Pile Design and Construction Practice, Fifth edition

ground surface is then given by

pz pozKqzcKcz (6.14)

where pozis the effective overburden pressure at depth z, cis the cohesion of the soil at depth
z, and Kqzand Kczare the passive pressure coefficients for the frictional and cohesive
components respectively at depth z. Brinch Hansen(6.12)has established values of Kqand Kc
in relation to the depth zand the width of the pile Bin the direction of rotation, as shown in
Figure 6.22.
The total passive resistance on each horizontal element is and, by taking
moments about the point of application of the horizontal load:

(6.15)

The point of rotation at depth xis correctly chosen when , that is, when the passive
resistance of the soil above the point of rotation balances that below it. Point X is thus
determined by a process of trial and adjustment. If the head of the pile carries a moment M
instead of a horizontal force, the moment can be replaced by a horizontal force Hat a
distance eabove the ground surface where M is equal to H  e.
Where the head of the pile is fixed against rotation, the equivalent height e 1 above ground
level of a force Hacting on a pile with a free head is given by

e 112 (ezf) (6.16)

M^0

M^ 

z x

z 0

pz Ln (ez)B 

z L

z x

pz Ln (ez)B

pzLnB

332 Piles to resist uplift and lateral loading

400

200

100

50

20

10

5

2

0 5 10 15 20

z/B

8.14

13.2

17.6

24.5

35.8

61.4

10.2

118

272

759

0 °

5 °

10 °

15 °

20 °

25 °

30 °

35 °

40 °

45 °

0

5 10 15 20

z/B

1

2

5

10

20

60

80

40

Kq Kc

5 °

10 °

15 °

20 °

25 °

30 °

35 °

40 °

45 °

222

81.4

17.7

35.3

9.91

5.88

3.50

1.93

0.62

f
 f

Kq
0 for f
 0 °

Figure 6.22Brinch Hansen’s coefficients Kqand Kc.