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1.
In this work, the macroscopic Richards equation for moisture transport is established in unsaturated porous media using periodic homogenization. By performing dimensional analysis on microscopic equations of moisture transfer, dimensional numbers characterizing moisture transport appear. The application of the asymptotic homogenization leads to the classical Richards equation, which is justified rigorously this way. Moreover, we obtain an accurate definition of the homogenized diffusion tensor of moisture involving the geometric properties of the microstructure and known transport properties of the material. A different behavior for the transport of water vapor between hygroscopic and super‐hygroscopic region is revealed. Finally, a simple 2D example where an analytical solution exists is addressed. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

2.
Field injectivity tests are widely used in the oil and gas industry to obtain key formation characteristics. The prevailing approaches for injectivity test interpretation rely on traditional analytical models. A number of parameters may affect the test results and lead to interpretation difficulties. Understanding their impacts on pressure response and fracture geometry of the test is essential for accurate test interpretation. In this work, a coupled flow and geomechanics model is developed for numerical simulation of field injectivity tests. The coupled model combines a cohesive zone model for simulating fluid-driven fracture and a poro-elastic/plastic model for simulating formation behavior. The model can capture fracture propagation, fluid flow within the fracture and formation, deformation of the formation, and evolution of pore pressure and stress around the wellbore and fracture during the tests. Numerical simulations are carried out to investigate the impacts of a multitude of parameters on test behaviors. The parameters include rock permeability, the leak-off coefficient of the fracture, rock stiffness, rock toughness, rock strength, plasticity deformation, and injection rate. The sensitivity of pressure response and fracture geometry on each parameter is reported and discussed. The coupled flow and geomechanics model provides additional advantages in the understanding of the fundamental mechanisms of field injectivity tests.  相似文献   

3.
An exact steady‐state closed‐form solution is presented for coupled flow and deformation of an axisymmetric isotropic homogeneous fluid‐saturated poroelastic layer with a finite radius due to a point sink. The hydromechanical behavior of the poroelastic layer is governed by Biot's consolidation theory. Boundary conditions on the lateral surface are specifically chosen to match the appropriate finite Hankel transforms and simplify the transforms of the governing equations. Ordinary differential equations in the transformed domain are solved, and then the analytical solutions in the physical space for the pore pressure and the displacements are finally obtained by using finite Hankel inversions. The analytical solutions at some special locations such as the top and bottom surfaces, lateral surface, and the symmetrical axis are given and analyzed. And a case study for the consolidation of a water‐saturated soft clay layer due to pumping is conducted. The analytical solution is verified against the finite element solution. Meanwhile, an analysis of coupled hydromechanical behavior is carried out herein. The presented analytical solution is an exact solution to the practical poroelastic problem within an axisymmetric finite layer. It can provide us a better understanding of the poroelastic behavior of the finite layer due to fluid extraction. Besides, it can be applied to calibrate numerical schemes of axisymmetric poroelasticity within finite domains. Copyright © 2017 John Wiley & Sons, Ltd.  相似文献   

4.
Thermo‐hydro‐mechanical responses around a cylindrical cavity drilled or excavated in a low‐permeability formation are studied when the cavity is subjected to a time‐dependent thermal loading. The cavity is considered backfilled after it is supported by casing or lining. Solutions of temperature, pore water pressure, stress, and displacement responses are analytically formulated based on Biot's consolidation theory with the assumption that the backfilling material, supporting material, and surrounding low‐permeability formation are poroelastic media. The solution is expressed in Laplace space, and numerical inversion techniques are used to find field variables in the real‐time domain. After the solution is verified with the numerical results, it is applied in a large‐scale in situ heating test – PRACLAY heating test – for a predictive reference calculation and an extensive parametric study. Another medium‐scale in situ heating test – ATLAS III heating test – is also analyzed using the solution, which provides reasonable agreement with measurements. The new analytical solution proves to be a convenient tool for a good understanding of the resulting coupled thermo‐hydro‐mechanical behavior and is therefore valuable for the interpretation of measured data in engineering practices and for a rational design of potential radioactive waste repositories. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

5.
Mathematical simulation of non‐isothermal multiphase flow in deformable unsaturated porous media is a complicated issue because of the need to employ multiple partial differential equations, the need to take into account mass and energy transfer between phases and because of the non‐linear nature of the governing partial differential equations. In this paper, an analytical solution for analyzing a fully coupled problem is presented for the one‐dimensional case where the coefficients of the system of equations are assumed to be constant for the entire domain. A major issue is the non‐linearity of the governing equations, which is not considered in the analytical solution. In order to introduce the non‐linearity of the equations, an iterative discretized procedure is used. The domain of the problem is divided into identical time–space elements that cover the time–space domain. A separate system of equations is defined for each element in the local coordinate system, the initial and boundary conditions for each element are obtained from the adjacent elements and the coefficients of the system of equations are considered to be constant in each step. There are seven governing differential equations that should be solved simultaneously: the equilibrium of the solid skeleton, mass conservation of fluids (water, water vapor and gas) and energy conservation of phases (solid, liquid and gas). The water vapor is not in equilibrium with water and different phases do not have the same temperature. The governing equations that have been solved seem to be the most comprehensive in this field. Three examples are presented for analyzing heat and mass transfer in a semi‐infinite column of unsaturated soil. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

6.
We present a second-order analytic solution [in terms of a heterogeneous log-transmissivity Y(r) = ln T(r)] for the hydraulic head field in a finite 2D confined heterogeneous aquifer under steady radial flow conditions assuming fixed head boundary conditions at the well and at a circular exterior boundary. The solution may be used to obtain the gradient used in calculation of solute transport to a well in a heterogeneous transmissivity field. The solution, obtained using perturbation methods coupled with Green's function techniques, leads us to postulate a more general form of the head for arbitrarily large-variance fields and may be used to obtain moment relations between the log-transmissivity and head under convergent flow conditions when Y(r) is expressed as a random space function. We present expressions for the mean head field when the log-transmissivity is Gaussian and conditioned on the transmissivity value at the well for an arbitrary ln T covariance. Finally, we look at the effect of parameter variations on the mean head behavior and present numerical simulations verifying the second-order mean head expressions.  相似文献   

7.
One major difficulty in seepage analyses is finding the position of phreatic surface which is unknown at the beginning of solution and must be determined in an iterative process. The objective of the present study is to develop a novel non‐boundary‐fitted mesh finite‐element method capable of solving the unconfined seepage problem in domains with arbitrary geometry and continuously varied permeability. A new non‐boundary‐fitted finite element method named as smoothed fixed grid finite element method (SFGFEM) is used to simplify the solution of variable domain problem of unconfined seepage. The gradient smoothing technique, in which the area integrals are transformed into the line integrals around edges of smoothing cells, is used to obtain the element matrices. The solution process starts with an initial guess for the unknown boundary and SFGFEM is used to approximate the field variable. The boundary shape is then modified to eventually satisfy nonlinear boundary condition in an iterative process. Some numerical examples are solved to evaluate the applicability of the proposed method and the results are compared with those available in the literature. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

8.
An analytical solution is proposed for transient flow and deformation coupling of a fluid‐saturated poroelastic medium within a finite two‐dimensional (2‐D) rectangular domain. In this study, the porous medium is assumed to be isotropic, homogeneous, and compressible. In addition, the point sink can be located at an arbitrary position in the porous medium. The fluid–solid interaction in porous media is governed by the general Biot's consolidation theory. The method of integral transforms is applied in the analytical formulation of closed‐form solutions. The proposed analytical solution is then verified against both exact and numerical results. The analytical solution is first simplified and validated by comparison with an existing exact solution for the uncoupled problem. Then, a case study for pumping from a confined aquifer is performed. The consistency between the numerical solution and the analytical solution confirms the accuracy and reliability of the analytical solution presented in this paper. The proposed analytical solution can help us to obtain in‐depth insights into time‐dependent mechanical behavior due to fluid withdrawal within finite 2‐D porous media. Moreover, it can also be of great significance to calibrate numerical solutions in plane strain poroelasticity and to formulate relevant industry norms and standards. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

9.
This paper presents a fracture mapping (FM) approach combined with the extended finite element method (XFEM) to simulate coupled deformation and fluid flow in fractured porous media. Specifically, the method accurately represents the impact of discrete fractures on flow and deformation, although the individual fractures are not part of the finite element mesh. A key feature of FM‐XFEM is its ability to model discontinuities in the domain independently of the computational mesh. The proposed FM approach is a continuum‐based approach that is used to model the flow interaction between the porous matrix and existing fractures via a transfer function. Fracture geometry is defined using the level set method. Therefore, in contrast to the discrete fracture flow model, the fracture representation is not meshed along with the computational domain. Consequently, the method is able to determine the influence of fractures on fluid flow within a fractured domain without the complexity of meshing the fractures within the domain. The XFEM component of the scheme addresses the discontinuous displacement field within elements that are intersected by existing fractures. In XFEM, enrichment functions are added to the standard finite element approximation to adequately resolve discontinuous fields within the simulation domain. Numerical tests illustrate the ability of the method to adequately describe the displacement and fluid pressure fields within a fractured domain at significantly less computational expense than explicitly resolving the fracture within the finite element mesh. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

10.
The governing differential equations of unsaturated soils considering the thermo‐poro‐mechanical behaviour consist of equilibrium, moisture air and heat transfer equations. In this paper at first, following some necessary simplifications, the thermal three‐dimensional fundamental solution for an unsaturated deformable porous medium with linear elastic behaviour in Laplace transform domain is presented. Subsequently, the closed‐form time domain fundamental solutions are derived by analytical inversion of the Laplace transform domain solutions. Then a set of numerical results are presented, which demonstrate the accuracies and some salient features of the derived analytical transient fundamental solutions. Finally, the closed‐form time domain fundamental solution will be verified mathematically by comparison with the previously introduced corresponding fundamental solution. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

11.
By using a complete set of poroelastodynamic spherical wave potentials (SWPs) representing a fast compressional wave PI, a slow compressional wave PII, and a shear wave S with 3 vectorial potentials (not all are independent), a solution scheme based on the method of fundamental solution (MFS) is devised to solve 3‐D wave scattering and dynamic stress concentration problems due to inhomogeneous inclusions and cavities embedded in an infinite poroelastic domain. The method is verified by comparing the result with the elastic analytical solution, which is a degenerated case, as well as with poroelastic solution obtained using other numerical methods. The accuracy and stability of the SWP‐MFS are also demonstrated. The displacement, hoop stress, and fluid pore pressure around spherical cavity and poroelastic inclusion with permeable and impermeable boundary are investigated for incident plane PI and SV waves. The scattering characteristics are examined for a range of material properties, such as porosity and shear modulus contrast, over a range of frequency. Compared with other boundary‐based numerical strategy, such as the boundary element method and the indirect boundary integral equation method, the current SWP‐MFS is a meshless method that does not need elements to approximate the geometry and is free from the treatment of singularities. The SWP‐MFS is a highly accurate and efficient solution methodology for wave scattering problems of arbitrary geometry, particularly when a part of the domain extends to infinity.  相似文献   

12.
An approximate analytical solution is presented for the coupled seepage and deformation problem of unsaturated soils. Because of the matric suction dependence of both saturation and permeability coefficient, the coupled governing equations are strongly nonlinear. To obtain an analytical solution, these coupled governing equations are linearized and analytically solved for a specified saturation using the eigenfunction method. Then, the obtained analytical solutions are extended to the entire saturation range. Comparison between the current solution and the previous theoretical solution indicates that the proposed solution yields excellent results. Due to its analytical nature, the proposed procedure can be effectively used to obtain the solution of the coupled seepage and deformation of unsaturated soils.  相似文献   

13.
The paper presents the analytical solution for the steady‐state infiltration from a buried point source into two types of heterogeneous cross‐anisotropic unsaturated half‐spaces. In the first case, the heterogeneity of the soil is modelled by an exponential relationship between the hydraulic conductivity and the soil depth. In the second case, the heterogeneous soil is represented by a multilayered half‐space where each layer is homogeneous. The hydraulic conductivity varies exponentially with moisture potential and this leads to the linearization of the Richards equation governing unsaturated flow. The analytical solution is obtained by using the Hankel integral transform. For the multilayered case, the combination of a special forward and backward transfer matrix techniques makes the numerical evaluation of the solution very accurate and efficient. The correctness of both formulations is validated by comparison with alternative solutions for two different cases. The results from typical cases are presented to illustrate the influence on the flow field of the cross‐anisotropic hydraulic conductivity, the soil heterogeneity and the depth of the source. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

14.
This paper presents a novel analytical solution to the transient, z‐dependent, and asymmetric problem of an infinite wellbore drilled into a fluid‐saturated porous medium. The formulations are based on Biot's linear theory of poroelasticity, in which the dependency of poroelastic field variables to spatial coordinates as well as time domain is considered in the most general form. This gives flexibility to the solution in cases that cannot be analyzed using the conventional plane strain or symmetric models. One such case is when calculating the stress variations around an inclined wellbore where the far‐field stresses are acting over a finite vertical section. The results of our solution to this case with a three‐dimensional state of far‐field stress are used to analyze the stability of inclined wellbores passing through abnormally stressed formations. The presented solution is capable of finding expressions for fundamental solutions with stress or flow boundary conditions at the wellbore. These solutions are here adopted to analyze the pressure disturbances generated by multiprobe formation tester, a standard wireline device that is designed for downhole fluid sampling as well as estimating the directional permeabilities of subsurface earth formations. A comparison with the conventional solution for the relevant pressure diffusion equation indicates that the poroelastic effect is relatively significant in relation to the transient response of the pore pressure. Further, it is shown that the finite dimensions of sink probe would, to a great extent, contribute to the formation's pore pressure variations at its immediate proximity. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

15.
This paper presents a non‐linear coupled finite element–boundary element approach for the prediction of free field vibrations due to vibratory and impact pile driving. Both the non‐linear constitutive behavior of the soil in the vicinity of the pile and the dynamic interaction between the pile and the soil are accounted for. A subdomain approach is used, defining a generalized structure consisting of the pile and a bounded region of soil around the pile, and an unbounded exterior linear soil domain. The soil around the pile may exhibit non‐linear constitutive behavior and is modelled with a time‐domain finite element method. The dynamic stiffness matrix of the exterior unbounded soil domain is calculated using a boundary element formulation in the frequency domain based on a limited number of modes defined on the interface between the generalized structure and the unbounded soil. The soil–structure interaction forces are evaluated as a convolution of the displacement history and the soil flexibility matrices, which are obtained by an inverse Fourier transformation from the frequency to the time domain. This results in a hybrid frequency–time domain formulation of the non‐linear dynamic soil–structure interaction problem, which is solved in the time domain using Newmark's time integration method; the interaction force time history is evaluated using the θ‐scheme in order to obtain stable solutions. The proposed hybrid formulation is validated for linear problems of vibratory and impact pile driving, showing very good agreement with the results obtained with a frequency‐domain solution. Linear predictions, however, overestimate the free field peak particle velocities as observed in reported field experiments during vibratory and impact pile driving at comparable levels of the transferred energy. This is mainly due to energy dissipation related to plastic deformations in the soil around the pile. Ground vibrations due to vibratory and impact pile driving are, therefore, also computed with a non‐linear model where the soil is modelled as an isotropic elastic, perfectly plastic solid, which yields according to the Drucker–Prager failure criterion. This results in lower predicted free field vibrations with respect to linear predictions, which are also in much better agreement with experimental results recorded during vibratory and impact pile driving. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

16.
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17.
This paper presents a model for the analysis of clay liner desiccation in a landfill barrier system due to temperature effects. The model incorporates consideration of fully coupled heat‐moisture‐air flow, a non‐linear constitutive relationship, the dependence of void ratio and volumetric water content on stress, capillary pressure and temperature, and the effect of mechanical deformation on all governing equations. Mass conservative numerical schemes are proposed to improve the accuracy of the finite element solution to the governing equations. The application of the model is then demonstrated by examining three test problems, including isothermal infiltration, heat conduction and non‐isothermal water and heat transport. Comparisons are made with results from literature, and good agreement is observed. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

18.
A new three-dimensional numerical model of coupled heat, moisture and air transfer in unsaturated soil is presented. In particular, the model accommodates moisture transfer in the form of liquid and vapour flow and heat transfer arising from conduction, convection and latent heat of vaporization. The bulk flow of dry air and the movement of air in a dissolved state are also included. The theoretical basis of the model, the finite element solution of the spatial terms and finite difference solution of the temporal terms are briefly presented. Attention is focused on the verification of the new numerical solution. This is achieved via comparisons with independent solutions of heat, moisture and air transfer in an unsaturated soil. The physical problem considered includes the highly non-linear hydraulic properties of sand. Thermal conductivity is also included as a function of soil moisture content. Excellent correlation of results is shown thus providing confidence in the new model. The new model is also applied to a number of test cases which illustrate the need for the development of a model which can fully include three-dimensional behaviour. In particular, three applications are presented each increasing in complexity. The first application illustrates three-dimensional heat transfer. This particular application is verified against existing commercial finite element software. Subsequent applications serve to illustrate how the coupled processes of heat moisture and air transfer combine to yield three-dimensional problems even within a simple geometric domain. Visualization of three-dimensional results is also addressed. © 1998 by John Wiley & Sons, Ltd.  相似文献   

19.
This paper introduces an exact analytical solution for governing flow equations for one‐dimensional consolidation in unsaturated soil stratum using the techniques of eigenfunction expansion and Laplace transformation. The homogeneous boundary conditions adopted in this study are as follows: (i) a one‐way drainage system of homogenous soils, in which the top surface is considered as permeable to air and water, whereas the base is an impervious bedrock; and (ii) a two‐way drainage system where both soil ends allow free dissipation of pore‐air and pore‐water pressures. In addition, the analytical development adopts initial conditions capturing both uniform and linear distributions of the initial excess pore pressures within the soil stratum. Eigenfunctions and eigenvalues are parts of the general solution and can be obtained based on the proposed boundary conditions. Besides, the Laplace transform method is adopted to solve the first‐order differential equations. Once equations with transformed domain are all obtained, the final solutions, which are proposed to be functions of time and depth, can be achieved by taking an inverse Laplace transform. To verify the proposed solution, two worked examples are provided to present the consolidation characteristics of unsaturated soils based on the proposed method. The validation of the recent results against other existing analytical solutions is graphically demonstrated. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

20.
A FEM model for analysis of fully coupled multiphase flow, thermal transport and stress/deformation in geological porous media was developed based on the momentum, mass and energy conservation laws of the continuum mechanics and the averaging approach of the mixture theory over a three phase (solid–liquid–gas) system. Six processes (i.e. stress–strain, water flow, gas flow, vapor flow, heat transport and porosity evolution processes) and their coupling effects are considered, which not only makes the problem well-defined, but renders the governing PDEs closed, complete, compact and compatible. Displacements, pore water pressure, pore gas pressure, pore vapor pressure, temperature and porosity are selected as basic unknowns. The physical phenomena such as phase transition, gas solubility in liquid, thermo-osmosis, moisture transfer and moisture swelling are modeled. As a result, the relative humidity and other related variables in porous media can be evaluated on a sounder physical basis. A three dimensional computer code, THYME3D, was developed, with eight degrees of freedom at each node. The laboratory CEA Mock-up test and the field scale FEBEX benchmark test on bentonite performance assessment for underground nuclear waste repositories were used to validate the numerical model and the software. The coupled THM behaviors of the bentonite barriers were satisfactorily simulated, and the effects and impacts of the governing equations, constitutive relations and property parameters on the coupled THM processes were understood in terms of more straightforward interpretation of physical processes at microscopic scale of the porous media. The work developed enables further in-depth research on fully coupled THM or THMC processes in porous media.  相似文献   

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