Concrete is a material similar in shape and appearance to natural limestone rock but formed by artificial binding together of natural or artificial stone (coarse aggregate) with sand (fine aggregate), cement and water (for hydration). In special cases certain materials known as admixtures may be added to the mixture to increase or retard setting time or improve some required properties. The water/cement ratio is usually the governing factor that determines the strength of hardened concrete. Other factors such as mix ratio, aggregate grading, and quality/type of cement also play significant role to determine the strength of concrete.

Due to the significant contribution of the mix ratio, mix design is usually done prior to the production of concrete. **The aim of the mix design is to determine the optimum quantities of cement, sand and aggregate that would produce the required strength**. In the hardened concrete, aggregate usually provide the strength to the concrete. The cement acts as binder to bind aggregates together and provide paste to fill voids. The water helps the cement to hydrate in order to do its function.

**Aggregate/Aggregate grading**

It is on record that the maximum particle size of aggregate used in concrete is limited by the type of work concerned but for reinforced concrete, it should not be more than 20 mm to enable aggregates pass through reinforcement. To use the best aggregate for works, the following points should be noted (Adams, 1976).

- The highest grades of concrete are made by using two or more sizes of single-sized coarse aggregate and a fine aggregate, each constituent being measured separately. This helps to ensure close control of the grading.
- Good concrete can also be made by combining a fine aggregate with a graded coarse aggregate. There is fair control of grading here.
- All-in aggregate which are not permitted to be used in structural works but only in mass concrete works because there is no control in grading.

We can learn from the foregoing that grading of aggregate is very important in concrete production. Table 1 provides the zones of fine aggregates.

Table 1; Percentage by weight using BS sieves for fine aggregate

The values in Table 1 are gotten by sieve analysis. From the results gotten in the sieve analysis, the grading curve would be plotted. The grading curve is basically used to classify the soil. By the classification, the particular use suited for each soil shall be determined. Soil gradation is an indication of other engineering properties such as **compressibility**, **shear strength** and **hydraulic conductivity**. Among the zones above, the coarsest zone is zone 1 while zone 4 have finer varieties. Zone 4 is not usually good for reinforced concrete because of extreme fines content but may be used if mix design requires that (Adams, 1976).

In this post I would show how to design a concrete mix based on Council for the Regulation of Engineering in Nigeria (COREN) mix design manual.

**Generally, the goal of mix proportioning** is to use the minimumquantity of cement that will lubricate themixture when fresh to allow for adequateplacing and at the same time, bind theaggregates together and fill up the voidsbetween them when the concrete has hardened.Any excess of paste results in a higher cost,higher drying shrinkage (COREN, 2017).

Four variable factors need to be considered inmix proportioning. These are:

**i. Water/Cement ratio**

**ii. Cement content**

**iii. Gradation of aggregates**

**iv. Consistency**

Typically, two or three factors above are specified and the others are adjusted to achieve minimum workability and economy. The design is done to achieve concrete with specified characteristics in accordance to EN 206.

**Water/Cement ratio: **According to Abram’s law, the higherthe water cement ratio, the lower the strength ofconcrete. It is generally accepted as a rule ofthumb that every 1% increase in quantity ofwater added reduces the strength of concrete by5%. Theoretically, a water cement ratio of 0.25 isrequired for the complete hydration of cement.Hence, it is very important to control the watercement ratio on site.

**Cement Content:** With regardsto durability, conditions of exposure govern themaximum cement contents required. Based on therelationship between cement content and watercement ratio, we see that a greater water cementratio would require a lower cement content.

**Gradation of Aggregates**

Aggregates in concrete are of two types: coarse aggregates which refer to materials retained on 4.75mm sieve size; and fine aggregates which are materials passing through 4.75mm sieve size. The proportion of fine aggregates to coarse aggregate in a concrete mix depend on the fineness of the fine aggregate, size/shape of coarse aggregates and the cement content. Fine aggregate grading zones as shown in Table 1 plays significant role in the design.

**Consistency**

A concrete mix is expected to be consistent and workable. Consistency which is a property of concrete is the degree of wetness of the concrete while workability is the ease with which the concrete is transported, cast in formwork, compacted and finished without segregation. The workability required for various types of construction is dependent on various factors. The Slump test is typically used to determine the degree of workability. For a given proportion of cement and aggregates, the higher the slump, the wetter the mixture and higher the workability.

**Note:** The crushing strength of the hardened concrete is normally used in mix design as it is a fairly good and convenient index of most of the important properties of dense concrete. The crushing strength is usually gotten from concrete cube/cylinder test.

The step by step procedure to design a concrete mix is as follows:

**Step 1: ****Determination of target mean strength**

As a result of the variability of concrete in production, it is necessary to design the mix to have a mean strength greater than the specified characteristic strength. Hence, the target compressive strength is obtained from the Equation 1:

f_{m} = f_{c} + ks

where f = the target mean strength ‘m’

f = the specified characteristic ‘c’ strength

k = a constant (taken as 1.64 for a 5% defective level)

s = standard deviation.

The standard deviation is obtained from the field by carrying out tests on a minimum of 20-30 samples taken from the site as early as possible. In cases of significant changes in production of concrete batches, the standard deviation value should be calculated for new batches. The standard deviation recommended is 6 Nmm^{-2 }(COREN, 2017). The manual recommends that the producer should use lesser value than 6 Nmm^{-2} should he/she get that from the tests.

**Step 2: ****Determination of Water-cement ratio**

The relationship between strength and water cement ratio should be established for the materials to be used. If this is not available, the free water/cement ratio corresponding to the target strength may be obtained from Figure 1

The water/cement ratio selected should be checked against the maximum water cement ratio for the requirements of durability and the lower of the two values is recommended. If all the above would not be used, equations relating target mean strength to water/cement ratio for two popular cement grades in Nigeria (32.5 and 42.5) could be used

For grade 32.5, r = (62 – σ)/64 (1)

For grade 42.5, r = (83 – σ)/84 (2)

Where, σ = target mean strength and r = water/cement ratio.

The formulas above have limitations as follows: for grades 32.5 and 42.5, the target mean strength are limited to 44 Nmm^{-2} and 57 Nmm^{-2} respectively for water/cement ratio between 0.3 and 0.9, otherwise, the limits would be 52 Nmm^{-2} for grade 32.5 and 68 Nmm^{-2} for grade 42.5.

**Step 3: ****Determination of water content**

The water content of concrete is dependent on the type and maximum size of concrete to give a specified workability. The ranges of slump covered in the manual are 30 to 60 mm and 60 to 180 mm (Table 2). Maximum aggregate sizes are also limited to 20 and 40 mm.

Table 2: Approximate Free water contents required to give various levels of workability

Table 3; Typical ranges of slump for different concrete mix (structx.com)

**Step 4: ****Determination of cement content**

The cement content is determined from the water-cement ratio and the quantity of water.

Cement Content = (free cement content) / (free water-cement ratio)

The resulting value should be checked against the maximum and minimum values specified.

If the specified maximum cement content is exceeded, a higher cement grade should be used to enable the producer meet this requirement. Alternatively, super plasticizers could be used to meet other requirement at the determined cement content.

If the minimum cement content is higher than the earlier calculated value, this minimum value should be adopted and the water content should be recalculated to provide the same water/cement ratio at the specified minimum cement content.

**Step 5: ****Determination of aggregate content**

To determine the total aggregate content, an estimate of the density of the fully compacted concrete should be known. From tests carried out, a density value of 2400 kgm^{-3} is recommended for use for all mixes using normal weight aggregates. The total aggregate is obtained from the relationship:

The fine and coarse aggregate content are determined by obtaining the proportion of fine aggregate in the total aggregate content. Due to the fact that many coarse aggregates available from the quarries in Nigeria do not fit into the BS 882 envelopes for coarse aggregates, the use of combined aggregate grading envelope is recommended. Two methods are recommended for determining the proportion of fine aggregates in the concrete.

The first involves plotting the grading curves of the fine and coarse aggregates on the same axis on the graph paper and determining the percentage combinations of the two aggregates which gives a grading very close to the median of the BS 882 envelope. The fine aggregate and coarse aggregate contents are calculated from the relationships.

**Trial Mixes**

The mix proportions obtained should bechecked using trial batches. The workability ofthe first trial mix should be measured and if it’sdifferent from the stipulated value, the watercontent should be adjusted suitably. With theadjusted water content, the mix design shouldbe recalculated with the original water-cementratio. Two more trial mixes should be made withthis adjusted water content but at varying watercement ratios of ±10% of the original value.The last three mixes provide sufficientinformation on the relationship betweencompressive strength and water-cement ratio.

This can be used to carry out mix proportions for field trials using actual methods of concrete production on site. The issue of trial mix must be taken very seriously due to the variables involved in concrete production.

**Example**

Design a concrete mix with the following data

Characteristic strength = 30 Nmm^{-2} at 28 days

Assume 5 % defective

Standard deviation = 6 Nmm^{-2}

Since 5 % defective was assumed, margin (k) = 1.64

Cement type = PLC (Portland Limestone Cement)

Cement grade = 42.5

Aggregate type = Coarse/fine aggregate (uncrushed)

Maximum free Water/Cement ratio = 0.55

Slump = 30 – 60 mm

Maximum aggregate size = 20 mm

Minimum cement content = 190 kgm^{-3}

Relative density of aggregate = 2.6

Grading of fine aggregate = Zone 3

**Solution**

**Step 1**

Margin = k x standard deviation = 1.64 x 6 = 9.84 Nmm^{-2}

Target mean strength = characteristic strength + margin = 30 + 9.84 = 39.84 Nmm^{-2}

**Step 2**

Free water/cement ratio = 0.53 (Figure 2)

Maximum free water/cement ratio = 0.55 (use the minimum)

**Step 3**

Slump = 30 – 60 mm

Maximum aggregate = 20 mm

Free water content = 180 kgm^{-3 }(Table 2)

**Step 4**

Cement content = (free water content)/(free water-cement ratio) 180/0.53 = 340 kgm^{-3}

Minimum cement content = 190 kgm^{-3}

Use 340 kgm^{-3} because it is greater than 190.

Note: if the calculated value is less than the minimum value of 190, use the minimum value of 190

**Step 5**

Concrete density = 2400 kgm^{-3}

Total aggregate content = Concrete density – cement content – water content = 2400-340-180 = 1880 kgm^{-3}

Grading of aggregate = Zone 3

Based on the zone, proportion of fine aggregate = 25-30, say 27% (Table 1). In this interval, we can use 26 or 27 or 28 or 29.

Using 27%, Fine aggregate = 1880 x 0.27 = 508 kgm^{-3}

Coarse aggregate content = 1880 – 508 = 1373 kgm^{-3}

Table 4; Trial mix ratio