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MATRIX METHOD TO SOLVE NONCOMPLIANCE OF STANDARD SAND IN INDIA

Mahendra Kapoor , A N Vyasa Rao and Pravesh Sharma

M/s Ambuja Cements Ltd, Mumbai________________________________________________________________

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1.0 Introduction

In a cement plant the compressive strength of cement is tested by casting cubes with standard sand.The standard sand plays a very significant role in the cement industry as it is required not only as areference testing material but also as a standard material to study the properties of other buildingmaterials like lime and pozzolanas, various admixtures to cement and also for determining theabrasive resistance. Hence, the standard sand shall have consistent uniform in quality and anyvariation will create havoc in the quality of cement and reproducibility of results.

In recent past, over and under sizes more than the permissible limits in three grades have beennoticed. This may be due to variation in naturally occurring product, which in turn depends ongeological strata, mineral composition, surface characteristics etc. As the various properties or testresults of cement are highly dependent on the standard sand quality, it is necessary to correct thenon-compliance by adopting suitable methodology.In the Table 1 variations noticed in threegrades of Ennore sand at different plants are presented. It clearly indicated in > 2mm size 4to 21% and in grade I ,60 to 98% instead of 100%,similarly in grade II & III it is 58 to72% & 51 to 89% respectively as against of 100% in each grade.

Table 1 Variation in standard sand at different cement plants

Standard Sand Sieve Analysis

PLANT A PLANT B PLANT C PLANT D

GRADE GRADE GRADE GRADESieve Size

1 2 3 1 2 3 1 2 3 1 2 3

(+) 2mm 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00(+) 1mm 97.00 7.00 7.00 100.00 9.00 0.00 60.54 1.25 0.05 98.34 2.22 2.14(+)0.5mm 2.00 58.00 41.00 0.00 72.00 11.00 32.11 62.22 14.81 1.60 53.08 30.84

(+) 90mic 0.00 35.00 51.00 0.00 19.00 89.00 7.03 36.47 84.67 0.00 44.60 66.90

(-) 90mic 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

SUM 99.00 100 99.00 100 100 100 99.68 99.94 99.53 99.94 99.90 99.88

(+) 2mm 18.8 0 0 21 0 0 4.09 0 0 21.58 0 0

(-) 90mic 0 0 0.001 0 0.35 0.98 0.089 0.29 1.76 0 1.31 1.69

MIXING%

28.90 19.93 51.17 29.56 41.94 28.50 54.47 19.02 26.51 32.36 53.60 14.04

CALI G 33.01 33.33 33.23 33.31

II G 33.12 33.33 33.25 33.30III G 33.07 33.33 33.21 33.30

2.0 Principles for using Microsoft Excel to Perform Matrix Operations

In this study, a novel method based on fundamental matrix principle, corrections for equalproportions are suggested.Many of the Microsoft Excel functions that we are using to complete these Matrix Operations areARRAY FUNCTIONS- returning more than one value at a time. To enter an ARRAY function intoa Microsoft Excel worksheet, we must hold down the CTRL and SHIFT keys while pressing theENTER key; CTRL+SHIFT+ENTER. Once this is done, braces (cells) will surround the arrayformula.

2.1 How to Ener data in matrices

A computor spreadshet is a series of small cells where the columns are labeled with ‘capital letters’and the rows are labeled by ‘numbers’ . To enter a matrix into Microsoft Excel ,simply type eachmatrix element into its own small ‘cell’.

Pressing ENTER after each entry will usually make the cursor go down to the next ‘cell’

Pressing the RIGHT ARROW after each entry will make the cursor move to the next cell to therightL

2.2 Application Of Matrix Method For Coorction In Sand Variation:

The above mentioned principle is adopted to solve variation in the standard sand. A case study ispresented to understand the method of calculation. The following procedure is suggested:

QUANTITY OF EACH GRADE OF SAND 10 BAGS OR ACCORDING TOCONSUMPTIONMIX THROUGHLY INDIVIDUALGRADE SANDTO GET UNIFORMITY

DISCARD SAND >2 MM AND < 90 MICRONCARRY OUT SIEVE ANALYSIS ON 1MM, 0.5 MM AND 90 MICRON

Randomly select 3 bags of each grade of the standard sand and thoroughly mix.Over sizes + 2mm and -90 micron to be discarded.

Carry out sieve analysis on 1mm,05 mm and 90 microns and the results are tabulated in excelformat as shown below ( Table 2)

Step.1. Enter data as per table given below

A B C D12 GR 1 GR 2 GR 33 + 1 mm 60.54 1.25 0.054 + 500 micron 32.11 62.22 14.815 + 90 micron 7.03 36.47 84.676 TOTAL 99.68 99.94 99.53

Step. 2. Convert to 100%G H I J

12 GR 1 GR 2 GR 33 + 1 mm 60.74 1.25 0.054 + 500 micron 32.22 62.26 14.885 + 90 micron 7.04 36.49 85.076 TOTAL 100.00 100.00 100.00

Step.3.Find the INVERSE of the matrix Highlight cells H9 to J11 Type: =MINVERSE(H3:J5) -Enter Press F2 followed by CTRL+SHIFT+ENTER

G H I J12 GR 1 GR 2 GR 33 + 1 mm 60.74 1.25 0.054 + 500 micron 32.22 62.26 14.885 + 90 micron 7.04 36.49 85.076 TOTAL 100.00 100.00 100.0089 0.0166515 -0.000366322 5.42419E-05

10 -0.00923385 0.018100424 -0.003160571

11 0.00258235 -0.007734101 0.01310633

Step.4. Multiply the “INVERSE MATRIX” by the constant matrix (desired value) Highlight cells L3 to L5 Type =MMULT(H9:J11,L3:L5)-Enter Press F2 followed by CTRL+SHIFT+ENTER

G H I J K L12 GR 1 GR 2 GR 3 Desired Answer3 + 1 mm 60.74 1.25 0.05 33.33 0.5446424 + 500 micron 32.22 62.26 14.88 33.33 0.1901955 + 90 micron 7.04 36.49 85.07 33.33 0.2651636 TOTAL 100.00 100.00 100.00 100.00 189 0.0166515 -0.000366322 5.42419E-05

10 -0.00923385 0.018100424 -0.00316057111 0.00258235 -0.007734101 0.01310633

Note: A matrix will have no inverse if its determinant is zero. So, before attempting to findthe inverse of a matrix,you may want to check the value of its determinant. If the matrix of asystem of linear equation has a determinant equal to zero,the system will not have a uniquesolution. And you will have to find the general solution by Hand-using the Gauss-JordanElimination Method.

Step.. Convert to 100%

G H I J K L12 GR 1 GR 2 GR 3 Desired Answer3 + 1 mm 60.74 1.25 0.05 33.33 0.5446424 + 500 micron 32.22 62.26 14.88 33.33 0.1901955 + 90 micron 7.04 36.49 85.07 33.33 0.2651636 TOTAL 100.00 100.00 100.00 100.00 18 RATIO (%) 54.46 19.02 26.52 100.00

9 0.0166515 -0.000366322 5.42419E-0510 -0.00923385 0.018100424 -0.00316057111 0.00258235 -0.007734101 0.01310633

4.0 Conclusion

Of late, a variation in the standard sand being used for cement mortar strength is noticed. Thecommon practice is to sieve the entire lot of sand before its use in testing. A new method basedon matrix principle is suggested to solve amicably this problem which ensures reliable andreproducible cement strength results.

6.0. Acknowledgements

The authors are thankful to their management M/s Ambuja cements Ltd for permitting to useR&D data and their encouragement. Special thanks to Mr C M Dordi, Corp.Head (PQM &CS) forhis valuable suggestions on the manuscript.