Normal Concrete Mix Design
1. Prescribed Mix (Standard Mix)
(Source: General Specification for Civil Engineering Works)
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2. Designed Mix
2.1 Variability of Strength

Design is based on the assumption of certain minimum properties of concrete,
such as strength.

Actual strength of the concrete produced is a variable quantity.

Source of variability include variations in mix ingredients, changes in concrete
making and placing; variations also occur in sampling procedure and testing.

Knowledge of variability is required so that the strength values can be
interpreted properly.
2.2 Target Strength and Characteristic Strength

It is generally accepted that the variation in concrete strengths or a particular
mix follows the normal distribution as shown below:
Figure 1
Normal distribution of concrete strength
(Source: Building Research Establishment)

In the figure above, the mean strength of the mix is 40 N/mm2.
That is, we can
expect half of the test results will be higher than 40 N/mm2 and half will be
lower.

In practice, we specify the quality of concrete not as a minimum strength, and
not as a mean strength, but as a characteristic strength below which a specified
percentage of the test results, often called defectives, may be expected to fall.
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
Characteristic strength may be defined as to have any proportion of defectives.
(BS 5328 – Guide to Specifying Concrete, and BS8110 – Structural Use of
Concrete adopt the 5% defective level.)

As a result, it is necessary to design a mix to have a target mean strength greater
than the specified characteristic strength by an amount termed the margin.
Target mean strength = characteristic strength + margin
fm = fk + k × s
where

fm
= target mean strength
fk
= characteristic strength
k×s
= margin
k
= constant
s
= standard deviation
Constant k is derived from the mathematics of the normal distribution.
Defective
Constant
1%
2.33
2.5 %
1.96
5%
1.64
Example 1
To design a concrete mix with characteristic strength of 30 MPa, what should the
target mean strength be?
Given that : defective level 5%, standard deviation 5 MPa.
Solution
fk = 30 MPa
k = 1.64
s = 5 MPa
fm = fk + k × s
= 30 + 1.64 x 5 MPa
= 38.2 MPa
The target mean strength should be 38.2 MPa
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2.3 BRE Mix Design Method (Formerly DoE Method)

“Design of Normal Concrete Mixes” was published by the Building Research
Establishment Ltd. in 1997.

(Formerly by Department of Environment).
The design procedure is summarized in chart below:
(Source: Building Research Establishment)
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(Source: Building Research Establishment)
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Equations for mix design
C1
M=kxs
where M = the margin
k = a value appropriate to the ‘percentage defectives’ permitted below the
characteristic strength
s = the standard deviation
C2
f m = fc + M
where fm = the target mean strength
fc = the specified characteristic strength
M = the margin
C3
C4
Cement content =
free - water content
free - water / cement ratio
Total aggregate content (saturated and surface–dry) = D – C – W
where D = the wet density of concrete (kg/m3)
C = the cement content (kg/m3)
W = the free water content (kg/m3)
C5
C6
Fine aggregate content = total aggregate content x proportion of fines
Coarse aggregate content = total aggregate content – fine aggregate content
Portland cement content =
(100  p) W
(100  0.7 p) [W / (C  0.3 F)]
where W = the free water content (kg/m3)
C = the cement content (kg/m3)
F = pfa content (of the mix) (kg/m3)
p = proportion of pfa specified as percentage of the combined weight of cement and
pfa
the ratio of W/(C+0.3F) is derived from Table 10 and Figure 4
C7
pfa content =
pC
100 - p
where C = the cement content (kg/m3)
p = proportion of pfa specified as percentage of the combined weight of cement and
pfa
C8
C9
W
for comparison of maximum free-water/cement ratio
CF
where W = the free water content (kg/m3)
C = the cement content (kg/m3)
F = pfa content (kg/m3)
Total aggregate content (saturated and surface dry) = D – (C + F) – W
where W = the free water content (kg/m3)
C = the cement content (kg/m3)
F = pfa content (of the mix) (kg/m3)
D = the wet density of concrete (kg/m3)
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Figure 3
Relationship between standard deviation
and characteristic strength
Figure 4
Relationship between
compressive strength and
free-water/cement ratio
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Figure 5 Estimated wet density of fully compacted concrete
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Figure 6
Recommended proportions of fine aggregate according to percentage passing 600 μm sieve
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Example 2 – unrestricted design
Specification of the mix:

Characteristic compressive strength 30 N/mm2 at 28 days

Defective rate 2.5 %

No previous control data

Cement: OPC class 42.5

Slump required, 10-30 mm

Maximum free-water/Cement ratio 0.55

Minimum cement content 290 kg/m3

Coarse aggregate:

Fine aggregate: Uncrushed with 70% passing 600 µm sieve

Relative density of aggregate : 2.6 (assumed)

Volume of trial mix : 0.05 m3
Uncrushed single sized 10 mm and 20 mm (1:2 by weight)
Example 3 – mix restricted by maximum water/cement ratio
Specification of the mix:

Characteristic compressive strength 25 N/mm2 at 28 days

No previous control data but a margin of 10 N/mm2 is specified

Cement: OPC class 42.5

Slump required, 30-60 mm

Maximum free-water/Cement ratio 0.5

Minimum cement content 290 kg/m3

Coarse aggregate:
Uncrushed single sized 10, 20 and 40 mm
(Suggested ratio 1 : 1.5 : 3 by weight)

Fine aggregate: Uncrushed with 90% passing 600 µm sieve

Relative density of aggregate : 2.5 (assumed)

Volume of trial mix : 0.08 m3
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Solution of Example 2
(Source: Building Research Establishment)
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Solution of Example 3
(Source: Building Research Establishment)
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Example 4 – mix restricted by minimum cement content
Specification of the mix:

Same as example, but

Slump required 0 -10 mm
Example 5 – mix restricted by maximum cement content
Specification of the mix:

Characteristic compressive strength 50 N/mm2 at 7 days

Defective rate 1 %

Previous control data: standard deviation 5 N/mm2

Cement: RHPC class 52.5

Slump required, 30-60 mm

Maximum cement content 550 kg/m3

Coarse aggregate:

Fine aggregate: Uncrushed with 45% passing 600 µm sieve

Relative density of aggregate : 2.7 (assumed)

Volume of trial mix : 0.08 m3
Crushed single sized 10 mm
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Solution of Example 4
(Source: Building Research Establishment)
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Solution of Example 5
(Source: Building Research Establishment)
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3
Trial Mixes
3.1 Moisture conditions of aggregates:
Aggregates may be in the following conditions:

Oven dry:- prolonged drying in an oven would eventually remove the moisture
completely.

Air dry:- when the aggregate is allowed to stand in dry air, some water will
evaporate so that the aggregate is air-dry.

Saturated surface dry (SSD):- all pores in the aggregate are full of water, i.e.,
saturated, but the surface of the aggregate is dry.

Damp or wet:- containing an excess of moisture on the surface (free water).
Moisture Condition of Aggregate
(Source: Design and Control of Concrete Mixtures Portland Cement Association)
3.2 Adjustment to mix proportion in trial mix

The batch quantities determined in the mix design are based on saturated
surface-dry (SSD) aggregates.

Very often, aggregates are in other conditions, adjustment of actual weights of
aggregates and water have to be made.
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3.3 Determination of mass of aggregate for trial mix
3.3.1
MT = MD × (
1  M.C.
)
1 A
where
MT
= the mass of aggregate to be weighed for trial mix
MD
= mass of aggregate designed, which the aggregate is assumed in SSD
condition.
M.C. = insitu moisture content of the aggregate (mass of water/mass of dry
aggregate) presented in decimal.
A
= water absorption of the aggregate (mass of absorbed water/mass of dry
aggregate) presented in decimal.
3.3.2
A simplified formula:
MT = MD × (1 + M.C. – A)

This formula gives an approximate result only but is accurate enough for most
practical purpose.
3.4. Determination of mass of water for trial mix
ΣMD = ΣMT
or
MTw + MTf + MT10 + MT20 + MT40 = MDw + MDf + MD10 + MD20 + MD40
MTw = MDw + MDf + MD10 + MD20 + MD40 - (MTf + MT10 + MT20 + MT40)
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Example 6
Quantities of the constituent materials for 0.05 m3 of a designed mix are:
Material
Designed Mass (kg)
Absorption (%)
Cement
17.0
-
Coarse aggregate (SSD)
69.2
1
Sand (SSD)
25.7
2
Water
8.0
-
If oven-dried aggregates are use, determine the mass of each constituent for trial mix.
Solution
MT = MD × (
1  M.C.
)
1 A
Coarse agg: MTc = 69.2 ×
1 0
1  0.01
Using
Using
MT = MD × (1 + M.C. –A)
MTc = 69.2 × (1 + 0 – 0.01)
= 68.5 kg
Sand:
MTs = 25.7 ×
1 0
1  0.02
= 68.5 kg
MTs = 25.7 × (1 + 0 – 0.02)
= 25.2 kg
= 25.2 kg
ΣMD = ΣMT
Water: Using
69.2 + 25.7 + 8 = 68.5 + 25.2 + MTw
MTw = 9.2 kg
Cement:
unchanged
Example 7
If moisture content of aggregates in example 6 are:
Coarse aggregate:
1.4 %
Sand
2.8%
determine the mass of each constituent for trial mix.
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3.5 Workability of trial mix

During the mixing of the trial mix, an experienced technician is able to adjust
the water content by eye inspection if the workability of the mix is much outside
the target range.

It is thus useful, initially, to withhold a small proportion, say 10% of the mixing
water until assessment of workability has been made to determine whether
deduction or addition of water is necessary.

Any adjustment of water ( MAw) must be recorded for later use.
4. Design iteration (Re-design)

The design tables and charts in the BRE method are based on the statistical data
in England.

Due to different sources of cement and aggregates, there may be deviation of
actual cube strength of trial mix from target strength. It is thus necessary to
undergo the re-design procedure.

The re-design procedure is same as the original design procedure excepted that
data obtained from tables and charts shall be replaced with actual measured data
in the first trial.
4.1 Free-water content

In Item 2.3 of the design table, use actual free-water content in the first trial
instead of obtaining from table 3.

Actual free water content (per m3) = (MDw  MAw) ÷ volume of first trial mix

Please note that any addition or deduction of water to bring the aggregate back
to SSD condition shall not be involved in the above calculation.
4.2 Density of fresh concrete

In Item 4.2, use actual measured fresh concrete density in the first trial.
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4.3 Free-water/cement ratio
In Item 1.7, the free-water/cement ratio shall be determined as follow:
a.
Determine the actual free-water/cement ratio in the first trial, which is
(MDw  MAw) ÷ Mcement
b. When the actual cube strength of the first trial is available, plot this result
together with the result in (a) on figure 4 to obtain a re-design water/cement ratio.
(Two examples are given as below.)
Example 8
Target mean strength 60 MPa
First trial

Free-water/cement ratio 0.37

No addition or deduction of water during first trial

Actual cube strength 70 MPa
Re-design

Plot point C1: W/C = 0.37, and
fc = 70 MPa

Get point D1: target = 60 MPa, and
W/C = 0.44
Example 9
Target mean strength 22 MPa
First trial

Free-water/cement ratio 0.62

Some water is added such that the actual free-water/cement ratio became 0.69

Actual cube strength 14 MPa
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Re-design

Plot point C2: W/C = 0.69, and
fc = 14 MPa

Get point D2: target = 22 MPa, and
W/C = 0.54
(Source: Building Research Establishment)
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