Conditional simulation for characterising the spatial variability of sand state

Abstract

Properties of soils are spatially variable and to describe the behaviour of soils as a response to loading, this variability appears crucial in giving the correct range of possible solutions for structure response. Because site investigation techniques only provide exact information at a limited part of the site, random field simulations are used to assess this variability over the full test site domain. The random fields use the spatial statistical characteristics that are derived from the site investigation, which in geotechnical application mainly consists of cone penetration tests (CPT’s). To reduce the range of possible solutions to be found for structure response analysis, the random fields can be conditioned by the actual CPT measurements. This report describes the conditioning of the random field in order to generate conditioned simulations of sand state fields. In order to derive the state parameter from the CPT tip resistance, the NorSand constitutive model is calibrated against the results of 55 triaxial tests of the test site. Different methods of calibration using triaxial test data are described and the results are discussed. 140 CPT’s of the test site are then transformed into state parameter profiles. The statistical characteristics of the profiles are determined to be used for the simulation of the spatially variable fields of sand state. The statistical characteristics of the profiles are used in the conditional simulation of the fields. A conditional simulation algorithm to generate realisations of spatially variable sand state fields is derived and demonstrated. Using unconditioned random fields, generated with the Local Average Subdivision (LAS) method, conditioned simulations of the field around the CPT profiles are generated in a post-processing algorithm. The algorithm uses the geometry-dependent property of the kriging estimation error for the exchange of noise terms between estimation fields. The specific properties of the kriging estimator are demonstrated to be suitable to be used for the conditioning. The decrease in uncertainty by the conditioning with respect to the unconditioned random fields is presented. This decrease in uncertainty is used to demonstrate that the effectiveness of the conditioning is a function of the number and location of conditioning points relative to the scales of fluctuation of the field. It is demonstrated that conditioning reduces the range of possible solutions for the simulation of sand state fields with respect to unconditioned fields. This reduction will lead to a smaller range of solutions to be found when the conditional simulations are used in structure response analysis, leading to less uncertainty in design. The conditional simulation is shown to produce fields that honour the initial distribution function, the correlation structure and the actual CPT profiles in the simulated fields. To demonstrate that conditional simulation can be applied on the test site, a stochastic characterisation of the test site is performed and conditional simulations of the state parameter fields are generated for a small part of the test site.