Spatial variability of soil properties is inherent in soil deposits, whether as a result of natural geological processes or engineering construction. It is therefore important to account for soil variability in geotechnical design in order to represent more realistically a soil's in situ state. This variability may be modelled as a random field, with a given probability density function and scale of fluctuation. A more convenient way to deal with the uncertainty of a soil property due to spatial variability, by constraining the generated random field at the locations of actual field measurements, is presented in this article. Conditioning the random field at known locations is a powerful tool, not only because it more accurately represents the observed variability on site, but also because it uses the available field information more efficiently. In situ cone penetration test (CPT) data from a particular test site are used to determine the input statistics for generating random fields, which are later constrained (conditioned) at the locations of actual CPT measurements using the Kriging interpolation method. The results from the conditional random fields are then analysed, to quantify how the number of field measurements used influences the reduction of uncertainty. It is shown that the spatial uncertainty relative to the original (unconditional) random field reduces with the number of CPTs used in the conditioning.
Variability in spatial distribution of mineral phases in the Lower Bowland Shale, UK, from the mm-to m-scale: quantitative characterization and modelling. Marine and Petroleum Geology.
A case study involving the assessment and re-design of an existing dyke, founded on a layered soil, has compared deterministic analysis based on 5-percentile property values and a reliability-based random finite element analysis consistent with the requirements of Eurocode 7. The results show that a consideration of the spatial nature of soil variability generally leads to higher computed factors of safety and, for those dyke sections requiring remedial action, to more economic designs. Back-figured characteristic values are shown to be considerably higher than the 5percentile soil properties; hence, a reduction in over-conservatism is achieved.
a b s t r a c tThis paper discusses the numerical results for a consolidation test studied by using a hydromechanical model formulated within a numerical homogenization approach, the so-called finite element squared method, FE 2 . This model is characterized by two observation scales: at the microscopic scale, the microstructure of the material is described as an assembly of hyperelastic grains connected by cohesive interfaces that define a network of channels in which fluid can percolate. This microstructure, periodically distributed in the small-scale, identifies the Representative Elementary Volume of the material. At the macroscopic scale, the material is treated as a continuum and the corresponding constitutive equations are obtained by means of a numerical homogenization process on the microscopic problem. In this manner, the total stress of the mixture, the density of the mixture, the fluid mass flow and the fluid mass content can be computed. The objective of this work is to compare the numerical results with the analytical solution of a classical oedometric test using the poroelastic theory of Biot (1941) [1]. For this purpose, it is shown that the hydromechanical behavior obtained with the selected FE 2 method is characterized by a classical Biot-like porous medium and the resulting macroscopic properties can be illustrated in light of the hydromechanical mechanisms at the microscopic scale.
For analysing low probability slope failures, a modified version of subset simulation, based on performance-based subset selection rather than the usual probability-based subset selection, is combined with the random finite element method. The application to an idealized slope is used to study the efficiency and consistency of the proposed method compared to classical Monte Carlo simulations and the shear strength reduction (SSR) method. Results demonstrate that failure events taking place without strength reduction have different modes of failure than stable slopes brought to failure by SSR. The correlation between sliding volume and factor of safety is also demonstrated.
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