Stochastic finite element modelling of flow and solute transport in dual domain system

Hydrological processes are greatly influenced by the characteristics of the domain through which the process occurs. It is generally accepted that earth materials have extreme variations from point to point in space. Consequently this heterogeneity results in high variation in hydraulic properties of soil. In order to develop a reliable predictive model for transport processes in soil, the effects of this variability must be considered. Soil heterogeneity due to presence of macropores (micro-) and to spatial variability in hydraulic properties (macro-heterogeneity) coexists in the real field conditions. The challenge is to incorporate the effects of both types of soil heterogeneity in simulation models. This thesis presents development and application of a 2D/3D numerical model for simulation of advection and diffusion-dispersion contaminant transport considering both types of soil heterogeneity. Stochastic finite element approach is used to incorporate the effects of the spatial variability of soil hydraulic properties on contaminant fate. The soil micro heterogeneity effects are modelled with a dual domain concept in which a first order kinetic expression is used to describe the transfer of the solute between the two domains. Also, the capability of the model in 3D simulation of field problems improves the accuracy of the results, since it is possible to avoid the generally applied assumption in 2D simulations. From comparison of the model results with experimental and analytical results, it is concluded that the model performs well in predicting contaminant fate and the incorporation of the both types of micro- and macro- heterogeneity in the simulation models improves the accuracy of the prediction. Also, capability of the model in evaluation of the concentration variation coefficient as an index of reliability of the model outputs makes it possible to estimate a probable interval (mean concentration minus and plus standard deviation) for the range of oscillations of possible realizations of solute distribution. Moreover, comparison of the results of the proposed method with the results obtained using the Monte Carlo approach yields a pronounced reduction in the computation cost while resulting in virtually the same response variability as the Monte Carlo technique

Rate-dependency and Stress-Relaxation of Unsaturated Clays

This paper presents the experimental program conducted for evaluation of the rate-dependent and stress-relaxation behavior of unsaturated reconstituted London clay. A series of drained constant rate of strain (CRS) compression-relaxation tests with single-staged (SS-CRS) and multistaged (MS-CRS) loading modes was performed in an innovative CRS oedometer cell where soil suction evolutions were monitored using two high-capacity tensiometers (HCTs). Specimens were tested at two strain rates of 4.8×10−7 and 2.4×10−6  s−1 and over a suction range of 0–1,905 kPa. The coupled and independent effects of strain rate and soil suction on one-dimensional stress–strain and stress-relaxation responses, including the effects of prerelaxation strain, stress, and strain rate under both saturated and unsaturated conditions, were evaluated. An increase in suction and strain rate resulted in an increase of the yield vertical net stress (σp). Furthermore, it was observed that the rate and magnitude of the relaxed stresses increased with increases in prerelaxation strain, stress, and strain rate, and decreased with an increase in soil suction. At constant suction, an increase in the prerelaxation strain rate by a factor of five resulted in an increase of the relaxed stresses by a factor of 2.2–3.6. Moreover, the coefficient of relaxation (Rα) was found to be suction dependent, falling within a range of 0.011–0.019 and 0.017–0.029, respectively, for slow and fast strain rates during MS-CRS tests. Comparing these results with the Cα/Cc ratio obtained from conventional multistage loading (MSL) oedometer test results revealed the validity of Rα=Cα/Cc correlation for unsaturated reconstituted specimens

Creep and consolidation of a stiff clay under saturated and unsaturated conditions

In this paper the one-dimensional (1D) time-dependent behaviour of natural and reconstituted London Clay samples under saturated and unsaturated conditions is studied. For this purpose, a set of 1D consolidation tests including multi-staged loading (MSL) oedometer tests and single-staged loading (SSL) long-term oedometer creep tests were carried out on saturated and unsaturated specimens. Conventional oedometer cells were used for tests on saturated specimens, whereas a newly designed unsaturated oedometer cell, equipped with two high-capacity tensiometers (HCTs) for suction measurements, was used for unsaturated tests. The tests results revealed stress- and suction-dependency of primary and secondary consolidation responses of the soil samples. Furthermore, counter to formerly acknowledged suggestions of independency of the slope of normal consolidation line to suction changes, it was observed that an increase in suction results in a decrease of the slope of compression curve (Cc) and the creep index (Cαe) values, and an increase in yield vertical net stress (σp). Moreover, the Cαe/Cc ratio for London Clay was found to be stress- and suction-dependent, unlike the previously suggested hypotheses

Transport in porous media with nonlinear flow condition

We investigate local aspects and heterogeneities of porous medium morphology and relate them to the relevant mechanisms of momentum transfer. In the inertial flow range, there are very few experimental data that allow to recognize the effects of porous structure on the flow and transport through porous media. An experimental analysis was performed in order to understand above processes at different Reynolds numbers in randomly structured porous media. The objective of the analysis is to explore the effects of porous media particle size on inertial and viscous forces and determine range of the Reynolds numbers in which the inertial flow predominantly contributes in dispersive processes. Transport characteristics of the randomly structured porous media and the influence of inertial force on longitudinal and transverse dispersion coefficients were studied

Creep analysis of an earth embankment on soft soil deposit with and without PVD improvement

In this paper, an anisotropic creep constitutive model, namely Creep-SCLAY1S is employed 10 to study the installation effects of prefabricated vertical drains (PVDs) on the behavior of a full 11 scale test embankment, namely Haarajoki embankment in Finland. The embankment was 12 constructed on a natural soft soil with PVD installed to improve the drainage under one half of 13 it. The Creep constitutive model used in this study, incorporates the effects of fabric 14 anisotropy, structure and time within a critical state based framework. For comparison, the 15 isotropic modified Cam clay (MCC) model and the rate-independent anisotropic S-CLAY1S 16 model are also used for the analyses. The numerical predictions are compared with field 17 measurements and the results indicate that the creep model provides an improved 18 approximation of field settlements, and excess pore pressure build-up and dissipations. In 19 addition, the application of two commonly used permeability matching techniques for two 20 dimensional (2D) plane-strain analysis of the PVD problem is studied and the results are 21 discussed highlighting their limitations and advantages

Multi-scale approach for modeling the transversely isotropic elastic properties of shale considering multi-inclusions and interfacial transition zone

Multiscale approach based explicit analytic predictions are obtained for the transversely isotropic properties of shale rock considering the multi-inclusion and interfacial transition zone (ITZ) effects. Representative volume elements (RVEs) are utilized to describe the material’s hierarchical microstructures from the nanoscale to the macroscale. A new multilevel micromechanical homogenization scheme is presented to quantitatively estimate the material’s transversely isotropic properties with the multi-inclusion and ITZ effects. The ITZ is characterized by the interphase material, whose effects are calculated by modifying the generalized self-consistent model. Furthermore, the explicit form solutions for the transversely isotropic properties are obtained by utilizing the Hill polarization tensor without numerical integration and the standard tensorial basis with the analytic inversions of fourth-rank tensors. To verify the proposed multiscale framework, predictions obtained via the proposed model are compared with experimental data and results estimated by the previous work, which show that the proposed multi-scaling approaches are capable of predicting the macroscopic behaviors of shale rocks with the multi-inclusion and ITZ effects. Finally, the influences of ITZ and inclusion properties on the material’s macroscopic properties are discussed based on the proposed multiscale framework

Effects of flow nonlinearity and spatial heterogeneity on dispersive solute transport in porous media : a pore-scale study

Quantifying nonlinear flow conditions and their influences on dispersive solute transport in heterogeneous porous media and characterising associated effective features are vital for the design of a variety of industrial, biological, and environmental systems. The present study illustrates the pore-scale effects of flow nonlinearity and spatial heterogeneity of porous structures on dispersive solute transport. Two pore-scale solvers resting on the finite volume method are developed for direct numerical simulation of pore flow and solute transport in three-dimensional porous samples. Employing the maximum likelihood method, the Darcy-scale dispersion parameters of the samples are inversely estimated for a series of Peclet numbers ranging from 110-2 to 5104, covering both linear (Darcy) and nonlinear (Forchheimer) flow regimes. The effect of the transition of the flow from linear to nonlinear regimes on the dispersion rate of the solute is studied to clarify mutual interactions of the advection and diffusion mechanisms on the overall solute transport. Two porous rocks, well-established micro-scale porous media (i.e., a Beadpack and a Bentheimer sandstone) imaged through a close packing approach and X-ray CT, with differing degrees of heterogeneity, are used for pore-scale simulations. Results highlight that the complexity of the flow field in a nonlinear flow regime enhances the solute dispersivity up to five orders of magnitude in heterogeneous porous media. Also, solute dispersion behaviour is more complex with higher dispersion for Bentheimer sandstone because of higher heterogeneity compared to the Beadpack sample. The pore-scale analyses emphasise the importance of incorporating the pore-scale flow features in the solute transport and spreading models

A simplified multiscale damage model for the transversely isotropic shale rocks under tensile loading

A simplified multiscale damage model is proposed for the transversely isotropic shale rocks under tensile loading. In this framework, the multiscale representations for the shale rocks are presented by introducing the microcrack-weakened equivalent solid with hierarchical microstructures, whose transversely isotropic properties are obtained by performing multilevel homogenization procedures. To simplify the calculation process for the damage-induced properties, the equivalent isotropic medium is attained by applying the Voigt–Reuss–Hill averaging process to the transversely isotropic solid. Subsequently, the microcrack-induced inelastic compliances are approximately derived in terms of microcrack opening displacements in the equivalent isotropic medium of the shale rock under tensile loading. The sizes and orientations of microcracks are taken as random variables. Both stationary and evolutionary damage models are considered. Microcrack kinetic equations are characterized through the use of a fracture mechanics-based stability criterion and microcrack geometry within a representative volume element. Numerical examples including experimental validations and comparisons with existing micromechanical models are presented to verify the proposed multiscale damage model. Finally, the influences of the silt inclusions and porosity on the material intrinsic and damage-induced properties are discussed

A surrogate modelling approach based on nonlinear dimension reduction for uncertainty quantification in groundwater flow models

In this paper, we develop a surrogate modelling approach for capturing the output field (e.g., the pressure head) from groundwater flow models involving a stochastic input field (e.g., the hy- draulic conductivity). We use a Karhunen-Lo`eve expansion for a log-normally distributed input field, and apply manifold learning (local tangent space alignment) to perform Gaussian process Bayesian inference using Hamiltonian Monte Carlo in an abstract feature space, yielding outputs for arbitrary unseen inputs. We also develop a framework for forward uncertainty quantification in such problems, including analytical approximations of the mean of the marginalized distri- bution (with respect to the inputs). To sample from the distribution we present Monte Carlo approach. Two examples are presented to demonstrate the accuracy of our approach: a Darcy flow model with contaminant transport in 2-d and a Richards equation model in 3-d