Input ground motion and mechanical properties are the two main categories of data required for dynamic structural analysis and, as shown hereafter, are both probabilistic entities.

The characteristics of seismic ground motion at a specific location (e.g. frequency content, amplitude) are mainly governed by (1) distance from the seismic source, (2) local soil conditions, and (3) magnitude of the event. As a consequence of wave propagation and loss of coherence, there is a certain spatial variation of seismic ground motion from one location to another. To this end, the earthquake ground motion over the domain of interest can be described by a non-stationary stochastic vector process with evolutionary power, each component of the vector process representing the motion at a certain spatial location (e.g. Deodatis (1996)).

Many physical systems in
general and soil materials in particular
exhibit relatively large variability in their properties,
even within so called homogeneous zones.
Deterministic descriptions of this spatial variability are not feasible
due to prohibitive cost of sampling and to uncertainties induced by
measurement errors.
A more rational approach to geotechnical design is made possible by use
of stochastic field based techniques of data analysis, which
rely more on analytical methods when
dealing with various uncertainties related to soil properties.
The relevant material properties over the
analysis domain can be modeled as a multi-variate, multi-dimensional
(*m*V-*n*D), non-Gaussian stochastic field

(e.g. Popescu (1995)).

The integrated procedure for fault-soil-structure system analysis presented in the following (Fig. 1) is intended for case studies related to the analysis of ground motion, assessment of soil liquefaction, and prediction of seismic response of buildings, bridges and underground structures. The statistics of the structural response are obtained by performing Monte Carlo simulations consisting of digital generation of ground motion and sample vector fields of soil material parameters, combined with nonlinear dynamic finite element analyses.

**Figure 1:** Flow chart of the integrated procedure for
fault-soil-structure analysis (**for a larger image click
here** - 26K).