For the mix design of concrete following data is required: 1. Characteristic (Targeted) Compressive Strength at 28 days 2. Degree of Workability (Selection of Water-Cement Ratio) 3. Estimation of Entrapped Air 4. Selection of Water-Cement and Fine to Total Aggregate Ratio 5. Calculation of Cement Content 6. Calculation for Aggregate Content and a Few Others.
1. Characteristic Compressive Strength at 28 Days:
The target mean compressive strength ft, at 28 days is given by the relation-
ft = fc + K.S. …(i)
where ft is the target mean strength at 28 days, fc is the characteristic strength at 28 days. As per IS-456- 2000 and IS-1343-1980, the characteristic strength of the concrete is that value of the concrete, below which not more than 5% results are expected to fall.
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where,
S = standard deviation. For the initial value of mix design the value of standard deviation may be adopted from table 20.32 below.
K = a statistical coefficient known as tolerance factor or risk factor. The value of K may be adopted from table 20.33.
From table 20.33, the value of K is taken as 1.65, putting the value of K is equation (i) we get.
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∴ ft = fc + 1.65 S…(ii)
2. Selection of Water-Cement Ratio:
Even when the water-cement ratio is fixed, the compressive strength of concrete is influenced by various factors such as type of cement and aggregate, maximum size of aggregate, surface texture of aggregate etc. Thus it is desirable to establish relation between the strength of concrete and free water/cement ratio for the materials to be used and site conditions. If it is not possible to establish such relation, then for the targeted strength of the concrete the free water/cement ratio may be obtained from the curve 20.7 given below.
In this method of mix design, the strength of cement has been incorporated. By incorporating the strength of cement, it is possible to effect economy in the concrete mix.
If the 28 days cement strength is known then for more accurate estimation of water/cement ratio curves shown in Fig. 20.8 can be used. However adoption of these curves will delay the work as for testing the 28 days strength; at least a delay of 28 days will be there in the whole process.
To cut down this delay, accelerated strength tests may be adopted. Since 1982 the quality and strength of Indian Cement has improved considerably. Hence for determining the water/cement ratio curve of Fig. 20.9 may be adopted instead of Fig. 20.8. The curves of Fig. 20.9 are not a part of the IS recommended method. They are taken from practice in Germany and may be more useful for getting better results.
The free water/cement ratio thus selected as discussed above, should also be checked from durability requirements as shown in Table 20.34, the lower value of the two should be adopted.
3. Estimation of Entrapped Air:
The air content is estimated as shown in Table 20.35 for the nominal aggregate used.
4. Selection of Water Content and Fine to Total Aggregate Ratio:
For medium strength concrete i.e. below M35 grade concrete and high grade concrete i.e. higher than M35 grade, the water content and percentage of sand in total aggregate by absolute volume basis can be determined from table 20.36 and 20.37 respectively.
ADVERTISEMENTS:
Both tables are based on the following conditions:
(a) Crushed coarse aggregates conforms to IS 383-1970
(b) Fine aggregate consisting of natural sand conforms to the grading of zone II of IS 383-1970.
(c) Workability corresponding to slump of about 30 mm (compacting factor 0.80).
The water/cement ratio of table 20.36 is 0.6 by mass and that of Table 20.37 as 0.35 by mass. For departure from above noted conditions corrections have to be applied as suggested in table 20.38.
5. Calculation of Cement Content:
The cement content per unit volume of concrete may be calculated from free water/cement ratio and the quantity of water per unit volume of concrete as-
Cement by mass = [(water content)/(w/c ratio)]
The cement content so calculated should by checked for durability requirement Table 20.34. Greater of the two values should be adopted.
6. Calculation for Aggregate Content:
Aggregate content may be calculated from the following relation:
where,
V = Absolute volume of fresh concrete, which is equal to vol. of concrete in m3 minus the volume of entrapped air.
W = mass of water (kg.) per m3 of concrete
C = mass of cement (kg) per m3 of concrete
Sc = specific gravity of cement
p = ratio of fine aggregate (F.A.) to total aggregate by absolute volume
fa = total mass of F.A. (kg.) per m3 of concrete
Ca = total mass of coarse aggregate (kg) per m3 of concrete
Sfa & Sca = sp. gravities of fine and coarse aggregate respectively.
7. Actual Quantities Required for the Mix:
The mix proportions calculated by the above noted method are based on the assumption that aggregates are saturated and surface dry. For any change than these conditions, i.e., when aggregates are moist or air dry or fully dry. Corrections in the quantity of mixing water as well as in aggregates have to be made.
8. The Calculated Mix Proportion should be Checked by Trial Batches:
For each trial, the mix should be sufficient to prepare at least three 150 mm cubes and workability should be as per IS 1199-59. If any change is required to be done, it should be done as per table 20.38.
The method is illustrated by following examples:
Example:
(a) Design Stipulation (Requirements):
(i) Characteristic compressive strength at 28 days in the field required = 25 MPa
(ii) Maximum size of crushed aggregate = 20 mm (angular)
(iii) Degree of workability = Medium, compacting factor 0.90 or slump 75 mm
(iv) Degree of quality control Good
(v) Type of exposure Mild
(vi) Grading zone of sand III (I.S. 385-1970)
(b) Characteristics of materials
Cement:
(i) Type of cement Ordinary port-land cement
(ii) Specific gravity 3.15
(iii) Bulk density of cement 1450 kg/m3
(iv) Compressive strength at 7 days Satisfies the requirements of IS 269-1989
(c) Mix Design. Target Mean Strength:
ft = fc + K S The values of K and S are taken from tables 20.32 and 20.33
= 25 + 1.6 x 4 = 25 + 6.4 = 31.4 Ma
(d) Selection of Water/Cement Ratio:
As the seven days strength is specified, use of Fig. 20.8 has been made.
For a targeted mean strength of 31.4 MPa, the w/c ratio is 0.48
This is lower than specified value of 0.55 for R.C.C. from durability consideration for mild exposure. Hence adopt w/c ratio as 0.48.
(e) Selection of Water and Sand Contents:
For 20 mm maximum aggregate size, sand conforming to the grading of zone II, from table 20.36, water content per cubic metre of concrete = 186 kg.
Sand content % of total aggregate = 35% For change in w/c ratio, compacting factor, for sand belonging to zone III, following adjustments must be made as per table 20.38
Thus required sand as percentage of total aggregate by absolute value 35.0 – 3.5 = 31.5%
Required water content = 186 + 3% of 186 kg = 186.0 + 5.58 = 191.58 kg = 191.6 kg.
(f) Determination of Cement Content:
Water/cement ratio = (0.60 – 0.12) = 0.48
Amount of water = 191.6 kg
= 191.6
Cement = [(Amount of water)/(w/c ratio)] = 191.6/0.48
= 399.2kg/m3 app.
Cement content from durability considerations from table 20.34 for mild exposure is adequate.
(g) Determination of Coarse and Fine Aggregate Contents:
From table 20.35, for the specified maximum size of aggregate of 20 mm, the amount of entrapped air is 2%.
Taking this into account and using equation no. 1 and 2 we get-
Absolute volume of concrete = 1 – 0.02 = 0.98%
For 50 kg of cement, the quantities worked are as follows:
Cement = 50 kg
Fine aggregate = 68 kg
Coarse aggregate = 140 kg fraction I 60% = 84 kg
fraction II 40% = 56 kg
(ii) Water:
1. For w/c ratio 0.48, water = 24 kg
2. Extra water for absorption by coarse aggregate 0.5% of mass = 0.70 litres.
(iii) Quantity of Water:
Quantity of water to be deducted for moisture present in sand at 2% by mass = 1.38 litres
∴ Actual quantity of water to be added = 24 + 0.7 – 1.38 = 23.3 litres
Actual quantity of sand after adding water content = 68 + 1.38 = 69.38 kg. Thus after allowing for free mass of moisture, sand quantity = 69.4 kg.
(iv) Actual Quantity of Coarse Aggregate:
Fraction (i) 84 – 0.42 = 83.68 kg Fraction
(ii) 56 – 0.28 = 55.72 kg.
Thus actual quantities of materials to be used are:
Water = 23.3 litres
Cement = 50.0 kg
Sand = 69.9 kg
Coarse aggregate fraction I = 83.58 kg
Coarse aggregate fraction II = 55.72 kg. Ans.