Concrete Mixed Design Method (BS Method)

Concrete Mix Design

• Finalize the proportions of concrete mix constituents (Cement, Fine aggregate (or normally Sand), Coarse aggregate, and Water).
• Produce concrete of  specified properties.

Figure 1: Concrete Mixer – Drum type 140L

Concrete Mix Design procedure

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).

Mix design procedure are described by the following steps:

step-1: Determining the  Water/ Cement Ratio

Set the required characteristic strength at a specified age, f_c
Calculation of the margin, M.

M = k * s     ….. [ 1 ]

Here;
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 Figure 1).

Figure 1: Relationship between standard deviation and characteristic strength.

step-2: Calculation of the target mean strength, f_m

f_m =   f_c + M     ….. [ 2 ]

where;
f_m = Target mean strength
f_c = The specified characteristic strength

Table. 1: Approximate compressive strength (N/mm2) of concrete mixes made with a  water/cement ratio of 0.5

Table 1 is used to obtain the compressive strength, at the specified age that corresponds to a free water/cement ratio of 0.5.

Figure. 2: Relationship between compressive strength and water/ cement ratio.

iv) a value is obtained from Table 1 for the strength of a mix made with a water/cement ratio of 0.5 according to the specified age, the strength class of the cement and the aggregate to be used. This strength value is then plotted on Figure 2 and a curve is drawn from this point and parallel to the printed curves until it intercepts a horizontal line passing through the ordinate representing the target mean strength.

Step-3: Determination of the Free-Water Content

 the free-water content can be determined from Table 2 depending upon the type and maximum size of the aggregate to give a concrete of the specified slump or Vebe time.

Table 2: Approximate free-water contents (kg/m3) required to give various levels of workability.

Note: When coarse and fine aggregates of different types are used, the free-water content is estimated by the following expression.

2⁄3*W_f + 1⁄3*W_c

Where,

 W_f  = free-water content appropriate to type of fine aggregate

W_c  =  free-water content appropriate to type of coarse aggregate.

Step-4: Determination of Cement Content

The cement content can be determined from equation 3...

Cement Content = Free Water Content / water-Cement Ratio     ….. [ 3 ]

The resulting value should be checked against any maximum or minimum value that may be specified. If the calculated cement content from equation 3 is below a specified minimum, this minimum value must be adopted and a modified free-water/cement ratio calculated.  

If the design method indicates a cement content that is higher than a specified maximum then it is probable that the specification cannot be met simultaneously on strength and workability requirements with the selected materials. Consideration should then be given to changing the type or strength class, or both, of cement, the type and maximum size of aggregate or the level of workability of the concrete, or to the use of a water-reducing admixture.

Step 5: Determining the Total Aggregate Content

 Density of fully compacted concrete can be estimated from Figure 3. 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.

Figure 3: Estimated wet density of fully compacted concrete.

The total aggregate content can be calculated using equation 4:

Total Aggregate Content = D – C – W     ….. [ 4 ]

where;
D = The wet density of concrete ( in kg/m³)
C = The cement content (in kg/m³)
W = The free-water content (in kg/m³)

Step 6: Determining of The Fine and Coarse Aggregate Contents

Current step demonstrate  how to find out total fine aggregate (materials smaller than 5 mm, i.e. the sand or fine aggregate content). The figure 4 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.

Figure 4: Recommended proportions of fine aggregate according to percentage passing a 600 μm sieve.

Determination of  fine and coarse aggregate can be made using the proportion of fine aggregate obtained from Figure 4 and the total aggregate content derived from Step-5

Fine Aggregate Content = Total Aggregate Content * Proportion of Fines ….. [ 5 ]

Coarse Aggregate Content = Total Aggregate Content – Fine Aggregate

Procedures of Design Mixing

Production of Trial Mix Design

1. 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.
2. 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.
3. The mixing of concrete is according to the procedures given in laboratory guidelines.
4. Firstly, cement, fine and course aggregate are mixed in a mixer for 1 minute.
5. Then, water added and the cement, fine and course aggregate and water mixed approximately for another 1 minute.
6. When the mix is ready, the tests on mix are proceeding.

Tests on Trial Mix Design

1. The slump tests are conducted to determine the workability of fresh concrete.
2. 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.
3. 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 22⁰C 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^oC until the testing date.
4. Compressive strength tests are conducted on the cubes at the age of 7 days. Then, the mean compressive strengths are calculated.

Slump Test apparatus for Concrete Workability

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/mm² at 7 days for the characteristic strength. Then, we obtained the standard deviation,s from the figure 1. So, s = 8 N/mm².

From the equation 1, k = 1.64 for 5 % defect. The margin, M is calculated as below:
M = k * s = 1.64 x 8 = 13.12 N/mm²

With the equation 2, target mean strength,  f_m is calculated as below:

Target mean strength, f_m = f_c + M
= 30 + 13.12 = 43.12 N/mm²

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 1. For OPC ( 7 days ) using crushed aggregate, water/cement ratio = 36 N/mm².

After that, from the figure 2, the curve for 42 N/mm² 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/mm². 

From the slump test result, 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 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/m³ and for the crushed aggregates is 205 kg/m³. 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
= ²/₃ W_f + ¹/₃ W_c
= (²/₃ x 180) + (¹/₃ x 205)
= 188.33 kg/m³

where,
W_f = Free-water content appropriate to type of fine aggregate
W_c = Free-water content appropriate to type of coarse aggregate

Cement content also can obtained from the calculation with the expression at equation 3:
Cement Content, C = Free Water Content / Free-water or Cement Ratio
= 188.33 / 0.45 = 418.52 kg/m³

We assumed that the relative density of aggregate (SDD) is 2.7. Then, from the Figure 3 with the free-water content 188.33 kg/m³, obtained that concrete density is 2450 kg/m³. The total aggregate content can be calculated by:

Total Aggregate Content = D – C – W
= 2450 – 418.52 – 188.33 = 1843.15 kg/m³

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 4, which is 38 %. Then, the fine and course aggregate content can be obtained by calculation:

Fine Aggregate Content
= Total Aggregate Content * Proportion of Fines
= 1868.74 x 0.38 = 700.40 kg/m³

Coarse Aggregate Content = Total Aggregate Content – Fine Aggregate
= 1843.15 – 700.40 = 1142.75 kg/m³

The quantity per m³ 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 m³

The quantities of trial mix = 0.00375 m³, in which is;
Cement                                      = 1.57 kg
Water                                         = 0.71 kg
Fine aggregate                       = 2.61 kg
Coarse aggregate (10 mm) = 4.29 kg