Tomasz Strzelecki

RELATION BETWEEN FILTRATION AND SOIL CONSOLIDATION THEORIES

Abstract This paper presents a different, than commonly used, form of equations describing the filtration of a viscous compressible fluid through a porous medium in isothermal conditions. This mathematical model is compared with the liquid flow equations used in the theory of consolidation. It is shown that the current commonly used filtration model representation significantly differs from the filtration process representation in Biot’s and Terzaghi’s soil consolidation models, which has a bearing on the use of the methods of determining the filtration coefficient on the basis of oedometer test results. The present analysis of the filtration theory equations should help interpret effective parameters of the non-steady filtration model. Moreover, equations for the flow of a gas through a porous medium and an interpretation of the filtration model effective parameters in this case are presented.

Thermal Consolidation Process of Multiphase Medium Consisting of Elastic Skeleton, Water, and Water Vapour

In the process of coal gasification, the phase transition from water to water vapour takes place as a result of high temperature. Thus, the parameters of the fluid flowing through the pores of the elastic skeleton change in a significant way. The goal of this work is to calculate the fluid flow process at a variable temperature using Finite Element Method and to determine the soil consolidation process taking place under its own weight and temperature changes. The mathematical model of thermal consolidation for a Biot body accounts for the phase transition of a liquid. Numerical calculations for a homogeneous and isotropic porous medium, consisting of two conventionally accepted layers, were carried out using the FlexPDE v. 6 software. The obtained results are a first approximation of the actual processes taking place under complex geological conditions. They make it possible to determine, in approximation, the range of the phase transition and the influence of water vapour filtration on soil consolidation.

Numerical 3D simulations of seepage and the seepage stability of the right-bank dam of the Dry Flood Control Reservoir in Racibórz

Abstract This article presents the results of numerical simulations of seepage through the body of the dam and the reservoir bed. The purpose of this study was to analyse the seepage stability during a flood as well as the impact on seepage stability of the diaphragm wall and gravel columns, on which the dam body is founded in selected segments. Simulations were conducted for three different locations, and the following 3D models of the dum were prepared: – a model containing the front and right-bank part of the dam, for which no diaphragm wall, gravel columns and drainage ditch were provided for – a model of a segment of the right-bank dam including a diaphragm wall, drainage ditch and gravel columns under the dam (two variants with differing diaphragm wall lengths) – a model of the water dam segment accounting for gravel columns and a drainage ditch, but without a diaphragm wall. In the case of founding on gravel columns, the base was modelled as an anisotropic medium in terms of seepage properties, macroscopically equivalent to the actual soil medium. The numerical model utilises the finite element method. The geometry of the dam and geological substrate was defined in the GIS tools in the form of a 3D model of the terrain and geology of the substrate.

Non-Isothermal Constitutive Relations and Heat Transfer Equations of a Two-Phase Medium

Abstract In the case of a two-phase medium – such as the soil, which consists of an elastic skeleton and is filled with pore fluids – stress and strain within the medium are dependent on both phases. Similarly, in the case of heat transfer, heat is conducted through the two phases at different rates, with an additional heat transfer between the phases. In the classical approach to modelling a porous medium, it is assumed that the fluid filling the pore space is water, which is incompressible. In the case of gas, the volume of which is strongly dependent on temperature and pressure, one should take this behavior into account in the constitutive relations for the medium. This work defines the physical relations of a two-phase medium and provides heat transfer equations, constructed for a porous, elastic skeleton with fluid-filled pores, which may be: liquid, gas, or mixture of liquid and a gas in non-isothermal conditions. The paper will present constitutive relations derived from the laws of irreversible thermodynamics, assuming that pores are filled with either a liquid or a gas. These relations, in the opinion of the authors, may be used as the basis for the construction of a model of the medium filled partly with a liquid and partly with a gas. It includes the possibility of independent heat transfer through any given two-phase medium phase, with the transfer of heat between the phases.

Numerical analysis of road pavement thermal deformability, based on Biot viscoelastic model of porous medium

Abstract The following study presents numerical calculations for establishing the impact of temperature changes on the process of distortion of bi-phase medium represented using Biot consolidation equations with Kelvin–Voigt rheological skeleton presented, on the example of thermo-consolidation of a pavement of expressway S17. We analyzed the behavior of the expressway under the action of its own weight, dynamic load caused by traffic and temperature gradient. This paper presents the application of the Biot consolidation model with the Kelvin–Voigt skeleton rheological characteristics and the influence of temperature on the deformation process is taken into account. A three-dimensional model of the medium was created describing the thermal consolidation of a porous medium. The 3D geometrical model of the area under investigation was based on data obtained from the land surveying and soil investigation of a 200 m long section of the expressway and its shoulders.

Analysis of the Foundation Slab Settlement of the “Africa Pavilion” Facility in Wrocław

Abstract This article presents the results of numerical calculations of soil consolidation underneath the “Africa Pavilion” structure in Wrocław Zoo, Poland. To determine the deformations of the baseplate of the “Africa Pavilion” and deformations of the subsoil, Biot’s consolidation theory for two-phase medium was applied. The calculations were carried out using the professional program FlexPDE v.6, which is based on the Finite Element Method. Numerical calculations performed were used to evaluate the design assumptions allowing for the laying of hydraulic conduits under the slab.

Building a Numerical Model of the Filtration Flow in the Żelazny Most Flotation Tailings Disposal Lake

Abstract The paper presents results of numerical computations of the filtration flow of liquid contaminated wastes through the Żelazny Most flotation tailings disposal lake. Unlike the preceding papers [5]-[7], it takes the geological structure of the subsoil into account. A three-dimensional numerical model of the lake was created for computing purposes. Data on some of the effective model parameters were acquired from laboratory tests of the material taken from the lake site. The other data were taken from the literature for media of similar properties. The results of the computations carried out using the model can be a basis for future numerical analyses aimed at determining the consolidation of the flotation tailings disposal lake and its subsoil, and the stability of the lake.

Effect of Variation of Temperature Field on the Process of Thermal Consolidation of Tailings Pond “Zelazny Most”

Abstract The following study presents numerical calculations for establishing an impact of temperature changes on the process of distortion of bi–phase medium. The Biot consolidation equations with Kelvin–Voigt rheological skeleton were used for that purpose. The process was exemplified by thermal consolidation of post floatation dump “–elazny Most”. We analyzed the behavior of the landfill under the action of its own weight, forces of floating filtration and temperature gradient. Values of certain effective parameters of model were obtained during laboratory tests on material obtained from the landfill. The remaining data for mediums with similar characteristics were taken from literature. The results obtained from the stress state in the landfill allow the magnitude of plasticity potential to be specified based on known strength criteria. Change in the value sign of the plasticity potential clearly testifies to the emergence of an area of plasticity of material from landfill, however, this does not indicate the loss of stability of this hydrotechnical structure.

Numerical calculation of deformation of three dimensional sample in triaxial apparatus under external load and temperature field

Abstract This study presents the results of calculations of the of thermo consolidation process of porous medium with the rheological Kelvin-Voigt skeleton, obtained numerically with the use of Flex.PDE. It is a continuation of the discussion on the phenomenon of thermal consolidation. A 3D problem considered boils down to solving the problem of the porous column filled with a liquid and treated by applying uniaxial compression load through a porous plate, allowing free flow of liquid from the center. To the sample affected by external lateral pressure. Numerical solution assumes compressing the sample at properly defined boundary conditions. The aim of this study was to describe the influence of external load and temperature gradient in the deformation tests for the case when the lateral surface is a good conductor of heat, and where the lateral surface of the sample does not conduct heat. The results obtained, in the context of further research, can also be used to determine the influence of other parameters of the state and model parameters on the process of thermo poroelasticity of the Biot model with rheological skeleton.

NUMERICAL MODELING OF VERTICAL WELLS IN UNSTEADY GROUNDWATER FLOW CONDITIONS

Abstract This article presents the results of numerical calculations of drainage of a large engineering construction - “Afrykarium” in Wrocław ZOO, Poland, based on a 2D numerical model for seepage flow. In the numerical simulations the real (natural) hydrogeological conditions, water-courses, surface reservoirs and time dependent seepage flow (during drainage) are taken into account. The aim of numerical calculations was to determine quantities (draining time, number of wells, spacing and arrangement of wells, flows for every well, and hydraulic head map) necessary to design an effective drainage system of construction site. The mathematical model adopted to illustrate and predict groundwater depression during pumping was the Boussinesq equation for unsteady 2D flow.