Optimisation of Limestone Calcined Clay Cement Based on Response Surface Method

Abstract

Limestone calcined clay cement (LC3) is a new type of cement that contains Portland cement, calcined clay, and limestone. Compared with traditional cement clinker, LC3 reduces CO₂ emissions by up to 40%, and is a promising technology for the cement industry to achieve its emission target. We used a numerical approach to predict the optimum composition of LC3 mortar. The experiments were performed using central composite rotational design under the response surface methodology. The method combined the design of mixtures and multi-response statistical optimization, in which the 28-day compressive strength was maximized while the CO₂ emissions and materials cost were simultaneously minimized. The model with a nonsignificant lack of fit and a high coefficient of determination (R²) revealed a well fit and adequacy of the quadratic regression model to predict the performance of LC3 mixtures. An optimum LC3 mixture can be achieved with 43.4% general purpose cement, 34.16% calcined clay, 20.6% limestone and 1.94% gypsum.

1 Introduction

Concrete is the most widely used construction material, and as an essential component, Portland cement (PC) production accounts for approximately 8% of annual anthropogenic greenhouse gas emissions [1]. Because there is no viable economic alternative to concrete, cement consumption is ever-growing. Currently, using supplementary cementitious materials (SCMs) to achieve a partial clinker replacement is the most effective strategy to reduce cement production. Nevertheless, the shortage of traditional SCMs (e.g., fly ash and slag) requires exploration of other types of cementitious materials [2].

Recently, researchers have worked on limestone calcined clay (LC3) cement, which consists of PC, calcined clay (metakaolin: MK), and limestone (LS). Such a combination of ingredients allows higher clinker replacement and leads to the development of a denser microstructure that gives LC3 excellent mechanical and durability performance [3]. Because LC3 cement has various components, the single-factor method is mainly used in the design of material proportions in LC3 cement, but this can only obtain an optimal mix design for a single performance and cannot achieve multi-objective optimization. In comparison, the response surface method (RSM) is especially advantageous for designing a competitive and more sustainable blended cement binder [4].

In this study, central composite rotation design (CCRD) in RSM was performed. The content of MK, LS and gypsum (GYP) was taken as the variables. The 28-day compressive strength, CO₂ emission, and materials cost were used as response values. The mathematical model was established by analysis of variance (ANOVA) to determine the interaction of various variables and model accuracy. The multi-objective optimization of LC3 mortar was achieved using the numerical-functional optimization model.

2 Methods

2.1 Materials

LS, MK, GYP, and general-purpose cement (GPC) were used to create the LC3 binder mixtures (Table 1). MK was obtained after calcination of kaolin clay at 800 °C for 2 h. The LS, MK and GYP were ground using a horizontal roller mill. Concrete sand with a particle size ranging from 75 to 2.36 mm and a specific density of 2.64 was collected from ResourceCO Australia. A polycarboxylate-based superplasticizer was used to maintain the same consistency for all mixtures (between 185 and 195 mm). Mortar samples with a binder to aggregate ratio of 1:2.75 were cast in accordance with ASTM C305.

Table 1 Chemical and physical characteristics of the binder materials

2.2 Design of Mixtures

CCRD is the most suitable technique in RSM to obtain a highly effective mathematical experiment design and develop a functional relationship between the variables and responses [5]. For the binder design of LC3 cement, MK content (x₁), LS content (x₂) and GYP content (x₃) were selected as the independent variables. The PC replaced by other ingredients was by mass and defined as a weight percentage of the total binder mass. The variable levels were selected to vary from 0 to 60% for MK, 0% to 30% for LS and 0% to 5% for GYP. The effect of each independent variable was assessed at five levels with a code value of –alpha, –1, 0, 1, + alpha (factorial, axial and central points). The spatial schematic illustration of CCRD is shown in Fig. 1. Three replicates are considered at the central point, resulting in 17 experimental runs. The mix proportions are shown in in Table 2.

Fig. 1

Schematic illustration of central composite rotational design

Table 2 Central composite design matrix and LC3 mortar mix proportions

The compressive strength of the mortar sample at 28 days (Y₁), CO₂ emissions (Y₂), and materials cost (Y₃) were taken as the response variables. The 28-day compressive strength was recorded experimentally, while the environmental responses, such as CO₂ emissions and materials cost, were evaluated based on per kg of mortar sample. The relevant information on CO₂ emission and the material cost was collected from previous publications or estimations of local materials’ market prices. All data used are shown in Table 3. The cost of mortar casting procedures and the emission from mortar service life were not taken into account.

Table 3 Relevant data on emission and cost for LC3 mortar manufacture

The Design-Expert 12.0.3.0 (Sat-Ease Inc., Minneapolis, MN, USA) software was used to develop the mathematical design and ANOVA of the experiments. The quadratic polynomial model was used to predict the optimal conditions, where Y is the response value, $\upbeta$ is the regression coefficient, $\upvarepsilon$ is the random error, ${\mathrm{X}}_{\mathrm{i}}$ and ${\mathrm{X}}_{\mathrm{j}}$ are the independent variables, and k is the number of variables.

$$\mathrm{Y}={\upbeta }_{0}+\sum_{\mathrm{i}=1}^{\mathrm{k}}{\upbeta }_{\mathrm{i}}{\mathrm{x}}_{\mathrm{i}}+\sum_{\mathrm{i}=1}^{\mathrm{k}}{\upbeta }_{\mathrm{ii}}{\mathrm{x}}_{\mathrm{i}}^{2}+\sum_{\mathrm{i}=1}^{\mathrm{k}}\sum_{\mathrm{j}>1}^{\mathrm{k}}{\upbeta }_{\mathrm{ij}}{\mathrm{X}}_{\mathrm{i}}{\mathrm{X}}_{\mathrm{j}}+\upvarepsilon $$

(1)

3 Mathematical Modelling and Statistical Analysis

3.1 ANOVA and Adequacy Checking

The ANOVA for the surface response model revealed the model’s accuracy and reliability. Specifically, the p-value and F-value at a 95% confidence level were computed to verify the model and the model’s terms significant degree for each response. A p-value < 0.05 and a larger F-value indicated the model terms have a significant influence, while p-values ≥ 0.05 are considered insignificant. In addition, the lack of fit test measured the degree of fitting between the predicted model and input variables. If the p-value for lack of fit is > 0.05 (non-significant), it implies that: (1) the generated model fits the experimental data well, and (2) the independent variables have considerable effects on the response. When the p-value is < 0.05, seriously insufficient fitting is recorded, indicating the model was not well fitted to the input data. The ANOVA results for Y₁ to Y₃ are shown in Table 4. The response for the model showed a p-value < 0.05 indicating a good fit; however, the response for the lack of fit had a p-value > 0.05, indicating an insignificant lack of fit.

Table 4 Analysis of variables of the test results

The regression coefficients (${\upbeta }_{0}, {\upbeta }_{\mathrm{i}}, {\upbeta }_{\mathrm{ii}} \& {\upbeta }_{\mathrm{ij}}$) were estimated by ANOVA, and the regression models for each response as functions of %MK, %LS and %GYP are summarised in Table 5. The coefficient of determination (R²) was obtained to ascertain the accuracy of the predicted function. For all responses, the R² values were >95%, which indicated a high degree of correlation to the experimental data.

Table 5 Regression models for each response

3.2 Interaction Effects on Response

The three-dimensional response surface plots (see Fig. 2) were shown to evaluate the influence of interactions of different variables on the corresponding response value. The plot presented the interaction of two variables considering that the third variable was fixed on the central point in the CCRD design. The significance of the variables interaction is denoted by the surface steepness and the variable interaction p-value [6]. Therefore, the variable interaction with the smallest p-value was considered to study the influence of two independent variables on the responses. Based on the ANOVA results shown in Table 4, the selected variable interaction is X₁X₂, X₁X₃ and X₁X₃ for 28-day compressive strength (Y₁), CO₂ emissions (Y₂) and materials cost (Y₃).

Fig. 2

Three-dimensional response surface plots. a 28-day compressive strength, b CO₂ emissions, c materials cost. GYP, gypsum; MK, metakaolin; LS, limestone

3.3 Response Surface Optimization Analysis

A multi-objective optimization scheme was conducted to determine an optimum formulation of %MK, %LS and %GYP, which satisfied the desired strength specifications while simultaneously minimizing the CO₂ emission and materials cost. The desirability function approach (range from 0 to 1) was used for this purpose. A desirability value of 1 represents the ideal case, while 0 indicates the responses are outside their acceptable limits. The optimal design was verified by the experimental result and shown in Table 6. An overall desirability of 0.72 indicated a reliable result.

Table 6 Optimization results and predicted desirability

4 Conclusion

This study examined the effects of formulation on strength performance, CO₂ emission, and production cost of LC3 cement. The following conclusions were drawn based on the experimental results.

• ANOVA showed satisfactory fit and accuracy of the developed quadratic models.

• The optimization results confirmed that the optimal percentages of MK, LS and GYP were 34.16%, 20.6% and 1.94%, respectively.