Using Conditional Random Fields for a Spatially Variable Liquefiable Foundation Layer in Nonlinear Dynamic Analyses of Embankments

Two-dimensional nonlinear dynamic analyses (NDAs) are performed for a series of hypothetical embankment dams on a spatially variable liquefiable foundation layer to evaluate the utility of representing the foundation layer with random fields conditioned on different levels of site characterization information. A set of two-dimensional parent models (PMs), each representing a true foundation condition, were generated using unconditional random fields of equivalent clean sand, corrected standard penetration test (N1)60cs values. Different levels of site characterization were then represented by combining different numbers of local borings (i.e., columns of data from the PM) with the optional inclusion of constraints on the geostatistical properties that might come from sitewide explorations. NDAs were performed using the same input motions for the PM (which represents perfect knowledge of soil conditions), a set of realizations conditioned on the local borings alone, and a set of realizations conditioned on the local borings with sitewide statistics. Embankment deformations obtained for the conditional realizations are compared to those for the PM to evaluate the potential benefits of increasing levels of site characterization in terms of deformation prediction accuracy. Parametric analyses include varying the embankment size, scales of fluctuation in the foundation stratum, number of conditioning borings, and ground motions. The results of these comparisons illustrate that the beneficial effects of using conditional random fields were generally limited to cases with the horizontal scale of fluctuation approaching the scale of the embankment base width and to cases with a large number of borings (more than three borings per horizontal scale of fluctuation), which may not be practical in many situations. Additional potential benefits and limitations of using conditional random fields for representing spatial variable liquefiable foundation layers in embankment dam NDAs are discussed