**Objective of Concrete Mix Design**

Two main objectives for concrete mix design:

- To determine the proportions of concrete mix constituents of; Cement, Fine aggregate (or normally Sand), Coarse aggregate, and Water.
- To produce concrete of the specified properties.
- To produce a satisfactory of end product, such as beam, column or slab as economically as possible.

**Theory of Mix Designs**

**The Process of Concrete Mix Design**

The method of concrete mix design applied here is in accordance to the method published by the Department of Environment, United Kingdom (in year 1988).

There are two categories of initial information required:

- Specified variables; the values that are usually found in specifications.
- Additional information, the values normally available from the material supplier.

Reference data consists of published figures and tables is required to determine the design values including;

- Mix parameters such as target mean strength, water-cement ratio and concrete density.
- Unit proportions such as the weight of materials.

The design process can be divided into 5 primary stages. Each stage deals with a particular aspect of the concrete mix design:

**Stage 1: Determining the Free Water/ Cement Ratio**

i) Specify the required characteristic strength at a specified age, f

_{c}

ii) Calculate the margin, M.

M = k x s ….. [ F1 ]

where;

k = A value appropriate to the defect percentage permitted below the characteristic strength. [ k = 1.64 for 5 % defect ]

s = The standard deviation (obtained from CCS 1).

k = A value appropriate to the defect percentage permitted below the characteristic strength. [ k = 1.64 for 5 % defect ]

s = The standard deviation (obtained from CCS 1).

iii) Calculate the target mean strength, f

_{m}f

_{m }= f_{c}+ M ….. [ F2 ]where;

f

f

f

_{m}= Target mean strengthf

_{c}= The specified characteristic strengthiv) Given the type of cement and aggregate, use the table of CCS 1 to obtain the compressive strength, at the specified age that corresponds to a free water/cement ratio of 0.5.

v) In figure CCS 4, follow the ‘starting line’ to locate the curve which passes through the point (the compressive strength for water/cement ratio of 0.5). To obtain the required curve representing the strength, it is necessary to interpolate between the two curves in the figure. At the target mean strength draw horizontal line crossing the curve. From this point the required free water/cement ratio can be determined.

**Stage 2: Determining the Free-Water Content**

Given the Concrete Slump or Vebe time, determine the free water content from table CCS 2.

**Stage 3: Determining the Cement Content**

Cement Content = Free Water Content / Free-water or Cement Ratio ….. [ F3 ]

The resulting value should be checked against any maximum or minimum value that may be specified. If the calculated cement content from F3 is below a specified minimum, this minimum value must be adopted resulting in a reduced water/cement ratio and hence a higher strength than the target mean strength. If the calculated cement content is higher than a specified maximum, then the specified strength and workability simultaneously be met with the selected materials; try to change the type of cement, the type and maximum size of the aggregate.

**Stage 4: Determining the Total Aggregate Content**

This stage required the estimate of the density of fully compacted concrete which is obtained from figure CCS 5. This value depends upon the free-water content and the relative density of the combined aggregate in the saturated surface-dry condition. If no information is available regarding the relative density of the aggregate, an approximation can be made by assuming a value of 2.6 for un-crushed aggregate and 2.7 for crushed aggregate.

With the estimate of the density of the concrete the total aggregate content is calculated using equation F4:

Total Aggregate Content = D – C – W ….. [ F4 ]

where;

D = The wet density of concrete ( in kg/m

C = The cement content (in kg/m

W = The free-water content (in kg/m

D = The wet density of concrete ( in kg/m

^{3})C = The cement content (in kg/m

^{3})W = The free-water content (in kg/m

^{3})**Stage 5: Determining of The Fine and Coarse Aggregate Contents**

This stage involves deciding how much of the total aggregate should consist of materials smaller than 5 mm, i.e. the sand or fine aggregate content. The figure CCS 6 shows recommended values for the proportion of fine aggregate depending on the maximum size of aggregate, the workability level, the grading of the fine aggregate (defined by the percentage passing a 600 μm sieve) and the free-water/ cement ratio. The best proportion of fines to use in a given concrete mix design will depend on the shape of the particular aggregate, the grading and the usage of the concrete.

The final calculation, equation F5, to determine the fine and coarse aggregate is made using the proportion of fine aggregate obtained from figure CCS 6 and the total aggregate content derived from Stage 4.

Fine Aggregate Content = Total Aggregate Content x Proportion of Fines ….. [ F5 ]

Coarse Aggregate Content = Total Aggregate Content – Fine Aggregate

**Procedures of Design Mixing**

**Production of Trial Mix Design**

- The volume of mix, which needs to make three cubes of size 100 mm is calculated. The volume of mix is sufficient to produce 3 numbers of cube and to carry out the concrete slump test.
- The volume of mix is multiplied with the constituent contents obtained from the concrete mix design process to get the batch weights for the trial mix.
- The mixing of concrete is according to the procedures given in laboratory guidelines.
- Firstly, cement, fine and course aggregate are mixed in a mixer for 1 minute.
- Then, water added and the cement, fine and course aggregate and water mixed approximately for another 1 minute.
- When the mix is ready, the tests on mix are proceeding.

**Tests on Trial Mix Design**

- The slump tests are conducted to determine the workability of fresh concrete.
- Concrete is placed and compacted in three layers by a tamping rod with 25 times, in a firmly held slump cone. On the removal of the cone, the difference in height between the uppermost part of the slumped concrete and the upturned cone is recorded in mm as the slump.
- Three cubes are prepared in 100 mm x 100 mm each. The cubes are cured before testing. The procedures for making and curing are as given in laboratory guidelines. Thinly coat the interior surfaces of the assembled mould with mould oil to prevent adhesion of concrete. Each mould filled with two layers of concrete, each layer tamped 25 times with a 25 mm square steel rod. The top surface finished with a trowel and the date of manufacturing is recorded in the surface of the concrete. The cubes are stored undisturbed for 24 hours at a temperature of 18 to 22
^{0}C and a relative humidity of not less than 90 %. The concrete all are covered with wet gunny sacks. After 24 hours, the mould is striped and the cubes are cured further by immersing them in water at temperature 19 to 21^{o}C until the testing date. - Compressive strength tests are conducted on the cubes at the age of 7 days. Then, the mean compressive strengths are calculated.

**The Calculations**

Here is one example of calculation from one of the concrete mix design obtained from the laboratory. We have to fill in all particulars in the concrete mix design form with some calculations…

Firstly, we specified 30 N/mm

^{2}^{ }at 7 days for the characteristic strength. Then, we obtained the standard deviation, s from the figure CCS 3. So, s = 8 N/mm^{2}.From the formula F1, k = 1.64 for 5 % defect. The margin, M is calculated as below:

M = k x s = 1.64 x 8 = 13.12 N/mm

M = k x s = 1.64 x 8 = 13.12 N/mm

^{2}With the formula F2, target mean strength, f

Target mean strength, f

= 30 + 13.12 = 43.12 N/mm

_{m}is calculated as below:Target mean strength, f

_{m}= f_{c}+ M= 30 + 13.12 = 43.12 N/mm

^{2}The type of cement is Ordinary Portland Cement (OPC). For the fine and course aggregate, the laboratory’s fine aggregate is un-crushed and for coarse aggregate is crushed before producing concrete.

Then, we obtain the free-water/ cement ratio from table CCS 1. For OPC ( 7 days ) using crushed aggregate, water/cement ratio = 36 N/mm

^{2}.After that, from the figure CCS 4, the curve for 42 N/mm

^{2}at 0.5 free-water ratio is plotted and obtained the free-water ratio is 0.45 at the target mean strength 43.12 N/mm^{2}.Next, we specified the slump test for slump about 20 mm and the maximum aggregate size we used in laboratory is 10 mm. For the specified above, we can obtained the free-water content from table CCS 2 at slump 10 – 30 mm and maximum size aggregate 10 mm, the approximate free-water content for the un-crushed aggregates is 180 kg/m

^{3 }and for the crushed aggregates is 205 kg/m^{3}. Because of the coarse and fine aggregates of different types are used, the free-water content is estimated by the expression:Free-water Content, W

=

= (

= 188.33 kg/m

=

^{2}/_{3}W_{f}+^{1}/_{3}W_{c}= (

^{2}/_{3}x 180) + (^{1}/_{3}x 205)= 188.33 kg/m

^{3}where,

W

W

W

_{f}= Free-water content appropriate to type of fine aggregateW

_{c}= Free-water content appropriate to type of coarse aggregateCement content also can obtained from the calculation with the expression at F3:

Cement Content, C = Free Water Content / Free-water or Cement Ratio

= 188.33 / 0.45 = 418.52 kg/m

Cement Content, C = Free Water Content / Free-water or Cement Ratio

= 188.33 / 0.45 = 418.52 kg/m

^{3}We assumed that the relative density of aggregate (SDD) is 2.7. Then, from the figure CCS 5 with the free-water content 188.33 kg/m

^{3}, obtained that concrete density is 2450 kg/m^{3}. The total aggregate content can be calculated by:Total Aggregate Content = D – C – W

= 2450 – 418.52 – 188.33 = 1843.15 kg/m

= 2450 – 418.52 – 188.33 = 1843.15 kg/m

^{3}The percentage passing 600 μm sieve for the grading of fine aggregate is about 60 %. The proportion of the fine aggregate can be obtained from the figure CCS 6, which is 38 %. Then, the fine and course aggregate content can be obtained by calculation:

Fine Aggregate Content

= Total Aggregate Content x Proportion of Fines

= 1868.74 x 0.38 = 700.40 kg/m

= Total Aggregate Content x Proportion of Fines

= 1868.74 x 0.38 = 700.40 kg/m

^{3}Coarse Aggregate Content = Total Aggregate Content – Fine Aggregate

= 1843.15 – 700.40 = 1142.75 kg/m

= 1843.15 – 700.40 = 1142.75 kg/m

^{3}The quantity per m

Cement = 418.52 kg

Water = 188.33 kg

Fine aggregate = 700.40 kg

Coarse aggregate (10 mm) = 1142.75 kg

^{3}can be obtained, which is;Cement = 418.52 kg

Water = 188.33 kg

Fine aggregate = 700.40 kg

Coarse aggregate (10 mm) = 1142.75 kg

The volume of trial mix for 3 cubes

= [(0.1 x 0.1 x 0.1) x 3] + [25% contingencies of trial mix volume]

= 0.003 + 0.00075

= 0.00375 m

= [(0.1 x 0.1 x 0.1) x 3] + [25% contingencies of trial mix volume]

= 0.003 + 0.00075

= 0.00375 m

^{3}The quantities of trial mix = 0.00375 m

Cement = 1.57 kg

Water = 0.71 kg

Fine aggregate = 2.61 kg

Coarse aggregate (10 mm) = 4.29 kg

^{3}, in which is;Cement = 1.57 kg

Water = 0.71 kg

Fine aggregate = 2.61 kg

Coarse aggregate (10 mm) = 4.29 kg

**The Results of Mix Design**

Slump Test = True Slump of 55 mm…

All the 3 concrete cubes produced were then cured for 7 days. After that, the compressive cube test is carried out. The results are as follows:

Sample | 1 | 2 | 3 |

Compressive Strength | 32.37 | 33.54 | 35.70 |

Average | (32.37 + 33.54 + 35.70) / 3 = 33.87 |

For cubes after 7 days of curing, compressive strength should not be less than 2/3 target mean strength.

= 2/3 × 43.12 = 28.75 N/mm

= 2/3 × 43.12 = 28.75 N/mm

^{2}< 33.9 N/mm^{2}After 7 days of curing, the compressive strength of concrete cubes produced by the mix design method pass the specific strength requirements.

**Discussions Upon Concrete Mix Designs**

Although our compressive strength passes the specific requirements, we still identified several factors which contribute to the lacking of compressive strength of concrete mixes produced in the experiment. However, the main factor is the condition of aggregates whether it is exposed to sunlight or rainfall.

When the free water/cement ration is high, workability of concrete is improved. However, excessive water causes “

*honey-comb*” effect in the concrete produced. The concrete cubes become porous, and hence its compressive strength is well below the design value. Other possible reasons include over compaction, improper mixing methods and some calculation errors.Few suggestion upon several steps to avoid the problems previously faced:

- All the raw materials, which is cement, aggregates, and sand should be protected from precipitation or other elements which may affect its physical properties.
- The quantity of ingredients may be adjusted if necessary, theoretical values are not always suitable. For example, if the aggregates are wet or saturated, less amount of water should be added, vice versa.
- Compaction should be done carefully, as either under or over-compaction will bring significant negative effect on the concrete produced.

**The Conclusion**

- By using the concrete mix design method, we have calculated the quantities of all ingredients, that is water, cement, fine and coarse aggregate according to specified proportion.
- The concrete produced did not fulfill the compressive strength requirements due to several reasons. Furthermore, some steps mentioned above should be taken into consideration to overcome this problem.

I need to pour a patio size slab of concrete. What will it cost me to rent a small mixer and supplies to make the cement slab? Is there a brand of cement that works best in this situation? How long will it take for the cement to settle with a 10x10 area?

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