of service life (Figure 7c–f).

3.6. Discussion

In contrast to previous studies, the suggested design framework revealed several improvements, as outlined below.

Firstly, previous mixture design studies did not pay enough attention to carbonation durability. In this study, it was found that carbonation durability is not a critical issue for high-strength concrete, but it has an effect on ordinary-strength concrete. Thus, it is vital to identify the threshold strength under which carbonation durability should be considered. This can be achieved using the proposed design method, which revealed that this threshold strength is dependent upon the goal and constraints of design. For low-CO₂ concrete, low-cost concrete, and low-cost concrete with global warming, the threshold strengths were 45.39 MPa, 31.28 MPa, and 33.44 MPa, respectively.

Secondly, previous mixture design studies did not consider the impact of global warming. This study found that global warming had a significant impact on the mixture design of ordinary-strength concrete (30 MPa), but it failed to influence the higher-strength mixtures (40, 50, and 60 MPa). Hence, for 30 MPa concrete, additional engineering techniques, such as increasing the cover depth, using additional coating, and increasing the design strength, should be used to improve the service life with respect to carbonation durability.

Thirdly, previous studies mainly focused on low-cost concrete or low-CO₂ concrete, whereas the difference between low-cost concrete and low-CO₂ concrete was not clarified. In this study, the proposed method enabled the design of low-cost concrete or low-CO₂ concrete, which were found to differ as a function of the SF content due to its higher price but lower CO₂ emissions. Thus, the proposed method was proven to be flexible in finding optimal mixtures for different goals.

Fourthly, the final application of this paper can be the optimal design of sustainable silica fume blended concrete. To use the proposed method, the aim of the optimal design (Equations (1)–(3)) should be established. Moreover, the constraints of optimal design should be added. Finally, optimal mixtures can be found considering both the aim and the constraints of optimal design. In addition, the sustainable design of silica fume blended concrete consists of many sub-aims, such as low-CO₂ and low-cost. The proposed method considers these different design aims and is suitable for various design cases.

Lastly, for various design codes, the calculation equations for strength, slump, and carbonation depth of SF-modified concrete might differ [10,17,18,22,23]. However, the genetic algorithm can be used as an optimization process for various constraint equations, thus allowing other researchers to determine the optimal mixture designs for their circumstances using the proposed integrated design framework. The findings are interesting and may be valuable in the design stage of construction to establish the cover depth in accordance with environmental exposure or the types of elements. Nevertheless, some further research based on laboratory tests may be relevant to validate the findings.

4. Conclusions

This study proposed an integrated mixture design framework for sustainable SF-modified concrete, which implemented the genetic algorithm to determine optimal mixtures. Strength, slump, and carbonation with or without global warming were considered as constraints of optimization, whereas CO₂ emissions, material cost, and total cost were established as the goals of optimization. According to the analysis of five design cases, the following conclusions could be drawn:

(1)

Case 1 (low-CO₂ concrete without carbonation) showed that the carbonation durability constraint could be fulfilled for high-strength concrete (Mixes 3 and 4, 50 MPa and 60 MPa, respectively) but not ordinary-strength concrete (Mixes 1 and 2, 30 MPa and 40 MPa, respectively). For all mixes, the SF/binder ratio was toward the upper limit due to the substantially lower CO₂ emissions of SF than cement.

(2)

Case 2 (low-CO₂ concrete with carbonation) showed variations in the actual strength of ordinary-strength concrete with respect to their design strength (Mixes 5 and 6, 45.39 MPa for both), suggesting that carbonation dominated the mixture design. Thus, to satisfy the carbonation durability, greater actual strength can be obtained. On the other hand, no such influence was found on high-strength concrete (Mixes 7 and 8).

(3)

Case 3 (low-material-cost concrete with carbonation) revealed that the SF/binder ratio was toward the lower limit for Mixes 9–12, due to the greater material price of SF compared to cement. Additionally, for Mix 9, the actual strength (31.28 MPa) was greater than the design strength (30 MPa), suggesting that carbonation dominated the mixture design. After 50 years of service life, the carbonation depth of Mix 9 was equal to the cover depth.

(4)

Case 4 (low-total-cost concrete with carbonation) revealed similar results for Mixes 13–16 to those for Mixes 9–12, respectively, as the cost of CO₂ emissions (12% of total cost) was substantially less than the material cost and, thus, did not influence the outcome.

(5)

Case 5 (low-total-cost concrete with carbonation and global warming) showed that, for Mix 17 (design strength of 30 MPa), global warming led to an increase in actual strength from 31.28 to 33.44 MPa. Thus, to fulfill the constraints of carbonation with global warming, a greater binder content or greater strength ought to be used. However, global warming was not found to influence the mixture design of higher-strength concretes (40, 50, and 60 MPa).

In the future, the following aspects should be considered: CO₂ emissions from production phase and transportation phase; a performance evaluation model considering the chemical content, mineralogical composition, specific gravity, particle size, or surface area of the silica fume; a performance evaluation model for hydration heat and long-term (90 or 360 days) strength.

In summary, the proposed framework is able to strive for different goals (CO₂ emission, material cost, or total cost) as a function of various constraints (strength, workability, and carbonation durability with or without global warming). The suggested technique can be used as a general process for the optimal design of sustainable SF-modified concrete.