Hydro-mechanical analysis of gas transport in compacted bentonite: uncertainty modelling

In the last years, transport of gases in clay buffer materials for Engineered Barrier Systems (EBS) has been deeply investigated by many research programs in the framework of nuclear waste storage. At present state, the coupled hydromechanical models to analyse this kind of problems provide qualitatively description of the gas transport phenomena but their predictive capabilities are still limited, indicating that the physical phenomena that rules the gas transport process are not understood in sufficient detail. The gas transport phenomenon is strongly influenced by material heterogeneities and by the hydromechanical coupling of the involved phenomena. From a modelling perspective, the hypothesis of perfect homogeneity of the buffer material is not realistic and leads to important errors in the assessment of material behaviour. In the present contribution, Lagamine has been used as a basic tool of a Stochastic Finite Element Method (SFEM) analysis. It represents a well-known approach to consider the effect of material uncertainties by using a deterministic FEM tool. A series of finite element analyses with increasing degree of complexity have been performed and compared with high-quality laboratory tests performed on compacted bentonite. The influence of the constitutive assumptions and of the material heterogeneity have been analysed in terms of hydration kinetics, swelling behaviour, breakthrough pressure, and kinetics of gas dissipation. The most relevant outcome of the study is the possibility of analyse each step of the finite element modelling to highlight critical points of the simulation process focusing the sources of uncertainty and orienting the subsequent experimental and modelling phases.

Numerical modeling of cohesive sediment transport and bed morphology in estuaries

Célestin Leupi

Two major lines of investigation have been pursued in this thesis: (1) More efficient, robust and realistic numerical techniques are designed for the simulation of complex turbulent fluid flows; (2) A new algorithm and its analysis is performed in the context of multiphasic fluid flow, for a cohesive fine-grained sediment (fluid mud) transport in estuaries. Estuaries exist between marine and freshwater system where waters of different physical, chemical and biological composition meet, combine and disperse primarily due to tidal influences. In the present thesis, the behavior of cohesive sediment in estuaries is reviewed based on the existing literature. Basic theories and recent developments are introduced to describe the formation of fluid mud from a very dilute suspension and its motion down a natural river bed with complex bathymetry. The present work contributes to the numerical simulation of complex turbulent multiphasic fluid flows encountered in estuarine channels, with the aim of the better understanding of the underlying physical processes as well as predicting realistically the cohesive sediment transport and bed morphology in such a zone. The model is based on the mass preserving method by using the so-called Raviart-Thomas finite element on the unstructured mesh in the horizontal plane. In the vertical, the computational domain is divided into number of layers at predefined heights and the method uses a conventional conforming P1 finite element scheme, with the advantage that the lowermost and uppermost layers variable height allow a faithful representation of the time-varying bed and free surface, respectively. Concerning the modeling of turbulence, the research effort focuses on the turbulence two-equation k - ε closure for the vertical parameterization of eddy viscosity. More precisely, a robust up-to-date algorithm is used for this issue. The new methodology is developed with the aim to account for more general relevant effects in the closure. The proposed model offers the capability to cope with the stiffness problem introduced by the large difference between the solid phase flow time scale and the hydrodynamic one, by using a sub-cycling strategy, whereas the splitting scheme is adopted with the aim of stability and the positivity of the relevant turbulent variables. The flexibility of the model and its performance are evaluated on several free-surface flow configurations with increasing complexity : homogeneous unsteady non-uniform flows in plane open channel flows, U-shaped (193°) curved open channel flow. Concerning the cohesive sediment transport, most of the existing models in the literature assume the analogous transport characteristics with that of the coarse sediment and adopt the relevant developed sediment transport for the latter to treat the former. Moreover, these existing models do not account for the consolidation of the mud-bed. The present research effort focused on a novel methodology based on the realistic empirical relationships, which accounts for the mutually exclusive processes for re-suspension and/or erosion and deposition of fine sediment, whereas only a limited range of bed shear stresses is allowed for simultaneous erosion and deposition to occur. Hence, on this basis, the new model investigated the bed morphology evolution by taking into account of the fluidization and/or consolidation of the fluid mud, which was handled by modeling the bed in three layers: (i) the mud-bed layer, (ii) the partially consolidated bed and (iii) the fully consolidated bed. The prediction of deposition/re-suspension using these two different methods lead to a non negligible difference in the results. Therefore, investigation of the true mechanism of erosion/deposition processes for cohesive sediments and their implementation in the numerical model is very important. This suggests that a realistic prediction must account for the fresh mud-bed re-suspension once deposited, as well as the consolidation and/or fluidization of the mud-bed deposits. Finally, the capability and improvements of the model are demonstrated, and its predicting performance is successfully evaluated by applying it to the simulation of the Po River Estuary (PRE) in Italy, which is the main source of river water discharge into the Northern Adriatic Sea. The analysis showed that the consolidation/fluidization process at the bed may have important influence on the prediction of bed morphology evolution. The three-layer approach used in this thesis is a first attempt to model these processes in detail within a numerical model.

EPFL2005

Numerical modeling and neural networks to identify constitutive parameters from in situ tests

Rafal Filip Obrzud

This study proposes a new advanced algorithm for determining material parameters based on in situ tests. In situ testing gives an opportunity to perform soil characterization in natural stress conditions on a representative soil mass. Most field techniques reduce soil disturbances to minimum, allowing investigating the response of virgin soil. Self-boring pressuremeter tests (SBPT) and standard piezocone tests (CPTU) are widely used to deduce properties of clayey soils through analytical and empirical correlations between soil properties and experimental measurements. Empirical correlations usually require some tuning based on reference laboratory data because first-order estimates for typical correlation coefficients may give unreliable evaluation of soil properties. Analytical correlations are mostly based on cavity expansion methods which are restricted to either fully drained or perfectly undrained problems, so that inverse closed-form solutions for relatively simple constitutive models can be derived. In practice, however, depending on physical and consolidation properties of the soil, partially drained conditions may occur during field testing, leading to an erroneous estimation of clay characteristics. Therefore, elaborating a generic parameter identification framework, which is based on the artificial neural network (NN) technique and which may improve the reliability of soil properties derived from in situ testing, is the main goal of this research. This study explores the possibility of using NNs to solve complex inverse problems including partially drained conditions. In other words, NNs are used to map experimental measurements onto set of soil properties. The development of NN-based inverse models is based on a training data sets which consists of pseudo-experimental measurements derived from numerical simulations of both the SBPT and the CPTU test in normally- and lightly overconsolidated clay type material. The study presents a generic two-level procedure designed for the calibration of constitutive models of soils. It is demonstrated that NN inverse models can be easily integrated into the classical back-analysis. At the first level, the NN approach is applied to achieve the first approximation of parameters. This technique is used to avoid potential pitfalls related to the conventional gradient-based optimization (GBO) technique, considered here as a corrector that improves predicted parameters. Trained NNs as parallel operating systems can provide output variables instantly and without a costly GBO iterative scheme. The proposed framework is verified for the elasto-plastic Modified Cam Clay (MCC) model that can be calibrated based on standard triaxial laboratory tests, i.e. the isotropic consolidation test and the consolidated isotropic drained compression test. The study presents formulations of the input data for the NN predictors, enhanced by a dimensional reduction of experimental data using principal component analysis (PCA). The determination of model characteristics is demonstrated, first on numerical pseudo-experiments and then on the experimental data. Furthermore, the efficiency of the proposed approach in terms of accuracy and computational effort is also discussed. The verified two-level strategy is applied to a numerical procedure of parameter identification for the boundary value problem (BVP) of the SBPT. The coupled hydro-mechanical finite element (FE) formulation allows the generated excess pore water pressure to be dissipated during simulations of the expansion test, followed then by a holding test. Numerical simulations demonstrate that volume changes that may occur in clay during the expansion test due to partial drainage, can cause local soil hardening near the cavity wall and affect parameter interpretation for pressuremeter tests. Therefore, the NN technique is applied to obtain an initial guess for model parameters, taking into account the possible partially drained conditions during the expansion test. Parameter identification based on measurements obtained through the pressuremeter expansion test and two types of holding tests is illustrated on the MCC model. NNs are trained using a set of synthetic test samples, which are generated by means of FE simulations based on constrained random permutations of input model parameters. The measurements obtained through expansion and consolidation tests are normalized by the proposed normalizing formulas so that NN predictors operate independently of the testing depth. Examples of parameter determination are demonstrated on both numerical data and field measurements from the Fucino clay deposit. The efficiency of the combined parameter identification in terms of accuracy, effectiveness and computational effort is also discussed. Finally, an application of NN predictors as a stand-alone support for soil profiling is presented for the piezocone test. By similarity to the SBPT problem, a number of NN inverse models are developed based on the results derived from rigorous FE analyzes. The FE model of piezocone penetration involves numerical formulation for the two-phase material obeying the MCC law and including the large strain theory, as well as the large deformation formulation for contact interface. It is demonstrated that a considerable computational effort related to the generation of the training database can be reduced by optimizing the mesh size and "steady-state" depth in function of soil rigidity index. Due to a severe loss of measurement accuracy observed in the finite elements adhered to the "rough" interface, an equivalent semi-numerical approach is proposed to account for frictional effects in different drainage conditions which are delineated from a number of numerical simulations. The validity of the developed penetration model is verified in detail by means of comparisons with other theoretical solutions and parametric studies synthesized from literature, as well as experimental evidence for both undrained and partially drained scenarios. An extended parametric study including influence analyzes of strength and stress anisotropy, rigidity index and cone roughness on two cone factors provides new insight into the analysis of cone penetration. The shortcomings of the FE model due to the limitations of the applied constitutive model are also discussed. As regards NN models, different configurations of input variables, including standard normalized piezocone metrics and other available soil characteristics are investigated in terms of feasibility of effective NN training. The post-training regression analyzes are performed for numerical data allowing the assessment of the influence of specific input variables on accuracy of parameters predictions. Finally, the developed NN models are applied to predict parameters based on field measurements for a number of characterization sites. Provided examples demonstrate that NN inverse models may constitute an effective complementary support during the first-order quantification of the MCC parameters from piezocone measurements.

EPFL2009

A posteriori error estimations for elliptic partial differential equations with small uncertainties

Diane Sylvie Guignard, Fabio Nobile, Marco Picasso

In this article, a finite element error analysis is performed on a class of linear and nonlinear elliptic problems with small uncertain input. Using a perturbation approach, the exact (random) solution is expanded up to a certain order with respect to a parameter that controls the amount of randomness in the input and discretized by finite elements. We start by studying a diffusion (linear) model problem with a random coefficient characterized via a finite number of random variables. The main focus of the article is the derivation of a priori and a posteriori error estimates of the error between the exact and approximate solution in various norms, including goal-oriented error estimation. The analysis is then extended to a class of nonlinear problems. We finally illustrate the theoretical results through numerical examples, along with a comparison with the Stochastic Collocation method in terms of computational costs.