Optimisation and prediction of compressive properties for concrete containing recycled aggregates and rice husk ash using response surface methodology (RSM)

Rice husk ash (RHA), an agricultural by‐product, has been added as supplementary cementitious material (SCM) in concrete mixture to improve the compressive properties of recycled aggregate concrete (RAC) in recent years. This study aimed to optimise the mixture design of RAC considering two variables: the replacement ratio (wt.%) of recycled aggregate (RA) to natural aggregate (NA) with three levels (0%, 50% and 100%) and the replacement ratio (wt.%) of RHA to cement with three levels (0%, 10% and 20%). Compression test was implemented at concrete age of 28 days based on the full factorial experiment. By means of response surface methodology (RSM), the optimised RA replacement ratio and RHA replacement ratio can be calculated with respect to the compressive strength and E‐modulus at 28 days, and vice versa the compressive strength and E‐modulus at 28 days of RAC containing RHA can also be predicted. According to response surface modelling, the compressive strength reaches the maximum value when the RA replacement ratio is 0% and the RHA replacement ratio is 7%, and the E‐modulus would reach the maximum when the RA replacement ratio is 17% and the RHA replacement ratio is 7%. The determination coefficient (R2) and adjusted coefficient (R2adj) for the compressive strength model are 0.9632 and 0.9544 respectively, and for the E‐modulus model are 0.9319 and 0.9157 respectively, showing that the models developed by RSM are relatively well correlated with the experimental results.


Introduction
A consensus has been reached that the reuse of construction and demolition waste (CDW) as recycled aggregate (RA) can reduce the consumption of natural stone and release land pressure caused by landfill.Given the wide distribution of masonry structures in Asia and Europe, the recycled aggregates used in these countries are usually in a mixed type, containing old concretes and old clay bricks.Both of the recycled concrete aggregate (RCA) and the recycled brick aggregate (RBA) have very porous structures.In terms of RCA, apart from the porous old mortar, the existence of more interfacial transition zones (ITZs) in the concrete containing RCA also has negative effect on mechanical properties of the concrete produced with RCA.As summarised by other researchers [1][2][3], by replacing 100% coarse natural aggregates with coarse recycled aggregates, the concrete compressive strength can be reduced by up to 30% and the E-modulus can be reduced by 23%.
Supplementary cementitious materials such as fly ash, silica fume, ground granulated blast slag and metakaolin have been applied for decades to improve mechanical properties of concrete.Rice husk ash (RHA), a by-product of the combustion of rice husk, has attracted people's attention due to its positive environmental impact and high percentage of silica content.By partially replacing cement with RHA, the carbon footprint resulting from cement production can be lowered, and the agricultural waste (rice husk) can be repurposed [4,5].Additionally, the concrete produced with RHA has been shown to have improved compressive properties, due to the filling effect and high pozzolanic activity of RHA.As summarised from the existing studies, with a replacement of up to 20 wt.% of cement by RHA, the concrete compressive strength and E-modulus can be improved by up to 16% and 14% at 28 days, respectively [6][7][8][9].A few studies also indicated that by replacing 15-20 wt.% cement with RHA in RAC, where 100% coarse aggregates were RAs, the compressive strength increased by up to 13% at 90 days [10,11].Ma et al. [12] also showed that with the addition of RHA (10% replacement ratio), there was no significant difference in compressive strength between the RAC (50% RA replacement ratio) and the normal natural aggregate concrete (without RHA).
It is clear that the compressive strength will decrease with the increasing RA replacement ratio, and many researchers presented linear correlation between RA replacement ratio and compressive strength [13][14][15].On the contrary, RHA can be typically used to replace up to 20-25% of the cement in concrete mixtures, and excessive RHA will result in reduction in compressive strength.However, the advisable replacement ratio of RHA varies depending on the properties of RHA including particle size, chemical composition and crystalline phase.It is hard to determine an exact optimal RHA replacement ratio by limited experiments.Thus, response surface methodology (RSM) can be an efficient technique for optimising the concrete mixture considering the replacement ratios of RA and RHA.In turn, the compressive strength can also be predicted with the input of the replacement ratios of RA and RHA.

Materials
The coarse recycled aggregates (RAs) used in this study were in a mixed form, in which the weight ratio between the recycled brick aggregate (RBA) and recycled concrete aggregate (RCA) was 3:5.The RAs were recycled and processed from CDW by Jinke Resource Recycling Co., Ltd. in China.Natural gravels and natural river sand were used as coarse natural aggregates and fine aggregates, respectively.The physical properties of the aggregates shown in Table 1, tested according to the Chinese standard JGJ 52-2006 [16].The raw RHA was sourced from a local power plant in Lingshou County, China, after 4-hour combustion of rice husk at 600 o C.They were then ground at the laboratory by a planetary ball mill with 300 rpm for 20 min.As tested by laser diffraction particle size analyser, over 70% of the RHA particles were finer than 10 μm, and the average particle size was 8.45 μm.Table 2 presents the chemical composition of the RHA measured by X-ray fluorescence (XRF) and its loss on ignition (LOI).The predominant chemical component of RHA is SiO2, which makes up 83.93% of the composition.Figure 1 displays the crystalline phase of RHA, as determined by X-ray diffraction (XRD) analysis using Cu-Kα radiation (λ = 1.5419A•, 40 kV, 40 mA).The XRD pattern reveals two distinct peaks at approximately 22 ° (2θ) and 36° (2θ), indicating the presence of crystalline silica, in addition to amorphous silica in the RHA.The other binder used in this study was the ordinary Portland cement of 42.5 Grade, which meets the specifications of the Chinese code GB/T 4131-2014 [17].

Design of experiment
A full-factorial experimental design was used to investigate the effects of the RA replacement ratio and RHA replacement ratio on the compressive properties (i.e., compressive strength and E-modulus) of concrete.Table 3 shows the design matrix, and for each combination of factors and levels there were 3 runs.The experimental data were analysed using response surface methodology (RSM) to explore the underlying relationships between the responses (i.e., compressive strength and E-modulus) and the input variables (RA% and RHA%), and to optimize the responses by adjusting the values of the input variables.

Concrete mixing
The concretes were formulated based on C40 concrete according to Chinese concrete standard JGJ 55-201 [18].The mixture proportions are shown in Table 4.Additional water was added according to the moisture content and water absorption ratio of the RAs.
Two-stage mixing approach [19] was adopted during concrete mixing procedure.To create the concrete paste, the NAs and RAs were initially blended with RHA for a period of 30 s. Subsequently, the sands were added and mixed for an additional 30 s.After this, ½ water was added and mixed for a duration of 60 s.The cement, along with the superplasticiser, was then added and mixed for 30 s. Finally, the remaining water was added and mixed for a duration of 60 s.The concretes were fabricated into 150 mm × 150 mm × 300 mm and cured in the standard concrete curing chamber ((20±2) °C, >95% RH) for 28 days.

Compression test setup
The compression test was carried out at a servo hydraulic compression testing machine with the stress rate of 0.5 MPa/s, according to Chinese standard GB/T 50081-2019 [20].Strain gauges were bonded longitudinally on the concrete surface to measure the axial strain.

Statistical analysis and modelling
Equation ( 1) and ( 2) provide the second-order polynomial equations which describe the relationships between the input variables (RA% and RHA%) and the responses (compressive strength and E-modulus), obtained by performing multiple regression analysis on the experimental results.
Table 5 is the analysis of variance (ANOVA) table showing the significance of factors and the fitness of the RSM models.It is revealed that both models show statistical significance (p-values < 0.0001), along with nonsignificant Lack of fit (p-values > 0.1).This implies that the models are good fit for the data.Additionally, the compressive strength model has a determination coefficient (R 2 ) of 0.9632 and an adjusted coefficient (R 2 adj) of 0.9544, while the E-modulus model has an R 2 of 0.9319 and an R 2 adj of 0.9157.These values indicate a relatively strong correlation between the experimental results and the models developed by RSM.ANOVA also revealed that the interaction between RA% and RHA% significantly affected the compressive strength at a significant level of 10% (p-value = 0.06), whereas the interaction was nonsignificant for Emodulus (p-value = 0.94).This corresponds with the previous study [12].The only difference is that the interaction between RA% and RHA% was significant for the compressive strength at a significant level of 5% in the previous study, due to more levels of the replacement ratios of RA and RHA that were investigated formerly.
In the previous study [12], a unified model for the compressive strength of concrete containing RA and RHA was developed.To compare the accuracy between the RSM model and the previous model, the tested compressive strength against the predicted compressive strength are shown in Figure 2. The mean absolute percentage error (MAPE) and root mean square error (RMSE) of the RSM model are slightly lower than that of the previous model, indicating a satisfactory goodness-of-fit for the RSM model.It is efficient to use RSM as it has a systematic approach to identify the critical factors as well as their interactions, and meanwhile shows a good fitness.However, it is difficult to interpret the physical relations between response and variables, and the physical meaning of the interaction among variables.On the contrary, the model in previous study [12], which was developed based on the Abram's law, reflects the fact that the pozzolanic reaction of RHA occurs at a slower rate than the hydration of cement, even though some of the coefficients in the model also require regression analysis.This also makes the model in previous study [12] more generally applicable.Additionally, concerning the model for the E-modulus, it also shows a good accuracy, with 1.7% MAPE and 0.63 RMSE.

Response surfaces for compressive strength and E-modulus
The response surfaces concerning the compressive strength and E-modulus as function of RA% and RHA% are shown in Figures 3 and 4. In Figure 3, it is obvious that the compressive strength tends to decrease with the increasing RA%, and the surface shows curvature in relation to the RHA% variable.According to the canonical analysis, the stationary point was estimated to be at RHA% = 7%, RA% = -20%.Given the constraint that the RA replacement ratio cannot be negative, the estimated optimum design for achieving maximum compressive strength is 0% for RA replacement ratio and 7% for RHA replacement ratio.
Figure 4, representing the response surface for the concrete E-modulus, shows a generally similar tendency to that for the compressive strength.However, curvature is observed on the surface with respect to both the RA% and RHA% variables.This indicates that the increase of the RA replacement ratio does not always reduce the E-modulus, according to the estimation from RSM.The contour in Figure 4 also shows that the design centre (where the maximum output was reached) is located within the testing range, and the stationary point was estimated to be at RHA% = 7%, RA% = 17%.This suggests that the optimal design for achieving maximum E-modulus corresponds to 17% for RA replacement ratio and 7% for RHA replacement ratio.However, this has a slight discrepancy with the tested results, since the tested E-modulus values decreased with the increasing RA replacement ratio.Moreover, E-modulus has been shown to have a strong correlation with concrete density [21].Increasing the amount of RA reduces concrete density and thus reduces the E-modulus.The explanation of this unexpected estimation could be that there is in fact no significant difference in E-modulus between M1 and M4.As also revealed by statistical analysis in previous study [12], replacing 30% or 50% NAs with RAs did not result in significant difference in E-modulus compared with NAC (both p-values > 0.1, by pairwise comparisons).This could potentially result in a misinterpretation by RSM that the stationary point is situated between the range of RA% = 0% to RA% = 50%.Nevertheless, it is not wrong that 17% was estimated to be the optimum RA replacement ratio, since the RA% does not significantly affect the E-modulus in the range of 0%-50%.

Conclusions
In this study, the compressive properties including compressive strength and E-modulus of RAC were analysed with varying levels of replacement of NAs with RAs (at 0%, 50% and 100%) and replacement of cement with RHA (at 0%, 10% and 20%).RSM was utilised to determine the optimal replacement ratios of RHA and RA, and to predict the compressive strength and E-modulus.The following key findings were obtained.
• ANOVA revealed that the proposed models were significant (p-values < 0.0001).In the proposed compressive strength model, RA%, RA% 2 and RHA% 2 were found to be the significant terms (pvalues ≤ 0.0001).RA% and RA% 2 were found to have significant effect (p-values < 0.0001) in the proposed E-modulus model.

•
Statistics showed a good reliability of the models developed by RSM.The MAPE and the RMSE for the proposed compressive strength model are 3.5% and 1.27 respectively, and for the E-modulus model are 1.7% and 0.63 respectively.

•
According to RSM analysis, the compressive strength achieves its highest value when the replacement ratio of RA is 0% and the replacement ratio of RHA is 7%, while the maximum E-modulus is obtained when the RA replacement ratio is 17% and the RHA replacement ratio is 7%.

Figure 3 Figure 4
Figure 3 Response surface for compressive strength

Table 3
Design matrix

Table 5
ANOVA and regression model statistics for compressive strength (fc) and E-modulus (E) [12]re 2Comparison of experimental vs. predicted compressive strength using the RSM model and the unified model in previous study[12]