STUDENT EXERCISE #2
Use the α-Method described in Section 9.7.1.2a and the Nordlund Method
described in Section 9.7.1.1c to calculate the ultimate pile capacity and
the allowable design load for a 12.75 inch O.D. closed end pipe pile driven
into the soil profile described below. The trial pile length for the calculation
is 63 feet below the bottom of pile cap excavation which extends 3 feet
below grade. The pipe pile has a pile-soil surface area of 3.38 ft2/ft and a
pile toe area of 0.89 ft2. Use Figure 9.18 to calculate the shaft resistance
in the clay layer. The pile volume is 0.89 ft3/ft. The effective overburden
at 56 feet, the midpoint of the pile shaft in the sand layer is 3.73 ksf, and
the effective overburden pressure at the pile toe is 4.31 ksf. Remember,
the soil strengths provided are unconfined compression test results (cu =
qu / 2).
Soil Profile
3 ft
Silty Clay
 = 127 lbs / ft3
46 ft
qu = 5.46 ksf
Set-up Factor = 1.75
Dense, Silty F-M Sand
20 ft
 = 120 lbs / ft3
 = 35˚
Set-up Factor = 1.0
Calculate the Shaft Resistance in the Clay
Layer Using α-Method
STEP 1 Delineate the soil profile and determine the pile
adhesion from Figure 9.18.
Layer 1: qu = 5.46 ksf so cu =
D/b =
2.73 ksf
43 ft / 12.75 in = 40.5
Therefore ca from Figure 9.18 = 1.47 ksf
ca = 1.47 ksf
cu = 2.73 ksf
Concrete, Timber, Corrugated Steel Piles
Smooth Steel Piles
9-45
D = distance from ground surface to bottom of
clay layer or pile toe, whichever is less
b = Pile Diameter
Figure 9.18
Calculate the Shaft Resistance in the Clay
Layer Using α-Method
STEP 2 Compute the unit shaft resistance, fs, for each
soil layer.
fs = ca = 1.47 ksf
STEP 3 Compute the shaft resistance in the clay layer.
Layer 1: Rs1 = ( fs1 )( As )( D1) =
Rs1 = (1.47 ksf)(3.38 ft2/ft)(43 ft)
= 213.6 kips
Calculate the Shaft Resistance in the Sand
Layer Using the Nordlund Method
STEP 1 The po diagram, soil layer determination, and the soil
friction angle, N, for each soil layer were presented in the
problem introduction.
STEP 2 Determine *.
a.
Compute volume of soil displaced per unit length of pile, V.
V = 0.89 ft3/ft (per problem description)
b. Determine */N from Figure 9.10.
V = 0.89 ft3/ft 6 */N =
or * =
N
Relationship Between Soil Displacement, V, and /
V = 0.89
/ = 0.62
a – closed-end pipe and non-tapered Monotube piles
b – timber piles
c – pre-cast concrete piles
d – Raymond Step-Taper piles
e – Raymond uniform piles
f – H-piles
g – tapered portion of Monotube piles
Calculate the Shaft Resistance in the Sand
Layer Using the Nordlund Method
STEP 1 The po diagram, soil layer determination, and the soil
friction angle, , for each soil layer were presented in the
problem introduction.
STEP 2 Determine *.
a.
Compute volume of soil displaced per unit length of pile, V.
V = 0.89 ft3/ft (per problem description)
b. Determine */N from Figure 9.10.
V = 0.89 ft3/ft
6 */N =0.62
or *0.62
=
N 0.62
= (35˚) = 21.7˚
Calculate the Shaft Resistance in the Sand
Layer Using the Nordlund Method
STEP 3 Determine K* for each soil layer based on displaced volume, V,
and pile taper angle, .
Layer 2: For  = 35˚, V = 0.89 ft3/ft and  = 0˚
From Figure 9.13:
Using log linear interpolation
K = 1.15 for V = 0.10 ft3/ft
K = 1.75 for V = 1.00 ft3/ft
K = 1.72 for V = 0.89 ft3/ft
STEP 4 Determine correction factor, CF, to be applied to K when  ≠ .
(Figure 9.15.)
Layer 2:
 = 35˚ and / = 0.62 CF =
Correction Factor for K when   
CF = 0.78
 = 35˚
Figure 9.15
Calculate the Shaft Resistance in the Sand
Layer Using the Nordlund Method
STEP 3 Determine K* for each soil layer based on displaced volume, V,
and pile taper angle, .
Layer 2: For  = 35˚, V = 0.89 ft3/ft and  = 0˚
From Figure 9.13:
Using log linear interpolation
K = 1.15 for V = 0.10 ft3/ft
K = 1.75 for V = 1.00 ft3/ft
K = 1.72 for V = 0.89 ft3/ft
STEP 4 Determine correction factor, CF, to be applied to K when  ≠ .
Layer 2:
 = 35˚ and / = 0.62
CF = 0.78
Calculate the Shaft Resistance in the Sand
Layer Using the Nordlund Method
STEP 5 Compute effective overburden pressure at midpoint of each soil
layer, pd.
From problem description, pd for layer 2 is 3.73 ksf.
STEP 6 Compute the shaft resistance for each soil layer.
Rs2= K CF pd sin  Cd D
=
(1.72) (0.78) (3.73 ksf) (sin 21.7˚) (3.38 ft2/ft) (20 ft)
= 125.1 kips
Compute the Ultimate Shaft Resistance, Rs
Rs = Rs1 + Rs2
Rs = 213.6 kips + 125.1 kips
Rs = 338.7 kips
Compute the Ultimate Toe Resistance, Rt
STEP 7 Determine αt coefficient and bearing capacity factor
N'q from  angle of 35˚ at pile toe and Figures
9.16(a) and 9.16(b)
At pile toe depth
D/b =
From Figure 9.16(a)
αt =
From Figure 9.16(b)
N'q =
66 ft / 12.75 in. = 62
αt Coefficient versus 
1
0.67
t
D/b = 20
D/b = 30
D/b = 45
 = 35˚
0.1
15
Figure 9.16a
20
25
30
 (degrees)
35
40
45
65
Figure 9.16b
Compute the Ultimate Toe Resistance, Rt
STEP 7 Determine αt coefficient and bearing capacity factor
N'q from  angle of 35˚ at pile toe and Figures
9.16(a) and 9.16(b)
At pile toe depth
D/b = 62
From Figure 9.16(a) αt = 0.67
From Figure 9.16(b) N'q = 65
STEP 8 Compute effective overburden pressure at pile toe.
pt = 4.31 ksf. However, maximum of 3.0 ksf governs.
Compute the Ultimate Toe Resistance, Rt
STEP 9 Compute the ultimate toe resistance, Rt.
a. Rt =αt N'q At pt
= (0.67)(65)(0.89 ft2)(3.0 ksf) = 116.3 kips
b. Rt =qL At (qL determined from Figure 9.17)
c.
Use lesser value of Rt from Step 9a and 9b.
Therefore, Rt =
Limiting Unit Toe Resistance
105
Figure 9.17
Compute the Ultimate Toe Resistance, Rt
STEP 9 Compute the ultimate toe resistance, Rt.
a. Rt =αt N'q At pt
= (0.67)(65)(0.89 ft2)(3.0 ksf) = 116.3 kips
b. Rt =qL At (qL determined from Figure 9.17)
= (105 ksf)(0.89 ft2) = 93.5 kips
c.
Use lesser value of Rt from Step 9a and 9b.
Therefore, Rt = 93.5 kips
Compute the Ultimate Pile Capacity, Qu
STEP 10
Qu = Rs + Rt
= 338.7 + 93.5 kips = 432.2 kips