Mix Design of Palm Bunch Ash-Cementitious Composite Using Regression Theory

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1 ISSN: Mix Design of Palm Bunch AshCementitious Composite Using Regression Theory Onwuka Davis Ogbonna, Anyanwu Timothy Uche, Awodiji Chioma Temitope Gloria,Onwuka Silvia Ulari. Senior Lecturer, Department of Civil Engineering,Federal University of Technology, Owerri, Imo State, Nigeria. Lecturer II, Department of Civil Engineering,Federal University of Technology, Owerri, Imo State, Nigeria. Onwuka, Assistant lecturer, Department of Civil Engineering,Federal University of Technology, Owerri, Imo State, Nigeria. Assistant lecturer, Department of Project Management,Federal University of Technology, Owerri, Imo State, Nigeria. ABSTRACT: This article presents a model developed from regression theory, for the design of Palm Bunch Ash (PBA)cement concrete mixtures. PBAcement concrete is actually a pozzolaniccementitious composite with five components. The achievement of a desired performance criterion of any pozzolaniccementitious composite is to a large extent, dependent on adequate proportioning of its components. The conventional mix design method of trial batches is too laborious, timeconsuming and expensive for designing mixtures of the five component pozzolaniccementitious composite i.e. PBAcement concrete. In this work, a model for designing of PBAcement concrete mixtures was developed from Osadebe s regression theory. The adequacy of the mix design model was verified using statistical ttest. The model is quite useful and practical for designer s to quickly get relatively accurate information on mix proportions and the corresponding strengths of PBAcement composite with fixed raw materials, and fixed curing conditions and periods. KEYWORDS: Mix design, Palm Bunch Ash (PBA), Pozzolana, Composite, Regression Theory. I. INTRODUCTION Some agricultural and industrial wastes contain significant portion of pozzolanic materials, and so can be used as SCMs. Palm bunch is an agricultural byeproduct, which is gradually finding its way into the construction industry. Its relevance in the construction industry stems from the pozzolanic property of its ash. Already, the ash of other wastes e.g. shells and fibre from oil palm trees, have been used for making cement [13]. Tests conducted on PBA by [4] showed that PBA is a pozzolanic material with a pozzolanic Activity Index (PAI) of 76.9 precent. This value is greater than the minimum value of 70 percent specified by [] for pozzolanic materials. Extensive research has shown that pozzolanas are known to have produced concrete having almost the same behaviour as normal concrete beyond the ages of 8 days [10]; [11] and [9]. In this work, a model was developed from regression theory by [1], for the mix design of the pozzolaniccementitious composite, PBAcement concrete II MATERIALS The five materials used in producing the test specimen i.e. PBAcement concrete cubes, are cement, fine aggregate, coarse aggregates, palm bunch ash and water. Ibeto brand of portland cement was used in producing cubic PBAcement concrete specimen tested in compression. The cement conforms to requirements of []. The physical and chemical properties of the cement were tested and presented in Table 1 and respectively.the PBA used for this investigation was obtained by burning empty palm bunches. Open burning method was used. The ashes were cooled, pulverized (by grinding) and sieved using a 10mm BS sieve. The physical and chemical properties of the PBA are shown in Table 1 and 3 respectively. The fine aggregate was sharp river sand obtained from Otamiri River in Imo State of Nigeria. In order to eliminate unwanted materials, it was washed and then dried for seven days. The grain size distribution of the sharp river sand shows that the sand is well graded and falls into zone of the grading chart. The coarse aggregate was crushed granite Copyright to IJARSET

2 ISSN: rock (chippings) sourced from Ishiagu quarry site in Ebonyi State of Nigeria. The maximum size of the coarse aggregate is 0mm. Piped municipal water supply conforming to [8] was used for the production of the PBAcement concrete cubes. Initial and final setting times are given in Table 8. The mix proportions of these constituent materials of concrete are shown in Table 4. TABLE 1: PHYSICAL PROPERTIES OF IBETO CEMENT AND PALM BUNCH ASH. Properties Values Moisture content Specific gravity 3.16 Finess 190 plus ph 9. PALM BUNCH ASH Water Absorption 79.31% Bulk density 334Kg/m 3 Apparent porosity 91.96% Shrinkage.63% Modulus of plasticity.64 Modulus of rupture 9.40Kg/cm 3 Specific gravity.6 < 10µm grain size < 38µm grain size 100% % Source: concrete properties.org TABLE : CHEMICAL COMPOSITION OF IBETO CEMENT S/No Oxides Mass Fraction % 1 Alumina (Al O 3) 6.04 Lime (CaO) Silicate (SiO ) Magnesium Oxide 1.30 Iron Oxide (Fe O 3).9 6 Potassium Oxide (K O) Sodium oxide (Na O) 0. 8 Titanium Oxide Loss on Ignition.6 Total 98.8 Source: Project development institute (PRODA) Emene. TABLE 3: CHEMICAL COMPOSITION OF PALM BUNCH ASH (PBA) S/No Oxide Percentage Mass (%) 1 Silicate (SiO ) 48.6 Alumina (Al O 3). 3 Iron oxide (Fe O 3) Lime (CaO) 14.0 Magnesium oxide (MgO) Potassium Oxide (K O) Manganese (MnO ) Sulphate (SO ).49 9 Titanium Oxide TiO ) Phosphorous (P O ) Loss on ignition (LOI) 0.13 Total 100% Source: properties.org Copyright to IJARSET

3 ISSN: TABLE 4: MIX PROPORTION OF CONSTITUENT MATERIALS USED IN PRODUCING THE CONCRETE BEAMS Point of observation Mix No. Watercement ratio Cement PBA Sand Granite chippings 1 Mix Mix Mix Mix Mix Mix Mix Mix Mix Mix Mix Mix Mix / Mix Mix C1 Mix C Mix C3 Mix C4 Mix C Mix C6 Mix C7 Mix C8 Mix C9 Mix C10 Mix C11 Mix C1 Mix C13 Mix C14 Mix C1 Mix III THEORITICAL BACKGROUND In the course of this work, the regression theory by [1], was used to formulate the response equation for the mix design of PBAcementitious composite. Osadebe assumed that the following response function, F(Z), is continuous and differentiable with respect to its predictors, Z i. F(Z) = F m (Z (0) ) * (Z i Z (0) ) / m! (1) Where 0 m α ;m = the degree of polynomial of the response function. Osadebe assumed that the response function, F(Z) is continuous and differentiable with respect to its predictors, Z i. By making use of Taylor s series, the response function could be expanded in the neighbourhood of a chosen point: Z (0) (0) (0) (0) (0) (0) = Z 1, Z/, Z 3, Z 4, Z Expanding Eqn. (1) up to the second order gives: () F(Z) = F o (Z (0) ) * (Z i Z (0) ) 0 / 0! + F 1 (Z (0) ) * (Z i Z (0) ) 1 + F 11 (Z (0) ) * (Z i Z (0) ) /! + F 11 (Z (0) ) * (Z i Z (0) )(Z j Z (0) )/! (3) Where 1 i Copyright to IJARSET

4 ISSN: For the sake of convenience, Z (0) is chosen as the origin. Let the predictor, Z i, be called fractional portion and S i be the actual portion of each mixture component. The total quantity of concrete, S, is obtained by summing up the actual portions of each mixture component, S i, that is: S i = S (4) S 1 + S +S 3 +S 4 /+S = S () To obtain a unit quantity of concrete, divide Eqn. () by S: S 1 /S + S /S + S 3 /S + S 4 /S + S /S = S/S (6) Let Si/S =z i (fractional portion) (7) Then, z 1 + z + z 3 + z 4 +z = 1 (8) Experience shows that when z i = 1, the values of the coefficients are so large that the regression becomes too sensitive. Consequently, the use of other predictors to determine the response gives outrageous values. To correct this shortcomings, a system of z that yields z = 10, is adopted. Thus Eqn. (8) is multiplied by 10: 10z z + 10z z z = 10 (9) Let 10z i = Z i (10) Therefore; Z 1 + Z + Z 3 + Z 4 + Z = 10 (11) The assumption that Z (0) is taken as the origin implies that: Z 1 (0) = Z (0) = Z 3 (0) = Z 4 (0) = Z (0) = 0 (1) Let: b o = F(0) (13) b i = F(0) / Z i (14) b ij = F(0) / Z i Z j (1) b ii = F(0) / Z i (16) Substituting Eqns. (13) to (16) into Eqn. (3), yields; F(Z) = b o + b i Z i + b ij Z i Z j + b ii Z i (17) Where 1 i for b i Z i 1 i 4 and 1 j for b ij Z i Z j 1 i for b ii Z i Multiplying Eqn. (8) by b o gives the following expression for b o ; b o = b o z 1 + b o z + b o z 3 + b o z 4 + b o z (18) Copyright to IJARSET 138

5 ISSN: Similarly, multiplying Eqn. (8) by Z i yields the following expressions for Z i : z 1 = z 1 + z 1 z + z 1 z 3 + z 1 z 4 + z 1 z (19) z = z 1 z + z + z z 3 + z z 4 + z z (0) z 3 = z 1 z 3 + z z 3 + z 3 + z 3 z 4 + z 3 z (1) z 4 = z 1 z 4 + z z 4 + z 3 z 4 + z 4 + z 4 z () z = z 1 z + z z + z 3 z + z 4 z + z 4 z (3) Rearranging the Eqns. (19) (3) gives the following expressions for Z i : z 1 = z 1 z 1 z z 1 z 3 z 1 z 4 z 1 z (4) z = z z 1 z z z 3 z z 4 z z () z 3 = z 3 z 1 z 3 z z 3 z 3 z 4 z 3 z (6) z 4 = z 4 z 1 z 4 z z 4 z 3 z 4 z 4 z (7) z = z z 1 z z z z 3 z z 4 z (8) Substituting Eqns. (4) (8) into Eqn. (16), and factorizing, yields Eqn. (9): Y = (b o + b 1 + b 11 )z 1 + (b o + b + b )z + (b o + b 3 + b 33 )z 3 + (b o + b 4 + b 44 )z 4 + (b o + b + b )z + (b 1 b 11 b )z 1 z + (b 13 b 11 b 33 )z 1 z 3 + (b 14 b 11 b 44 )z 1 z 4 + (b 1 b 11 b )z 1 z + (b 3 b b 33 )z z 3 + (b 4 b b 33 )z z 4 + (b b b )z z + (b 34 b 33 b 44 )z 3 z 4 + (b 3 b 33 b )z 3 z + (b 4 b 44 b )z 4 z (9) Let, α i =b o + b i + b ii (30) and, α ij = b ij + b ii + b jj (31) Substituting Eqns. (30) (31) into Eqn. (9) gives; Y = α 1 z 1 + α z + α 3 z 3 + α 4 z 4 + α z + α 1 z 1 z + α 13 z 1 z 3 + α 14 z 1 z 4 + α 1 z 1 z + α 3 z z 3 + α 4 z z 4 + α z z + α 34 z 3 z 4 + α 3 z 3 z + α 4 z 4 z (3) Presenting it in a compact form, Eqn. (3) becomes: Y = α i z i + α ij z i z j (33) The Eqns. (3) and (33) are the regression equations when the system of z = 1 is used. Thus for the system of z = 10 adopted in this work, Y = α i Z i + α ij Z i Z j (34) Where 10z i =Z i ; and 1 i j The Eqn. (33) is the response function at any point of observation. α i andα ij are the coefficients of the regression equation, while Z i and Z j are the predictors when the system z = 10. Coefficient of the Regression Equation The different points of observation will have different predictors at constant coefficients. At the nth observation point, the response function, Y (n) will have corresponding predictor, Z i (n). That is to say; Y (n) = α i Z i (n) + α ij Z i (n) Z (n) (3) where 1 i j and n = 1,, 3,, 1. Eqn. (3) can be put in matrix form as follows; Copyright to IJARSET

6 ISSN: [Y (n) ] = [Z (n) ][α] (36) Expanding Eqn. (36) gives the following matrix; Y (1) (1) (1) (1) (1) Z 1 Z Z 3 Z n α 1 Y () () Z 1 Z () () () Z 3 Z n α Y (3) (3) (3) (3) (3) = Z 1 Z Z 3. Z n α Y (1) (1) Z 1 Z (1) (1) (1) Z 3.. Z n α 4 (37) Rearranging the above Eqn. (37) gives Eqn. (38) α 1 (1) Z 1 (1) Z (1) Z 3 (1) Z n Y (1) α () () Z 1 Z () Z 3 () Z n α 3 = (3) Z 1 Z (3) (3) Z 3 (3). Z n Y (3) Y () α 4 (1) Z 1 (38) Z (1) Z 3 (1).. Z n (1) Y (1) The Table shows the actual mix proportions, S i (n) and their corresponding fraction portions, Z i (n). The values of the fractional portions, Z i (n), were used to develop the Z (n) matrix and inverse Z (n) matrix given in Tables 6 and 7 respectively. The values of the Y (n) matrix are determined from laboratory compressive strength tests on concrete specimen. With the values of the matrices Y (n) and Z (n) known, the values of the constant coefficients, α i. of Eqn. (3) can be determined. Copyright to IJARSET

7 ISSN: TABLE : VALUES OF ACTUAL MIX PROPORTIONS AND THEIR CORRESPONDING FRACTIONAL PORTIONS WHEN Z = 10 S1 S S3 S4 S S Z1 Z Z3 Z4 Z Copyright to IJARSET 138

8 ISSN: TABLE 6: VALUES OF MATRIX OF ACTUAL MIX PROPORTIONS AND CONTROL MIX PROPORTIONS WHEN Z = 10 Z 1 Z Z 3 Z 4 Z Z 1 Z Z 1 Z 3 Z 1 Z 4 Z 1 Z Z Z 3 Z Z 4 Z Z Z 3 Z 4 Z 3 Z Z 4 Z Copyright to IJARSET

9 ISSN: TABLE 7: VALUES OF INVERSE MATRIX OF ACTUAL MIX PROPORTIONS WHEN Z = 10 Z 1 Z Z 3 Z 4 Z Z 1 Z Z 1 Z 3 Z 1 Z 4 Z 1 Z Z Z 3 Z Z 4 Z Z Z 3 Z 4 Z 3 Z Z 4 Z / E E E E E IV EXPERIMENTAL WORKS. The test specimen were concrete cubes that were cast in steel moulds measuring 10x10x10mm. A total of ninety concrete cubes were produced and tested in compression.three concrete cubes were produced from each mix proportion. The base of each mould was clamped in order to prevent leakage of mortar during concrete casting. Then, a thin layer of engine oil was applied to the inner walls of the mould to ease the removal of concrete cubes. Each mould was filled with concrete in three equal layers as specified by [6] and each layer was given 3 blows with a tamping rod. Then, the concrete cubes were cured in water for 8 days. Thereafter, the concrete cubes were demoulded and tested in compression. The concrete specimen were loaded at a constant rate in the compression testing machine until fracture occurred. The load causing failure was recorded in each case, and then the compressive strength calculated and reported to the nearest 0.N/mm. V EXPERIMENTAL RESULTS AND ANALYSIS The compressive strength results obtained from laboratory test, are given in Table 9. Copyright to IJARSET

10 ISSN: TABLE 8: INITIAL AND FINAL SETTING TIMES FOR DIFFERENT PERCENTAGE REPLACEMENT OF CEMENT WITH PBA S/No Percentage of Cement Replacement Initial Time (Minutes) Final Setting Time (Minutes) TABLE 9: 8 TH DAY COMPRESSIVE STRENGTH RESULTS OF PBACEMENT CONCRETE MIXTURES. Point of observation Mix No. Replicates of compressive strengths (N/mm ) Mean compressive strength (N/mm ) Mix Mix Mix Mix Mix Mix Mix Mix Mix Mix Mix Mix Mix Mix Mix C1 Mix C Mix C3 Mix C4 Mix C Mix C6 Mix C7 Mix C8 Mix C9 Mix C10 Mix C11 Mix C1 Mix C13 Mix C14 Mix C1 Mix Determination of the coefficients of the Regression Equation The value of the mean compressive strengths for Mix01 to Mix1 (given in Table 9), were substituted into Eqn. (31) to obtain the following coefficients of the regression equation: α 1 = α = α 3 = α 4 = α = α 6 = α 7 = α 8 = α 9 = α 10 = α 11 = α 1 = α 13 = α 14 = α 1 = Copyright to IJARSET

11 ISSN: Determination of the final Regression Equation Substituting the above regression coefficients into the Eqn. (3) yeilds the following regression equation; Y = Z Z Z Z Z Z 1 Z Z 1 Z Z 1 Z Z 1 Z Z Z Z Z Z Z Z 3 Z Z 3 Z Z 4 Z (39) The Eqn. (39) is the final regression equation needed for the mix design of palm bunch ashcementitious composite. Specifically, it can be used to determine the mix proportions of the constituents of palm bunch ashcementitious composite when the compressive strength of the palm bunch ashcementitious composite is known. Test of Adequacy The Ftest was used to check the adequacy of the formulated regression equation at 9 percent confidence level. The F test calculations are as follows: TABLE 10: FTEST CALCULATION Control Mix No. Y e Y m Y e Ŷ e Y m Ŷ m (Y e Ŷ e) (Y m Ŷ m) points C1 Mix C Mix C3 Mix C4 Mix C Mix C6 Mix C7 Mix C8 Mix C9 Mix C10 Mix C11 Mix C1 Mix C13 Mix C14 Mix C1 Mix Sum Mean The varince of the replicates of the compressive strength test results at any arbitrary point can be calculated from the Eqn.(40 ) as given by [7]; S e = [Σ(Y e Ŷ e ) ]/(n 1) (40) = (8.738)/14 = 0.64 = S 1 Similarly, S m = [Σ(Y m Ŷ m ) ]/(n 1) (41) = (7.498)/14 = 0.37 = S Therefore the calculated Fvalue is given by: F cal = S 1 / S (4) = (0.64) / 0.37 = From standard statistical table, the value of F =.44 and 1/F = Since the value of F cal (i.e ) is greater than the value of 1/F and less than the value of F i.e. the condition 1/F S 1 / S F (i.e ), is satisfied. Thus, the null hypothesis is accepted. This implies that, there is no significant difference between the experimental results and the results obtained from the formulated regression equation. Copyright to IJARSET

12 ISSN: Comparison of Experimental and Predicted Results The results from the controlled laboratory tests and those obtained from the formulated regression equation are compared in Table (11). The comparison show that the percentage difference ranges from a minimum of % to a maximum of.7046%.since the maximum percentage difference between the predicted value and the controlled experimental values is negligible, the formulated regression equation can be used for the designing of mixtures of palm bunch ashcementitious composites. TABLE 11: COMPARISON OF EXPERIMENTAL AND PREDICTED RESULTS PTS. OF MIX EXPERIMENTAL PREDICTED DIFFERENCE PERCENTAGE OBSER NOS. COMPRESSIVE STRENGTH COMPRESSIVE STRENGTH DIFFERENCE VATION (MPA) (MPA) C1 Mix C Mix C3 Mix C4 Mix C Mix C6 Mix C7 Mix C8 Mix C9 Mix C10 Mix C11 Mix C1 Mix C13 Mix C14 Mix C1 Mix VI CONCLUSION Test conducted on PBACementitious composite shows that it has the same behaviour as normal concrete beyond the ages of 8 days. A response function based on the Regression Theory by Osadebe, has been formulated for the mix desi/gn of PBACementitious composite.the formulated regression function was tested for adequacy and found adequate.the use of the regression function will simplify the process and reduce the cost of the mix design of PBAcement concrete mixtures. REFERENCES [1] Aggarwal, M. I. Mixture Experiments Design Workshop Lecture Note,University of Delhi, India. Pp [] American Society for Testing and Materials (ASTM) International: Standard Specification for Coal Flyashand Raw Calcined Natural Pozzolans for use in Concrete. ASTM C618 [3] Anyanwu, T. U. Mathematical Models for the Optimization of the compressive strength of Palm Bunch AshCement Concrete, An unpublished M.Eng Thesis submitted to the Department of Civil Engineering, Federal University of Technology, Owerri, Imo State, Nigeria. 01. [4] Arimanwa, M. C. PalmBunch Ash Cement Concrete An unpublished thesis submitted to the post graduate school, Federal University of Technology, Owerri, Imo State.006. [] British Standard Institute: Specification for Portland Cement.BS 1 (1996). [6] British Standard Institute: Method for making Fresh cubes from fresh concrete.bs 1881 (1983), Part 108. [7] Cramer, H, Mathematical Methods of Statistics, Princeton University Press, USA [8] European Standard: Mixing water for concrete. Specification for sampling, testing and assessing the suitability of water including water recovered from processes in the concrete industry, as mixing water for concrete. EN 1008: 00 [9] Elinwa, A. U. and Mahmood, Y. A., Ash from Timber waste as Cement Replacement Material, Cement and Concrete Composite. 4, pp [10] Okpala, D. C., Rice Husk Ash (RHA) as Partial Replacement of Cement in Concrete,Proceedings of Annual Conference, Nigeria Society of Engineers [11] Marina, A., Julian, S., and Janer, Properties of Concrete Made With Fly Ash,International Journal of Cement and Lightweight Concrete. 10 pp , Copyright to IJARSET

13 ISSN: [1] Osadebe, N. N., Generalized Mathematical Model for Normal Concrete as a Multivariate Function of the Properties of its Constituents A paper delivered at the Faculty of Engineering, University of Nigeria Nsukka [13] Price, W. H., Pozzolans A Review, ACI Journal. Vol., pp [14] Tay, J. H., Ash From Oilpalm Waste as /Concrete Material, Journal of Material in Civil Engineering. (), pp Copyright to IJARSET