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SyllabusConcrete Mix Design• Mix Design for compressive strength by I.S. Method, Road
Note Method, British method, Mix Design for flexuralStrength
Concrete Mix Design• Concrete mix design may be defines as the art of selecting
suitable ingredients of concrete and determining theirrelative proportions with the object of producing concrete ofcertain minimum strength & durability as economically aspossible.
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 ofthe structure being built. Mix design should ensure followingobjectives.
• 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
Basic ConsiderationsCost• 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 aimat as lean a mix as possible. Therefore, all possible steps should be taken toreduce the cement content of a concrete mixtures without sacrificing thedesirable properties of concrete such as strength and durability.
Basic ConsiderationsSpecifications• 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
Basic ConsiderationsWorkability• 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 ratherthan the addition of more water
• Wherever possible, the cohesiveness and finishibility of concrete should beimproved by increasing sand/ aggregate ratio than by increasing theproportion 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 atgiven cement content. Water demand can by lowered by throughoutcontrol of the aggregate grading and by using water reducingadmixtures.
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 M10M15M20
101520
Standard Concrete M25M30M35M40M45M50M55
25303540455055
High Strength Concrete M60M65M70M75M80
6065707580
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 15N/mm2
• The minimum grade of reinforced Concrete ( RCC) shall be20 N/mm2
Nominal Concrete Mixes and
Design mix concreteNominal Mix Concrete• The wide use of concrete as construction materials has led to
the use of mixes of fixed proportion, which ensuresadequate 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.
Proportions of Ingredients in Nominal Mixes• The proportions of materials for nominal mix shall be in accordance
Grade ProportionsC: FA: CA
M5 1: 5:10M 7.5 1:4:8M 10 1:3:6M 15 1:2:4M 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 invariety of important structures, because of better strength, reducedvariability, leaner mixed with consequent economy, as well asgreater 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.
Factors Influencing Choice of Mix DesignGrade of Concrete• The grade of concrete gives characteristic compressive
strength of concrete. It is one of the important factorinfluencing the mix design• The grade M 20 denotes characteristic compressive strength
fck of 20 N/mm2. Depending upon the degree of controlavailable at site, the concrete mix is to be designed for atarget mean compressive strength (fck) applying suitablestandard deviation.
Factors Influencing Choice of Mix DesignType 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 53grade of cement, gives saving in cement consumption asmuch as 15 % and 25 % respectively, as compared to 33grade of cement. For concrete of grade M25 it is advisable touse 43 and 53 grade of cement.
Factors Influencing Choice of Mix DesignMaximum 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 isretained. The maximum nominal size of C.A. should not be more than one-forthof 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 sumless than the minimum clear distance between the main bars or 5 mm less theminimum cover to the reinforcement, whoever is smaller.
• The workability of concrete increases with an increase in the maximum size ofaggregate. But the smaller size of aggregates provide larger surface area forbonding with the mortar matrix which gives higher strength.
Factors Influencing Choice of Mix DesignGrading of Combined Aggregates• The relative proportions of the fine and coarse aggregate in
a concrete mix is one of the important factors affecting thestrength of concrete.• For dense concrete, it is essential that the fine and coarse
aggregate be well graded. In the case when the aggregateavailable from natural sources do not confirm to thespecified grading, the proportioning of two or moreaggregate become essential
Factors Influencing Choice of Mix DesignMaximum 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 onwater/cement ratio. The lower the water/Cement ratio, the greater isthe compressive strength
Workability• Workability of fresh concrete determines the case with which a
concrete mixture can be mixed, transported, placed, compacted andfinished without harmful segregation and bleeding.
Factors Influencing Choice of Mix DesignDurability• Durability require low water/Cement ratio. It is usually
achieved not by increasing the cement content, but bylowering 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 workcarried 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.
IS Method of Mix Design• Target Strength for Mix Design• The target average compressive strength (fck) of concrete at 28 days is
given by
• Fck= f ck + t.sWhere,• 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.
IS Method of Mix Design• According to Is 456: 2000 and IS 1343:1980 te
characteristic strength is defined as the value below whichnot more than 5 percent of results are expected to fall. Insuch cases the above equation reduced to• Fck= fck + 1.65 s• The value of standard deviation is obtained from the table
IS Method of Mix DesignStep-IISelection of Water –Cement Ratio• Since different cements and aggregates of different maximum sizes,
grading, surface texture shape and other characteristics may produceconcrete of different compressive strength for the same free watercement ratio, the relationship between strength and free watercement ratio should preferable be established for the materialactually to be used. In the absence of such data, the preliminary freewater-cement ratio corresponding to the target strength at 28 daysmay be selected from the relationship shown below
IS Method of Mix Design• Alternatively, the preliminary free water cement ratio by
mass corresponding to the average strength may be selectedfrom the relationship shown below using the curvecorresponding to the 28 days cement strength to be used forthe purpose. However, this will need 28 days for testing ofcement.
IS Method of Mix Design• The free water-cement ratio thus selected should be checked
against limiting water-cement ratio for the requirements ofdurability as per table 5.4 and the lower of the two valuesshould be adopted.
IS Method of Mix DesignStep 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 %
IS Method of Mix DesignSelection 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 totalaggregate by absolute volume are to be estimated from table below asapplicable. Depending upon the nominal maximum size and type ofaggregate.
IS Method of Mix Design• 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 4020 186 3540 165 30
IS Method of Mix Design• 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 absolutevolume of (%)
10 200 2820 180 25
IS Method of Mix Design• Adjustment of values in water content and sand percentage for other
conditionsChange in Condition Adjustment Required
Water Content Percentage sand in total aggregateFor 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 compactingfactor 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 instep- 2, and the quantity of water per unit volume ofconcrete obtained in step-4• The cement content so obtained should be checked against
the minimum cement content for the requirement ofdurability as per table 5 IS 456:2000 and the greater of thetwo 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 aggregatecontent per unit volume of concrete may be calculated from the followingequations
• V= [ W + C + 1 x fa ] x 1 for fine aggregate …………………………1Sc p Sfa 1000
AndV = [ W + C + 1 x Ca ] x 1 for coarse aggregate …………..2
Sc (1-p) Sca 1000
Step -6 Calculation of Aggregate ContentWhere,• 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 sufficientfor 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
ExampleStep-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)
ExampleStep-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
ExampleStep –III• Estimation of Air Content• For maximum Size of aggregate of 20 mm, the air content is taken as
2 %
ExampleStep-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 metreof concrete = 186 kg and sand content as percentage of totalaggregate 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 aggregateFor Decrease in water cement ratio(0.6-0.5) that is 0.10.1 x 1 = 2.00.05
0 -2.0
For increase in compacting factor (0.9 -0.8) = 0.10.1 x 3 = 30.1
+ 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 absolutevolume= 35 – 3.5= 31.5 %
ExampleDetermination 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.
ExampleDetermination 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
1001- 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 aggregatecontent per unit volume of concrete may be calculated from the followingequations
• V= [ W + C + 1 x fa ] x 1 for fine aggregate ………………1Sc p Sfa 1000
0.98 = [ 191.6 + 383 + 1 + fa ] x 13.15 0.315 2.66 1000
980 = 313.187 + 1.19 fafa= 558.75 kg mass of F.A
ExampleAndV = [ W + C + 1 x Ca ] x 1 for coarse aggregate …………..2
Sc (1-p) Sca 10000.98 = [ 191.6 + 383 x 1 x Ca ] x 1
3.15 (1-0.315) 2.75 1000980 = 313.187 + 0.5308 CaCa= 1256.24 kg mass of C.A
ExampleWater Cement F.A C.A191.6 li 383 kg 558.75 kg 1256.24 kg0.5 1 1.46 3.28
Water Cement F.A C.A383 = 0.264 m 3
1450558.75 = 0.328 m 3
17001256.24 = 0.698 m 3
18000.5 1.0 1.242 2.644
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
ExampleTest 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
ExampleStep-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
ExampleStep-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= 0.44C
ExampleStep III Estimation of air Content• For maximum Size of Aggregate of 20 mm, the air content is taken as
2.0 %
ExampleStep-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 metreof concrete = 186 kg and sand content as percentage of totalaggregate 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 RequiredWater Content Percentage Sand in total
Aggregate(i) For Decrease in Water-Cement ratio (0.6
– 0.44) that is 0.16Therefore 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 = 3.00.1
+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 absoluterVolumep= 35 – 1.7= 33.3 %
ExampleStep- V Determination of Cement Content• Water Cement Ratio = 0.44• Water = 191.6 lit = 191.6 kg• Therefore,• W= 0.44
C191.6 = 0.44
CC= 435.45 kg/m3 > 300 kg /m3
This cement content is adequate for ‘Moderate Exposure’ condition,according to table 5 IS 456-2000)
ExampleDetermination 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 – 0.02V= 0.98 m3
Therefore,
Example• V= [ W + C + 1 x fa ] x 1 for fine aggregate…1
Sc p Sfa 1000And0.98= [ 191.6 + 436 + 1 + fa ] x 1
3.15 0.33 2.6 1000980 = 191.6 + 138.41 + 1.15 fafa= 562.76 kg= 563 kg mass of F.A.
ExampleSimilarly,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 1000980 = 191.6 + 138.41 + 0.5657 CaCa= 1149 kg/m3 mass of C.A.
Example• Mix Proportions (By Mass)
Water Cement F.A. C.A191.6 li 436 kg 563 kg 1149 kg0.44 1 1.29 2.64
ExampleStep 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 massQuantity 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
Water Cement F.A. C.A21.50 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
ExampleStep-I Target mean Strength• Fck=35 N/mm2
Step-II Selection of Water-Cement Ratio:• W/C ratio = 0.43Step-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
ExampleStep-V• Cement Content• Water-Cement Ratio = 0.43• Water = 190 kg• W = 0.43
c190 = 0.43
CC= 441 .86 kg/m3
ExampleDetermination 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
100V= 0.98 m3
Example• V= [ W + C + 1 x fa ] x 1 for fine aggregate ………………1
Sc p Sfa 10000.98 = [ 190 + 442 + 1 + fa ] x 1
3.15 0.35 2.6 10000.98 = [ 190 + 140.32 + 1.098 fa] x 1
1000fa= 591.69 kg/m3
fa= 592 kg/m3 Mass of FA
ExampleSimilarly,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
Water Cement F.A C.A190 442 592 11420.43 1 1.34 2.58
Water Cement F.A C.A21.5 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 equallywell, and with more or less identical procedure to roundedor angular aggregate, to normal or lightweight aggregateand 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 independentof mix proportions, i.e. Water content regardless ofvariation in water/cement ratio and cement content.
The ACI Method of Mix Design• This method assumes that the optimum ratio of the bulk
volume of coarse aggregates and on the grading of finenessaggregates regardless of shape of particles. This method alsoassumes that even after complete compaction is done, adefinite percentage of air remains which is inverselyproportional to the maximum size of aggregate.
The ACI Method of Mix Design• The steps by steps operation in the ACI method areStep-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
The ACI Method of Mix DesignStep-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
The ACI Method of Mix DesignStep-3 Estimation of Water-Cement Ratio• Water Cement ratio is estimated from table 9.10 for the mean design
Strength.
The ACI Method of Mix DesignAverage Compressive Strength at
28 daysEffective Water-Cement Ratio (By Mass)
Non-Air Entrained Concrete Air-entrained Concrete
45 0.38 -40 0.43 -35 0.48 0.430 0.55 0.4625 0.62 0.5320 0.7 0.6115 0.8 0.71
The ACI Method of Mix Design• The water Cement ratio obtained from Strength point of
view is to be checked against maximum W/C Ratio given forspecial exposure condition given in table 9.11 and minimumof the two is to be adopted.
The ACI Method of Mix Design• Requirement of ACI for W/C Ratio and Strength for Special Exposure
Condition
Exposure Condition Maximum W/C ratio, normal densityaggregate concrete
Minimum Design Strength, lowDensity aggregate Concrete, MPA
Concrete Intended to be Watertight(a) Exposed to fresh Water(b) Exposed to brackish or sea Water
0.50.45
2530
Concrete Exposed to freezing and Thawing in a moist Condition:
(a) Kerbs, gutters, guard rails or thinsections
0.45 30
Other elements 0.5 25In presence of de-icing chemicals 0.45 30For corrosion protection ofreinforced concrete exposed to de-icing salts, brackish water, sea wateror spray from the sources.
0.4 30
The ACI Method of Mix Design• 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.
The ACI Method of Mix DesignType of Construction Range of slump mm
Reinforced foundation walls and footings 20-80Plain footing, cassions and substructure wall 20-80
Beams and Reinforced Wall 20-100Building Column 20-100
Pavement and Slabs 20-80Mass Concrete 20-80
The ACI Method of Mix DesignStep-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 asgiven in table 9.12
The ACI Method of Mix DesignStep-5 Cement Content• Cement Content is computed by dividing the water content by the
water/ Cement RatioStep-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 aircontent.
Table 9.13Workability Water Content, kg/m 3 of Concrete for indicated maximum aggregate Size
Non- air entrained ConcreteWorkability 10
mm12.5 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 140150-180 mm 240 230 210 205 185 180 170 -Approxentrapped air content
3 2.5 2 1.5 1 0.5 0.3 0,2
Table 9.13Workability Water Content, kg/m 3 of Concrete for indicated maximum aggregate Size
Air entrained ConcreteWorkability 10
mm12.5 mm 20mm 25 mm 40 mm 50 m 70 mm 150 mm
Slump 30-50mm
180 175 165 160 145 140 135 120
80-100 mm 200 190 180 175 160 155 150 135150-180 mm 215 205 190 185 170 165 160 -
Table 9.13Workability Water Content, kg/m 3 of Concrete for indicated maximum aggregate Size
Air entrained ConcreteWorkability
Water Content, kg/m 3 of Concrete for indicated maximum aggregate SizeAir entrained Concrete
10 mm 12.5 mm 20mm 25 mm 40 mm 50 m 70 mm 150 mmSlump30-50mm
180 175 165 160 145 140 135 120
80-100mm
200 190 180 175 160 155 150 135
150-180mm
215 205 190 185 170 165 160 -
Recommended 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
The ACI Method of Mix Design• Knowing the values of maximum size of coarse aggregates and
fineness modulus (FM) of fine aggregate, bulk volume of dry roddedaggregate per unit volume of concrete is selected from table 9.14
• Dry Bulk of Coarse Aggregate per unit Volume of Concrete as Givenby 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 3.010 0.5 0.48 0.46 0.44
12.5 0.59 0.57 0.55 0.5320 0.66 0.64 0.62 0.625 0.71 0.69 0.67 0.6540 0.75 0.73 0.71 0.6950 0.78 0.76 0.74 0.7270 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
The ACI Method of Mix DesignStep-7• The weight of CA per cubic metre of Concrete is Calculated by
multiplying the bulk Volume with bulk density of CAStep-8 Estimate of Density of fresh Concrete• Knowing the maximum Size of Coarse Aggregates, the density of
fresh Concrete is estimated as
The ACI Method of Mix Design• 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 219012.5 2315 223520 2355 228025 2375 231540 2420 235550 2445 237570 2465 2400
The ACI Method of Mix DesignStep-9• Absolute volumes of ingredients per cubic metre of concrete are obtained
by knowing the specific gravity of cement, water CA and FAStep- 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 compressivestrength. The proportion of CA and FA may be changed to get desiredproperties.
Example-IDesign 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-ISolutionStep-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-IStep-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
The ACI Method of Mix DesignAverage Compressive Strength at
28 daysEffective Water-Cement Ratio (By Mass)
Non-Air Entrained Concrete Air-entrained Concrete
45 0.38 -40 0.43 -35 0.48 0.430 0.55 0.4625 0.62 0.5320 0.7 0.6115 0.8 0.71
Exposure Condition Maximum W/C ratio, normal densityaggregate concrete
Minimum Design Strength, lowDensity aggregate Concrete, MPA
Concrete Intended to be Watertight(a) Exposed to fresh Water(b) Exposed to brackish or sea Water
0.50.45
2530
Concrete Exposed to freezing and Thawing in a moist Condition:
(a) Kerbs, gutters, guard rails or thinsections
0.45 30
Other elements 0.5 25In presence of de-icing chemicals 0.45 30For corrosion protection ofreinforced concrete exposed to de-icing salts, brackish water, sea wateror spray from the sources.
0.4 30
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 9.13Workability Water Content, kg/m 3 of Concrete for indicated maximum aggregate Size
Non- air entrained ConcreteWorkability 10
mm12.5 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 140150-180 mm 240 230 210 205 185 180 170 -Approxentrapped air content
3 2.5 2 1.5 1 0.5 0.3 0,2
Table 9.13Workability Water Content, kg/m 3 of Concrete for indicated maximum aggregate Size
Air entrained ConcreteWorkability 10
mm12.5 mm 20mm 25 mm 40 mm 50 m 70 mm 150 mm
Slump 30-50mm
180 175 165 160 145 140 135 120
80-100 mm 200 190 180 175 160 155 150 135150-180 mm 215 205 190 185 170 165 160 -
Table 9.13Recommended 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-IStep-4• Cement Content• W/C ratio = 0.45• 200 = 0.45
CC= 445 kg/m3
Water = 200 kg/m3 of concrete
Example-IStep-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
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 3.010 0.5 0.48 0.46 0.44
12.5 0.59 0.57 0.55 0.5320 0.66 0.64 0.62 0.625 0.71 0.69 0.67 0.6540 0.75 0.73 0.71 0.6950 0.78 0.76 0.74 0.7270 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
Example-IStep-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-IStep-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-ISr.no Ingredient Mass, kg/m3 Absolute Volume m31 Cement 445 445 = 0.141 m3
3.15 x 10002 Water 200 200= 0.2 m3
1 x 10003 CA 992 992 = 0.367 m3
2.7 x 10004 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
Water Cement F.A C.A200 445 kg 721 kg 992 kg0.45 1 1.62 2.23
Water Cement F.A C.A22.5 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/m3CA 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 MethodStep-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-IIDetermination 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 0.5Type of Cement
Type of Coarse Aggregate
3 7 28 91
Ordinary or SulphateResisting Cement
UncrushedCrushed
2227
3036
4249
4956
Rapid HardeningPortland Cement
UncrushedCrushed
2934
3743
4855
5461
CONCRETE MIX DESIGN
• Now adopt the pair of data i.e. compressive strength read from table9.16 and w/c ratio mark point ‘P’. Through this point draw a dottedcurve parallel to neighbouring curve. Using this new curve we readthe w/c ratio as against target strength ft calculated in step 1
• Check this w/c ratio for durability considerations and adopt thelower value
Minimumgrade
30 35 40 45 50
Maximum w/cratio
0.65 0.6 0.55 0.5 0.45
Maximum cementcontent
275 300 325 350 400
CONCRETE MIX DESIGN
Fig.1 Relation betweencompressive strengthand free water cementratio mark a point corresponding tostrength f1, at water cement ratio 0.5. draw a curve parallel to the nearestcurve, through this pointUsing the new curve,Read off ( abscissa) the water cement
ratiocorresponding to the target meanstrength (ordinate)
Free water-cement ratio
CONCRETE MIX DESIGN
Step-3Determination 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 60-180Vee-bee >12 12-6 6-3 3-0Compaction 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 225Crushed 180 205 230 250
20 Uncrushed 135 160 180 195Crushed 170 190 210 225
40 Uncrushed 115 140 160 175Crushed 155 175 190 205
CONCRETE MIX DESIGN
• Reduction in water content when fly ash is Used
% of fly ash Reduction in Water content Kg/m310 5 5 5 1020 10 10 10 1530 15 15 20 2040 20 20 25 2550 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-5Determination of aggregate Cement Ratio• Absolute volume occupied by the aggregate• = 1- Cement Content (kg) – Water Content (kg)
1000 x Sc 1000 x SwWhere, Sc= Specific gravity of cement particlesTherefore Total aggregate content (kg/m3)= absolute volume occupied by the aggregate x 1000x SaWhere 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 isdetermined from fig 9.5 (a), 9.5 (b) and 9.5 (c)
• Once the proportion of FA is obtained, multiplying by the weight of totalaggregate gives the weight of fine aggregate. Then coarse aggregate iscalculated as
• Fine aggregate content = total aggregate content x proportion of fineaggregate
• Coarse aggregate content = Total aggregate content – fine aggregatecontent
CONCRETE MIX DESIGN
Proportion of Different sizes of CAAggregate 4.75- 10 mm 10-20 mm 20-40 mm
Type-I 33 67 -Type-II 18 27 55
CONCRETE MIX DESIGN
Step-7Determination 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
ExampleDetermination 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 thisnew 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 is0.6
• Hence Adopt the minimum w/c ratio as 0.48
CONCRETE MIX DESIGN
ExampleStep-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
ExampleStep-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
CTherefore C= 375 kg/m3 of ConcreteThis is satisfactory as it is greater than minimum Cement Content of300 kg/m3
CONCRETE MIX DESIGN
ExampleStep: 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 1Therefore total Aggregate Content= 0.7009 x 1000 x 2.65= 1875 kg/m3
CONCRETE MIX DESIGN
ExampleStep-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
ExampleStep 7• The estimated Quantity are:
Water Cement F.A C.A180 kg 375 kg 557 kg 1300 kg0.48 1 1.485 3.46
CONCRETE MIX DESIGN
ROAD NOTE No. 4 METHOD OF MIX DESIGN
Proposed by the Road Research Laboratory, UK (1950)
IntroductionIn 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
Procedure1. 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 20mm.
4. If the aggregate available differs from the standard grading, combine FA and CA so as to produce one ofthe standard grading.
5. The proportion of cement, water, FA and CA is determined from knowing the water/cement ratio and theaggregate/cement ratio.
6. Calculate the quantities of ingredients required to produce 1 m3 of concrete, by the absolute volumemethod, using the specific gravities of cement and aggregates.
CONCRETE MIX DESIGN 157
CONCRETE MIX DESIGN 158
Method In DetailFind The Target Mean Strength
Concrete is designed for strength higher than characteristic strengthas a margin for statistical variation in results and variation in degree ofcontrol exercised at site. This higher strength is defined as the target meanstrength.
Target mean strength = Characteristic strength + K * s
Determine water/cement ratioThe relation between Target Mean Strength and water cement ratio
for different cement curves is given in IS 10262
CONCRETE MIX DESIGN 159
CONCRETE MIX DESIGN 161
The Relative Proportion Are Worked Out
A trial proportion is taken and combined gradation is worked out fore.g.35% fine aggregate 20% 10mm down aggregate, 45% 20mm downaggregate.
CONCRETE MIX DESIGN 162
Combined gradation is plotted and pushed towards Ideal curveby increasing or decreasing the sand content
CONCRETE MIX DESIGN 163
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 aggregateSca20=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 beC +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 becomingobsolete.
In many cases use of gap graded aggregate becomes unavoidable. In manyparts of the country the practice is to use 20mm coarse aggregates without10mm aggregates. This is because of quality of 10mm aggregates producedfrom jaw crusher is very poor .Gap grading does not fit in to the standardcombined grading curves of RRL method.
Sand available in some parts of country is graded that it is high on coarsefraction (1.18mm and above) and low on fines (600micron and below). Itis difficult to adjust the sand content to match any of the standardcombined grading curves .The combined grading curve often cuts acrossmore than one standard curves in such cases
CONCRETE MIX DESIGN 164
Different aggregate to cement ratios are given fordifferent levels of workability ranging from low tohigh. But these levels of workability are not definedin terms of slump, compaction factor or Vee Bee timeas in case of other methods.
The fine aggregate content cannot be adjusted fordifferent cement contents. Hence the richer mixesand leaner mixes may have same sand proportion,for a given set of materials.
CONCRETE MIX DESIGN 165
References• Concrete Technology by: R.P. Rethaliya• Concrete Technology by . M.S. Shetty
• Internet websites• http://www.foundationsakc.org/