The following points highlight the five methods of concrete mix design. The methods are: 1. American Method of Mix Design 2. Graphic Method of Mix Design 3. Mix Design by Indian Standard Method 4. American Concrete Institute Method of Mix Design 5. Rapid Method of Mix Design.
1. American Method of Mix Design:
The American Concrete Institute (ACI) method is based on the fact that for a given maximum size of aggregate the water content in kilogram per cubic metre of concrete determines the workability of concrete mix, usually independent of the mix proportions. The relative water contents for various work-abilities are given in Table 20.2. Table 20.24 gives the actual content of water for a reference (plastic) consistency of table 20.23. It is thus possible to start the mix design by selecting the water content from these tables.
Further it is also assumed that the optimum ratio of bulk volume of coarse aggregate to the total volume of concrete depends only on the maximum size of aggregate and on the grading of fine aggregate. Table 20.25 gives the maximum bulk volume of coarse aggregate per unit volume of concrete. For other consistency the values of Table 20.23 should be multiplied by a factor given in Table 20.26. The actual procedure is explained with the help of the following example.
Example 1:
Concrete of compressive strength of350 kg/Cm2 (35 MPs) and 5 cms slump is required for a particular job, ordinary Portland cement being used. The maximum size of aggregate used is 38 mm (1½”) its bulk density is 1600 kg/m and specific gravity 2.64. The fineness modulus of fine aggregate is 2.60and its specific gravity 2.58. The absolute density in kg/m3 is 1000 times larger than the specific gravity.
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Procedure:
After fixing the maximum size and type of aggregate, the workability is determined with the help of water content obtained from given tables 20.23 and 20.24, and bulk volume of coarse aggregate from table 20.25. From given specific gravity of coarse aggregate, its absolute volume is determined.
Now the water/cement ratio is chosen from strength as well as durability requirements and the quantity of cement is computed dividing water content by water/cement ratio. Thus the absolute volumes of water, coarse aggregate, are known. The absolute volume of fine aggregate can be determined by subtracting the above weights from the weight of concrete.
Solution:
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For the required slump of 50 mm, the concrete is of stiff plastic degree. For this concrete having a maximum size of aggregate as 38 mm to 40 mm water content is taken from table 20.23 and 20.24 as 175 x 0.92 = 161 kg. per cubic metre of concrete.
Air entrainment is assumed as 1%. For this condition the water/cement ratio is taken from table 20.19 as 0.47 by extra polation.
Hence cement content = Weigh of water/Water/cement ration = 161/0.47 = 342.55 kg.
For a fineness modulus of 2.60 for fine aggregate (using the given fine aggregate) the bulk volume of coarse aggregate from table 20.25). is given as 0.73 m3.
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∴ Weight of coarse aggregate per cubic metre of concrete = 0.73 x 1600 = 1168 kg.
Hence absolute volumes–of ingredients are calculated as follows:
∴ Weight of fine aggregate = 0.02779 x 2.58 x 1000 = 700.6 kg.
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Hence the weights of materials per cubic metre of concrete are:
1. Cement = 342.55 kg.
2. Water = 161.00 kg.
3. Fine aggregate = 700.6 kg.
4. Coarse aggregate = 1168.0 kg.
Total = 2372.55 kg.
Hence density of concrete = 2372.6 kg. Ans.
2. Graphic Method of Mix Design:
This method has been developed by Road Research Laboratory, London and its detailed procedure has been explained in Road Note No. 4. Here this method is explained with the help of Fig. 20.5 and 20.6. The aggregates to be mixed together are served and their percentage passing through standard serves for fine aggregate serve 4.75 mm, 2.36 mm, 1.18 mm. 600 micron, 300 micron and 150 micron are used. For coarse aggregate maximum size allowed, say 38 mm, 19 mm, 9.5 mm 4.75 mm, 2.36 mm serve used.
Procedure:
1. The percentage passing through each serve of the coarse and fine aggregate or two fractions of coarse aggregate which are to be mixed to obtain the desired grading curve are noted along the two opposite vertical sides of a square from top to bottom as shown in Fig. 20.5. The points corresponding to the same serve size are joined by the straight lines. If the serve size does not exist on any of the vertical axis, then the line should be joined to the 100% point on the left hand axis and 0% point on the right hand axis.
2. Now a vertical line is drawn through the point of intersection of the line joining the same serve size point and the horizontal line representing the correct percentage of aggregate smaller than the desired serve or the vertical line drawn from the appropriate point along the scale at the top of the diagram (this scale represents the ratio of fine to total aggregate) and the combined grading is given by the inter section of this line and the serve size lines joining the pairs of points. If two coarse aggregate are to be combined with sand then the two C.A sizes to be combined using the % passing 20 mm sieve as a criterion. Its two sands are to be combined then 600 micron sieve should be taken as criterion.
Let us illustrate the procedure with the help of an example. Let the serve analysis of the material is given as shown in Table 20.30.
I.S. 383-1970 has given the limits of grading for all in aggregate and the range is shown in the following Table 20.31.
5. Now draw a horizontal line through 41% line parallel to x-axis.
6. Draw a vertical line through the point of inter-section of line joining the percentages of 4.75 mm line and horizontal line of 41% intersecting all lines as shown.
7. Measure the corresponding percentages indicated by these points of inter-section as shown in the Fig. 20.5. These will be the percentages of each fraction. These percentages are shown on the lines.
8. Now let us combine two fractions of coarse aggregate. In this case the percentage passing through 19:0 or (20) mm sieve size is taken as the criterion. The percentages passing each sieve are marked along the two opposite sides of the square as shown in Fig. 20.6 and the points corresponding to same sieve size are joined by straight lines Fig. 20.6.
Now a vertical line is drawn through the point where the line joining the 19.0 mm value intersect the horizontal line representing the correct percentage of aggregate smaller than 19.0 mm as in our case say it is 39%.
3. Mix Design by Indian Standard Method:
The bureau of Indian standards has recommended a procedure for mix design of concrete based on the experimental work carried out in the national laboratories. The mix design procedure is given in IS-10262- 1982. After that no revision has been done in this procedure, whereas IS 456-1968 has been revised in 2000. Hence IS 10262-1982 needs revision as the strength of cement available in the country has improved significantly.
Thus following changes need to be effected:
1. The 28 day strength of A, B, C, D, E & F category of cements needs to be revised.
2. The relation between the different strengths of cement and w/c ratio should be re-established.
3. The relation between 28 days compressive strength and w/c ratio should be extended upto a compressive strength of 80 MPa (800 kg/cm2), if the graph is to be used for high strength concrete.
4. As per the revised IS 456-2000 the degree of workability is expressed in terms of slump in place of compacting factor. This change needs new values of sand and water content to be used for normal concrete upto 35 MPa and higher strength Concrete above 35 MPa.
However in the absence of any revision in IS 10262-1982, the existing procedure of IS 10262 is described below step wise.
The IS recommendations for mix design include the design for nominal concrete mixes (non-air entrained) for both medium and high strength concrete.
The method of mix design consists of determining the followings:
(a) Water content
(b)Percentage of fine aggregate corresponding to the maximum nominal size of aggregate for the reference value of workability
(c) Water-cement ratio, and
(d) Grading of fine aggregate.
The water content and percentage of fine aggregate is then adjusted for any difference in workability. Finally the mass of ingredients per unit volume of concrete is calculated by absolute volume method. This method is applicable to both ordinary port-land and port-land pozzolana cements. The final mix proportions selected after trial mixes, may need minor adjustment. In case of fly ash cement concrete, water content may be reduced by about 3 to 5% and proportion of fine aggregate may be reduced by 2 to 4%.
4. American Concrete Institute Method of Mix Design:
Though ACI committee published its method of mix design in 1944 and almost all Indian multipurpose concrete dams have been designed using then prevalent ACI committee method of mix design. Since then many improvements have been incorporated in the original method. Here the latest method of concrete mix design based on ACI 211-1 of 1991 manual of concrete practice part-I recommendations is discussed.
The ACI committee has assumed the following basic assumptions:
1. Fresh concrete of a given slump and containing a reasonably well graded aggregate of given maximum size will have practically a constant water content, regardless of variation in w/c ratio and cement content which are inter related over a considerable range of practical proportions.
2. The optimum dry rodded volume of coarse aggregate per unit volume of concrete depends on its maximum size and the fineness modulus of the fine aggregate as shown in table 20.39 regard less of shape of particles. The effect of angularity is reflected in the void contents. Thus angular coarse aggregates require more mortar than rounded aggregates.
3. Irrespective of methods of compaction, even after complete compaction is done, a definite percentage of air remains in the concrete and is inversely proportional to the maximum size of the aggregate.
Procedure of Mix Design:
For the design of the mix, following data is required data to be collected:
(a) Fineness modulus of selected fine aggregate.
(b) Unit weighs of dry selected fine aggregate.
(c) Specific gravity of coarse and fine aggregate in saturated, surface dry conditions.
(d) Absorption of coarse and fine aggregates.
(e) Specific gravity of cement.
Note:
(a) The values given in the above table 20.39 are suitable for R.C.C. construction. For less workable concrete the values may be increased by 1.0%. For more workable concrete such as pumpable concrete the values may be reduced upto 1.0%.
(b) From specified minimum strength, estimate the average design strength either using standard deviation or using coefficient of variation.
(c) Find the w/c ratio for the given strength from the table 20.40 given below. Check the w/c from durability point of view from table 20.41. Adopt the lower of the two values.
Note:
The values are measured on standard cylinders. The values given are for a max. size of aggregate of 20 and 25 mm and ordinary port-land cement and for recommended percent of air entrained shown in Table 20.43.
(d) Decide max. size of aggregate to be used. Generally for R.C.C. works 20 mm and for pre-stressed concrete work 10 mm size aggregate is used.
(e) Decide workability in terms of slump for the job in hand from the following table 20.42.
(f) The total water required in concrete in kg/m3 is read from above table 20.43 for the max. size of aggregate and the given slump. Table 20.43 gives the approximate amount of accidentally entrapped air.
(g) The cement content required is calculated by dividing the amount of water required by the w/c ratio.
(h) The bulk value of dry rodded coarse aggregate per unit volume of concrete is selected from table 20.39 for the particular max size of coarse aggregate and fineness modulus of the fine aggregate.
(i) The weight of coarse aggregate per cubic metre of concrete is calculated by multiplying the bulk volume with bulk density.
(j) The solid volume of coarse aggregate in one cubic metre of concrete is calculated by knowing the specific gravity of coarse aggregate.
(k) Similarly the solid volume of cement, water and volume of air is calculated per cubic metre of concrete.
(l) The solid volume of sand is computed by subtracting the solid volume of cement, coarse aggregate, water and entrapped air from the total volume of concrete.
(m) The weight of fine aggregate is calculated by multiplying the solid volume of fine aggregate by specific gravity of fine aggregate.
Table 20.45 Required increases in strength (mean strength) for specified design strength when no tests records are available as per ACI 318-1989.
5. Rapid Method of Mix Design:
To estimate the preliminary water-cement ratio corresponding to the target mean strength a more realistic approach will be to correlate it with the 28 days compressive strength of cement. The characteristic strength is found to be better related to characteristic 28 days strength of cement rather than at earlier ages. Thus this approach will need 28 days for determining the characteristic strength of cement and next 28 days for trial mixes strength of concrete. The 28 day strength of cement can be taken as that given by curves of Fig. 20.8.
The 28 days or 56 days is too long a period for a contractor to wait for the results of the trial mix. There is a tendency to use mix directly without trying trial mixes. To reduce the time required for trial mixes, the cement Research Institute of India (CRI) has developed a method called rapid method, by which the compressive strengths of cement and concrete are obtained by using accelerated curing method as discussed in IS 9013-1978. This method reduces the period for finding the strength of trial mixes from 28 days to 3 days only.
The 28 days compressive strength of concrete is found to be statistically significantly related to its accelerated strength. Thus the trial mixes are correlated to the target mean accelerated strength rather than to the target mean 28 days strength, with the help of correlation between the two. A typical relation is shown in Fig. 20.16.
This correlation is found to be independent of type or characteristics of cement used i.e. the correlation is not affected by the type of cement used, presumably due to the fact that they affect both the accelerated and normal 28 days strength of concrete in a proportionate manner, so that the effect is neutralised when their ratios are compared. More over for individual application such correlations can be established for the type of the materials and mix proportions to be used.
On the other hand, results of accelerated compressive strength tests on standard cement mortar as per IS 4932-1968 have not been found reliable. This problem has been overcome by testing cement also in an accelerated manner and determining its accelerated strength.
The reference concrete mix or accelerated strength of concrete mix has w/c ratio as 0.35 and workability very low with slump 0 to 10 or compacting factor 0.8 with the available cement i.e. (cement in hand).
The nominal maximum size of natural crushed aggregate should be 10 mm and fine aggregate should conform to zone II of table 4 of IS-383-1970.
The typical composition of such as reference concrete mix per cubic metre of concrete is as follows:
Cement = 570 kg
Fine aggregate = 400 kg
Coarse aggregate = 1178 kg
Water = 200 kg
or Cement : F.A. : C.A
1 : 0.7 : 2.07
Water/cement ratio = 0.35
Using the above proportions, 150 mm cube specimens of reference concrete are prepared with the available cement and cured by boiled water method. The accelerated strength is determined. Corresponding to this accelerated strength of the reference concrete, the water/cement ratio is determined from Fig. 20.17.
Using this water/cement ratio, the accelerated strength of the trial mix is compared with the characteristic target strength using the correlation between accelerated and normal 28 day strength of concrete.
Step by Step Procedure:
1. The accelerated strength of standard or reference concrete is determined using the available cement. For determining the standard concrete strength 150 mm cubes are prepared from the above mentioned proportions and cured by boiling water method in accordance to IS 9013-1978.
2. For the required target mean strength of normal concrete, the water/cement ratio is determined by using the corresponding accelerated strength of standard concrete obtained in step (i).
3. The mix proportions are determined by any of the accepted methods of mix design and checked for workability of fresh concrete for the desired value.
4. W/c ratio for the required target strength of the mix is determined from Fig. 20.17.
5. The accelerated compressive strength of the trial mix is determined by preparing 150 mm cubes and curing by boiling water method as per IS 9013-1978.
6. The 28 day compressive strength of normal concrete is determined from the accelerated strength obtained in step (4) above by the following relations-
F28 = 8.25 + 1.64 Fa …(1) For boiling water (100°C) curing
F28 = 13 + Fa …(2) For warm water (55 ± 1°C) curing
where,
F28 = 28 day compressive strength of normal concrete
Fa = Accelerated strength of concrete.
The curve is shown in Fig. 20.18
To Judge the suitability of the trial mix, the compressive strength, so obtained is compared with the target mean strength.
The accelerated curing method as per IS 9013-1978 is given below:
1. Boiling Water Method:
(a) Specimens are cured at 27 ± 2°C for 23 ± 1/4 hours under standard moist conditions.
(b) At the end of this period the specimens are cured in boiling water (100°C) for 3½ hours ± 5 minutes.
(c) Specimens are cooled to a normal temperature of 27 ± 2°C in two hours before testing.
2. Warm Water Methods:
(a) 1½ to 3½ hours after casting, the specimens are immersed in water at a temperature of (55 ± 1°C) and cured for 20 hours ± 10 min.
(b) The specimen are de-moulded and cooled at 27 ± 2°C for one hour before testing.
The average correlation is shown in Fig. 20.19 which is generally used for different concrete.
A correlation between 28 days strength and accelerated strength of cement is established as shown in Fig. 20.19 using all types of cements available in the country and different grades of concrete using boiling water curing method.
Example 5:
Design a mix for 28 days strength of 35 MPa if accelerated strength of standard concrete is 24.0 MPa.
Solution:
1. Find out the w/c ratio from Fig. 20.17. From the curve D, for 28 days strength of 35 MPa, the w/c = 0.45.
2. From this w/c, find out the remaining proportions from any accepted method and check the workability of fresh concrete for the desired value.
3. Find out the accelerated compressive strength of the trial mix.
4. Find out the 28 days compressive strength from the accelerated strength determined in step 3 by using the relation from Fig. 20.17 and compare it with the target strength.