IRJET- A Statistical Approach to Obtain the Best Blend of Aggregates

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

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.

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.

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
i1
M  1

M
(YT 
2
i
Y )

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

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

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
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2. Shilstone, J.M (1990). “Concrete Mixture Optimization.” Concrete International 12(6):33-39.
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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
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13. Karthik H. Obla and Haejin Kim., (2008), “On Aggregate GradingIs good concrete performance dependent on meeting
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