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Kinematic response of pipe piles subjected to vertically propagating seismic P-waves

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Abstract

This paper presents an analytical solution for determining the time-harmonic response of single open-ended pipe piles subjected to vertically propagating seismic P-waves. Following the presentation of the formulation, we employ the solution to derive closed-form expressions of seismic pipe pile displacements, as well as robust expressions to determine the depth- and frequency-dependent parameters of complex Winkler springs, for use with beam-on-dynamic-Winkler-foundation models. Finally, the importance of considering the contribution of the inner soil in the seismic analysis of pipe piles is quantified via a parametric sensitivity analysis.

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Abbreviations

a 1 :

Dimensionless frequency

A ~ D, A n :

Undetermined coefficients

A p :

Cross-sectional area of pipe pile

c 1 :

Damping coefficient of outer soil

c 2 :

Damping coefficient of inner soil

E p :

Young’s modulus of pile

f :

Vertical soil resistance

H :

Pile length

I v :

Kinematic response factor

\( I_{0} \left( {} \right) \) :

The first kind of zero-order modified Bessel function

k 1 :

Dynamic stiffness of outer soil

k 2 :

Dynamic stiffness of inner soil

K :

Winkler modulus of soil

r, \( \theta \), z :

Radial, circumferential and vertical directions in the cylindrical coordinate system

r 1 :

Pile outer radius

r 2 :

Pile inner radius

Subscripts 1 and 2:

Parameters referring to outer and inner soil respectively

t :

Time

u :

Vertical displacement of soil

u g :

Amplitude of seismic wave

u p :

Vertical displacement of pipe pile

u r p :

Relative displacement of pipe pile to rigid base

u r :

Relative displacement of soil to rigid base

V p :

One-dimensional wave propagation velocity in pipe pile

\( u_{g} \text{e}^{{\text{i} \omega t}} \) :

Time-harmonic displacement

\( V_{\text{l}}^{*} \) :

Complex propagation velocity of damped longitudinal wave in soil

\( V_{{s}}^{*} \) :

Complex propagation velocity of damped shear wave in soil

\( \nu \) :

Poisson’s ratio of soil

β :

Hysteretic damping of soil

λ *, G * :

Complex Lame’s constants of soil

ρ :

Mass density of soil

ρ p :

Mass density of pile

\( \eta \), \( u_{1\hom }^{r} \), \( q_{{}}^{2} \), \( u_{1par}^{r} \), b n , T n :

Temporary variables

ω :

Circular frequency

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 51708064, 51878173 and 41977259) and the Scientific Research Starting Foundation of Fujian University of Technology (GY-Z19097).

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Authors and Affiliations

  1. Fujian Provincial Key Laboratory of Advanced Technology and Informatization in Civil Engineering, School of Civil Engineering, Fujian University of Technology, Fuzhou, 350118, China

    Changjie Zheng

  2. Priority Research Centre for Geotechnical Science and Engineering, Faculty of Engineering and Built Environment, The University of Newcastle, Callaghan, NSW, 2308, Australia

    George Kouretzis

  3. College of Environmental Science and Technology, Ocean University of China, Qingdao, 266100, China

    Lubao Luan

  4. Key Laboratory of New Technology for Construction of Cities in Mountain Areas, College of Civil Engineering, Chongqing University, Chongqing, 400045, China

    Xuanming Ding

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  1. Changjie Zheng
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  2. George Kouretzis
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  3. Lubao Luan
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  4. Xuanming Ding
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Correspondence to Lubao Luan.

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Zheng, C., Kouretzis, G., Luan, L. et al. Kinematic response of pipe piles subjected to vertically propagating seismic P-waves. Acta Geotech. 16, 895–909 (2021). https://doi.org/10.1007/s11440-020-01050-3

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