We present a set of ground motion prediction equations (GMPEs) derived for the geometrical mean of the horizontal components and the vertical, considering the latest release of the strong motion database for Italy. The regressions are performed over the magnitude range 4 -6.9 and considering distances up to 200 km. The equations are derived for peak ground acceleration (PGA), peak ground velocity (PGV) and 5%-damped spectral acceleration at periods between 0.04 and 2 s. The total standard deviation (sigma) varies between 0.34 and 0.38 log 10 unit, confirming the large variability of ground shaking parameters when regional data sets containing small to moderate magnitude events (M < 6) are used. The between-stations variability provides the largest values for periods shorter than 0.2 s while, for longer periods, the between-events and between-stations distributions of error provide similar contribution to the total variability.

The increasing interest in performance-based earthquake engineering has promoted research on the improvement of hazard-consistent seismic input definition and on advanced criteria for strong motion record selection to perform nonlinear time history analyses. Within the ongoing research activities to improve the representation of seismic actions and to develop tools as a support for engineering practice, this study addresses the selection of displacement-spectrum-compatible real ground motions, with special reference to Italy. This involved (1) the definition of specific target displacement spectra for Italian sites, constrained—both at long and short periods—by results of probabilistic seismic hazard analyses; (2) the compilation of a high-quality strong ground motion database; and (3) the development of a software tool for computer-aided displacement-based record selection. Application examples show that sets of unscaled, or lightly scaled, accelerograms with limited record-to-record spectral variability can also easily be obtained when a broadband spectral compatibility is required.

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SUMMARYThe problem of ampliÿcation of seismic waves by surface topographic irregularities is addressed through analytical and numerical investigations. First, a closed-form expression for estimating the fundamental vibration frequency of homogeneous triangular mountains is obtained, using Rayleigh's method. Subsequently, numerical modelling based on the spectral element approximation is used to study the 3D seismic response of several real steep topographic irregularities excited by vertically propagating plane S-waves. A topographic ampliÿcation factor is obtained for each case, by a suitable average of the ratio of acceleration response spectra of output vs input motion. The 3D ampliÿcation factors are then compared with those derived by 2D analyses as well as with the topographic factors recommended in Eurocode 8 for seismic design.

SUMMARYThe capability of a simplified approach to model the behaviour of shallow foundations during earthquakes is explored by numerical simulation of a series of shaking table tests performed at the Public Works Research Institute, Tsukuba, Japan. After a summary of the experimental work, the numerical model is introduced, where the whole soil-foundation system is represented by a multi-degrees-of-freedom elastoplastic macro-element, supporting a single degree-of-freedom superstructure. In spite of its simplicity and of the large intensity of the excitation involving a high degree of nonlinearity in the foundation response, the proposed approach is found to provide very satisfactory results in predicting the rocking behaviour of the system and the seismic actions transmitted to the superstructure. The agreement is further improved by introducing a simple degradation rule of the foundation stiffness parameters, suitable to capture even some minor details of the observed rocking response. On the other hand, the performance of the model is not fully satisfactory in predicting vertical settlements.

Stimulated by the recent advances in computational tools for the simulation of seismic wave propagation problems in realistic geologic environments, this paper presents a 3D physics-based numerical study on the prediction of earthquake ground motion in the Po Plain, with reference to the M W 6.0 May 29 2012 earthquake. To respond to the validation objectives aimed at reproducing with a reasonable accuracy some of the most peculiar features of the near-source strong motion records and of the damage distribution, this study required a sequence of investigations, starting from the analysis of a nearly unprecedented set of near-source records, to the calibration of an improved kinematic seismic source model, up to the development of a 3D numerical model of the portion of the Po Plain interested by the earthquake, including the irregular buried morphology, with sediment thickness varying from few tens of m to some km. The spatial resolution of the numerical model is suitable to propagate up to about 1.5 Hz. Numerical simulations were performed using the open-source highperformance code SPEED, based on the Discontinuous Galerkin Spectral Elements (DGSE) method. The 3D numerical model coupled with the updated slip distribution along the rupturing fault proved successful to reproduce with reasonable accuracy, measured through quantitative goodness-offit criteria, the most relevant features of the observed ground motion both at the near-and far-field scales. These include: (i) the large fault normal velocity peaks at the near-source stations driven by up-dip directivity effects; (ii) the small-scale variability at short distance from the source, resulting in the out-of-phase motion at stations separated by only 3 km distance; (iii) the propagation of prominent trains of surface waves, especially in the Northern direction, induced by the irregular buried morphology in the near-source area; (iv) the map of earthquake-induced ground uplift with maximum values of about 10 cm, in substantial agreement with satellite measurements; and (v) the two-lobed pattern of the peak ground velocity map, well correlated with the distribution of macroseismic intensity.

Using selected sets of high-quality digital strong motion data from different regions (Taiwan, Japan, Italy, and Greece), the salient features of displacement response spectra in the long-period range are illustrated (up to 10 s period) as a function of magnitude, source distance, and site conditions. By means of simple analytical models of displacement waveforms, we have derived analytical expressions for the displacement spectra that provide satisfactory fits to the observations. These expressions also demonstrate that the moment magnitude and distance control the shape of the spectra consistent with the commonly accepted models of the seismic source. Furthermore, we derived from simple physical considerations an analytical expression of the variation of peak ground displacement with magnitude and distance that reasonably fits the observations. The findings of this study are believed to be particularly useful in the formulation of design elastic displacement spectra for seismic codes, and in zoning studies of seismic hazard for long-period structures.

SUMMARYIn this paper, different formulations of a macro-element model for non-linear dynamic soil-structure interaction analyses of structures lying on shallow foundations are first reviewed, and secondly, a novel formulation is introduced, which combines some of the characteristics of previous approaches with several additional features. This macro-element allows one to model soil-footing geometric (uplift) and material (soil plasticity) non-linearities that are coupled through a stiffness degradation model. Footing uplift is introduced by a simple non-linear elastic model based on the concept of effective foundation width, whereas soil plasticity is treated by means of a bounding surface approach in which a vertical load mapping rule is implemented. This mapping is particularly suited for the seismic loading case for which the proposed model has been conceived. The new macro-element is subsequently validated using cyclic and dynamic large-scale laboratory tests of shallow foundations on dense sand, namely: the TRISEE cyclic tests, the Public Works Research Institute and CAMUS IV shaking table tests. Based on this comprehensive validation process against a set of independent experimental results, a unique set of macro-element parameters for shallow foundations on dense sand is proposed, which can be used to perform predictive analyses by means of the present model.