Concrete Mix Design

Syllabus
Concrete Mix Design
• Mix Design for compressive strength by I.S. Method, Road
Note Method, British method, Mix Design for flexural
Strength

Concrete Mix Design
• Concrete mix design may be defines as the art of selecting
suitable ingredients of concrete and determining their
relative proportions with the object of producing concrete of
certain minimum strength & durability as economically as
possible.

Objectives of Mix Design
• The purpose of concrete mix design is to ensure the most optimum
proportions of the constituent materials to fulfill the requirement of
the structure being built. Mix design should ensure following
objectives.
• To achieve the designed/ desired workability in the plastic stage
• To achieve the desired minimum strength in the hardened stage
• To achieve the desired durability in the given environment
conditions
• To produce concrete as economically as possible.

Basic Considerations
• The following point must be considered while designing concrete
mixes
• Cost
• Specification
• Workability
• Strength and Durability

Cost
• The cost of concrete is made up of
• Material Cost
• Equipment Cost
• Labour Cost
• The variation in the cost of materials arises from the fact that cement is
several times costlier than aggregates. So it is natural in mix design to aim
at as lean a mix as possible. Therefore, all possible steps should be taken to
reduce the cement content of a concrete mixtures without sacrificing the
desirable properties of concrete such as strength and durability.

Specifications
• The following point may be kept in mind while designing concrete
mixes
• Minimum Compressive Strength required
• Minimum water/ cement ratio
• Maximum cement content to avoid shrinkage cracks
• Maximum aggregate / cement ratio
• Maximum density of concrete in case of gravity dams

Workability
• The following points related to workability shall be kept in mind while
designing concrete mixes.
• The consistency of concrete should no more than that necessary for
placing, compacting and finishing.
• For concrete mixes required high consistency at the time of placing, the
use of water-reducing and set-retarding admixtures should be used rather
than the addition of more water
• Wherever possible, the cohesiveness and finishibility of concrete should be
improved by increasing sand/ aggregate ratio than by increasing the
proportion of the fine particles in the sand.

Strength and Durability
Strength and durability
• Strength and durability require lower w/c ratio. It is usually achieved
not by increasing the cement content, but by lowering the water at
given cement content. Water demand can by lowered by throughout
control of the aggregate grading and by using water reducing
admixtures.

Grade of Concrete
• The concrete shall be in grades designated
Group Grade designation Characteristics compressive strength
of 150 mm cube at 28 days, N/mm2
Ordinary Concrete M10
M15
M20
10
15
20
Standard Concrete M25
M30
M35
M40
M45
M50
M55
25
30
35
40
45
50
55
High Strength Concrete M60
M65
M70
M75
M80
60
65
70
75
80

What is M 20 ?
• M refers to Mix
• 20 refers to characteristic compressive strength of 150 mm
cube at 28 days in N/mm2
• The minimum Grade of Plain Concrete (PCC) shall be 15
N/mm2
• The minimum grade of reinforced Concrete ( RCC) shall be
20 N/mm2

Nominal Concrete Mixes
and
Design mix concrete
Nominal Mix Concrete
• The wide use of concrete as construction materials has led to
the use of mixes of fixed proportion, which ensures
adequate strength. These mixes are called nominal mixes.
• They offer simplicity and Under normal circumstances, has
margin of strength above that specified.
• Nominal mix concrete may be used for concrete of grades
M5, M 7.5, M10, M15 and M20.

Nominal Concrete Mixes
and
Design mix concrete

Proportions of Ingredients in Nominal Mixes
• The proportions of materials for nominal mix shall be in accordance
Grade Proportions
C: FA: CA
M5 1: 5:10
M 7.5 1:4:8
M 10 1:3:6
M 15 1:2:4
M 20 1:1.5:3

Design Mix Concrete
• The concrete mix produced under quality control keeping in view
the strength, durability, and workability is called the design Mix.
• Others factors like compaction equipment's available, curing method
adopted, type of cement, quality of fine and coarse aggregate etc.
have to be kept in mind before arriving at the mix proportion.
• The design mix or controlled mix is being used more and more in
variety of important structures, because of better strength, reduced
variability, leaner mixed with consequent economy, as well as
greater assurance of the resultant quality.

Factors Influencing Choice of Mix Design
• According to IS 456:2000 and IS 1343:1980 the important influencing the
design of concrete mix are
• Grade of Concrete
• Type of Cement
• Maximum nominal Size of Aggregate
• Grading of Combined aggregate
• Maximum Water/ Cement Ratio
• Workability
• Durability
• Quality Control.

Grade of Concrete
• The grade of concrete gives characteristic compressive
strength of concrete. It is one of the important factor
influencing the mix design
• The grade M 20 denotes characteristic compressive strength
fck of 20 N/mm2. Depending upon the degree of control
available at site, the concrete mix is to be designed for a
target mean compressive strength (fck) applying suitable
standard deviation.

Type of Cement
• The rate of development of strength of concrete is
influenced by the type of cement.
• The higher the strength of cement used in concrete, lesser
will be the cement content. The use of 43 grade and 53
grade of cement, gives saving in cement consumption as
much as 15 % and 25 % respectively, as compared to 33
grade of cement. For concrete of grade M25 it is advisable to
use 43 and 53 grade of cement.

Maximum Nominal Size of Aggregates
• The maximum size of C.A is determined by sieve analysis. It is designated by the
sieve size higher than larger size on which 15 % or more of the aggregate is
retained. The maximum nominal size of C.A. should not be more than one-forth
of minimum thickness of the member.
• For heavily reinforced concrete members as in the case of ribs of main beams,
the nominal maximum size of the aggregate should usually be restricted to sum
less than the minimum clear distance between the main bars or 5 mm less the
minimum cover to the reinforcement, whoever is smaller.
• The workability of concrete increases with an increase in the maximum size of
aggregate. But the smaller size of aggregates provide larger surface area for
bonding with the mortar matrix which gives higher strength.

Grading of Combined Aggregates
• The relative proportions of the fine and coarse aggregate in
a concrete mix is one of the important factors affecting the
strength of concrete.
• For dense concrete, it is essential that the fine and coarse
aggregate be well graded. In the case when the aggregate
available from natural sources do not confirm to the
specified grading, the proportioning of two or more
aggregate become essential

Grading of Combined Aggregates

Maximum Water/ Cement Ratio
• Abram’s water/Cement ratio states that for any given condition of
test, the strength of a workability concrete mix is dependent only on
water/cement ratio. The lower the water/Cement ratio, the greater is
the compressive strength
Workability
• Workability of fresh concrete determines the case with which a
concrete mixture can be mixed, transported, placed, compacted and
finished without harmful segregation and bleeding.

Durability
• Durability require low water/Cement ratio. It is usually
achieved not by increasing the cement content, but by
lowering the water demand at a given cement content.
• Water demand can be lowered by through control of the
aggregate grading and by using water reducing admixtures

Method of Concrete Mix Design
• Some of the commonly used mix design methods are
• I.S. Method
• A.C.I method
• Road Note 4 method ( U.K. Method)
• IRC 44 method
• Arbitrary method
• Maximum Density method
• Fineness modulus method
• Surface area Method
• Nix design for high strength Concrete
• Mix design for pumpable Concrete
• DOE (British) Mix design method

IS Method of Mix Design
• The Bureau of Indian Standards, recommended a set of procedure for
design of concrete mix. The procedure is based on the research work
carried out at national laboratories.
• Data for mix design
• The following basic data are required to be specified for design a concrete
mix
• Characteristic Compressive strength only a few specified proportions of
test results are expected to fall of concrete at 28 days (fck)
• Degree of workability desired
• Limitation on water/Cement Ratio with the minimum cement to ensure
adequate durability
• Type and maximum size of aggregate to be used.
• Standard deviations of compressive strength of concrete.

• Target Strength for Mix Design
• The target average compressive strength (fck) of concrete at 28 days is
given by
• Fck= f ck + t.s
Where,
• Fck= target average compressive strength at 28 days
• F ck= characteristics compressive strength at 28 days
• s= Standard deviation
• t= a stastical value, depending upon the accepted proportion of low results
and the number of tests.

• According to Is 456: 2000 and IS 1343:1980 te
characteristic strength is defined as the value below which
not more than 5 percent of results are expected to fall. In
such cases the above equation reduced to
• Fck= fck + 1.65 s
• The value of standard deviation is obtained from the table

Step-II
Selection of Water –Cement Ratio
• Since different cements and aggregates of different maximum sizes,
grading, surface texture shape and other characteristics may produce
concrete of different compressive strength for the same free water
cement ratio, the relationship between strength and free water
cement ratio should preferable be established for the material
actually to be used. In the absence of such data, the preliminary free
water-cement ratio corresponding to the target strength at 28 days
may be selected from the relationship shown below

• Alternatively, the preliminary free water cement ratio by
mass corresponding to the average strength may be selected
from the relationship shown below using the curve
corresponding to the 28 days cement strength to be used for
the purpose. However, this will need 28 days for testing of
cement.

• The free water-cement ratio thus selected should be checked
against limiting water-cement ratio for the requirements of
durability as per table 5.4 and the lower of the two values
should be adopted.

Step 3 Estimation of Air Content
• Approximate amount of entrapped air to be expected in normal
concrete is given in table 9.6
Nominal Maximum Size of Aggregates Entrapped Air, as percentage of volume
of concrete
10 3 %
20 2 %
40 1 %

Selection of Water Content and fine to total aggregate ratio
• For the desired workability the quantity of mixing water per unit
volume of concrete and the ratio of fine aggregate (sand) to total
aggregate by absolute volume are to be estimated from table below as
applicable. Depending upon the nominal maximum size and type of
aggregate.

• Approximate Sand and water Content per Cubic Metre of Concrete
for Grades up to M 35 W/C = 0.6 Workability= 0.8 C.F
Nominal Maximum size
of aggregate (mm)
Water Content per
cubic metre of concrete
(kg)
Sand as percentage of
total aggregate by
absolute volume
10 208 40
20 186 35
40 165 30

• Approximate Sand and Water Content per cubic metre of concrete
for grades above M 35 W/C = 0.35 Workability= 0.8 C.F.
Nominal Maximum size
of Aggregates
Water Content per cubic
metre of concrete (kg)
Sand as percentage total
aggregate by absolute
volume of (%)
10 200 28
20 180 25

• Adjustment of values in water content and sand percentage for other
conditions
Change in Condition Adjustment Required
Water Content Percentage sand in total aggregate
For sand confirming to
grading Zones I , III
and IV
0 + 1.5 percent for zone I
-1.5 percent for zone III
-3.0 for zone IV
Increase or decrease in
values of compacting
factor by 0.1
± 3 % 0
Each 0.05 increase or
decrease in free water
cement ratio
0 ± 1 %
-15 kg/m 3 -7 %
For rounded
aggregates

Calculation of Cement Content
• The cement content per unit volume of concrete may be
calculated from the free water-cement ratio obtained in
step- 2, and the quantity of water per unit volume of
concrete obtained in step-4
• The cement content so obtained should be checked against
the minimum cement content for the requirement of
durability as per table 5 IS 456:2000 and the greater of the
two value is adopted.

Step -6 Calculation of Aggregate Content
• With the quantities of water and cement per unit volume of concrete and
the ratio of fine to total aggregate already determined, the total aggregate
content per unit volume of concrete may be calculated from the following
equations
• V= [ W + C + 1 x fa ] x 1 for fine aggregate …………………………1
Sc p Sfa 1000
And
V = [ W + C + 1 x Ca ] x 1 for coarse aggregate …………..2
Sc (1-p) Sca 1000

Step -6 Calculation of Aggregate Content
Where,
• V= Absolute volume of fresh concrete (m3)
• W= Mass of Water (kg) per m3 of concrete
• C= Mass of Cement (Kg) per m3 of concrete
• Sc= Specific gravity of cement say 3.15
• P= ratio of fine aggregate to total aggregate by absolute volume
• Fa and Ca = Total masses of fine aggregate and coarse aggregate (kg) / m3
of concrete mass respectively
• Sfa, Sca= Specific gravities of saturated surface dry fine aggregate and
coarse aggregate respectively
• Normally Sfa= 2.6 and Sca= 2.7

Trial Mixes
• The Calculated mix proportions shall be checked by means
of trial batches. The quantity of material should be sufficient
for at least three 150 mm size cube concrete specimens

Example
• Using I.S Method design a concrete mix for reinforced concrete
structure for the following requirement.
• Design data
• Characteristic compressive strength= 20 N/mm 2
• Maximum size of aggregates= 20 mm (angular)
• Degree of workability= 0.9 CF
• Degree of quality Control= Good
• Type of exposure= Mild

Example
• Test data for Material
• Cement used= Ordinary Portland cement of grade 43 with 28 days
strength 51 N/mm2
• SG= 3.15
• Bulk Density = 1450 kg/m3
• Aggregate Fine Aggregate Coarse Aggregate
• SG 2.66 2.75
• Bulk Density 1700 1800
• Water absorption 1 0.5
• Free Moisture 2 Nil

Example
Step-I Target Mean Strength
• Fck= fck + ts
• fck= 20 N/mm2
• T= 1.65
• S= 4 from table 9.5 for M 20
• Therefore
• Fck= 20 + 1.65 x 4
• = 26.6 N/mm2 (Mpa)

Example
Step-II
• Selection of Water Cement Ratio
• From the fig the free water cement ratio required for the target mean
strength of 26.6 N/ mm2 is 0.5
• From fig, for 28 days strength of cement 51 N/mm2, for curve D the
free water cement ratio is 0.52
• From table the maximum free water cement ratio for mild exposure
is 0.55
• Hence the free water cement ratio is taken as the minimum of above
three values i.e. w/c = 0.5

Example
Step –III
• Estimation of Air Content
• For maximum Size of aggregate of 20 mm, the air content is taken as
2 %

Example
Step-4 Selection of water and Sand Content
• From table 9.7 for 20 mm nominal maximum size aggregate and
sand confirming to grading zone –II water content per cubic metre
of concrete = 186 kg and sand content as percentage of total
aggregate by absolute volume= 35 %
• Water= 186 kg/m3 of concrete
• Sand= 35 % of total aggregate by absolute volume

Example
• For change in values in water cement ratio, compaction factor and
sand belonging to zone III the following adjustments required.
Change in Condition Water Content Percentage Sand in
total aggregate
For Decrease in water cement ratio
(0.6-0.5) that is 0.1
0.1 x 1 = 2.0
0.05
0 -2.0
For increase in compacting factor (0.9 -
0.8) = 0.1
0.1 x 3 = 3
0.1
+ 3 0
For Sand conforming to Zone III 0 -1.5
+3 -3.5

Example
• Required Water Content = 186 + ( 186 x 3 / 100)
• = 186 + 5.58
• = 191.6 lit /m3
= required sand content as percentage of total aggregate by absolute
volume= 35 – 3.5
= 31.5 %

Example
Determination of Cement Content
• Water Cement ratio= 0.5
• Water = 191.6 lit= 191.6 kg
• Therefore W/c = 0.5
• 191.6 = 0.5
• C
• C=383.4 kg/m3
• = 383kg/m3 > 300 kg / m3 therefore O.K.

Example
Determination of fine and coarse Aggregates
• Consider volume of Concrete= 1 m3
• But entrapped air in wet concrete = 2 %
• Therefore volume of fresh concrete= 1 – 2
100
1- 0.02
V= 0.98 m3

Example
• With the quantities of water and cement per unit volume of concrete and
the ratio of fine to total aggregate already determined, the total aggregate
content per unit volume of concrete may be calculated from the following
equations
• V= [ W + C + 1 x fa ] x 1 for fine aggregate ………………1
Sc p Sfa 1000
0.98 = [ 191.6 + 383 + 1 + fa ] x 1
3.15 0.315 2.66 1000
980 = 313.187 + 1.19 fa
fa= 558.75 kg mass of F.A

Example
And
V = [ W + C + 1 x Ca ] x 1 for coarse aggregate …………..2
Sc (1-p) Sca 1000
0.98 = [ 191.6 + 383 x 1 x Ca ] x 1
3.15 (1-0.315) 2.75 1000
980 = 313.187 + 0.5308 Ca
Ca= 1256.24 kg mass of C.A

Example
Water Cement F.A C.A
191.6 li 383 kg 558.75 kg 1256.24 kg
0.5 1 1.46 3.28
383 = 0.264 m 3
1450
558.75 = 0.328 m 3
1700
1256.24 = 0.698 m 3
1800
0.5 1.0 1.242 2.644

Example
25 li 50 kg 73 kg 164 kg

Example
• Design a Concrete mix for M 25 grade as per IS 10262 for the
following data:
• Characteristic Compressive Strength in the field at 28 days 25
N/mm2
• Maximum Size of Aggregate= 20 mm
• Degree of Workability 0.9 CF
• Degree of Quality Control= Good
• Type of Exposure = Moderate

Example
Test data for Material
• Cement Used : Ordinary Portland Cement of Grade 33 satisfying the requirement of IS: 269-1989
• Specific Gravity of Cement: 3.15
• Specific Gravity;
• Coarse Aggregate=2.65
• Fine Aggregate= 2.6
• Water absorption
• Coarse Aggregate 0.6 %
• Fine aggregate= 1.2 %
• Free moisture
• Coarse aggregate Nil
• Fine aggregate 2 %
• CA conform to table 2 of IS 383-1970 FA is natural river Sand Confirming to Zone I of Table 383-1970

Example
Step-I
• Target mean Strength of Concrete
• Fck= fck + ts
• fck= 25 N/mm2
• T= 1.65 from table 9.4
• S= 4.0 from table 9.5 for M 25 grade of concrete
• Fck= 25 + 1.65 x 4
• = 31.6 N/mm2

Example
Step-2
• Selection of Water-Cement Ratio
• From fig 9.1 the free water cement ratio required for the target mean
strength of 31.6 N/mm 2 is 0.44
• Now, from table 5.4 the maximum free water cement ratio for moderate
exposure is 0.5
• Hence, the free water cement ratio is taken as the minimum of above two
value i.e
• W= 0.44
C

Example
Step III Estimation of air Content
• For maximum Size of Aggregate of 20 mm, the air content is taken as
2.0 %

Example
Step-4
• Selection of Water and Sand Content
• From table 9.7 for 20 mm nominal maximum size aggregates and
sand confirming to grading Zone-II, water content per cubic metre
of concrete = 186 kg and sand content as percentage of total
aggregate by absolute volume = 35 % i.e.
• Water = 186 kg/m3
• Sand = 35 % of total aggregate by absolute Volume.

Example
• For Change in values in water-Cement ratio, compaction factor and
sand belonging to zone I the following adjustments are required.

Change in Condition Adjustment Required
Water Content Percentage Sand in total
Aggregate
(i) For Decrease in Water-Cement ratio (0.6
– 0.44) that is 0.16
Therefore 0.16 x 1 = 3.2
0.05
0 -3.2
(ii) For Increase in Compacting factor (0.9 -
0.8)= 0.1
Therefore 0.1 x 3 = 3.0
0.1
+3 0
(iii) For Sand Conforming to Zone-I of table
4 of IS 383-1970
0 +1.5

Example
• Required water Content = 186 + ( 186 x 3 )
100
= 191.6 lit / m3
Required Sand Content as Percentage of Total aggregate by absoluter
Volume
p= 35 – 1.7
= 33.3 %

Example
Step- V Determination of Cement Content
• Water Cement Ratio = 0.44
• Water = 191.6 lit = 191.6 kg
• Therefore,
• W= 0.44
C
191.6 = 0.44
C
C= 435.45 kg/m3 > 300 kg /m3
This cement content is adequate for ‘Moderate Exposure’ condition,
according to table 5 IS 456-2000)

Example
Determination of fine and Coarse content:
• Consider volume of concrete = 1 m3
But, entrapped air in wet concrete= 2 %
Therefore, absolute volume of fresh concrete= 1 – 2
100
= 1 – 0.02
V= 0.98 m3
Therefore,

Example
• V= [ W + C + 1 x fa ] x 1 for fine aggregate…1
Sc p Sfa 1000
And
0.98= [ 191.6 + 436 + 1 + fa ] x 1
3.15 0.33 2.6 1000
980 = 191.6 + 138.41 + 1.15 fa
fa= 562.76 kg
= 563 kg mass of F.A.

Example
Similarly,
V = [ W + C + 1 x Ca ] x 1 for coarse aggregate……..2
Sc (1-p) Sca 1000
• 0.98 = [ 191.6 + 436 x 1 x Ca ] x 1
3.15 (1-0.333) 2.65 1000
980 = 191.6 + 138.41 + 0.5657 Ca
Ca= 1149 kg/m3 mass of C.A.

Example
• Mix Proportions (By Mass)
Water Cement F.A. C.A
191.6 li 436 kg 563 kg 1149 kg
0.44 1 1.29 2.64

Example
22 li 50 kg 64.5 kg 132 kg

Example
Step 8 Adjustment for water absorption and free surface moisture in F.A. and C.A
• For water Cement ratio of 0.44 quantity of water required = 22 lit
• C.A absorbs 0.6 % of water by mass
• Therefore extra quantity of water to be added
• 0.6 x 132 = 0.792 lit (+)
100
F.A contains 2 % free moisture by mass
Quantity of water to be deducted
= 2 x 64.5 = 1.29 (-)
100
Actual quantity of water to be added
= 22 + 0.792 – 1.29
= 21.5 lit

Example
• Actual quantity of sand (FA) required after allowing for mass of free
water
• = 64.5 + 1.29 = 65.79 kg
• Actual quantity of C.A required
• = 132 - 0.792
• = 131.21 kg
21.50 li 50 kg 65.79 kg 131.21 kg

Example
• Design a concrete mix from the following data by I.S. method
• Target mean Strength= 35 N/mm2
• Maximum Size of Aggregate = 20 mm
• W/C ratio = 0.43
• Water required per m3 of concrete= 190 kg
• Sand as percentage of total aggregate by absolute Volume = 35 %
• Entrapped air in concrete= 2 %
• Sp gravity of Cement= 3.15
• Sp gravity of fine aggregate= 2.6
• Sp gravity of Coarse aggregate.= 2.7

Example
Step-I Target mean Strength
• Fck=35 N/mm2
Step-II Selection of Water-Cement Ratio:
• W/C ratio = 0.43
Step-III Estimation of air Content
• Entrapped air = 2 %
Step-IV
• Selection of water and sand Content
• Quantity of water per m3 of concrete = 190 kg
• Sand Content = 35 % of total aggregate by absolute Volume

Example
Step-V
• Cement Content
• Water-Cement Ratio = 0.43
• Water = 190 kg
• W = 0.43
c
190 = 0.43
C
C= 441 .86 kg/m3

Example
Determination of F.A and C.A Content
• Consider Volume of Concrete = 1 m 3
• But, entrapped air = 2 %
• Therefore Absolute Volume of press Concrete
• V= 1 – 2
100
V= 0.98 m3

Example
• V= [ W + C + 1 x fa ] x 1 for fine aggregate ………………1
Sc p Sfa 1000
0.98 = [ 190 + 442 + 1 + fa ] x 1
3.15 0.35 2.6 1000
0.98 = [ 190 + 140.32 + 1.098 fa] x 1
1000
fa= 591.69 kg/m3
fa= 592 kg/m3 Mass of FA

Example
Similarly,
V = [ W + C + 1 x Ca ] x 1 for coarse aggregate……..2
Sc (1-p) Sca 1000
• 0.98 = [ 190 + 442 x 1 x Ca ] x 1
• 3.14 (1-0.35) 2.7 1000
• 980 = 190 + 140.32 + 0.569 Ca
• Ca= 1142 kg/m3 Mass of CA

Example
• Mix Proportion (by mass)
• Quantity for 1 bag of Cement
190 442 592 1142
0.43 1 1.34 2.58
21.5 50 67 129

The ACI Method of Mix Design
• In the USA the method suggested by ACI is widely used. It
has the advantages of simplicity in that it applies equally
well, and with more or less identical procedure to rounded
or angular aggregate, to normal or lightweight aggregate
and to air-entrained or non-air-entrained concretes.
• The ACI method is based on the fact that for a given size of
well graded aggregates water content is largely independent
of mix proportions, i.e. Water content regardless of
variation in water/cement ratio and cement content.

• This method assumes that the optimum ratio of the bulk
volume of coarse aggregates and on the grading of fineness
aggregates regardless of shape of particles. This method also
assumes that even after complete compaction is done, a
definite percentage of air remains which is inversely
proportional to the maximum size of aggregate.

• The steps by steps operation in the ACI method are
Step-1 Data to be collected
• Fineness modulus of FA
• Unit weight of dry CA
• Specific gravity of FA and CA saturated surface dry condition.
• Specific gravity of Cement
• Absorptions characteristics of both CA and FA

Step-2
• Calculation mean design Strength, from the minimum strength
specified, using standard deviation:
• fm= fmin + K.S
• Where,
• F m= Specified minimum strength (Characteristic Strength)
• K= Constant dependency upon the probability of certain no of results
likely to fall fck= taken from table 9.4
• S= Standard Deviation from table 9.5

Step-3 Estimation of Water-Cement Ratio
• Water Cement ratio is estimated from table 9.10 for the mean design
Strength.

Average Compressive Strength at
28 days
Effective Water-Cement Ratio (By Mass)
Non-Air Entrained Concrete Air-entrained Concrete
45 0.38 -
40 0.43 -
35 0.48 0.4
30 0.55 0.46
25 0.62 0.53
20 0.7 0.61
15 0.8 0.71

• The water Cement ratio obtained from Strength point of
view is to be checked against maximum W/C Ratio given for
special exposure condition given in table 9.11 and minimum
of the two is to be adopted.

• Requirement of ACI for W/C Ratio and Strength for Special Exposure
Condition

Exposure Condition Maximum W/C ratio, normal density
aggregate concrete
Minimum Design Strength, low
Density aggregate Concrete, MPA
Concrete Intended to be Watertight
(a) Exposed to fresh Water
(b) Exposed to brackish or sea Water
0.5
0.45
25
30
Concrete Exposed to freezing and Thawing in a moist Condition:
(a) Kerbs, gutters, guard rails or thin
sections
0.45 30
Other elements 0.5 25
In presence of de-icing chemicals 0.45 30
For corrosion protection of
reinforced concrete exposed to de-
icing salts, brackish water, sea water
or spray from the sources.
0.4 30

• Decide maximum size of aggregate to be Used. Generally RCC work
20 mm and Pre-stressed Concrete 10 mm Size are Used
• Decide Workability in terms of slump for the type of job in hand.
General guidance can be taken from table 9.12.

Type of Construction Range of slump mm
Reinforced foundation walls and footings 20-80
Plain footing, cassions and substructure wall 20-80
Beams and Reinforced Wall 20-100
Building Column 20-100
Pavement and Slabs 20-80
Mass Concrete 20-80

Step-4 Minimum Water Content and entrapped air content:
• Decide maximum size of aggregate to be used. Generally for RCC
work 20 mm and for pre-stressed concrete 10 mm size are used.
• Decide workability in terms of slump for the type of job in hand.
Recommended value of slump for various types of construction as
given in table 9.12

Step-5 Cement Content
• Cement Content is computed by dividing the water content by the
water/ Cement Ratio
Step-6
• Bulk Volume of Dry Rodded Coarse Aggregate per Unit Volume of
Concrete
• Table 9.13 for a decided value of slump and maximum size of
aggregate, decide the mixing water content and entrapped air
content.

Table 9.13
Workability Water Content, kg/m 3 of Concrete for indicated maximum aggregate Size
Non- air entrained Concrete
Workability 10
mm
12.5 mm 20mm 25 mm 40 mm 50 m 70 mm 150 mm
Slump 30-50
mm
205 200 185 180 160 155 145 125
80-100 mm 225 215 200 195 175 170 160 140
150-180 mm 240 230 210 205 185 180 170 -
Approx
entrapped air
content
3 2.5 2 1.5 1 0.5 0.3 0,2

Table 9.13
Air entrained Concrete
Workability 10
mm
12.5 mm 20mm 25 mm 40 mm 50 m 70 mm 150 mm
Slump 30-50
mm
180 175 165 160 145 140 135 120
80-100 mm 200 190 180 175 160 155 150 135
150-180 mm 215 205 190 185 170 165 160 -

Table 9.13
Workabili
ty
Water Content, kg/m 3 of Concrete for indicated maximum aggregate Size
10 mm 12.5 mm 20mm 25 mm 40 mm 50 m 70 mm 150 mm
Slump
30-50
mm
180 175 165 160 145 140 135 120
80-100
mm
200 190 180 175 160 155 150 135
150-180
mm
215 205 190 185 170 165 160 -
Recomme
nded air
Content
Mild
Exposure
4.5 4 3.5 3.0 2.5 2.0 1.5 1.0
Moderate
Exposure
6.0 5.5 5.0 4.5 4.5 4.0 3.5 3.0
Extreme
Exposure
7.5 7.0 6.0 6.0 5.5 5.0 4.5 4.0

• Knowing the values of maximum size of coarse aggregates and
fineness modulus (FM) of fine aggregate, bulk volume of dry rodded
aggregate per unit volume of concrete is selected from table 9.14
• Dry Bulk of Coarse Aggregate per unit Volume of Concrete as Given
by ACI

Maximum Size of
Aggregate
Bulk Volume of Dry Rodded Coarse Aggregate per unit volume of concrete for fineness
modulus of sand
FM 2.4 2.6 2.8 3.0
10 0.5 0.48 0.46 0.44
12.5 0.59 0.57 0.55 0.53
20 0.66 0.64 0.62 0.6
25 0.71 0.69 0.67 0.65
40 0.75 0.73 0.71 0.69
50 0.78 0.76 0.74 0.72
70 0.82 0.8 0.78 0.76
150 0.87 0.85 0.83 0.81
(a) The value given will produce a mix that is suitable for reinforced concrete construction. For less workable
concrete the value may be increased by 10 percent for workable concrete such as pumpable concrete the
value may be reduced by upto 10 percent
(b) From the minimum strength specified estimate the average design strength either by using coefficient of
variation
(c) Find the water/cement ratio from the table 9.14

Step-7
• The weight of CA per cubic metre of Concrete is Calculated by
multiplying the bulk Volume with bulk density of CA
Step-8 Estimate of Density of fresh Concrete
• Knowing the maximum Size of Coarse Aggregates, the density of
fresh Concrete is estimated as

• First Estimate of Density of Fresh Concrete as Given by ACI
Maximum Size of
Aggregates
Non air-entrained air
kg/m3
Airentrained kg/m3
10 2285 2190
12.5 2315 2235
20 2355 2280
25 2375 2315
40 2420 2355
50 2445 2375
70 2465 2400

Step-9
• Absolute volumes of ingredients per cubic metre of concrete are obtained
by knowing the specific gravity of cement, water CA and FA
Step- 10
• Trial mix proportions are calculated and adjustments for field conditions
like free moisture and water absorption by aggregates are made.
Step-11
• A trial mix is then made to study the properties of concrete in respect of
workability, cohesiveness, finishing quality and 28 days compressive
strength. The proportion of CA and FA may be changed to get desired
properties.

Example-I
Design a Concrete mix Using ACI method for a multi-Storied building for the following data
• 28 days characteristic Compressive Strength= 30 Mpa
• Type of Cement Available= Ordinary Portland Cement
• Desired Slump= 80-100 mm
• Maximum Size of aggregate = 20 mm
• Standard Deviation from past Records = 4.5 Mpa
• Specific Gravities for FA= 2.65
• Specific Gravity for CA= 2.7
• For Cement= 3.15
• Bulk density of CA= 1600 kg/m3
• Fineness modulus of FA= 2.8
• CA absorbed 1 % moisture and sand
• Contains 1.5 % free surface moisture
• Assume any other data

Example-I
Solution
Step-I
• Mean Design Strength
• fm= fmin + K.S
• = 30 + 1.65 x 4.5
• = 37.425 Mpa
• From table 9.4
• Assume 5 % of test results are expected fall
• K= 1.65

Example-I
Step-II
• Estimation of Water-Cement Ratio
• From table 9.1 for mean design strength of 37.425 Mpa, the
estimated W/C ratio is 0.45
• From table 9.11, for exposure condition “concrete intended to be
watertight and exposed to fresh water”, the maximum
• w/C ratio is 0.5
• Hence adopt a water cement ratio of 0.45

Example-I
• Mixing water content and entrapped air content
• Maximum size of aggregates = 20 mm
• Desired Slump= 80-100
• Therefore from table 9.13
• Mixing water Content = 200 kg/m3 of Concrete
• Entrapped air Content = 2 %

Table 9.13
Recomme
nded air
Content
Mild
Exposure
4.5 4 3.5 3.0 2.5 2.0 1.5 1.0
Moderate
Exposure
6.0 5.5 5.0 4.5 4.5 4.0 3.5 3.0
Extreme
Exposure
7.5 7.0 6.0 6.0 5.5 5.0 4.5 4.0

Example-I
Step-4
• Cement Content
• W/C ratio = 0.45
• 200 = 0.45
C
C= 445 kg/m3
Water = 200 kg/m3 of concrete

Example-I
Step-5
• Bulk Volume of Dry Rodded CA:
• Maximum Size of CA= 20 mm
• Fineness modulus of FA= 2.8
• Therefore table 9.14
• The bulk volume of dry rodded CA is 0.62 per unit volume of
Concrete

Example-I
Step-6
• Weight of CA = 0.62 x 1600
• = 992 kg/m3
• Therefore density of CA is 1600 kg/m3

Example-I
Step-7
• Dry density of fresh Concrete
• For maximum Size of CA = 200 mm and non air entrained Concrete,
• From table 9.15 dry density of fresh Concrete
= 2355 kg/m3

Example-I
Step-8
• Mass of all the known Ingredient of Concrete
• Mass of water= 200 kg/m3
• Mass of Cement= 445 kg/m3
• Mass of CA= 992 kg/m3
• Mass of FA = 2355-[ 200 + 445 + 992]
= 718 kg/m3

Example-I
Sr.no Ingredient Mass, kg/m3 Absolute Volume m3
1 Cement 445 445 = 0.141 m3
3.15 x 1000
2 Water 200 200= 0.2 m3
1 x 1000
3 CA 992 992 = 0.367 m3
2.7 x 1000
4 Entrapped Air 2 % 2 x 1 = 0.02 %
100
Total Absolute Volume 0.728 m3

• Hence, Volume of FA required = 1-0.728
• = 0.272 m 3
• Mass of FA = 0.272 x 2.65 x 1000
• = 720.8 kg/m 3
• Adopt mass of FA = 720.8 kg/m 3
• = 721 kg/m 3
• Estimated quantities of material per cubic metre of concrete are
• Cement= 445 kg
• FA= 721 kg
• CA= 992 kg
• Water= 200 kg
• Total 2358 kg/m3 of Concrete

Example-I
• Density of fresh Concrete is 2358 kg/m3 as against 2355
200 445 kg 721 kg 992 kg
0.45 1 1.62 2.23
22.5 kg 50 kg 81 kg 111.5

Example-I
• Adjustment for water absorption and free surface moisture
• F.A Contains 1.5 % free surface moisture
• Total surface moisture of FA = 1.5 x 721
100
= 10.82 kg (-)
Mass of FA in field condition = 721 + 10.82
= 731.83 kg/m3
Say 732 kg/m3
CA absorbs 1 % of moisture,
Quantity of water absorbed by CA = 1 x 992
100
= 9.92 kg (+)
Therefore mass of CA in field Condition = 992 – 9.92
= 982 kg/m3

Example-I
• Net Quantity of Mix Water = 200 -10.82+ 9.92
= 199.10 kg
• Final mix proportions (for 1 m3 of concrete)
Water Cement F.A. C.A.
199.10 kg 445 kg 732 kg 982 kg

The British Method
• The traditional British method has been replaced by the department of the
environment for normal mixes, known as DOE(British) mix design method.
• The following steps are Involved in DOE Method
Step-I
• Find the target mean strength from the specified Characteristic Strength
• ft= fck + k.S
• Where,
• ft= target mean strength
• fck= characteristic Strength
• S= Standard Deviation
• K= risk factor or probability factor
CONCRETE MIX DESIGN

Step-II
Determination of free water cement ratio
• From the given type of cement and aggregate, obtain the compressive
strength of concrete corresponding to free w/c ratio of 0.5
Type of
Cement
Type of Coarse
Aggregate
3 7 28 91
Ordinary or
Sulphate
Resisting
Cement
Uncrushed
Crushed
22
27
30
36
42
49
49
56
Rapid
Hardening
Portland
Cement
Uncrushed
Crushed
29
34
37
43
48
55
54
61
CONCRETE MIX DESIGN

• Now adopt the pair of data i.e. compressive strength read from table
9.16 and w/c ratio mark point ‘P’. Through this point draw a dotted
curve parallel to neighbouring curve. Using this new curve we read
the w/c ratio as against target strength ft calculated in step 1
• Check this w/c ratio for durability considerations and adopt the
lower value
Minimum
grade
30 35 40 45 50
Maximu
m w/c
ratio
0.65 0.6 0.55 0.5 0.45
Maximu
m cement
content
275 300 325 350 400
CONCRETE MIX DESIGN

Fig.1 Relation between
compressive strength
and free water cement
ratio
 mark a point corresponding to
strength f1, at water cement ratio 0.5.
 draw a curve parallel to the nearest
curve, through this point
Using the new curve,
Read off ( abscissa) the water cement
ratio
corresponding to the target mean
strength (ordinate)
Free water-cement ratio
CONCRETE MIX DESIGN

Step-3
Determination of water Content
• Depending upon the type and maximum nominal size of aggregate
and workability the water content is estimated as
• W= 2 W fa + 1 W ca
3 3
• Where,
• W fa= free water content appropriate to the type of fine aggregate
• W ca= free water content appropriate to the type of coarse aggregate
CONCRETE MIX DESIGN

Level of
Workability
Very Low Low Medium High
Description Slump 0-10 10-30 30-60 60-180
Vee-bee >12 12-6 6-3 3-0
Compaction
Factor
0.75- 0.85 0.85-0.9 0.9- 0.93 >0.93
Maximum
Size of Agg
Type of
aggregate
Water Content
10 mm Uncrushed 150 180 205 225
Crushed 180 205 230 250
20 Uncrushed 135 160 180 195
Crushed 170 190 210 225
40 Uncrushed 115 140 160 175
Crushed 155 175 190 205
CONCRETE MIX DESIGN

• Reduction in water content when fly ash is Used
% of fly ash Reduction in Water content Kg/m3
10 5 5 5 10
20 10 10 10 15
30 15 15 20 20
40 20 20 25 25
50 25 25 30 30
CONCRETE MIX DESIGN

Step 4 - Determination of Cement Content
• The Cement Content if the mix is calculated from the selected w/c
ratio
• Cement Content = water content
W/C ratio
CONCRETE MIX DESIGN

Step-5
Determination of aggregate Cement Ratio
• Absolute volume occupied by the aggregate
• = 1- Cement Content (kg) – Water Content (kg)
1000 x Sc 1000 x Sw
Where, Sc= Specific gravity of cement particles
Therefore Total aggregate content (kg/m3)
= absolute volume occupied by the aggregate x 1000x Sa
Where Sa= Specific gravity of aggregate

Step-6 Determination of FA and CA
• Depending on the free water cement ratio, the nominal maximum size of
coarse aggregate, the workability and grading zone of fine aggregate is
determined from fig 9.5 (a), 9.5 (b) and 9.5 (c)
• Once the proportion of FA is obtained, multiplying by the weight of total
aggregate gives the weight of fine aggregate. Then coarse aggregate is
calculated as
• Fine aggregate content = total aggregate content x proportion of fine
aggregate
• Coarse aggregate content = Total aggregate content – fine aggregate
content
CONCRETE MIX DESIGN

FIG3-Recommendedproportionoffineaggregateasa
functionoffreewater–cementratio

Proportion of Different sizes of CA
Aggregate 4.75- 10 mm 10-20 mm 20-40 mm
Type-I 33 67 -
Type-II 18 27 55
CONCRETE MIX DESIGN

Step-7
Determination of final Proportion
• The proportion so worked out should be tried for their specified
strength and suitable adjustment are made to obtain the proportion.
CONCRETE MIX DESIGN

Example
• Design a Concrete mix Using, DOE Method for a reinforced Concrete Work for
the following data:
• Required Characteristic Compressive Strength= 35 Mpa at 28 days
• Type of Cement Used= Sulphate Resisting Portland Cement
• Desired Slump= 50 mm
• Maximum Size of Aggregate= 20 mm
• Type of Aggregate= Uncrushed
• Specific Gravity = 2.65
• Fine aggregate conforms to grade Zone III with percent passing 600 micron
sieve being 70 %
• Exposure Condition = Moderate
• Standard Deviation= 5.0 Defective Rate= 5 %
CONCRETE MIX DESIGN

Example
• Mix Design Without fly ash:
• Target Mean Strength:
• Ft= fck+ kS
• fck= 35 N/mm 2
• Standard Deviation= 5.0
• K= 1.65
• ft= 35 + 1.65 x 5
• = 43.25 N/mm 2
CONCRETE MIX DESIGN

Example
Determination of free Water-Cement Ratio
• For type of Cement Sulphate resisting Portland cement and uncrushed
aggregate 28 days compressive strength from table 9.16 is 42 MPA
• For Compressive Strength equal to 42 MPA and w/c ratio 0.5, mark ‘P’ in
fig and draw a dotted curve parallel to the neighbouring curve Using this
new curve again ft= 43.25 N/mm2 the W/C ratio is read as 0.48
• From table 9.17 from durability point of view the maximum w/c ratio is
0.6
• Hence Adopt the minimum w/c ratio as 0.48
CONCRETE MIX DESIGN

Example
Step-3
• Determination of Water Content:
• For Desired slump = 50 mm
• Maximum size of CA= 20 mm
• From table 9.18 water content is 180 kg/m3
CONCRETE MIX DESIGN

Example
Step-4 Determination of Cement Content:
• W/C ratio obtained from step 2 is 0.48 and water is 180 kg/m3
• W/C = 0.48
• 180 = 0.48
C
Therefore C= 375 kg/m3 of Concrete
This is satisfactory as it is greater than minimum Cement Content of
300 kg/m3
CONCRETE MIX DESIGN

Example
Step: 5
• Aggregate Cement Ratio
• Specific gravity of aggregate is 2.65
• Therefore fig 9.4 wet density of concrete is 2400 kg/m3
• Therefore mass of total aggregate
• = 2400 – 180- 375
• = 1845 kg/m3
• Alternatively Volume occupied by aggregate
• = 1- 375 – 180 = 0.7009 m3
100x 3.15 1000 x 1
Therefore total Aggregate Content
= 0.7009 x 1000 x 2.65
= 1875 kg/m3
CONCRETE MIX DESIGN

Example
Step-6 Determination of FA and CA Content
• For, Maximum size of aggregate = 20 mm
• Slump= 50 mm
• Free W/C ratio = 0.48
• Percent aggregate Passing
• 600 micron sieve = 70 %
• From fig 9.5 (b) the proportion of fine aggregate i.s 30 %
• Mass of FA = 30 x 1875 = 557 kg/m3
• 100
• Mass of CA = 1875 – 557.1
• = 1299.9 kg/m3
• = 1300 kg/m3
CONCRETE MIX DESIGN

Example
Step 7
• The estimated Quantity are:
180 kg 375 kg 557 kg 1300 kg
0.48 1 1.485 3.46
CONCRETE MIX DESIGN

RoadNote No. 4
Method Of Mix Design
CONCRETE MIX DESIGN

ROAD NOTE No. 4 METHOD OF MIX DESIGN
Proposed by the Road Research Laboratory, UK (1950)
Introduction
In this method, the aggregate to cement ratios are worked out on the basis of type of
aggregate, max size of aggregate and different levels of workability.
The relative proportion of aggregates is worked on basis of combined grading curves. This
method facilitates use of different types of fine and coarse aggregates in the same mix.
The relative proportion of these can be easily calculated from combined grading curves.
The values of aggregate to cement ratio are available for angular rounded or irregular
coarse aggregate.
CONCRETE MIX DESIGN 156

Procedure
1. The average compressive strength of the mix to be designed is obtained by applying control factors to the
minimum compressive strength.
2. w/c ratio is read from compressive strength v/s w/c ratio graph.
3. Proportion of combined aggregates to cement is determined from tables, for maximum size 40 mm and 20
mm.
4. If the aggregate available differs from the standard grading, combine FA and CA so as to produce one of
the standard grading.
5. The proportion of cement, water, FA and CA is determined from knowing the water/cement ratio and the
aggregate/cement ratio.
6. Calculate the quantities of ingredients required to produce 1 m3 of concrete, by the absolute volume
method, using the specific gravities of cement and aggregates.

Method In Detail
Find The Target Mean Strength
Concrete is designed for strength higher than characteristic strength
as a margin for statistical variation in results and variation in degree of
control exercised at site. This higher strength is defined as the target mean
strength.
Target mean strength = Characteristic strength + K * s

Determine water/cement ratio
The relation between Target Mean Strength and water cement ratio
for different cement curves is given in IS 10262

 Finding cement content

 The Relative Proportion Are Worked Out
A trial proportion is taken and combined gradation is worked out for
e.g.
35% fine aggregate 20% 10mm down aggregate, 45% 20mm down
aggregate.

Combined gradation is plotted and pushed towards Ideal curve
by increasing or decreasing the sand content

 Calculation Of Cement Content
Plastic Density =
(1x Sc + 1.45x Sfa +0.75x Sca10 +1.6 x Sca20 + w/c)x 1000 x (1− Ea)
5.26
Sc= Specific gravity of cement
Sfa =Specific gravity of fine aggregate
Sca10=Specific gravity of 10mm coarse aggregate
Sca20=Specific gravity of 20mm coarse aggregate
W/c = water to cement ratio
Ea = Entrapped air %
Cement Content (Kg/m3) = Plastic density /(1+a/c ratio + w/c ratio)
If weight of cement is “C” the total weight per m3 will be
C +1.45C + 0.75C +1.6C + 0.46C=5.26C

Drawbacks Of Road Note No. 4 Method
This method leads to very high cement contents and thus is becoming
obsolete.
In many cases use of gap graded aggregate becomes unavoidable. In many
parts of the country the practice is to use 20mm coarse aggregates without
10mm aggregates. This is because of quality of 10mm aggregates produced
from jaw crusher is very poor .Gap grading does not fit in to the standard
combined grading curves of RRL method.
Sand available in some parts of country is graded that it is high on coarse
fraction (1.18mm and above) and low on fines (600micron and below). It
is difficult to adjust the sand content to match any of the standard
combined grading curves .The combined grading curve often cuts across
more than one standard curves in such cases

Different aggregate to cement ratios are given for
different levels of workability ranging from low to
high. But these levels of workability are not defined
in terms of slump, compaction factor or Vee Bee time
as in case of other methods.
The fine aggregate content cannot be adjusted for
different cement contents. Hence the richer mixes
and leaner mixes may have same sand proportion,
for a given set of materials.

References
• Concrete Technology by: R.P. Rethaliya
• Concrete Technology by . M.S. Shetty
• Internet websites
• http://www.foundationsakc.org/

Concrete Mix Design

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