One of the most utilised construction materials in the world is concrete. The concrete industry is also a significant source of CO₂ gas emissions (1-3). Approximately one cubic meter of concrete is produced per person annually (4). Ordinary Portland cement (OPC) has traditionally been the binder material in concrete, whereas aggregate, water and chemical admixtures have been used as the mix constituents in the production of normal concrete. As a result, CO₂ is emitted from concrete, in the range of 800 kg-820 kg per one ton of produced cement (5). Some studies have indicated that CO₂ emissions can be as high as 700 kg-1000 kg to produce 1000 kg of cement (6, 7). The production of coarse aggregate and fine aggregate also emits 45.9 kg-CO₂-e/ton (5) and 13.9 kg CO₂-e/ton (5), respectively.

Statistical methods, such as a design of experiments (DOE), are an accurate framework used to understand the connections between variables, for instance, those affecting mix design proportion (8-10). However, casting several trial mixtures in the laboratory requires a notable quantity of raw materials, including cement, water, chemical admixtures, coarse aggregate and fine aggregate. Thus, CO₂ emission will increase (1). The production of the raw materials and transport can also increase the consumption of energy, and thereby lead to increased CO₂ emissions (11). Therefore, the aim of this study is to optimise mixture design for normal concrete using a DOE along with PSO methods to reduce CO₂ emissions. Additionally, compressive strength, flexural strength, and splitting-tensile strength were tested to evaluate the mechanical properties of the concrete.

Concrete properties can be affected by the physical properties of the aggregate and the cement paste. These factors can significantly influence the mechanical properties of concrete, including the compressive, flexural and splitting strength. Other factors can influence the mechanical properties of normal concrete, such as the water/cement ratio, the coarse aggregate/fine aggregate ratio, and the cement quantity. Due to using the same material properties in all 47 mixtures in this study, the physical and micromechanical properties of the concrete did not change from sample-to-sample. Therefore, very little effect can be achieved in final model equations, thus, using another factors instead of materials quantities can led to the similar results in the final models equations of DOE and PSO methods. By utilising a statistical method in this study, the quantities of materials will be easy to control as the main factors in the analysis. The five main control factors in the DOE and the PSO methods included the material quantities of cement, coarse aggregate, fine aggregate, the water-cement ratio, and the chemical admixtures/superplasticiser (SP).

The DOE method, using a response surface methodology (RSM) technique defines a suitable model necessary to create a relationship between the factors and the various responses (9, 10, 12). Generally, artificial intelligence (AI) techniques are adopted within prediction, optimisation, classification, and visualization. DOE has been widely used in engineering fields (13). The main objective of optimisation methods is to achieve values from a set of parameters, which maximise and minimise objective functions subject to constraints. Some studies have suggested using the particle swarm optimisation (PSO) algorithm to improve the techniques (14, 15). Optimisation methods using PSO apply the behaviour of flocking birds. The PSO method is based on a randomly initialised population. It can solve engineering problems using very few parameters, avoiding trial and error, to find the appropriate coefficients of the proposed model. PSO has been used successfully in structural engineering (16-20).

In this study, factorial design of experiments (DOE) and PSO were applied to evaluate several factors in different concrete mixtures. A 47 mixture design was used in the DOE program and the PSO method solved the appropriate equations required to assess concrete strength, splitting strength, and flexural strength. The purpose of this study was to identify the best mixture recipe in order to achieve optimum performance of the concrete, while decreasing CO₂ emissions. The interaction between the mixture contents was modelled using central composite design (CCD). The predicted accuracy of these equations was expected to be up to 94.00% of the experimental results. The equations can be used in future to determine the required compressive strength, splitting strength and flexural strength of concrete, thereby saving time and reducing concrete material waste resulting from a number of trial and error mixtures.

The CO₂ emissions ranged from 820 kg-CO₂-e/ton to 927 kg-CO₂-e/ton for the production of one ton of cement (21). In contrast, other studies have cited that the CO₂ emissions reached 1000 kg-CO₂-e/ton (6, 7). The manufacture of one ton of coarse aggregate and one ton of fine aggregate produce 45.90 kg-CO₂-e/ton (5) and 13.90 kg- CO₂-e/ton (5), respectively. One litre of SP produces 5.20 x 10^-3 kg-CO₂-e (22). Thus, by using the equations from this study, instead of conducting multiple experimental trials, the overall cost and the CO₂ emissions will be greatly reduced. The prediction/optimisation was conducted to estimate the cement content recipe in order to produce the required performance. Generally, the predicted values will provide lower cement content than an experimental result, owing to the number of iterations.

RSM involves the optimisation of parameters using experimental results in order to understand the interactions between the parameters and reduce the number of runs required in experiments (24-27). Hence, it has been used for many applications in civil engineering to evaluate the optimisation of mix proportions in concrete and pavement design (12, 28, 29). RSM has become more popular in recent years (9, 10, 12, 28-30). Accordingly, Design-Expert version 10.0 was used in this study to determine the optimum equations for the responses of the concrete through experimental and statistical analyses. For the purpose of this study, the effect of five factors and four responses were investigated utilising a 47 mixture matrix by applying Central Composite Design (CCD). The numerical variables were transferred to the coded form using equation [1]:

where, x_i defines the i_th independent factor using the coded value, Xi and X_o are the actual values at the centre point, and ΔX is defined as the change in the i_th variable.

A 47 experimental mixtures run were adopted to determine the relationship between the factors and the responses. The dependent variables were calculated using equation [2] (31, 32):

where Y refers to the response value through calculation, and β₀ is a constant. x_i and x_j represent independent variables in coded form. The coefficient β_i represents the linear term, while β_ii represents the quadratic term. e is the random error, β_ij is the coefficient of interaction term, and n represents the number of studied factors. An analysis of variance (ANOVA) was applied to evaluate the output. The coefficient R² and R²_adj determined from equations [3] and [4], were calculated to evaluate the accuracy of the suggested model (33). The preferred values of R² and R²_adj should be greater than 0.80.

where SS is the squares summation and DF represents the degrees of freedom. In order to evaluate the significance of the model, the adequate precision (AP) was checked using equations [5] and [6] and an F-test.

where p is the parameter number of the model, Y refers to the response of the predicted value, n is the number of experiments, and σ² is the mean of the residual square. Upon completion of the F-test, the insignificant terms in the model were identified and eliminated, which was followed by the introduction of the finalized model.

Optimisation is required to create a two-dimensional (2D) method for 47 mixtures of normal concrete. The key points taken into account in its enhancement are as follows:

The itemised points are further expanded upon in the next sections.

Table 4 presents the mixture proportions of the concrete. Cylindrical samples of 300 mm in height and 150 mm in diameter and cubes of 100 x 100 x 100 mm were stacked into three layers and compacted with vibration in compliance with the specifications of BS EN 12390-1 (2000) (37). Experimental tests were conducted after 28 days of curing the concrete samples in water. Compression tests were performed to comply with BS EN 12390-1, 3, and 4 (2009) (37, 38). In addition, flexural strength tests complied with BS EN 12390-5 (2009)(39) and splitting tensile strength tests complied with BS EN 12390-6 (2009)(40). The results reported were the average of three samples.

Pure error calculations were performed if exact duplicates could be detected, unless the duplicates were in separate blocks. In such cases, an independent estimate of pure error is obtained, which Design-Expert can use for evaluation of the statistical significance. The program pools the pure error, with error estimated from the unselected effects. Design-Expert labels the error estimated from the non-significant effects as “lack of fit”. That value is then tested against the pure error to check if the model adequately fits the response data. Models with large lack of fit F-values (small probability values) may be inadequate as representations of the true surface. The analysis should have pure error, with several degrees of freedom from true replicates in order to proceed it. Otherwise, the analysis will be rejected. Moreover, pure error and residual error should each estimate the same experimental variability. The program includes the error estimate from replicate points on the probability plots used to choose factorial model effects. Based on the slope calculated from the pure standard error, Design-Expert constructs an initial reference line, as depicted in Figure 7. As a result, the error is very small and the probability was 96.00%.

The most popular method applied to predict the output response with respect to input parameters is Central Composite Design (CCD). CCD has three groups of design points, namely a) two-level factorial design points, b) axial points, and c) centre points. The analysis using CCD requires five levels of each factor in order to assess the experimental results, such as –α, −1, 0, +1 and +α; see Figure 6.

A graphical optimisation tool was used for the concrete responses. The experimental results were analysed using the central composite method to obtain the best fit empirical mathematical model. The type of polynomial model obtained for the responses were linear and quadratic interactions. The mathematical equations, which corresponded in terms of coded factors with materials units in kg/m³ were as follows.

where C is cement amount, FA is fine aggregate amount, CA is coarse aggregate amount, W is water amount and SP are the chemical admixtures amount. Here, C, FA, CA, W, and SP must all be greater than zero. Section 10 presented the material ranges, which can be applied in the model equations of the DOE and PSO.

Moreover, using these equations was very accurate, with 94.00% accuracy compared to the experimental results. Thus, the equations can be used with confidence, saving time and money, while decreasing CO₂ emissions.

Figure 7 presented the responses across selected factors, which can also be used to predict responses. The red coloured area shows the maximum effect of the parameter on the response. The parameters that had the highest effect on the compressive strength and splitting-tensile strength were cement, SP, water, coarse aggregate and fine aggregate, in that particular order. Fine aggregate had a larger effect than coarse aggregate on flexural strength. The percentage accuracy of the results is presented in Table 7.

The accuracy of the results that used the equations, as presented in Table 7, revealed that the flexural strength, compressive strength, and splitting-tensile strength had slightly higher average values than the experimental results. The 3D surfaces of the responses are depicted in Figure 8. The response changed when other factors were added into each level, as shown in Figure 9. The figure also presents the effect of cement and fine aggregate factors. Water and SP significantly influenced the result of the responses. The values of the response increased when the quantity of water decreased and quantity of SP increased. Additionally, the fine aggregate had a larger effect on controlling concrete paste strength than SP or coarse aggregate. Increasing the coarse aggregate quantity enhanced the splitting strength value.

Based on the (2D) contour plots and (3D) surface responses, the results improved by increasing the quantities of cement, SP, coarse aggregate, and fine aggregate, as well as when decreasing the water ratio. The optimum contents of the concrete mixture in order to obtain the best mechanical properties are presented in Figure 9.

Four PSO models were built to optimise the compressive, flexural, and splitting strengths of concrete. The parameters of these models represented the quantities of cement, water, SP, fine aggregate, and coarse aggregate. The target of the PSO objective function was to minimise the variance of the predicted and measured strength. PSO provided the models to evaluate the strength capacity within the range of the maximum and minimum quantities of the experimental results. The PSO algorithm was updated until a suitable g_best was achieved or the maximum number of iterations was reached. The objective function variances were constant after 1200 iterations. Thus, the number of iterations was fixed at 2000, as depicted in Figure 10. In this study, 10, 20, 30, 40 and 50 particles were used to explore the effect of the number of particles on the accuracy of the models. The swarm sizes are presented in Figure 10, though 10, 20, 30, 40, and 50 were used for MAE to estimate the differences between the measured and predicted mechanical properties of concrete. Figure 10 also shows the performance measure variation values of the objective function for particles of different sizes. The best solution of the PSO algorithm was provided by a swarm size of 40, as illustrated in Figure10. The remaining swarm sizes indicated higher errors and were more time consuming. Finally, equations [16] to [19] presents the best factors to evaluate the mechanical properties of normal concrete.

where C is cement amount, FA is fine aggregate amount, CA is coarse aggregate amount, W is water amount and SP are the chemical admixtures amount. All values should be greater than zero.

The compressive strength, flexural strength, and splitting-tensile strength using equations [16] to [19] can give good agreement about the accuracy values required to find the mechanical properties within the maximum and minimum quantities of the factors as mentioned in Table 4.

Table 8 presents the average accuracy values using equations [16 to 19] in the PSO method. The correlation factor (R) exceeds 0.8 based on the logical hypothesis, thus a strong correlation is achieved between the predicted and actual values (36). Therefore, a satisfactory degree of accuracy is obtained from the analysis results of the DOE and PSO methods, as depicted in Figure11. The results of the analysis using PSO algorithm have shown that the predicted values are close to the actual results of the experimental tests. This shows a high accuracy as presented in Table 8. Therefore, applying PSO and RSM as optimisation methods in this study is quite useful to identify the best mix proportion based on the mechanical properties of the concrete. In addition, the results of the equations using both RSM and PSO methods can be applied within the range of the 47 concrete mixes constituents. The material quantities in the DOE and PSO model equations should not be equal to zero. The range of the cement contents in the 47 experimental mixtures of concrete used was from 380 kg/m³ to 550 kg/m³. The water-cement ratio (W/C) ranged from 0.30 to 0.40. The coarse aggregate range was 758.00 kg/m³ to 1293.00 kg/m³. The fine aggregate sizes were less than 4.75 mm and its content ranged between 441.75 kg/m³ and 925.00 kg/m³. The ratio of the chemical admixtures or superplasticiser (SP) type © Sika^® ViscoCrete ® 2044 was 3.25 kg/m³ to 6.50 kg/m³, which is equivalent to 0.68% to 1.44% of the weight of the cement. Therefore, equations [12] to [19] were valid for these ranges of materials and can be applied in order to determine the compressive, flexural, and splitting-tensile strengths.

The clinker in the cement production process uses mineral raw materials and fuel, which require a high temperature. Both fuel and raw materials emit CO₂ and the clinker production requires 3.2 GJ per ton using a wet rotary kiln (41, 42). Electricity of 0.06 GJ/ton was used to produce the clinker, due to the need for grinding. Cement binders can also be used, instead of a clinker (42). Coarse aggregates and fine aggregates typically take up 80% of a concrete mixture. The production process of aggregate involves extraction, crushing, sieving, and transportation. Extraction of one ton of natural aggregate requires 20 MJ of oil and 9 MJ of electricity, while one tonne of crushed coarse aggregate requires 120 MJ of oil and 50 of MJ electricity (43). The CO₂ emissions resulting from the production of cement ranges between 820 kg- CO₂-e/ton and 927 kg- CO₂-e/ton (21), and occasionally reaches 1000 kg- CO₂-e/ton (6, 7). One ton of coarse aggregate produces 45.90 kg-CO₂-e/ton (5) and one ton of fine aggregate emits 13.90 kg- CO₂-e/ton (5). In addition, one litre of SP produces 5.20 x 10^-3 kg-CO₂-e (22); see Figure 12.

The total quantity of materials used in the experimental works are presented in Table 9. The CO₂ emissions from materials were calculated using equation [20] and presented in Table 10.

where, Qi is the quantity of material, such as cement, coarse aggregate, fine aggregate, water, and SP, and CO_2-em is the CO₂ emission rate, as presented in Table 9.

The CO₂ emissions due to the materials used were 6.133 ton-CO₂-e/ton, 0.612 ton-CO₂-e/ton, 0.126 ton-CO₂-e/ton, 0.771 ton-CO₂-e/ton, and 0.3(30) x 10^-3 ton-CO₂-e/ton for cement, coarse aggregate, fine aggregate, water and chemical admixtures, respectively. Thus, the CO₂ emission ratios were equivalent to 80.25%, 8.01%, 1.6%, 10.09%, and 0.00431% for cement, coarse aggregate, fine aggregate, water, and chemical admixtures, respectively.

This study aimed to evaluate the effect of concrete mixture parameters on the response results and CO₂ emissions. The parameters represented the mixture proportions and the responses referred to the mechanical properties of concrete. RSM and PSO algorithm methods were used to find the optimum models to reduce CO₂ emissions. The predicted results showed good agreement with actual results. Thus, the following conclusions can be drawn from the results of the study.