ASSIGNMENT NUMBER 3 – SOLUTION KEY

 

Problem:  Do a proportion a trial mixture that will meet the following conditions and specifications.

 

Conditions and Specifications: Concrete is required for a pavement that will be exposed to chlorides from seawater. A specified compressive strength, f'c, of 40 MPa is required at 28 days. Slump should be between 25 mm and 75 mm. A nominal maximum size aggregate of 25 mm is required. No statistical data on previous mixes are available. The materials available are as follows:

Cement: Type I with relative density of 3.0.

Coarse aggregate: Well graded, 25-mm nominal maximum-size rounded gravel with ovendry relative density of 2.7, absorption of 0.5% and ovendry rodded bulk density of 1700Kg/m3. The laboratory sample for trial batching has a moisture content of 1.5%.

Fine aggregate: Natural sand with ovendry relative density of 2.60 and absorption of 0.6%. The laboratory sample moisture content is 5%. The fineness modulus is 2.80.

Water reducer: reduces water demand by 10% when used at a dosage rate of 4 g per Kg of cement. Assume that density is that of water.

 

SOLUTION:

 

Strength. The minimum design compressive strength for concrete exposed to chlorides from sea water is given as 35 MPa. (Table 9-1).

 

 Table 9-1. Maximum Water-Cementitious Material Ratios and Minimum Design Strengths for Various Exposure Conditions

 

Exposure Condition

Maximum water-cementitious material ratio by mass for concrete

Minimum design compressive strength, f' c , MPa (psi)

Concrete protected from exposure  to freezing and thawing, application of deicing chemicals, or aggressive substances.

Select water-cementitious material ratio on basis of strength, workabilty, and finishing needs

Select strength based on structural requirements

Concrete intended to have low permeability when exposed to water

0.50

28 (4000)

Concrete exposed to freezing and thawing in a moist condition or deicers

0.45

31 (4500)

For corrosion protection for reinforced concrete exposed to chlorides from deicing salts, salt water, brackish water, seawater, or spray from these sources

0.40

35 (5000)

Thus, we see here that the required design strength is 40 MPa. Since no statistical data is given , as per table 9-11,

The required compressive strength for proportioning f'cr is given by: 1.10f'c + 5.0

i.e. f'cr = 1.10*40 + 5.0 = 49.0 MPa.

 

Table 9-11. (Metric). Required Average Compressive Strength When Data are Not Available to Establish a Standard deviation

 

Specified compressive strength, f'c , Mpa

Required average compressive strength, f' cr, Mpa

Less than 21

f' c + 7.0

21 to 35

f' c + 8.5

Over 35

1.10 f' c + 5.0

 

 

w/c ratio: According to Table 9-1, the maximum w/c ratio for concrete exposed to chlosrides from sea water is 0.40. However , the recommended w/c ratio on basis of compressive strength as per Fig 9-2 or table 9-3 is :

0.38 as per table 9-3 or 0.35 as per Fig 9-2

Therefore w/c ratio = 0.35 (lower value governs)

 

Table 9-3 (Metric). Relationship Between Water to Cementitious Material Ratio and Compressive Strength of Concrete

 

Compressive Strength at 28 days, Mpa

Water-cementitious materials ratio by mass

Non-air-entrained concrete

Air-entrained concrete

45

0.38

0.30

40

0.42

0.34

35

0.47

0.39

30

0.54

0.45

25

0.61

0.52

20

0.69

0.60

15

0.79

0.70

                                                                                                                                                                                                                                                                                                                   

 

 

Air Content: According to Table 9-5, a target air content of 1.5% is recommended for aggregate of size 25-mm.Therefore, we can design the mix for 1%- 3% air and use 3% for batch proportions. The trail batch air content must be within ±0.5 % of the maximum allowable air content.

 

 

 

 

 

 

 

 

Table 9-5 (Metric). Approximate Mixing Water and Target Air Content Requirements for Different Slumps and Nominal Maximum Sizes of Aggregate

 

Slump, mm

Water, Kilograms per cubic meter of concrete, for indicated sizes of aggregate

9.5 mm

12.5 mm

19 mm

25 mm

37.5 mm

50 mm

75 mm

150 mm

 

Non-air-entrained concrete

25 to 50

207

199

190

179

166

154

130

113

75 to 100

228

216

205

193

181

169

145

124

150 to 175

243

228

216

202

190

178

160

-

Appropriate amount of entrapped air in non-air-entrained concrete, percent

3.0

2.5

2.0

1.5

1.0

0.5

0.3

0.2

 

Air-entrained concrete

25 to 50

181

175

168

160

150

142

122

107

75 to 100

202

193

184

175

165

157

133

119

150 to 175

216

205

197

184

174

166

154

-

Recommended average total air content, percent, for level of exposure:

 

Mild exposure

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

Moderate exposure

6.0

5.5

5.0

4.5

4.5

4.0

3.5

3.0

Severe exposure

7.5

7.0

6.0

6.0

5.5

5.0

4.5

4.0

 

 

 

Slump: The slump is specified at 25-mm to 75-mm. However, for proportioning purpose, we shall use 75mm ± 20mm.

 

Water content: In accordance with Table 9-5 or Fig 9-5, the required water content for a 75-mm slump, Non-air-entrained concrete with 25-mm aggregate size is about 193 Kg/m3. However, the rounded gravel would need only 168 Kg/m3. (193 – 25). Also, the water reducers would also result in reduction of 10%. Thus the final water content would be:

168 – (10% of 168) = 151.2 Kg/m3.

 

 

 

 

Cement Content:  On basis of w/c ratio of 0.35 and water content of 151.2 Kg/m3,

 The cement content required will be:

151.2/0.35 = 432 Kg/m3.

This is greater than the 310 Kg/ m3 on basis of aggregate size and also greater than 335 Kg/m3 required for severe conditions (Table 9-7).

 

Table 9-7. Minimum Requirements of Cementing Materials for Concrete Used in Flatwork

 

Nominal maximum size of aggregate, mm (in.)

Cementing materials, Kg/m3 (lb/yd3)*

37.5   (11/2)

280   (470)

25       (1)

310   (520)

19     (3/4)

320   (540)

12.5  (1/2)

350   (590)

9.5    (3/8)

360   (610)

*cementing materials quantities may need to be greater for severe exposure. For example, for deicer exposures, concrete should contain at least 335 Kg/m3 (564 lb/yd3) of cementing materials.

 

Coarse aggregate content: The bulk volume of CA (of 25-mm size) recommended when using sand with fineness 2.80 is 0.67. (Table 9-4 or Fig 9-3).

Therefore the ovendry mass of CA for a cubic meter of concrete will be density times the volume.

i.e. 1700 * 0.67 = 1139 Kg.

 

 

 

Table 9-4. Bulk Volume of Coarse Aggregate Per Unit Volume of Concrete

 

Nominal maximum size of aggregate, mm (in.)

Bulk volume of dry-rodded coarse aggregate per unit volume of concrete for different fineness moduli of fine aggregate

2.40

2.60

2.80

3.00

9.5       (3/8)

0.5

0.48

0.46

0.44

12.5     (1/2)

0.59

0.57

0.55

0.53

19        (3/4)

0.66

0.64

0.62

0.6

25         (1)

0.71

0.69

0.67

0.65

37.5    (11/2)

0.75

0.73

0.71

0.69

50         (2)

0.78

0.76

0.74

0.72

75         (3)

0.82

0.8

0.78

0.76

150       (6)

0.87

0.85

0.83

0.81

 

 

 

Admixture Content:

The amount of water reducer per cubic meter of concrete is: 4 * 432 = 1728 g or      1.728 Kg.

 

 

 

Fine Aggregate content:

At this point, we have calculated the amount required of all the ingredients except fine aggregate.

By the Absolute volume method, FA content can be obtained by subtracting the absolute volumes of the known ingredients from 1 cubic meter.

 

Absolute volume is calculated by dividing the mass of ingredient by the product of its relative density and the density of water:

 

Water                   =             = 0.1512 m3.                                

Cement                =            = 0.144 m3.           

Air                       =                  = 0.030 m3.                    

Coarse aggregate =        = 0.422 m3.

                                                         ---------------

Total Volume of known ingredients = 0.747 m3.

Hence, absolute volume of FA is: 1 – 0.747 = 0.253m3.

The mass of dry FA is: 2.60*0.253*1000 = 657.8 Kg.

 

Thus, the proportions before trial mixing per cubic meter of concrete are:

Water                                       151.2 Kg

Cement                                    432.0 Kg

Coarse aggregate (dry)          1139.0 Kg

Fine aggregate (dry)                  657.8 Kg

                                           --------------

Total mass                              2380.0 Kg

 

Water reducer                       1.728 Kg

 

Slump 75 mm (±20 mm for trial batch)

 

Estimated concrete density (using SSD aggregate) =

151.2 + 432 + (1139*1.005) + (657.8*1.006)

= 2389.64 Kg/m3.

 

Note: (0.5% absorption / 100) + 1 = 1.005

          (0.6% absorption / 100) + 1 = 1.006

 

Correction for moisture:

Test indicates that for this example, CA moisture content is 1.5 % and FA moisture content is 5 %.

Now the trial batch aggregate proportions become:

CA = 1139.0*1.015 = 1156.09 Kg.

FA = 657.8*1.05 = 690.69 Kg.

Note that water absorbed by the aggregate does not become part of mixing water and hence must be excluded from water adjustment.

Surface moisture contributed by CA = 1.5 % - 0.5 % = 1.0 %. = 0.010

                                                     FA= 5 % - 0.6 % = 4.4 %. = 0.044

Thus, the estimated requirement for added water becomes:

151.2 – (1139*0.010)-(657.8*0.044) = 110.87 Kg.

 

Now the revised proportions of batch taking moisture into consideration are:

Water (to be added)                                 110.87 Kg

Cement                                                     432.00 Kg

Coarse aggregate (1.5% MC, wet)         1156.09 Kg

Fine aggregate (5% MC, wet)                    690.69 Kg

                                                            --------------

Total mass                                               2389.65 Kg

                                        

Water reducer                                             1.728 Kg