Polymorphic uncertainty quantification for stability analysis of fluid saturated soil and earth structures

Abstract

Nowadays, numerical simulations enable the description of mechanical problems in many application fields, e.g. in soil or solid mechanics. During the process of physical and computational modeling, a lot of theoretical model approaches and geometrical approximations are sources of errors. These can be distinguished into aleatoric (e.g. model parameters) and epistemic (e.g. numerical approximation) uncertainties. In order to get access to a risk assessment, these uncertainties and errors must be captured and quantified. For this aim a new priority program SPP 1886 has been installed by the DFG which focuses on the so called polymorphic uncertainty quantification. In our subproject, which is part of the SPP 1886 (sp12), the focus is driven on quantification and assessment of polymorphic uncertainties in computational simulations of earth structures, especially for fluid-saturated soils. To describe the strongly coupled solid-fluid response behavior, the theory of porous media (TPM) will be used and prepared within the framework of the finite element method (FEM) for the numerical solution of initial and boundary value problems [2,3]. To capture the impacts of different uncertainties on computational results, two promising approaches of analytical and stochastic sensitivity analysis will enhance the deterministic structural analysis [6][7][8].A simple consolidation problem already provided a high sensitivity in the computational results towards variation of material parameters and initial values. The variational and probabilistic sensitivity analyses enable to quantify these sensitivities. The variational sensitivities are used as a tool for optimization procedures and capture the impact of different parameters as continuous functions. An advantage is the accurate approximation of the solution space and the efficient computation time, a disadvantage lies in the analytical derivation and algorithmic implementation. In the probabilistic sensitivity analysis from the field of statistics, the expense only increases proportionally to the problems dimension. Instead of a constant value, the model parameters are defined as probability distribution, which provides random values. Thus, a set of solution data is built up by several cycles of the simulation. Different approaches of the Bayes statistics will enable to receive accurate information with just a few simulations. The overall objective is the development of more efficient methods and tools for the sizing of earth structures in the long-run.

Analysis of polymorphic data uncertainties in engineering applications

“…For a detailed derivation the reader is referred to Stieghan [17] and Henning and Ricken. [20] The resulting material sensitivity matrix S  contains the sensibility of the system response behavior to changes in the initial material parameters. In the following, the focus is on the Local Impact Analysis (LIA), representing the percentage, location-dependent impact of a parameter on the output with The local material sensitivity matrix S loc contains the ratios of each entry S ij to the row total ∑ k (S) ki of its respective row position i.…”

Challenges of order reduction techniques for problems involving polymorphic uncertainty

“…It follows that the total variation of the physical residual R have to vanish. The discretized form provides the linear approximation of the relation between an additional change in the expected value Δ m and the resulting change in the field quantities Δ u (for a detailed derivation, the reader is referred to Stieghan and Henning and Ricken) with …”

Polymorphic Uncertainty Quantification of Computational Soil and Earth Structure Simulations via the Variational Sensitivity Analysis

“…However, the high computational effort due to the large number of simulation runs required, builds a main drawback of this approach. Consequently, the total variation of the equilibrium state towards the unknown field quantities u and the material parameters m has to vanish [7]. It provides detailed information about the current equilibrium state of a given problem and thus provides prior knowledge for reducing the parameter space of a subsequent probabilistic or fuzzy analysis.…”

“…The equilibrium state is required to be stable, which implies that a small deflection towards any arbitrary quantity must not destabilize the mechanical system. Consequently, the total variation of the equilibrium state towards the unknown field quantities u and the material parameters m has to vanish [7]. This requirement is used for the development of the material sensitivities and results in the linear approximation of the current equilibrium state.…”