Autocorrelation

Random field

Pure mathematics

Statistics

Geotechnical engineering

Field (mathematics)

Probabilistic logic

Stability (learning theory)

Stratum

Computer science

Geology

Spatial analysis

Mathematics

Remote sensing

Monte Carlo method

Machine learning

Borehole

Computers and Geotechnics

Due to the complexity and inherent spatial variability of the strata and the limited availability of borehole information, the subsurface stratigraphic configuration at a site is hard to characterize accurately, which gives rise to stratigraphic uncertainty. This paper presents a random field-based approach for modelling the stratigraphic uncertainty, in which, the spatial correlation of the stratum existence between different subsurface elements is characterized by an autocorrelation function, and the probability of the existence of a particular stratum in a given non-borehole element is determined according to the derived spatial correlations. With the existence probabilities calculated, Monte Carlo simulation (MCS) is used for sampling the possible realizations of the stratigraphic configuration. The number of the MCS samples is determined based upon an information entropy analysis. To illustrate the effectiveness of this new approach, a set of hypothetical examples (with different stratigraphic settings) are studied; and, the advantages of this new approach over the existing stratigraphic uncertainty modelling approaches are depicted through a comparative analysis. Finally, this new approach is applied to Majiagou Landslide for a probabilistic stability analysis. The influences of the stratigraphic uncertainty on the stability of this landslide and the location of the slip surface are revealed.

Stratigraphic uncertainty modelling with random field approach