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 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.

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.

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/m3 X3 = Fa fine paragraph kg/m3 X4 = Ca coarse Aggregate kg/m0 Slump dry mm
Xnar Highest level (+) 300 7 690 1380
Xim Lowest level (-) 207 5 414 953
Xer Central Level (0) average 254 6 552 1167
δ Interval of Change Δ 46 1 138 213
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
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 X3 = X4 Slump
Water Cement Kg/m3 Fine Aggregate Coarse SDRY
Kg/m3 Aggregate
Highest Level (+) 300 0.7 690 1380
Xmin Lowel level (-) 207 0.5 414 953
Xmin Control level(0) 2.54E+02 0.6 552 1167
Δ Interval of Change 4.60E+01 0.1 138 213 Y2
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

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.

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 2.03E-01 -0.17 0.864
X2 -9.118 8.272 -1.1 0.283
X3 0.02685 0.06349 0.42 0.677
X4 -0.05011 4.30E-02 -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 DF Seq SS

Source DF Seq SS
X1 1 132
X2 1 2694
X3 1 126
X4 1 1500

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

Figure 2 :Residual Plots for Y2

Figure 3:Main Effects Plot for Y2

Figure 4:Interaction Plot for Y2

Figure 5:Contour Plots of Y2

Figure 6:Surface Plots of Y2

Response optimization

Parameters

Goal Lower Target Upper Weight Import

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

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.

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 th matlab 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.