DHARM
PILE FOUNDATIONS 687
abutments, tall structures subjected to wind loads and as anchors for wharves, bulkheads and
other waterfront structures. The batter may be up to 30° with the vertical. Depending on the
direction of the lateral force relative to the direction of inclination with respect to the vertical,
the batter may be termed ‘positive’ or ‘negative’. If the tendency of the force is to ‘right’ the pile
(bring it nearer vertical), the batter is considered positive; otherwise, it is considered negative
(Fig. 16.20).
b
Qh
b
Qh
b: Angle of batter
(a) Positive batter (b) Negative batter
Fig. 16.20 Batter piles with positive batter and negative batter
A rational analysis of the action of batter piles is difficult because the problem is statically
indeterminate to a high degree. One approximate method assumes the piles to be hinged at
their tips and at their butts. A batter and vertical pile combination that is usually employed in
sheet-pile bulkhead construction is shown in Fig. 16.21.
a Hinge
Hinge
Batter pile Rigid surface
Concrete
bulb
Tension
pile
1 Reinforcement
2.5
c
t a
t c
Triangle of forces
(a) Batter and vertical piles for
a sheet-pile bulkhead
(b) Simplified analysis for combined
vertical and batter piles
Fig. 16.21 Batter and vertical pile combination
Hrennikoff (1949) and Vesic (1970) have advanced theoretical analyses for batter piles.
The former assumes the coefficient of a sub grade reaction as constant with the depth for all
soils, while the latter assumes it as constant for clays and as varying linearly with depth for