2. Example 1:
A 400 mm square prestressed concrete pile is to be
driven 19 m into the soil profile shown in the figure.
a) Compute the net load transferred to the ground
through toe bearing
b) Compute the nominal side friction capacity
c) Compute the ASD downward load capacity using a
factor of safety of 2.8.
6. Example 2:
A straight drilled shaft of diameter 1 m is
installed in a soil profile, as shown in the figure.
SPT were performed at intervals of
approximately 1 m below the base. Determine
the toe bearing capacity.
7. Solution 2:
Use average N60 value over a depth of 2D from the base or tip.
OâNeill and Reese (1999)
8. Example 3:
The drilled shaft shown is to be designed
without the benefit of any on-site static load
tests. The soil conditions are uniform and the
site characterization program was average.
Unit weights of soil layers above the water
table are 17kN/m3 and below are 20kN/m3.
Compute the allowable downward load
capacity.
11. Example 4:
A concrete pile 40 cm in diameter and 10 m long is driven into a homogenous mass of clayey soil of medium
consistency. The water table is at the ground surface.The undrained shear strength is 80 kPa and the
adhesion factor α = 0.75. Compute the ultimate load bearing capacity.
Solution 4:
12. Example 5:
It is designed that the steel pile having a
diameter 40cm given in the figure below has
to have an allowable bearing capacity which
should be maximum 490 kN. Calculate the
length of the pile by considering the factor of
safety as 3.
Solution 5:
ðð¢ðð¡ = ðð + ðð
ðð = 9 â ðð¢ â ðŽð = 9 â 125 â
0.42 â ð
4
= 141.4 ðð
ðð = à· ðð¢ â ðŒ â ð â âð
According to Randolph and Murphy (1985),
ðâ²ð§ð· 1 = 3 â 17 = 51ððð â
ðð¢
ðâ²
ð§ð· 1
=
50
51
â 1 â ðŒ1 â 0.5 (ððð¢ð)
ðâ²ð§ð· 2 = 6 â 17 + 2 â 19 â 9.8 = 120.4ððð â
ðð¢
ðâ²
ð§ð· 2
=
50
120.4
â 0.41 â ðŒ2 â 0.78 (ððð)
14. Example 6:
The load-settlement data shown in the figure were
obtained from a full-scale static load test on a 400mm
square, 17m long concrete pile (fÂŽc=40MPa). Use
Davissonâs method to compute the ultimate
downward load capacity.
17. Example 7:
Given that n1 = 4, n2 = 3, D = 305 mm, d = 1220 mm,
and L = 15 m. The piles are square in cross section
and embedded in a homogenous clay with ɣ = 15.5
kN/m3 and cu = 70 kN/m2. Using a factor of safety
equal to 4, determine the allowable load bearing
capacity of the group pile.
21. Example 8:
A group pile in clay is shown in the figure on
the right. Determine the consolidation
settlement of the pile groups.
Assume that all the clay layers are normally
consolidated.
30. Deep Foundations-Pile Axial Load Capacity
-Shaft resistance (Undrained condition, clayey soil, non-free draining)
ï¶ Î±-method (ðððð£ðð ððððð )
ðð = α(ðð¢)ðŽð
As= shaft area of the of the pile
α= adhesion factor and f(slenderness, shear strength)
ð¹ðð
ðð¢
Ïâ²ð£0
†1; α = 0.5Fp
ðð¢
Ïâ²ð£0
â0.5
†1
ð¹ðð
ðð¢
Ïâ²ð£0
⥠1; α = 0.5Fp
ðð¢
Ïâ²ð£0
â0.25
Fp = 1.0 if
ð¿ð
ðµ
†50
= 0.7if
ð¿ð
ðµ
⥠120
31. Deep Foundations-Pile Axial Load Capacity
-Shaft resistance (Undrained condition, clayey soil, non-free draining)
ï¶ Î±-method (ððððð ððððð )
ðð = α(ðð¢)ðŽð
As= shaft area of the of the pile
α= adhesion factor and f(shear strength)
α = 1.0 ððð ð𢠆30
α = 1. 16 â
ðð¢
185
ððð 30 < ð𢠆150
α = 0.35 ððð ðð¢ > 150
32. Deep Foundations-Pile Axial Load Capacity
-Shaft resistance (Drained condition, granular soil, free draining)
ðð = ðŸð Ïâ²ð£0 tan ÎŽâ² ðŽð (ððððð ððð ðððð£ðð ððððð )
As= shaft area of the of the pile
Ks= coefficient of horizontal soil stress
ÎŽ'= the angle of friction b/w pile and soil
ÎŽâ² = Ï = 0.75Ïâ²
ðŸ0 = 1 â ð ððÏâ²
33. Deep Foundations-Pile Axial Load Capacity
-Shaft resistance (Drained condition, granular soil, free draining)
ðð = βÏâ²ð£0ðŽð
β=0.18+0.65Dr
Dr=relative density in decimal form
ï¶ Î²-method (ðððð£ðð ððððð )
ðð = βÏâ²ð£0ðŽð
β=1.5-0.245 ð§
z= depth to the mid-layer (m)
ï¶ Î²-method (ððððð ððððð )
34. Ex1: A bridge pier is to be supported by 1.0 ð diameter driven-cast in place concrete
piles. The design load per pile is determined as 700 ðð by the structural engineer.
Calculate the total pile length using a factor of safety of 3.0 against failure.
Deep Foundations- Single Pile Capacity
6 m Sand γ=17 kN/m3 Ï'=36Ë
Clay γ=20 kN/m3 cu=100 kPa
Ïð£0 (ððð) ð¢ (ððð) Ïâ²ð£0 (ððð)
51
102
102 + 20âððððŠ 10âððððŠ
51
102
102 + 10âððððŠ
35. Ex1: A bridge pier is to be supported by 1.0 ð diameter driven-cast in place concrete
piles. The design load per pile is determined as 700 ðð by the structural engineer.
Calculate the total pile length using a factor of safety of 3.0 against failure.
Deep Foundations- Single Pile Capacity
6 m Sand γ=17 kN/m3 Ï'=36Ë
Clay γ=20 kN/m3 cu=100 kPa
â¢
ð¿ð
ðµ
⥠12, ð¡âð¢ð ð¿ð,ððð ⥠12 ð
ð»ðððð ðððððððð ðð¢ðð¡ = âðð + ðð
⢠ð¹ðð ð ððð ðððŠðð
ðð = ðŸð Ïâ²ð£0 tan ÎŽâ² ðŽð
ðŸð = 0.41 1.5 = 0.62 ÎŽâ² = Ï = 0.75 Ïâ² = 27Ë
ðŸ0 = 1 â ð ððÏâ² = 0.41
38. Ex2: A bridge pier is to be supported by bored-cast in place concrete piles (C30). The
design load per pile is determined as 2000 ðð by the structural engineer. Calculate the
total pile length using a factor of safety of 3.0 against failure.
Deep Foundations- Single Pile Capacity
6 m Sand γ=17 kN/m3 Ï'=28Ë
Clay γ=18 kN/m3 cu=30 kPa
Ïð£0 (ððð) ð¢ (ððð) Ïâ²ð£0 (ððð)
51
102
210 60
Sand γ=19 kN/m3 Ï' =38Ë
Clay γ=18 kN/m3 cu=150 kPa
6 m
6 m
120
324
51
102
150
204
39. Ex2: A bridge pier is to be supported by bored-cast in place concrete piles (C30). The
design load per pile is determined as 2000 ðð by the structural engineer. Calculate the
total pile length using a factor of safety of 3.0 against failure.
Deep Foundations- Single Pile Capacity
6 m Sand γ=17 kN/m3 Ï'=28Ë
Clay γ=18 kN/m3 cu=30 kPa
Ïð£0 (ððð) ð¢ (ððð) Ïâ²ð£0 (ððð)
51
102
210 60
Sand γ=19 kN/m3 Ï' =38Ë
Clay γ=18 kN/m3 cu=150 kPa
6 m
6 m
120
324
51
102
150
204
⢠ðžð¶7 Ïðððð ðððð =
ððððð
ðŽð
â€
Ïð,ð
4
Ïðððð ðððð â€
30
4
= 7.5 ððð
ððððð
ðŽð
=
2000000
ðŽð
= 7.5 ðððð ðððððð¡ðð â ðµ = 600ðð
42. -Load vs settlement: Load controlled test, to obtain ultimate load
ï¶ Load increment= 25% of working load
ï¶ Ultimate load= 200% of working load
Deep Foundations- Pile Load Test (Davisson Approach)
1) Clayey soil
2) Granular soil
Total
settlement
Elastic
settlement
Net settlement=Total settlement- pile elastic settlement
ÎŽðððð ðððð ð¡ðð =
(ðð€ð+0.6ðð€ð )ð¿ð
ðŽððžðððð
ðð€ð = ð€ðððððð ðððð
ðð€ð = ð âððð¡ ððð ðð ð¡ððð ðððð @ð€ðððððð
43. -Load vs settlement
ï¶ Use net settlement values
Deep Foundations- Pile Axial Load Test
ÎŽð¢ðð¡ = 0.012 ðµððð + 0.1
ðµ
ðµððð
+
ðð¢ð¿ð
ðŽððžð
K M
K
M
Net settlement (mm)
ðð¢ðð¡ = ððð¡ðððð¡ð ðððð (ðð)
ðµ = ðððð ðððððð¡ðð (ðð)
ðµððð = ð ðððððððð ðððð ð€ððð¡â ðð
= 300 mm
ð¿ð = ðððð ððððð¡â (ðð)
ðŽð = ðžðð ððððððð ðððð ðð2
ðžð = ðððð ðððð ð¡ðð ðððð¢ðð¢ð (ðºðð)
ÎŽð¢ðð¡
ðð¢ðð¡
44. -Ex3: Lp= 20 m, BxB=406x406 mm, Ep=30 GPa (C30 concrete), Qult ?
Deep Foundations- Pile Axial Load Test
ÎŽð¢ðð¡ = 0.012 ðµððð + 0.1
ðµ
ðµððð
+
ðð¢ð¿ð
ðŽððžð
K=3.735
Net settlement (mm)
ÎŽð¢ðð¡ = 0.012 300 + 0.1
406
300
+
ðð¢20000
(406)(406)(30)
ðð¢ðð¡ = 1460 ðð
45. -Downdrag force acting on pile: force exerted by settling soil on pile (ÎŽsoil> ÎŽpile)
Deep Foundations- Negative Skin Friction
ï¶ Placement of fill (granular) settlement of the fill by selfweight
additional consolidation of soft clayey layers beneath fill
ï¶ Lowering of GWT Ï' and settlement increases
additional
settlement
for the pile
46. -Downdrag force acting on pile
Deep Foundations- Negative Skin Friction
⢠ðð = ð0 + ðð ððð ð€ðððâð¡ + ðððð€ððððð
ðððð€ððððð = 0.25 Ïâ²ð£(ÏðµðððððŠ ðððŠðð)
⢠For clay layer upon consolidation
⢠For sand layer upon settling
ðððð€ððððð = ðŸ0Ïâ²ð£ tan ÎŽâ² (Ïðµðð ððð)
ÎŽâ² = (0.6)Ïâ²
Resistance
Load
Force
P0
Qb
ð¹ð =
ðð + ðð
ð0 + ðð ððð ð€ðððâð¡ + ðððð€ððððð
⥠2.0
ðð + ðð
47. Ex2 (cont.): 2 m height of a very large fill (γ=20 kN/m3) will be placed next to the pile
on the behalf of approach fill. Check whether adequate FS exists or not?
Deep Foundations- Negative Skin Friction
6 m Sand γ=17 kN/m3 Ï'=28Ë
6 m
6 m
Clay γ=18 kN/m3 cu=30 kPa
Sand γ=19 kN/m3 Ï' =38Ë
Clay γ=18 kN/m3 cu=150 kPa
⢠ð¹ð =
ðð +ðð
ð0+ðð ððð ð€ðððâð¡+ðððð€ððððð
⥠2.0
ð¹ð =
6614.3
2000 + 80.6 + ðððð€ððððð
ðððð€ððððð = 0.25 Ïâ²ð£(Ïð·ðððððŠ ðððŠðð)
Ïâ²ð£0 =
102 + 150
2
+ (2)(20) = 166 ððð
Fill
ðððð€ððððð = 0.25 166 Ï 0.6 6 = 469 ðð
ð¹ð =
6614.3
2000 + 80.6 + 469
= 2.59
48. Piles working under tension:
Deep Foundations- Uplift Capacity
⢠ð¹ð =
ðð +ðð ððð ð€ðððâð¡
ðð¢ðð€ððð
⥠3.0~6.0
ï¶ Ship building docks ï¶ Wind turbines, chimneys or any structures
exposed to lateral loads
49. -Group action: zone of soil or rock which is stressed by the entire group extends to a
much greater width and depth than the zone beneath the single pile. Spacing (s) between
adjacent piles should be increased (>5B)
Deep Foundations- Piles in Group
ï¶ (# of piles) x Qult (single pile) > Qult (group) under same displacement
ï¶ Even though loading tests made on a single pile have indicated satisfactory performance, failure or
excessive settlement may take place
Friction pile
(clayey soil, adhesion)
End bearing pile
(granular soils)
50. -Group capacity:
Deep Foundations- Piles in Group
Group Efficiency Approach
Qult, group = (η) x (# of piles) x Qult (single pile)
η (efficiency)=1âÏ
[ ð â 1 ð + ð â 1 ð]
90(ð)(ð)
Ï in degrees = tanâ1
ðµ
ð
B
B
B
B B
ð = ðð ðð ððð€ð
ð = ðð ðð ðððð¢ððð
s = spacing b/w piles measured from center to center
51. -Group capacity:
Deep Foundations- Piles in Group
Terzaghi-Peck Block Approach
ï¶ shallow spread foundation
ï¶ Crucial for soil profiles consisting of soft clay layers (low cu values)
ï¶ ðð¢ðð¡ = âðð + ðð
ðð = 2 ð¿ððððð + ðµððððð âð·ðα(ðð¢) or ðð = 2 ð¿ððððð + ðµððððð âð·ððŸð Ïâ²ð£0 tan ÎŽâ²
clayey soil granular soil
ðð = (ð¿ððððððµððððð) ð ððððð¢ ðð = (ð¿ððððððµððððð) ððÏâ²ðð ð
clayey soil granular soil
ð· = ð¿ð
52. -Ex4: A group of bored-cast in place piles are constructed in a deep layer of clay. Find
Qult, group? B=0.6 m
Deep Foundations- Piles in Group
ðºððð¢ð ððððððððððŠ ðððððððâ
s=1.8 m
⢠ðð¢ðð¡,ð ððððð ðððð = ðð + ðð
Ïâ²ð£0 (ððð)
114
228
ðð = ðŽð ð ððððð¢ = Ï 0.3 2 9 60 = 152.7 ðð
ðð = α(ðð¢)ðŽð = 1.16 â
60
185
60 Ï 0.6 12 = 1134.2 ðð α = 1. 16 â
ðð¢
185
ððð 30 < ð𢠆150
Pile layout
s=1.8 m
53. -Ex4: A group of bored-cast in place piles are constructed in a deep layer of clay. Find
Qult, group? B=0.6 m
Deep Foundations- Piles in Group
Pile layout
s=1.8 m
⢠Qð¢ðð¡,ð ððððð ðððð = ðð + ðð = 152.7 + 1134.2 = 1286.9 ðð
⢠Qult, group = (η) x (# of piles) x Qult (single pile)
η (efficiency)=1âÏ
[ ð â 1 ð + ð â 1 ð]
90(ð)(ð)
Ï in degrees = tanâ1
ðµ
ð
= tanâ1
0.6
1.8
= 18.4Ë
η =1â18.4
[ 3 â 1 4 + 4 â 1 3]
90(4)(3)
= 0.71
ð = 3
ð = 4
⢠Qult, group = (0.71)(12)(1286.9)=10964.4 kN
s=1.8 m
54. -Ex4: A group of bored-cast in place piles are constructed in a deep layer of clay. Find
Qult, group? B=0.6 m
Deep Foundations- Piles in Group
Pile layout
s=1.8 m
s=1.8 m
TerzaghiâPeck Block ðððððððâ
ðð = 2 ð¿ððððð + ðµððððð α(ðð¢)
ï¶ ðð¢ðð¡,ððððð = ðð + ðð
ðð = 2[ 1.8 3 + 1.8 2 12 0.84 60 = 10886.4 kN
α = 1. 16 â
ðð¢
185
ððð 30 < ð𢠆150
ðð = ð¿ððððððµððððð ð ððððð¢ = ð¿ððððððµððððð 9ðð¢
ðð = 5.4 3.6 9 60 = 10497.6ðð
ï¶ ðð¢ðð¡,ððððð = ðð + ðð = 10886.4 + 10497.6 = 21384 ðð
ï¶ ðð¢ðð¡,ððððð = min ðºððð¢ð ððððððððððŠ ðððððððâ, ðððð§ððâð â ðððð ððððð ðððððððâ = 10694.4 ðð