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 Kto increase linearly with depth z; that is, Knhz, where nh
coefficient of horizontal subgrade reaction. A characteristic pile length Tis cal-
culated from

(4.3)

whereEIpile stiffness. The lateral deflection yof a pile with head free to
move and subject to a lateral load Ptand moment Mtapplied at the ground line
is given by

(4.4)

whereAyandByare nondimensional coefficients. Nondimensional coefficients
are also available for evaluation of pile slope, moment, shear, and soil reaction
along the shaft.
For positive moment,

(4.5)

PositiveMtandPtvalues are represented by clockwise moment and loads
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 zdistance 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

(4.6)

where (^) srad represents the counterclockwise () rotation of the pile head and
A andB are coefficients (see Table 4.1). The influence of the degrees of fixity
Mt
A PtT
B



(^) sEI
B T
MAmPtTBmMt
yAyPt

T^3

EI

ByMt

T^2

EI

T

B

EI

nh

TABLE 4.1 Percentage of Base Load Transmitted to

Rock Socket

Er/Ep

Ls/ds 0.25 1.0 4.0

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 ratio0.26.