MIX DESIGN OF CONCRETE

WHAT IS MIX DESIGN ?The process of selecting suitable ingredients of concrete and determining their relative amounts with the objective of producing a concrete of the required, strength, durability, and workability as economically as possible “is termed the concrete mix design.”

NOMINAL MIXES A nominal mix concrete is a prescribed concrete It means the proportions of the ingredients are specified by the engineer usually without testing the materialsA 1:2:4 mix concrete means a concrete consisting of 1 part cement. 2 parts fine aggregate and 4 parts coarse aggregate by volumeThe water cement ratio may or may not be specified There is no guarantee that a nominal mix will give a desired strength

STANDARD MIXES The nominal mixes of fixed cement-aggregate ratio (by volume) vary widely in strength and may result in under- or over-rich mixes. For this reason, the minimum compressive strength has been included in many specifications. These mixes are termed standard mixes.M10, M15, M20, M25, M30, M35 and M40. In this designation the letter M refers to the mix and the number to the specified 28 day cube strength of mix in N/mm2. The mixes of grades M10, M15, M20 and M25 correspond approximately to the mix proportions (1:3:6), (1:2:4), (1:1.5:3) and (1:1:2) respectively.

VARIABLES IN PROPORTIONING Water-Cement ratioCement content or cement-aggregate ratioGradation of the aggregatesconsistency

PROBABILISTIC CONCEPT IN MIX DESIGN APPROACH :It will be very costly to have very rigid criteria to reject the structure on the basis of a single or a few standard samples. The basis of acceptance of a sample is that a reasonable control of concrete work can be provided, by ensuring that the probability of test result falling below the design strength is not more than a specified tolerance level.If a number of cube test results are plotted on histogram, the results are found so follow a bell shaped curve known as "Normal Distribution Curve".

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DOE( DEPARTMENT OF ENVIRONMENT) OR BRITISH

MIX DESIGN METHOD

STEP 1: FIND THE TARGET MEAN STRENGTH FROM THE SPECIFIED CHARACTERISTIC STRENGTH = + ksWhere = the target mean strength

And = the specified characteristic strengthK= risk factorS = standard deviationk for 10% defectives = 1.28k for 5% defectives = 1.64 (recommended )k for 2.5% defectives = 1.96k for 1% defectives = 2.33

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EXAMPLE For the 5 % defectives k = 1.64, and hence formula becomes = + 1.64sfigure1 relates to a concrete having a specified characteristic strength of 30 N /m m 2 and a standard deviation o f 6.1 N /m m 2. Hence:Target mean strength = 30 + (1.64 x 6.1)= 30 + 10 = 40 N /m m 2 as shown Go back

STEP 2: CALCULATE THE WATER CEMENT RATIO Table 1 gives the approximate compressive strength of concretes made with a free w/c ratio of 0.50.

table 1

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CONTINUE… > Using this table1 find out the 28 days strength for the approximate type of cement and types of C.A.(course aggregate )

> Mark a point on the “Y” axis in figure 2 equal to the compressive strength read form table 1 which is at a water cement ratio of 0.50.

> Through this intersection point, draw a parallel dotted curve nearest to the intersection point. Using this curve we read the water cement ratio as against target mean strength.

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FIGURE2

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EXAMPLEAs an example, referring to Table 1 for sulphate resisting cement, crushed aggregate, approximate compressive strength, with a free W/C ratio of 0.5 at 28 days is 49 MPa. In figure2 intersection point of 49 MPa and W/C ratio of 0.50 is marked. A parallel dotted curve is drawn to the neighboring curve. Water/Cement ratio is read off on this new dotted curve for any target mean strength. This Water/Cement ratio must be compared to the maximum W/C requirement for durability (refer Table D1 or Table D2, depending upon whether it is RCC or plain concrete).And lower of the two is taken Go back

STEP 3 Next decide water content for the required workability expressed in slump or vebe time , taking into consideration the size of the aggregate and its type from table 3.

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STEP 4: FIND THE CEMENT CONTENT KNOWING THE WATER/CEMENT RATIO AND WATER CONTENT.

Cement content = The cement content so calculated should be compared with the minimum cement content specified from the durability consideration (Table D1 )and higher of the two should be adopted. Sometime maximum cement content is also specified. The calculated cement content must be less than the specified maximum cement content

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STEP 5: NEXT FIND OUT THE TOTAL AGGREGATE CONTENTThis requires an estimate of the wet density of the fully compacted concrete. This can be found out from Figure 3 for approximate water content and specific gravity of aggregate. If sp. gr. is unknown, the value of 2.6 for uncrushed aggregate and 2.7 for crushed aggregate can be assumed. The aggregate content is obtained by

Total aggregate content = wet density of concrete – the cement content – the free water content

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FIGURE 3 Go back

STEP 6: THEN, PROPORTION OF FINE AGGREGATE IS DETERMINED IN THE TOTAL AGGREGATE USING FIGURE4

The parameters involved in Fig. 4 are maximum size of coarse aggregate, the level of workability(slump, vebe time), the water/cement ratio, and the grading of the fine aggregate (defined by its percentage passing a 600 μm sieve.Now, fine aggregate content = total aggregate content * proportion of fines

And coarse aggregate content = total aggregate content – fine aggregate content

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Figure 4

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Figure 4 continued

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Figure 4 continued

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EXAMPLE Example—DOE Method Design a concrete mix for a reinforced concrete work which will be exposed to the moderate condition. The concrete is to be designed for a mean compressive strength of 30MPa at the age of 28 days. A requirement off 25 mm cover is prescribed. Maximum size of aggregate is 20 mm uncrushed aggregate will be used. Sieve analysis shows that 50% passes through 600 μ Sieve. The bulk specific gravity of aggregate is found to be 2.65(by DOE or British method)

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STEP 1 : TARGET STRENGTH = + 1.64s(Where s =5 N/mm² is standard deviation for good quality control and k = 1.64 ) छलफलHere = 30 Mpa (mean compressive strength )

Example 1

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STEP 2 WATER CONTENT Referring to Table1, for OPC, uncrushed aggregate, for W/C ratio of 0.5, 28 days compressive strength is 42MPa.

In Fig. 2 find an intersection point for 42MPa and 0.5 W/C ratio. Draw a dotted line curve parallel to the neighboring curve. From this curve read off the W/C ratio for a target mean strength of 30MPa.

The Water/cement ratio is = 0.62 (Check this W/C ratio from durability consideration from Table D1. The maximum W/C ratio permitted is 0.50.)

Adopt the lower of the two (adopt 0.5)

Example 1

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STEP 3 Decide the water content for slump of 75 mm (assumed) 20 mm uncrushed aggregate from Table 3.

The water content is 195 kg/m3

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Example 1

STEP4 With W/C of 0.5 and water content of 195 kg/m3, the cement content is

= 390 kg/m3

(Check this cement content with that of durability requirements given in TableD1) Minimum cement content from durability point of view is 350 kg/m3.

Adopt greater of the two Therefore adopt cement content = 390 kg/m3

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Example 1

STEP5 Find out the density of fresh concrete from Fig.3. for water content of 195 kg/m3

20 mm uncrushed aggregate ofsp.gr. 2.65 The wet density = 2400 kg/m3

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Example 1

STEP6 find the weight of total aggregate 2400 - (195 +390) = 1815 kg/m3

Next, find the percentage of fine aggregate from Fig.4. For 20 mm aggregate size, W/C ratio of 0.50, Slump of 75 mm, for 50% fines passing through 600 μ sieve, the percentage of FA. = 40 percent

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Example 1

CONT… Weight of F A. = 1815 x40/100 = 726 kg/m3 .•. Weight of C.A.= 1815-726 = 1089 kg/m3 Estimated quantities in kg/m3 : Cement = 390 FA. = 726 C.A. = 1089 Water = 195 Wet density = 2400 The above quantities are required to be adjusted for the field moisture content and absorption characteristics of aggregates

Lastly trial mixes are made to arrive at the correct quality of concrete. Go back

Example 1

5.3.2. IS METHOD OF MIX DESIGN : IS 456:2000 AND IS 10262:2009

* DATA FOR MIX PROPORTIONINGThe following data are required for mix proportioning of a particular grade of concrete:Grade designation;Type of cement;Maximum nominal size of aggregate;Minimum cement content;Maximum water-cement ratio;Workability;Exposure conditions as per Table 4 and Table5 of IS 456;Maximum temperature of concrete at the time of placing;Method of transporting and placing;Early age strength requirements, if required;Type of aggregate; Maximum cement content; and Whether an admixture shall or shall not be used and the type of admixture and the condition of use.

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STEP1: TARGET MEAN STRENGTH = + 1·65 s Where = characteristic compressive strength at 28 days. S = standard deviation The value of the standard deviation has to be worked out from the trials conducted. Where sufficient test results for a particular grade of concrete is not available the value of standard deviation can be adopted from Table 1 to facilitate initial mix design. As soon as enough test results become available, standard deviation should be worked out and the mix design is modified accordingly.

Design steps

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TABLE 1 : STANDARD DEVIATION

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STEP2 : SELECTION OF WATER CEMENT RATIOWater cement ratio may be fixed by experience or that of used in the neighboring project. We can use the generalized relationship established and given in text books, one such graph is shownThe water cement ratio selected by whatever method should be checked against the limiting water cement ratio for durability as per table D1.Go back

STEP 3 : WATER CONTENT

The water content in Table 2 is for angular coarse aggregate and for 25 to 50 mm slump range. The water estimate in Table 2 can be reduced by approximately 10 kg for sub-angular aggregates, 20 kg for gravel with some crushed particles and 25 kg for rounded gravel to produce same workability.

For the desired workability (other than 25 to 50 mm slump range), the required water content may be established by trial or an increase by about 3 percent for every additional 25 mm slump or alternatively by use of chemical admixtures conforming to IS 9103. Water reducing admixtures or superplasticizing admixtures usually decrease water content by 5 to 10 percent and 20 percent and above respectively at appropriate dosages Go back

TABLE 2

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STEP 4 : CALCULATION OF CEMENTITIOUS MATERIAL CONTENT

It can be determined from the free water cement ratio and quantity of water per unit volume of concrete

The cementitious material so calculated should be checked for durability requirements (table D1 )greater of the two value is adopted.

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STEP 5 :

Approximate values for this aggregate volume are given in Table 3 for a water-cement ratio of 0.5, which may be suitably adjusted for other water- cement ratios. For every decrease of w\c ratio by 0.05 the coarse aggregate volume may be increased by 1.0 percent to reduce the sand content and for every increase of w\c ratio by 0.05 the coarse aggregate volume may be decreases by 1.0 percent to increase the sand content.

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STEP 6

With the completion of step 5, all the ingredients have been estimated except the coarse and fine aggregate content. As a next step, find out the absolute volume of all the so far known ingredients. Deduct the sum of all the known absolute volume from unit volume (1m3), the result will be the absolute volume of coarse and fine aggregates put together.

We know the volume of coarse aggregate and hence volume of fine aggregate can be calculated.

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2.ILLUSTRATIVE EXAMPLE ON CONCRETE MIX PROPORTIONING

Design a concrete mix for M45 grade of concrete with following data

a) Grade designation:M 45 b) Type of cement : OPC 43 grade conforming to IS 8112

c) Maximum nominal size of aggregate: 20 mm

d) Minimum cement content: 320 kg/m3 e) Maximum water-cement ratio:0.45 0 Workability: 125 mm (slump) g) Exposure condition: Severe (for reinforced concrete)

h) Method of concrete placing: Pumping j) Degree of supervision : Good k) Type of aggregate :Crushed angular aggregate

l) Superplasticizer will be used m) Specific gravity of; 1) Coarse aggregate:2.80 2) Fine aggregate:2.70 n) Water absorption: 1) Coarse aggregate:0.5 percent 2) Fine aggregate:1.0 percent o) Free (surface) moisture:

Coarse aggregate Fine aggregate

p) Grading of course aggregate conforming to table 2 of IS 383

q) Grading of fine aggregate conforming to grading zone IIGo back

1. TARGET STRENGTH FOR MIX PROPORTIONING = + 1.65S From Table 1, standard deviation, s= 5 N/mm2. Therefore, target strength = 45 + 1.65 x 5 = 53.25 N/mm2.

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Example 2

2. SELECTION OF WATER-CEMENT RATIO From Table D1 of IS 456, maximum water-cement ratio = 0.45. Based on experience, adopt water-cement ratio as 0.42. 0.402< 0.45, hence O.K.

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Example 2

3. SELECTION OF WATER CONTENT From Table 2, maximum water content =186 liter (for 25 to 50 mm slump range) for 20 mm aggregate

Estimated water content for 120 mm slump = 186 + x 186* =203 liter (or simply increase 3% for every 25 mm slump over above 50mm slump .i.e. = 186+186*3%+186*3%+186*3%=203 liter)

Superplasticizer is assumed to reduce water content of 25 percent . Hence, the arrived water content = 203*75% = 152 liter

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Example 2

STEP 4 : CALCULATION OF CEMENT CONTENT Water-cement ratio = 0.42 Water used = 152 liter Cement content = = 362 kg/m3 From Table D1 ( check for durability) minimum cement content for ‘severe’ exposure condition = 320 kg/m3 350 kg/m3 > 320 kg/m3, hence, O.K.

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Example 2

STEP 5 : CALCULATION OF COARSE AND FINE AGGREGATE CONTENT

From Table 3, volume of coarse aggregate corresponding to 20 mm size aggregate and fine aggregate (Zone II) for water-cement ratio of 0.50 = 0.62

In the present case water-cement ratio is 0.42. As the water-cement ratio is lower by 0.08, the proportion of volume of coarse aggregate is increased by 0.016 (at the rate of 0.01 for every decrease in water cement ratio of 0.05: increase in proportion =). Therefore, corrected proportion of volume of coarse aggregate = 0.62+0.016=0.636

Since it is angular aggregate and the concrete is Pumpable , these values should be reduced by 10 percent.

Therefore, volume of coarse aggregate = 0.636 x 0.9 = 0.572 say 0.57. Volume of fine aggregate content = 1 - 0.57 = 0.43 Go back

Example 2

STEP 6 : CALCULATION OF MIX PROPORTIONS

The mix calculations per unit volume of concrete shall be as follows: Volume of concrete = 1 Absolute volume of cement (mass of cement)/(specific gravity of cement)*1/1000 0.115 Volume of water = 152 liter = 0.152 Volume of chemical admixture =(1.2*362)/(100*1.1)*1/1000 =0.004

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Example 2

Specific gravity =Density of cement = ?Volume of cement =

FINALLY Mix proportions are: Cement 362 kg / Water 152 kg/ FA 846 kg/ CA 1163 kg/ Chemical admixture 4 kg/ Water/cement ratio 0.42 Site correction is also required. Go back

Example 2