Question 31.4: This example concerns a single pile in a uniform sand layer,...
This example concerns a single pile in a uniform sand layer, for the case where there is groundwater present. A 0.5 m diameter, 10 m long round concrete pile is driven into a sandy soil stratum as shown in Fig. 31.8. The groundwater level is located 3 m below the surface. Compute the ultimate bearing capacity of the pile.
STEP 1: Compute the end bearing capacity.
Q_{ultimate} = (\sigma^{\prime}_t \times N_q \times A) + [K \times \sigma^{\prime}_v \times \tan \delta \times (\pi \times d) \times L]
End bearing term Skin friction term
end bearing term = \sigma^{\prime}_t \times N_q \times A
where
\sigma^{\prime}_t = effective stress at the tip of the pile
\sigma^{\prime}_t = 17.3 \times 3 + (17.3 – \gamma_w)\times 7
where
\gamma_w = density of water = 9.8 kN/m³
\sigma^{\prime}_t= 17.3 \times 3 + (17.3 – 9.8)\times 7 = 104.4 kN/m^2 (2,180 psf)
Find N_q using Table 31.1. For a friction angle of 30° N_q = 21 for driven piles.
end bearing capacity = \sigma^{\prime}_t \times N_q \times A \\ = 104.4 \times 21 \times (\pi \times 0.5^2/4) \\ =403.5 kN(96.8 kip)
STEP 2: Compute the skin friction (A to B).
The computation of skin friction has to be done in two parts. First find the skin friction from A to B and then find the skin friction from B to C.
skin friction term = K \times \sigma^{\prime}_v \times \tan \delta \times (\pi \times d) \times L
Obtain the K value. From Table 31.4, for driven round piles, the K value lies between 1.0 and 1.5. Hence, assume that K = 1.25.
Obtain the \sigma^{\prime}_v (effective stress at the perimeter of the pile). The effective stress along the perimeter of the pile varies with the depth. Hence, obtain the \sigma^{\prime}_P value at the midpoint of the pile from point A to B. The length of the pile section from A to B is 3 m. Hence, find the effective stress at 1.5 m below the ground surface.
Obtain the skin friction angle, δ. From Table 31.3, the skin friction angle for steel piles is 20°.
skin friction = K \times \sigma^{\prime}_v \times \tan \delta \times (\pi \times d) \times L
where
\sigma^{\prime}_v = effective stress at midpoint of section A to B (1.5 m below the surface)
\sigma^{\prime}_v = 1.5 \times 17.3 = 25.9 kN/m^2(0.54 ksf)
And since
K = 1.25
δ = 20°
The skin friction (A to B) can be calculated as
skin friction (A to B) = 1.25 × (25.9) × (tan 20°) × (π × 0.5) × 3
= 55.5 kN (12.5 kip)
Find the skin friction of the pile from B to C.
skin friction = K \times \sigma^{\prime}_v \times \tan \delta \times (\pi \times d) \times L
\sigma^{\prime}_v = effective stress at midpoint of section B to C
= 3 × 17.3 + (17.3 – 9.8) × 3.5
= 78.2 kN/m² (1,633 psf)
Since
K = 1.25
δ = 20°
The skin friction (B to C) can be calculated as
skin friction (B to C) = 1.25 × (78.2) × tan(20° ) × (π × 0.5) × 7
= 391 kN (87.9 kip)
STEP 3: Compute the ultimate bearing capacity of the pile.
Q_{ultimate} = ultimate bearing capacity of the pile
Q_{ultimate} = end bearing capacity + skin friction
Q_{ultimate} = 403.5 + 55.5 + 391 = 850 kN
Assume a factor of safety of 3.0. Hence, the allowable bearing capacity of the pile can be calculated as
Q_{ultimate}/F.O.S. = 850.1/3.0 = 283 kN
allowable pile capacity = 283 kN (63.6 kip)
Note that 1 kN is equal to 0.225 kip.
Table 31.1
Friction angle vs. N_q
| φ | 26 | 28 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |
| N_q (for driven piles) | 10 | 15 | 21 | 24 | 29 | 35 | 42 | 50 | 62 | 77 | 86 | 12 | 145 |
| N_q (for bored piles) | 5 | 8 | 10 | 12 | 14 | 17 | 21 | 25 | 30 | 38 | 43 | 60 | 72 |
Source: NAVFAC DM 7.2 (1984).
Table 31.3
Pile type and pile skin friction angle
| Pile type | δ |
| Steel piles | 20° |
| Timber piles | 3/4 φ |
| Concrete piles | 3/4 φ |
Source: NAVFAC DM 7.2 (1984).
Table 31.4
Pile type and lateral earth pressure coefficient
| Pile type | K (piles under compression) | K (piles under tension, uplift piles) |
| Driven H-piles | 0.5-1.0 | 0.3-0.5 |
| Driven displacement piles (round and square) | 1.0-1.5 | 0.6-1.0 |
| Driven displacement tapered piles | 1.5-2.0 | 1.0-1.3 |
| Driven jetted piles | 0.4-0.9 | 0.3-0.6 |
| Bored piles (less than 24 in. diameter) | 0.7 | 0.4 |
Source: NAVFAC DM 7.2 (1984).