Dynamic Stability Analysis of Pile Foundation under Wave Load
Publication: International Journal of Geomechanics
Volume 21, Issue 4
Abstract
The main load on a pile foundation in the ocean is the wave load. Presently, few reports exist on the dynamic stability of pile foundations in the ocean. This paper investigated the dynamic stability of pile foundations under wave loads. The foundation reaction force was calculated using a double-parameter model and considering pile side soil softening under a cyclic load. By establishing the energy equation of the entire pile, the Hamiltonian principle was used to obtain the dynamic differential equations of the pile in four different situations (vertical harmonic, transverse harmonic, longitudinal and transverse harmonic, and longitudinal and horizontal harmonic loads with different frequencies). Then, the nonhomogeneous Mathieu equation was obtained by arranging the dynamic differential equations, and the parametric resonance critical frequency and instability load were obtained by solving this equation. The analytical solution was verified by comparing the results obtained by the finite-element software simulation with the analytical solution and analyzing the influence of several different factors on the critical frequency and amplitude. The research indicated that the amplitude of the pile body increases linearly with an increase of wave height, the effect of wavelength on amplitude increases nonlinearly, and the amplitude increases much rapidly with an increase of wavelength. The critical frequency calculated by the double-parameter method was lower than that calculated by the Winkler model, and the result of double-parameter model was more practical and safe.
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Acknowledgments
This work was supported by the Key projects of National Natural Science Foundation of China (Grant No. 11932010).
Notation
The following symbols are used in this paper:
- A
- amplitude;
- b1
- calculated width;
- C
- damping parameter;
- D
- damping potential energy;
- d
- pile diameter;
- d1
- the length of the pile in the water (not including the part of the pile that enters the soil);
- E
- elastic modulus of pile;
- Es
- elastic modulus of the foundation soil;
- fz
- wave load;
- G
- shear stiffness of soil;
- Gp
- Gb1;
- g
- acceleration of gravity;
- H
- wave height;
- h
- length of the pile in the water;
- hg
- thickness of the shear layer of the foundation soil;
- first-order Bessel function of the first kind;
- K
- 2π/L;
- k
- pile side soil resistance coefficient;
- k0
- pile–soil stiffness ratio;
- L
- wavelength;
- l
- pile length;
- M0
- initial bending moment of the pile top;
- m
- mass of pile;
- m0
- coefficient of the soil around the pile;
- N
- number of cycles of load;
- Ntcr
- instability load;
- P0
- vertical static load;
- Pt
- vertical harmonic load;
- q0
- hydrostatic pressure;
- T
- kinetic energy;
- TN
- period;
- t
- time;
- U
- potential energy of the internal force of the pile;
- Us
- strain energy of the soil at the side of the pile;
- V
- external force potential energy;
- pile top bending moment potential energy;
- Vp
- pile top load potential energy;
- Vq0
- hydrostatic pressure potential energy;
- first-order Bessel function of the second kind;
- z1
- water depth;
- θ
- vertical harmonic load frequency;
- ρ
- density of seawater;
- νb
- lateral displacement of soil;
- νs
- Poisson’s ratio of the foundation soil; and
- ξ
- P/m;
- ϕ
- internal friction angle of the soil; and
- ω
- frequency of the wave load.
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Published In
International Journal of Geomechanics
Volume 21 • Issue 4 • April 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: May 9, 2020
Accepted: Nov 8, 2020
Published online: Jan 29, 2021
Published in print: Apr 1, 2021
Discussion open until: Jun 29, 2021
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