Analysis and Experimental Design of Slump Dry Concrete Mix...

Advances in Engineering & Scientific Research

AESR 12|Volume 1|Issue 1|2015

1

Research Article

ANALYSIS AND EXPERIMENTAL DESIGN OF SLUMP DRY

CONCRETE MIX IN WARM AND HOT HUMID ZONES, SOUTH

EASTERN NIGERIA

John U. Ezeokonkwo1, Chukwuemeka Daniel Ezeliora

2, F. O. Ezeokoli

1

1Department of Building, NnamdiAzikiwe University, Awka, Anambra State 2Department of Mechanical Engineering, NnamdiAzikiwe University, Awka, Anambra State

Correspondence should be addressed to John U. Ezeokonkwo

Received August 14, 2015; Accepted August 22, 2015; Published September 05, 2015;

Copyright: © 2015 John U. Ezeokonkwo et al. This is an open access article distributed under the Creative

Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium,

provided the original work is properly cited.

Cite This Article: U. Ezeokonkwo, J., Daniel Ezeliora, C., Ezeokoli, F.(2015). Analysis and Experimental Design of Slump Dry Concrete Mix in Warm and Hot Humid Zones, South Eastern Nigeria. Advances in Engineering &

Scientific Research, 1(1).1-12

ABSTRACT

In the research work, the use of factorial mathematical model was adopted for the slumps dry of concrete mix in a Hot and

Warm humid zones as functions of quantity of cement, water-cement ratio and quantity of aggregates, the composition of

the concrete mix was optimized by varying the independent factors (variables) for various seasons within the zones through

Box Wilson’s composite mathematical method. The optimum value for factors X1 and X2 and X3 and X4 were obtained for

the Hot and Warm humid zones as Y2 = 106.8221. The electronic (computer) manipulations of the data generated from the

experiments, the following graphs (1 – 8) were generated for a better understanding of interactions between the factors and

value generated as a result.

KEYWORDS:Concrete mix, matlab, Climatic Conditions, factorial design, Quality, Production

INTRODUCTION

Conceptual framework is the operationalization of the

variables that hold the research together. It helps one to

make logical sense of the relationship among variables or

factors that have been identified as significant to the

problem under investigation. The quality control

management of building materials with emphases on

concrete works is examined based on the following:

Concept of Quality Control in Building

Production,

Factors affecting Quality of Concrete Work.

Climatic conditions and their effect on Quality of

Concrete Work

Concrete Mix Design and Production

Quality Control Measures of Concrete Works

Concept Of Quality Control In Building Production

Quality Control is a process employed in other to ensure

that a product or service conforms to established standards

or specifications. It may include whatever actions a

business deems necessary to provide for control and

verification of certain characteristics of a product or

service. The basic goal of quality control is to ensure that

the products, services, or processes provided meet specific

requirements and are dependable, satisfactory and fiscally

sound.

Essentially, quality control involves the examination of a

product, services, or process for certain minimum levels of

quality. The goal of a quality control team is to identify

products or services that do not meet a specified standard

of quality. If a problem is identified, the job of a quality

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2

k k k

control team or professional may involve stopping

production temporarily. Depending on the particular

service or product as well as the type of problem identified,

production or implantation may not cease entirely.

Wisegeek, (2010).

The concept of quality control in building production is the

quality of the production which involves the quality of

integrated action due to human, material, machinery,

process methodology and work environment. This is also

known as process quality which reflects the quality of the

finished work or product. In order to ensure the quality of

production, the quality of each process must be controlled,

which is the focus of quality control during construction

Shilian, (2004).

HUMAN FACTORS IN QUALITY CONTROL

Since human activities, form part of production process,

the overall quality control and individual ability of humans

would determine to large extent the results of all quality

control activities. Therefore, human are considered as both

the controlled targets and controlling motivation of other

quality control activities Cheng, (2004). The contents of

human control includes the overall quality of the set up or

company and individual knowledge, ability, physical

condition, psychological state, quality consciousness,

behaviour, concept of organizational discipline, and

professional ethics. The main measures and approach of

human control on production sites are summarized as

follows:

The management objectives and

responsibilities of the project manager or

supervisor being considered as the centre the

organization of project management should be

set up reasonably with appropriate

management personnel.

The operating workers should be asked to

have relevant qualifications, particularly

important technical trades, special trades etc.

There should be very strict on-site

management system and production

discipline and the standard of operation

technology and management activities.

Incentives and communication activities should be

promoted to arouse staff’s enthusiasm.

REGRESSION MODEL

In accordance with the experimental method (Box

Wilson’s Mathematical Theory of Experiment), 25

experiments were carried out for effective study of the

mutual interactions of various factors (variables)

considered in the experiment. Both the experimental and

theoretical values of the slump in mm, density and

compressive strength of the concrete measured during the

wet and dry seasons obtained as contained in tables 1 and 2

for the two zones (Hot and Warm humid zones). From the

results obtained regressional model for the factors –

dependent variables were derived in the form.

Y =bo + ΣbiXi+ΣbijXi

2

+Σbij XiXj 1

i=1 i=1 i-j

The main objective in the regression analysis is to determine the statistical relevance of the derived mathematical

expression for the studied subject of this research, which in summary is as a check and balance apparatus for the reliability

of measured results of the experiment on one hand, and the adequacy of the derived Mathematical Model (MM) for the

observations made.

Critical Values of Regression Coefficient based on the Regression Mathematical Model is shown in the equation 1.1.

Y2=208–0.035X1–9.12X2+0.0268X3–0.0501X4 ..... Equation 1.1

The equation 1.1 is the regression equation of the slump dry season under which the experiments were performed.

THE RESEARCH METHOD

used in this work is the application of Factorial design Analysis of Mathematical Models for Variables in the Zones. The

method is used to study the relative influence of each of the factors on the slumps (workability) of concrete, density and

compressive strength for each climatic season, quasi or mono factorial models were obtained. From the analysis, it is

possible to make the following deductions on the influence of the different factors over the workability density and strength

of concrete.



3

Computer Analysis Of The Experimental Results From The Two Zones

Table 1:Values of Results from Hot Humid Zone (Awka)

Level of factors and test X1 = C Cement kg/m3

X2= w water content kg/m

3

X3 = Fa fine paragraph kg/m3

X4 = Ca coarse Aggregate kg/m0

Slump dry mm

Xnar Highest level (+)

Xim Lowest level (-)

Xer Central Level (0) average

𝜹Interval of Change Δ

300

207

254

46

7

5

6

1

690

414

552

138

1380

953

1167

213

Test No X1 X2 X3 X4 Y2

1 207 5 414 953 85

2 207 7 690 953 103

3 207 5 690 953 157

4 207 5 690 953 150

5 300 7 414 953 63

6 300 5 690 1380 80

7 207 7 690 1380 97

8 207 7 690 1380 51

9 207 6 552 1167 64

10 300 7 552 1167 58

11 254 5 552 1167 78

12 254 7 552 1167 94

13 254 6 414 953 159

14 300 5 690 953 152



4

15 207 7 414 1380 112

16 254 6 552 1167 170

17 207 5 414 953 100

18 207 5 690 953 98

19 254 7 552 1167 92

20 254 5 552 1167 92

21 254 7 690 953 99

22 254 6 414 1167 99

23 254 6 552 1380 101

24 254 6 552 953 97

25 254 6 552 1167 142

Source: Researcher’s Field Work

Table 2:Values of Result obtained from Experiment in Warm Humid Zone (Owerri)

Level (of Factors and tests)

X1 = C Cement Kg.m3

X2 = c

Water Cement Kg/m3

X3 =

Fine Aggregate

Kg/m3

X4

Coarse

Aggregate

Slump

SDRY

Highest Level (+) 300 .7 690 1380

Xmin Lowel level (-) 207 .5 414 953

Xmin Control level(0) 254 .6 552 1167

Interval of Change 46 .1 138 213 Y2



5

Source: Researcher’s Field Work

After experimentally generating data on Tables 1 and 2, the data was subjected to electronic manipulation with Minitab

software and the following results with appropriates tables and figures were obtained.

S/N0

1 - - - - 85

2 + + - - 110

3 - + - - 159

4 - + - - 157

5 + + - - 125

6 + - + + 73

7 - + + + 101

8 + + + + 163

9 - 0 0 0 72

10 + 0 0 0 58

11 0 - 0 0 87

12 0 + 0 0 68

13 0 0 - - 159

14 + - + - 157

15 - + - + 109

16 0 0 0 0 167

17 - - - 0 105

18 - + - 0 97

19 0 + 0 0 91

20 0 - 0 0 99

21 + + 0 0 98

22 0 0 - 0 101

23 0 0 0 + 94

24 0 0 0 0 102

25 0 0 0 0 99



6

Regression Analysis: Y2 versus X1, X2, X3, X4

The regression equation is

Y2 = 208 - 0.035 X1 - 9.12 X2 + 0.0268 X3 - 0.0501 X4

Predictor Coef SE Coef T P

Constant 207.59 83.75 2.48 0.022

X1 -0.0352 0.2026 -0.17 0.864

X2 -9.118 8.272 -1.10 0.283

X3 0.02685 0.06349 0.42 0.677

X4

-0.05011

0.04300

-1.17

0.258

S = 33.2274 R-Sq= 16.8% R-Sq(adj) = 0.1%

Analysis of Variance

Source DF SS MS F P

Regression 4 4452 1113 1.01 0.427

Residual Error 20 22081 1104

Total 24 26533

Source DFSeq SS

Source DF Seq SS

X1 1 132

X2 1 2694

X3 1 126

X4 1 1500



7

Unusual Observations

Obs X1 Y2 Fit SE Fit Residual St Resid

16 254 170.00 100.29 7.43 69.71 2.15R

R denotes an observation with a large standardized residual.

Figure 1:Effects Plot for Y2

3210-1-2-3

99

95

90

80

70

60

50

40

30

20

10

5

1

Standardized Effect

Pe

rce

nt

A X1

B X2

C X3

D X4

Factor Name

Not Significant

Significant

Effect Type

Normal Plot of the Standardized Effects(response is Y2, Alpha = 0.05)

Figure 2 :Residual Plots for Y2

50250-25-50

99

90

50

10

1

Residual

Per

cent

1501251007550

60

30

0

-30

Fitted Value

Res

idua

l

6040200-20-40

8

6

4

2

0

Residual

Freq

uenc

y

24222018161412108642

60

30

0

-30

Observation Order

Res

idua

l

Normal Probability Plot Versus Fits

Histogram Versus Order

Residual Plots for Y2



8

Figure 3:Main Effects Plot for Y2

300207

120

115

110

105

100

75

690414

120

115

110

105

100

1380953

X1

Me

an

X2

X3 X4

Main Effects Plot for Y2Data Means

Figure 4:Interaction Plot for Y2

75 690414 1380953

120

100

80

120

100

80

120

100

80

X1

X2

X3

X4

207

300

X1

5

7

X2

414

690

X3

Interaction Plot for Y2Data Means



9

Figure 5:Contour Plots of Y2

X2*X1

300260220

7.0

6.5

6.0

5.5

5.0

X3*X1

300260220

650

600

550

500

450

X4*X1

300260220

1300

1200

1100

1000

X3*X2

765

650

600

550

500

450

X4*X2

765

1300

1200

1100

1000

X4*X3

640560480

1300

1200

1100

1000

X1 207

X2 5

X3 414

X4 953

Hold Values

>

–

–

–

–

< 20

20 70

70 120

120 170

170 220

220

Y2

Contour Plots of Y2

Figure 6: Surface Plots of Y2

7100

6

150

200

200250 5

300

Y2

X2

X1

720

600100

150

200

200 480250

300

Y2

X3

X1

1400

50 1200

100

150

200

200 1000250300

Y2

X4

X1

720

600100

120

140

5

160

4806

7

Y2

X3

X2

1400

1200100

120

140

5

160

100067

Y2

X4

X2

1400

0 1200

50

100

150

480 1000600 720

Y2

X4

X3

X1 207

X2 5

X3 414

X4 953

Hold Values

Surface Plots of Y2

RESPONSE OPTIMIZATION

Parameters

Goal Lower Target Upper Weight Import



10

Y2 Target 50 106.58 200 1 1

Local Solution

X1 = 285.194

X2 = 5.16162

X3 = 656.545

X4 = 1181.60

Predicted Responses

Y2 = 106.82 , desirability = 0.997409

Composite Desirability = 0.989775

Figure 7:optimization plot

CurHigh

Low0.98977D

Optimal

d = 0.99835

Targ: 112.460Y1

y = 112.6046

d = 0.99741

Targ: 106.580Y2

y = 106.8221

d = 0.99915

Targ: 7.4072Y3

y = 7.4069

d = 0.99448

Targ: 2223.5020Y4

y = 2230.5515

d = 0.95765

Targ: 11.8322Y5

y = 11.7123

d = 0.99228

Targ: 28.6832Y6

y = 28.7706

0.98977Desirability

953.0

1380.0

414.0

690.0

5.0

7.0

207.0

300.0X2 X3 X4X1

[285.1943][5.1616][656.5455][1181.5960]



11

Figure 8:Root Mean Square Test for Non linear Regression Analysis

Non-linear results/graphs using matlabY2 results

Figure 9:Coefficient of relationship Test for Non linear Regression Analysis

Model Fitting And Validation For Strength After assessing the data graphically, the second step in

analysis is to estimate an appropriate model for each

response.

1 2 3 4 5 6 784

86

88

90

92y

Data point

RMS training set error: 0.09279 Variation explained: 99.8299 %

Predicted y (training values)

Actual y (training values)

1 2 3 4 5 6 7 860

70

80

90

100

y

Data point

RMS test set error: 6.9458 Variation explained: -704.0647 %

Predicted y (test values)

Actual y (test values)

Bias Gene 1 Gene 2-50

0

50

100Gene weights

Bias Gene 1 Gene 20

0.5

1

1.5

2x 10

-5 P value (low = significant)

R squared = 0.9983 Adj. R squared = 0.99745



12

The adequacy of each fitted model was validated

quantitatively by calculating statistical measures such as

residual standard deviation and (PRESS), and graphically

by examining residual plots. The residual standard

deviation S, for this model is O.99mpa. A value of s near

the repeatability value (replicate standard deviation

calculated from centre points) is an indication of an

adequately fitting model.

CONCLUSION AND RECOMMENDATION

Factorial design mathematical model and a non-linear

matlab least square regression model were developed to

study and analyze the results. it is possible to analyze

accurately the positive effects of the various factors

responsible for better slumps dry (workability) and

strength of concrete produced and to optimize those factors

for quick determination of the optimum factorial

composition of concrete for any given climatic condition.

The factorial design shows the optimal production mix of

the concrete production in hot and warm climatic condition

while thmatlab non-linear regression approach was used to

see the effect of linearity and non-linearity of the data.

From the results, it shows that the dat is more of non-linear

with the coefficient of determination of the dependent and

independent variables (R2

) of 0.9963. also when adjusted

the R2

, it shows a coefficient of 0.99745. The results

however, where recommended to the construction

industries, builders and Civil engineers for their

applicability of the Optimal results and its relationships in

hot and warm humid zones of south east Nigeria.

REFERENCES

[1] Chang Hu, 2004: Construction Project Management.

Second Edition, China Construction Industry Publisher,

22-32.

[2] Koehler, E.P. and Fowler D.W. (2003): ICAR 105,

Measuring the Workability of High Fines, concrete

International Centre for Aggregates research. The

University of Texasat Austin.

[3] Liang, Shilian, (2004): Engineering Project

Management, Second edition, China: Dongbei

University of Finance and Economics. 71-79.

[4] Mahmood, K.(2005): Factors Affecting Reinforced

Concrete Construction Quality in Pakistan. CBM-CI

International Workshop, Karachi, Pakistan.

[5] Mcpharlin, (2012): Weather and How to Minimize the

Effect on Concrete Qranite Rock.

[6] Scanton, J. M. (1994): Factors Influencing Concrete

Workability P. Klieger, and J. F. Lamond, ed.

Significance of Tests Properties of Concrete and

Concrete-Making. American Society for Testing and

Materials. STP 169c, Philadelphia. P. A.

[7] WiseGeek, http://www.wisegeek.com/what-is-quality-

control.htm (14.04.2010).

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