Elastic halfspace under impulsive, distributed, vertical loading at the surface: exact solution at the center for a punch-like distribution

The exact analytical solution for the vertical displacement at the center of the surface of an elastic half space under an impulsive loading having the same spatial distribution as the contact stresses arising underneath a smooth, rigid disk when subjected to a static, vertical load, is obtained using Eason's method. The solution can be used to study the dynamical interaction and contact problems between soil and structures and can also be used to assess numerical computations with a finite element or boundary element program.     

Vibrations of square and circular foundations with concentric openings on elastic half space

A study on the dynamic characteristics of rigid foundations with special geometries such as square or circular with concentric internal holes, is presented. The foundations are resting on a homogeneous, linear elastic halfspace and are subjected to external forces or seismic wave excitation. Both ‘relaxed’ and ‘non-relaxed’ boundary conditions at the interface between the foundation and the halfspace are considered, and several parametric studies are conducted to assess the influence of either type of boundary conditions upon each of the possible modes of vibration. Results for massive and massless foundations are presented in time and frequency domains for impulsive and harmonic excitations, respectively. A time domain boundary element method (BEM) developed by the authors for the solution of a class of 3-D soil-structure interaction (SSI) problems is used for all the analyses reported in this work. The accuracy and efficiency of the method and the BEM models developed in this work are assessed on the basis of comparison studies with published results.     

Analytical solution for frequency response of equipment in laterally loaded multistorey buildings

An analytical and closed-form frequency response of equipment mounted on multistorey buildings subjected to horizontal ground motion is proposed. In this study, the dynamics of the equipment and the building is expressed as a state-flow graph model, in which the interaction effect between the equipment and the building is considered. Based on the graph model, the analytical results for the frequency response of the acceleration of the equipment and the internal force in the support are derived. One of the advantages of this method is that the closed-form solutions of the frequency response expressed by polynomial form will be easily examined by analytical and numerical computations without complex operation. Moreover, the dynamic of the primary and secondary systems and their dynamic interaction are expressed separately in the derived formula. Thus most of the items in the formula need not be computed repeatedly for different supports of the equipment in design. Copyright © 1999 John Wiley & Sons, Ltd.     

Effects of the dynamic cross-interaction in the seismic analysis of multiple embedded foundations

A boundary element formulation of the substructure deletion method is presented for the seismic analysis of the dynamic cross-interaction between multiple embedded foundations. This approach is particularly suitable for three-dimensional foundations of any arbitrary geometrical shape and spatial location, since it requires only the discretization of the foundations’ surfaces. The surrounding soil is represented by a homogeneous viscoelastic half-space while the foundations are assumed to be rigid and subjected to incoming SH-, P-, and SV-waves arbitrarily inclined in both the horizontal and vertical planes. The proposed methodology is tested for the case of two identical embedded square foundations for different values of the foundations’ embedment and distance. The effects of the cross-interaction are outlined in the components of the impedance matrix and of the foundation input motion. © 1997 John Wiley & Sons, Ltd.     

Seismic response of a bridge–soil–foundation system under the combined effect of vertical and horizontal ground motions

Different levels of model sophistication have recently emerged to support seismic risk assessment of bridges, but mostly at the expense of neglecting the influence of vertical ground motions (VGMs). In this paper, the influence of VGMs on bridge seismic response is presented and the results are compared with the case of horizontal‐only excitations. An advanced finite element model that accounts for VGMs is first developed. Then, to investigate the effect of soil–structure interaction (SSI) including liquefaction potential, the same bridge with soil‐foundation and fixed boundary conditions is also analyzed. Results show that the inclusion of the VGMs has a significant influence on the seismic response, especially for the axial force in columns, normal force of bearings, and the vertical deck bending moments. However, VGMs do not have as much influence on the seismic demand of the pile cap displacements or pile maximum axial forces. Also, the significant fluctuation of the column axial force can reduce its shear and flexural capacity, and a heightened reversal of flexural effects may induce damage in the deck. In addition, relative to the fixed base case, SSI effects tend to reduce response quantities for certain ground motions while increasing demands for others. This phenomenon is explained as a function of the frequency content of the ground motions, the shift in natural vertical periods, and the VGM spectral accelerations at higher modes. Moreover, the mechanisms of liquefaction are isolated relative to SSI effects in nonliquefiable soils, revealing the influence of liquefaction on bridge response under VGMs. Copyright © 2012 John Wiley & Sons, Ltd.