Efficient random field modeling of soil deposits properties

The autocorrelation function (ACF) of the soil profile in some sites in Shandong province, China is studied using cone penetration test (CPT) data. This is done in the context of a random field modeling of the soil deposits. It is found that the different types of soil profile have different stochastic parameters, and there is no obvious trend along the depth of the soil profile. Thus, the soil profile is examined within each layer. Numerical values for three existing analytical (ACF) models are derived by the least squares fitting approach for the different types of soil. Further, comparisons of the autocorrelation function between the tip resistance and sleeve friction were examined. Based on the autocorrelation data analysis, a new autocorrelation model, named linear-exponential-cosine (LNCS), is considered with differentiability at the origin of the spatial lag axis, and alternating sign along this axis. For all of the four ACF models, a related integral equation is numerically solved for determining the associated Karhunen-Loeve (K-L) representation. In this regard, it is noted that the new model is not only more physics-consistent, but also yields quite good computational efficiency. In the end, the random field of the soil profile is modeled using a two-dimensional K-L expansion with the new model, assuming separability in two dimensions.