I need detailed explanation to solve the exercise below. There are some formulas and hints, I also added some tables from the book.
Meyerhof's method, Coyle and Castello's method and Vesic's method were already solved.
$A 20 m long concrete pile with a rectangular cross section of 460 mm × 460 mm fully embedded in sand is shown in Figure P 12.2. Estimate the ultimate point load or tip resistance Qp by each of the following 4 methods and discuss. Necessary variables and formulae: Area of the pile tip Effective vertical stress at the level of the pile tip Atmospheric pressure 100 kN/m² Ap q' Pa o'o Irr Ir A Ms Mean effective normal ground stress at the level of the pile point Reduced rigidity index for the soil Rigidity index for the soil Average volumetric strain in the plastic zone below the pile point Poisson's ratio of soil 1) Terzaghi's method (Use Ng = 2) Meyerhof's method (Use Table 12.6 for interpolation of Na) Sand: Qp = min (q', 0.5påtanp') · No Ap 3) Vesic's method (Use Table 12.8 for interpolation of N and modulus of elasticity of soil of Es = 600pa) Sand: Qp = ¯'。No Ap where ' = 0 exp[(37-4¹) tand 2 1-sin o' 1+2Ko 3 q', K. = 1 - sino', Irr = 20 m Ir 1+1,Δ FIGURE P 12.2 9 Ir = For 25° ≤ ø' ≤ 45°, µs = 0.1 +0.3 (25¹), A = 0.005 (1 – $¹_25") '-25° q' { 20° 20° Pa Es 2(1+μ₂)q'tand' 4) Coyle and Castello's method (Use Figure 12.20 for extrapolation of Na) Sand: Qp = q'N Ap Concrete pile 460 mm X 460 mm Loose sand φί = 30° y = 18.6 kN/m³ Dense sand $'2 = 42° y = 18.5 kN/m³$
Transcribed Image Text:A 20 m long concrete pile with a rectangular cross section of 460 mm × 460 mm fully embedded in sand is shown in Figure P 12.2. Estimate the ultimate point load or tip resistance Qp by each of the following 4 methods and discuss. Necessary variables and formulae: Area of the pile tip Effective vertical stress at the level of the pile tip Atmospheric pressure 100 kN/m² Ap q' Pa o'o Irr Ir A Ms Mean effective normal ground stress at the level of the pile point Reduced rigidity index for the soil Rigidity index for the soil Average volumetric strain in the plastic zone below the pile point Poisson's ratio of soil 1) Terzaghi's method (Use Ng = 2) Meyerhof's method (Use Table 12.6 for interpolation of Na) Sand: Qp = min (q', 0.5påtanp') · No Ap 3) Vesic's method (Use Table 12.8 for interpolation of N and modulus of elasticity of soil of Es = 600pa) Sand: Qp = ¯'。No Ap where ' = 0 exp[(37-4¹) tand 2 1-sin o' 1+2Ko 3 q', K. = 1 - sino', Irr = 20 m Ir 1+1,Δ FIGURE P 12.2 9 Ir = For 25° ≤ ø' ≤ 45°, µs = 0.1 +0.3 (25¹), A = 0.005 (1 – $¹_25") '-25° q' { 20° 20° Pa Es 2(1+μ₂)q'tand' 4) Coyle and Castello's method (Use Figure 12.20 for extrapolation of Na) Sand: Qp = q'N Ap Concrete pile 460 mm X 460 mm Loose sand φί = 30° y = 18.6 kN/m³ Dense sand $'2 = 42° y = 18.5 kN/m³
Transcribed Image Text:TABLE 12.6 Interpolated Values of Ng Based on Meyerhof's Theory 25 26 27 28 29 Soil friction angle, ø' (deg) 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 10 39 40 41 42 43 20 44 45 TABLE 12.8 Bearing Capacity Factors N. Based on the Theory of Expansion of Cavities 15.95 17.47 19.12 20.91 22.85 24.95 27.22 29.68 32.34 35.21 38.32 41.68 45.31 49.24 53.50 58.10 63.07 68.46 74.30 80.62 87.48 N₂ 12.4 13.8 15.5 17.9 21.4 26.0 29.5 34.0 39.7 46.5 56.7 68.2 81.0 96.0 40 115.0 143.0 168.0 194.0 231.0 60 276.0 346.0 420.0 525.0 650.0 780.0 930.0 Embedment ratio, L/D 0 ITT 10 20 30 40 50 60 70 10 T T T Bearing capacity factor, N* 9 20 40 60 80 100 $' = 30° 80 300 400 12.12 20.98 24.64 27.61 39.70 46.61 52.24 13.18 23.15 27.30 30.69 44.53 52.51 59.02 14.33 25.52 30.21 34.06 49.88 59.05 66.56 15.57 28.10 33.40 37.75 55.77 66.29 74.93 16.90 30.90 36.87 41.79 62.27 74.30 84.21 30 18.24 33.95 40.66 46.21 69.43 83.14 94.48 31 19.88 37.27 44.79 51.03 77.31 92.90 105.84 32 21.55 40.88 49.30 56.30 85.96 103.66 118.39 33 23.34 44.80 54.20 62.05 95.46 115.51 132.24 34 25.28 49.05 59.54 68.33 105.90 128.55 147.51 35 27.36 53.67 65.36 75.17 117.33 142.89 164.33 36 29.60 58.68 71.69 82.62 129.87 158.65 182.85 37 32.02 64.13 78.57 90.75 143.61 175.95 203.23 38 34.63 70.03 86.05 99.60 158.65 194.94 225.62 39 37.44 76.45 94.20 109.24 175.11 215.78 250.23 40 40.47 83.40 103.05 119.74 193.13 238.62 277.26 41 43.74 90.96 112.68 131.18 212.84 263.67 306.94 42 47.27 99.16 123.16 143.64 234.40 291.13 339.52 43 51.08 108.08 134.56 157.21 257.99 321.22 375.28 44 55.20 117.76 146.97 172.00 283.80 354.20 414.51 45 59.66 128.28 160.48 188.12 312.03 390.35 457.57 Based on data from "Design of Pile Foundations," by A. S. Vesic. Synthesis of Highway Practice by American Association of State Highway and Transportation, 1977 32° 36° 100 30.16 33.60 37.37 41.51 46.05 51.02 56.46 62.41 68.92 76.02 83.78 92.24 101.48 111.56 122.54 134.52 147.59 161.83 177.36 194.31 212.79 34° FIGURE 12.20 Variation of N with L/D (Based on Coyle and Castello, 1981) 38° 40° 200 200 500 57.06 64.62 73.04 82.40 92.80 104.33 117.11 131.24 146.87 164.12 183.16 204.14 227.26 252.71 280.71 311.50 345.34 382.53 423.39 468.28 517.58

Question

I need detailed explanation to solve the exercise below. There are some formulas and hints, I also added some tables from the book.
Meyerhof's method, Coyle and Castello's method and Vesic's method were already solved.

A 20 m long concrete pile with a rectangular cross section of 460 mm × 460 mm fully embedded in sand is shown in
Figure P 12.2. Estimate the ultimate point load or tip resistance Qp by each of the following 4 methods and discuss.
Necessary variables and formulae:
Area of the pile tip
Effective vertical stress at the level of the pile tip
Atmospheric pressure 100 kN/m²
Ap
q'
Pa
o'o
Irr
Ir
A
Ms
Mean effective normal ground stress at the level of the pile point
Reduced rigidity index for the soil
Rigidity index for the soil
Average volumetric strain in the plastic zone below the pile point
Poisson's ratio of soil
1) Terzaghi's method (Use Ng
=
2) Meyerhof's method (Use Table 12.6 for interpolation of Na)
Sand: Qp = min (q', 0.5påtanp') · No Ap
3) Vesic's method (Use Table 12.8 for interpolation of N and modulus of elasticity of soil of Es = 600pa)
Sand: Qp = ¯'。No Ap
where ' =
0
exp[(37-4¹) tand
2
1-sin o'
1+2Ko
3
q', K. = 1 - sino', Irr
=
20 m
Ir
1+1,Δ
FIGURE P 12.2
9
Ir
=
For 25° ≤ ø' ≤ 45°, µs = 0.1 +0.3 (25¹), A = 0.005 (1 – $¹_25")
'-25°
q'
{
20°
20° Pa
Es
2(1+μ₂)q'tand'
4) Coyle and Castello's method (Use Figure 12.20 for extrapolation of Na)
Sand: Qp = q'N Ap
Concrete pile
460 mm X 460 mm
Loose sand
φί = 30°
y = 18.6 kN/m³
Dense sand
$'2 = 42°
y = 18.5 kN/m³

TABLE 12.6 Interpolated Values of Ng Based on
Meyerhof's Theory
25
26
27
28
29
Soil friction angle, ø' (deg)
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
10
39
40
41
42
43
20
44
45
TABLE 12.8 Bearing Capacity Factors N. Based on the Theory of Expansion of Cavities
15.95
17.47
19.12
20.91
22.85
24.95
27.22
29.68
32.34
35.21
38.32
41.68
45.31
49.24
53.50
58.10
63.07
68.46
74.30
80.62
87.48
N₂
12.4
13.8
15.5
17.9
21.4
26.0
29.5
34.0
39.7
46.5
56.7
68.2
81.0
96.0
40
115.0
143.0
168.0
194.0
231.0
60
276.0
346.0
420.0
525.0
650.0
780.0
930.0
Embedment ratio, L/D
0
ITT
10
20
30
40
50
60
70
10
T
T
T
Bearing capacity factor, N*
9
20
40 60 80 100
$' = 30°
80
300
400
12.12
20.98
24.64
27.61
39.70
46.61
52.24
13.18
23.15
27.30
30.69
44.53
52.51
59.02
14.33
25.52
30.21
34.06
49.88
59.05
66.56
15.57
28.10
33.40
37.75
55.77
66.29
74.93
16.90
30.90
36.87
41.79
62.27
74.30
84.21
30
18.24
33.95
40.66
46.21
69.43
83.14
94.48
31
19.88
37.27
44.79
51.03
77.31
92.90
105.84
32
21.55
40.88
49.30
56.30
85.96
103.66
118.39
33
23.34
44.80
54.20
62.05
95.46
115.51
132.24
34
25.28
49.05
59.54
68.33
105.90
128.55
147.51
35
27.36
53.67
65.36
75.17
117.33
142.89
164.33
36
29.60
58.68
71.69
82.62
129.87
158.65
182.85
37
32.02
64.13
78.57
90.75
143.61
175.95
203.23
38
34.63
70.03
86.05
99.60
158.65
194.94
225.62
39
37.44
76.45
94.20
109.24
175.11
215.78
250.23
40
40.47
83.40
103.05
119.74
193.13
238.62
277.26
41
43.74
90.96
112.68
131.18
212.84
263.67
306.94
42
47.27
99.16
123.16
143.64
234.40
291.13
339.52
43
51.08
108.08
134.56
157.21
257.99
321.22
375.28
44
55.20
117.76
146.97
172.00
283.80
354.20
414.51
45
59.66
128.28
160.48
188.12
312.03
390.35
457.57
Based on data from "Design of Pile Foundations," by A. S. Vesic. Synthesis of Highway Practice by American Association of State Highway and Transportation, 1977
32° 36°
100
30.16
33.60
37.37
41.51
46.05
51.02
56.46
62.41
68.92
76.02
83.78
92.24
101.48
111.56
122.54
134.52
147.59
161.83
177.36
194.31
212.79
34°
FIGURE 12.20 Variation of N with L/D
(Based on Coyle and Castello, 1981)
38°
40°
200
200
500
57.06
64.62
73.04
82.40
92.80
104.33
117.11
131.24
146.87
164.12
183.16
204.14
227.26
252.71
280.71
311.50
345.34
382.53
423.39
468.28
517.58

Accepted Answer

L = 20 m B = 460mm