10.4. Proportioning concrete mixtures

One of main task of concrete technology is determination of optimum composition of concrete. Under the optimum composition of concrete, as a rule, the content of materials per 1 m³ of concrete mixture which provides the required properties of concrete at the least expense of cement is understood.

The composition of concrete for dry materials is called nominal one(laboratory), for materials with certain humidity – working one. The nominal composition is found at first, as a rule, and then transfers it taking into account the aggregate humidity, on the worker composition.

In the conditions of production the calculation of the concrete composition is add up to determination of material expenses for the batch of concrete mixer. A volume of batch is a less than the total volume of separate friable materials as a result of filling the voidage between grains of coarse aggregate.

, (10.11)

where - coefficient of concrete yield, for a heavy-weight concrete equals 0.55...0.75; - accordingly volumes of cement, sand and coarse aggregate.

Proportioning of the concrete mixtures can be realized by experimental or calculation-experimental methods. For proportioning of the heavy-weight concrete the required slump or rigidity of concrete and also class of concrete strength are specified. If it is required the grades of concrete are also specified according to the frost resistance and water impermeability and so on.

The experimental methods of concrete mixtures proportioning are expedient at the large volumes of concrete works and heterogeneity of materials.

Calculation-experimental methods accelerate the mixtures proportioning due to the empirical formulas, accumulated graphic and tabular information using. But the expected composition should be experimentally corrected on required indexes before the recommendation to the production.

The method of absolute volumes is the most common among the calculation-experimental methods of determination of concrete composition.

The calculation of composition of heavy-weight concrete begins with determination of required C/W or W/C.

The approximately needed C/W can be found from the formula:

, (10.12)

where - concrete strength at the 28 days; C/W - cement-water ratio; А - coefficient which depends on the quality of materials.

The formula (10.12) indicates the rectilinear dependence between the concrete strength, cement strength and cement-water ratio. It is just for C/W ≤ 2,5. At C/W > 2,5 ( < ) the next formula can be used:

(10.13)

Depending on the material quality the next values of coefficients can be used:

	А	А1
High quality	0.65	0.45
Ordinary quality	0.6	0.4
Satisfactory quality	0.55	0.37

Water-cement ratio should be limited at action of salt and fresh water on structures and also in other cases when the concrete density is specified (Table 10.10).

Таble 10.10

The W/C limitation at the action of salt and fresh water

Condition of exposure	W/C for the non-massive concrete structures		W/C for the external surface of massive concrete structures
	Salt water	Fresh water	Salt water	Fresh water
Area of variable water level at climatic conditions:
Especially severe	0.42	0.47	0.45	0.48
Severe	0.45	0.50	0.47	0.52
Mild	0.50	0.55	0.55	0.56
Parts of structures which are constantly under water pressure	0.55	0.58	0.56	0.58
non-pressure	0.6	0.62	0.62	0.62

For the concrete of ordinary density W/C can be no more than 0.6; high dense - no more than 0.55 and especially dense - no more than 0.45.

After the water-cement ratio selecting, the required amount of water can be determined to achieve the required slump or rigidity of concrete mixture. Usually for water content determination graphic (Fig. 10.5) or tabular data is used, taking into account influence of the cement type and coarse aggregate and also the water demand of sand.

If the content of water and water-cement ratio are known, it is possible to define the cement content (C):

C=W/(W/C) or C = W·(C/W) (10.14)

The cement content should be not less than some minimum values to prepare the homogeneous concrete mixture. The minimum value of cement content is accepted not less than 200 kg/m³ for the non-reinforced concrete. The decline of cement content is assumed to 150 kg/m³ at the use of fly ash additive. It is effective to add, also other dispersible mineral additives to provide the minimal binder content.

The contents of sand and coarse aggregate can be found by solving the system of two equations:

, (10.15)

де C, S, C.S, W - accordingly contents of cement, sand, crushed stone (gravel) and water; , , - absolute densities of cement, sand and crushed stone (gravel); - bulk density of the crushed stone (gravel); - voidage of the crushed stone (gravel) ;  - coefficient of the coarse aggregate grains separation by the cement-sand mortar.

Coefficient α characterizes the mortar surplus for filling the emptinesses between the coarse aggregate grains and for plastic concrete mixes depends on the cement content, water-cement ratio and water demand of sand (Table 10.11).

Таble 10.11

Coefficient α for plastic concrete mixes

Cement content, kg/m3	Value of  depending on W/C
	0.4	0.5	0.6	0.7	0.8
250	—	—	1.26	1.32	1.38
300	—	1.3	1.36	1.42	—
350	1.32	1.38	1.44	—	—
400	1.4	1.45	—	—	—

Notes: 1. The values given in Table are true for sands with the water demand 7 %. At the increasing of sand water demand on every percent a diminishes on 0.03, and at diminishing of sand water demand grows accordingly on 0,03.

2. For non-plastic (rigid) concrete (C < 400 kg/m³)  = 1.05...1.15.

The first equation in system (10.15) state that 1 m³ of concrete mix (1000 litres) equals the sum of absolute volumes of four components (cement, sand, crushed stone or gravel and water). From the second equation follows that volume of mortar in a concrete should fill the voidage between grains of coarse aggregate.

Calculation formulas for determination of crushed stone (gravel) and sand contents can be obtained by solving the system (10.15):

, (10.16)

. (10.17)

The determination of optimum water amount as a result of testing of few series of specimens with different water content is the most responsible for light-weight concrete. At the optimum water amount is possible to get maximum strength of concrete at defined grain composition of aggregates, cement content and conditions of compaction.

There are some other calculation-experimental ways of concrete mixtures proportioning, used in construction practice.