A paper presented at the Nigerian Institute of Building (NIOB) Mandatory Workshop

1. Design of Concrete Mix and FieldApplications
Bldr. (Dr.) Olawuyi Babatunde James
Department of Building, Federal University of Technology, Minna, Nigeria
babatunde@futminna.edu.ng; babatundeolawuyi@yahoo.com
Being a Paper presented at the 2-Day National Workshop of the Nigerian Institute of Building
(NIOB) with the theme “Building Production and Structural Stability”.
NB: The various Tables and Chart quoted from Neville (2012) and the Nigerian ‘Concrete Mix
Design Manual’ has to be provided for all participants during the Workshop for hand-on training.
1.0 INTRODUCTION:
Design of concrete mix refers to the appropriate selection of different ingredients of concrete to be
designed for specific purpose (Addis & Goodman). This exercise must result in a mixture that
meets the following requirements:
• In the fresh state, can be transported without segregation, placed, compacted and finished
(if necessary) with available equipments.
• In the hardened state, satisfactorily meet the required strength, durability and dimensional
stability (Beushausen & Dehn, 2009; Neville, 2012).
The concept of design of concrete mix implies determination of an appropriate and economical
combination of concrete constituents that can be used for a first trial batch to produce a concrete
close to that which can achieve a good balance between the various desired properties of the
concrete at the lowest possible cost (Aītcin, 1998).
Concrete in the recent times are specified in the form of minimum required strength and this come
along with material specification and expected water/cement (w/c) or water/binder (W/B) ratio
depending on the type and category of concrete being prepared. A summary classification of
concrete in the recent code of practice (Euroced 2 – BS EN 206-1-2001) and based on best practices
are presented in Table 1 below.
Table 1: Strength classes for normal weight concrete according to BS EN 206-1:2001 and classification
according to fib Model Code 2010 (Dehn, 2012)
Concrete type Strength class 𝑓𝑐𝑘,𝑐𝑦𝑙
/𝑓𝑐𝑘,𝑐𝑢𝑏𝑒
Low strength concrete C8/10 C12/15 C16/20
Normal strength concrete C20/25 C25/30 C30/37 C35/45 C40/50 C45/55 C50/60
High strength concrete C55/67 C60/75 C70/85 C80/95 C90/105 C100/115
Ultra-high strength concrete*
C110/130, C120/140
*not included in BS EN 206-1:2001;

2. 𝑓𝑐𝑘,𝑐𝑦𝑙
= the Cylinder strength while 𝑓𝑐𝑘,𝑐𝑢𝑏𝑒
= cube strength.
The strength classes might guide the requisite approach to the mix proprtioning and materials
selection for pactical application which is the focus of this workshop.
2.0 APPROCAHES TO DESIGN OF CONCRETE MIXES
Selection of concrete mix ingredients and their proportions is referred to as mix design in the British
usage while the Americans term for it is mixture proportioning. It is different from the structural
design process of concrete whose concern is about required performance of the concrete and not
the detailed proportioning of the materials which will ensure that performance. The output from a
structural design process for a Beam for instance in recent times comes as use 25 – 410 concrete
with the reinforcement details attached. This implies a concrete that will produce minimum 28-day
cube strength of 25 N/mm2
is required while the reinforcement bars should be of minimum yield
strength of 410 N/mm2
. The onus is thereby on the Professional Builder on site to select appropriate
materials from the neighbourhood, at appropriate proportion which must give the requisite strength
and durability performance. The mix selection process will be expected to take cognisance of the
workability (in terms of slump and slump retention) as required for the construction procedure
(handling, transporting and placing). Also, of importance is the curing method to be adopted for
achieving the performance specified for the concrete.
The mix selection can therefore be summarised as the process of choosing suitable ingredients of
concrete and determining their relative quantities with the object of producing as economically as
possible a concrete of certain minimum properties, notably strength, durability and a required
consistency (Neville, 2012).
The basic factors of consideration in material selection process for normal strength concrete (NSC)
generally can be explained as shown in the flow chart presented in Figure 1

3. Figure 1: Basic Factors in the process of mix selection
The traditional mix proportioning approach popular in Nigeria has been prescribed proportion of
cement to fine and coarse aggregates (e.g. 1:2:4 mix), but this approach, many times had resulted
in varying strength despite working with fixed cement-aggregate proportion and a given
workability. The inclusion of minimum strength to concrete mix prescription thereby calls for good
understanding of the material properties and the selection procedure. The usual range of properties
in mix selection as outlined by Neville (2012) are;
i. ‘Minimum’ compressive strength necessary for structural consideration.
ii. Maximum w/c ratio and/or minimum cement content and, in certain conditions of
exposure, a minimum content of entrained air to give adequate durability.
iii. Maximum cement content to avoid cracking due to temperature cycle in mass concrete;
Durability
requirement
Method of
Transportation
Method of
compaction
Size of section and
spacing of
reinforcement
Quality
control
Minimum
strength
Required
workability
Maximum
size of
Aggregate
s
Aggregate
shape and
texture
Mean
strength
Thermal
Requirement
Age at which
strength is
required
Nature of
Cementitious
Material
Water/Cement
Ratio
Cement
Content
Overall
Grading of
Aggregate
Proportion of
each size
fraction
Mix Proportions
Capacity of
concrete mixer
Mass of ingredient
per batch

4. iv. Maximum cement content to avoid shrinkage cracking under conditions of exposure of
low humidity; and
v. Minimum density for gravity dams and similar structures.
In reference to the above the properties, approaches to design of NSC mixes are basically two.
i. American Method
ii. British Method
2.1 American Method of Mix Proportion
The ACI Standard Practice ACI 211.1 – 91 otherwise referred to as American Method provides a
first approximation of mix proportions to be used in trial mixes. The method consists of sequence
of logical eight (8) steps outlined as follows:
2.1.1 Step 1: Choice of slump
This require determination of the slump range (minimum and maximum slump value) at the time
of mix proportion. This is governed by the workability requirements and avoidance of segregation
of mix.
2.1.2 Step 2: Choice of maximum size of aggregate
This is often decided by the structural designer bearing in mind the geometric requirements of
member size and spacing of reinforcement or based on availability.
2.1.3 Step 3: Estimate of water content and air content
Governing factors for this step are maximum size of aggregate, its shape, texture and grading; the
content of entrained air, the use of admixtures with plasticizing or water reducing properties and
temperature of concrete. Table 14.5 of Neville (2012) can be used here.
2.1.4 Step 4: Selection of water/cement ratio
Selection of w/c ratio is guided by the strength and durability requirements. In regards to strength,
the average value aimed at (i.e. ‘target strength’ – 𝑓𝑐𝑟
’
) must exceed the specified ‘minimum’
strength (𝑓𝑐) by an approximate margin as shown in the formulae below:

5. 𝑓
𝑐𝑟
′
= 𝑓
𝑐 + 1.343𝜎 (1)
𝑓
𝑐𝑟
′
= 𝑓
𝑐 + 2.33𝜎 − 3.5 (2)
Where: 𝜎 𝑖𝑠 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛; 𝑓
𝑐𝑟
’
is target strength at maturity (often 28 days) and 𝑓
𝑐 is the
characteristic strength obtained from previous onsite data (ACI 318-02 and ACI 322).
Equation 1 ensures that there is a 99% probability that the average of all sets of three consecutive
compressive strength tests will be equal to or greater than 𝑓
𝑐. The second equation ensures that there
is a 99% probability that no single test will have a compressive strength lower than 𝑓𝑐 - 3 MPa (ACI 363
R-92).
2.1.5 Step 5: Calculation of cement content
This is obtained using the outcome of Step 3 and 4. Durability consideration however requires a
certain minimum cement content. This implies the larger of the two values should be used.
2.1.6 Step 6: Estimate of coarse aggregate content
Here assumption is made that the optimum ratio of the bulk volume of coarse aggregate to the total
volume of concrete depends only on the maximum size of aggregate and on the grading of fine
aggregate. Shape of the coarse aggregate particle is taken to be of no consequence. Table 14.6,
Neville (2012) gives the values of optimum volume of coarse aggregate in relation to the fineness
moduli of fine aggregate.
2.1.7 Step 7: Estimate of fine aggregate content
The absolute volume of the fine aggregate can be obtained by subtracting the sum of absolute
volumes of water, cement, entrained air and coarse aggregate from the volume of concrete. We
then convert the absolute volume of fine aggregate into mass by multiplying this volume by the
specific gravity of the fine aggregate and by the density of water.
Alternatively, the mass of fine aggregate can be obtained directly by subtracting the total mass of
other ingredients from the mass of a unit volume of concrete.

6. 2.1.8 Step 8: Adjustments to mix proportions
This involves making trial mixes and adjustment made appropriately with slump check used as
guide.
2.2 British Method
The British method otherwise referred to as Department of the Environment (DOE) method just as
the American ACI 211 approach also recognize the durability requirements in mix selection. It
consists of five (5) steps outlined in Neville (2012) as follows:
2.2.1 Step 1: Compressive strength for the purpose of determining water/cement ratio
Here the concept of mean target strength (fm) is introduced, similar to minimum compressive
strength (𝑓𝑐𝑟) of the ACI 318R – 92 as shown in Equation 1 and 2 of Section 2.1.4.
The Equation for mean target strength here is determined using the formulae
𝑓
𝑚 = 𝑓
𝑐 + 𝑘𝜎 (3)
The k-value here is taken as 1.64 while 𝑓
𝑚 now replace 𝑓
𝑐𝑟 of Equations 1 and 2.
Table 14.9 of Neville (2012) gives strength assumed at a w/c ratio of 0.5 for different cements and
types of aggregate. These values applied to a hypothetical concrete of medium richness cured in
water at 20 o
C. The approximate value of strength (at w/c of 0.5) corresponding to the type of
cement, type of aggregate and age of concrete are to be used in Figure 14.12 of Neville (2012) to
get the required w/c for the target strength of interest.
2.2.2 Step 2: Determination of water content
The required workability expressed either as slump or Vebe time, recognising the influence of the
maximum aggregate size and its type (crushed or uncrushed) guides the choice – refer Table 14.10
of Neville (2012).

7. 2.2.3 Step 3: Determination of cement content
This is similar to Step 5 of the American method. It is simply output from Step 1 divided by output
for Step 2.
2.2.4 Step 4: Determination of the total aggregate content
This requires an estimate of the fresh density of fully compacted concrete which can be read off
from Figure 14.13 Neville (2012) for the appropriate water content (from Step 2) and specific
gravity of the aggregate. If this is unknown, Neville (2012) specify the value of 2.6 for uncrushed
and 2.7 for crushed aggregate can be assumed. The aggregate content can then be obtained by
subtracting the value of cement content and water content from the fresh density arrived at.
2.2.5 Step 5: Determination of proportion of fine aggregate from total aggregate content
This involves using Figure 14.14, Neville (2012) which gives data for only 20 and 40-mm
aggregates. The governing factors here are the maximum size of aggregate, the level of workability,
the w/c and the percentage of fine aggregate passing the 600 µm sieve. Once the proportion of fine
aggregate has been obtained, multiplying it by the total aggregate content give the content of fine
aggregate.
The coarse aggregate content can then be calculated by subtracting the fine aggregate content from
the total aggregate content. Table 14.11 of Neville (2012) further gives a general guide for dividing
the coarse aggregate into appropriate fractions depending on the aggregate shape.
2.3 Nigerian Concrete Mix Design Manual
The Nigerian version of the mix selection approach termed “Concrete Mix Design Manual”
developed by the Council for the Regulation of Engineering in Nigeria (COREN) published in
2017 also adopts five (5) Steps similar to the British method as outlined below;
Step 1: Determination of target strength
Step 2: Determination of water-cement ratio

8. Step 3: Determination of water content
Step 4: Determination of cement content and
Step 5: Determination of aggregate content.
A closer look at the Nigerian “Concrete Mix Design Manual” revealed it as a modified form of
the British method in which case Steps 1 of the British method now becomes Steps 1 and 2 in the
Nigerian manual while Steps of 4 and 5 of the British method now becomes merged into Step 5
of the ‘Concrete Mix Design Manual’. The Nigerian Concrete Mix Design Manual also maintains
the target mean strength (𝑓
𝑚) with same formulae (Equation 3) as the British method while
Tables and Charts applicable for British method now developed in simplified form in consonance
with the observed data on available local materials for use in Nigeria. A good understanding of
the British method as discussed above will enhance effective use of the Nigerian ‘Concrete Mix
Design Manual’ too. An attempt will be made at the NIOB Workshop to have worked examples
discussed using the Nigerian ‘Concrete Mix Design Manual’.
2.4 Mix Selection for High Strength/High Performance Concrete
Strength classes above the C50/60 as stated in Table 1 above requires special handling in material
selection and mix proportioning. This category of concrete is referred to as High Strength/
High-performance concrete (HSC/HPC). HPC on the other hand is defined by ACI (1999) as
concrete meeting special combinations of performance and uniformity requirements that cannot
always be achieved routinely using conventional constituents and normal mixing, placing, and
curing practice (ACI THPC/TAC, 1999). HPC is a type of concrete specially designed to meet a
combination of performance and requirements which specifically includes high strength or high
early strength, durability and high elastic modulus (Kosmatka et al, 2002; Neville, 2012). Its
application includes precast pylons, piers and girders of many long span bridges in the world;

9. tunnels, tall and ultra-high buildings; shotcrete repairs, poles, parking garages and agricultural
applications (Kosmatka et al, 2002).
Neville (2012) pointed out that a generalised systematic approach of mix proportioning for HPC is
yet to be developed. The peculiarity and performance requirements in HPC have however made
the known mix design approaches to be inadequate due to the following reasons identified in
literature (Aītcin, 1998; Addis & Goodman, 2009; Neville, 2012).
• The use of superplasticisers now, enhances low W/B in HPC.
• HPC often contains one or more SCM which in many cases replaces a significant amount
of cement.
• The presence of SF in HPC causes significant changes in properties of fresh and hardened
concrete.
• Workability of HPC can be adjusted using superplasticisers without altering the W/B.
The American Concrete Institute offers a method of design for HSC in their state-of-the-art-report
on high-strength concrete (ACI 363 R-92, reapproved in 1997). The procedure like the known
method for NSC (the D.O.E and ACI 211-1) specified the required target strength fcr
’
(MPa) same
as in ACI 211-1 stated in Equation 1 and 2 earlier.
Mehta & Monteiro (2014) also proposed a simplified mixture proportioning procedure applicable
for concrete of compressive strength range 60 MPa to 120 MPa. It is said to be suitable for coarse
aggregate having maximum size range of 10 to 15 mm and slump range of 200 to 250 mm. It
assumes a 2 % entrapped air volume for non-air entrained HPC, which can be increased to 5 to 6 %
and suggested an optimum aggregate volume of 65%.
Aītcin (1998) on the other hand presented a design approach for HPC said to be initiated by five
different mix characteristics beginning with decision on W/B ratio. The sequence of Aītcin (1998)
approach is as follows:
• No. 1 – the W/B;
• No. 2 – the water content;

10. • No. 3 – the superplasticiser dosage;
• No. 4 – the coarse aggregate content and
• No. 5 – the entrapped air content (assume value).
The procedure is presented in the chart shown in Figure 2.1.
Figure 2: Mix Design Process for HPC (Aītcin, 1998)
The cement content in HPC mixtures is often very high but Neville (2012) advise against excessive
content of cementitious material and recommends 500 – 550 kg/m3
of which 10 % being silica
fume as advisable maximum. Fine aggregate type specified for HPC is expected to be of round
particle shape having fineness modulus of 2.5 to 3 while of importance is the compatibility of the
superplasticizer to the binder combination/type. The conventional slump test cannot serve as check
STEP 1 STEP 2 STEP 3 STEP 4 STEP 5
Binder content
Final composition
Strength
Workability
Trial batch
Sand content
Adjustment
Change W/B
ratio
Air content
Coarse aggregate
content
W/B selection Water selection
Superplasticisers
dosage
Yes
No
Yes
No

11. for workability/consistency but rather a slump flow test giving slump flow result of 400 – 600 mm
is specified in Neville (2012) for HPC as a check for the trial mix.
3.0 Worked Examples
3.1 Example 1: American Method
If we require a mix with a mean 28-day cylinder compressive strength of 35 MPa and a slump of
50 mm, ordinary Portland cement being used. The maximum size of well-shaped, angular
aggregate is 20 mm, its bulk density is 1600 kg/m3
, and its specific gravity is 2.64. The available
fine aggregate has a fineness modulus of 2.60 and a specific gravity of 2.58. No air entrainment is
required.
Solution:
Step 1: Slump as specified is 50 mm.
Step 2: Maximum size of aggregate specified is 20 mm.
Step 3: From Table 14.5 (Neville, 2012) – water requirement is 190 kg/m3
of concrete.
Step 4: water/cement (w/c) for cylinder strength of 35 MPa is 0.48 (from experience); there is no
durability requirement stated.
Step 5: Cement content =
𝑤𝑎𝑡𝑒𝑟 𝑐𝑜𝑛𝑡𝑒𝑛𝑡
𝑤/𝑐
= 190/0.48 = 395 kg/m3
Step 6: From Table 14.6, using fine aggregate having a fineness modulus of 2.60, the bulk volume
of oven-dry rodded coarse aggregate with a maximum size of 20 mm is 0.64.
Given that the bulk density of the coarse aggregate is 1600 kg/m3
; the mass of the coarse aggregate
is 0.64 x 1600 = 1020 kg/m3
.
Step 7: Estimate of fine aggregate content
We calculate the mass of all the constituent and then subtract from unit mass of the concrete.
Volume of water is 190/1000 = 0.190 m3

12. Solid volume of cement, assuming usual specific gravity of 3.15, is 395/ (3.15 x 1000) = 0.126 m3
Solid volume of coarse aggregate is 1020/ (2.64 x 1000) = 0.396 m3
Volume of entrapped air, (see Table 14.5) is 0.02 x 1000 = 0.020 m3
Hence, total volume of all ingredients except fine aggregate = 0.732 m3
Therefore, the required volume of fine aggregate is 1.000 – 0.732 = 0.268 m3
The mass of the fine aggregate is then 0.268 x 2.58 x 1000 = 690 kg/m3
.
From the various steps, we can list the estimated mass of each of the ingredients in kilograms per
cubic metre of concrete as follows:
Water 190
Cement 395
Coarse 1020
Fine aggregate, dry 690
Therefore, the density of concrete is 2295 kg/m3
.
It is this material proportion that will then be used for trial mix and slump checked to decide if
there will be need for adjustment or not as required by Step 8.
3.2 Example 2: British Method
Select a mix to satisfy requirements of a 28-day cube compressive strength of 44 MPa; a slump of
50 mm; uncrushed aggregate with a maximum size of 20 mm; specific gravity of aggregate of 2.64;
60 % of the fine aggregate passes the 600 um sieve; no air entrainment required; ordinary Portland
cement (OPC) to be used.
Solution:
Step 1: Table 14.9, Neville (2012) – OPC; uncrushed aggregate gives 28-day strength as 42 MPa.
Using Figure 14.12 (Neville, 2012) we got w/c of required concrete (𝑓𝑐𝑘,𝑐𝑢𝑏𝑒
of 44 MPa) = 0.48
Step 2: From Table 14:10, for 20 mm uncrushed and 50 mm slump, water content = 180 kg/m3
Step 3: The cement content =
𝑤𝑎𝑡𝑒𝑟 𝑐𝑜𝑛𝑡𝑒𝑛𝑡
𝑤/𝑐
= 180/0.48 = 375 kg/m3

13. Step 4: Figure 14.13, for water content of 180 kg/m3
and aggregate specific gravity of 2.64, we
read off the fresh density of concrete as = 2400 kg/m3
The total aggregate content is therefore = 2400 – 375 – 180 = 1845 kg/m3
Step 5: Figure 14.14, using maximum aggregate size of 20 mm and a slump 50 mm, 60 % of fine
aggregate passing 600 um sieve at a w/c of 0.48 gives proportion of fine aggregate as 32 % (by
mass of total aggregate). Hence the fine aggregate content is 0.32 x 1845 = 590 kg/m3
The coarse aggregate content therefore is 1845 – 590 =1255 kg/m3
.
The material to be used for trial mix are therefore summarised as follows:
Water = 180
Cement = 375
Fine aggregate = 590
Coarse aggregate = 1255
Density of concrete = 2400 kg/m3
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