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IRJET- A Statistical Approach to Obtain the Best Blend of Aggregates
1.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 12 | Dec 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.34 | ISO 9001:2008 Certified Journal | Page 1400 A STATISTICAL APPROACH TO OBTAIN THE BEST BLEND OF AGGREGATES N. Lalith Vamsi1, and Dr K.Narasimhulu2 1,2Department of Civil Engineering, Annamacharya Institute of Technology and Sciences, Tirupati, India ---------------------------------------------------------------------***---------------------------------------------------------------------- Abstract - Aggregate gradation is the particle size distribution of both the coarse aggregates and fine aggregates present in the concrete matrix. This is an aggregate property which has been profoundly researched formorethanacentury butthe impactsthis property on concrete properties is still to some degree misunderstood. Past research has revealed that aggregate gradation dictates the proportion of aggregate to cement paste in concrete mix, and greatly influences the overall durability of the construction material. For more than half a century, the 0.45 PowerChart(Talbot’sGradingCurvewithannvalueof0.45(Richart, 1923)) has been the method taken as a standardized method by the Federal Highway Administration (FHWA) for aggregate gradations design of hot mix asphalt industry since the 1960s (Virtual Superpave Laboratory, 2005). It is now more freely being applied to concrete mix designs. However, the selection of the suitable range for the exponent n, must consider the standard deviation of actual aggregates gradations from the theoretical gradations. The combined aggregates gradations can also do by using coarseness factor (Cf) and a workability factor (Wf). The optimum concrete mix is one whose coarseness factor is around 65 and workability factor is above 35. The standard deviation is calculated by utilizing the Wf and Cf factors as guidelines. The principal objective of this investigation was to find N based on the lowest standard deviation from theoretical and actual aggregate gradations. Key Words: Coarse Aggregate, Sieve analysis, Standard deviation, least value, DIN curves 1. INTRODUCTION High-Performance Concrete (HPC) is defined (Russell, 1999) as “Concrete meeting special combinations of performance and uniformity requirements that cannot always be achieved routinelyusingconventional constituentsand normal mixing,placing and curing practices”. Thus HPC should necessarily have improved strength and durability properties than ordinary Portland cement concrete (PCC). Mostly attempts were made to achieve durability by increasing the cementitiousmaterial contentand reducing the water-cementitious material ratio. But very few have attempted to achieve HPC by using combined well-graded aggregates in concrete. The most important feature of mix design is aggregate content. The resulting mix designshouldhavea strong aggregate skeleton for permanent deformation resistance andanoptimumamountofcement,whichactsasa binderfor the aggregates. The void space in the aggregate skeleton can be changed by varying the gradation(particlesizedistribution) of a mixture. A well-graded combined aggregate gradation requires graded coarse aggregates and coarser fine aggregates. But today fine aggregates do not contain predominantly coarse particles.HPCcanbeachievedbycombiningaggregates ofdifferent sizes and blending them, thus reducing the requirement for additional water and cementitiousmaterials.Optimizedaggregate gradation should be the most basic goal of achieving HPC 2. LITERATURE REVIEW The particle size distribution of the aggregates is called gradation. To obtain the gradation curve for aggregate, sieve analysis has to be conducted in accordance with ASTM C136. The gradations of aggregates are classified into three types, well-graded, gap-graded, and uniformly graded, which are illustrated in Figure 6-1 Fig 2.1 Grading Aggregate
2.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 12 | Dec 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.34 | ISO 9001:2008 Certified Journal | Page 1401 In uniformly graded aggregates, only a few sizes govern the bulk material and the aggregates are ineffectively packed. The result is porous concrete requiring more cement paste. Gap graded aggregates constitutes in shortages of few intermediate sizes. This grading results in good concrete in the cases of comparatively low workability, where as in the cases of high workability, this leads to segregation problems. It would require a higher amount of fines, more water, and would increase vulnerability to shrinkage. Well-graded aggregates are appropriate for preparing good concrete mix, as the voids between larger sized particles is thoroughly filled by smaller sized particlestoproducea well-packedstructure, requiringlesseramount of cement paste. This gradation would reduce the needfor excesswaterstill maintains adequateworkability.Achievinga better gradation may require the use of three or more different aggregate sizes. An optimized gradation is termed as thegradationin which operational and economic constraints are consideredtoobtaina mixofaggregatesparticlesizesthatresultsinimproved workability, durability, and strength (Popovics, 1973). An optimum graded aggregate is the key to the mixture performance and constructability, and would provide the workability needed for placement and finishing with the lowest water- cement ratio. The 1923 ASTM C33standardincluded requirements that contributed to well- graded mixtures. The 1986 ASTM C33 standard contributes to near gap grading with its inherent placement problems. The major difference in these two standardsisinthesandgradation.The1923standardrequiredthatthe sand be “predominately coarse particles” and have 85 percent passing the No.4 (4.75 mm) sieve. Today’s sands are finer with 95 to 100 percent passing the No.4 (4.75 mm) sieve (Richart, 1923) 3. METHODOLOGY 3.1 Methods for Optimizing Aggregate Gradation 1. 0.45 Power Chart Method 2. Shilstone Method 3.1.1. 0.45 Power Chart Method Aggregate gradation can be characterized by drawing a gradationplotona 0.45power chart,whichalsoincludesthemaximum density line. 0.45 power chart was adopted by Superpave for graphical display of the aggregate gradations as per FHWA recommendations. Fig 3.1 0.45 power chart for 1 inch Aggregate 3.1.2 Shilstone Method There are three principal factors upon which mixtureproportionscan be optimizedforagivenneedwithagivencombinationof aggregate characteristics: • The relationship between the coarseness of two larger aggregate fractions and the fine fraction. Total amount of mortar. Aggregate particle distribution. Shilstone developed a grading chart showing the aggregate gradationsand the combined gradationsforthecoarsest,finest,and optimum mixtures. The chartused is divided into three segmentsidentifiedasQ,I,W.Thiswasbasedoncommentsbyothermix researchers about the amount and function of the “intermediate aggregate” particles.
3.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 12 | Dec 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.34 | ISO 9001:2008 Certified Journal | Page 1402 Fig 3.2 Combined Aggregate Gradations 3.2 PROBLEM STATEMENT Engineers and researchers use the 0.45 power gradation for obtaining the densest possible (maximum density) packing of aggregates. There is a concern whether plotting of the sieve size raised to 0.45 power may not be universally applicable to all aggregates. Thus there is a need to evaluate the validity of the 0.45 power chart using an aggregate (other than the granite aggregate that was used to develop the 0.45 power curve), to determine whether the chart is universally applicable for all aggregates. 4. MATERIALS In the total volume of concrete, aggregates constitute to 60-90%. So the main properties of the concrete- workability and mechanical strength, permeability, durability, depends predominantly on the selection of aggregates and its particle size distribution which has a direct effect on the total cost of hardened concrete. Hence, the aggregates mixture design becomes a main part of the concrete mix-design and optimization. Aggregate mix composition can be obtained either by means of the “ideal grading curves” method or by means of practical and theoretical determination of aggregate packing value. Aggregate gradation is defined as the relation between standard sieve size Xi (mm) and the total amount aggregates passing through the sieve Yi(Xi). This relation can be replicated by tables, formulas or graphics. Aggregate grading optimization is pronounced by means of “ideal” grading curves which offer the best fresh and hardened concrete properties as well as good aggregate packing. Fig 4.1 Aggregate "ideal" grading The “ideal” aggregate grading curve can also be defined with the help of restricting curves in graphics. Varied of transformed “ideal” curves with various degrees and the restricting curves in accordance with DIN 1045 are depicted in Fig. 5. Determination of optimum aggregate mix by analytical and numerical methods N varieties of aggregates are provided (grading curves for the aggregates are determined). Fractions of each aggregate in the mix are to be determined to obtain the best correlation with the “ideal” grading curve.
4.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 12 | Dec 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.34 | ISO 9001:2008 Certified Journal | Page 1403 The equation of the combined grading curve Yi is as given below: N Yi = Σ KjYji j=1 Here Kj – the proportion of j-st aggregate in mix; Yji – real grading of j-st aggregate. Coefficients Kj can be calculated by minimizing the squared sum of deviation between an “ideal” ( theoretical) and a real grading curve: ΣM (YTi − Yi)2 min i=1 Here M – number of sieves The most stable and reliable results are determined using thenumerical methodtodeterminetheoptimumaggregatemix. This method facilitates in calculating the possible proportions of each aggregate in the mixture. An optimum aggregate mix will be obtained by calculating the average squared root deviation between real and “ideal” aggregate curves calculated for all sieves With the usage of a computer program which was written in the python programming language is utilized for 5 aggregate combination has been worked out. In general practice from 2 to 4 aggregates is usually used in a concrete mix. The average squared deviation S is used as a criterion of suitability of the given aggregate combination and allows to compare the possibilities to use different aggregate combinations. Table 5.1 Standard Deviation of Samples 1 to 10. Slno N Value Standard Deviation Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample 6 Sample 7 Sample 8 Sample 9 Sample 10 1 0.3 6.49 9.897 7.147 4.717 8.555 6.49 7.746 9.513 7.659 9.436 2 0.35 5.691 8.466 5.438 3.719 7.086 5.691 6.973 7.817 6.109 8.132 3 0.4 5.276 7.541 4.232 3.037 6.139 5.276 6.515 6.579 5.059 7.366 4 0.45 5.083 6.945 3.308 2.568 5.626 5.083 6.248 5.685 4.43 6.968 5 0.5 4.992 6.607 2.611 2.297 5.376 4.992 6.078 5.031 4.059 6.777 6 0.55 4.921 6.411 2.185 2.165 5.326 4.921 5.962 4.711 3.939 6.722 7 0.6 4.839 6.299 1.932 2.135 5.378 4.839 5.874 4.535 3.943 6.707 8 0.65 4.733 6.199 1.813 2.155 5.502 4.733 5.838 4.505 3.991 6.708 9 0.7 4.601 6.109 1.802 2.224 5.618 4.601 5.793 4.576 4.082 6.714 10 0.75 4.445 6.033 1.868 2.321 5.764 4.445 5.787 4.707 4.244 6.721 11 0.8 4.267 5.936 1.954 2.432 5.913 4.267 5.777 4.893 4.393 6.713 12 0.85 4.08 5.831 2.071 2.573 6.067 4.08 5.819 5.098 4.541 6.694 13 0.9 3.88 5.717 2.162 2.683 6.025 3.88 5.876 5.335 4.691 6.694 14 0.95 3.676 5.592 2.292 2.831 6.355 3.676 5.973 5.577 4.867 6.683 15 1 3.474 5.459 2.411 2.987 6.912 3.474 6.061 5.833 5.049 6.68 i1 M 1 M (YT 2 i Y )
5.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 12 | Dec 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.34 | ISO 9001:2008 Certified Journal | Page 1404 Table 5.2 Standard Deviation of Samples 11 to 24. Sln o Standard Deviation N Val ue Samp le 11 Samp le 12 Samp le 13 Samp le 14 Samp le 15 Samp le 16 Samp le 17 Samp le 18 Samp le 19 Samp le 20 Samp le 21 Samp le 22 Samp le 23 Samp le 24 1 0.3 8.014 6.594 5.036 5.68 6.253 7.145 5.274 8.963 4.523 5.037 9.436 6.701 5.036 5.207 2 0.35 5.697 5.4 4.171 4.471 5.749 5.634 4.279 7.271 3.612 4.17 8.132 6.283 4.171 5.05 3 0.4 3.888 4.589 3.639 3.636 5.438 4.574 3.667 6.061 3.028 3.615 7.366 6.024 3.639 5.241 4 0.45 3.888 4.091 3.313 3.134 5.236 3.953 3.318 5.254 2.698 3.301 6.968 5.829 3.313 5.53 5 0.5 1.879 3.828 3.085 2.827 5.09 3.644 3.206 4.724 2.548 3.15 6.777 5.642 3.085 5.818 6 0.55 1.742 3.736 2.942 2.692 4.983 3.54 3.208 4.397 2.478 3.111 6.722 5.459 2.942 6.056 7 0.6 2.018 3.769 2.872 2.696 4.901 3.542 3.284 4.207 2.514 3.168 6.707 5.257 2.872 6.233 8 0.65 2.384 3.874 2.833 2.718 4.849 3.678 3.417 4.095 2.593 3.254 6.708 5.068 2.833 6.348 9 0.7 2.764 4.046 2.819 2.795 4.81 3.806 3.562 4.03 2.671 3.429 6.714 4.88 2.819 6.427 10 0.75 3.069 4.244 2.86 2.922 4.852 4.01 3.74 3.997 2.793 3.569 6.721 4.702 2.86 6.469 11 0.8 3.307 4.454 2.907 3.041 4.881 4.185 3.933 3.98 2.902 3.776 6.713 4.56 2.907 6.501 12 0.85 3.481 4.696 2.994 3.19 4.937 4.403 4.133 3.974 3.053 3.952 6.694 4.407 2.994 6.509 13 0.9 3.621 4.913 3.057 3.351 5.069 4.623 4.34 3.989 3.193 4.164 6.694 4.319 3.057 6.502 14 0.95 3.72 5.163 3.171 3.518 5.186 4.838 4.547 4.005 3.365 4.342 6.683 4.241 3.171 6.501 15 1 3.761 5.422 3.32 3.674 5.344 5.079 4.743 4.037 3.557 4.573 6.68 4.199 3.32 6.515 Table 5.3 Least Values Slno: Samples & N Value Lowest standard deviation Lowest Wf and Cf N Value Standard Deviation N Value Standard Deviation 1 Sample1 - 0.7 0.70 1.802 0.99 5.245 2 Sample2 - 0.6 0.60 2.135 0.92 2.745 3 Sample3 - 0.55 0.55 5.326 0.51 5.351 4 Sample4 - 0.8 0.80 5.777 0.78 5.794 5 Sample5 - 0.65 0.65 4.505 0.9 5.335 6 Sample6 - 0.55 0.55 3.939 0.96 4.926 7 Sample7 - 0.6 0.60 6.707 0.48 6.833 8 Sample8 - 0.55 0.55 1.742 0.48 6.833 9 Sample9 - 0.55 0.55 3.736 0.85 4.696 10 Sample10 - 0.7 0.70 2.81 0.84 2.96 11 Sample11 - 0.55 0.55 2.692 0.83 3.127 12 Sample12 - 0.7 0.70 4.81 0.99 5.017 13 Sample113 - 0.55 0.55 3.54 0.99 5.017 14 Sample14 - 0.5 0.50 3.206 0.78 5.741 15 Sample15 - 0.85 0.85 3.974 0.83 3.385 16 Sample16 - 0.55 0.55 2.478 0.8 2.902 17 Sample17 - 0.55 0.55 3.111 0.81 3.789 18 Sample18 - 0.6 0.60 6.707 0.86 4.405 19 Sample19 - 0.7 0.70 2.819 0.84 2.96 20 Sample20- 0.33 0.33 5.05 0.46 5.6 Average 0.61 3.8433 0.795 4.633 Average of two 0.7
6.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 12 | Dec 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.34 | ISO 9001:2008 Certified Journal | Page 1405 Fig 5.1 Standard Deviation Based on standard deviation and N value we considered a DIN curve to get an maximum size of aggregate to increase workability, strength, probability and durability. Table 5.4 DIN Curves Sieve Size Standard deviation N Value d/D N=0.5 N=0.6 N=0.7 25 1 100 100 100 20 0.8 89.4427 87.469 85.5388 16 0.64 80 76.5082 73.1688 12.5 0.5 70.7107 65.9754 61.5572 10 0.4 63.2456 57.708 52.6553 4.75 0.19 43.589 36.9192 31.27 2.36 0.0944 30.7246 24.2652 19.1638 1.18 0.0472 21.7256 16.009 11.7967 0.6 0.024 15.4919 10.6691 7.34764 0.3 0.012 10.9545 7.03896 4.523 0.15 0.006 7.74597 4.64398 2.78424 Fig 5.2 combined Grading for N values
7.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 12 | Dec 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.34 | ISO 9001:2008 Certified Journal | Page 1406 6. CONCLUSIONS Use of numerical method of aggregate mix design with aid of transformed Fuller’s curve allows to calculateaggregate mixes for different types of concrete as well as to use natural, non-fractional aggregates. Average squared deflection between the “ideal” and the real grading curve S is efficiently used as the criterion of packing quality of the aggregate. Use of granulation number method of concrete mix design allowsprotectingthephysical andmechanical properties of concrete (Strength and workability) with coefficient of correlation not less than 0.95. At the same time, correlation coefficient between practical and experimental results of the standard method is 0.85 to 0.9. A system of concrete mix optimization gives a possibility to estimate more objectively and find a compromise variant between economy on the one hand and property on the other hand REFERENCES 1. Shiltone, J.M (1989). “A Hard Look at concrete.” Civil Engineering: 47-49. 2. Shilstone, J.M (1990). “Concrete Mixture Optimization.” Concrete International 12(6):33-39. 3. Shilstone, J.M. (1990). Mixture Optimization for Fast-Track. 69thannual Transportation Research Board meeting, wahington, D.CA 4. Talbot and F.E Richart (1923).“The Strength Concrete and its Relation to the Cement, Aggregate and Water.” Bulletin No 137:1-116. 5. Taylor, M.A. (1986). “Concrete Mix Proportioning by Modified FinenessModulusMethod.”ConcreteInternational:47- 52. 6. Washingtone DOT (2004). “Combined Aggregate Gradation for Portland Ceement Concrete, Standard Specifications, Section 9-03.1(5)”1. 7. Wilson,P. and D.N. Richardson (2001). “Aggregate Optimization of Concrete Mixtures.”Rolla, Missouri, University of Missouri-Rolla: 18. 8. S.D. Baker, C.F. Scholar, (1973). “Effect of Variations in Coarse-aggregate Gradation on properties of PortlandCement Concrete.” Highway Research Board, Issue No 441. 9. Sandor Popovics, (1973) “ Aggregate Grading and the Internal Structure Of Concrete” Highway ResearchBoard,Issue No 441 10. S.B. Hudson, H.F. Waller, (1969) “Evaluation of Construction Control Procedures: AggregateGradationVariationsand Effects.” NCHRP Report, Issue No. 69, Publisher- Transportation research Board. 11. Shu-T‟ien Li, V. Ramakrishnan, 1973. “Gap Graded Aggregates for High StrengthConcretes”HighwayResearchBoard, Issue No 441 12. C.P. Marais, E. Otte, L.A. Bloy 1973 “The Effect of Grading on Lean Mix Concrete”. Highway Research Board, Issue No 441 13. Karthik H. Obla and Haejin Kim., (2008), “On Aggregate GradingIs good concrete performance dependent on meeting grading limits” Concrete Iinternational, pp 4550. 14. Harrison, P.J., 2004, For Ideal SlabonGround Mixture, Concrete International, 26(3), pp 4955. 15. Shilstone, J. M. Sr., 2002, Performance based concrete mixtures and specifications for today, Concrete International
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