12.4.2 Mathematical Model for Descending Stage of Rapid
Piling
This section mainly establishes the mathematical model of hydraulic–pneumatic
pile driving hammer in descending stage.
(1) Taking the direction of gravity as the positive direction, the force equilibrium
equation of the hydraulic hammer in the descending stage is as follows.
mg þ p u A u À p d A d ¼ m
d
2 y
dt 2 þ B
dy
dt
þ Ky
ð12:37Þ
A d ¼ p D
2
À d
2
À
Á =4; A d ¼ pD
2
=4
ð12:38Þ
where
m Mass of movable part of hydraulic hammer;
B Viscous damping coefficient;
y Drop displacement of hammer body;
t Descending time;
K Spring stiffness coefficient;
D Piston diameter;
d Piston rod diameter.
Fig. 12.24 Hydraulic system diagram of pressure-retaining stage in hydraulic hammer piling
process
300
12 Pneumatic–Hydraulic Pile Driving Hammer