Pile capacity in sand, group effect, load test

Bearing capacity of a pile in sand

The ultimate capacity is the sum of end bearing and shaft friction, $Q_u = Q_p + Q_s$.

Static formula

$$Q_p = A_p\,q'N_q^{*} \le A_p\,q_l,\qquad q_l = 50N_q^{*}\tan\phi\ (\text{kN/m}^2)$$ $$Q_s = \sum K\sigma'_v\tan\delta\,(\pi D)\,\Delta L$$

where $q'$ is the effective overburden pressure at the tip (limited to the critical depth, $15D$ to $20D$), $K$ the earth pressure coefficient (about 1 for loose, 2 for dense sand), $\delta \approx 0.75\phi$ the pile–soil friction angle, and $\sigma'_v$ the average effective stress over each layer. The allowable load is $Q_u/FS$ with $FS = 2.5$ to $3$.

SPT (Meyerhof) method: $Q_p = 40N\dfrac{L}{D}A_p \le 400NA_p$ and $f_s = 2\bar N$ (kN/m², driven piles), $Q_s = f_sA_s$.

Group effect

When piles are close together, the stress zones overlap, so the group behaves differently from the sum of single piles. The efficiency is $\eta = \dfrac{\text{capacity of group}}{n \times \text{capacity of one pile}}$.

  Single pile            Pile group (overlapping zones)
     |  |                 | | | | |
     |  |                 | | | | |
    /    \               /         \
   / small\             /  wide and \
  /  bulb  \           /  deep zone  \

• In loose sand a driven group compacts the soil, so $\eta \ge 1$ (taken as 1 for design); in dense sand or bored piles in sand, $\eta \le 1$.
• Group capacity: $Q_g = \eta\,nQ_{u}$, with $\eta$ found from the Converse–Labarre formula $\eta = 1 - \theta\dfrac{(n-1)m + (m-1)n}{90mn}$, where $\theta = \tan^{-1}(D/s)$, or taken as 1 for driven piles at $s \ge 2.5D$.
• Settlement of a group is larger than that of a single pile at the same load per pile, because a larger zone of soil is stressed.

Pile load test: application and limitations

Application: carried out by applying load in increments (usually through a hydraulic jack against a kentledge or anchor piles) and recording the settlement (IS 2911 Part 4).

• It gives the actual ultimate load (the load at which settlement reaches about 10% of the pile diameter, or the point of a break in the curve) and the safe load, i.e. the smaller of 50% of the load at 10% $D$ settlement or two-thirds of the load at 12 mm settlement.
• It checks the design assumptions, and verifies the quality of the installed pile.
• Used to determine the settlement under working load, lateral load capacity (horizontal test) and uplift capacity (pullout test).

Limitations:

• It is costly and time-consuming (the test takes days).
• It shows the behaviour of a single pile; a group has a different capacity (deeper stress zone), and group settlement is not found.
• Time effects (set-up, consolidation in clay) may not be reflected unless the test is carried out after a rest period.
• The test depends on the correctness of the test set-up; it covers only the test location.