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• Author: Tomasz Strzelecki
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## 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.

## Abstract

With a view to protecting areas lying near the Nysa Kłodzka river and in order to reduce flood wave in Wrocław Waterway System, construction of a water reservoir near Kamieniec Ząbkowicki is being planned. After analysing the hydrology and hydraulics of the river Nysa Kłodzka and the function of reservoirs in Kamieniec Ząbkowicki cascade, a numerical seepage model, based on finite element method (FEM) and taking into account bedrock geology, drainage design and dam sealing, has been proposed. Boussinesq’s mathematical model was used to calculate unconfined groundwater table and vector field of seepage velocity. Building a numerical terrain model and visualisation of the water table in GIS tools enabled presenting calculation results in 3-D space.

## Abstract

In this paper, the results of numerical analysis of the thermal consolidation of a two phase medium, under the assumption of independent heat transfer in fluid and the solid phase of the medium, are presented. Three cases of pore fluid were considered: liquid, represented by water, and gas, represented by air and carbon dioxide. The mathematical model was derived from irreversible thermodynamics, with the assumption of a constant heat transfer between the phases. In the case of the accepted geometry of the classical dimensions of the soil sample and boundary conditions, the process leads to equalization of temperatures of the skeleton on the pore fluid. Heat transfer is associated with the fluid flow in the pores of the medium. In the case of gas as the pore fluid, a non-linear mathematical model of gas filtration through the pores of the medium was accepted. For the computing process, relationships between viscosity or density and temperature proposed by other authors were taken into account. Despite accepting mechanical constants of the solid phase that do not depend on temperature, the obtained model is nonlinear and develops the classical Biot–Darcy model.

## 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:

1. 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
2. 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)
3. 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.

## 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.

## 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.

## Abstract

This study presents calculations results of thermal consolidation process of the porous medium with the rheological Kelvin-Voigt skeleton, obtained numerically with the use of Flex.PDE software. The investigated calculation scheme consisted of the porous column filled with a liquid. The vertical load was applied to the top surface of the column through a porous plate allowing the free flow of liquid through this surface. Numerical solution is based on compression of the sample at appropriately defined boundary conditions. The aim of this study was to describe the influence of external load and temperature gradient on the deformation tests progress at different values of three parameters: λ, rs and cv. The results obtained, in the context of further research, can also be used for the determination of the influence of other parameters of the state and model parameters on the process of thermo poroelasticity of Biot model with rheological skeleton.

## 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.

## 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.

## 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.