Frequency-independent Springs Research Articles

A case study on the soil–pile–structure interaction of a long span arched structure

Different concepts for modelling of soil-foundation in complete dynamic interaction analysis for a 110-m height 70-m span arched structure on 180 piles were investigated in this paper. The modelling approaches consisted of a sophisticated procedure to account for soil compliance and foundation flexibility by defining frequency-dependent springs and dashpots; namely, flexible-impedance base model. The results of this model were compared with those of the conventional modelling procedures; namely, fixed base model and flexible base model by defining frequency-independent springs. In the flexible-impedance base model, the substructure approach was employed through finite element modelling. To account for the kinematic interaction, the numerical model of the soil, foundation and piles were developed using a verified finite element model in ABAQUS. The free field time history and design spectrum were modified to obtain the foundation input motion. The impedance of pile groups with different length was obtained by the finite element model to assess the inertial interaction. The comparison of the results of the employed models showed that rocking and torsional responses were greatly affected by soil–structure interaction, indicating redistribution of seismic demands. It was also proven that the internal demands of the conventional model considering frequency-independent Winkler springs might be higher than those of the model including pile–soil–structure interaction effects.

Nested Lumped-Parameter Model for Foundation with Strongly Frequency-dependent Impedance

A nested lumped-parameter model (LPM) consisting of frequency-independent springs and dashpots is proposed to represent the foundation-soil dynamic system with strongly frequency-dependent impedance in time domain. Due to the convergence and robustness of the complex Chebyshev polynomial, it is used to approximate the dynamic flexibility of the foundation by least-square curve-fitting technique. The comparisons with existing LPMs show that the present model can express the impedance by using a small number of elements and reduce oscillation of the solution appearing in simple polynomial approximations. Finally, several examples of foundations with irregular geometries are presented to show the application of nested LPMs.

Simplified methods in Soil Dynamics

After a brief description of the main characteristics that define Soil Dynamics and its engineering applications, the role of Simplified Methods is discussed. Despite the current wide availability of powerful computer simulations, it is concluded that Simplified Methods will continue to play an important role in Soil Dynamics as they do in the rest of Geotechnical Engineering. Simplified Methods allow the engineer to conduct calculations by hand or with a minimum computational effort, including parametric variations. In the process, the engineer has the possibility to develop a feel for the physical meaning and relative importance of the various factors, with more personal control of calculations and decisions including use of engineering judgment as needed. A list of simplified procedures proposed by the author is provided, covering systems that range from the free field and earth dams to shallow and deep foundations, subjected to excitations that include both seismic shaking and machine vibrations. Basic understanding of the basic theory and simplifications behind the simplified procedure can be very helpful to engineers, including Dynamics and Wave Propagation concepts. Some of this understanding is developed in the paper, with focus on shallow machine foundations and other dynamic soil–structure interaction applications.The Lecture concentrates on shallow machine foundations on a half-space subjected to dynamic loads in any of the six degrees of freedom of the foundation, and the Simplified Methods that have been proposed over the years to characterize the corresponding equivalent soil springs and dashpots. This includes both frequency-dependent and frequency-independent springs and dashpots. It started with the circular surface foundation which was studied over much of the 20th Century, until the breakthroughs by Lysmer and others in 1966–1971, and continued with the cases of surface and embedded foundations of arbitrary shape that culminated in the two summary publications by Gazetas in 1990 and 1991. The development of these simplified equivalent springs and dashpots for both surface and embedded foundations of arbitrary shape is discussed in some detail, including the contribution of the author in the early part of the process.

Seismic response analysis of highway overcrossings including soil–structure interaction

AbstractThis paper presents a systematic procedure for the seismic response analysis of highway overcrossings. The study employs an elementary stick model and a more sophisticated finite element formulation to compute response quantities. All dynamic stiffnesses of approach embankments and pile groups are approximated with frequency‐independent springs and dashpots that have been established elsewhere. A real eigenvalue analysis confirms the one‐to‐one correspondence between modal characteristics obtained with the three‐dimensional finite element solutions and the result of the simpler stick‐model idealization. A complex eigenvalue analysis yields modal damping values in the first six modes of interest and shows that modal damping ratios assume values much higher than those used by Caltrans. The validity of the proposed method is examined by comparing the computed time response quantities with records from the Meloland Road and Painter Street overcrossings located in southern and northern California, respectively. The proposed procedure allows for inexpensive parametric analysis that examines the importance of considering soil–structure interaction at the end abutments and centre bent. Results and recommendations presented by past investigations are revisited and integrated in comprehensive tables that improve our understanding of the dynamic characteristics and behaviour of freeway overcrossings. The study concludes with a step‐by‐step methodology that allows for a simple, yet dependable dynamic analysis of freeway overcrossings, that involves a stick model and frequency‐independent springs and dashpots. Copyright © 2002 John Wiley & Sons, Ltd.

A hybrid time frequency domain formulation for non-linear soil-structure interaction

Methods that combine frequency and time domain techniques offer an attractive alternative for solving Soil-Structure-interaction problems where the structure exhibits non-linear behaviour. In the hybrid-frequency-time-domain procedure a reference linear system is solved in the frequency domain and the difference between the actual restoring forces and those in the linear model are treated as pseudo-forces. In the solution scheme explored in this paper, designated as the hybrid-time-frequency-domain (HTFD) procedure, the equations of motion are solved in the time domain with due consideration for non-linearities and with the unbounded medium represented by frequency-independent springs and dampers. The frequency dependency of the impedance coefficients is introduced by means of pseudo-forces evaluated in the frequency domain at the end of each iteration. A criterion of stability for the HTFD approach is derived analytically and its validity is sustained numerically. As is often the case, the criterion takes the form of a limit of unity on the spectral radius of an appropriately defined matrix. Inspection of the terms in this matrix shows that convergence can be guaranteed by suitable selection of the reference impedance. The CPU times required to obtain converged solutions with the HTFD are found, in a number of numerical simulations, to be up to one order of magnitude less than those required by the alternative hybrid-frequency-time-domain approach.

Discrete model for dynamic through-the-soil coupling of 3-D foundations and structures

An efficient discrete model for predicting the dynamic through-the-soil interaction between adjacent rigid, surface foundations supported by a homogeneous, isotropic and linear elastic half-space is presented. The model utilizes frequency-independent springs and dashpots, and the foundation mass, for the consideration of soil–foundation interaction. The through-the-soil coupling of the foundations is attained by frequency-independent stiffness and damping functions, developed in this work, that interconnect the degrees of freedom of the entire system of foundations. The dynamic analysis of the resulting coupled system is performed in the time domain and includes the time lagging effects of coupled dynamic input due to wave propagation using an appropriate modification of the Wilson-θ method. The basic foundation interaction model is also extended to the evaluation of coupled building-foundation systems. © 1998 John Wiley & Sons, Ltd.