Concrete Mix Design Using DoE Method
23/09/19 Engineering Reference this
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Concrete Mix Design Using DoE Method
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Contents Page
1. Introduction
1.1. In this report I will calculate the exact amount of materials required to produce 1m^{3} of concrete, designed to the Department of Environment (DoE) method. This method of concrete design was first introduced in 1950, under the name “Road Note No 4”, which was later replaced by “Design of Normal Concrete Mixes” in 1975 by the British Department of Environment (DoE). The design guidance was updated in 1988 to account for changes in the then current British Standards and is still used today, often being referred to as the British Standard concrete mix design.
1.2. The DoE method for concrete mix design works by calculating the values of 8 fundamental processes:
 Mean target compressive strength
 Water/Cement ratio
 Water content using required slump value and aggregate size
 Cement content
 Concrete density
 Aggregate content
 Proportion of fine & course aggregate
 Course aggregate
2. Design Requirements and Assumptions
2.1. Below is a list of design requirements/assumptions that have been used for the concrete mix design:
 A slump of 10mm to 30mm.
 A characteristic 28day compressive strength of 30 N/mm^{2} (5% failures permitted).
 The standard deviation of the tests is σ = 6.1 N/mm^{2}.
 Ordinary Portland cement (42.5 N).
 Crushed sand of 2.7 density and 60% passing through a 600 µm sieve.
 Crushed coarse aggregate 2.6 density and 20mm are used.
3. Mean Compressive Strength
3.1. The target mean compressive strength
$\left({f}_{m}\right)$can be calculated by:
$\mathit{characteristic\; strength}\left({f}_{c}\right)+\left(\mathit{risk\; factor}\left(k\right)\mathit{x\; standard\; deviation}\right(\sigma \left)\right)$
Table 1. Risk factor values used in statistical control (G.D.Taylor, 2000)
Percentage failure permitted 
Risk factor value 
16 
1.00 
10 
1.28 
5 
1.64 
2.5 
1.96 
2 
2.05 
1 
2.33 
${f}_{m}={f}_{c}+(1.64\mathit{x\; \sigma})$
${f}_{m}=30+\left(1.64\mathit{x}8\right)=\mathit{40}\mathit{N}\mathit{/}{\mathit{mm}}^{\mathit{2}}$
4. Water / Cement Ratio
4.1. The water / cement ratio is determined by using data from table 2.
Table 2. Approximate compressive strength of concrete made with a free Water/Cement ratio of 0.50 (G.D.Taylor, 2000)
Type of cement 
Type of coarse aggregate 
Compressive Strength (N/mm2) 

Age (days) 

3 
7 
28 
91 

Ordinary Portland Cement (OPC) Or Sulphateresisting Portland (SRPC) 
Uncrushed 
22 
30 
42 
49 
Crushed 
27 
36 
49 
56 

Rapidhardening Portland (RHPC) 
Uncrushed 
29 
37 
48 
54 
Crushed 
34 
43 
55 
61 

1 N/mm2 = 1 MN/m2 = 1 MPa 
4.2. One of the requirements of the design mix stated that the mix will use ordinary Portland cement, with crushed aggregate, therefore, the 28day strength value of 49 N/mm^{2} from the above table can be used to calculate the water / cement ratio:
 0.5 is used for the freewater/cement axis as this value is used in table 2.
 At the point of intersection of compressive strength value of 49 N/mm^{2} with the freewater / cement value 0.5 (orange), the nearest curve is offset parallel to the point of intersection (blue).
 A horizontal line is drawn starting at the desired compressive strength of 40 N/mm^{2}, until it intersects with the parallel curve, with a vertical line drawn from this point of intersection to find the desired freewater / cement ratio of 0.57 (red).
Figure 1. Desired freewater / cement ratio (G.D.Taylor, 2000)
5. Water Content
5.1. To calculate the required water content to achieve a suitable concrete workability, the following factors are used:
 Slump value (10 mm – 30 mm)
 Aggregate size (20 mm)
The values of these factors have been provided in the design requirements and can be found in table 3.
5.2. Using the information provided in Table 3 (below), we can determine that the required water content is 190 kg/m^{3}by intersecting the value at 20 mm aggregate size and 10 mm – 30 mm slump value for crushed aggregate.
Table 3: Workability and approximate freewater content (G.D.Taylor, 2000)
Slump (mm)
Vebe (seconds) 
Very Low 0 – 10 >12 
Low 10 – 30 6 – 12 
Medium 30 – 60 3 – 6 
High 60 – 180 0 – 3 



Maximum size of aggregate (mm) 
Type of aggregate 
Water content (kg/m^{3}) 

10 
Uncrushed Crushed 
150 180 
280 205 
205 230 
225 250 
20 
Uncrushed Crushed 
135 170 
160 190 
180 210 
195 225 
40 
Uncrushed Crushed 
115 155 
140 175 
160 190 
175 205 


Percentage of fly ash in cementitious material 
Reduction in water content (kg/m^{3}) 

10 
5 
5 
5 
10 

20 
10 
10 
10 
15 

30 
15 
15 
20 
20 

40 
20 
20 
25 
25 

50 
25 
25 
30 
30 
6. Cement Content
6.1. To calculate the amount of cement required, the following formula is used
$\mathit{Cement\; content\; per}{m}^{3}=\frac{\mathit{water\; content\; per}{m}^{3}}{\mathit{free}\u2013\mathit{water}/\mathit{cement\; ratio}}$
The values for both water content and freewater / cement ratio are known, so it is easily calculated.
$\mathit{Cement\; content\; per}{m}^{3}=\frac{190}{0.57}=333\mathit{kg}/{m}^{3}$
7. Density of Concrete
7.1. The DoE method uses a graphical system for calculating the density of the fresh concrete, using the relative aggregate density and freewater content.
7.2. The relative aggregate density has been provided at 2.6, and the freewater content is 190 kg/m^{3}, therefore the density can be calculated to be 2370 kg/m^{3}, as shown in figure 2.
Figure 2. Fresh Concrete Density (G.D.Taylor, 2000)
8. Aggregate Content
8.1. Using the fresh concrete density of 2370 kg/m^{3}, and the aggregate content can be calculated using the following formula:
$\mathit{Aggregate\; content}=\mathit{fresh\; density}\u2013(\mathit{cement\; content}+\mathit{water\; content})$
These values have already been calculated, therefore:
$\mathit{Aggregate\; content}=2370\u2013\left(333+190\right)\mathit{Aggregate\; content}=\mathit{1847}\mathit{kg}\mathit{/}{\mathit{m}}^{\mathit{3}}$
9. Fine aggregate content
9.1. The proportion of fine aggregate in the concrete mix will depend on:
 The grading of the sand
 Maximum aggregate size
 Workability of the concrete
 Freewater / cement ratio
9.2. Figure 3 (below) shows the graphical method of calculating the proportion of fine aggregate, which gives a result of 30% by starting at 0.5 freewater/cement ratio and drawing a line vertically upwards to the percentage of fine aggregate passing through a 600 µm sieve (60%). A horizontal line is then drawn to find the proportion of fine aggregate.
Figure 3. Recommended proportions of sand according to percentage passing a 600 µm sieve (G.D.Taylor, 2000)
Using the total aggregate content 1847 kg/m^{3}, the proportion of fine aggregate can be calculated.
$1847\mathit{x}0.3=\mathit{554}\mathit{kg}\mathit{/}{\mathit{m}}^{\mathit{3}}$
10. Coarse Aggregate Content
10.1. Once the fine aggregate content has been calculated, we can simply deduct this value from the total aggregate content to determine the amount of coarse aggregate required.
$1847\u2013554=\mathit{1293}\mathit{kg}\mathit{/}{\mathit{m}}^{\mathit{3}}$
11. Summary
11.1. From the calculations above, it can be determined that for each m^{3} of concrete, the correct amounts for each component are as follows:
Table 4. Quantity of materials required to produce 1m^{3} of concrete with a 28day compressive strength of 30 N/mm^{2}, designed to the DoE method.
Material 
Quantity (kg/m^{3}) 
Cement 
333 
Water 
190 
Fine Aggregate 
554 
Coarse Aggregate 
1293 
References
 G.D.Taylor, 2000. Materials in Construction – An Introduction. 3rd ed. Essex: Pearson Education Limited.
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