On characterizing spatially variable soil Young's modulus using spatial average

The purpose of this study is to investigate whether the effective Young's modulus (Eeff) for a spatial variable soil mass can be strongly correlated to any spatial average. The spatially variable Young's modulus of the soil mass is modeled as a stationary lognormal random field, and the Eeff of the soil mass is simulated by random field finite element analysis. Spatial averages are calculated from the input random field. If a strong correlation exists, it is possible to replace a random field analysis by a simpler random variable analysis. Two classes of problems are considered: a soil cube subjected to displacement-controlled compression and a footing problem. For the soil cube problem, Eeff is found to be strongly correlated to a suitable spatial average. However, for the footing problem, only the statistics (mean and standard deviation) of Eeff can be well approximated by a suitable spatial average, but the correlation is not strong. It is possible that the two classes of problems behave differently because the finite elements in the soil cube are mobilized uniformly, whereas those in the footing problem are mobilized non-uniformly. This leads to a weighted spatial average model that applies a different weight on the log modulus of each finite element over the domain being averaged.