design mix proportion of wmm mix

Royal University of Bhutan

College of Science and Technology

Rinchending: Bhutan

Highway Engineering

Academic Year 2014, Winter Semester

Tutor: Sangey Pasang

Department of Civil Engineering and Architecture

Practical Report:

Aggregate Job Mix Proportion for WMM

Submitted By: Group ID: B-1

EDC2011041; Sanjit Kumar

EDC2011051; Tashi Zangmo

EDC2011052; Tenzin Norbu

EDC2011053; Tenzin Zam

EDC2011054; Thinley Gyelmo

EDC2011055; Tshering Cheki

Sieve Analysis of Sample A: 20mm Aggregate

Sample A1: 20mm Aggregate

I.S Sieve Size (mm)

Wt. of empty Sieve (Kg)

Wt. of Sample with Sieve (Kg)

Wt. of Sample retained (Kg)

Cumulative Wt. retained

Cumulative Wt. % Retained

Cumulative wt. passing (%)

37.5 0.4465 0.4465 0.0000 0.0000 0.00 100.00

26.5 0.3735 0.3735 0.0000 0.0000 0.00 100.00

20 0.4265 0.581 0.1545 0.1545 7.73 92.28

12.5 0.5035 2.022 1.5185 1.6730 83.65 16.35

4.75 0.4580 0.7765 0.3185 1.9915 99.58 0.42

2.36 0.3730 0.3745 0.0015 1.9930 99.65 0.35

0 0.3100 0.317 0.0070 2.0000 100.00 0.00

Sample A2: 20mm Aggregate

I.S Sieve Size (mm)

Wt. of empty Sieve (Kg)

Wt. of Sample with Sieve (Kg)

Wt. of Sample retained (Kg)

Cumulative Wt. retained

Cumulative Wt. % Retained

Cumulative wt. passing (%)

37.5 0.4465 0.4465 0.0000 0.0000 0.00 100.00

26.5 0.3735 0.3735 0.0000 0.0000 0.00 100.00

20 0.4265 0.515 0.0885 0.0885 4.43 95.58

12.5 0.5035 2.119 1.6155 1.7040 85.20 14.80

4.75 0.4580 0.747 0.2890 1.9930 99.65 0.35

2.36 0.3730 0.376 0.0030 1.9960 99.80 0.20

0 0.3100 0.314 0.0040 2.0000 100.00 0.00

Average Cumulative wt. passing for Sample A

I.S Sieve Size (mm)

Cumulative wt. passing for Sample A1 (%)

Cumulative wt. passing for Sample A2 (%)

Average Cumulative wt. passing for Sample A (%)

37.5 100.00 100.00 100.00

26.5 100.00 100.00 100.00

20 92.28 95.58 93.93

12.5 16.35 14.80 15.58

4.75 0.42 0.35 0.39

2.36 0.35 0.20 0.27

0 0.00 0.00 0.00

Sieve Analysis for Sample B: 10mm Aggregate

Sample B1: 10mm Aggregate

I.S Sieve Size (mm)

Wt. of empty Sieve (Kg)

Wt. of Sample with Sieve

Wt. of Sample retained (Kg)

Cumulative Wt. retained

Cumulative Wt. % Retained

Cumulative wt. passing (%)

12.5 0.4205 0.4225 0.0020 0.0020 0.10 99.90

4.75 0.4410 2.1245 1.6835 1.6855 84.28 15.73

2.36 0.3910 0.5060 0.1150 1.8005 90.03 9.98

0.3 0.4070 0.4300 0.0230 1.8235 91.18 8.83

0.075 0.2195 0.3670 0.1475 1.9710 98.55 1.45

Pan 0.3485 0.3775 0.0290 2.0000 100.00 0.00

Sample B2: 10mm Aggregate

I.S Sieve Size (mm)

Wt. of empty Sieve (Kg)

Wt. of Sample with Sieve

Wt. of Sample retained (Kg)

Cumulative Wt. retained

Cumulative Wt. % Retained

Cumulative wt. passing (%)

12.5 0.4205 0.4295 0.0090 0.0090 0.45 99.55

4.75 0.4410 2.2480 1.8070 1.8160 90.80 9.20

2.36 0.3910 0.4905 0.0995 1.9155 95.78 4.22

0.3 0.4070 0.4295 0.0225 1.9380 96.90 3.10

0.075 0.2195 0.2565 0.0370 1.9750 98.75 1.25

Pan 0.3485 0.3735 0.0250 2.0000 100.00 0.00

Average Cumulative wt. Passing for Sample B: 10mm Aggregate

I.S Sieve Size (mm)

Cumulative wt. passing for Sample B1 (%)

Cumulative wt. passing for Sample B2 (%)

Average Cumulative wt. passing for Sample B (%)

12.5 99.90 99.55 99.73

4.75 15.73 9.20 12.46

2.36 9.98 4.22 7.10

0.3 8.83 3.10 5.96

0.075 1.45 1.25 1.35

0 0.00 0.00 0.00

Sieve Analysis of Sample C: Sand

Sample C1: Sand

I.S Sieve Size (mm)

Wt. of empty Sieve (Kg)

Wt. of Sample with Sieve

Wt. of Sample retained (Kg)

Cumulative Wt. retained

Cumulative Wt. % Retained

Cumulative wt. passing (%)

4.75 0.4410 0.4410 0.0000 0.0000 0.00 100.00

2.36 0.3910 0.4402 0.0492 0.0492 2.46 97.54

0.3 0.4070 2.2795 1.8725 1.9217 96.09 3.92

0.075 0.2195 0.2848 0.0653 1.9870 99.35 0.65

Pan 0.3485 0.3615 0.0130 2.0000 100.00 0.00

Sample C2: Sand

I.S Sieve Size (mm)

Wt. of empty Sieve (Kg)

Wt. of Sample with Sieve

Wt. of Sample retained (Kg)

Cumulative Wt. retained

Cumulative Wt. % Retained

Cumulative wt. passing (%)

4.75 0.4410 0.4410 0.0000 0.0000 0.00 100.00

2.36 0.3910 0.4350 0.0440 0.0440 2.20 97.80

0.3 0.4070 2.2055 1.7985 1.8425 92.13 7.88

0.075 0.2195 0.3569 0.1374 1.9799 99.00 1.01

Pan 0.3485 0.3686 0.0201 2.0000 100.00 0.00

Average Cumulative Wt. Passing for Sample C: Sand

I.S Sieve Size (mm)

Cumulative wt. passing for Sample C1 (%)

Cumulative wt. passing for Sample C2 (%)

Average Cumulative wt. passing for Sample C (%)

4.75 100.00 100.00 100.00

2.36 97.54 97.80 97.67

0.3 3.92 7.88 5.90

0.075 0.65 1.01 0.83

Pan 0.00 0.00 0.00

Grain Size Distribution Diagram of Sample A, B and C

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GRAIN SIZE DISTRIBUTION (DIAMETER MM)

Gradation Curve for Sample A

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Grain Size Distribution (Diameter mm)

Gradation Curve for Sample B

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GRAIN SIZE DISTRIBUTION

Gradation Curve for Sample C

Gradation Curve Without Mix-proportion

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Grading requirements for WMM Sample A Gradation

Sample B Gradation Sample C Gradation

Sieve Sizes

Avg. % by weight passing the IS sieve for 20mm aggregate

A

Avg. % by weight passing the IS sieve for 10mm aggregate

B

Avg. % by weight passing the IS sieve

for sand C

Avg. Combined % by weight passing the IS

sieve for sand

Avg. % by weight passing the IS sieve for standard WMM

45 100.00 100.00 100.00 100.00 97.50

22.4 93.93 100.00 100.00 97.98 70.00

11.2 15.58 99.73 100.00 71.77 50.00

4.75 0.39 12.46 100.00 37.62 32.50

2.36 0.27 7.10 97.67 35.01 22.50

0.6 0.00 5.96 5.90 3.95 15.00

0.075 0.00 1.35 0.83 0.73 4.00

Let, x1, x2, x3 represent the proportions of sample A, B, C respectively.

Then the respective linear equations are as follows:

x1 + x2 + x3 = 0.975

0.9393x1 + x2 + x3 = 0.7

0.1558x1 + 0.9973x2 + x3 = 0.5

0.0039x1 + 0.1246x2 + x3 = 0.325

0.0027x1 + 0.071x2 + 0.9767x3 = 0.225

0.0596x2 + 0.059x3 = 0.15

0.0135x2 + 0.0083x3 = 0.04

Computation of Mix-Proportion Solving Linear Equations by Mat-Lab

>> A=[1 1 1; 0.9393 1 1; 0.1558 0.9973 1; 0.0039 0.1246 1; 0.0027 0.071 0.9767; 0 0.0596 0.059;0

0.0135 0.0083]

A =

1.0000 1.0000 1.0000

0.9393 1.0000 1.0000

0.1558 0.9973 1.0000

0.0039 0.1246 1.0000

0.0027 0.0710 0.9767

0 0.0596 0.0590

0 0.0135 0.0083

>> B=[0.975; 0.7; 0.5; 0.325; 0.225; 0.15; 0.04]

B =

0.9750

0.7000

0.5000

0.3250

0.2250

0.1500

0.0400

>> A\B

ans =

0.4151

0.1806

0.2581

>>

Result:

Mix proportion of the Sample A : Sample B : Sample C = 0.4151 : 0.1806 : 0.2581

= 1 : 0.435 : 0.622

Sieve Sizes (mm)

Avg. Combined % by weight passing the IS sieve for sand (after

mix proportion)

Avg. % by weight passing the IS sieve for standard WMM

45 85.38 97.50

22.4 84.86 70.00

11.2 77.98 50.00

4.75 32.94 32.50

2.36 29.62 22.50

0.6 4.56 15.00

0.075 0.90 4.00

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SIEVE SIZES (GRAIN SIZES MM)

Standard and Designed Gradation of Aggregates (A -B-C)

Design Field Gradation Average Standard GradationRatio: A:B:C = 1 : 0.435 : 0.622