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Modern Approaches on Material Science

Research Article

Mathematical Model to Monitor Application Of Silica Fumes, Iron Slag And Rice Husk Ash on Compressive

Strength For Partial Replacement of Cement

Eluozo SN* and Ebirim S

Department of Civil Engineering, College of Engineering, Gregory University Uturu Abia State, Nigeria

*Corresponding author: Eluozo SN, 1Department of Civil Engineering, College of Engineering, Gregory University Uturu Abia State, Nigeria

Received: December 30, 2020 Published: January 21, 2021

ISSN: 2641-6921DOI: 10.32474/MAMS.2021.03.000168

AbstractThe study has expressed the rate on strength development of concrete as it partially replaced cement with silica fumes, iron

slag and Rice husk Ash. Modeling and simulation were adopted to monitor the growth rate of compressive strength, the predictive values that was generated experienced gradual growth rate with slight curve to the optimum level recorded at 28 days of curing. The study monitor the system by improving on the previous work done by other experts, such improvement were carried out by predicting the compressive strength of concrete that partially replaced cement with silica fumes iron slag and Rice husk Ash at the 14 days of curing, while other existing work was carried out on experimental procedure that monitored the compressive within 7 and 28days, there is no literature that has applied this mathematical techniques to monitor the compressive strength analytically, the developed compressive strength generated predictive values that was in agreement with Chaudhary et al. [1] for 7 and 28 days, this generated compressive strength was a model concrete that partially replaced cement with silica fumes, Iron Slag and Rice husk Ash, the predictive model observed silica fumes to attained the optimum compressive strength, followed with iron slag and Rice Husk Ash that experienced the lowest compressive strength, the growth rate of these materials shows that these additives have the highest siliceous content and pozzolanic properties, these study also monitor the system based on the dosage which shows that 5 and 10% experienced the required percentage that developed silica fume as the highest compressive strength. While Iron Slag maintained stable strength above Rice husk Ash which experienced the lowest compressive strength, other concrete properties was monitored to determined there variations influence on the development rates of the concrete model, the model reflected the compressive growth rate on variation of concrete porosities, these were examined from the variation established in the simulation, there rates of influenced monitored were determined in the system, the study is imperative because the behaviour of the model concrete that partially replaced cement in different admixtures has been predicted, there various pressure from other parameters in concrete properties has been examined. Experts will fine these tools as another conceptual technique in developing different concrete model with partial replacement of silica fumes, Iron Slag and Rice husk Ash to attain any designed concrete model.

Keywords: Mathematical model; silica fumes; iron slag; rice husk; ash compressive cement

IntroductionNumerous studies have carried out to observe the application

some localized materials such as iron slag waste tyre and Rice husk Ash as partial replacement of cement. other materials are fine and coarse aggregates in strength development, these concept are available in the literature [2-9] the concept has definitely generated high percentage result, the application of waste tyre has demonstrated tremendous feasibility applying gargantuan amounts from waste tyre in concrete products. Other materials are the use of plastic waste, these are one of the most familiar

environmental issues that is contemporary around the globe Choi et al. [10] most current studies carried out has examined the effect of waste PET bottles aggregate on properties of concrete. The yield of these studies explained how this concept of applying waste tyre and bottles can be reducing by 2 – 6% of normal weight concrete. Marzouk et al. [11] carried out research studied on the applications of consumed plastic bottle waste material as sand replacement; it was observed from the study monitored that density was lowered when the PET aggregate exceeding 50% by

Citation: Eluozo SN, Ebirim S. Mathematical Model to Monitor Application Of Silica Fumes, Iron Slag And Rice Husk Ash on Compressive Strength For Partial Replacement of Cement. Mod App Matrl Sci 3(4)- 2021. MAMS.MS.ID.000168. DOI: 10.32474/MAMS.2021.03.000168.

Volume 3 - Issue 4Mod App Matrl Sci. Copyrights @ Eluozo SN, et al.

407

volume of sand. Suganthy et al. [12] investigated the declined in weight of concrete just as plastic content experienced an increase Ode and Eluozo [13]. Marzouk [11] more so studies were carried out to monitor the reduction of compressive strength from plastic concrete; this concept was the application of sand replaced with plastic. Al-Manasser and Dalal other investigation was carried out by studying the influence of plastic on concrete mix. It was observed that the splitting tensile strength experienced decreased as the plastic content increased. Batayneh et al. [14] express splitting tensile strength and the flexural strength of concrete mix slump on the replacement and observed that the plastic content went up. Several experts have investigated the strengths of plastic concrete Batayneh et al. [14] mentioned that the incorporation of ground plastic in concrete had effect on its compressive strength [15,16] investigated the effect of post-consumer waste plastic in concrete as a soft filer [17-19].

Theoretical Background

( ) ( )dc dd V y c y cd ddx

+ = Φ (1.0)

Dividing equation (1.0) all through by we have

1( ) ( )dcn ndc v x c yd ddx

− −+ = Φ (1.1)

Let

1 nP cd−= (1.2)

(1 )

dcdp n dn cddy dy−= −

1

1

dc dpn dcd dy n dy− =

− (1.3)

Substituting equation (1.2) and (1.3) into equation (1.1) we have that.

1

( ) ( )1

dpV y p y

n dx+ = Φ

− (1.4)

Integrating both sides we have

( )(1 ) ( )(1 )[ ] ( )(1 )

v y n yp v y n yd e y n e dy− −∫ = Φ − ∫

( ) ( )(1 )( )

y Vu y n yp Aevu y

Φ − −= + (1.5)

Substituting equation (1.2) into equation (1.13) we have

( ) ( )(1 )1( )

y Vu y n yncd Vu y

Φ − −− = + (1.6)

Materials and Method

Experimental Procedures

Compressive Strength Test Concrete cubes of size 150mm×150mm×150mm were cast with and without copper slag. During casting, the cubes were mechanically vibrated using a table vibrator. After 24 hours, the specimens were demoulded and subjected to curing for 1-90 days and seven-day interval to 28 days in portable water. After curing, the specimens were tested for compressive strength using compression testing machine of 2000KN capacity. The maximum load at failure was taken. The average compressive strength of concrete and mortar specimens was calculated by using the following equation 5.1.

Compressive strength (N/mm2) = Ultimate compressive load (N)

Area of cross section of specimen (mm2)

Results and Discussion The study expressed the behaviour of the model concrete from

figure one to twelve based on the mixed design approach for the study, the trend in most of the figures displayed slight curve were gradual increase were observed to the optimum values recorded at twenty eight days of curing, while some figures displayed linear increase in gradual process to the optimum level, slight fluctuation was also experienced in a figures, while predominant figures observed linear growth rate, the predictive model thoroughly developed this variation, similar condition were observed on the experimental values, this were applied to validated the model, but displayed predominant linear growth rate, the study explained the level of concrete mixed designed proportion in various figures, the study developed model that was applied by Silica fume, Rice Husk Ash and Iron Slag, the experimental values were he applied at different admixtures to develop compressive strength of concrete, the study monitored the developed of concrete that partially replaced cement with these materials, the study predict at various modifiers such as Silica fume, Rice Husk Ash and Iron Slag used Chaudhary et al. [20] experimental values, the experimental values between 7 and 28 days were in agreement with predictive parameters, these validated the simulation parameters, the dosage percentage for Silica fume, Rice Husk Ash and Iron Slag was between 5%-20% , the predictive simulation values at different admixture observed that observed the highest compressive was generated from silica fumes flowed by iron slag, while Rice husk ash developed the lowest compressive strength, these was much lower than the compressive strength without replacement of cement by Chaudhary et al. [20] , the study monitored the compressive strength from various admixtures by replacing cement with these addictives, at different dosage and curing age. More so, the simulation was able to monitor the effect from other concrete characteristic that developed mechanical

Volume 3 - Issue 4Mod App Matrl Sci.

Citation: Eluozo SN, Ebirim S. Mathematical Model to Monitor Application Of Silica Fumes, Iron Slag And Rice Husk Ash on Compressive Strength For Partial Replacement of Cement. Mod App Matrl Sci 3(4)- 2021. MAMS.MS.ID.000168. DOI: 10.32474/MAMS.2021.03.000168.

Copyrights @ Eluozo SN, et al.

408

properties, this simulation generated variations influence from these parameters, it was observed that the system was affected by these variables and it was reflected on the growth rate of the compressive from different curing age Tables 1-12 (Figures 1-12).

Table 1: Predictive and Experimental Values of Compressive Strength at Different Curing Age.

Curing Age

Predictive Values for W/C of 0.43 Silica Fumes 5%

Experimental Values for W/C of 0.43 Silica Fumes 5%

7 37.53406172 24.5

14 36.23966492 33.608832

28 37.96231669 40.6

Table 2: Predictive and Experimental Values of Compressive Strength at Different Curing Age.

Curing Age

Predictive Values [W/C of [ 0.43] RHA 5%

Experimental Values [W/C of [ 0.43] RHA 5%

7 32.28023967 22.3

14 33.13988231 32.71

28 35.1531108 32

Table 3: Predictive and Experimental Values of Compressive Strength at Different Curing Age.

Curing Age

Compressive Predictive Values [W/C 0.43 5%

Experimental Values [W/C of [ 0.43] Slag Iron 5%

7 24.66831142 26.3

14 25.06067644 24.338

28 26.23593467 31.2

Table 4: Predictive and Experimental Values of Compressive Strength at Different Curing Age.

Curing Age

Predictive Values for W/C of 0.43 Silica Fumes 10%

Experimental Values for W/C of 0.43 Silica Fumes

10%

7 34.93132681 27.2

14 35.45579774 31.808

28 37.17844952 41.1

Table 5: Predictive and Experimental Values of Compressive Strength at Different Curing Age.

Curing Age

Compressive Predictive Values [W/C 0.43 RHA10%

Experimental Values for W/C of 0.43 [RHA] 10%

7 29.00883764 21.4

14 29.44463004 27.578

28 30.79211932 31

Table 6: Predictive and Experimental Values of Compressive Strength at Different Curing Age.

Curing Age

Compressive Predictive Values [W/C 0.43 Iron Slag

10%

Experimental Values for W/C of 0.43 Iron Slag 10%

7 29.4897028 23

14 29.9480847 27.576

28 31.388179 35

Table 7: Predictive and Experimental Values of Compressive Strength at Different Curing Age.

Curing Age

Compressive Predictive Values [W/C 0.43 [Silica

Fumes] 15%

Experimental Values for W/C of 0.43 Silica Fumes

15%

7 35.82733973 27

14 36.27533135 33.39

28 37.67257667 42

Table 8: Predictive and Experimental Values of Compressive Strength at Different Curing Age.

Curing Age

Compressive Predictive Values [W/C 0.43 [Silica

Fumes] 15%

Experimental Values for W/C of 0.43 Silica Fumes

15%

7 35.82733973 27

14 36.27533135 33.39

28 37.67257667 42

Table 9: Predictive and Experimental Values of Compressive Strength at Different Curing Age.

Curing Age

Compressive Predictive Values [W/C 0.43 [RHA]

15%

Experimental Values for W/C of 0.43 RHA 15%

7 23.51371098 17

14 24.01492234 21.016

28 25.63617084 29.1

Table 10: Predictive and Experimental Values of Compressive Strength at Different Curing Age.

Curing Age

Compressive Predictive Values [W/C 0.43 [Iron

Slag] 15%

Experimental Values for W/C of 0.43 Iron Slag 15%

7 31.17997553 22.3

14 31.68118689 30.686

28 33.30243539 37

Table 11: Predictive and Experimental Values of Compressive Strength at Different Curing Age.

Curing Age

Compressive Predictive Values [W/C 0.43 [RHA]

20%

Experimental Values for W/C of 0.43 RHA 20%

7 26.9873657 16

14 27.28560578 27.792

28 28.11444625 27.5

Table 12: Predictive and Experimental Values of Compressive Strength at Different Curing Age.

Curing Age

Compressive Predictive Values [W/C 0.43 [Iron

Slag] 20%

Experimental Values for W/C of 0.43 [Iron Slag] 20%

7 26.55353459 21.4

14 26.85177467 27.352

28 27.68061513 30

Citation: Eluozo SN, Ebirim S. Mathematical Model to Monitor Application Of Silica Fumes, Iron Slag And Rice Husk Ash on Compressive Strength For Partial Replacement of Cement. Mod App Matrl Sci 3(4)- 2021. MAMS.MS.ID.000168. DOI: 10.32474/MAMS.2021.03.000168.

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409

Figure 1: Predictive and Experimental Values of Compressive Strength at Different Curing Age.

Figure 2: Predictive and Experimental Values of Compressive Strength at Different Curing Age.

Figure 3: Predictive and Experimental Values of Compressive Strength at Different Curing Age.

Volume 3 - Issue 4Mod App Matrl Sci.

Citation: Eluozo SN, Ebirim S. Mathematical Model to Monitor Application Of Silica Fumes, Iron Slag And Rice Husk Ash on Compressive Strength For Partial Replacement of Cement. Mod App Matrl Sci 3(4)- 2021. MAMS.MS.ID.000168. DOI: 10.32474/MAMS.2021.03.000168.

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410

Figure 4: Predictive and Experimental Values of Compressive Strength at Different Curing Age.

Figure 5: Predictive and Experimental Values of Compressive Strength at Different Curing Age.

Figure 6: Predictive and Experimental Values of Compressive Strength at Different Curing Age.

Citation: Eluozo SN, Ebirim S. Mathematical Model to Monitor Application Of Silica Fumes, Iron Slag And Rice Husk Ash on Compressive Strength For Partial Replacement of Cement. Mod App Matrl Sci 3(4)- 2021. MAMS.MS.ID.000168. DOI: 10.32474/MAMS.2021.03.000168.

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411

Figure 7: Predictive and Experimental Values of Compressive Strength at Different Curing Age.

Figure 8: Predictive and Experimental Values of Compressive Strength at Different Curing Age.

Figure 9: Predictive and Experimental Values of Compressive Strength at Different Curing Age.

Volume 3 - Issue 4Mod App Matrl Sci.

Citation: Eluozo SN, Ebirim S. Mathematical Model to Monitor Application Of Silica Fumes, Iron Slag And Rice Husk Ash on Compressive Strength For Partial Replacement of Cement. Mod App Matrl Sci 3(4)- 2021. MAMS.MS.ID.000168. DOI: 10.32474/MAMS.2021.03.000168.

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412

Figure 10: Predictive and Experimental Values of Compressive Strength at Different Curing Age.

Figure 11: Predictive and Experimental Values of Compressive Strength at Different Curing Age.

Figure 12: Predictive and Experimental Values of Compressive Strength at Different Curing Age.

Citation: Eluozo SN, Ebirim S. Mathematical Model to Monitor Application Of Silica Fumes, Iron Slag And Rice Husk Ash on Compressive Strength For Partial Replacement of Cement. Mod App Matrl Sci 3(4)- 2021. MAMS.MS.ID.000168. DOI: 10.32474/MAMS.2021.03.000168.

Volume 3 - Issue 4Mod App Matrl Sci. Copyrights @ Eluozo SN, et al.

413

ConclusionThe study has modified a model concrete that is applied at

different admixtures with variations of dosage and curing age. the study expressed the growth rate of compressive strength at constant water cement ratio, but with variation of these admixtures within 7 and 28 days of curing, while the dosage was within 5 to 20%, the concept adopted was developed modeling techniques, the study express the behaviour of the model concrete by simulating the derived model to generated the predictive values, these were applicable to other addictives, the behaviour of the materials express various growth rate based on different factors, this concept were observed to monitor other concrete characteristics that could affect the concrete model, this application adopted were validated with experimental values generated by Chaudhary et al. [20]. The study improved on the model concrete whereby 14days of curing was integrated, this application was integrated in the system, the predictive values simulated for 14days and observation from the growth rate at 14 days were experienced, the variation influenced from 14 days of curing were observed before the reflection growth rate of 28 days of curing, the study expressed the correlation between 7,14, and 28days, this development expressed the behaviour of the model concrete in different dimensions, these strength development from predictive and experimental values was based on the fact that it serve as fillers within the void of concrete, these are through the particles of the admixtures to generated high strength base on the concrete grades. The lowest values from the predictive and experimental values were that of RHA, that obtained the lowest even at 5%, but lower than concrete compressive developed without admixtures, this can be used in local areas for low-cost housing.

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Volume 3 - Issue 4Mod App Matrl Sci.

Citation: Eluozo SN, Ebirim S. Mathematical Model to Monitor Application Of Silica Fumes, Iron Slag And Rice Husk Ash on Compressive Strength For Partial Replacement of Cement. Mod App Matrl Sci 3(4)- 2021. MAMS.MS.ID.000168. DOI: 10.32474/MAMS.2021.03.000168.

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DOI: 10.32474/MAMS.2021.03.000168