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By
Kaushal Kishore, Materials Engineer, Roorkee
ABSTRACT:
The stresses induced in concrete pavements are mainly flexural. Therefore flexural strength is more often specified than compressive strength in the design of concrete mixes for pavement construction. A simple method of concrete mix design based on flexural strength for normal weight concrete mixes is described in the paper.
INTRODUCTION:
Usual criterion for the strength of concrete in the building industry is the compressive strength, which is considered as a measure of quality concrete. However, in pavement constructions, such as highway and airport runway, the flexural strength of concrete is considered more important, as the stresses induced in concrete pavements are mainly flexural. Therefore, flexural strength is more often specified than compressive strength in the design of concrete mixes for pavement construction. It is not perfectly reliable to predict flexural strength from compressive strength. Further, various codes of the world specified that the paving concrete mixes should preferably be designed in the laboratory and controlled in the field on the basis of its flexural strength. Therefore, there is a need to design concrete mixes based on flexural strength.
The type of aggregate can have a predominant effect, crushed rock aggregate resulting in concrete with higher flexural strength than uncrushed (gravel) aggregates for comparable mixes, assuming that sound materials are used. The strength of cement influences the compressive and flexural strength of concrete i.e. with the same watercement ratio, higher strength cement will produce concrete of higher compressive and flexural strength.
1  Characteristic Flexural Strength at 28 days  :  4.5 N/mm^{2} 
2  Cement  :  Three mixes are to be designed 
MIXA
With PPC (Flyash 18 percent based) conforming to IS:1489partI1991. 7 days strength 37.5 N/mm^{2}. Specific Gravity : 3.00 

MIXB
With OPC43 Grade conforming to IS: 81121989. 7 days strength 40.5 n/mm^{2}. Specific Gravity : 3.15 

MIXC
With OPC of MixB and Fly ash conforming to IS:3812 (PartI)2003 Specific Gravity : 2.20 

Note: Requirements of all the three mixes are the same. Fine Aggregate, Coarse Aggregate and Retarder Super plasticizer are the same for all the three mixes.  
3  Fly ash replacement  :  20% Fly ash is required to be replaced with the total cementitious materials. 
4  Maximum nominal size of aggregates  :  31.5 mm Crushed aggregate 
5  Fine aggregate and coarse aggregate grading  :  Given in Table 1 
6  Minimum cement content for 4.5 N/mm2 characteristic flexural strength:  :  (a) OPC shall not be less than 360 kg/m^{3}.
(b) PPC shall not be less than 425 kg/m^{3}. Fly ash in it 20% maximum by weight of total cementitious materials (c) OPC + Fly ash mix OPC shall not be less than 340 kg/m^{3}. Fly ash 20% maximum by weight of cementations material 
7  Maximum free W/C Ratio  :  (a) For OPC 0.45
(b) For PPC 0.50 
8  Workability  :  40 mm slump at pour the concrete will be transported from central batching plant through transit mixer, at a distance of 15 Km during June, July months. The average temperature last year during these months was 30^{0}C. 
9  Exposure condition  :  Moderate 
10  Method of placing  :  Fully mechanised construction 
11  Degree of supervision  :  Good 
12  Maximum of cement content  :  (a) OPC 425 kg/m^{3}
(b) PPC 425 kg/m^{3} 
13  Chemical admixture  :  Retarder Super plasticizer conforming to IS:91031999. With the given requirements and materials, the manufacturer of Retarder Super plasticizer recommends dosages of 1% bw of OPC, which will reduce 15% of water without loss of workability. For fly ash included cement dosages will be required to be adjusted by experience/ trials.2% maximum by weight of cementitious material 
14  Values of Z x (for National Highway)  :  1.96 x 0.40 
TEST DATA FOR MATERIALS AND OTHER DETAILS
1. The grading of fine aggregate, 1 & 2 aggregates are as given in Table. 1.
2. Properties of aggregates
Tests 
Fine aggregate 
Aggregate 1 
Aggregate 2 
Specific Gravity 
2.65 
2.65 
2.65 
Water Absorption % 
0.8 
0.5 
0.5 
3. Target average flexural strength for all A, B and C mixes
S = S+ Zq
=4.5 + 1.96 x 0.40
= 5.3 N/mm^{2} at 28 days age
4. For Mix A, B and C free W/C ratio with crushed aggregate and required average flexural target strength of 5.3 N/mm^{2} at 28 days from Fig. 1 Curve D found to be 0.42. This is lower than specified maximum W/C ratio value of 0.45 for OPC and 0.50 for PPC.
Note:
In absence of cement strength, but cement conforming to IS Codes, assume from Fig. 1
Curve C and D for OPC 43 Grade
Take curves C and D for PPC, as PPC is being manufactured in minimum of 43 Grade of strength.
5. Other data’s: The Mixes are to be designed on the basis of saturated and surface dry aggregates. At the time of concreting, moisture content of site aggregates are to be determine. If it carries surface moisture this is to be deducted from the mixing water and if it is dry add in mixing water the quantity of water required for absorption. The weight of aggregates are also adjusted accordingly.
DESIGN OF MIXA WITH PPC
a) Free W/C ratio for the target flexural strength of 5.3 N/mm^{2} as worked out is 0.42 for first trial.
b) Free water for 40 mm slump from Table 2 for 31.5 mm maximum size of aggregate.
2/3×170 + 1/3×200= 180 kg/m^{3}
From trials it is found that Retarder Super plasticizer at a dosages of 1.3% bw of PPC may reduce 15% water without loss of workability
Then water = 180 – (180 x 0.15) = 153 kg/m^{3}
c) PPC = 153/0.42 = 364 kg/m^{3} (Required minimum PPC is 425 kg/m^{3})
d) Formula for calculation of fresh concrete weight in kg/m^{3}
U_{m} = 10 x G_{a} (100 – A) + C_{m}(1 – G_{a}/G_{c}) – W_{m} (Ga – 1)
Where,
U_{m}=Weight of fresh concrete kg/m3
G_{a}=Weighted average specific gravity of combined fine and coarse aggregate bulk, SSD
G_{c}=Specific gravity of cement. Determine actual value, in absence assume 3.15 for OPC and 3.00 for PPC (Fly ash based)
A=Air content, percent. Assume for trial entrapped air 1.5%
Note: The exact density may be obtained by filling and fully compacting constant volume suitable metal container from the trial batches of calculated design mixes. The mix be altered with the actual obtained density of the mix.
U_{m} =10 x G_{a} (100 – A) + C_{m} (1 – G_{a}/G_{c}) – W_{m} (G_{a} – 1)
=10 x 2.65 (100 – 1.5) + 425(1 2.65/3.00) – 153 (2.65 1)
=2409 kg/m^{3}
e) Aggregates = 2409 – 425 – 153 = 1831 kg/m^{3}
f) Fine aggregate = 1831 x 0.45 = 824 kg/m^{3}
Aggregate 1 = 1831 x 0.29 = 531 kg/m^{3}
Aggregate 2 = 1831 x 0.26 = 476 kg/m^{3}
g) Thus for 4.5 N/mm2 flexural strength quantity of materials per cu.m. of concrete on the basis of saturated and surface dry aggregates:
Water = 153 kg/m^{3}
PPC = 425 kg/m^{3}
Fine Aggregate (sand) = 824 kg/m^{3}
Aggregate (1) = 531 kg/m^{3}
Aggregate (2) = 476 kg/m^{3}
Retarder Super Plasticizer 1.3% bw of PPC = 5.525 kg/m^{3}
MIX B WITH OPC
a) Water = 180 – (180 x 0.15) = 153 kg/m^{3}
b) OPC = 153/0.42 = 364 kg/m^{3}
c) Density: 10 x 2.65 (100 – 1.5) + 364 (1 – 2.65/3.15) – 153 (2.65 – 1)= 2416 kg/m^{3}
d) Total Aggregates = 2416 – 364 – 153 = 1899 kg/m^{3}
Aggregate 1 = 1899 x 0.29 = 551 kg/m^{3}
Aggregate 2 = 1899 x 0.26 = 494 kg/m^{3}
Fine Aggregate = 1899 x 0.45 = 854 kg/m^{3}
e) Thus for 4.5 N/mm^{2} flexural strength quantity of materials per cu.m of concrete on the basis of SSD aggregates are given below:
Water = 153 kg/m^{3}
OPC = 364 kg/m^{3}
Fine Aggregate (sand) = 854 kg/m^{3}
Aggregate (1) = 551 kg/m^{3}
Aggregate (2) = 494 kg/m^{3}
Retarder Super Plasticizer 1% bw OPC = 3.640 kg/m3
MIXC WITH OPC + FLY ASH
With a total cementitious material of 430 kg/m^{3},
OPC = 430 x 0.80 = 344 kg/m^{3}
Fly ash = 430 x 0.20 = 86 kg/m^{3}
Mix on the basis of SSD Aggregates,
(1) Water as worked out earlier = 153 kg/m^{3}
(2) OPC = 344 kg/m^{3}
(3) Fly ash = 86 kg/m3
Density = 10 x 2.65 (100 – 1.5) + 430 (1 – 2.65/3.00) – 153 (2.65 – 1) = 2410 kg/m^{3}
Total Aggregates = 2410 – 153 – 344 – 86 = 1827 kg/m^{3}
(4) Fine aggregate 0.45 x 1827 = 822 kg/m^{3}
(5) Aggregate (1) 0.29 x 1827 = 530 kg/m^{3}
(6) Aggregate (2) 0.26 x 1827 = 475 kg/m^{3}
(7) Retarder super plasticizer 1.5% bw of cementitious material = 6.450 kg/m^{3}
Note:
(1) Cementitious material worked out as per IRC : 152011, which specified: In case fly ash (as per IS: 3912 Part 1) is blended at site, the quantity of fly ash shall be restricted to 20 percent by weight of cementitious material and the quantity of OPC in such a blend shall not be less than 340 kg/m^{3} .
(2) After the first trial mix, its actual density is to be determined, as specified elase where in this paper. The mix proportions shall then be worked out accordingly including the water content, the dosages of Retarder SP for required workability keeping the free w/c ratio with in the permissible limits and adjusting it according to the required flexural strength.
(3) The mix proportions given in this paper are for first trial and to be adjusted as per actual site materials, conditions and requirements.
Materials 
MIX. ‘A’ with PPC 
Mix. ‘B’ with OPC 
Mix. ‘C’ with OPC+Flyash 
Water kg/m^{3} 
153 
153 
153 
PPC kg/m^{3} 
425 
— 
— 
OPC kg/m^{3} 
— 
364 
344 
Flyash kg/m^{3} 
— 
— 
86 
Fine Agg. kg/m^{3} 
824 
854 
822 
Agg. (1) kg/m^{3} 
531 
551 
530 
Agg. (2) kg/m^{3} 
476 
494 
475 
Retarder Super plasticizer kg/m^{3} 
5.525 
3.640 
6.450 
W/ Cementitious ratio 
0.36 
0.42 
0.356 
Note:
1. For exact W/C ratio the water in admixture should also be taken into account.
2. PPC reduces 5% water demand. If this is found by trial then take reduce water for calculation.
3. If the trial mixes does not gives the required properties of the mix, it is then required to be altered accordingly. However, when the experiences grows with the particular set of materials and site conditions very few trials will be required, and a expert of such site very rarely will be required a 2nd trial.
CONCLUSION
1. For 4.5 N/mm^{2} flexural strength concrete having same material and requirement, but without water reducer, the OPC required will be 180/0.42 = 429 kg/m^{3}
2. With the use of superplasticizer the saving in OPC is 65 kg/m^{3} and water 27 lit/m^{3}.
3. In the financial year 20092010 India has produces 200 million tonnes of cement. In India one kg of cement produce emitted 0.93 kg of CO_{2}. Thus the production of 200 million tonnes of cement had emitted 200 x 0.93 = 186 million tonnes of CO_{2} to the atmosphere.
4. If 50 million tonnes cement in making concrete uses Water Reducers 7500000 tonnes of cement can be saved. 3750000 KL of potable water will be saved and the saving of Rs. 3300 crores per year to the construction Industry. 6975000 tonnes of CO_{2} will be prevented to be emitted to the atmosphere. The benefits in the uses of water reducers not limited to this. When water reduces shrinkage and porosity of concrete are reduces which provides the durability to concrete structures.
5. India is facing serious air, water, soil, food and noise pollution problems. Every efforts therefore are necessary to prevent pollution on top priority basis.
6. As the stress induced in concrete pavements are mainly flexural, it is desirable that their design is based on the flexural strength of concrete. The quality of concrete is normally assessed by measuring its compressive strength. For pavings, however, it is the flexural strength rather than the compression strength of concrete which determine the degree of cracking and thus the performance of road, and it is imperative to control the quality on the basis of flexural strength.
7. As per IRC: 152011, in case of small size projects, where facilities for testing beams with three print loading are not available, in such cases, the mix design may be carried out by using compressive strength values and there after flexural strength will be determined as per correlation between flexural strength with compressive strength given the following equation.
Where fcr is the flexural strength in MPa or N/mm^{2} and fck is the characteristic compressive strength in MPa or N/mm^{2} as per IS: 4562000.
REFERENCES:
1  IS : 3831970  Specifications for coarse and fine aggregates from natural sources for concrete (second revision) BIS, New Delhi  
2  IS: 4562000  Code of practice for plain and reinforced concrete (fourth revision), BIS, New Delhi  
3  IS: 91031999  Specification for admixtures for concrete (first revision) BIS, New Delhi  
4  IS: 81121989  Specifications for 43 Grade ordinary portland cement (first revision) BIS, New Delhi  
5  IS: 2386 (PartIII) 1963  method of test for aggregate for concrete. Specific gravity, density, voids, absorption and bulking, BIS, New Delhi  
6  IS: 3812 (PartI) 2003  Specification for pulverized fuel ash: PartI for use as pozzolana in cement, cement mortar and concrete (second revision) BIS, New Delhi  
7  IS: 1489PartI 1991  Specifications for portland pozzolana cement (PartI) Flyash based. (Third revision), BIS, New Delhi  
8  IRC: 152011 – Standard specifications and code of practice for construction of concrete road (Fourth revision)  
9  Kishore Kaushal, “Concrete Mix Design Based on Flexural strength for AirEntrained Concrete”, Proceeding of 13^{th} Conference on our World in Concrete and Structures, 2526, August, 1988, Singapore.  
10  Kishore Kaushal, “Method of Concrete Mix Design Based on Flexural Strength”, Proceeding of the International Conference on Road and Road Transport Problems ICORT, 1215 December, 1988, New Delhi, pp. 296305.  
11  Kishore Kaushal, “Mix Design Based on Flexural Strength of AirEntrained Concrete”. The Indian Concrete Journal, February, 1989, pp. 9397.  
12  Kishore Kaushal, “Concrete Mix Design Containing Chemical Admixtures”, Journal of the National Building Organization, April, 1990, pp. 112.  
13  Kishore Kaushal, “Concrete Mix Design for Road Bridges”, INDIAN HIGHWAYS, Vol. 19, No. 11, November, 1991, pp. 3137  
14  Kishore Kaushal, “ Mix Design for Pumped Concrete”, Journal of Central Board of Irrigation and Power, Vol. 49, No.2, April, 1992, pp. 8192  
15  Kishore Kaushal, “Concrete Mix Design with Fly Ash”, Indian Construction, January, 1995, pp. 1617  
16  Kishore Kaushal, “HighStrength Concrete”, Bulletin of Indian Concrete Institute No. 51, AprilJune, 1995, pp. 2931  
17  Kishore Kaushal, “Concrete Mix Design Simplified”, Indian Concrete Institute Bulletin No. 56, JulySeptember, 1996, pp.2530.  
18  Kishore Kaushal, “Concrete Mix Design with Fly Ash & Superplasticizer”, ICI Bulletin No. 59, AprilJune 1997, pp. 2930  
19  Kishore Kaushal. “Mix Design for Pumped Concrete”, CE & CR October, 2006, pp. 4450. 
Table. 1: Grading of Aggregates
IS Sieve Designation 
Percentage of passing by mass 

Fine aggregate from river
45% 
Crushed aggregate  Combined grading of mix  IRC: 152011 recommended grading of combined aggregates for pavement quality concrete (PQC)  
(1)
29% 
(2)
26% 

31.50 mm 
100 
100 
100 
100 
100 
26.50 mm 
100 
100 
98 
99 
85 – 95 
19.0 mm 
100 
100 
25 
81 
68 – 88 
9.50 mm 
100 
46 
0 
58 
45 – 65 
4.75 mm 
94 
5 

44 
30 – 55 
600 micron 
42 
0 

19 
8 – 30 
150 micron 
10 


5 
5 – 15 
75 micron 
2 


1 
0 – 5 
Table. 2: Approximate freewater content (kg/m3) required to give various levels of workability for nonairentrained (with normal entrapped air) concrete.
Maximum size of aggregate (mm) 
Type of aggregate 
Slump (mm) 
25 + 10

40 + 1031.5 
Uncrushed
Crushed 
160 190 
170 200 
Note: When coarse and fine aggregate of different types are used, the free water content is estimated by the expression.
2/3W_{f}+1/3W_{c}
Where,
W_{fsub>= Free water content appropriate to type of fine Aggregate
And Wc= Free water content appropriate to type of coarse aggregate.}
We at engineeringcivil.com are thankful to Er. Kaushal Kishore for submitting the revised mix design as per IRC:152011. This will be of great help to all civil engineering students and faculty who are seeking information on mix design based on revised IRC.
Thank you sir for your valuable information
What is volume of materials to be used in 1cubic meter of concrete
One (1 cubic meter) of concrete is how many kilograme of materials inside
J.C.Sharma May 12,2016
Thank you sir for your PQC design in .design calculation some abbreviation is being used but not clear.Please.tell us about those.Some constant used in design plz let us know which stand for.
Thanks
J.C.Sharma
Illustrated example In is code mix design for m40 concrete the cement content is given 350 kg but for m20 grade cement content is given 380 kg why so , Is m20 concrete is more costly than m 40 grade?