Page 169 - Civil Engineering Formulas

106 CHAPTER FOUR

The lateral-load versus pile-head deflection relationship is developed from
charted nondimensional solutions of Reese and Matlock. The solution assumes
the soil modulus K to increase linearly with depth z; that is, K n z, where n
h
h
coefficient of horizontal subgrade reaction. A characteristic pile length T is cal-
culated from
EI
T (4.3)
B n h
where EI pile stiffness. The lateral deflection y of a pile with head free to
move and subject to a lateral load P and moment M applied at the ground line
t
t
is given by
T 3 T 2
y A y P t B y M t (4.4)
EI EI
where A and B are nondimensional coefficients. Nondimensional coefficients
y
y
are also available for evaluation of pile slope, moment, shear, and soil reaction
along the shaft.
For positive moment,
(4.5)
M A m P t T B m M t
Positive M and P values are represented by clockwise moment and loads
t
t
directed to the right on the pile head at the ground line. The coefficients applic-
able to evaluation of pile-head deflection and to the maximum positive moment
and its approximate position on the shaft, z/T, where z distance below the
ground line, are listed in Table 4.1.
The negative moment imposed at the pile head by pile-cap or another struc-
tural restraint can be evaluated as a function of the head slope (rotation) from
A P t T s EI
M t (4.6)
B B T
where rad represents the counterclockwise ( ) rotation of the pile head and
s
A and B are coefficients (see Table 4.1). The influence of the degrees of fixity

TABLE 4.1 Percentage of Base Load Transmitted to
Rock Socket
E /E p
r
L /d 0.25 1.0 4.0
s s
0.5 54* 48 44
1.0 31 23 18
1.5 17* 12 8*
2.0 13* 8 4
*Estimated by interpretation of finite-element solution;
for Poisson’s ratio 0.26.