WORLD FOR CIVIL

Laterally loaded vertical piles

Vertical-pile resistance to lateral loads is a function of both the flexural stiffness of the shaft, the stiffness of the bearing soil in the upper 4 to 6D length of shaft, where D=pile diameter and the degree of pile-head fixity.

The lateral-load vs. 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_h ,z where n_h coefficient of horizontal subgrade reaction. A characteristic pile length T is calculated as:

T=(EI/n_h)^1/2

where
EI= pile stiffness.

The lateral deflection y of a pile with head free to move and subject to a lateral load P_t and moment M_t applied at the ground line is given by

y=A_y P_t T³ / EI+ B_y M_t T² / EI

where
A_y and B_y are nondimensional coefficients. Non- dimensional coefficients are also available for evaluation of pile slope, moment, shear, and soil reaction along the shaft.

For positive moment,

M=A_m P_t T+B_m M_t

Positive M_t and P_t values are represented by clockwise moment and loads directed to the right on the pile head at the ground line. The coefficients applicable 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 and are given in the tabular form

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 ratio
0.26.

The negative moment imposed at the pile head by pile- cap or another structural restraint can be evaluated as a function of the head slope (rotation) from

-M_t=A_?P_tT/B_?-?_sEI/B_?T

where
?_s rad represents the counterclockwise ( + ) rotation of the pile head and A_? and B_? are coefficients . The influence of the degrees of fixity of the pile head on y and M can be evaluated by substituting the value of M_t from the preceding equation into the earlier y and M equations. Note that, for the fixed-head case,

y_f=[P_tT³/EI]*[A_y-A_?B_y/B_?]