The process of relative proportions of cement, sand, coarse aggregate
and water, so as to obtain a concrete of desired quality is known as
the

*proportioning of concrete.*The proportions of coarse aggregate, cement and water should be such that the resulting concrete has the following properties:- When concrete is fresh, it should have enough workability so that it can be placed in the formwork economically.
- The concrete must possess maximum density or in the other words, it should be strongest and most water-tight.
- The cost of materials and labor required to form concrete should be minimum.

The determination of the proportions of cement, aggregates and water to obtain the required strengths shall be made as follows:

a) By designing the concrete mix, such concrete shall be called design mix concrete, or

b) By adopting nominal mix, such concrete shall be called nominal mix concrete.

- Design mix concrete is preferred to nominal mix.
- Concrete of each grade shall be analysed separately to determine its standard deviation.

Where, Δ = deviation of the individual test strength from the average strength of n samples.

n = Number of sample test results.

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**METHODS OF PROPORTIONING CONCRETE**

**(1) Arbitrary Method**

The general expression for the proportions of cement, sand and coarse aggregate is 1 : n : 2n by volume.

1 : 1 : 2 and 1 : 1.2 : 2.4 for very high strength.

1 : 1.5 : 3 and 1 : 2 : 4 for normal works.

1 : 3 : 6 and 1 : 4 : 8 for foundations and mass concrete works.

**Recommended Mixes of Concrete**

M10 | 1 : 3 : 6 |

M15 | 1 : 2 : 4 |

M20 | 1 : 1.5 : 3 |

M25 | 1 : 1 : 2 |

**(2) Fineness Modulus Method:**

The
term fineness modulus is used to indicate an index number which is
roughly proportional to the average size of the particle in the entire
quantity of aggregates. The fineness modulus is obtained by adding
the percentage of weight of the material retained on the following
sieve and divided by 100. The coarser the aggregates, the higher the fineness modulus.

Sieve is adopted for:

All aggregates : 80 mm, 40 mm, 20 mm, 10 mm, and Nos. 480, 240, 120, 60, 30 and 15.

Coarse aggregates : mm, 40 mm, 20 mm, 10 mm, and No. 480.

Fine aggregates : Nos. 480, 240, 120, 60, 30 and 15.

Where, P = desired fineness modulus for a concrete mix of fine and coarse aggregates.

P1 = fineness modulus of fine aggregate

P2= fineness modulus of coarse aggregate.

**(3) Minimum Void Method**(Does not give satisfactory result)

The
quantity of sand used should be such that it completely fills the voids
of coarse aggregate. Similarly, the quantity of cement used shown such
that it fills the voids of sand, so that a dense mix the minimum voids
is obtained.

In actual practice, the quantity of fine aggregate
used in the mix is about 10% more than the voids in the coarse aggregate
and the quantity of cement is kept as about 15% more than the voids in
the fine aggregate.

**(4) Maximum Density Method:**

Where, D = maximum size of aggregate (i.e. coarse aggregate)

P = percentage of material finer than diameter d (by weight)

d = maximum size of fine aggregate.

A
box is filled with varying proportions of fine and coarse aggregates.
The proportion which gives heaviest weight is then adopted.

**(5) Water – Cement Ratio Method:**

According
to the water – cement ratio law given by Abram as a result of many
experiments, the strength of well compacted concrete with good
workability is dependent only on the ratio.

- The lower water content produces stiff paste having greater binding property and hence the lowering the water-cement ratio within certain limits results in the increased strength.
- Similarly, the higher water content increases the workability, but lower the strength of concrete.
- The optimum water-cement ratio for the concrete of required compressive strength is decided from graphs and expressions developed from various experiments.
- Amount of water less than the optimum water decreases the strength and about 10% less may be insufficient to ensure complete setting of cement. An increase of 10% above the optimum may decrease the strength approximately by 15% while an increase in 50% may decrease the strength to one-half.
- According to
**Abram’s water-cement law**, lesser the water-cement ratio in a workable mix greater will be the strength. - If water cement ratio is less than 0.4 to 0.5, complete hydration will not be secured.
- Some practical values of water cement ratio for structural reinforced concrete are

0.45 for 1 : 1 : 2 concrete

0.5 for 1 : 1.5 : 3 concrete

0.5 to 0.6 for 1 : 2 : 4 concrete.

Concrete vibrated by efficient mechanical vibrators require less water cement ratio, and hence have more strength.

**Thumb Rules**for deciding the quantity of water in concrete:

(i) Weight of water = 28% of the weight of cement + 4% of the weight of total aggregate

(ii) Weight of water = 30% of the weight of cement + 5% of the weight of total aggregate

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