MAIN REFERENCES
1.
Teychene D C et al "Design of Normal Concrete Mixes" Department of
Environment, Building Research Establishment, 1992
2.
Neville A et al "Concrete Technology", revised reprint 1990, Longman Scientific and Technical. (Chapter 19 Mix Design and Chapter 17 Compliance with specifications are particularly relevant to the topic. Since design of concrete mix involved a wide range of knowledge of the constituent materials and testing methods and their influence on fresh and hardened concrete, other chapters may also referenced, particularly Chapters 2, 3, 5, 6,10, 16)
INTRODUCTION
In this lecture, design of concrete mixes is discussed based on the approach proposed by the Department of Environment, Building Research Establishment of United
Kingdom, which sometimes is referred to as DOE approach. Students are therefore recommended to refer Building Research Report, BR 106 "Design of Normal
Concrete Mixes", for more details. Concrete mix design involves a wide range of knowledge concerning the properties and interactive influences of constituent materials, influence of ambient conditions and concrete technology. Students are recommended to read Neville's "Concrete Technology" when needed.
Concrete mix design is to select suitable constituent materials and determine proportions of the materials to meet specifications for that concrete. The specifications normally include requirement on strength, durability of hardened concrete and workability of fresh concrete.
Many factors affect the properties of concrete. It is not necessary, and indeed it is not possible, to include all of them in a mix design. The design method introduced in this lecture considers a few factors that possess relatively significant influences, namely water/cement ration, water content, types of cement, size, grading and density of aggregates. These factors are briefly discussed in the following sections. Relations of these factors are reflected in figures and tables attached.
It should be noted that the figures and tables are for UK materials, practice and conditions and may not directly applicable to the Hong Kong concrete. For example, the compressive strengths at early ages may higher than those given in the design table for concrete mix design due to higher temperature here. The principle of the design approach, however, equally applies to local concrete.
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SPECIFIED STRENGTH AND TARGET STRENGTH FOR MIX DESIGN a. Variation and probability of concrete strength
Table a is a collection, or a sample, of testing records of concrete cube tests for a construction project. Fig. 1 shows the histogram of the sample. It is now generally accepted that the strength of concrete follows normal distribution. The standard deviation of the sample, s, may be calculated using equation (1).
Table a Compressive strength of 60 cubes from a construction site
24.1 20.8 21.1 14.6 20.6 22.0 28.1 17.1 22.1 26.4
19.6 28.8 23.5 19.1 28.9 31.5 24.4 28.3 32.6 17.2
26.7 35.7 21.6 26.0 31.6 15.4 26.9 22.8 27.0 15.1
30.0 38.4 18.5 31.1 22.3 23.8 18.6 25.5 17.5 12.8
23.2 19.7 26.1 12.7 27.4 25.0 27.4 39.2 34.0 17.0
32.4 22.9 20.9 31.8 21.6 14.2 25.9 22.3 19.8 23.3 s

  x
 m

2 n

1
(1) where x = an individual test result n = the number of results m = the mean of the n results. m of the sample in Table a is 24.08 N/mm
2
, and s is 6.13 N/mm
2
.
Figure a.
Histogram and normal distribution curve based on the data in Table a
Normal distribution is expressed as follows. p ( m , s )
 s
1
2

 e

 x
 m

2
2 s
2
(2)
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Normal distribution curve with m and s obtained from data I Table a is plotted in Fig. a for comparison with the histogram.
Fig. b normal distribution curve for the data in Table a
Fig b shows the normal distribution curve based on the data in Table a. The shaded area beneath the curve equals one, and the proportion of results less than some specified value is represented by the area beneath the curve to the left-hand side of a vertical line drawn through the specified value. The proportion below a specified value, normally expressed as the mean minus a constant times the standard deviation, can be determined through integration of Equation (2) or using mathematics handbook. Some typical values are given below.
Specified value f c f c
= m - 1.28s f c
= m - 1.64s
Proportion of results below f
10%
5% c f c
= m - 1.96s f c
= m - 2.33s
2.5%
1%
For example, from the theoretical distribution obtained from Table a, there are 10% of the concrete below 24.08 - 1.28

6.13 = 16.2 N/mm
2
. b. Characteristic strength
Probability and statistics have been widely adopted in engineering to describe structure failure and material properties. In the old practice, concrete strength is specified using "minimum strength". From the probability theory adopted today, there is always a posibility, however remote, that the strength of concrete falls below a specified strength. Therefore concrete strength is specified in term of " Characteristic
Strength ". The characteristic strength is the strength below which a specified proportion of test results, often called "defectives", may be expected to fall. The characteristic strength may be defined to have any proportion of defectives, BS 5328
"Concrete" and BS8110 "Structure use of concrete" adopt 5% defectives level for the determination of characteristic strength.
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Example: Based on the test results in Table a, the characteristic strength of that concrete is 24.08 - 1.64

6.08 = 14.1 N/mm
2
. c. Target strength for mix design
As a results of variability of concrete it is necessary to design the mix to have a mean strength greater than the specified characteristic strength by an amount termed the margin . Thus the target strength , f m
, is f m
= f c
+ ks where
(3) f c
= specified characteristic strength s = standard deviation k = constant depending on the defective level associated with the specified strength. ks is termed the margin.
For example, for a specified characteristic strength of 40 N/mm
2
in a design comply to BS8110 (5% defective level), and standard deviation is 7 N/mm
2
, the target mean strength is f m
= f c
+ ks = 40 + 1.64

7 = 51.5 N/mm 2 ,
Standard deviation should be based on previous record of the concrete produced by the concerned concrete plant or supplier. In the absence of such record, DOE recommended to use the value from the attached Fig. 3.
DURABILITY REQUIREMENT
Durability requirement specified by, for example, minimum cement content and maximum water/cement ratio, etc. The durability requirement specified in BS8110 for structural concrete is exacted as an example.
Durability requirement for concrete cover (extracted from BS8110)
Conditions of exposure Nominal cover
Mild
Moderate mm
25
- mm
20
35 mm
20
30 mm
20
25
Mm
20
20
Severe
Very severe
Extreme
Max Free water/cement ratio
Min cement content (kg/m 3 )
-
-
-
-
40
50
30
40
25
30
- - - 60 50
0.65 0.6 0.55 0.5 0.45
275 300 325 350 400
Lowest grade of concrete C30 C35 C40 C45 C50
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PROCEDURES OF MIX DESIGN
DOE mix design generally involves the following stages.

Determine the target strength

Determine the water/cement (W/C) ratio according to the target strength, types of cement and aggregate.

Determine the water content , W, from required workability, size and type of aggregate.

Determine cement content, C, from W/C ratio and water content.

Estimate the density of wet fresh concrete, D, based on relative density of combined aggregate and water content.

Determine the total aggregate content from D, C, and W.

Determine the proportion of fine aggregate according to the fineness of fine aggregate, maximum aggregate size, slump/Vebe time and W/C.
Note: For course aggregate using combined 10mm, 20mm and 40mm size, DOE recommendation is as forllows.
1:2 for combination of 10mm and 20mm material
1:1.5:3 for combination of 10mm, 20mm and 40mm material
DOE design a "Concrete mix design form" to facilitate the design. The procedure is illustrated in Figure 2 of reference [1].
EXAMPLES
Refer to reference [1] Examples 1 and 2.
TRIAL MIXES
The design gives only an estimated proportion of the mix for the expected properties.
Since there are many factors that affect the performance of concrete and not include in the design consideration. Trial mixes have to be produced to verify the designed mix.
The mix design approach is based on the aggregate in a saturated and surface-try condition (SSD). If the aggregate used for the trial mixes is not in such condition, adjustment to the proportion of the mix must be made.
For example, if water absorption of the aggregate is 2%, the moisture content of the aggregate on the basis of dry aggregate is 8% and the amount of aggregate for one cubic meter of concrete is 540kg. The actual water added to the mix should be reduced by
540

(0.08-0.02) = 32.4 kg
Accordingly the actual amount of aggregate added to the mix should be
Mix - 5

M wet

1

(
M
SSD
M

A )

540
1

( 0 .
08

0 .
02 )

574 kg where
M
M wet
SSD
= mass of wet aggregate with a moisture content of M
= mass of aggregate at SSD condition
M = moisture content
A = water absorption of the aggregate.
Water absorption of a aggregate in defined as the ratio of water required to bring an aggregate from dry condition to SSD condition to the mass of dry aggregate.
QUESTIONS
1.
Discuss the influence the following factors on the workability of a normal concrete mix.
Shape of aggregate
Maximum size of aggregate
Grading of course aggregate
Grading of fine aggregate
2.
The following is results from a sieve analysis test,
(a) calculate the per cent passing 600
 m sieve, and
(b) draw grading chart (size distribution chart) of the aggregate.
Sieve Size
(mm or
 m)
5 mm
2.36 mm
1.18 mm
600
 m
300
 m
150
 m
Mass Retained (g) 11 110 230 273 286 69
75
 m
7
Receiver
3.
The following is a set of result from cube compressive strength tests on a construction site. Determine the mean, standard deviation and characteristic strength of the concrete at 2.5% defective level.
Results cube compressive strength on 150

150 mm cubes (N/mm 2 )
19.6 20.8 26.5 23.4 31.2 29.5 31.5 32.4 22.1 27.8
22.9 23.5 20.9 22.2 23.2 18.3 25.3 29.5 25.0 25.9
21.5 24.4 17.5 22.1 26.2 13.9 19.2 25.4 20.8 27.9
34.1 21.1 18.5 24.7 23.5 19.0 16.0 30.1 26.0 30.9
20.8 25.6 25.4 29.8 21.7 27.0 22.0 23.4 30.5 19.9
20.5 29.9 26.8 31.9 23.2 26.6 24.2 30.6 21.6 18.6
2
4.
Based on the record in Question 3, if a specified characteristic cube strength is
40N/mm 2 , what should be the target mean strength when design a concrete mix.
5.
How crushed and uncrushed coarse aggregate affect the strength of concrete?
Explain why.
6.
Define the term Saturated and surface-dry condition.
7.
Define the term "aggregate absorption".
8.
Define the term "Free water" in the context of concrete mix proportions. Why use free water instead of total water when design a concrete mix?
9.
What is "relative density" of an aggregate? What is "bulk density of an aggregate?
What is "percentage void of an aggregate?
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10.
If water absorption of course aggregate is 2 per cent; moisture content of the aggregate is 4 percent; the water absorption of the fine aggregate is 3% and moisture content of the fine is 6%. The designed mix proportion of the concrete is given in the following table, calculate the amount of water that should be added for one cubic meter of concrete. (Answer 94.2kg)
Proportion of a concrete mix (Per cubic meter)
Cement (kg)
Fine Aggregate (kg)
Course Aggregate (kg)
Superplasticiser (l)
Water (kg)
350
720
980 (20mm granite)
7
135.4
11.
For the materials in Question 9, how other materials shall be adjusted in order to achieve the required proportions?
12.
If water absorption of course aggregate is 2 per cent, moisture content of the aggregate is 0.5 percent, the water absorption of the fine aggregate is 3% and moisture content of the fine is 1%. How the proportions of each material should be adjusted in order to achieve the proportion of the mix in Question 9.
13.
When mix concrete using dry aggregate, BS1881:Part 125 recommends that about half of the total water be added first and mix a certain period of time before adding the cement. What is the consideration?
14.
In a trial mix, the cement content has reached the maximum specified quantity. To achieve the specified concrete strength, the water/cement ration has to be kept low, but the water added can not achieve the specified workability. What measures you may taken so that both strength and workability requirement be satisfied.
15.
Proportions of a concrete mix is shown in the following Table.
Proportions of a concrete mix (for 1 cubic meter)
Crushed Crushed Crushed
Cement
400kg
20mmAgg
700
10mmAgg.
350
fine
420
River
Sand
280
Water
210
Estimate the density of fresh concrete.
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