Kinematic response of pipe piles subjected to vertically propagating seismic P-waves
- PDF / 859,512 Bytes
- 15 Pages / 595.276 x 790.866 pts Page_size
- 74 Downloads / 174 Views
(0123456789().,-volV)(0123456789(). ,- volV)
RESEARCH PAPER
Kinematic response of pipe piles subjected to vertically propagating seismic P-waves Changjie Zheng1 • George Kouretzis2 • Lubao Luan3 • Xuanming Ding4 Received: 4 February 2020 / Accepted: 27 July 2020 Ó Springer-Verlag GmbH Germany, part of Springer Nature 2020
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 depthand 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. Keywords Pipe piles P-waves Seismic response Soil–pile interaction Winkler springs List of symbols a1 A * D, An Ap c1 c2 Ep f H Iv
I0 ðÞ Dimensionless frequency Undetermined coefficients Cross-sectional area of pipe pile Damping coefficient of outer soil Damping coefficient of inner soil Young’s modulus of pile Vertical soil resistance Pile length Kinematic response factor
& Lubao Luan [email protected] 1
2
k1 k2 K r, h, z
r1 r2 Subscripts 1 and 2 t u ug up urp
Fujian Provincial Key Laboratory of Advanced Technology and Informatization in Civil Engineering, School of Civil Engineering, Fujian University of Technology, Fuzhou 350118, China Priority Research Centre for Geotechnical Science and Engineering, Faculty of Engineering and Built Environment, The University of Newcastle, Callaghan, NSW 2308, Australia
3
College of Environmental Science and Technology, Ocean University of China, Qingdao 266100, China
4
Key Laboratory of New Technology for Construction of Cities in Mountain Areas, College of Civil Engineering, Chongqing University, Chongqing 400045, China
ur Vp
ug eixt Vl
The first kind of zero-order modified Bessel function Dynamic stiffness of outer soil Dynamic stiffness of inner soil Winkler modulus of soil Radial, circumferential and vertical directions in the cylindrical coordinate system Pile outer radius Pile inner radius Parameters referring to outer and inner soil respectively Time Vertical displacement of soil Amplitude of seismic wave Vertical displacement of pipe pile Relative displacement of pipe pile to rigid base Relative displacement of soil to rigid base One-dimensional wave propagation velocity in pipe pile Time-harmonic displacement Complex propagation velocity of damped longitudinal wave in soil
123
Acta Geotechnica
Vs m b k*, G* q qp g, ur1 hom , q2 , ur1par , bn, Tn x
Complex propagation velocity of damped shear wave in soil Poisson’s ratio of soil Hysteretic damping of soil Complex Lame’s constants of soil Mass density of soil Mass density of pile Temporary variables Circular frequency
1 Introduc
Data Loading...
