PROJECT KISALA

SCHOOL OF SCIENCE

DEPARTMENT OF CHEMISTRY AND BIOCHEMISTRY

RESEARCH PROJECT ANC 417

PREDICTION OF CEMENT STRENGTH USING MULTIPLE LINEAR REGRESSION MODELS AND A COMPARATIVE

ANALYSIS OF LOCAL KENYAN CEMENT BRANDS

BRIAN JAMES KISALA

ANC/007/11A research project dissertation submitted in partial fulfilment of the requirements for

the award of an undergraduate bachelors degree in Analytical Chemistry with Computing

AUGUST 2016

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TABLE OF CONTENT

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SDECLARATION................................................................................................................................. vi

ACKNOWLEDGMENTS................................................................................................................... vii

ABSTRACT..................................................................................................................................... viii

GLOSSARY....................................................................................................................................... x

CHAPTER ONE: INTRODUCTION................................................................................................... 1

1.1. Background to study............................................................................................................ 1

1.2. Problem statement............................................................................................................... 1

1.3. Justification.......................................................................................................................... 2

1.4. Objectives............................................................................................................................ 3

1.4.1. General objective.............................................................................................................. 3

1.4.2. Specific objective.............................................................................................................. 3

1.4.3. Statement of hypothesis................................................................................................... 3

CHAPTER TWO: LITERATURE REVIEW.........................................................................................4

2.1. Constituents of cement........................................................................................................4

2.2. Cement impurities................................................................................................................ 5

2.3. Previous research on cement..............................................................................................6

2.4. Regression model for cement strength prediction................................................................8

CHAPTER THREE: MATERIALS AND METHODOLOGY..............................................................10

3.1. Source of data.................................................................................................................... 10

3.2. Data collection method....................................................................................................... 10

3.3. Model creation.................................................................................................................... 11

CHAPTER FOUR: RESULTS AND ANALYSIS...............................................................................12

4.1. Regression model 32.5......................................................................................................13

4.2. Regression model 42.5......................................................................................................15

4.3. Regression model 32.5 and 42.5.......................................................................................17

4.4. Days of setting anova analysis 32.5 and 42.5....................................................................19

4.5. Cement comparison 32.5 and 42.5....................................................................................23

CHAPTER FIVE............................................................................................................................... 25

5.1. Discussion.......................................................................................................................... 25

5.2. Limitation............................................................................................................................ 27

CHAPTER SIX................................................................................................................................. 28

6.1. Conclusion......................................................................................................................... 28

6.2. Recommendation............................................................................................................... 28

6.3. Future work........................................................................................................................ 29

REFERENCES................................................................................................................................ 33iii | P a g e

LIST OF APPENDICESAppendix 1A: Cement chemical composition raw data..................................................................a

Appendix 1B: Cement strength raw data.........................................................................................d

Appendix 1C: Cement composition averages..................................................................................f

Appendix 1D: Cement strength averages........................................................................................g

Appendix 2A: 32.5 28 days residual diagnostics............................................................................g

Appendix 2B: 32.5 all days residual diagnostics.............................................................................h

Appendix 2C: 42.5 28 days residual diagnostics............................................................................h

Appendix 2D: 42.5 all days residual diagnostics..............................................................................i

Appendix 2E: Composite 28 days residual diagnostics.................................................................. j

Appendix 2F: Composite all days residual diagnostics.........................................................................j

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LIST OF TABLESTable 4.1: Model Summary for regression model 32.5 vs components....................................13

Table 4.2: Coefficients summary for regression model 32.5 vs components............................13

Table 4.2: Model summary for regression model 32.5 vs components and days........................14

Table 4.3: Coefficient summary for regression model 32.5 vs components and days................14

Table 4.4: Model Summary for regression model 42.5 vs components....................................15

Table 4.6: Coefficients summary for regression model 42.5 vs components............................15

Table 4.5: Model summary for regression model 42.5 vs components.....................................16

Table 4.8: Coefficient summary for regression model 42.5 vs components..............................16

Table 4. 9: Model summary for regression model 32.5 and 42.5 vs components.....................17

Table 4.10: Coefficients summary for regression model 32.5 and 42.5 vs components...........17

Table 4.11: Model summary for regression model 32.5 and 42.5 vs components and days...18

Table 4.6: Coefficients summary for regression model 32.5 and 42.5 vs components and days........................................................................................................................18

Table 4.13: Anova test on the days of setting at 32.5 strength class........................................19

Table 4.14: Separation of means of 32.5 strength using LSD method......................................20

Table 4.15: Anova test on the days of setting at 42.5 strength class........................................21

Table 4.16: Separation of means of 42.5 strength using LSD method......................................21

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LIST OF FIGURESFigure 4.1: Box Plot of 32.5 strength class mean strengths versus days..................................20

Figure 4.2: Box Plot of 42.5 strength class mean strengths versus days..................................22

Figure 4.3: Comparison of cements strengths vs days for all 32.5 brands................................23

Figure 4.4: Comparison of cements strengths vs days for all 42.5 brands................................24

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DECLARATIONDeclaration by the student:

I declare that this is my original work and it has not been presented to any other institution for

the award of a Bachelor of Science in Analytical Chemistry with Computing

Brian James Kisala Adm. No. ANC/007/11

Signature..................... Date................................

Declaration by the supervisor:

This project has been submitted with our approval

Dr. Naomi. J. Bisem

Signature..................................... Date..............................

School of Science,

University of Eldoret

Dr. Argwings Otieno

Signature.................................... Date.........................

School of Science,

University of Eldoret

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ACKNOWLEDGEMENTSI would like to acknowledge the following people for their invaluable help

Almighty God for His Grace

The University of Eldoret for this opportunity as well as the support

My supervisor Dr. Bisem for her invaluable help in so many ways

My supervisor Dr. Argwings Otieno for making statistics not only simple but enjoyable

along with his valuable innovative input

Mr. Njoroge, Mr. Namu, Mr. Karoga, Mrs. Faith and Mrs. Josephine From Ministry of

Transport: Materials, testing and Research Division They gave me skills and information

that one can never really forget

Finally my family for the financial and moral support. It was neither easy nor cheap but

they supported me nonetheless

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ABSTRACTCement is the civil construction adhesive that binds the concrete (sand, aggregate and water)

to the building stones so as to form a solid construction mass. It is made up of various

chemical components like calcium oxide (CaO or simply calcium in this study) and silica (SiO2)

which are known to add to the strength. It also contains impurities like magnesia (MgO),

chloride (Cl-) as well as other components like carbon dioxide (CO2), hydration water (H2O)

manganese etc according to the Ministry of Transport and Infrastructure, Materials Testing and

Research Division (MoTI- MTRD). There are also inert crystals like quartz (collectively known

as insoluble residue) that don’t add to the compressive strength of the cement. Cement in

Kenya is tested based on its compressive strength at 2 days, 7 days and 28 days and the

percentage level of the above mentioned chemical components. The method of testing for

strength however is problematic since it is both an expensive and time consuming process. On

the other hand, all the chemical components above are tested in about 10 days at a cheaper

cost. The objective of this study is to use a linear multiple regression to create a prediction

model so as to test whether the above chemical components can be used to determine the

strength of the cement thus reducing both cost and time. Data for 60 samples of the 6 popular

brands in Kenya was gotten from the MoTI- MTRD physics and chemistry laboratories to

conduct the analysis and design the model. The model was used to determine if any of the

chemical components along with the number of days of setting do contribute significantly to the

cement strength and thus can be used as predictors. Six models were designed and the model

that best fulfilled the expectations based on theoretical facts was chosen. The model chosen

was the “32.5 and 42.5 regressed against calcium oxide, silica, insoluble residue and days of

setting” model. An anova test was also done on the days of setting to verify if there really is a

significant difference in strength of cement at different days of setting as per the model of the

model. Based on the model, the only significant contributor to the strength at 5% level of

significance was the number of days of setting. But theoretically, all the chemical components

chosen do affect cement strength. The discrepancy therefore could be due to errors,

uncontrolled variables or variables that had not been factored in (lurking variables). It was

concluded that based on the model, the chemical components did shared some correlation

with the cement strength but not sufficient for them to be predictors of strength but the number

of days of setting did have a significant relationship with strength. The limitation to this was that

the data was too small and sourced from various sources and at various times. This led to

introduction of a lot of uncontrolled variables that affected the model quality. Also, there were ix | P a g e

other variables which should have been factored in the model but could not be tested, for

example the density of the cement and volume of water of hydration. Also, the linear multiple

regression equation could not account for the interaction of the variables (in these case the

chemical components) and as such there was no way of empirically finding out what effect that

had on the overall strength of the cement. A comparison of all the local brands in Kenya was

also performed to find out the best from a compressive strength stand point. It was also

concluded that at 32.5 cement strength class, Mombasa Cement is the best while at 42.5

cement strength class, Bamburi Cement is the best. The limitation to this was that the

comparison of the cement was based purely on the strength and did not factor in other

variables like cost and nationwide availability

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GLOSSARY32.5Nm-2: The expected compressive strength of cement after 28 days of setting as

indicated on commercial cement packages. Usually written simply as 32.5

42.5Nm-2: The expected compressive strength of cement after 28 days of setting as

indicated on commercial cement packages. Usually written simply as 42.5

MoTI MTRD: Ministry of Transport and Infrastructure, Materials Testing and Research Division

Chemistry and Physics lab. Sometimes referred in this project as simply Ministry

of Transport and Infrastructure

SPSS: Statistical Package for Social Sciences. The statistical analysis software that is

used in this study

CALCIUM: A representative term used to mean calcium oxide (lime) in this study

OPC: Ordinary Portland Cement

W/C: Ratio of water to cement weight for weight in a concrete mix

W/B: Ratio of water to concrete binder in a concrete mix

Rebar: Reinforcement bar. Steel bars put in concrete support beams to support the

weight of the structure and transmit it to the ground

Chemical components: The chemical components tested during this study namely silicon

dioxide, calcium oxide and insoluble residue (non-reactive mass) sometimes

simply called components

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CHAPTER ONE: INTRODUCTION1.1.BACKGROUND TO STUDY Cement is used as a binding agent in almost all civil construction endeavours. It is made of

several chemical components, the major ones being calcium oxide (CaO), calcium sulphate

(CaSO4), silica (SiO2), alumina (Al2O3), and ferrite (Fe2O3). In addition, there are other

impurities like, carbon dioxide and water (collectively known as volatile components), chloride

and others like sodium and magnesium (which are generally not tested in Kenya due to the

very low levels). There are also other inert components collectively known as insoluble residue

that do not affect the cement at all but lower the strength to weight ratio of the cement [1]

Cement is graded based on the compressive strength of a 70.6mm cube after 28 days of

setting [2] which gives rise to four different strength classes 32.5N/m2, 42.5N/m2, 52.5N/m2 and

62.5N/m2. It is also graded based on its setting time giving rise to the R class (for rapidly

setting cement) and N class (for cement setting at a normal rate). The standard testing of

cement also includes the testing of the chemical components which takes about 10 days and

costs about 5,000/= per sample (quotation from the MoTI- MTRD).

Since testing for strength takes much longer and costs much more, it raised the question

whether the chemical components can actually be used to predict the strength of the cement.

This can be confirmed using the linear multivariate regression model. This is an equation that

that can be used to predict the value of a dependent variable using several independent

variables. For example determining the date using a reference date and the number of

seconds elapsed since that date

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1.2. PROBLEM STATEMENTEvery cement company advertises its product as the best in the market and the primary way of

determining cement quality is its strength. Conventionally, there is a way to test the strength of

the cement which has led a strength based grading system written as Megapascals of

compressive strength after 28 days of hardening time (i.e 32.5, 42.5 52.5 and 62.5) [3]

The problem with this testing method is that it takes at least a month to determine cement

strengths (since it must set for 28 days before the strength is measured) and will cost 20,000/=

per sample. While it may take about 10 days to determine the levels of chemical components

in the cement depending on the standard operating procedure that one uses and will only cost

5000/= per sample (quotations from the MoTI- MTRD)

On the other hand, from a chemical standpoint, there are only standards for threshold levels

for the constituent cement compounds that affect the quality of the product. This is in spite of

the fact that these standards do demand that many of the chemical components that affect the

strength of cement be measured. As such there is no simple and fast way of knowing the

cement strength and thus quality simply by looking at the chemical components

1.3. JUSTIFICATIONThe Kenyan government requires that every civil work have every batch of cement tested

before use, waiting for 28 days to get results on the cement batch will severely slow down the

construction process not to mention prove very expensive.

Observations have been made at MoTI- MTRD that 32.5 grade cement generally has a higher

insoluble residue content and lower calcium content than 42.5 cement (52.5 was very rare to

find while 62.5 cannot be found in Kenya).

Therefore the purpose of this research project is to try and create a simple and fast and robust

model that can predict the cement strength using the chemical components [3]. This will serve

as a cheaper and faster interim approval for the construction to continue while the contractors

wait for the results on the official strength test (should it still be necessary afterwards).

The second purpose of this project is to find out of the known local brands, which is the best

from a physical standpoint in order to give the consumer an informed choice on quality.

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1.4.OBJECTIVES

1.4.1. GENERAL OBJECTIVE To create a prediction model for cement strength using the level of chemical components

and the number of days of setting

To determine the best local cement in Kenya

1.4.2. SPECIFIC OBJECTIVE To use linear multiple regression equation based model to predict the cement strengths of

the common known Kenyan brands using silica insoluble residue and lime (calcium oxide)

and the number of days of setting as the prediction parameters (variables)

To conduct an ANOVA test on the number of days of setting to verify the significance of the

variable at 5% level of significance as per the chosen model

To determine which of the common Kenyan brands is the best from a compressive strength

standpoint both on the 32.5 and 42.5 compressive strength scales

1.4.3. STATEMENT OF HYPOTHESISThe general hypotheses will be:

H01: There is no relationship between the compressive strength of cement and the chemical

components silica insoluble residue and lime as well as the number of days of setting at 5%

level of significance

HA1: there is a relationship between the compressive strength of cement and the chemical

components silica insoluble residue and lime as well as the number of days of setting at 5%

level of significance

H02: There is no difference between the strength of the different cement brands at the different

strength classes 32.5 and 42.5.

HA2: There is a difference between the strength of the different cement brands at the different

strength classes 32.5 and 42.5.

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CHAPTER TWO: LITERATURE REVIEW2.1. CONSTITUENTS OF CEMENTThe major components of Portland cement are (in approximations) [4] [1] :

Silica approximately 18.6-36.3%

Alumina approximately 2.4-6.3%

Iron oxide approximately 1.3-6.1%

Calcium oxide approximately 60.2-66.3% (written as either lime or simply calcium)

Magnesia approximately 0.6-4.8%

Sulphate (measured as sulphite SO3) approximately 1.7-4.6%

Chlorides approximately 0.97%

Insoluble residue approximately1.50%

Loss on ignition approximately 4.00%

However, these levels vary from standard to standard and from strength class to strength

class. The standard shown above are the ones KEBS uses (KS EAS 18-1: 2001 EAS 198.2) [5]

which are in line with the global standard (Global ICS 91.100-10) [6]

These components react during clinkering to form more complex substances namely C2S, C3S,

C3A, and C4AF. Where C stands for calcium oxide, S stands for silicon oxide, A stands for

aluminum oxide and F stands for iron oxide. The silicates, C3S andC2S, are the most important

compounds, which are responsible for the strength of hydrated cement paste [7].

Hydration of the cement with water forms and adhesive paste that holds concrete together

according to the equation 2Ca3SiO5 + 7H2O → 3(CaO)·2(SiO2)·4(H2O)(gel) + 3Ca(OH)2 [8]

Apart from these, there are also other components which are considered impurities. These are:

sodium oxide, potassium oxide, titanium dioxide, phosphorus pentoxide, zinc oxide, Insoluble

residue, Carbon Dioxide and moisture. However of these, sodium potassium, titanium

phosphorous and zinc oxide are only considered in special cases and are thus insignificant in

this case[8]. The impurities of interest here are insoluble residue, carbon dioxide and moisture

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The cement when mixed with water during concrete mixing is hydrated and hardens infinitely.

The process only stops when the water for hydration is depleted. Too much calcium oxide

(lime) in the cement leads to unsoundness in the cement while too little leads to a lower early

setting strength [5].

2.2. CEMENT IMPURITIESThe major Impurities in cement include Alumina, magnesia, chloride and sulphite as well as

insoluble residue and volatile contents like water and carbon dioxide according to the MoTI

MTRD

Alumina is considered an impurity due to the formation of tricalcium aluminates which cause

rapid setting as well as tetracalcium iron aluminates which has no effect on the hardening of

the cement and just adds to the cement bulk [5].

Magnesia (also known as periclase MgO) is considered a toxic impurity because during

hydration of the cement, it undergoes hydration to form magnesium hydroxide. This is a slow

process and the MgOH2 crystals are larger than the periclase crystals. Therefore, the hydration

of the magnesia causes the cement to expand at the places where the magnesia particles

exist, long after the cement has set. This leads to the formation of cracks in the cement that

significantly weaken the cement. This phenomenon is called magnesia expansion [5]

Chloride is another toxic impurity as it reacts with the lime to form calcium chloride which has

no cementing properties. It is also the highest cause of rebar corrosion in concrete structures

by penetrating the layer of protective oxide film formed by the hydrated lime on the rebar [10].

This therefore greatly affects the overall integrity of the structures by significantly weakening

both the cement and the steel bars [9].

Insoluble residue is mostly any other component that doesn’t have cementing properties and is

insoluble in acids and bases (usually crystals like quartz which have been rendered inert due

to their ceramic properties [10].) They eventually end up in the cement maybe during

manufacturing packaging etc. Since they don’t have any cementing properties; they affect the

compressive strength of the cement by lowering its strength to weight ratio. [5] [2]. This effect

gradually reduces with age when in low levels [2].]

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The volatile substances are compounds, specifically moisture and CO2 that may have

percolated into the cement. They are good indicators of premature hydration possibly due to

improper storage or handling [5]. They are toxic to the cement in the sense that during

hydration, the lime forms calcium hydroxide that raises the pH of the concrete thus forming a

thin film of oxides on the rebar that prevent rusting. However, dissolved CO2 slowly reacts with

the slated lime to form calcium carbonate. This lowers the pH from about 12-13 to about 8.5.

This not only depletes the protective film on the rebar but also lowers the threshold content of

chlorides required to rust the rebar from about 7000-8000ppm to about 100ppm [10]. The volatile

substances are collectively known as loss on ignition (since they are tested by weighing the

cement before and after igniting it to evolve the volatile components). Their levels are

deducted from the general cement matrix in this study in order to remove any errors due to

storage or mishandling.

2.3. PREVIOUS RESEARCH ON CEMENTZain et. al. (2008) [3] designed a prediction model for concrete by using power multivariable

regression equation on the various constituents of concrete to predict the strength at 7 and 28

days. Their variables were ordinary Portland cement (OPC), sand, water volume and density

and coarse aggregate as well as the water to cement ratio (w/c). This was a deviation from the

usual regression that only factors water to cement ratio f=b0+b1wc since, they argue that the

other components of the mix do in fact affect the overall strength.

In order to factor in the other mix components (sand and aggregate) they designed a model

with power multivariable equation f=α . X1β1 X2

β2…….X Nβ N ε where ά and β are coefficients and

‘x’ is the concrete mix components.

The models he acquired were: f 28=0.34262 .C−28.7310W 28.0856F . A−28.3023C . A−1.9259 ρ0.72819 W

C

1.61814

ε

f 7=0.2335 .C−4.8139W 4.0703F . A−4.1368C . A−3.9896 ρ2.5945W /C1.4920ε

Where f7= strength at 7 daysF28= strength at 28 daysC= cement levelF.A= sand levelC.A= aggregate levelΡ= density of the cementW/C= water to cement ratioε = error margin

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The adjusted R2 for the 7 days model was .99047 while the R2 was .995. on the other hand, the

28 days model had an R2 value of .994 and an adjusted R2 value of .988 which meant they

were very good models

Abd et. al. (2008) [11] did a similar study on foam concrete using the following variables:

Cement level Sand level Foam level Water volume Fly ash level Silica fume Slag level Water to cement ratio (w/c) Water to binder ratio (w/b) density

The model they acquired was

f 28=0.528661 .cement−6.39575 sand 60.9302 foam0.173423water−23.33702 flyash−63.2764

silica fume35.56460 slag66.46551w /c−2.23569w/b−71.9172density−18.0283∗4.112102,

Where 4.112102 was the error margin`

The correlation coefficient was 0.99990 while the adjusted R2 was 0.99979

They did go further to confirm the validity of using linear multiple regression models as a widely

used model for determination of cement strength. The equation used in the linear multiple

regression models is: f=ao+a1C3S+a2C2S+a3C3 A+a4C4 AF+ε

It is from these studies that the model in this study was birthed. However, both the studies

above use power multivariable regression which is more complex to perform while the aim of

this study was to produce a simple and fast method hence the use of the linear multivariate

regression models.

Also the linear multivariable regression highlighted above used the crystal phase complexes of

cement whose levels are difficult to acquire while the model in this study uses individual

component oxides which are easy to isolate and measure

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2.4.REGRESSION MODEL FOR CEMENT STRENGTH PREDICTION

There have been many models designed to predict cement strength but most of them use

concrete mix ratios to predict strength with age [3] [12]. The purpose of this study is to use

regression to predict strength using chemical components and not concrete mix ratios as the

variables.

The prediction model used was the linear multiple regression model [12]. This is a model for

predicting cement strength using chemical compositions. It is gotten by the equation

Y=α+β1 X1+ β2X2+β3 X3+β4 X4+ε

Where

βi (where i= 1,2,3,4) are regression coefficients

X1 is calcium level

X2 is silica level

X3 is insoluble residue level

X4 is the number of days of setting

ε is an error term

These four were chosen because the calcium and silica form complexes (C3S C2S) which give

the cement the strength while the insoluble residue lowers the cement strength to weight ratio.

The iron oxide and alumina complexes are either undesirable (C3A) or make a very marginal

addition to cement strength (C4AF) hence they weren’t considered [5], [13].

To assess the fit (goodness) of the model we use the coefficient determinant- adjusted R2

value.

The R2 is an accounting factor which shows us how much of the variables have been

accounted for (that is, how much of the total variation in the dependent variables can be

explained by the independent variable). Values can be between 0 and 1 and the higher the

factor the better the model [14].

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The adjusted R2 adjusts the R2 value to account for the increase in number of parameters to

give a better result since by default more variables means greater R2 value whether or not the

variable actually have a significant effect on the model. Thus the adjusted R2 eliminates the

effect of the useless variable to give a more truthful factor [15]

The R factor is gotten by: R2=regression∑ of squares

total∑ of squares

Residuals are the difference between the actual strength (dependent variable) and the strength

that is predicted by the model. The higher the residual, the more ‘off’ the prediction is. This

could be an indicator of either the low quality of the prediction or errors in the measurements of

the strength [13] [15]

Outliers are data entries that are either too large or too small to fit the data set. They are

obvious proofs of errors in measurements or anomalies. For example, in the measurement of

the height of men, a height of 4 feet is an outlier which could either be an error or a dwarf.

Usually outliers are removed to get more truthful results [13]

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CHAPTER THREE:MATERIALS AND METHODOLOGY

3.1. SOURCE OF DATAThe source of data was The Ministry of Transport and Infrastructure: Materials Testing and

Research Division (MoTI- MTRD). Samples sources were the samples that had been brought

for analysis by the various manufacturing companies as well as contractors of various civil

works

3.2. DATA COLLECTION METHODDue to the duration it takes to conduct one strength test (about 28 days) as well as the cost

(20,000/= per sample according to the MoTI MTRD), data could only be collected from the

records of the samples that had been analysed earlier. Only datasets which had both

compressive strength data and chemical composition data were taken

The chemical data acquired were the silica, insoluble residue, and calcium as well as loss on

ignition (in order to eliminate the error due to storage). The physical data acquired were the

compressive strengths at 2, 7 and 28 days setting time.

The brands gotten were:

1. Athi River Mining (ARM)- Rhino Cement 32.5

2. Athi River Mining (ARM)- Rhino Cement 42.5

3. East African Portland Cement- Blue Triangle 32.5

4. East African Portland Cement- Blue Triangle 42.5

5. Bamburi- Nguvu Cement 32.5

6. Bamburi- Power Max 42.5

7. National Cement- Simba 32.5

8. National Cement- Simba 42.5

9. Mombasa Cement- Nyumba 32.5

10.Mombasa Cement- Nyumba 42.5

11.Savannah Cement 32.5

12.Savannah Cement 42.5

Each brand had 5 samples for each compressive strength, thus the total samples were 5

samples x 2 compressive strengths x 6 brands = 60 samples

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3.3. MODEL CREATIONThe model was created using the linear multiple regression equation. The independent

variables were silica, insoluble residue and calcium. The dependent variables were the

strengths at 2, 7 and 28 days setting times for both 32.5 and 42.5 cement strength class.

The model designed were regression models for

1. 32.5 regressed against silica insoluble residue and calcium at 28 days setting time

2. 42.5 regressed against silica insoluble residue and calcium at 28 days setting time

3. 32.5 regressed against silica insoluble residue and calcium at 2, 7 and 28 days setting

time

4. 42.5 regressed against silica insoluble residue and calcium at 2, 7 and 28 days setting

time

5. 32.5 and 42.5 regressed against silica insoluble residue and calcium at 28 days setting

time

6. 32.5 and 42.5 regressed against silica insoluble residue and calcium at 2, 7 and 28

days setting time

The model closest to expectation (that is with the highest adjusted R2 value and coefficients

that are closest to theoretical facts) was then chosen as the preferred model.

The expectation in this case would be:

A relatively high positive calcium coefficient (β1) since calcium adds to the cement

strength in a big way theoretically

A relatively high negative insoluble residue coefficient (β2) since insoluble residue is the

greatest retardant to cement strength theoretically

A relatively low positive silica coefficient (β3) since silica adds to the cement strength

albeit not as greatly as calcium theoretically

A relatively very high positive number of days coefficient (β4) since cement strength

increases with increase in the number of days of setting theoretically

A zero alpha coefficient α since no chemical components should mean no strength

theoretically

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CHAPTER FOUR:RESULTS AND ANALYSIS

Appendix 1A shows the content of select components (namely silica, insoluble residue and

calcium) for the major brands in Kenya for both 32.5 and 42.5 strength class. The data in red

are outliers (erroneous data that didn’t fit the general data set) that had to be removed in order

to calculate the mean.

There were several datasets that didn’t meet the 5 sample mark. That is, only 1 sample for

Rhino 32.5; 4 samples for Mombasa Nyumba 32.5; 2 samples for Blue Triangle 32.5; 3

samples for National Cement 32.5 could be gotten. The rest of the brands however had 5

samples per strength class.

Appendix 1B shows the strengths of the cement samples in 1A after 2 days 7 days and 28

days of setting. The sets in red are outliers that had to be removed in order to calculate the

mean

Appendix 1C and 1D shows the average of the 5 samples per brand of the chemical

composition and strength respectively. For the brands which didn't have 5 samples, an

average of the samples that were available was made. That is, an average of 4 samples for

Mombasa Nyumba 32.5; 2 samples for Blue Triangle 32.5; 3 samples for National Cement

32.5 and only one entry for ARM rhino

The outliers were identified using the SPSS software.

Appendix 2A-2F analyses the residuals in the model. This is achieved by using the model to

predict the very same strengths used to create the model using their chemical components

and/or the number of days of setting. This is then compared with the actual strength to see the

deviation (residual)

The 32.5 and 28 days residual analysis analysed all the 6 brands from appendix 1D (case no

1-6 in order given in appendix 1D). The 32.5 and all days, residual analysis analysed all the 6

brands from appendix 1D using first the 2 days compressive strengths (case no 1-6) then 7

days (case no 7-12) then 28 days compressive strength (case no 13-18)

12 | P a g e

4.1. REGRESSION MODEL 32.5From table 4.1 it is visible that the adjusted R2 is .816 which means 81.6% of the dependent

variables can be accounted for by the independent variables. Thus this is a generally good

model. However from table 4.2 it is seen that none of the components had a p value of less

than 0.05 thus none of the chemical components were a significant predictor to cement

strength.

Table 4. 7: Model Summary for regression model 32.5 regressed against components

Model R R2 Adjusted R2

Std. Error of the

Estimate Durbin-Watson

1 .963 .927 .816 .26540 2.050

Table 4. 8: Coefficients summary for regression model 32.5 regressed against components

Model

Coefficients

t P- valueB Std. Error

1 (Constant) 44.075 5.231 8.425 .014

CALCIUM -.067 .083 -.806 .505

SILICA -.146 .165 -.884 .470

INSOLUBLE_RESIDUE -.142 .050 -2.865 .103

Based on the table, the regression model will be

Strength=44.075 – 0.067 calcium level – 0.146 silica level – 0.142 insoluble residue level

This means that if the insoluble residue, for example, is increased by 1% then the strength will

reduce by approximately 1.536. However, calcium had a negative coefficient contrary to

expectation which means this was not a suitable model

There were small residuals in the data as seen in appendix 2A (minimum -0.20 maximum 0.26)

which shows minimal error in prediction. Residuals are the difference between the actual

strength and the predicted strength based on the chemical components

13 | P a g e

Factoring in the days as per the table 4.3 the adjusted R2 becomes 0.685 which shows that the

quality of the model has reduced. Based on the significance on table 4.4, only the numbers of

days of setting was a significant contributor to cement strength.

Table 4. 9: Model summary for regression model 32.5 regressed against components and days


Std. Error of the


1 .871 .759 .685 4.87205 1.042

Table 4. 10: Coefficient summary for regression model 32.5 regressed against components and days

Model

Coefficients

t P valueB Std. Error

1 9.062 55.450 .163 .873

CALCIUM .018 .880 .021 .984

SILICA .115 1.753 .066 .949

INSOLUBLE_RESIDUE .142 .526 .269 .792

DAYS .688 .108 6.389 .000


Strength = 9.062+ .018 calcium level + 0.115 silica level + 0.142 insoluble residue level +

0.688 days of setting

This shows that the only significant contributor to the cement strength was the number of days

of setting. However, insoluble residue had a positive coefficient contrary to expectations thus

making the model not suitable

There were large residuals as shown in appendix 2B (maximum 2.02 minimum – 5.98) in the

data compared to the previous model which show the reason for the small R factor in that the

model was not a good quality

14 | P a g e

4.2. REGRESSION MODEL 42.5From the table 4.5 the adjusted R2 is .026. This is a poor model. Also none of the chemical

components had a p value of less than 0.05 as shown in table 4.6 thus none of the chemical

components were a significant predictor to cement strength.


Table 4. 11: Model Summary for regression model 42.5 regressed against components


Std. Error of the


1 .781 .610 .026 .89580 3.052

Table 4. 12: Coefficients summary for regression model 42.5 regressed against components

Model

Coefficients


1 (Constant) 22.964 40.050 .573 .624

CALCIUM .364 .529 .689 .562

SILICA -.101 .461 -.220 .846

INSOLUBLE_RESIDUE .437 .278 1.571 .257

Based on the table the model will be

Strength=22.964 + 0.364 calcium level – 0.101 silica level + 0.437 insoluble residue level

The model however had a positive insoluble residue coefficient thus the model was not very

suitable

15 | P a g e

There were small residuals in the data as seen in appendix 2C (minimum -0.62 maximum

0.93) which shows minimal error in predictions.

Factoring in the days as per table 4.7 the adjusted R2 becomes 0.890 which shows that the

quality of the model has increased. But from table 4.8 it is seen that, only the number of days

of setting was a significant predictor of cement strength.

Table 4. 13: Model summary for regression model 42.5 regressed against components


Std. Error of

the Estimate Durbin-Watson

1 .957 .916 .890 3.49423 .952

Table 4. 14: Coefficient summary for regression model 42.5 regressed against components

Model

Coefficients


1 (Constant) -21.376 90.200 -.237 .816

CALCIUM .719 1.191 .604 .556

SILICA -.051 1.038 -.049 .962

INSOLUBLE_RESIDUE -.144 .626 -.230 .822

DAYS .868 .073 11.868 .000

Based on table 4.8, the regression model will be

Strength = -21.376+ .719 calcium level - 0.051 silica level - 0.144 insoluble residue level +


This shows that the biggest contributor to cement strength is the number of days. However, the

alpha coefficient was negative which is unrealistic thus the model was not suitable

16 | P a g e

There were large residuals as seen in appendix 2D (maximum 6.11 minimum -4.38) in the

data which show errors in predictions.

4.3. REGRESSION MODEL 32.5 AND 42.5When designing a model from both 32.5 and 42.5 as per table 4.9, the adjusted R2 is .889

which is the best model for the prediction at 28 days. However based on table 4.10, none of

the chemical components had a p value of less than 0.05 thus no one of the chemical

components was a significant contributor to cement strength.

Table 4. 15: Model summary for regression model 32.5 and 42.5 regressed against components


Std. Error of


1 .959 .919 .889 1.79194 1.916

Table 4. 16: Coefficients summary for regression model 32.5 and 42.5 regressed against components

Model

Coefficients


1 (Constant) 13.803 29.178 .473 .649

CALCIUM .479 .405 1.182 .271

SILICA .070 .512 .136 .895


Based on table 4.10, the regression model will be

Strength=13.803 + 0.479 calcium level + 0.070 silica level – 0.055 insoluble residue level

This means that the model was relatively good since all the coefficients met the expectations.

However, the high alpha coefficient made the model unsuitable17 | P a g e

There were relatively large residuals in the data (minimum -3.33 maximum 1.93) which shows

relatively large error in predictions.

Factoring in the days as per table 4.11 the adjusted R2 becomes 0.92 which shows that the

quality of the model has increased, thus it is the best model for prediction factoring in all days

and the best model in general. Based on table 4.12, we see that only the number of days of

setting was a significant contributor to cement strength.

Table 4. 17: Model summary for regression model 32.5 and 42.5 regressed against components and days


Std. Error of


1 .964 .929 .920 2.98605 1.129

Table 4. 18: Coefficients summary for regression model 32.5 and 42.5 regressed against components and days

Model

Coefficients


1 (Constant) 5.048 28.077 .180 .858

CALCIUM .311 .390 .799 .430

SILICA -.082 .493 -.166 .869


DAYS .801 .044 18.139 .000


Strength = 5.048+ 0.311 calcium level - 0.082 silica level - 0.138 insoluble residue level +


This shows that the only significant predictor of cement strength was the number of days of

setting. However, the silica coefficient had a negative value which could mean some error in

the measurement of strength either at 2 days or 7 days

There were large residuals as per appendix 2F (maximum 6.27 minimum – 5.52) in the data

which show possible errors in the predictions

18 | P a g e

In all cases the only significant predictor to cement strength is the number of days of setting

which is contrary to the theoretical fact that all the chemical components should be significant

predictors of cement strength

4.4.DAYS OF SETTING ANOVA ANALYSIS 32.5 AND 42.5

The purpose of the anova analysis is to confirm if the number of days of setting does have a

considerable effect on the cement strength (i.e. is there a significant difference in the strength

between each set of days)

The anova analysis is done according to the equation Yij= µ + ti + εij

Where Yij = strength

µ = grand mean strength

ti = days of setting

εij= error margin

Thus the anova test confirms the significance of the effect of the number of days of setting on

the mean strength

Therefore, the null hypothesis will be that the days of setting have no effect on the strength i.e:

H0: t1 =t2 = t3 = 0

HA: t1 ≠t2 ≠ t3 ≠ 0

Conducting an anova test on the 32.5 data set using the number of days as the factor as per

table 4.13, it is seen that there is a significant difference in the mean strength of the cement at

different days (p value <0.05). Separating the means as per table 4.14 it is seen that there is a

significant difference in mean strength between the individual days (p value <0.05) (about

6N/m2 increase from 2-7 days and 13 N/m2 from 7-28 days).

19 | P a g e

Table 4. 19: Anova test on the days of setting at 32.5 strength class

Strength

Sum of

Squares df

Mean

Square F P value

Between

Groups1264.163 2 632.081 537.310 .000

Within Groups 17.646 15 1.176

Total 1281.809 17

Table 4. 20: Separation of means of 32.5 strength using LSD method

(I)

days

(J)

days Mean Difference (I-J) Std. Error P value

2 7 -6.39333 .62620 .000

28 -20.09000 .62620 .000

7 2 6.39333 .62620 .000

28 -13.69667 .62620 .000

28 2 20.09000 .62620 .000

7 13.69667 .62620 .000

A box plot of the same dataset shows that there is a significant change in strength with

increase in days of setting. E.A.P.C shows to be the weakest cement at 2 days (lower outlier)

and 7 days of setting shows the most even distribution.

20 | P a g e

Figure 4. 1: Box Plot of 32.5 strength class mean strengths versus days

Conducting an anova test on the 42.5 data set using the number of days as the factor (table

4.15) it is seen that the means of the strengths are different at the different days of setting (p

value of less than 0.05) and that there is a significant difference between 2days, 7 days and 28

days setting time (about 10N/m2 increase from 2-7 days and 13 N/m2 from 7-28 days).

Table 4. 21: Anova test on the days of setting at 42.5 strength class

21 | P a g e

STRENGTH

Sum of

Squares df

Mean

Square F P value

Between

Groups1905.517 2 952.759 342.607 .000

Within Groups 41.714 15 2.781

Total 1947.231 17

Table 4. 22: Separation of means of 42.5 strength using LSD method

A box plot of the same

dataset shows that

there is a significant

change in strength

with increase in days

of setting. There were

no outliers but, national

cement proved to be

the weakest cement

at 28 days setting time

22 | P a g e

(I)

DAYS

(J)

DAYS Mean Difference (I-J) Std. Error P value

2 7 -10.83167* .96279 .000

28 -25.12333* .96279 .000

7 2 10.83167* .96279 .000

28 -14.29167* .96279 .000

28 2 25.12333* .96279 .000

7 14.29167* .96279 .000

Figure 4. 2: Box Plot of 42.5 strength class mean strengths versus days

23 | P a g e

4.5. CEMENT COMPARISON 32.5 AND 42.5A graph of the mean strength across the days for all the cement brands at 32.5 N/m2 shows a

linear increase that spurts at the beginning and then levels off over time. This is consistent with

the strength plot of Portland cement [14]. The best cement is one which is high from the

beginning all through to the end.

In our case, the best cement for 32.5 cement strength is Mombasa Nyumba cement.

Figure 4. 3: Comparison of cements strengths vs days for all 32.5 brands

24 | P a g e

On the other hand, the best cement for 42.5 cement strength is Bamburi Power Max (although

the strongest cement is East African Portland- Blue Triangle) cement

Figure 4. 4: Comparison of cements strengths vs days for all 42.5 brands

25 | P a g e

CHAPTER FIVE5.1. DISCUSSION

The model closest to expectation (that is with the highest adjusted R2 value and coefficients

that are the closest representation of the theoretical facts) as well as having all components as

significant contributors to cement strength was to be chosen as the preferred model.

In this case, since no components means no cement strength, a zero alpha coefficient

(constant) was expected. The model with the closest to zero alpha constant was the preferred

model

Also since calcium and silica increase cement strength both should have a positive beta

coefficient, with calcium having a higher one. On the other hand since insoluble residue

reduces cement strength it should have a negative coefficient. The number of days of setting

should have the highest positive coefficient.

The 32.5 model for 28 days had a low R2 value due to insufficient data to improve the quality of

the model. Adding the other days brought in further errors into the model thus reducing the

quality even more.

The 42.5 model for 28 days had the poorest quality due to the unusually low value of the

national cement average strength at 28 days. Adding the days however balanced out the low

value by adding the relatively high values for national cement at 2 and 7 days thus improving

the quality of the model.

When the two data sets for 28 days were combined, the model greatly improved since the

change in composition of the cements from 32.5 to 42.5 was factored in the model. Factoring

in the days also improved the model even further. Thus, the model for composite 32.5-42.5

model for all days was chosen.

The model showed that calcium has a high positive value which is in line with the theoretical

fact that calcium is the largest contributor to cement strength. Insoluble residue had the highest

negative value which is in line with the theoretical fact that it reduces cement strength. The

silica had a negative value coefficient (though it had a positive value coefficient in the 28 days

model) probably due to an error in measurements of strength at 2 or 7 days setting time since

theoretically, silica should increase cement strength albeit minimally.

26 | P a g e

The model had a non-zero constant coefficient which is erroneous, since theoretically,

removing all the components should give you zero constant (i.e. no components means no

cement and thus no strength). This could be probably due a significant variable which was

unaccounted for that ended up being featured in the alpha coefficient (e.g setting water:

cement ratio etc) [10].

However the main thing is that based on the model, the only variable that actionably affects

the strength is the number of days of setting.

From the anova and box plot analyses it is visible that the number of days of setting does in

fact increase strength linearly which is in line with the theoretical fact that strength increases

with age provided that all other factors are held constant

It was not possible to do an anova test on the chemical components since the level of the

components was measured not predetermined. However, all the models showed that none of

the chemical components were significant predictors of cement strength. But theoretically the

chemical components should be significant predictors of strength. The discrepancy between

the theoretical facts and the regression could be due to a lurking variable (variable that affects

the cement strength but has not been included in the equation as a variable) [13]. Some of the

possible variables are the density and volume of the water used to make the concrete for

cement strength test among other variables

In comparison to the model proposed by the other studies quoted in chapter 2, It is seen that

the model proposed in this study had a marginally lower quality (R2= 0.92) than the one

proposed by Zain et. al. (2008) [3] (R2= 0.988) and Abd et. al. (2008) [12] (R2= 0.99979). This

means that the proposed model was a relatively competitive model

Both studies reflected above however did also point out the validity of the linear multiple

regression equation and its wide use in the determination of strength albeit with different

variable than the one used in this study

Both studies also did reflect the importance of water to cement ratio as well as concrete

density as variables in the regression model. However, these variables could not be factored

into the models since the data for these variables was not available

27 | P a g e

In the second part of this study, a multiple line graph of the different cement brands showed

that at 32.5Nm-2 Mombasa cement is the best, which is in line with its relatively high calcium

level (second highest at 48.43%) and low insoluble residue level (lowest at 20.77%) compared

to the rest. At 42.5Nm-2, the best cement was Bamburi which is in line with its relatively high

calcium (second highest at 62.39%) and low insoluble residue level (2.7%) compared to the

rest.

Ali. M. S. et. al. (2008) [5] did a comparison of 5 cement brands in Bangladesh (Holcim, Shah,

Crown, King and Anwar) using the British standard for cement as a benchmark. However, they

compared quality in terms of conformity of the chemical components to standard while this

study compares quality in terms of the cement strength and consistency of increase in

strength.

5.2. LIMITATIONThe fact that the cements’ data was gotten from varying dates of analysis introduces

determinate errors in the data. However since according to MoTI MTRD, the only thing that

changes with time in the cement is the weight due to absorption of water and carbon dioxide

(all factors held constant), the calculation factor was added which removes the volatile

components from the cement sample and presents the cement data as it should have been

before storage.

The cement samples were too few which led to a lot of noise in the data model. But since

these were the only consistent records, there was a need for improvisation.

There are other variables which could not be measured but have a great effect on the cement

strength. For example, the amount of water used for setting and cement density [3], which led to

the presence of a non- zero coefficient. However, no data for such variables were present

While the linear multiple regression equation is generally helpful it is unable to account for the

fact that the variables (apart from days) interact chemically in a complex manner (e.g. in

forming calcium silicates and calcium aluminates). This leads to the inadequacy of the linear

regression model and thus the need for more complex models (e.g. multivariable power

equation models and logarithmic linear multiple regression models) and even the use of

artificial intelligence in the prediction [3]. However the purpose of this project was to produce a

simple, fast and easy to use model hence it was avoided.

The comparison of the different cement brands was based purely on cement strength and did

not factor in other things like cost and availability across the country

28 | P a g e

CHAPTER SIX6.1. CONCLUSION

Thus based on the results, and based on the model, the null hypothesis is accepted that

there is no relationship between the chemical components of cement and cement strength at

5% level of significance

It is also accepted that the number of days of setting is the only contributor to cement strength

From the data, it is concluded that the best cement at 32.5N/m2 compression strength is

Mombasa Nyumba cement, while the best cement at 42.5 N/m2 compression strength is

Bamburi Power Max

6.2. RECOMMENDATIONA larger data set should be used for the analysis in order to improve the model, preferably

straight from the manufacturer in order to minimize errors

The volume of the hydration water and density of the concrete should be factored in as a

model parameter as this seems to be a major contributor based on the regressions done on

concrete [3].

Other regression models should be tried out in order to get one that better fits the model than

the linear regression model.

The model should be validated by conducting blind sampling and comparing the strength of the

samples to the predictions

More funds should be availed in order to facilitate easier mobility as well pay as for cement

strength analysis (20,000/= per sample) in order to minimize errors and improve on model

Further research and more time should be availed for this kind of project as it is both time and

labour intensive.

29 | P a g e

6.3. FUTURE WORK In the model, 5 samples were used per strength class per brand from the MoTI MTRD

records giving a total of 60 samples. The model however could be improved using more

data preferably direct from the sources to reduce noise and also errors as well as

minimize uncontrolled variables.

In the model used, it was impossible to factor in the density of cement and volume of

water used in the making of concrete since it wasn’t tested. The model could be

improved by factoring in the amount of the water used in setting and the density of the

concrete or by using a fixed amount of water in order to eliminate it as a variable. This

could serve to remove the discrepancy between the model and the theoretical facts as

well as remove the non- zero alpha coefficient.

There may also be a need to conduct a blind experiment by taking the chemical

compositions of a sample of known strength and try to predict the strength using the

improved model. This would serve well as a method validation system.

Seeing as the linear multiple regression equation does have its own limitation as

pointed out by Zain et. al (2008) a model using power multivariable regression equation

in a simplified way could be used in the model above in order to see if it will give a

better prediction

The comparison test done factored in only the cement strength as a quality marker.

Factoring in other markers like the relative costs of each brand and the nationwide

availability could better the comparisons

30 | P a g e

APPENDICESAPPENDIX 1A CEMENT CHEMICAL COMPOSITION RAW DATA

NAME CALCIUM IN % SILICA IN %INS RES IN % L.O.I C.F

ATHI RIVER MINING- RHINO 32.5

3.15SAMPLE 1 49.00 50.59 17.56 18.13 20.73 21.40 0.97

SAMPLE 2 N/A N/A N/A N/A N/A





3.41SAMPLE 1 58.24 60.30 16.54 17.12 19.18 19.86 0.97

SAMPLE 2 63.00 64.77 17.43 17.92 2.56 2.63 2.73 0.97

SAMPLE 3 63.00 64.71 19.89 20.43 1.88 1.93 2.65 0.97

SAMPLE 4 56.58 58.08 18.73 19.23 1.42 1.46 2.58 0.97

SAMPLE 5 63.98 65.28 19.87 20.27 1.48 1.51 1.99 0.98

MOMBASA- NYUMBA 32.5

0.97SAMPLE 1 39.62 40.79 14.55 14.98 19.44 20.01 2.87

SAMPLE 2 45.36 46.31 16.29 16.63 22.60 23.08 2.06 0.98

SAMPLE 3 46.84 48.09 16.86 17.31 19.59 20.11 2.59 0.97

SAMPLE 4 56.84 58.53 16.38 16.87 19.30 19.87 2.89 0.97



0.97SAMPLE 1 58.43 59.97 18.00 18.47 10.68 10.96 2.57

SAMPLE 2 54.45 55.62 18.99 19.40 9.53 9.74 2.11 0.98

SAMPLE 3 58.66 61.21 20.89 21.80 1.20 1.25 4.16 0.96

SAMPLE 4 60.34 61.39 20.84 21.20 2.57 2.61 1.71 0.98

SAMPLE 5 70.98 72.46 18.97 19.37 2.80 2.86 2.04 0.98

a | P a g e

EAST AFRICAN PORTLAND CEMENT- BLUE TRIANGLE 32.5

27.48SAMPLE 1 41.16 42.51 16.69 17.24 28.38 3.18 0.97

SAMPLE 2 40.74 41.93 16.01 16.48 29.12 29.97 2.83 0.97





9.14SAMPLE 1 55.44 56.94 20.55 21.11 9.39 2.64 0.97

SAMPLE 2 59.30 61.01 18.98 19.53 4.28 4.40 2.80 0.97

SAMPLE 3 60.48 63.00 19.09 19.89 4.29 4.47 4.00 0.96

SAMPLE 4 57.82 58.65 19.25 19.53 4.87 4.94 1.42 0.99

SAMPLE 5 60.48 61.26 22.70 22.99 1.06 1.07 1.27 0.99

NATIONAL CEMENT- SIMBA 32.5

SAMPLE 1 40.60 41.95 16.05 16.58 33.64 34.76 3.22 0.97

SAMPLE 2 42.56 44.51 14.93 15.62 31.08 32.51 4.39 0.96

SAMPLE 3 35.56 36.63 12.62 13.00 42.78 44.07 2.92 0.97




SAMPLE 1 52.64 53.27 20.80 21.05 3.31 3.35 1.18 0.99

SAMPLE 2 56.28 56.87 20.67 20.89 3.16 3.19 1.03 0.99

SAMPLE 3 59.64 61.41 16.91 17.41 5.73 5.90 2.89 0.97

SAMPLE 4 63.00 64.71 21.48 22.06 1.93 1.98 2.64 0.97

SAMPLE 5 61.38 61.66 21.27 21.37 1.80 1.81 0.45 1.00

SAVANNAH CEMENT 32.5

SAMPLE 1 51.26 51.98 18.84 19.11 18.42 18.68 1.39 0.99

SAMPLE 2 41.86 42.69 15.69 16.00 30.88 31.49 1.95 0.98

SAMPLE 3 42.56 43.94 19.18 19.80 27.86 28.77 3.15 0.97

SAMPLE 4 54.74 55.94 17.82 18.21 22.74 23.24 2.14 0.98

SAMPLE 5 40.58 41.37 15.37 15.67 29.64 30.21 1.90 0.98

b | P a g e


SAMPLE 1 60.90 61.76 21.22 21.52 1.62 1.64 1.39 0.99

SAMPLE 2 61.74 62.48 21.00 21.25 2.67 2.70 1.18 0.99

SAMPLE 3 59.36 60.17 19.38 19.65 5.40 5.47 1.35 0.99

SAMPLE 4 60.90 61.87 20.15 20.47 1.77 1.80 1.57 0.98

SAMPLE 5 62.44 63.33 21.20 21.50 1.46 1.48 1.40 0.99

BAMBURI- NGUVU 32.5

SAMPLE 1 39.76 40.87 21.71 22.31 33.95 34.90 2.71 0.97

SAMPLE 2 39.16 40.07 11.34 11.60 34.77 35.58 2.27 0.98

SAMPLE 3 39.62 40.87 12.56 12.96 35.38 36.50 3.06 0.97

SAMPLE 4 41.72 42.61 15.90 16.24 30.18 30.83 2.10 0.98

SAMPLE 5 48.30 49.08 17.33 17.61 28.75 29.21 1.58 0.98

BAMBURI- POWER MAX 42.5

SAMPLE 1 59.64 61.78 15.39 15.94 3.71 3.84 3.46 0.97

SAMPLE 2 60.76 62.89 15.81 16.36 1.43 1.48 3.39 0.97

SAMPLE 3 60.19 62.28 18.54 19.18 2.45 2.54 3.36 0.97

SAMPLE 4 60.50 62.73 17.86 18.52 2.63 2.73 3.55 0.96

SAMPLE 5 60.20 62.28 18.24 18.87 2.74 2.83 3.34 0.97

INDEXCALCIUM Content of Calcium in 1g of Cement

SILICA Content of Silicon Dioxide in 1g of Cement

INS RES Level of Insoluble Residue in 1g Of Cement

LOI loss of weight on ignition of cement to remove volatile substances

absorbed during storage

C.F calculation factor gotten from removing loss on ignition values from the cement

matrix i.e. If L.O.I is 3% then the actual cement is97%

IN % percentage content of chemical component using C.F as 100% (that is,

determining what the component level would have been had there been no

volatile substances in the matrix)

e.g actual silica content=silica content∈matix

C .F∗100∗100

c | P a g e

APPENDIX 1B CEMENT STRENGTH RAW DATANAME 2 DAYS 7 DAYS 28 DAYS


SAMPLE 1 17.50 21.70 37.10

SAMPLE 2 16.10 18.20 35.10

SAMPLE 3 14.20 18.20 32.90

SAMPLE 4 11.60 24.20 34.10

SAMPLE 5 12.80 20.00 34.80


SAMPLE 1 24.20 33.50 45.20

SAMPLE 2 20.60 39.80 43.20

SAMPLE 3 23.40 38.10 43.20

SAMPLE 4 19.20 31.50 44.20

SAMPLE 5 15.00 30.20 46.30


SAMPLE 1 12.40 18.90 36.80

SAMPLE 2 13.20 18.40 35.20

SAMPLE 3 17.50 24.40 34.10

SAMPLE 4 14.00 22.60 35.40

SAMPLE 5 19.60 23.80 36.10


SAMPLE 1 18.40 20.90 44.10

SAMPLE 2 17.40 29.60 44.20

SAMPLE 3 19.50 33.60 47.60

SAMPLE 4 18.50 27.30 43.00

SAMPLE 5 18.80 33.80 47.00


SAMPLE 1 14.80 22.60 34.20

SAMPLE 2 10.50 17.50 35.60

SAMPLE 3 12.60 23.20 35.60

SAMPLE 4 8.10 16.80 33.40

SAMPLE 5 10.50 20.50 34.50

d | P a g e


SAMPLE 1 22.10 30.00 47.70

SAMPLE 2 19.80 31.90 47.40

SAMPLE 3 20.10 33.40 45.20

SAMPLE 4 12.30 28.60 45.20

SAMPLE 5 13.40 30.60 43.20


SAMPLE 1 16.90 20.70 33.90

SAMPLE 2 17.10 21.50 34.10

SAMPLE 3 13.70 20.50 33.40

SAMPLE 4 13.60 18.40 33.80

SAMPLE 5 14.60 24.70 33.80


SAMPLE 1 20.80 31.20 44.80

SAMPLE 2 20.70 33.10 45.10

SAMPLE 3 23.20 32.30 43.70

SAMPLE 4 19.60 29.80 45.50

SAMPLE 5 23.80 32.40 47.20


SAMPLE 1 17.30 22.30 36.40

SAMPLE 2 13.80 21.90 33.80

SAMPLE 3 17.50 28.50 35.70

SAMPLE 4 15.40 21.40 34.10

SAMPLE 5 14.10 21.70 34.10


SAMPLE 1 22.40 34.20 46.20

SAMPLE 2 22.80 33.10 43.80

SAMPLE 3 22.60 31.50 45.20

SAMPLE 4 22.10 29.80 45.30

SAMPLE 5 19.20 20.30 44.10

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BAMBURI- NGUVU 32.5

SAMPLE 1 16.90 20.70 33.90

SAMPLE 2 17.10 21.50 34.10

SAMPLE 3 13.70 20.30 33.40

SAMPLE 4 13.60 18.40 33.80

SAMPLE 5 14.60 24.70 33.80

BAMBURI- POWER MAX 42.5

SAMPLE 1 20.80 31.20 44.80

SAMPLE 2 20.70 33.10 45.10

SAMPLE 3 23.20 32.30 43.70

SAMPLE 4 19.60 29.80 45.50

SAMPLE 5 23.80 32.40 47.20

APPENDIX 1C CEMENT COMPOSITION AVERAGES

NAMECALCIUM

LEVEL

SILICA

LEVEL

INSOLUBLE RESIDUE

LEVELATHI RIVER MINING 32.5 50.59 18.13 21.40

MOMBASA CEMENT 32.5 48.43 16.45 20.77

EAST AFRICAN PORTLAND

CEMENT 32.5 42.22 16.86 29.18

NATIONAL CEMENT 32.5 41.03 15.07 37.11

SAVANNAH 32.5 47.18 17.76 26.48

BAMBURI 32.5 41.10 16.14 34.45

ATHI RIVER MINING 42.5 62.63 18.99 1.88

MOMBASA CEMENT 42.5 60.86 20.05 6.14


CEMENT 42.5 60.17 20.61 4.60

NATIONAL CEMENT 42.5 59.58 21.34 2.50

SAVANNAH 42.5 61.92 20.88 2.90

BAMBURI 42.5 62.39 17.77 2.70

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APPENDIX 1D CEMENT STRENGTH AVERAGESNAME 2 DAYS 7 DAYS 28 DAYSATHI RIVER MINING 32.5 14.44 20.46 34.8

MOMBASA CEMENT 32.5 15.34 21.62 35.52


CEMENT 32.5 11.3 20.12 34.66

NATIONAL CEMENT 32.5 15.18 20.28 33.9

SAVANNAH 32.5 15.62 21.82 34.82

BAMBURI 32.5 15.18 21.12 33.9

ATHI RIVER MINING 42.5 20.48 34.62 44.42

MOMBASA CEMENT 42.5 18.52 29.04 45.18


CEMENT 42.5 17.54 30.9 45.74

NATIONAL CEMENT 42.5 21.62 31.76 45.26

SAVANNAH 42.5 22.48 29.78 44.92

BAMBURI 42.5 21.62 31.76 45.26

APPENDIX 2A 32.5 28 DAYS RESIDUAL DIAGNOSTICS

Case Number Std. Residual STRENGTH

Predicted

Value Residual

1 -.754 34.80 35.0001 -.20011

2 .152 35.52 35.4796 .04042

3 .080 34.66 34.6389 .02111

4 .180 33.90 33.8522 .04780

5 .981 34.82 34.5597 .26027

6 -.639 33.90 34.0695 -.16949

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APPENDIX 2B 32.5 ALL DAYS RESIDUAL DIAGNOSTICS

Case Number Std. Residual STRENGTH Predicted Value Residual

1 -.419 14.44 16.4798 -2.03983

2 -.168 15.34 16.1578 -.81776

3 -1.228 11.30 17.2812 -5.98118

4 -.615 15.18 18.1756 -2.99559

5 -.302 15.62 17.0936 -1.47361

6 -.563 15.18 17.9236 -2.74357

7 .111 20.46 19.9191 .54087

8 .415 21.62 19.5971 2.02294

9 -.123 20.12 20.7205 -.60048

10 -.274 20.28 21.6149 -1.33488

11 .264 21.82 20.5329 1.28709

12 -.050 21.12 21.3629 -.24287

13 .089 34.80 34.3642 .43582

14 .303 35.52 34.0421 1.47790

15 -.104 34.66 35.1655 -.50553

16 -.443 33.90 36.0599 -2.15993

17 -.032 34.82 34.9780 -.15796

18 3.138 33.90 18.6114 1.52886E1

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APPENDIX 2C 42.5 28 DAYS RESIDUAL DIAGNOSTICS


1 -.298 44.42 44.6873 -.26734

2 -.687 45.18 45.7953 -.61530

3 1.033 45.74 44.8146 .92539

4 -.512 43.15 43.6086 -.45860

5 .265 44.92 44.6827 .23734

6 .199 45.26 45.0815 .17851

APPENDIX 2D 42.5 ALL DAYS RESIDUAL DIAGNOSTICS


1 -1.056 20.48 24.1689 -3.68892

2 -1.061 18.52 22.2288 -3.70881

3 -1.255 17.54 21.9260 -4.38601

4 -.677 19.40 21.7672 -2.36718

5 -.268 22.48 23.4157 -.93572

6 -.664 21.62 23.9400 -2.32000

7 1.749 34.62 28.5076 6.11236

8 .708 29.04 26.5675 2.47248

9 1.327 30.90 26.2647 4.63527

10 .808 28.93 26.1059 2.82411

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11 .580 29.78 27.7544 2.02557

12 .996 31.76 28.2787 3.48128

13 -.661 44.42 46.7302 -2.31022

14 .112 45.18 44.7901 .38989

15 .359 45.74 44.4873 1.25269

16 -.337 43.15 44.3285 -1.17848

17 -.303 44.92 45.9770 -1.05702

18 -.355 45.26 46.5013 -1.24130

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APPENDIX 2E COMPOSITE 28 DAYS RESIDUAL DIAGNOSTICS


1 -.339 44.42 45.0277 -.60767

2 .647 45.18 44.0208 1.15916

3 1.075 45.74 43.8137 1.92631

4 -.305 43.15 43.6969 -.54695

5 .087 44.92 44.7638 .15617

6 .266 45.26 44.7826 .47740

7 -1.860 34.80 38.1324 -3.33240

8 -.834 35.52 37.0148 -1.49479

9 .587 34.66 33.6087 1.05132

10 .793 33.90 32.4798 1.42022

11 -.767 34.82 36.1952 -1.37520

12 .651 33.90 32.7336 1.16641

APPENDIX 2F COMPOSITE ALL DAYS RESIDUAL DIAGNOSTICS

Minimum Maximum Mean Std. Deviation N

Predicted Value 13.0776 45.1758 27.8050 10.15499 36

Std. Predicted Value -1.450 1.711 .000 1.000 36

Standard Error of Predicted

Value.764 1.473 1.098 .184 36

Adjusted Predicted Value 12.6587 45.3062 27.8070 10.16018 36

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Residual -5.52582 6.27368 .00000 2.81024 36

Std. Residual -1.851 2.101 .000 .941 36

Stud. Residual -1.940 2.214 .000 1.006 36

Deleted Residual -6.07603 6.96761 -.00200 3.21526 36

Stud. Deleted Residual -2.037 2.374 .001 1.030 36

Mahal. Distance 1.322 7.550 3.889 1.607 36

Cook's Distance .000 .120 .029 .032 36

Centered Leverage Value .038 .216 .111 .046 36

REFERENCES

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1) Kraiwood, K, Jaturapitakkul. C and Tangpagasit. J, Effect of Insoluble Residue on Properties of Portland Cement. Cement and Concrete Research, 2000. 30(8): p. 1209- 1214.2) Compressive strength test of cement | IS 4031-Part 6 ProBCGuide. 2015 [cited 2016; Available from: http://www.probcguide.com/civil-works/plain-and-reinforced-concrete/compressive-strength-test-of-cement-is-4031-part-6/.

3) Clear, C.A., Specifying Cement- Standards and Nomenclature, B.C. Association, Editor. 2010: London

4 Ali, M.S., Khan. I.A, and Hossain. M.I, Chemical Analysis of Portland Cement in Bangladesh, in Department of Chemical Engineering. 2008, Bangladesh University of Engineering and Technology: Bangladesh, India.

5) Cement — Part 1: Composition, specification and conformity criteria for common cement, in EAS 18-1:2001, K.B.o. Statistocs, Editor. 2001, Kenya Beareau of Statitics

6 Cement -- Test methods -- Part 1: Analysis by wet chemistry., in ISO 29581-1:2009, I.S. Organization, Editor. 2009: Geneva, Switzerland.

7) Michaux, M., E. Nelson, and Vidick. B, Cement Chemistry and Additives. Well Completion, 1989. 1(1): p. 18- 25

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9) Corrosion of Embedded Material. 2015 [cited 2016 11th February 2:54 pm]; Available from: http://www.cement.org/for-concrete-books-learning/concrete-technology/durability/corrosion-of-embedded-materials.

10) Thomas, J. and Jennings. H. 3.6 - Mineral and Oxide Composition of Portland Cement. 2008 [cited 2016 25th May 2:34 pm]; Available from: http://iti.northwestern.edu/cement/monograph/Monograph3_6.html.

11) Abd, S.M, Mohd. M.F, and Hamid. R. A, Modelling the Prediction of Cement of Compressive Strength for Cement and Foam Concrete. ICCBT 2008, 2008. B(31): p. 343- 354.

12) Linear Regression. 1997 [cited 2016 28th April 9:31 am]; Available from: http://www.stat.yale.edu/Courses/1997-98/101/linreg.htm.

13) Thomas, J. and Jennings. H, The Science of Cement and Concrete. 2008 [cited 2016 May 25th 2:50pm]; Available from: http://iti.northwestern.edu/cement/monograph/scicem_chap3.doc.

14) Correlation. 1997 [cited 2016 25th May 12:10 pm]; Available from: http://www.stat.yale.edu/Courses/1997-98/101/correl.htm.

15) Lund, A. and Lund. M. Linear Regression Analysis using SPSS Statistics. 2013 [cited 2016 28th April 10:22am]; Available from: https://statistics.laerd.com/spss-tutorials/linear-regression-using-spss-statistics.php.

http://www.stat.yale.edu/Courses/1997-98/101/linreg.htm

http://iti.northwestern.edu/cement/monograph/Monograph3_6.html

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