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. The proportioning of ingredient of concrete is governed by the required performance of concrete in 2 states namely the plastic and the hardened states. If the plastic concrete is not workable, it cannot be properly placed and compacted. The property of workability, therefore, becomes of vital importance
The
compressive strength of hardened concrete which is generally considered to be
an index of its other properties, depends upon many factors, e.g. quality and
quantity of cement, water and aggregates; batching and mixing placing,
compaction and curing. The cost of concrete is made up of the cost of
materials, plant and labour. The variations in the cost of materials arise from
the fact that the cement is several times costly than the aggregate, thus the
aim is to produce as lean a mix as possible. From technical point of view the
rich mixes may lead to high shrinkage and cracking in the structural concrete,
and to evolution of high heat of hydration in mass concrete which may cause
cracking.
The
actual cost of concrete is related to the cost of materials required for
producing a minimum mean strength called characteristic strength that is
specified by the designer of the structure. This depends on the quality control
measures, but there is no doubt that the quality control adds to the cost of
concrete. The extent of quality control is often an economic compromise, and
depends on the size and type of job. The cost of labour depends on the
workability of mix, e.g., a concrete mix of inadequate workability may result
in a high cost of labour to obtain a degree of compaction with available
equipment.
Requirements
of concrete mix design
The
requirements which form the basis of selection and proportioning of mix
ingredients are
The
minimum compressive strength required from structural consideration
The
adequate workability necessary for full compaction with the compacting
equipment available.
Maximum
water-cement ratio and/or maximum cement content to give adequate durability
for the particular site conditions
Maximum
cement content to avoid shrinkage cracking due to temperature cycle in mass
concrete
Types of Mixes
Nominal Mixes
In the past the specifications for concrete
prescribed the proportions of cement, fine and coarse aggregates. These mixes
of fixed cement-aggregate ratio which ensures adequate strength are termed
nominal mixes. These offer simplicity and under normal circumstances, have a
margin of strength above that specified. However, due to the variability of mix
ingredients the nominal concrete for a given workability varies widely in
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.
IS 456-2000 has designated the concrete mixes into
a number of grades as 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.
Designed Mixes
In these mixes the performance of the concrete is
specified by the designer but the mix proportions are determined by the
producer of concrete, except that the minimum cement content can be laid down.
This is most rational approach to the selection of mix proportions with
specific materials in mind possessing more or less unique characteristics. The
approach results in the production of concrete with the appropriate properties
most economically. However, the designed mix does not serve as a guide since
this does not guarantee the correct mix proportions for the prescribed
performance.
For the concrete with undemanding performance
nominal or standard mixes (prescribed in the codes by quantities of dry
ingredients per cubic meter and by slump) may be used only for very small jobs,
when the 28-day strength of concrete does not exceed 30 N/mm2. No
control testing is necessary reliance being placed on the masses of the
ingredients
Factors affecting the choice of mix proportions
The
various factors affecting the mix design are:
Compressive strength
It is one
of the most important properties of concrete and influences many other
describable properties of the hardened concrete. The mean compressive strength
required at a specific age, usually 28 days, determines the nominal
water-cement ratio of the mix. The other factor affecting the strength of
concrete at a given age and cured at a prescribed temperature is the degree of
compaction. According to Abraham’s law the strength of fully compacted concrete
is inversely proportional to the water-cement ratio
Workability
The
degree of workability required depends on three factors. These are the size of
the section to be concreted, the amount of reinforcement, and the method of
compaction to be used. For the narrow and complicated section with numerous
corners or inaccessible parts, the concrete must have a high workability so
that full compaction can be achieved with a reasonable amount of effort. This
also applies to the embedded steel sections. The desired workability depends on
the compacting equipment available at the site
Durability
The
durability of concrete is its resistance to the aggressive environmental
conditions. High strength concrete is generally more durable than low strength
concrete. In the situations when the high strength is not necessary but the
conditions of exposure are such that high durability is vital, the durability
requirement will determine the water-cement ratio to be used.
Maximum nominal size of aggregate
In
general, larger the maximum size of aggregate, smaller is the cement
requirement for a particular water-cement ratio, because the workability of
concrete increases with increase in maximum size of the aggregate. However, the
compressive strength tends to increase with the decrease in size of aggregate
IS
456:2000 and IS 1343:1980 recommend that the nominal size of the aggregate
should be as large as possible
Grading and type of aggregate
The
grading of aggregate influences the mix proportions for a specified workability
and water-cement ratio. Coarser the grading leaner will be mix which can be
used. Very lean mix is not desirable since it does not contain enough finer
material to make the concrete cohesive
The type
of aggregate influences strongly the aggregate-cement ratio for the desired
workability and stipulated water cement ratio. An important feature of a
satisfactory aggregate is the uniformity of the grading which can be achieved
by mixing different size fractions
Quality Control
The
degree of control can be estimated statistically by the variations in test
results. The variation in strength results from the variations in the
properties of the mix ingredients and lack of control of accuracy in batching,
mixing, placing, curing and testing. The lower the difference between the mean
and minimum strengths of the mix lower will be the cement-content required. The
factor controlling this difference is termed as quality control
Mix Proportion designations
The
common method of expressing the proportions of ingredients of a concrete mix is
in the terms of parts or ratios of cement, fine and coarse aggregates. For
e.g., a concrete mix of proportions 1:2:4 means that cement, fine and coarse
aggregate are in the ratio 1:2:4 or the mix contains one part of cement, two
parts of fine aggregate and four parts of coarse aggregate. The proportions are
either by volume or by mass. The water-cement ratio is usually expressed in
mass
Factors to be considered for mix design
The grade
designation giving the characteristic strength requirement of concrete
The type
of cement influences the rate of development of compressive strength of
concrete
Maximum
nominal size of aggregates to be used in concrete may be as large as possible
within the limits prescribed by IS 456:2000
The
cement content is to be limited from shrinkage, cracking and creep
The
workability of concrete for satisfactory placing and compaction is related to
the size and shape of section, quantity and spacing of reinforcement and technique
used for transportation, placing and compaction
Procedure
Determine
the mean target strength ft from the specified characteristic compressive
strength at 28-day fck and the level of quality control.
ft =
fck + 1.65 S
where S
is the standard deviation obtained from the Table of approximate contents given
after the design mix
Obtain
the water cement ratio for the desired mean target using the emperical
relationship between compressive strength and water cement ratio so chosen is
checked against the limiting water cement ratio. The water cement ratio so
chosen is checked against the limiting water cement ratio for the requirements
of durability given in table and adopts the lower of the two values
Estimate
the amount of entrapped air for maximum nominal size of the aggregate from the
table
Select
the water content, for the required workability and maximum size of aggregates
(for aggregates in saturated surface dry condition) from table
Determine
the percentage of fine aggregate in total aggregate by absolute volume from
table for the concrete using crushed coarse aggregate
Adjust
the values of water content and percentage of sand as provided in the table for
any difference in workability, water cement ratio, grading of fine aggregate
and for rounded aggregate the values are given in table
Calculate
the cement content form the water-cement ratio and the final water content as
arrived after adjustment. Check the cement against the minimum cement content
from the requirements of the durability, and greater of the two values is
adopted
From the
quantities of water and cement per unit volume of concrete and the percentage
of sand already determined in steps 6 and 7 above, calculate the content of
coarse and fine aggregates per unit volume of concrete from the following
relations
where V =
absolute volume of concrete = gross volume (1m3) minus the volume of
entrapped air
Sc =
specific gravity of cement
W = Mass
of water per cubic metre of concrete, kg
C = mass
of cement per cubic metre of concrete, kg
p = ratio
of fine aggregate to total aggregate by absolute volume
fa,
Ca = total masses of fine and coarse aggregates, per cubic
metre of concrete, respectively, kg, and
Sfa,
Sca = specific gravities of saturated surface dry fine and coarse
aggregates, respectively
Determine the concrete mix proportions for the first trial mix.
Prepare the concrete using the calculated proportions and cast three
cubes of 150 mm size and
test them wet after 28-days moist curing and check for the strength
Prepare trial mixes with suitable adjustments till the final mix
proportions are arrived at
Example
Parameters for mix design M40
Grade Designation = M-40
Type of cement = O.P.C-43 grade
Brand of cement = …………………………………
Admixture = ……………………..
Fine Aggregate = Zone-II (assumed)
Sp. Gravity Cement = 3.15
Fine Aggregate = 2.61
Coarse Aggregate (20mm) = 2.65
Coarse Aggregate (10mm) = 2.66
Minimum Cement (As per contract) = 400 kg / m3
Maximum water cement ratio (As per contract) = 0.45
Mix Calculation
Target Mean Strength = 40 + (5 X 1.65) =
48.25 Mpa
Selection of water cement ratio
Assume water cement ratio = 0.4
Calculation of cement content
Assume cement content 400 kg / m3
(As per contract Minimum cement content 400 kg / m3)
Calculation of water: -
400 X 0.4 = 160 kg Which is less than 186 kg (As per Table No. 4, IS: 10262)
Hence o.k.
5. Calculation for C.A. & F.A.: – As
per IS : 10262 , Cl. No. 3.5.1
V = [ W + (C/Sc) + (1/p) . (fa/Sfa)
] x (1/1000)
V = [ W + (C/Sc) + {1/(1-p)} .
(ca/Sca) ] x (1/1000)
Where
V = absolute volume of fresh concrete,
which is equal to gross volume (m3) minus the volume of entrapped
air ,
W = mass of water ( kg ) per m3 of
concrete ,
C = mass of cement ( kg ) per m3 of
concrete ,
Sc = specific gravity of
cement,
(p) = Ratio of fine aggregate to total
aggregate by absolute volume ,
(fa) , (ca) = total mass of fine aggregate
and coarse aggregate (kg) per m3 of
Concrete respectively, and
Sfa , Sca = specific gravities of saturated
surface dry fine aggregate and Coarse aggregate respectively.
As per Table No. 3 , IS-10262, for 20mm
maximum size entrapped air is 2% .
Assume F.A. by % of volume of total
aggregate = 36.5 %
0.98 = [ 160 + ( 400 / 3.15 ) + ( 1 / 0.365
) ( Fa / 2.61 )] ( 1 /1000 )
=> Fa = 660.2 kg
Say Fa = 660 kg.
0.98 = [ 160 + ( 400 / 3.15 ) + ( 1 / 0.635
) ( Ca / 2.655 )] ( 1 /1000 )
=> Ca = 1168.37 kg.
Say Ca = 1168 kg.
Considering 20 mm : 10mm = 0.6 : 0.4
20mm = 701 kg .
10mm = 467 kg .
Hence Mix details per m3
Cement = 400 kg
Water = 160 kg
Fine aggregate = 660 kg
Coarse aggregate 20 mm = 701 kg
Coarse aggregate 10 mm = 467 kg
Admixture = 0.6 % by weight of cement = 2.4 kg.
Recron 3S = 900 gm
Water: cement: F.A.: C.A. = 0.4: 1:
1.65: 2.92
Observation: -
A. Mix was cohesive and homogeneous.
B. Slump = Masured
C. No. of cube casted = __ Nos.
7 days average compressive strength = ___ MPa.
28 days average compressive strength = ____ MPa which is greater than 48.25MPa
Hence the mix is accepted