Probabilistic analyses of slopes and footings with spatially variable soils considering cross-correlation and conditioned random field

M. K. Lo, Yat Fai Leung

Research output: Journal article publicationJournal articleAcademic researchpeer-review

27 Citations (Scopus)


This paper presents probabilistic analyses of slopes and strip footings, with spatially variable soil modeled by the random field theory. Random fields are simulated using Latin hypercube sampling with dependence (LHSD), which is a stratified sampling technique that preserves the spatial autocorrelation characteristics. Latin hypercube sampling with dependence is coupled with polynomial chaos expansion (PCE) to approximate the probability density function of model response. The LHSD-PCE approach is applied to probabilistic slope analyses for soils with cross-correlated shear strength parameters, and is shown to be more robust than raw Monte Carlo simulations, even with much smaller numbers of model simulations. The approach is then applied to strip footing analyses with conditioned random fields of Young's modulus and shear strength parameters, to quantify the reductions in settlement uncertainty when soil samples are available at different depths underneath the footing. The most influential sampling depth is found to vary between 0.25 and 1 times the footing width, depending on the strength mobilization and spatial correlation features. Design charts are established with practical guidelines for quick estimations of uncertainty in footing settlements.
Original languageEnglish
Article number04017044
JournalJournal of Geotechnical and Geoenvironmental Engineering
Issue number9
Publication statusPublished - 1 Sep 2017


  • Conditioned random field
  • Probabilistic analyses
  • Sampling location
  • Shallow foundation
  • Slope stability

ASJC Scopus subject areas

  • Environmental Science(all)
  • Geotechnical Engineering and Engineering Geology

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