Toe resistance

Along with the shaft resistance, the toe resistance $Q_p$ makes up a pile’s ultimate capacity, $Q_u = Q_s + Q_p$. Units, symbols and assumptions are set out in Method and assumptions.

$Q_p = q_p A_p$, with $q_p$ from the stratum the toe rests on; a toe exactly on a boundary rests on the stratum below. Both cases follow Meyerhof.

In sand

$q_p = \min(q' N_q^{\ast}, \; 0.5 \, p_a N_q^{\ast} \tan\phi')$, where $q' = \sigma'_v(L)$ is the effective stress at the toe, not limited by the critical depth $z_c$.

$N_q^{\ast}$ is interpolated linearly in $\phi'$ from Meyerhof’s values, as Das & Sivakugan (2017) tabulate them from 20° to 45°. Outside that range the end value holds: 12.4 below 20°, 930 above 45°.

$\phi'$	$N_q^{\ast}$	$\phi'$	$N_q^{\ast}$
20°	12.4	33°	96.0
21°	13.8	34°	115.0
22°	15.5	35°	143.0
23°	17.9	36°	168.0
24°	21.4	37°	194.0
25°	26.0	38°	231.0
26°	29.5	39°	276.0
27°	34.0	40°	346.0
28°	39.7	41°	420.0
29°	46.5	42°	525.0
30°	56.7	43°	650.0
31°	68.2	44°	780.0
32°	81.0	45°	930.0

As $N_q^{\ast}$ multiplies both terms, the limit governs once $q' > 0.5 \, p_a \tan\phi'$, between 29 and 42 kPa for $\phi'$ from 30° to 40°. Past the first few metres, $q_p$ no longer grows with depth.

In clay

$q_p = 9 \, c_u$. In a pile group, the block’s toe takes Skempton’s factor in place of the 9.