where eis 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 zfis the depth from the ground surface to the
point of virtual fixity. The depth zfis 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 zf should be taken as 1.4Rfor stiff, over-consoli-
dated clays and 1.8Tfor 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 Hucan be obtained by taking moments about
the point of rotation, when
(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 Muof the pile shaft.
The appropriate load factors are applied to the horizontal design force to obtain the ultimate
force Hu.
When applying the method to layered soils, assumptions must be made concerning the
depth zto obtain Kqand Kcfor the soft clay layer, but zis measured from the top of the stiff
clay stratum to obtain Kcfor this layer, as shown in Figure 6.23.
The undrained shearing strength cuis 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
(cand ) 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.
Hu(ex) (^)
x
0
pz LnB(xz)
xL
x
pz LnB(zx)
Piles to resist uplift and lateral loading 333
H
e
Stiff clay
z (for soft clay)
z (for stiff clay)
Soft clay
Figure 6.23Reactions in layered soil on vertical pile under horizontal load.