53
5.1. See Section 5.2.
5.3. See Section 5.5.
5.6. See Section 5.5.4.
5.7. Sample A: Total moisture content = [(521.0 –491.6) / 491.6] x 100 = 5.98%
5.9. Since moisture content and absorption are related to the aggregate dry weight, the first
step of the solution is WRdetermine the dry weight of WKHcoarse and fine aggregates.
54
5.10.a.Bulk dry specific gravity = 5216/(5227-3295) = 2.6998
5.11. Volume = 2000 x 48 x 0.5 = 48,000 ft3
5.12. The bulk dry specific gravity considers the total particle volume, whereas the dry-rodded
unit weight considers the volume of the container.
0.88
5.13. The bulk dry specific gravity considers the total particle volume, whereas the dry-rodded
unit weight considers the volume of the container.
5.72
5.14. a. Dry-rodded unit weight for trial 1 = (76.6–20.3)/0.5 = 112.6 lb/ft3
b. Percent volume of particles = 112.6/(2.620 x 62.3) x 100 = 69.0 %
5.15. See Section 5.5
55
5.16. Bulk dry specific gravity = 3862.1/(3923.4-2452.1) = 2.625
5.17. Bulk dry specific gravity = 495.5/(623+500-938.2) = 2.681
5.18.
Size No.
Maximum sieve size
Nominal maximum sieve size
357
63 mm (2.5 in.)
50 mm (2 in.)
57
37.5 mm (1.5 in.)
25 mm (1 in.)
8
12.5 mm (0.5 in.)
9.5 mm (3/8 in.)
56
5.19.
Sieve
Amount
Retained (g)
Cumulative Percent
Retained
Percent
Passing
25 mm
0
0
100
9.5 mm
47.1
7.3
93
4.75 mm
239.4
44.8
55
2.00 mm
176.5
72.4
28
0.425 mm
92.7
86.9
13
0.075 mm
73.5
98.4
1.5
Pan
9.6
100
0.0
Total
638.8
Note that the values of the percent passing are rounded off to the nearest 1%, except the
percent passing the 0.075 mm sieve is rounded off to the nearest 0.1%.
Semi-log gradation chart:



57
5.20.
.Sieve size
Amount
Cumulative
Cumulative
Percent
Retained,
Amount
Percent
Passing
g
Retained, g
Retained
Plus 37.5 mm
0.0
0.0
0.0
100
37.5 mm to 25 mm
315.0
5.4
5.4
95
25 mm to 19 mm
782.0
13.3
18.7
81
19 mm to 9.5 mm
1493.0
25.5
44.2
56
9.5 mm to 4.75 mm
677.0
11.6
55.8
44
4.75 mm to 0.60 mm
1046.0
17.8
73.6
26
0.60 mm to 0.075 mm
1502.0
25.6
99.2
0.8
Pan
45.0
0.8
100.0
0.0
Total
5860.0
The 0.45 power gradation chart:










Sieve Size, mm
Percent Passing, %







Note: In order to plot the 0.45 power gradation chart the horizontal axis represents the sieve
size raised to 0.45, (di)0.45. The vertical axis represents the percent passing calculated
using Equation 5.16. The values on the x-axis are then deleted and the text box feature is
used to label the x-axis with the actual sieve values. In addition, the drawing tool is used to
add vertical lines between the axis and the data points. The following table is used to plot
the 0.45 gradation chart:
58
(di)0.45
Pi= 100(di/D) 0.45
5.11
100
4.26
95
2.75
81
2.02
56
1.37
44
0.68
26
0.31
0.8
5.21.
Sieve Size,
mm
Amount
Retained,
g
Cumulative
Amount
Retained, g
Cumulative
Percent
Retained
Percent
Passing
25
0.0
0.0
0.0
100
19
376.7
5.5
5.5
94
12.5
888.4
13.0
18.6
81
9.5
506.2
7.4
26.0
74
4.75
1038.4
15.3
41.3
59
2.36
900.1
13.2
54.5
46
1.18
891.5
13.1
67.6
32
0.6
712.6
10.5
78.0
22
0.3
625.2
9.2
87.2
13
0.15
581.5
8.5
95.8
4
0.075
242.9
3.6
99.3
0.7
Pan
44.9
0.7
100.0
0.0
Total
6808.4
59
Semi-log gradation chart










   
Sieve Size, mm
Percent Passing, %
b. 0.45 gradation chart










Sieve Size, mm
Percent Passing, %











The Maximum Size = 25 mm
The Nominal Maximum Size = 19 mm
5.22.
Sieve
Sieve size
(in.)
Amount
Retained (lb)
Percent
Retained
Cumulative
Percent
Retained
Percent
Passing
3 in.
3
0.0
0.0
0.0
100
2 in.
2
0.0
0.0
0.0
100
1-1/2 in.
1.5
3.7
4.4
4.4
96
1 in.
1
15.9
19.1
23.6
76
3/4 in.
0.75
12.0
14.4
38.0
62
1/2 in.
0.5
13.5
16.2
54.2
46
3/8 in.
0.375
26.7
32.1
86.3
14
No. 4
0.187
10.1
12.1
98.4
1.6
Pan
1.3
1.6
100.0
0.0
Total
83.2
d. Semi-log gradation chart

61
e. 0.45 power gradation chart.




5.23. See Figure 5.15.
5.24.The maximum size is 25 mm.
5.25.
Gradation
A
B
C
Mx. Size (mm)
12.5
19.0
19.0
Nominal Max. Size (mm)
9.5
12.5
12.5
Classification
Open
Dense
Gap
Percent Passing
Size, mm
25
19
12.5
9.5
4.75
1.18
0.60
0.30
0.15
Agg. A
100
100
100
77
70
42
34
28
20
Agg. B
100
85
62
43
24
13
7
0
0
Agg. C
100
100
84
51
29
19
8
14
9
Blend
100
96
81
53
34
21
12
13
8
The grain size distribution of the blend is shown below


63
5.27.
The maximum size of aggregate A is
25.0 mm.
The maximum size of aggregate B is
19.0 mm.
Sieve Size,
mm
% Passing
Aggr. A
% Passing
Aggr. B
(di)0.45
P
Ai= (di
/D)0.45
P
Bi
= (di/D)0.45
25
100
100
4.257
100
19
92
100
3.762
88
100
12.50
76
92
3.116
73
83
9.50
71
65
2.754
65
73
4.75
53
37
2.016
47
54
2.36
38
31
1.472
35
39
1.18
32
30
1.077
25
29
0.600
17
29
0.795
19
21
0.300
10
28
0.582
14
15
0.150
5
21
0.426
10
11
0.075
3.0
15.4
0.312
7
8
0.45 Gradation chart for aggregate A:
64
0.45 Gradation chart for aggregate B:
The figure above shows that the gradation curve of aggregate B is deviated from the
straight line (maximum density line). Therefore, aggregate B is not well graded.
5.28. Pi= 0.35 Ai+ 0.40 Bi+ 0.25 Ci(Equation 5.17)
Sieve Size (mm)
% Passing
Agg. A
% Passing
Agg. B
% Passing
Agg. C
% Passing
Blended Agg.
9.5
85
50
40
60
4.75
70
35
30
46
0.6
35
20
5
22
0.3
25
13
1
14
0.15
17
7
0
9
65
5.29. Using Equation 5.17, Pi = a Ai+ b Bi , the following table can be developed by trial and
error:
Size
(mm)
19
12.5
9.5
4.75
2.36
0.60
0.30
0.15
0.075
Specs.
100
80-100
70-90
50-70
35-50
18-29
13-23
8-16
4-10
Target
Gradation
100
90
80
60
42.5
23.5
18
12
7
Agg. A
100
85
55
20
2
0
0
0
0
Agg. B
100
100
100
85
67
45
32
19
11
50/50
100
93
78
53
35
23
16
10
6
45/55
100
93
80
56
38
25
18
10
6
40/60
100
94
82
59
41
27
19
11
7
The best combination is obtained by blending 40 % of material A and 60 % of material B.
1
66
5.31. Using Equation 5.17, Pi = a Ai+ b Bi , the following table can be developed by trial and
error:
Size
(mm)
19
12.5
9.5
4.75
2.36
0.60
0.30
0.15
0.075
Specs.
100
80–100
70–90
50–70
35–50
18–29
13–23
8–16
4–10
Target
Gradation
100
90
80
60
42.5
23.5
18
12
7
Agg. A
100
100
100
79
66
41
38
21
12
Agg. B
100
92
54
24
3
1
0
0
0
50/50
100
96
77
52
35
21
19
11
6
45/55
100
96
75
49
31
19
17
9
5
40/60
100
96
79
54
38
23
21
12
7
The best combination is obtained by blending 55 % of material A and 45 % of material B.










   
Sieve Size, mm
Percent Passing, %
/6/
86/
$JJ$
$JJ%
%OHQG
5.32.
Input data
output data
ABCD
20% 15% 25% 40%
Sieve Size
(mm)
Sieve Size
^0.45 (mm)
37.5 5.11
100 100 100 100
100
25 4.26
100 100 100 100
100
19 3.76
95 100 100 100
99
12.5 3.12
89 100 100 100
98
9.5 2.75
50 85 100 100
88
4.75 2.02
10 55 100 100
75
2.36 1.47
2158898
64
1.18 1.08
2 5 55 45
33
0.6 0.79
2 3 35 34
23
0.3 0.58
2 2 22 25
16
0.15 0.43
2 2 15 14
10
0.075 0.31
2165
4.1
Aggregate
Blend
Percent Passing
Blend Percent










3HUFHQW3DVVLQJ
6LHYH6]HPP





















3HUFHQW3DVVLQJ

68
5.36. The sieves used to calculate the fineness modulus are 19, 12.5, 9.5, 4.75, 2.36, 1.18, 0.6,
Sieve, mm
Percent
Passing
Cumulative Percent
Retained
25
100
0
19
92
8
12.50
76
24
9.50
71
29
4.75
53
47
2.36
38
62
1.18
32
68
0.600
17
83
0.300
10
90
0.150
5
95
Total
506
Fineness modulus = 506 / 100 = 5.06
No, it is not within the typical range (2.3 –3.1) indicating it is coarse aggregate.
5.37. The sieves used to calculate the fineness modulus are 9.5, 4.75, 2.36, 1.18, 0.6, 0.3, and
Sieve, mm
Percent
Passing
Cumulative Percent
Retained
9.5
100
0
4.75
85
15
2.36
67
33
1.18
56
44
0.6
45
55
0.3
32
68
0.15
19
81
Total
296
Fineness modulus = 296 / 100 = 2.96
It is within the typical range of 2.3 –3.1.
69
5.38.
Sieve, mm
% Passing
for Sand
% Passing
for Gravel
40% Passing
for Sand
60% Passing
for Gravel
% Passing
for Blend
50
100
100
40
60
100
37.5
100
97.5
40
58.5
99
19
100
52.5
40
31.5
72
9.5
100
20
40
12
52
4.75
97.5
2.5
39
1.5
41
2.36
90
0
36
0
36
1.18
67.5
0
27
0
27
0.6
42.5
0
17
0
17
0.3
20
0
8
0
8
0.15
6
0
2.4
0
2
0.45 gradation chart
5.39. See Table 5.3
70
5.40. Since sand is not considered in coarse aggregate angularity, use Equation 5.18b,
)(
)(
2211
222111
nn
nnn
pPpPpP
pPxpPxpPx
)90)(25()90)(55(
)
90
)(
25
)(
87
()
90
)(
55
)(
100
(
From Equation 5.19,
614.2
20.0
711.2
25.0
631.2
55.0
1
From Equation 5.19,
712.2
20.0
765.2
25.0
732.2
55.0
1
5.41. Since sand is not considered in coarse aggregate angularity, use Equation 5.18b,
)(
)(
2211
222111
nn
nnn
pPpPpP
pPxpPxpPx
)90)(60()90)(25(
)
90
)(
60
)(
95
()
90
)(
25
)(
73
(
From Equation 5.19,
552.2
15.0
390.2
60.0
774.2
25.0
1
From Equation 5.19,
1
609.2
20.0
331.2
30.0
702.2
50.0
5.43. See Section 5.5.10.