On Probability in Geotechnics. Random Calculation Models Exemplified on Slope Stability Analysis and Ground-Superstructure Interaction

Doctoral thesis, 1998

The thesis deals with uncertainty in calculation modelling. Emphasis is put on the design state. Design is a chain of decisions under uncertainty. A probabilistic approach is used to describe the uncertainty and calculations as a way to reveal the uncertainty. Thus, a calculation method becomes an operative tool in a risk analysis, not merely a verification of a prescribed minimum level. The work is a combination of elements from three different academic disciplines; geotechnics, structural mechanics and statistics. Different aspects from two fields of geotechnical modelling are discussed; slope stability as an example of ultimate limit state problems, and interaction ground /superstructure as an example of serviceability limit state problems. For the mathematical solution different algorithms are used; mathematical analysis, point estimate method, Monte-Carlo simulation and reliability analysis. Soil properties are described as random variables. Different uncertainties are accounted for; natural variations, systematic testing errors, random testing errors and errors due to limited testing. Pre-knowledge and test results are combined systematically using Bayesian statistics. Three different levels of complexity of both slope stability analysis and ground/superstructure interaction are given. In both cases, structural models of the soil are given for the third level. For a slope a constant degree of mobilisation is not a prerequisite. Instead the deformation properties of the soil are considered. In the interaction analysis the soil is described as a continuous shear beam on elastic supports. The structural model of the soil can be calibrated against a more rigorous geotechnical model. To determine volumetric creep deformations in clay a simple creep model is presented, in which the soil deformations can be determined as a sum of elastic/plastic deformations and creep deformations.