design mix proportion of wmm mix
DESCRIPTION
Wet Mix Macadam, Computation of Mix-Proportion Solving Linear Equations by Mat-LabTRANSCRIPT
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
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
100.00
0.1 1 10 100
PER
CEN
T FI
NER
BY
WEI
GH
T
GRAIN SIZE DISTRIBUTION (DIAMETER MM)
Gradation Curve for Sample A
0.00
20.00
40.00
60.00
80.00
100.00
120.00
0.01 0.1 1 10 100
Pe
rce
nt
Fin
er
by
We
igh
t
Grain Size Distribution (Diameter mm)
Gradation Curve for Sample B
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
100.00
110.00
0.01 0.1 1 10
PER
CEN
T FI
NER
BY
WEI
GH
T
GRAIN SIZE DISTRIBUTION
Gradation Curve for Sample C
Gradation Curve Without Mix-proportion
0
20
40
60
80
100
0.01 0.1 1 10 100
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
0.00
20.00
40.00
60.00
80.00
100.00
120.00
0.01 0.1 1 10 100
PER
CEN
T FI
NER
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