Evaluation of predictors of non‐linear seismic demands using ‘fishbone’ models of SMRF buildings

Predictors (or estimates) of seismic structural demands that are less computationally time‐consuming than non‐linear dynamic analysis can be useful for structural performance assessment and for design. In this paper, we evaluate the bias and precision of predictors that make use of, at most, (i) elastic modal vibration properties of the given structure, (ii) the results of a non‐linear static pushover analysis of the structure, and (iii) elastic and inelastic single‐degree‐of‐freedom time‐history analyses for the specified ground motion record. The main predictor of interest is an extension of first‐mode elastic spectral acceleration that additionally takes into account both the second‐mode contribution to (elastic) structural response and the effects of inelasticity. This predictor is evaluated with respect to non‐linear dynamic analysis results for ‘fishbone’ models of steel moment‐resisting frame (SMRF) buildings. The relatively small number of degrees of freedom for each fishbone model allows us to consider several short‐to‐long period buildings and numerous near‐ and far‐field earthquake ground motions of interest in both Japan and the U.S. Before doing so, though, we verify that estimates of the bias and precision of the predictor obtained using fishbone models are effectively equivalent to those based on typical ‘full‐frame’ models of the same buildings. Copyright © 2003 John Wiley & Sons, Ltd.     

Assessment of predictions of the response of the Hualien containment model during forced vibration tests

Blind predictions for the response of the 1/4-scale reinforced concrete Hualien (Taiwan) containment model during forced vibration tests are compared with the observed data. The predictions obtained by the CLASSI approach reflect the experimental conditions prior to and after backfill of the soil surrounding the embedded foundation. The experimental data show a strong and unexpected coupling between the response in the NS and EW directions which is not present in the results for the axisymmetric theoretical models. Also, significant differences can be seen between the experimental responses in the two orthogonal horizontal directions which minimize cross-axis coupling. Although these differences are not accounted for in the theoretical models, the discrepancies between predictions and observations are within the uncertainty of the structural and geotechnical data. The obtained differences between predictions and observations give an excellent measure of the prediction error that can be expected in this type of analysis from uncertainty in the data. A detailed assessment of the initial structural and geotechnical data based on extensive comparisons with the results of previous identification studies is also presented. Finally, comparisons between the observed response and calculations based on revised models for the structure and the soil show that current methods of analysis can account accurately for the observed response.     

Dynamic displacements and stresses in the vicinity of a cylindrical cavity embedded in a half-space

The two-dimensional response of a viscoelastic half-space containing a buried, unlined, infinitely long cylindrical cavity of circular cross-section subjected to harmonic plane SH, P, SV and Rayleigh waves is obtained by an indirect boundary integral method based on the two-dimensional Green's functions for a viscoelastic half-space. An extensive critical review of the existing numerical results obtained by other techniques is presented together with some new numerical results describing the motion on the ground surface and the motion and stresses on the wall of the cavity for P, SV, SH and Rayleigh waves.     

Seismic response of a cylindrical shell embedded in a layered viscoelastic half-space. I: Formulation

A method to obtain the three-dimensional harmonic response of a infinitely long cylindrical shell of circular cross-section embedded in a layered viscoelastic half-space and subjected to harmonic plane waves impinging at an oblique angle with respect to the axis of the shell is presented. The procedure combines an indirect integral representation for the field in the exterior half-space with a model of the pipeline or tunnel based on Donnell shell theory. The integral representation for the soil is based on the use of moving Green's functions for the layered viscoelastic half-space. The accuracy of the formulation is tested by comparison of results obtained by using different discretizations. Extensive comparisons with previous two- and three-dimensional results for the case of a shell embedded in a uniform half-space and some new numerical results for a shell embedded in a multilayered half-space are presented in a companion paper.     

Seismic response of a cylindrical shell embedded in a layered viscoelastic half-space. II: Validation and numerical results

A procedure to calculate the three-dimensional harmonic response of a infinitely long cylindrical shell of circular cross-section embedded in a layered viscoelastic half-space and subjected to harmonic plane waves impinging at an oblique angle with respect to the axis of the shell is validated by extensive comparisons with previous two- and three-dimensional results for the particular case of a shell embedded in a uniform half-space. New numerical results describing the motion and stresses within a shell embedded in a multilayered half-space and subjected to obliquely incident P-, SV- and SH-waves with different horizontal angles of incidence are presented and discussed.     

Discrete models for vertical vibrations of surface and embedded foundations

A five-parameter discrete model that approximates the dynamic force4isplacement relationship for rigid foundations undergoing vertical vibrations on a uniform elastic half-space is presented. The model involves a combination of two springs, two viscous dampers and a mass. Values of the parameters for circular, square and rectangular foundations placed on the surface or embedded in an elastic half-space are listed. The parameters are obtained by minimizing the discrepancy between the force4isplacement relation for the model and that obtained by solution of the mixed boundary-value problem of the rigid foundation on an elastic half-space. The definition of an appropriate input motion to represent wave excitation is also discussed. The input motion to the discrete model differs from the input motion that should be used in a continuum model.     

Response of a circular foundation on a uniform half-space to elastic waves

An alternative technique to obtain the dynamic response of a massless rigid circular foundation resting on a uniform elastic half-space when subjected to harmonic plane waves is presented. The technique relies on the use of an integral representation involving the free-field ground motion and the contact tractions obtained in the course of calculating the dynamic force–displacement relationship of the foundation for external forces. Tables listing the translational and rotational components of the response of the foundation for non-vertically incident SH, P, SV and Rayleigh waves are presented.     

Active control of the seismic response of structures by combined use of base isolation and absorbing boundaries

The relative advantages of several control strategies to reduce the seismic response of multi-storey structures are studied. The strategies involve the separate or combined use of passive base isolation mechanisms and active control forces. The base isolation mechanism is modelled as an equivalent linear soft storey with high damping. The active control forces are selected so that an absorbing boundary is obtained at the top of the structure and non-reflecting or reflecting boundaries are obtained at the base of the building. It is found that the best results are obtained when a passive base isolation system is combined with an active absorbing boundary placed at the top of the building. However, the incremental gains resulting from adding a base isolation system to a structure already controlled by a roof-top active absorbing boundary are significant only for relatively soft base isolation systems. Also, the incremental gains appear to decrease as the number of storeys of the structure increases.     

Dynamic response of rigid foundations of arbitrary shape

An approximate numerical procedure for calculation of the harmonic force-displacement relationships for a rigid foundation of arbitrary shape placed on an elastic half-space is presented. This procedure is used to evaluate the vertical, rocking and horizontal compliance functions for rigid rectangular foundations and the vertical compliance for a rigid square foundation with an internal hole. Several comparisons between the results obtained by the proposed approach and other methods are also presented.     

Contact stresses and ground motion generated by soil-structure interaction

A study has been made of the dynamic contact stresses that the foundation of a nine-storey reinforced concrete building exerts on the soil during forced vibration tests. The effects of the flexibility of the foundation on the contact stress distribution and on the force-displacement relationship for the foundation have been examined in an attempt at testing several simplifying assumptions commonly used in soil-structure interaction studies. Comparisons of calculated and observed ground displacements induced by soil-structure interaction in the immediate neighbourhood of the building have also been presented.