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# 2a-Concrete Mix Design - Vocational Training Counciltycnw01.vtc.edu.hk/cbe2022/2a-Concrete Mix...

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Normal Concrete Mix Design 1. Prescribed Mix (Standard Mix)

(Source: General Specification for Civil Engineering Works)

• 2/21

2. Designed Mix 2.1 Variability of Strength Design is based on the assumption of certain minimum properties of concrete,

such as strength.

Actual strength of the concrete produced is a variable quantity.

Source of variability include variations in mix ingredients, changes in concrete

making and placing; variations also occur in sampling procedure and testing.

Knowledge of variability is required so that the strength values can be

interpreted properly.

2.2 Target Strength and Characteristic Strength It is generally accepted that the variation in concrete strengths or a particular

mix follows the normal distribution as shown below:

In the figure above, the mean strength of the mix is 40 N/mm2. That is, we can

expect half of the test results will be higher than 40 N/mm2 and half will be

lower.

In practice, we specify the quality of concrete not as a minimum strength, and

not as a mean strength, but as a characteristic strength below which a specified

percentage of the test results, often called defectives, may be expected to fall.

Figure 1 Normal distribution of concrete strength

(Source: Building Research Establishment)

• 3/21

Characteristic strength may be defined as to have any proportion of defectives.

(BS 5328 Guide to Specifying Concrete, and BS8110 Structural Use of

Concrete adopt the 5% defective level.)

As a result, it is necessary to design a mix to have a target mean strength greater

than the specified characteristic strength by an amount termed the margin.

Target mean strength = characteristic strength + margin

fm = fk + k s

where fm = target mean strength

fk = characteristic strength

k s = margin

k = constant

s = standard deviation

Constant k is derived from the mathematics of the normal distribution.

Defective Constant

1 % 2.33

2.5 % 1.96

5 % 1.64

Example 1 To design a concrete mix with characteristic strength of 30 MPa, what should the

target mean strength be?

Given that : defective level 5%, standard deviation 5 MPa.

Solution

fk = 30 MPa k = 1.64 s = 5 MPa

fm = fk + k s

= 30 + 1.64 x 5 MPa

= 38.2 MPa

The target mean strength should be 38.2 MPa

• 4/21

2.3 BRE Mix Design Method (Formerly DoE Method) Design of Normal Concrete Mixes was published by the Building Research

Establishment Ltd. in 1997. (Formerly by Department of Environment).

The design procedure is summarized in chart below:

(Source: Building Research Establishment)

• 5/21

(Source: Building Research Establishment)

• 6/21

Equations for mix design

C1 M = k x s

where M = the margin k = a value appropriate to the percentage defectives permitted below the

characteristic strength s = the standard deviation

C2 fm = fc + M

where fm = the target mean strength fc = the specified characteristic strength M = the margin

C3 Cement content =

ratiocement water / -free

contentwater -free

C4 Total aggregate content (saturated and surfacedry) = D C W

where D = the wet density of concrete (kg/m3) C = the cement content (kg/m3) W = the free water content (kg/m3)

C5 Fine aggregate content = total aggregate content x proportion of fines Coarse aggregate content = total aggregate content fine aggregate content

C6 Portland cement content =

F)] 0.3 (C[W / p) 0.7 (100

Wp) (100

where W = the free water content (kg/m3) C = the cement content (kg/m3) F = pfa content (of the mix) (kg/m3) p = proportion of pfa specified as percentage of the combined weight of cement and

pfa the ratio of W/(C+0.3F) is derived from Table 10 and Figure 4

C7 pfa content =

p - 100

C p

where C = the cement content (kg/m3) p = proportion of pfa specified as percentage of the combined weight of cement and

pfa

C8

F C

W

for comparison of maximum free-water/cement ratio

where W = the free water content (kg/m3) C = the cement content (kg/m3) F = pfa content (kg/m3)

C9 Total aggregate content (saturated and surface dry) = D (C + F) W

where W = the free water content (kg/m3) C = the cement content (kg/m3) F = pfa content (of the mix) (kg/m3) D = the wet density of concrete (kg/m3)

• 7/21

Figure 3 Relationship between standard deviation and characteristic strength

Figure 4 Relationship between compressive strength and free-water/cement ratio

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Figure 5 Estimated wet density of fully compacted concrete

• 9/21

Figure 6 Recommended proportions of fine aggregate according to percentage passing 600 m sieve

• 10/21

Example 2 unrestricted design Specification of the mix:

Characteristic compressive strength 30 N/mm2 at 28 days

Defective rate 2.5 %

No previous control data

Cement: OPC class 42.5

Slump required, 10-30 mm

Maximum free-water/Cement ratio 0.55

Minimum cement content 290 kg/m3

Coarse aggregate: Uncrushed single sized 10 mm and 20 mm (1:2 by weight)

Fine aggregate: Uncrushed with 70% passing 600 m sieve

Relative density of aggregate : 2.6 (assumed)

Volume of trial mix : 0.05 m3

Example 3 mix restricted by maximum water/cement ratio Specification of the mix:

Characteristic compressive strength 25 N/mm2 at 28 days

No previous control data but a margin of 10 N/mm2 is specified

Cement: OPC class 42.5

Slump required, 30-60 mm

Maximum free-water/Cement ratio 0.5

Minimum cement content 290 kg/m3

Coarse aggregate: Uncrushed single sized 10, 20 and 40 mm

(Suggested ratio 1 : 1.5 : 3 by weight)

Fine aggregate: Uncrushed with 90% passing 600 m sieve

Relative density of aggregate : 2.5 (assumed)

Volume of trial mix : 0.08 m3

• 11/21

Solution of Example 2

(Source: Building Research Establishment)

• 12/21

Solution of Example 3

(Source: Building Research Establishment)

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Example 4 mix restricted by minimum cement content Specification of the mix:

Same as example, but

Slump required 0 -10 mm

Example 5 mix restricted by maximum cement content Specification of the mix:

Characteristic compressive strength 50 N/mm2 at 7 days

Defective rate 1 %

Previous control data: standard deviation 5 N/mm2

Cement: RHPC class 52.5

Slump required, 30-60 mm

Maximum cement content 550 kg/m3

Coarse aggregate: Crushed single sized 10 mm

Fine aggregate: Uncrushed with 45% passing 600 m sieve

Relative density of aggregate : 2.7 (assumed)

Volume of trial mix : 0.08 m3

• 14/21

Solution of Example 4

(Source: Building Research Establishment)

• 15/21

Solution of Example 5

(Source: Building Research Establishment)

• 16/21

3 Trial Mixes 3.1 Moisture conditions of aggregates: Aggregates may be in the following conditions:

Oven dry:- prolonged drying in an oven would eventually remove the moisture

completely.

Air dry:- when the aggregate is allowed to stand in dry air, some water will

evaporate so that the aggregate is air-dry.

Saturated surface dry (SSD):- all pores in the aggregate are full of water, i.e.,

saturated, but the surface of the aggregate is dry.

Damp or wet:- containing an excess of moisture on the surface (free water).

3.2 Adjustment to mix proportion in trial mix The batch quantities determined in the mix design are based on saturated

surface-dry (SSD) aggregates.

Very often, aggregates are in other conditions, adjustment of actual weights of

aggregates and water have to be made.

Moisture Condition of Aggregate (Source: Design and Control of Concrete Mixtures Portland Cement Association)

• 17/21

3.3 Determination of mass of aggregate for trial mix

3.3.1 MT = MD ( A 1M.C. 1

)

where

MT = the mass of aggregate to be weighed for trial mix

MD = mass of aggregate designed, which the aggregate is assumed in SSD

condition.

M.C. = insitu moisture content of the aggregate (mass of water/mass of dry

aggregate) presented in decimal.

A = water absorption of the aggregate (mass of absorbed water/mass of dry

aggregate) presented in decimal.

3.3.2 A simplified formula: MT = MD (1 + M.C. A) This formula gives an approximate result only but is accurate enough for most

practical purpose.

3.4. Determination of mass of water for trial mix MD = MT or MTw + MTf + MT10 + MT20 + MT40 = MDw + MDf + MD10 + MD20 + MD40 MTw = MDw + MDf + MD10 + MD20 + MD40 - (MTf + MT10 + MT20 + MT40)

• 18/21

Example 6 Quantities of the constituent materials for 0.05 m3 of a designed mix are: Material Designed Mass (kg) Absorption (%)

Cement 17.0 -

Coarse aggregate (SSD) 69.2 1

Sand (SSD) 25.7 2

Water 8.0 -

If oven-dried aggregates are use, determine the mass of each constituent for trial mix. Solution

Using MT = MD ( A 1M.C. 1

) Using MT = MD (1 + M.C. A)

Coarse agg: MTc = 69.2 0.01 10 1

MTc = 69.2 (1 + 0 0.01)

= 68.5 kg = 68.5 kg

Sand: MTs = 25.7 0.02 10 1

MTs = 25.7 (1 + 0 0.02)

= 25.2 kg = 25.2 kg

Water: Using MD = MT

69.2 + 25.7 + 8 = 68.5 + 25.2 + MTw MTw = 9.2 kg

Cement: unchanged

Example 7

If moisture content of aggregates in example 6 are:

Coarse aggregate: 1.4 %

Sand 2.8%

determine the mass of each constituent for trial mix.

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3.5 Workability of trial mix During the mixing of the trial mix, an experienced technician is able to adjust

the water content by eye inspection if the workability of the mix is much outside

the target range.

It is thus useful, initially, to withhold a small proportion, say 10% of the mixing

water until assessment of workability has been made to determine whether

deduction or addition of water is necessary.

Any adjustment of water ( MAw) must be recorded for later use.

4. Design iteration (Re-design) The design tables and charts in the BRE method are based on the statistical data

in England.

Due to different sources of cement and aggregates, there may be deviation of

actual cube strength of trial mix from target strength. It is thus necessary to

undergo the re-design procedure.

The re-design procedure is same as the original design procedure excepted that

data obtained from tables and charts shall be replaced with actual measured data

in the first trial.

4.1 Free-water content In Item 2.3 of the design table, use actual free-water content in the first trial

instead of obtaining from table 3.

Actual free water content (per m3) = (MDw MAw) volume of first trial mix

Please note that any addition or deduction of water to bring the aggregate back

to SSD condition shall not be involved in the above calculation.

4.2 Density of fresh concrete

In Item 4.2, use actual measured fresh concrete density in the first trial.

• 20/21

4.3 Free-water/cement ratio

In Item 1.7, the free-water/cement ratio shall be determined as follow:

a. Determine the actual free-water/cement ratio in the first trial, which is

(MDw MAw) Mcement

b. When the actual cube strength of the first trial is available, plot this result

together with the result in (a) on figure 4 to obtain a re-design water/cement ratio.

(Two examples are given as below.)

Example 8 Target mean strength 60 MPa First trial

Free-water/cement ratio 0.37

No addition or deduction of water during first trial

Actual cube strength 70 MPa

Re-design

Plot point C1: W/C = 0.37, and

fc = 70 MPa

Get point D1: target = 60 MPa, and

W/C = 0.44

Example 9 Target mean strength 22 MPa First trial

Free-water/cement ratio 0.62

Some water is added such that the actual free-water/cement ratio became 0.69

Actual cube strength 14 MPa

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Re-design

Plot point C2: W/C = 0.69, and

fc = 14 MPa

Get point D2: target = 22 MPa, and

W/C = 0.54

(Source: Building Research Establishment) Embed Size (px)
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