Managing Geotechnical Uncertainty With Simulation Models: An Introduction

Burt G. Look

In a standard deterministic analysis discrete scenarios are considered, and a moderately conservative “characteristic” value is used as a design basis. However, fixed or exact values in a real-world geotechnical site seldom occurs. Deterministic approaches may not explicitly consider the ground uncertainty. Simulations using various probabilities provides for this uncertainty as each parameter input is treated as a random variable within certain measured ranges or ability to evaluate. Monte Carlo (MC) sampling is a traditional technique for generating random numbers to sample from a probability distribution. When low probability events occur, a small number of MC iterations might not sample sufficient quantities of these outcomes for inclusion in the simulation model. Latin Hypercube (LH) sampling uses stratification of the input probability distributions, to overcome the limitations of Monte Carlo sampling. The simulation results show low probability outcomes are included in the sampling for the simulation model. At a high number of simulation iterations both provide similar outputs, but at low simulation iterations the LH is more reliable. However, both the MC and LH sampling suffer from impractical values at low or high probability events when the normal probability density function (PDF) is adopted. The normal PDF is commonly used in statistical modelling. Non-normal PDFs often represent the best fit PDF when a goodness of fit test is carried out. The errors associated with using the common normal PDF are shown with the above-mentioned simulation models. This best fit PDF applies whether simulation models as described above is used or even with simple “what if” sensitivity models in traditional analysis.