Geotechnical Engineering

DHARM

658 GEOTECHNICAL ENGINEERING

For piles in sands:

qb =

1

2

γ bNγ + q. Nq ...(Eq. 16.5)

(for square or rectangular piles)

qb = 0.3 γ DNγ + q. Nq ...(Eq. 16.6)

(for circular piles with diameter D)

With driven piles the term involving the size of the pile is invariably negligible com-

pared with the surcharge term q. Nq. Thus, for all practical purposes,

qb = q. Nq ...(Eq. 16.7)

The surcharge pressure q is given by

q = γ.z if Z < Zc, and

q = γ.Zc if Z > Zc ...(Eq. 16.8)

Z being the embedded length of pile and Zc the critical depth.

This indicates that the vertical stress at the tip of a long pile tends to reach a constant
value and the depth beyond which the stress does not increase linearly with depth is called the
critical depth. This is due to the mechanics of transfer of load from a driven pile to the sur-
rounding soil. Large-scale tests by Vesic (1967) in the U.S.A. and Kerisel (1967) in France
indicate that the critical depth Zc is a function of density index. For ID < 30%, Zc = 10D ; for ID

70%, Zc = 30 D ; and, for intermediate values, it is nearly proportional to density index (D is
the dimension of the pile cross-section).
The bearing capacity factor Nq is related to the angle of internal friction of the sand in
the vicinity of the pile tip (several pile diameters above and below the pile tip), and the ratio of
the pile depth to pile width. Values of Nq presented by different investigators show a wide
range of variation because of the assumptions made in defining the shear zones near the pile
tip; for example, while Meyerhof assumes the shear zones to extend back to the pile shaft,
Vesic assumes punching shear in which the shear zones do not extend to the pile shaft. Values
of Nq attributed to Berezantzev et al. (1961), which take into account the effect of z/b ratio, are
believed to be the most applicable for the most commonly encountered field conditions. The
angle of internal friction for the soil in the vicinity of the pile tip is determined from the
standard penetration test. If Dutch cone resistance data are available, these values are corre-
lated directly to the end-bearing resistance of the pile, qb.
Values of Nq given by different investigators are shown in Fig. 16.3.
These values of Nq are based on the assumption that the soil above the pile tip is
comparable to the soil below the pile tip. If the pile penetrates the compact layer only slightly,
and loose material exists above the compact soil, an Nq value for a shallow foundation will be
more appropriate than a value from Fig. 16.3.
If Eq. 16.5 or 16.6 is to be used, the value of Nγ for a deep foundation can be conserva-
tively taken as twice the Nγ value used for shallow foundation; otherwise, it may be taken
from Fig. 16.3, the values given by Berezantzev et al.
According to Nordlund and Tomlinson (1969), Berezantzev’s values of Nq increase rap-
idly for high values of φ. Further, the decrease in Nq with increase in z/b also will be signifi-
cant for high values of φ.