It is well recognised that the dynamic interaction between structure, foundation and supporting soil can affect significantly the seismic behaviour of buildings. Among other effects, embedded and deep foundations can filter the seismic excitation, causing the foundation input motion (FIM) to differ substantially from the free-field motion. This paper presents a theoretical and numerical investigation on the filtering effect induced by rigid massless embedded foundations. Based on the results of dimensional analysis and numerical simulations, it is shown that the problem can be reasonably described by two sole dimensionless groups, namely: (i) H/VS, relating the wave length of the signal to the embedment depth of the foundation, and (ii) the aspect ratio of the foundation, B/H, where B is the foundation width in the polarization plane. New simplified and physically sound expressions are derived for the kinematic interaction factors, = uFIM/uff0 and = FIMH/uff0, which are frequencydependent transfer functions relating the harmonic steady-state motion experienced by the foundation to the amplitude of the corresponding free-field surface motion. Standard methods for using these functions in the evaluation of the FIM are critically reviewed, with reference to both static and dynamic procedures for the seismic design of structures.

This paper describes an experimental investigation of the behaviour of embedded retaining walls under seismic actions. Nine centrifuge tests were carried out on reduced-scale models of pairs of retaining walls in dry sand, either cantilevered or with one level of props near the top. The experimental data indicate that, for maximum accelerations that are smaller than the critical limit equilibrium value, the retaining walls experience significant permanent displacements under increasing structural loads, whereas for larger accelerations the walls rotate under constant internal forces. The critical acceleration at which the walls start to rotate increases with increasing maximum acceleration. No significant displacements are measured if the current earthquake is less severe than earthquakes previously experienced by the wall. The increase of critical acceleration is explained in terms of redistribution of earth pressures and progressive mobilisation of the passive strength in front of the wall. The experimental data for cantilevered retaining walls indicate that the permanent displacements of the wall can be reasonably predicted adopting a Newmark-type calculation with a critical acceleration that is a fraction of the limit equilibrium value.

1Some remarks on the seismic behaviour of embedded cantilevered retaining walls R. CO NTI Ã , G . M. B. V IGGIANI † and F. B URALI D 'AREZZO ‡ This paper is a numerical investigation of the physical phenomena that control the dynamic behaviour of embedded cantilevered retaining walls. Recent experimental observations obtained from centrifuge tests have shown that embedded cantilevered retaining walls experience permanent displacements even before the acceleration reaches its critical value, corresponding to full mobilisation of the soil strength. The motivation for this work stems from the need to incorporate these observations in simplified design procedures. A parametric study was carried out on a pair of embedded cantilevered walls in dry sand, subjected to real earthquakes scaled at different values of the maximum acceleration. The results of these analyses indicate that, for the geotechnical design of the wall, the equivalent acceleration to be used in pseudo-static calculations can be related to the maximum displacement that the structure can sustain, and can be larger than the maximum acceleration expected at the site. For the structural design of the wall, it is suggested that the maximum bending moments of the wall can be computed using a realistic distribution of contact stress and a conservative value of the pseudostatic acceleration, taking into account two-dimensional amplification effects near the walls.

Summary This paper deals with the effect of the foundation mass on the filtering action exerted by embedded foundations. The system under examination comprises a rigid rectangular foundation embedded in a homogeneous isotropic viscoelastic half‐space under harmonic shear waves propagating vertically. The problem is addressed both theoretically and numerically by means of a hybrid approach, where the foundation mass is explicitly included in the kinematic interaction between the foundation and the surrounding soil, thus referring to a “quasi‐kinematic” interaction problem. Based on the results of an extensive parametric study, it is shown that the filtering problem depends essentially on three dimensionless parameters, i.e.: the dimensionless frequency of the input motion, the foundation width‐to‐embedment depth ratio, and the foundation‐to‐soil mass density ratio. In complements to the translational and rotational kinematic interaction factors that are commonly adopted to quantify the filtering effect of rigid massless foundations on the free‐field motion, an additional kinematic interaction factor is introduced, referring to the horizontal motion at the top of a rigid massive foundation. New analytical expressions for the above kinematic interaction factors are proposed and compared with foundation‐to‐free‐field transfer functions computed from available earthquake recordings on two instrumented buildings in LA (California) and Thessaloniki (Greece). Results indicate that the foundation mass can have a strong beneficial effect on the filtering action with increasing foundation‐to‐soil mass density and foundation width‐to‐embedment depth ratios.

Soil-structure interaction (SSI) phenomena are typically studied in the frequency-domain using the substructure approach, involving several simplifications. In this study, SSI effects for a 20-storey building are studied numerically performing time-domain 3D non-linear dynamic analyses, using an elastoplastic nonlinear constitutive model for the soil. Three foundation systems-a relatively shallow, a deeply embedded and a pile foundation-and two soil profiles are investigated and compared. Specifically, relative merits of site amplification, kinematic interaction and inertial interaction are isolated, and the role of foundation deformability and local stratigraphy is highlighted. To isolate such features, the results of the complete 3D models are compared with those provided by 3D numerical analyses of the sole building, of the foundation-soil systems and of the free-field soil deposit. Numerical results show that, for tall buildings, an increase in foundation deformability leads to a decrease of the maximum base shear force (seismic demand), to a higher rigid rotation of the foundation, but not to appreciably higher displacements of the structure. Moreover, possible situations where a (decoupled) substructure approach can lead to a misinterpretation of SSI phenomena are highlighted, as in the case of deep foundations crossing very soft soil layers. In addition, the use of embedded pile elements was proven to be an effective strategy in reducing the computational cost when performing complex 3D simulations of dynamic SSI problems.