Design of single piles - Piling Engineering - page 167

lateral load, the increase in normal stress in front of the pile will be at least partially
offset by a reduction in normal stress behind the pile.
In practical terms, the axial and lateral response of a pile may be treated indepen-
dently, although Hanna and Nguyen (2003) found that the shaft capacity of raking
piles in sand decreases slightly with increasing rake angle. The response of a raking
pile to load applied at a particular angle may then be assessed by taking the compo-
nents of load parallel and normal to the axis of the pile. The overall capacity of a
pile will be determined by taking the axial and lateral components of the applied load
and comparing them with the respective capacities. Thus for the general case shown
in Figure 4.52, where a pile raking at an angle

ψ to the vertical is subjected to a load

inclined at θ to the vertical, axial failure will occur when

Q cos( θ − ψ ) = Q a (axial failure) (4.88)

or when

Q sin( θ − ψ ) = Q l (lateral failure) (4.89)

It may be seen that the maximum capacity will be achieved when both axial and lateral
pile capacities are mobilized simultaneously. This occurs for

tan( θ − ψ ) = Q l / Q a (4.90)

when the overall capacity will be

( Q a + Q l ) 1 / 2 Q = (4.91)

Evangelista and Viggiani (1976) showed that the axial and lateral deformation
response of a pile is virtually independent of the angle that the pile makes with the
ground surface, for angles of rake up to about 30 ◦ . Thus, as for the calculation of the
pile capacity, the deformation response may be assessed by considering the compo-
nents of the applied load parallel and normal to the pile axis. For vertical piles, the

Figure 4.52 Oblique loading of a ranking pile.