Cement concrete is a very useful constructional material whose properties can be modified readily at will. The desired properties of concrete can be obtained by using ingredients in a certain proportion. Thus determining the relative amount of materials is known as mix design. Hence mix design can be defined as the process of selecting suitable ingredients of concrete and determining their relative quantities for producing concrete of certain minimum properties as strength, durability and consistency etc., as economically as possible.
Purpose of Mix Design:
From the definition of mix design, it can be seen that the purpose of mix design is twofold as follows:
1. To achieve the stipulated minimum strength and durability.
2. To make the concrete in the most economical way. Cost wise all concretes depend mainly on two factors – (a) Cost of materials and (b) Cost of labour.
ADVERTISEMENTS:
The cost of form work, batching, mixing, transporting, and curing etc. is nearly the same for good as well as bad concrete work.
Thus to achieve economy, the main attention should be directed to the cost of materials. As the cost of cement is many times more than other ingredients, thus the attention mainly should be directed to the use of as little amount of cement as possible consistent with the strength and durability. Mix proportions provided by the designs are called as prescribed mix.
Objects of Mix Design:
The object of mix design is to decide the proportions of materials which will produce concrete of required properties. The mix proportions should be selected in such a way that the resulting concrete is of desired workability while fresh and it could be placed and compacted easily for the intended purpose. The fresh concrete should be fluid enough to fill the form work and surround the reinforcement fully and the hardened concrete should develop required strength and durability.
Factors Affecting the Choice of Mix Proportion:
According to IS 456-1978 and IS-1345-1980, the design of concrete should be based on the following factors:
ADVERTISEMENTS:
1. Grade designation
2. Type of cement
3. Max nominal size of aggregate
4. Grading of combined aggregates
ADVERTISEMENTS:
5. Water-cement ratio
6. Workability
7. Durability, and
8. Quality control.
ADVERTISEMENTS:
1. Grade Designation:
Grade designation specifies the characteristic compressive strength of concrete. As per IS-456-1978, the characteristic compressive strength is that value of concrete strength below which not more than 5% of the test results are expected to fall. It is the major factor which influences the mix design. Depending upon the degree of control at site, the concrete mix should be designed for the mean compressive strength, which is a little higher than the characteristic strength.
2. Type of Cement:
The type of cement is important as the rate of strength development depends mainly on cement. The choice of the type of cement depends upon the requirements of its performance. When very high compressive strength is required, port-land cement conforming to IS 8112-1976 is suitable. In case where an early strength is required, rapid hardening port-land cement conforming to IS 8041-1978 and for mass concrete work, low heat port-land cement conforming to IS 269-1979 is to be used.
ADVERTISEMENTS:
3. Maximum Nominal Size of Coarse Aggregate:
The maximum nominal size of coarse aggregate is determined by sieve analysis and is designated by the sieve size higher than the largest size on which 15% or more the aggregate is retained. It is governed by the size of the section and the spacing of the reinforcement.
According to IS 456-1978 and IS 1345-1980, the max size of the aggregate should be as follows:
(a) It should not be more than 1/4th of the minimum thickness of the member.
(b) It should be less by 5 mm than the minimum clear distance between the main reinforcement.
(c) It should be less by 5 mm than the minimum cover to the reinforcement.
(d) It should be less by 5 mm than the spacing between the pre-stressing cables.
For normal structural concrete work, the maximum size of aggregate may be used as 38 mm whereas for high strength concrete it may be 10 mm to 20 mm.
4. Grading of Combined Aggregate:
In a concrete mix, the relative proportions of the fine and coarse aggregates are one of the important factors which affect the strength of the concrete. For dense concrete, it is essential that the fine and coarse aggregates be well graded. The locally available aggregates generally do not conform to the standard grading’s. In such situations the aggregates should be combined in suitable proportions, so that the resulting grading is close to the desired grading.
The aim of combining the aggregates is to obtain a grading close to the coarset grading of the standard grading curves, the most economical mix having the highest permissible aggregate cement ratio. The aggregates can be combined either by analytical calculations or graphically, using the method of Road Note 4. The recommended e limits to the coarset and finest aggregate grading’s as per IS-383-1963 are shown in Table 20.1.
5. Water /Cement Ratio:
The compressive strength of concrete at a given age under normal conditions of curing mainly depends upon water/cement ratio, Lower the water-cement ratio within limits, greater the compressive strength and vice-versa. A number of relationships between compressive strength and water cement ratio are available, which are valid for a wide range of conditions. The generalized relationship between water-cement ratio and compressive strength of concrete is shown in Fig, 20.1.
6. Workability:
For satisfactory placing and compacting of concrete the workability is controlled by many factors as shape and size of the section to be concreting, quantity and spacing of reinforcement, method of transportation, placing and compaction of concrete etc. The aim should be to have minimum possible workability consistent with satisfactory placing and compaction of concrete. The insufficient workability will result in incomplete compaction, resulting in less strength and durability.
There are various methods of determining the workability of concrete, but there is no rigid correlation between work-abilities of concrete measured by different methods. Hence it is desirable to decide the test method before starting the concrete work. For comparable concretes workability measured by different methods is shown in Table 20.1.
7. Durability:
It can be defined as the resistance to internal and external deteriorating influences. The requirements of durability may be achieved by restricting the minimum cement content and minimum water-cement ratio as given in Table 20.2.
8. Quality Control:
The strength of concrete is never constant. It varies from batch to batch. This variation may be due to the variation in the quality of constituent materials, variations in mix proportions, variation in the quality of batching and mixing equipment available, quality of workmanship and supervision etc. Controlling these factors is important to minimise the difference between the minimum strength and characteristic mean strength of the mix, thus reducing the cement content. The method of controlling these differences is called quality control.
Analytical Method of Calculating % of Fine and Coarse Aggregate:
Let the fine aggregate is designated as aggregate = I whose percentage is β
and coarse aggregate is designated as aggregate = II whose percentage is γ
Let the percentage of combined aggregate is α.
These percentages are taken, and mixed. Let these percentages pass through the sieve corresponding to the point on the standard grading curve taken as criterion i.e., the combined aggregate should be very approximately near to this point.
Let x and y be the proportions of two aggregates in the combined state. Then to satisfy the condition that α % of combined aggregate passes through the criterion point, then-
The grading of the resultant combined aggregate is determined by first multiplying the grading of aggregate I and aggregate II by 1 and K respectively. The sum of corresponding products of the percentages passing the sieve sizes are divided by (1 + K) and the values are rounded off to the nearest percentage.
The method is illustrated by the following example:
Example:
The grading’s of fine and coarse aggregates available at a site are listed in columns 2 and 3 of table 20.3 below. These aggregates are to be combined in a suitable proportion to give the specified grading chosen from the standard curve which is listed in Column 4 of the same table 20.3.
Solution:
Let one kg of the fine aggregate be combined to x kg of coarse aggregate to get the desired grading. Let percentage passing through 4.75 mm sieve is taken as the criterion. In the standard grading curve 44% of the total aggregate passes through the IS 4.75 mm sieve. Hence using the Table 20.3.
95(1) + 4(x) = 44(1 + x)
4x – 44x = 44 – 95
– 40x = –51
or x = 51/40 = 5.1/4 = 1.275
Thus the fine and coarse aggregates must be combined in the proportion of 1:1.275. The grading of resulting combined aggregate is obtained by multiplying column 2 and 3 of the above table 20.1, by 1 and 1.275 respectively and dividing the sum of these products by (1 + 1.275) = 2.275. The respective values obtained are put in columns 5 of the table 20.1 as shown. Comparing the results of combined aggregate grading with the standard specified grading, it will be seen that the percentage passing through 4.75 mm sieve is same and the other values are very close to the specified grading.
In this method the percentage passing through the criterion sieve must necessarily agree, whereas others may not. If the variations are very small, they should be ignored and should be taken as such. In case the discrepancies are large the proportions may be changed by adopting another criterion point. This method can also be used to combine more than two aggregate.
Methods of Mix Design:
There are various methods of mix design as follows:
1. Arbitrary method
2. Minimum void method
3. Maximum density method
4. Water-cement ratio method
5. Fineness modulus method
6. Standard deviation method
7. American method of mix design
8. Graphic or Road Note 4 method of mix design
9. Indian Road Congress IRC-44 method
10. High strength concrete mix design
12. Mix design based on flexural strength
13. ACI committee 211-1 method
14. Department of Environment (DOE) mix design method
15. Mix design for pumpable concrete
16. Indian standard recommended (IS 10262-1982) method, and
17. Rapid method of mix design.
Nowadays out of the above methods following methods are commonly used:
1. ACI committee 211 method
2. DOE method
3. Indian Standard method, and
4. Rapid method of mix design.
Before discussing the mix design let us look on the grades of concrete.
The mix should be designed to produce the grade of concrete having the required workability and characteristic strength not less than as given in Table 20.5.
Note 1: Preliminary Test:
It is defined as the test conducted in a laboratory on the trial mix of concrete produced in the laboratory for designing a concrete mix before actual concreting at site to verify the strength of concrete and determining the adjustments required in the mix if needed. Thus a concrete for which mix is designed after carrying out preliminary test is called controlled concrete, and the concrete mixes adopted without carrying out preliminary tests is called ordinary concrete. For all important works controlled concrete should be used.
Works Test:
A test conducted either in the field or in a laboratory on the specimen made on actual site of works, out of concrete being used in the works is called works tests.
The 7 day strength may be adopted as given in Table 20.6:
Note 2:
In international system of units (S.I. units) the units of force or pressure is Newton and denoted by ‘N’. It can be defined as a force applied to a body having a mass of one kilogram gives an acceleration of one metre per second per second.
(Hence the reader must familiarize himself with the relation).
(b) Nominal Mix Concrete:
Where it is not practical to use controlled concrete, ordinary concrete of nominal mix is used. Nominal Mix grade for this concrete vary from M 5, M 7.5, M 10, M 15 & M 20 as per I.S. 456-1978, (M 50, M 75, M 100, M 150 and M 200).
The proportions of these mixes are given in Table 20.7:
Note:
1. The proportion of fine to coarse aggregate should be adjusted from upper limit to lower limit progressively as the grading of the fine aggregate becomes finer and the maximum size of coarse aggregate becomes larger. Graded coarse aggregate should be used. The proportions should be 1:1½, 1:2,1:2½ for maximum size of aggregate 10 mm, 20 mm and 40 mm respectively.
2. It may be noted for general guidance that M 10, M 15, M 20 and M 25 of ordinary concrete correspond approximately to 1:3:6, 1:2:4, 1:1½ : 3 and 1:1:2 nominal mixes of ordinary concrete.
3. M 5 and M 7.5 grades concrete may be used for lean concrete bases and simple foundations for masonry walls. These mixes need not to be designed. Grades of concrete lower than M 15 should not be used for reinforced concrete.