Assessment of the influence of micro and nanosilica on the behavior of selfcompacting lightweight concrete using full factorial design
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Abstract
The effects of different replacement levels of microsilica (MS), colloidal nanosilica (CS) and also the combined addition of MS and CS on the behavior of selfcompacting lightweight concrete (SCLC) were studied using the general full factorial design method. Three factors, including water to binder ratio (w/b) with two levels of 0.35 and 0.45, CS with four replacement levels of 0, 1, 3 and 5%, and MS with two replacement levels of 0% and 10% were chosen and three tests were conducted for each response. The modulus of elasticity, compressive strength and water absorption were selected as the responses at the age of 28 days. Also, using multiple regression analysis, acceptable prediction regression models were derived. The analysis of variance (ANOVA) showed that the effects of all three factors on fresh and hardened properties of SCLCs were significant. The results displayed that the mentioned properties for the SCLC specimens containing MS or CS improved, but the best performance was obtained in ternary mixes which were created by adding both MS and CS simultaneously. The optimal condition for having the best result of SCLC was obtained when the amounts of MS and CS were 10% and 3%, respectively.
Keywords
Optimization Factorial design Selfcompacting lightweight concrete Colloidal nanosilica Modulus of elasticity Water absorptionIntroduction
Selfcompacting lightweight concrete (SCLC) is defined as a category of highperformance concrete that combines the desirable properties of selfcompacting concrete (SCC) and lightweight concrete (LWC) (Wu et al. 2009; Mazloom and Mahboubi 2017). SCLC can spread into place and be compacted in dense reinforced formworks, while segregation or bleeding does not occur (Ranjbar and Mousavi 2015). Moreover, because of the ability to reduce dead loads, using SCLC can be favorable for structures. Properties such as the compressive strength and durability of SCLC are comparable to normal weight selfcompacting concrete (NWSCC) (Lachemi et al. 2009). Therefore, the technical, environmental and economic advantages of SCLC encourage researchers to pay more attention to the significant features of this kind of concrete (Mazloom et al. 2017, 2018; Karamloo et al. 2016b, 2017; Salehi and Mazloom 2018a, b; AfzaliNaniz and Mazloom 2018; Mazloom and Yoosefi 2013).
In recent years, the special effects of different admixtures on the properties of NWSCC have been investigated. Many researchers have concentrated on the use of cementitious materials as partial replacements of cement to advance the rheological, mechanical and durability of NWSCC. In fact, to accomplish highperformance selfcompacting concrete, it is required to use microscale or nanoscale of mineral admixtures (Bernal et al. 2018). In microscale, microsilica (MS) is a popular pozzolan (Mazloom et al. 2004, 2015), and nanosilica is the most widely used nanoparticle for producing cementbased materials (Singh et al. 2013). The strength of mortar and concrete can be enhanced by nanosilica in different ways including (Hosseinpourpia et al. 2012; Bahadori and Hosseini 2012; Hosseini et al. 2010): controlling crystallization which prevents the crystallization of weak crystals such as ettringite and calcium hydroxide; benefiting from the microfilling effect of nanosilica particles which causes them to fill small voids; creating a calcium–silicate–hydrate (C–S–H) dense gel, which changes the weak crystals into strong ones; benefiting from the nucleuslike act, which makes the nanoparticles create bonds due to their highly specific surface area. Nanosilica can be used in the form of dry powder or colloidal suspension. In fact, colloidal suspension can provide a better dispersion of the particles, so in comparison with the powder form it is more efficient and much easier to use (Mukharjee and Barai 2014; Chithra et al. 2016).
Few studies have been performed to investigate the properties of NWSCC containing micro/nanosilica. Bernal et al. (2018) studied the effects of micro and nanosilica as an extra cementitious material, and not as a cement replacement material, on the fresh and mechanical properties of NWSCC. Jalal et al. (2015) investigated the effects of some admixtures including fly ash, nanosilica and microsilica on the behavior of highperformance selfcompacting concrete (HPSCC). They reported that the strength properties improved via the blend of mineral admixtures and nanopowders. Also, Puentes et al. (2015) reported that silicabased micro and nano additions improved NWSCC performance at early ages with respect to the chemical reaction and the structure development.
However, researches on selfcompacting lightweight concrete have been far less than those on normal weight selfcompacting concrete. The importance of SCLC cannot be neglected due to its remarkable benefits for many applications and structures. Also, it should be mentioned that benefiting from all aspects of this material requires a deep understanding of its performance. In all these few researches that have been done on selfcompacting lightweight concrete, various parameters of this concrete have been investigated (Güneyisi et al. 2015, 2016; Karamloo et al. 2016a), but still there are parameters that have not been discussed. SCLC may have different behavior in comparison with normal concrete (NC) and NWSCC due to different materials such as the type of aggregate and the volume of paste. Moreover, it is obvious that compressive strength is an important mechanical property, but it is worth noting that the modulus of elasticity is also another vital property that affects the service life, durability and safety of the concrete structures (Parra et al. 2011).
Factorial design method is an applicable technique due to its benefits such as reducing the number of experiments, being time saving and being effective in reducing the cost of the overall research. In fact, this technique is a method of distinguishing the factors with significant effects on a response as well as distinguishing how the effects of one factor differ based on the level of others (Ashenai Ghasemi et al. 2017). In this paper, the general full factorial design technique is used considering parameters such as W/b ratio, CS (%) and MS (%) for analyzing their effects on the compressive strength, the modulus of elasticity and water absorption of SCLC. According to the analysis of variance (ANOVA), the key parameters affecting the mentioned properties were determined and appropriate prediction regression models were obtained. Furthermore, the effects of each parameter on the mentioned properties were discussed and the optimal value of all the factors was found.
Experimental program
Materials
Technical characteristics of colloidal nanosilica
Color  Specific gravity  Solid content  Particle size  Thermal stability  PH value 

White  1.2 g/cm^{3}  30%  10–20 nm  5–35 °C  9–10.5 
Chemical analysis of cement and microsilica
Component (%)  SiO_{2}  Al_{2}O_{3}  Fe_{2}O_{3}  CaO  MgO  SO_{3}  Na_{2}O  K_{2}O  CI  L.O.I  Residue 

Cement  21.32  3.83  2.96  62.02  3.44  2.09  0.42  0.71  0.04  2.4  0.77 
Microsilica  91.7  1.2  1.1  1.7  0.9  0.2  0.5  0.7  –  2  – 
Mix proportions and test specimens
The mix proportions of SCLC for factorial design optimization
Mixture  w/b  Cement (kg/m^{3})  MS (%)  CS (%)  LECA (kg/m^{3})  Powder (kg/m^{3})  Free water (kg/m^{3})  Sand (kg/m^{3})  SP (kg/m^{3}) 

LM0C0  0.35  450  0  0  270  230  157.5  800  9 
LM0C1  0.35  445.5  0  1%  270  230  157.5  800  9.45 
LM0C3  0.35  436.5  0  3%  270  230  157.5  800  11.7 
LM0C5  0.35  427.5  0  5%  270  230  157.5  800  13.5 
LM10C0  0.35  405  10%  0  270  230  157.5  800  10.8 
LM10C1  0.35  400.5  10%  1%  270  230  157.5  800  12.15 
LM10C3  0.35  391.5  10%  3%  270  230  157.5  800  14.4 
LM10C5  0.35  382.5  10%  5%  270  230  157.5  800  16.2 
HM0C0  0.45  400  0  0  270  230  180  800  3.6 
HM0C1  0.45  396  0  1%  270  230  180  800  4.05 
HM0C3  0.45  388  0  3%  270  230  180  800  5.85 
HM0C5  0.45  380  0  5%  270  230  180  800  7.2 
HM10C0  0.45  360  10%  0%  270  230  180  800  4.5 
HM10C1  0.45  356  10%  1%  270  230  180  800  5.4 
HM10C3  0.45  348  10%  3%  270  230  180  800  7.65 
HM10C5  0.45  340  10%  5%  270  230  180  800  9 
Design of experiments
Factorial design of experiments (DOE) is an effective method of experimentation with the possibility for all factors to differ at the same time over various sets of experimental runs (Montgomery 2017). In this paper, the general full factorial design was used to develop the design of the experiments. The input factors, namely CS (%), MS (%) and w/b, were considered at two, two and four levels, respectively. For each level, three replicates were carried out. The 16 different compositions were analyzed by Minitab statistical software.
Results and discussion
Fresh properties
The fresh properties of SCLC
Mix  Slump flow (mm)  T50 (s)  Jring (mm)  Vfunnel (s)  Ubox (h2–h1) (mm) 

LM0C0  720  3.6  665  9  14 
LM0C1  705  3.8  600  10.8  18 
LM0C3  690  4.8  610  9.5  20 
LM0C5  625  4.7  560  11.8  35 
LM10C0  700  4  615  8.6  25 
LM10C1  710  4.6  590  11.2  25 
LM10C3  605  5.4  520  15.1  36 
LM10C5  560  6.5  480  15.3  40 
HM0C0  785  2.3  690  5.4  5 
HM0C1  750  3.5  645  6.8  10 
HM0C3  770  3.2  640  8.4  16 
HM0C5  650  4.5  580  10.7  25 
HM10C0  755  3  635  6.3  15 
HM10C1  715  4.9  600  9.6  17 
HM10C3  650  4.3  550  10.7  22 
HM10C5  625  5  535  12.5  30 
Statistical evaluation of fresh properties of SCLC
Dependent variable  Independent variable  df  p value  Significance 

Slump flow diameter  Microsilica  1  0.005  Yes 
Colloidal nanosilica  3  0.000  Yes  
w/b  1  0.004  Yes  
Error  10  –  –  
Total  15  –  –  
T50 slump flow time  Microsilica  1  0.002  Yes 
Colloidal nanosilica  3  0.001  Yes  
w/b  1  0.003  Yes  
Error  10  –  –  
Total  15  –  –  
Vfunnel time  Microsilica  1  0.004  Yes 
Colloidal nanosilica  3  0.001  Yes  
w/b  1  0.001  Yes  
Error  10  –  –  
Total  15  –  –  
Jring diameter  Microsilica  1  0.000  Yes 
Colloidal nanosilica  3  0.000  Yes  
w/b  1  0.005  Yes  
Error  10  –  –  
Total  15  –  –  
Ubox (h2–h1)  Microsilica  1  0.000  Yes 
Colloidal nanosilica  3  0.000  Yes  
w/b  1  0.000  Yes  
Error  10  –  –  
Total  15  –  – 
Measured hardened SCLC properties and statistical analysis
Experimental results of hardened SCLCs
Mix  Compressive strength (MPa)  Modulus of elasticity (MPa)  Water absorption (%) 

LM0C0  39.35 (1.1)  23.05 (0.34)  4.34 
LM0C1  43.8 (2.1)  24.7 (0.46)  3.98 
LM0C3  46.9 (0.4)  25.9 (0.6)  3.87 
LM0C5  46 (1.3)  25.45 (1)  3.88 
LM10C0  43.7 (0.6)  24.70 (0.36)  4.08 
LM10C1  48.5 (1.05)  26.15 (0.4)  3.45 
LM10C3  51.7 (1.3)  27 (0.6)  3.23 
LM10C5  47.15 (0.9)  25.80 (0.8)  3.29 
HM0C0  28.8 (1)  19.8 (0.3)  5.34 
HM0C1  32.4 (0.6)  21.2 (0.17)  4.81 
HM0C3  34.85 (1)  22.1 (0.64)  4.27 
HM0C5  33.8 (0.7)  21.45 (0.95)  4.38 
HM10C0  31.5 (1.15)  20.75 (0.6)  4.74 
HM10C1  34.7 (0.5)  22.05 (0.42)  4.1 
HM10C3  37.1 (0.8)  22.50 (0.68)  3.56 
HM10C5  33.9 (1.5)  22.00 (0.37)  3.62 
Compressive strength
As shown in Table 6 and Fig. 3, the replacement of cement with MS and CS increased the 28day compressive strength of SCLC.
The analysis of variance for 28day compressive strength of SCLCs
Source  df  Seq SS  Adj SS  Adj MS  F  p 

w/b  1  1876.88  1876.88  1876.88  2302.47  0.000 
MS  1  93.66  93.66  93.66  114.90  0.000 
CS  3  285.79  285.79  95.26  116.86  0.000 
w/b × MS  1  10.97  10.97  10.97  13.46  0.001 
w/b × CS  3  6.02  6.02  2.01  2.46  0.080 
MS × CS  3  18.82  18.82  6.27  7.69  0.001 
w/b × MS × CS  3  1.09  1.09  0.36  0.45  0.721 
Error  32  26.09  26.09  0.82  
Total  47  2319.31 
Modulus of elasticity
The Analysis of variance for the 28day modulus of elasticity of SCLC
Source  df  Seq SS  Adj SS  Adj MS  F  p 

w/b  1  179.027  179.027  179.027  614.03  0.000 
MS  1  9.992  9.992  9.992  34.27  0.000 
CS  3  33.563  33.562  11.187  38.37  0.000 
w/b × MS  1  0.608  0.608  0.608  2.08  0.159 
w/b × CS  3  0.471  0.471  0.157  0.54  0.660 
MS × CS  3  1.341  1.341  0.447  1.53  0.225 
w/b × MS × CS  3  0.428  0.428  0.143  0.49  0.693 
Error  32  9.330  9.330  0.292  
Total  47  234.757 
Water absorption
Water absorption is among the properties that are connected to concrete durability (Lukic et al. 2015). Moreover, Schutter and Audenaert (2004) stated that the water absorption could indicate the amount of pore volume of concrete; however, the permeability of the concrete cannot be indicated.
The analysis of variance for the 28day water absorption of SCLC
Source  df  Seq SS  Adj SS  Adj MS  F  p 

w/b  1  4.1536  4.1536  4.1536  450.26  0.000 
MS  1  4.3200  4.3200  4.3200  468.29  0.000 
CS  3  5.9805  5.9805  1.9935  216.10  0.000 
w/b × MS  1  0.1102  0.1102  0.1102  11.95  0.002 
w/b × CS  3  0.4833  0.4833  0.1611  17.46  0.000 
MS × CS  3  0.1155  0.1155  0.0385  4.17  0.013 
w/b × MS × CS  3  0.0282  0.0282  0.0094  1.02  0.397 
Error  32  0.2952  0.2952  0.0092  
Total  47  15.4866 
Multiresponse optimization
The response optimization technique, by Minitab, was used to determine an optimal solution. The optimized properties by a response optimization technique are known as the desirability (D) function. In this technique, all predictors of responses are required to be converted into an individual desirability function (d), which is in the range of 0–1 and must be optimized for all the responses (Ashenai Ghasemi et al. 2017; George et al. 2005). More explanation about this technique can be found in the book by George et al. (2005).
Conclusions

Although the replacement of cement with MS and CS decreased the flowability of SCLC and also in some cases led to the use of a high dosage of superplasticizer (SP), the results show that almost all of the fresh properties of SCLCs were in the range of EFNARC. The decrease in flowability of SCLCs could be attributed to the high water demand of MS and CS.

According to ANOVA analysis, w/b, MS and CS significantly influenced the compressive strength and modulus of elasticity of SCLC. The main effect plots and interaction plots of compressive strength and the modulus of elasticity at the age of 28 days indicated that these properties decreased with the increase of w/b ratio and increased with increase in the content of MS and CS, but the optimum amount of CS (regardless of MS content and w/b ratio) was 3%. Moreover, the interaction plots and ANOVA tables of the mentioned properties depict that the interaction occurred between MS and CS factors for the compressive strength and the modulus of elasticity.

The comparison of the modulus of elasticity with the previous studies showed that at a given compressive strength, the modulus of elasticity of SCLC was lower than that of normal weigh selfcompacting concrete (NWSCC) and normal concrete (NC). This difference can be attributed to the type of aggregate, the volume of aggregate and the volume of paste in the mentioned concrete.

The 28day water absorption of SCLC improved with the increase in w/b ratio and was reduced by the addition of MS and CS. The optimum dosage of CS was 3%, which can be seen from the main effect plots.

The interaction plots of the compressive strength, the modulus of elasticity and water absorption show that in all of these properties of SCLCs, the combined addition of MS and CS, ternary mixtures, provide better performance than adding only one of them. When cement was replaced with both MS and CS (ternary mixes), the filler effect and the pozzolanic activity of the particles were enhanced.

The maximum value of compressive strength and the modulus of elasticity and the minimum value of water absorption were measured for SCLC with the blend of 10% MS and 3% CS in w/b ratio of 0.35. The results of the desirability function analysis in the optimization plot, with the composite desirability (D = 0.9342), confirmed these observations. The maximum increases for compressive strength and modulus of elasticity were 31% and 17%, respectively. The maximum decrease for water absorption was 34%.
Notes
Acknowledgements
The authors wish to acknowledge the supports of the Shahid Rajaee Teacher Training University.
Compliance with ethical standards
Conflict of interest
The authors declare no conflict of interest.
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