Finite element modelling of the effective elastic properties of partially saturated rocks

Simulation of effective physical properties from microtomographic 3D images of porous structures allows one to relate properties of rocks directly to their microstructure. A static FEM code has been previously used to estimate effective elastic properties of fully saturated monomineralic (quartz) rock under wet and dry conditions. We use the code to calculate elastic properties under partially saturated conditions. The numerical predictions are compared to the Gassmann theory combined with Wood's formula (GW) for a mixture of pore fluids, which is exact for a monomineralic macroscopically homogeneous porous medium. Results of the numerical simulations performed for two Boolean sphere pack distributions show significant deviation from the GW limit and depend on the spatial distribution of fluids. This is shown to be a numerical artefact caused by incomplete equilibration of fluid pressure, which is primarily due to insufficient spatial resolution. To investigate the effect of pore-size and pore geometry, we perform FEM simulations for a model with regular pore geometry, where all pore channels have the same size and shape. Accuracy of these simulations increases with the total cross-section area of the channels and the size of individual channels. For the case where the total cross-section of the channels is large enough (on the same order as total porosity), there is a minimum of 4 voxels per channel diameter required for adequate fluid pressure equilibration throughout the pore space. Increasing the spatial resolution of the digital models reduces the discrepancy between the simulations and theory, but unfortunately increases the memory and CPU requirements of the simulations

Poroelastic Modelling of Wavefields in Heterogeneous Media. Poroelastische Modellierung von Wellenfeldern in Heterogenen Medien

Numerical modelling of seismic waves in heterogeneous, porous reservoir rocks is an important tool in the field of reservoir engineering. A new 2-D velocity-stress finite-differences scheme is presented that allows to simulate waves and coupled diffusion processes within poroelastic media as described by Biot theory. The presented numerical methods allow to further develop rock physics theories of wave-induced fluid flow and contribute to the interpretation of new laboratory experiments

Forward Modelling and Inversion of the Ultrasonic Wave Propagation Through a Homogeneous and Porous Rock

The aim of my work is to estimate viscoelastic parameters of rock samples from waveforms of ultrasonic waves propagating through these samples. To this end, I develop an automated Python modules in Finite Element Modelling software Abaqus, and tailored it specifically for a controlled transmission experiment using ultrasonic source and receiver. The approach is verified using test Aluminium samples, and then applied to real rocks to estimate ultrasonic attenuation using Prony formulation of viscoelasticity

Behaviour of stiff clayey soils using fracture mechanics approach

Most of the conventional elastic plastic models of soils are based on continuum mechanics, however, for stiff, hard soils and soft rocks discontinuities develop under load, and since the models assume continuity, they would cease to apply. These discontinuities had not been accounted for in the continuum-based elastic plastic models. On the other hand, fracture mechanical theory may be used to advantage to replicate their behaviour. The behaviour of soil commonly is interpreted from conventional triaxial apparatus, whereas, testing of soil using the plane strain device would be more useful information, as more geotechnical field problems are basically occur in these situations.The present study has dealt with the investigation on the behaviour of saturated over consolidated clay as well as partially saturated clay, which represent the stiff and hard brittle clay by the use of a new biaxial device modified from conventional triaxial apparatus. In general, the apparatus was able to produce data which are in a good accordance with known soil behaviour of stiff clay. Shear band localization occurred in all test specimens of over consolidated clay. Specimen initiated to be discontinuous upon reaching the peak stresses. It is evident that specimen of partially saturated containing fissures had weaker shear strength as well as compressive strength.From point of view of the discontinuities that take places in the stiff clay, a model based on the unified model (Lo et al, 1996) and the elasto-plastic shear fracture model (Lo, et al, 2005) was used in this study. The problem may be dealth with one of brittle fracture of a three-phase specimen, where the matric suction is disrupted by tensile or shear loading. As a result the fracture toughness of the specimen would vary according to matric suction changes. A problem of plane strain compression testing was carried out to implement the model. The crack propagation simulation was resulted the same pattern with the experimental results on partially saturated kaolin clay

Squirt flow in partially saturated cracks: a simple analytical model

This is a pre-copyedited, author-produced PDF of an article published in Geophysical Journal International following peer review. The version of record ``Santiago G Solazzi, Simón Lissa, J Germán Rubino, Klaus Holliger, Squirt flow in partially saturated cracks: a simple analytical model, Geophysical Journal International, Volume 227, Issue 1, October 2021, Pages 680–692’ is available online at: https://doi.org/10.1093/gji/ggab249

Numerical and Physical Modeling of Cone Penetration in Unsaturated Soils and Numerical Simulation of Fracture Propagation in Shale Rock during Brazilian Test

Partially water saturated condition in soils may change the cone penetration resistance comparing with that of dry or saturated conditions. This effect was investigated in this study using numerical finite element modeling and experimental centrifuge testing. The results showed suction in unsaturated soil significantly influenced the soil resistance to cone penetration. Two approaches were implemented to numerically consider the partially saturated soil condition; i.e. modifying simple constitutive models using an apparent cohesion strategy and implementing Barcelona Basic Model for unsaturated soils. Both successfully captured the cone resistance profiles inside a calibration chamber and also in free field. In addition, details of developing a miniature cone setup capable of for cone penetration inside geotechnical centrifuge was explained. Further, the use of Linear Softening Cohesive Model (LCFM) to predict the fracture growth in shale rocks during Brazilian Test was examined. The application and importance of considering two different compressive and tensile elastic modulus and soil anisotropy during the fracture modeling of shales were demonstrated

Numerical modelling of slope–vegetation–atmosphere interaction: an overview

The behaviour of natural and artificial slopes is controlled by their thermo-hydro-mechanical conditions and by soil–vegetation–atmosphere interaction. Porewater pressure changes within a slope related to variable meteorological settings have been shown to be able to induce soil erosion, shrinkage–swelling and cracking, thus leading to an overall decrease of the available soil strength with depth and, ultimately, to a progressive slope collapse. In terms of numerical modelling, the stability analysis of partially saturated slopes is a complex problem and a wide range of approaches from simple limit equilibrium solutions to advanced numerical analyses have been proposed in the literature. The more advanced approaches, although more rigorous, require input data such as the soil water retention curve and the hydraulic conductivity function, which are difficult to obtain in some cases. The quantification of the effects of future climate scenarios represents an additional challenge in forecasting slope–atmosphere interaction processes. This paper presents a review of real and ideal case histories regarding the numerical analysis of natural and artificial slopes subjected to different types of climatic perturbations. The limits and benefits of the different numerical approaches adopted are discussed and some general modelling recommendations are addressed

Characterisation of ground thermal and thermo-mechanical behaviour for shallow geothermal energy applications

Increasing use of the ground as a thermal reservoir is expected in the near future. Shallow geothermal energy (SGE) systems have proved to be sustainable alternative solutions for buildings and infrastructure conditioning in many areas across the globe in the past decades. Recently novel solutions, including energy geostructures, where SGE systems are coupled with foundation heat exchangers, have also been developed. The performance of these systems is dependent on a series of factors, among which the thermal properties of the soil play one of major roles. The purpose of this paper is to present, in an integrated manner, the main methods and procedures to assess ground thermal properties for SGE systems and to carry out a critical review of the methods. In particular, laboratory testing through either steady-state or transient methods are discussed and a new synthesis comparing results for different techniques is presented. In-situ testing including all variations of the thermal response test is presented in detail, including a first comparison between new and traditional approaches. The issue of different scales between laboratory and in-situ measurements is then analysed in detail. Finally, thermo-hydro-mechanical behaviour of soil is introduced and discussed. These coupled processes are important for confirming the structural integrity of energy geostructures, but routine methods for parameter determination are still lacking

Revisiting the thermodynamics of hardening plasticity for unsaturated soils

A thermodynamically consistent extension of the constitutive equations of saturated soils to unsaturated conditions is often worked out through the use a unique 'effective' interstitial pressure, accounting equivalently for the pressures of the saturating fluids acting separately on the internal solid walls of the pore network. The natural candidate for this effective interstitial pressure is the space averaged interstitial pressure. In contrast experimental observations have revealed that, at least, a pair of stress state variables was needed for a suitable framework to describe stress-strain-strength behaviour of unsaturated soils. The thermodynamics analysis presented here shows that the most general approach to the behaviour of unsaturated soils actually requires three stress state variables: the suction, which is required to describe the invasion of the soil by the liquid water phase through the retention curve; two effective stresses, which are required to describe the soil deformation at water saturation held constant. However a simple assumption related to the plastic flow rule leads to the final need of only a Bishop-like effective stress to formulate the stress-strain constitutive equation describing the soil deformation, while the retention properties still involve the suction and possibly the deformation. Commonly accepted models for unsaturated soils, that is the Barcelona Basic Model and any approach based on the use of an effective averaged interstitial pressure, appear as special extreme cases of the thermodynamic formulation proposed here

Effect of fluid distribution on compressional wave propagation in partially saturated rocks

Partial saturation of porous rock by two fluids substantially affects compressional wave propagation. In particular, partial saturation causes significant attenuation and dispersion due to wave-induced fluid flow. Such flow arises when a passing wave induces different fluid pressures in regions of rock saturated by different fluids. When partial saturation is mesoscopic, i.e. existing on a length scale much greater than pore scale but less than wavelength scale, significant attenuation can arise for frequencies 10-1000 Hz. Models for attenuation and dispersion due to mesoscale heterogeneities mostly assume fluids are distributed in a regular way. Recent experiments indicate mesoscopic heterogeneities have less idealised distributions and distribution affects attenuation/dispersion. Thus, theoretical models are required to simulate effects due to realistic fluid distributions.The thesis focus is to model attenuation and dispersion due to realistic mesoscopic fluid distributions and fluid contrasts. First X-ray tomographic images of partially saturated rock are analysed statistically to identify spatial measures useful for describing fluid distribution patterns. The correlation function and associated correlation length for a specific fluid type are shown to be of greatest utility. Next a new model, called 3DCRM (CRM stands for continuous random media) is derived, utilizing a correlation function to describe the fluid distribution pattern. It is a random media model, is accurate for small fluid contrast and approximate for large fluid contrast. Using 3DCRM attenuation and dispersion are shown to depend on fluid distribution.Next a general framework for partial saturation called APS (acoustics of partial saturation) is extended enabling estimation of attenuation and dispersion due to arbitrary 1D/3D fluid distributions. The intent is to construct a versatile model enabling attenuation and dispersion to be estimated for arbitrary fluid distributions, contrasts and saturations. Two crucial parameters within APS called shape and frequency scaling parameters are modified via asymptotic analysis using several random media models (which are accurate for only certain contrasts in fluid bulk moduli and percent saturation). For valid fluid contrasts and saturations, which satisfy certain random media conditions there is good correspondence between modified APS and the random media models, hence showing that APS can be utilized to model attenuation and dispersion due to more realistic fluid distributions.Finally I devise a numerical method to test the accuracy of the analytical shape parameters for a range of fluid distributions, saturations and contrasts. In particular, the analytical shape parameter for randomly distributed spheres was shown to be accurate for a large range of saturations and fluid contrasts