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= nh ,z where nh coefficient of horizontal subgrade reaction. A characteristic pile length T is calculated as:
T=(EI/nh)1/2
where
EI= pile stiffness.
The lateral deflection y of a pile with head free to move and subject to a lateral load Pt and moment Mt applied at the ground line is given by
y=Ay Pt T3 / EI+ By Mt T2 / EI
where
Ay and By 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=Am Pt T+Bm Mt
Positive Mt and Pt 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 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
piles-formula
where
theta 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 Mt from the preceding equation into the earlier y and M equations. Note that, for the fixed-head case,
piles-formula-2
