12.5.2 Finite Element Solution of Pile and Soil
12.5.2.1 Dynamic Model Parameter Setting
During the impact process of hydraulic hammer and pile, the hammer transfers the
strike energy to the pile through the form of impact. After the impact process, the
strike energy propagates in the form of stress wave in the pile and soil. First, the
energy is transmitted in the pile, and then the energy is transmitted to the whole soil
through the contact between the pile and the soil. Soil is in a complex stress state,
and yield condition is a function of stress or strain state. In the theoretical analysis
of soil elastic–plastic constitutive relationship, it is assumed that the soil material is
isotropic, so the principal stress can be transferred to all directions of action. As
long as the magnitude of the principal stress acting at a point is studied, the
magnitude of the stress transferred in all directions can be known. The three
principal stresses can be described intuitively in three-dimensional space. The
Cartesian space coordinate system consisting of three principal stresses as axes is
called principal stress space. In the principal stress space, the space diagonal line
which is equal to the three coordinate axes is called the isobaric line, while the
plane perpendicular to the isobaric line is called the partial plane, and the intersection line between the yield surface and the partial plane is called the yield curve.
Drucker–Prager (D-P) yield criterion of DP soil material is adopted in ANSYS. The
plastic behavior of soil is assumed to be ideal elastic–plastic and the yield function
of soil is
f I 1 ;
ffiffiffiffi ffi
J 2
p
À
Á ¼
ffiffiffiffi ffi
J 2
p À aI 1 À k ¼ 0
ð12:53Þ
where
a; k Constants related to cohesion C and internal friction angle u of soil materials;
I 1
First invariant of soil stress tensor;
J 2 Second invariant of soil stress tensor.
The expressions of I 1 , J 2 , a; k are as follows:
I 1 ¼ r 1 þ r 2 þ r 3
ð12:54Þ
J 2 ¼
1
6
r 1 À r 2
ð
Þ
2 þ r 2 À r 3
ð
Þ
2 þ r 3 À r 1
ð
Þ
2
h
i
ð12:55Þ
a ¼
sin u
ffiffi ffi
3
p
ffiffi ffi
3
p
cos h r À sin h r sin u
À
Á
ð12:56Þ
k ¼
ffiffi ffi
3
p
c cos u
ffiffi ffi
3
p
cos h r À sin h r sin u
ð12:57Þ
310
12 Pneumatic–Hydraulic Pile Driving Hammer
12.5.2.1 Dynamic Model Parameter Setting
During the impact process of hydraulic hammer and pile, the hammer transfers the
strike energy to the pile through the form of impact. After the impact process, the
strike energy propagates in the form of stress wave in the pile and soil. First, the
energy is transmitted in the pile, and then the energy is transmitted to the whole soil
through the contact between the pile and the soil. Soil is in a complex stress state,
and yield condition is a function of stress or strain state. In the theoretical analysis
of soil elastic–plastic constitutive relationship, it is assumed that the soil material is
isotropic, so the principal stress can be transferred to all directions of action. As
long as the magnitude of the principal stress acting at a point is studied, the
magnitude of the stress transferred in all directions can be known. The three
principal stresses can be described intuitively in three-dimensional space. The
Cartesian space coordinate system consisting of three principal stresses as axes is
called principal stress space. In the principal stress space, the space diagonal line
which is equal to the three coordinate axes is called the isobaric line, while the
plane perpendicular to the isobaric line is called the partial plane, and the intersection line between the yield surface and the partial plane is called the yield curve.
Drucker–Prager (D-P) yield criterion of DP soil material is adopted in ANSYS. The
plastic behavior of soil is assumed to be ideal elastic–plastic and the yield function
of soil is
f I 1 ;
ffiffiffiffi ffi
J 2
p
À
Á ¼
ffiffiffiffi ffi
J 2
p À aI 1 À k ¼ 0
ð12:53Þ
where
a; k Constants related to cohesion C and internal friction angle u of soil materials;
I 1
First invariant of soil stress tensor;
J 2 Second invariant of soil stress tensor.
The expressions of I 1 , J 2 , a; k are as follows:
I 1 ¼ r 1 þ r 2 þ r 3
ð12:54Þ
J 2 ¼
1
6
r 1 À r 2
ð
Þ
2 þ r 2 À r 3
ð
Þ
2 þ r 3 À r 1
ð
Þ
2
h
i
ð12:55Þ
a ¼
sin u
ffiffi ffi
3
p
ffiffi ffi
3
p
cos h r À sin h r sin u
À
Á
ð12:56Þ
k ¼
ffiffi ffi
3
p
c cos u
ffiffi ffi
3
p
cos h r À sin h r sin u
ð12:57Þ
310
12 Pneumatic–Hydraulic Pile Driving Hammer