A non‐linear coupled finite element–boundary element model for the prediction of vibrations due to vibratory and impact pile driving

This paper presents a non-linear coupled finite element–boundary element approach for the prediction of free field vibrations due to vibratory and impact pile driving. Both the non-linear constitutive behavior of the soil in the vicinity of the pile and the dynamic interaction between the pile and the soil are accounted for. A subdomain approach is used, defining a generalized structure consisting of the pile and a bounded region of soil around the pile, and an unbounded exterior linear soil domain. The soil around the pile may exhibit non-linear constitutive behavior and is modelled with a time-domain finite element method. The dynamic stiffness matrix of the exterior unbounded soil domain is calculated using a boundary element formulation in the frequency domain based on a limited number of modes defined on the interface between the generalized structure and the unbounded soil. The soil–structure interaction forces are evaluated as a convolution of the displacement history and the soil flexibility matrices, which are obtained by an inverse Fourier transformation from the frequency to the time domain. This results in a hybrid frequency–time domain formulation of the non-linear dynamic soil–structure interaction problem, which is solved in the time domain using Newmark's time integration method; the interaction force time history is evaluated using the θ-scheme in order to obtain stable solutions. The proposed hybrid formulation is validated for linear problems of vibratory and impact pile driving, showing very good agreement with the results obtained with a frequency-domain solution. Linear predictions, however, overestimate the free field peak particle velocities as observed in reported field experiments during vibratory and impact pile driving at comparable levels of the transferred energy. This is mainly due to energy dissipation related to plastic deformations in the soil around the pile. Ground vibrations due to vibratory and impact pile driving are, therefore, also computed with a non-linear model where the soil is modelled as an isotropic elastic, perfectly plastic solid, which yields according to the Drucker–Prager failure criterion. This results in lower predicted free field vibrations with respect to linear predictions, which are also in much better agreement with experimental results recorded during vibratory and impact pile driving. Copyright © 2008 John Wiley & Sons, Ltd.

[1]  Jean-Lou Chameau,et al.  Measured Effects of Vibratory Sheetpile Driving , 1980 .

[2]  D. C. Rizos,et al.  Dynamic and Seismic Analysis of Foundations based on Free Field B-Spline Characteristic Response Histories , 2002 .

[3]  Otto von Estorff,et al.  Iterative coupling of FEM and BEM in 3D transient elastodynamics , 2005 .

[4]  W. Mansur,et al.  A linear θ method applied to 2D time‐domain BEM , 1998 .

[5]  Stavros A. Savidis,et al.  Soil–structure interaction in the time domain using halfspace Green's functions , 2002 .

[6]  Hal Amick,et al.  Construction Vibrations and Their Impact on Vibration-Sensitive Facilities , 2000 .

[7]  The θ scheme for time‐domain BEM/FEM coupling applied to the 2‐D scalar wave equation , 2000 .

[8]  A. Peirce,et al.  Stability Analysis of Model Problems for Elastodynamic Boundary Element Discretizations , 1996 .

[9]  Mounir Mabsout,et al.  Study of Pile Driving by Finite-Element Method , 1995 .

[10]  P. C. Pelekis,et al.  Ground vibrations from sheetpile driving in urban environment: measurements, analysis and effects on buildings and occupants , 2000 .

[11]  L. Neil Frazer,et al.  On a generalization of Filon's method and the computation of the oscillatory integrals of seismology , 1984 .

[12]  Mark Randolph,et al.  Numerical modelling of the driving response of thin‐walled open‐ended piles , 2001 .

[13]  A linear θ time-marching algorithm in 3D BEM formulation for elastodynamics , 1999 .

[14]  A. Frangi,et al.  On the numerical stability of time-domain elastodynamic analyses by BEM , 1999 .

[15]  E. Kausel,et al.  Coupling of boundary and finite elements for soil‐structure interaction problems , 1989 .

[16]  Mark Randolph,et al.  Analytical modelling of hammer impact for pile driving , 1993 .

[17]  J.A.M. Carrer,et al.  A MORE STABLE SCHEME FOR BEM/FEM COUPLING APPLIED TO TWO-DIMENSIONAL ELASTODYNAMICS , 2001 .

[18]  Dimitri E. Beskos,et al.  Boundary Element Methods in Dynamic Analysis: Part II (1986-1996) , 1997 .

[19]  J. F. Wiss,et al.  CONSTRUCTION VIBRATIONS: STATE-OF-THE-ART , 1981 .

[20]  Dimitris L. Karabalis,et al.  Non-singular time domain BEM with applications to 3D inertial soil–structure interaction , 2004 .

[21]  T. S. Thandavamoorthy.  Piling in fine and medium sand—a case study of ground and pile vibration , 2004 .

[22]  D. Karabalis,et al.  Inertial soil-foundation interaction by a direct time domain BEM , 1991 .

[23]  W. Mansur,et al.  Time weighting in time domain BEM , 1998 .

[24]  John P. Wolf,et al.  Non‐linear soil‐structure‐interaction analysis using dynamic stiffness or flexibility of soil in the time domain , 1985 .

[25]  W. Mansur,et al.  Time discontinuous linear traction approximation in time-domain BEM: 2-D elastodynamics , 2000 .

[26]  Alain Holeyman,et al.  A Method to Predict the Drivability of Vibratory Driven Piles , 1996 .

[27]  Björn Birgisson,et al.  Elastodynamic direct boundary element methods with enhanced numerical stability properties , 1999 .

[28]  Geert Lombaert,et al.  Prediction of free field vibrations due to pile driving using a dynamic soil–structure interaction formulation , 2007 .