- Article
- Open Access
Prediction of Compressive Strength of Concretes Containing Silica Fume and Styrene-Butadiene Rubber (SBR) with a Mathematical Model
- M. Shafieyzadeh^{1}Email author
https://doi.org/10.1007/s40069-013-0055-y
© The Author(s) 2013
- Received: 12 January 2013
- Accepted: 26 August 2013
- Published: 10 September 2013
Abstract
This paper deals with the interfacial effects of silica fume (SF) and styrene-butadiene rubber (SBR) on compressive strength of concrete. Analyzing the compressive strength results of 32 concrete mixes performed over two water–binder ratios (0.35, 0.45), four percentages replacement of SF (0, 5, 7.5, and 10 %) and four percentages of SBR (0, 5, 10, and 15 %) were investigated. The results of the experiments were showed that in 5 % of SBR, compressive strength rises slightly, but when the polymer/binder materials ratio increases, compressive strength of concrete decreases. A mathematical model based on Abrams’ law has been proposed for evaluation strength of SF–SBR concretes. The proposed model provides the opportunity to predict the compressive strength based on time of curing in water (t), and water, SF and SBR to binder materials ratios that they are shown with (w/b), (s) and (p).This understanding model might serve as useful guides for commixture concrete admixtures containing of SF and SBR. The accuracy of the proposed model is investigated. Good agreements between them are observed.
Keywords
- concrete
- silica fume
- SBR
- compressive strength
- mathematical modeling
1 Introduction
Compressive strength of concrete is affected by many factors, such as cement composition and fineness, water-to-cement ratio, aggregate, age and temperature of curing. There is as yet no such formula (mathematical model) that could reproduce the effects of all these factors adequately in a quantitative manner, primarily due to a high number of variables (Zelic et al. 2004).
Abrams’ water–cement ratio law in 1918 is still considered as a milestone in the history of concrete technology, it is accepted that the largest single factor that governs the strength of concrete is the water to cement ratio. Originally, concrete was made by mixing cement, aggregates and water, and use of admixtures was unknown. The only cementation material was cement. The present-day, new-generation concretes contain mineral admixtures and latexes for a variety of reasons. These materials increase abrasion strength or durability and decrease permeability (Bhikshma et al. 2009; Rozenbaum et al. 2005; Wang et al. 2005; Bhanjaa and Sengupta 2003), and Abrams’ formulation needs to be modified or the validity of this relationship for concrete with supplementary materials (silica fume (SF), styrene-butadiene rubber (SBR), etc.) should be investigated. The more knowledge be available about the concrete composition versus strength relationship, the better the nature of concrete is understood and how to optimize the concrete mixture.
Silica fume reduces the workability of fresh concrete due to its very specific surface area. It improves a lot of properties of hardened concrete (Bhikshma et al. 2009). SBR latex can reduce water binder ratio, effectively enhance both flexural strength and tensile strength but reduces compressive strength. The previous researches showed that SBR-modified mortars had good mechanical properties and frost resistance (Rozenbaum et al. 2005; Wang et al. 2005). Some researchers have indicated that there is a great potential of combined usage of SF and SBR latex in the increase in the performance of the concrete properties (Rossignol 2009).
- 1.
Keeping the water-to-cement ratio (w/c) constant to obtain a similar hydration of the cement paste.
- 2.
Fitting the consistency of the composite, by adjusting the w/c.
In this research, the water to binder ratio is constant (0.35, 0.45) and the effects of SBR emulsion and SF on fluidity and compressive strength of concrete are investigated and a relationship between compressive strength of concrete with the ratios of polymer, SF, water to binder materials and time of curing in water is proposed. By the way, using mathematical models to take and describe experiences from experimental data of concrete mixes behaviors are most reliable, accurate, scientific, and applicable recommended methods.
2 Experimental Work
2.1 Properties of Materials
The materials used in this research were: Ordinary Portland cement (Type 1) produced by Tehran Factory, and SF, a by-product of the ferrosilicon Deligan Factory.
Coarse aggregate with a maximum particle size of 17 mm and fine aggregate with a 3.01 finesse modulus were used in the experiment. The specific gravity and water absorption of coarse and fine aggregates were 2.55 and 1.6 %, 2.25 and 2.4 %, respectively. A water reducer agent with the commercial name of Gelenium 110p from Iranian BASF Construction Chemicals was used to adjust the workability of the concrete mixtures.
Properties of SBR.
Density (g/cm³) | Mean particle size (μ) | Butadiene content | pH |
---|---|---|---|
1.01 | 0.17 | 40 % | 10.5 |
2.2 Testing Program and Procedure
In this research, Cubes 150 × 150 × 150 mm were cast for compressive strength test. Before casting, coarse aggregate, sand and mixture of water and SF were mixed first. Then, cement, SBR latex and rest water together with superplasticizer were put in the mixer and completely mixed.
- 1.
7 days immersed in 20 ± 2 °C water and then cured in air at 20 ± 2 °C with 20 ± 10 % of relative humidity for 53 days (7W53D).
- 2.
14 days immersed in 20 ± 2 °C water and then cured in air at 20 ± 2 °C with 20 ± 10 % of relative humidity for 46 days (14W46D).
- 3.
28 days immersed in 20 ± 2 °C water and then cured in air at 20 ± 2 °C with 20 ± 10 % of relative humidity for 32 days (28W32D).
Cement hydration process is retarded by the polymer and surfactants. This is visible especially in the compressive strength (Beeldens et al. 2005).
The cement hydration and polymer film in the modified concretes develop with prolongation cured age, which results in enhanced strength (Wang et al. 2005). Although, the slope of increasing compressive strength of polymer modified concrete declines from 28 to 90 days (Chen and Liu 2007).
Also, combination of wet and dry curing is effective for the strength development of the polymer-modified concretes. A co-matrix is formed by both processes (Jun et al. 2003).
Details of mix proportions.
Water (l/m^{3}) | SBR (l/m^{3}) | Silica fume (kg/m^{3}) | Cement (kg/m^{3}) | SP (l/m^{3}) | Slump (mm) | Compressive strength (MPa) | ||
---|---|---|---|---|---|---|---|---|
7W53D | 14W46D | 28W32D | ||||||
180 | 0 | 0 | 400 | 2 | 50 | 25.2 | 27.8 | 30.9 |
180 | 0 | 20 | 380 | 2 | 40 | 27.9 | 30.1 | 32.8 |
180 | 0 | 30 | 370 | 2 | 30 | 30.6 | 32.7 | 34.2 |
180 | 0 | 40 | 360 | 2 | 25 | 29.6 | 31.7 | 33.3 |
168 | 20 | 0 | 400 | 0 | 35 | 26.6 | 29.8 | 32.4 |
168 | 20 | 20 | 380 | 0 | 25 | 29.1 | 31.2 | 34 |
168 | 20 | 30 | 370 | 2 | 90 | 27.6 | 29.4 | 32.2 |
168 | 20 | 40 | 360 | 2 | 80 | 26.3 | 28.4 | 31.5 |
156 | 40 | 0 | 400 | 0 | 90 | 24 | 26.8 | 29.2 |
156 | 40 | 20 | 380 | 0 | 85 | 26.5 | 29.2 | 31.8 |
156 | 40 | 30 | 370 | 0 | 80 | 28.6 | 30.7 | 33.1 |
156 | 40 | 40 | 360 | 0 | 75 | 27.4 | 29.6 | 32.4 |
144 | 60 | 0 | 400 | 0 | 160 | 21.5 | 24.1 | 26.7 |
144 | 60 | 20 | 380 | 0 | 155 | 23.9 | 26.9 | 29.5 |
144 | 60 | 30 | 370 | 0 | 155 | 26.4 | 28.8 | 31.6 |
144 | 60 | 40 | 360 | 0 | 150 | 24.6 | 27.5 | 30.2 |
140 | 0 | 0 | 400 | 3 | 80 | 31.8 | 36 | 40.4 |
140 | 0 | 20 | 380 | 3.2 | 70 | 33.8 | 37.1 | 42.5 |
140 | 0 | 30 | 370 | 3.2 | 70 | 35.9 | 40.4 | 45.1 |
140 | 0 | 40 | 360 | 3.4 | 60 | 34.5 | 38.4 | 43.3 |
128 | 20 | 0 | 400 | 2 | 80 | 32.7 | 37 | 41.4 |
128 | 20 | 20 | 380 | 2.2 | 70 | 35.1 | 39 | 44.2 |
128 | 20 | 30 | 370 | 2.2 | 60 | 37 | 42.4 | 47.5 |
128 | 20 | 40 | 360 | 2.4 | 60 | 36.1 | 40.7 | 45.8 |
116 | 40 | 0 | 400 | 1 | 90 | 30.2 | 32.6 | 37.3 |
116 | 40 | 20 | 380 | 1.2 | 80 | 32.3 | 36.1 | 40.2 |
116 | 40 | 30 | 370 | 1.2 | 70 | 34.2 | 37.4 | 42.8 |
116 | 40 | 40 | 360 | 1.4 | 60 | 33.5 | 35.8 | 42.2 |
104 | 60 | 0 | 400 | 0 | 50 | 27 | 29.4 | 34.1 |
104 | 60 | 20 | 380 | 0 | 60 | 29.3 | 31.4 | 36.1 |
104 | 60 | 30 | 370 | 0 | 65 | 30.2 | 32.7 | 38.2 |
104 | 60 | 40 | 360 | 0 | 70 | 30.2 | 32.2 | 37.8 |
3 Test Results and Discussion
3.1 Effects of SF and SBR on Fluidity of Concrete
Silica fume decreases fluidity of concrete but SBR increases fluidity of concrete. Adding of 15 % of SBR to samples with water to binder materials ratio 0.45 induces self-compacting concrete (concrete with slump of 150 mm). The effect of SBR in increasing fluidity of concrete is more than the decreasing effect of SF in fluidity (Table 2).
3.2 Effects of SBR on Compressive Strength
3.3 Effects of SF on Compressive Strength
3.4 Interaction Effects of SF and SBR on Compressive Strength of Concrete
3.5 Investigation of Main Effects and Interaction Effects of Factors in Compressive Strength
Numeric values of the rate constants from above equation.
A | B | C | D | E |
---|---|---|---|---|
2.637 | 0.999 | 0.98 | 1.005 | 0.977 |
4 Mathematical Model
The results obtained from an experiment can be shown by a mathematical model. Here, the primary factors that affected the compressive strength of concrete are the ratios of water, SBR, SF to binder materials and time of curing in water. (In modeling, from effects of superplastysizer on compressive strength is neglected.)
Relationship compressive strength with main effective factors can be determined by regression. But before regression needs to determine each factor how influence in compressive strength.
A, B are constant coefficients and $\left(\frac{\mathit{w}}{\mathit{c}}\right)$ is the ratio of water to cement.
Bihanja and Khan (Bhanja and Sengupta 2002; Iqbal khan 2009) proposed power equations for the effect of SF on compressive strength of concrete. Bhanja (Bhanja and Sengupta 2002) proposed a three degree function for prediction compressive strength of SF concrete. When the percentage of replacement of SF is less than 10, the relationship between compressive strength and SF can be considered with a parabola curve. (Base on Bhanja’s relationship, the maximum error will be less than 2.5 %.)
5 Conclusion
- 1.
The effect of SBR in increasing of fluidity of concrete is greater than the effect of SF in decreasing of fluidity of concrete.
- 2.
In constant water to binder ratio and combined curing system, the compressive strength of concrete in 5 % SBR rises slightly, but when polymer/binder ratio increases, the compressive strength of concrete decreases.
- 3.
Cement replacement up to 7.5 % with SF leads to increase in compressive strength.
- 4.
The decrease of compressive strength is compensated by the reduction of w/b due to the plasticizer effect of SBR. Both phenomena together remain compressive strength approximately constant.
- 5.
The percentage of SF that optimizes the compressive strength with adding SBR doesn’t change.
- 6.Abram’s law with some modification is applicable to the compressive strength of concretes contain of SF and SBR. Also, according to main effects of diagram can be proposed the following equation:The proposed model provides the opportunity to predict the compressive strength based on the time of curing in water (t), and water, SF and SBR to binder materials ratios that they are shown with (w/b), (s) and (p), briefly.$${f}_{c}=\frac{49.2}{{10}^{\left(\frac{w}{\mathit{b}}\right)}}\times \left(0.546\times log\left(\mathit{t}\right)+1\right)\left(-17.22{\mathit{s}}^{2}+2.74\mathit{s}+1\right)(-10{\mathit{p}}^{2}+0.54\mathit{p}+1)$$
Declarations
Open AccessThis article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
Authors’ Affiliations
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