where
E t Energy of hydraulic hammer before hitting, that is, strike energy of pile
hammer;
M Mass of Hammer;
v Pre-impact velocity of hydraulic hammer.
The energy received by the pile is related to the efficiency coefficient g of the
hydraulic hammer in the process of driving the pile. The key to the finite element
analysis of bearing capacity of single pile is to determine the mechanical properties
of soil and the contact condition between pile and soil. The mechanical properties
of soil materials are complex and changeable, and the stress–strain relationship of
the same soil body is nonlinear. In this section, Drucker–Prager model for elastic–
plastic soil and degree of freedom elastic body model for pile are adopted, and
friction characteristics between soil and pile are considered. It is assumed that the
interface between pile and soil is a contact element without thickness or thin layer,
and it is a rigid–flexible contact form. In the process of modeling and calculation,
the following assumptions are made: (1) The hammer body is rigid and the pile is a
mass-free deformed body. The material deformation obeys Hooke’s law during the
impact process, and the impact coefficient is zero during the impact process. (2) In
the process of impact, only the transformation between kinetic energy, potential
energy and deformation energy is possible, and other energy losses are neglected.
(3) Without considering the propagation of stress wave in the component, it is
assumed that the component deforms at the same time everywhere in every instant.
The energy method is used to calculate the impact of hammer and pile. When the
hammer impacts the pile head with velocity v, the impact force F d obtained by the
pile can be expressed as
F d ¼ kd d
ð12:49Þ
k ¼ EA=l
ð12:50Þ
d d ¼ K d d st ¼ 1 þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 þ
v 2
gd st
s
!
d st
ð12:51Þ
d st ¼ G=k
ð12:52Þ
where
k
Stiffness of pile as elastic bar;
d d Maximum deformation of piles under impact load when they are elastic rods.
E Elastic modulus of pile as impact member;
A Section area of impact member;
l
Length of pile as impact member;
K d Dynamic load coefficient of pile under impact;
308
12 Pneumatic–Hydraulic Pile Driving Hammer
E t Energy of hydraulic hammer before hitting, that is, strike energy of pile
hammer;
M Mass of Hammer;
v Pre-impact velocity of hydraulic hammer.
The energy received by the pile is related to the efficiency coefficient g of the
hydraulic hammer in the process of driving the pile. The key to the finite element
analysis of bearing capacity of single pile is to determine the mechanical properties
of soil and the contact condition between pile and soil. The mechanical properties
of soil materials are complex and changeable, and the stress–strain relationship of
the same soil body is nonlinear. In this section, Drucker–Prager model for elastic–
plastic soil and degree of freedom elastic body model for pile are adopted, and
friction characteristics between soil and pile are considered. It is assumed that the
interface between pile and soil is a contact element without thickness or thin layer,
and it is a rigid–flexible contact form. In the process of modeling and calculation,
the following assumptions are made: (1) The hammer body is rigid and the pile is a
mass-free deformed body. The material deformation obeys Hooke’s law during the
impact process, and the impact coefficient is zero during the impact process. (2) In
the process of impact, only the transformation between kinetic energy, potential
energy and deformation energy is possible, and other energy losses are neglected.
(3) Without considering the propagation of stress wave in the component, it is
assumed that the component deforms at the same time everywhere in every instant.
The energy method is used to calculate the impact of hammer and pile. When the
hammer impacts the pile head with velocity v, the impact force F d obtained by the
pile can be expressed as
F d ¼ kd d
ð12:49Þ
k ¼ EA=l
ð12:50Þ
d d ¼ K d d st ¼ 1 þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 þ
v 2
gd st
s
!
d st
ð12:51Þ
d st ¼ G=k
ð12:52Þ
where
k
Stiffness of pile as elastic bar;
d d Maximum deformation of piles under impact load when they are elastic rods.
E Elastic modulus of pile as impact member;
A Section area of impact member;
l
Length of pile as impact member;
K d Dynamic load coefficient of pile under impact;
308
12 Pneumatic–Hydraulic Pile Driving Hammer