Page 313 - Numerical Analysis and Modelling in Geomechanics

294 ANALYSIS AND DESIGN OF PILE GROUPS

(10.8)

where K is the passive earth pressure coefficient, equal to (1+sinф≥)/(1—sinф≥).
p
Group “shadowing” effect

Under lateral loads, closely spaced pile groups are subjected to a reduction of
lateral capacity. This effect, commonly referred to as “shadowing”, is related to
the influence of the leading row of piles on the yield zones developed in the soil
ahead of the trailing row of piles. Because of this overlapping of failure zones,
the front row will be pushing into virgin soil while the trailing row will be
pushing into soil which is in the shadow of the front row piles. A consequence of
this loss of soil resistance for piles in a trailing row is that the leading piles in a
group will carry a higher proportion of the overall applied load than the trailing
piles. This effect also results in gap formation behind the closely spaced piles
and an increase in group deflection. It has been shown both theoretically and
experimentally that the shadowing effect becomes less significant as the spacing
between piles increases and is relatively unimportant for centre-to-centre spacing
greater than about six pile diameters (Cox et al., 1984; Brown and Shie, 1990;
Ng et al., 2001).
The shadowing effect has been modelled into the PGROUPN analysis using
the approach outlined by Fleming et al. (1992). Following this approach, it has
been assumed that a form of block failure will govern when the shearing
resistance of the soil between the piles is less than the limiting resistance of an
isolated pile. Referring to Figure 10.1, the limiting lateral resistance for the pile
which is in the shadow of the front pile may be calculated from the lesser of the
limiting bearing stress for a single pile (as calculated from Equations (10.5) and
(10.8)) and , where s is the centre-to-centre pile spacing, d is the pile diameter
and t is the friction on the sides of the block of soil between the two piles. The
s
value of t may be taken as C for cohesive soil and tan ф≥ for cohesionless soil.
s
u
The outlined approach provides a simple yet rational means of estimating the
shadowing effect in closely spaced groups, as compared with the purely
empirical “p-multiplier” concept which is employed in load-transfer analyses
(e.g. in GROUP andFLPIER).

Extension to non-linear soil behaviour
Non-linear soil behaviour is incorporated, in an approximate manner, by
assuming that the soil Young’s modulus varies with the stress level at the pile-
soil interface. A simple and popular assumption is to adopt a hyperbolic stress-
strain relationship, in which case the tangent Young’s modulus of the soil E tan
may be written as (Duncan and Chang, 1970; Poulos, 1989; Randolph, 1994):