Pile Design and Construction Practice, Fifth edition

where e is the height from the ground surface to the point of application of the load at the
fixed head of the pile (Figure 6.21a), and z f is the depth from the ground surface to the
point of virtual fixity. The depth z f is not known at this stage but for practical design
purposes it can be taken as 1.5 m for a compact granular soil or stiff clay (below the
zone of soil shrinkage in the latter case), and 3 m for a soft clay or silt. The American
Concrete Institute (6.13) recommend that z f should be taken as 1.4R for stiff, over-consolidated
clays and 1.8T for normally consolidated clays, granular soils and silt, and peat (see
equations 6.11 and 6.12).
Having obtained the depth to the centre of rotation from equation 6.15, the ultimate lateral
resistance of the pile to the horizontal force H u can be obtained by taking moments about
the point of rotation, when
H u(e � x) � � x
0
pz L nB(x � z) � �
x�L
pz x
L n � B(z � x)
Piles to resist uplift and lateral loading 333
(6.17)
The final steps in Brinch Hansen’s method are to construct the shearing force and bending
moment diagrams (Figure 6.21b and c). The ultimate bending moment, which occurs at the
point of zero shear, should not exceed the ultimate moment of resistance M u of the pile shaft.
The appropriate load factors are applied to the horizontal design force to obtain the ultimate
force H u.
When applying the method to layered soils, assumptions must be made concerning the
depth z to obtain K q and K c for the soft clay layer, but z is measured from the top of the stiff
clay stratum to obtain K c for this layer, as shown in Figure 6.23.
The undrained shearing strength c u is used in equation 6.14 for short-term loadings such
as wave or ship-berthing forces on a jetty, but the drained effective shearing strength values
(c� and ��) are used for long-term sustained loadings such as those on retaining walls.
A check should be made to ensure that there is an adequate safety factor for undrained
conditions in the early stages of loading. The step-by-step procedure using the Brinch
Hansen method is illustrated in worked Example 6.4.
e
H
Soft clay
Stiff clay
z (for soft clay)
z (for stiff clay)
Figure 6.23 Reactions in layered soil on vertical pile under horizontal load.