SUMMARYAn important aspect of earthquake loads exerted on extended structures, or structures founded on several foundations, is the spatial variability of the seismic motion. Hence, a rigorous earthquake resistant design of lifeline structures should account for the spatial character of the seismic input, at least in an approximate way.A procedure is proposed which enables addressing the problem of multiply supported structures, subjected to imperfectly correlated seismic excitations, by means of an extension to the response spectrum method. A modified response spectrum model is developed for the design of extended facilities subjected to single and multicomponent ground motion. The modification procedure is based on adjusting each spectral value of the given design response spectrum by means of a correction factor, which depends on the structural properties and on the characteristics of the wave propagation phenomenon. Finally, the theoretical model is validated through digital simulation of seismic ground motion, whereby model predictions are found to be in good agreement with exact results.

In this paper, the Thin Layer Method (TLM) is adapted for solving one-dimensional primary consolidation problems. It is also combined with a stochastic formulation integrating Monte Carlo simulations to investigate primary consolidation of a random heterogeneous soil profile. This latter is modeled as a set of superposed layers extending horizontally to infinity, and having random properties. Spatial variability of soil properties is considered in the vertical direction only. Soil properties of interest are elastic modulus and soil permeability, modeled herein as spatially random fields. Lognormal distribution is chosen because it is suitable for strictly non-negative random variables, and enables analyzing the large variability of such properties. The statistics regarding final settlement and its corresponding time are investigated by performing a parametric study, which integrates the influence of variation coefficient of both elastic modulus and soil permeability, and vertical correlation length. Obtained results indicate that heterogeneity significantly influences primary consolidation of the soil profile, generating a quite different way of soil grain rearrangement and water pressure dissipation in comparison to the homogeneous case, and causing a delay in the consolidation process.

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SUMMARYThe spatial variability of seismic ground motion is an important aspect for the earthquake resistant design of extended facilities. A modified response spectrum model, which addresses the problem of multiply supported structures subjected to imperfectly correlated seismic excitations, has already been developed (see References 1 and 2). The present paper proposes a modal combination rule for the case of non-uniform seismic input, which would be used together with the modified response spectrum model in order to compute physical responses. This rule, which accounts for modal cross-correlations, is an extension to an existing rule for the case of uniform seismic motions. It modifies the existing modal cross-correlation coefficients through a correction factor which depends on structural properties and on the characteristics of the wave propagation phenomenon. Finally, some practical considerations on the theoretical development are addressed. They aim at suggesting reasonable simplifications which render the modal combination rule more appealing for engineering purposes. The proposed practical combination rule is validated through a numerical experiment which also characterizes the effect of non-uniform seismic input on modal cross-correlation.