In old deep abandoned mines, the problem of separation of the layers of a different nature needs ... more In old deep abandoned mines, the problem of separation of the layers of a different nature needs to be solved. The problem discussed in this paper relates to mines situated near Prague, capital of the Czech Republic and is concerned with a separation of two kinds of underground water, one being salt (saline) and the other sweet (fresh) water. The layer of the sweet water is positioned at approximately 200 m below the surface, then there was originally a layer of watertight clay (hydrogeological insulator) and from some 300 m downwards, salt water occurs. A problem arose when the shafts, at a depth of 1000 m, have been abandoned due to canceling the mine workings. During mining, pumps were used and no permeability was enabled. Since the mining has stopped, there is no reason to continue pumping and the danger of mixing both kinds of water has occurred. It was decided, in order not to damage the sweet water which is also used for wells and subsoil irrigation, that a stopper should be added into the clay layers to suppress any possibility of mixing both kinds of water. The problem then was oriented to answer several questions. One of the most important that was put forward was on the relationship between permeability coefficients and the thickness of the stopper. Another one was concerned with the optimization of expenses involving the required permeability, expressed in terms of economic indicators, the thickness depending on expenses, etc. As a numerical model has been prepared and it was necessary to feed it by reasonable input data, a scale model from physically equivalent materials was created and tested. The mutual influence of both models, mathematical and experimental, offered a very powerful tool for well-prepared reports on how the stopper should be constructed.
WIT transactions on engineering sciences, Jun 7, 2001
The goal of this paper is to introduce an energy-based approach to interaction between 0 a creepi... more The goal of this paper is to introduce an energy-based approach to interaction between 0 a creeping upper structure, and a subsoil undergoing consolidation. Following the variational formulation the numerical. finite element-based procedure, is proposed. We start by analysing interaction between individual phases characterzing transport processes in porous media. A set of differential equations describing these phenomena is derived. T h e main difficulty occurs when linking both the upper structure and subsoil. The displacement field might e incompatible along the interface between the two parts of the system considered. T h e remedy is to apply the modified Lagrange principle t o the quilibrium equations pertaining to both subdomains separately. Conversion of the principle of virtual work t,o the Lagrange principle requires that the displacement field be continuous along the interface surface. his constraint can be incorporated into the Lagrange principle to arrive a t its modified version 0 either by introducing a new variable (Lagrange multiplier), which repesents the interface tractions related to the interface boundary 0 or by approximating the Lagrange multiplier introducing an approprite penalty function. Since the process of deformation, describing t,he history of deformation n both subdomains (upper structure and subsoil) is time-dependant; an ppropriate algorithm affording the time history is necessary. It is known hat numerical solution of structure-subsoil interaction problems leads to arge system of equations. This disadvantage can be overcome and the
WIT Transactions on the Built Environment, May 4, 2005
In the problem of cracking of composite structures of several sorts, the pullout problem has freq... more In the problem of cracking of composite structures of several sorts, the pullout problem has frequently been solved. In some previous papers by the authors, curvilinear fibers reinforcing concrete mainly during its curing process have been studied. It was shown that the fibers of Dramix type proved to have a higher local bearing capacity than the straight fibers. The problem was solved in 3D on a unit cell assuming a periodicity of fiber placing. The linear behavior of concrete was taken into account and the pullout test was simulated by the finite element method. In this paper the optimal slope of fibers is sought. Using similar computations as those which were carried out in the above-mentioned papers, the optimum conditions have been added. They obey the typical Mohr-Coulomb law along the fiber-concrete interfacial zones and the compressive strength in the concrete cannot be exceeded at any point. The study is carried out on different unit cells, i.e. different positioning of fibers is considered. A different fiber ratio is also considered to show the mechanical behavior and to limit analysis of the composite aggregate.
WIT transactions on modelling and simulation, Feb 21, 2005
The paper deals with the debonding fiber-matrix process in composite materials. A couple of paper... more The paper deals with the debonding fiber-matrix process in composite materials. A couple of papers has been focused on this problem by the authors of this paper. As usual, the influence of separate pure normal and pure shear energy has been studied for obtaining the overall material properties. Such an approach is a simplification of the problem describing the mechanical behavior of the interface between fibres and the matrix in composite materials, since the standard procedure consisting of the superposition of both normal and shear influences is no longer admissible due to the strongly nonlinear behavior of the process. In this paper a more complex development of the debonding zones is shown, namely, responses of successively applied normal and then shear load and also first shear load and then normal load are observed. The physical behaviour of the interface is non-convex. This assertion immediately follows from the penalty formulation of the problem as published recently by the first author. The penetration of fiber into the matrix is not allowed in every case. In this contribution we start with a definition of the model describing the transfer of elastic stresses from the matrix to the fiber. Then, the contact problem is formulated in a manner leading to a very fast Uzawa's algorithm for its solution. In order to speed up the iterative solution influence matrices are created before the iteration. The approach turns to a similar one known as generalized transformation field analysis. Debonding processes in the interfacial zone are illustrated by examples.
WIT transactions on modelling and simulation, Jun 11, 2007
In some previous papers of the author coupled numerical-experimental modeling of tunnels embedded... more In some previous papers of the author coupled numerical-experimental modeling of tunnels embedded in surrounding rock was based on minimization of a certain functional describing the steepest descend mode of differences of measured and computed values of stresses or displacements at selected points. The idea consisted of a choice of subdomains (patches), the eigenstrains in which were introduced using the unit impulse technique. Influence matrices were generated and the linear hull of eigenstrain effects together with the optimization problem lead to the identification of plastic stresses inside the domain describing the surrounding rock. Consequently, a nonlinear model in numerical analysis can be improved using eigenparameters as design parameters in optimization. The only problem remaining is how to select the patches. In this paper inverse variational principles are applied to help solve this principal problem. The 2D problem is solved with moving patches (support subdomains) with uniformly introduced eigenstrains.
WIT Transactions on the Built Environment, Apr 23, 2007
Shape optimization of fibers based on the highest bearing capacity of composite aggregate on a un... more Shape optimization of fibers based on the highest bearing capacity of composite aggregate on a unit cell is studied using Inverse variational principles. They have been applied mostly in connection with finite elements. It appears now that boundary elements are much more efficient. On the other hand, it is necessary to find an appropriate function, which describes boundary density of potential energy and at the same time variational bounds or homogenization of the composite have to be carried out. If one starts with homogenization, a mathematical formulation has to prove that a solution exists and is unique. The latter problem seems not to be as simple as it first seems. Additional constraints must be introduced to ensure the uniqueness of the solution. If bounds are sought, we start with extended Hashin-Shtrikman principles. A study is carried out for different relations of fibers and matrices. Keynotes: optimization, Inverse variational principles, classical composites.
WIT transactions on modelling and simulation, Feb 21, 2005
Numerical methods seem to be the cheapest tool for assessing underground structures. However, the... more Numerical methods seem to be the cheapest tool for assessing underground structures. However, there exists one obstacle in applications of any numerical method which is a lack of information concerning the input data, particularly the knowledge of material properties. If the theory of damage should be involved in the formulation of the problem to be solved, special treatment is required. The methods, which are extensively used, start with realization of the trial body by a continuum. We can name "Cohesive zone method", which deals with Barenblatt's theory, for example. In our problem such methods are difficult to apply and exhibit unreal behavior, according to a couple of test examples. This is why test experiments have been carried out to gain further information towards a reasonable approach for solving the problem. The free hexagon method seems to be very promising. The method will be described and basic formulas will be derived, and then applications to assessment of structural strength will be presented.
WIT Transactions on the Built Environment, May 25, 2005
There are number of structures that either require local reinforcement or even have been locally ... more There are number of structures that either require local reinforcement or even have been locally reinforced during their construction. For example, a number of historic buildings in Prague, the capital of the Czech Republic, are built up with different local reinforcement, such as goat hair, fibers of different kinds (steel, plastic, glass, etc.). The historic buildings are exposed to current climate conditions and heavy traffic pollution, which are both very damaging to the quality of the original mortars. This is why the necessity of refurbishment of the old building is obvious. The fibers locally reinforce concrete, particularly in exacting conditions, such as shotcrete in tunnel construction, foundation engineering, etc. The aim of this paper is to compare experimental data with results from a numerical model to get information on the mechanical behavior of the locally reinforced material for further theoretical studies.
WIT transactions on modelling and simulation, Aug 27, 2009
In the paper a new procedure for effective properties of nonlinear composites will be proposed. B... more In the paper a new procedure for effective properties of nonlinear composites will be proposed. Based on boundary element method various ratios of phase stiffnesses are studied. Special properties of the stress distribution (or concentration factors) on a unit cell are utilized. The overall properties start with Hashin-Shtrikman idea, which is transformed to a numerical framework. Without loss of generality geometrical boundary conditions on the boundary of a unit cell are prescribed in this study. A special case of the presented approach is the effect of pore pressure, occurring in fiber reinforced concrete, for example. Also nonlinear behavior of the phases is taken into consideration, especially the von Mises-Huber-Hencky criterion is adopted in the model of matrix. The examples are exclusively prepared for two-phase materials.
WIT transactions on modelling and simulation, Apr 17, 2001
Rock burnps or rock bursts occur mostly a t decp excavations: during mining. tunneling a t high e... more Rock burnps or rock bursts occur mostly a t decp excavations: during mining. tunneling a t high enough overburden, and shaft excavalions. As an effect of instability of thnnel or shaft face, t8he extrusion of t,he rock mass into free space is studied both experimentally and mat,hematically. Frictional ignit,ion and t,ensilc overstressing of the mass rnay also cause t,he rock burst. This paper focuses on this phenomenon, starting with a specially prcparr~l experiment and a new numerical procedure. Both these t,ools provide a new view a t process of initiation of the failure of rock at tunnel face. T h e experimental study model simulatas the situation on sitme. while niinlerical model informs about clet,ailecl inatarial brhavior a t local zones endangered by the overstressing. Correctness of the numerical rnodrl is vcrific4 l>y distribution of stresses (forces) along the upper part of lining.
WIT Transactions on the Built Environment, Aug 25, 2008
Underground spaces offer large areas or volumes for establishment of underground nuclear power st... more Underground spaces offer large areas or volumes for establishment of underground nuclear power stations, underground halls, underground deposits of nuclear waste, and underground sewerage plants, etc. The roofing of such structures requires thick walled structures, in most cases being created from fiber reinforced concretes. Additionally, standard rebars serve as a bearing reinforcement while the fibers keep off moisture, chemical gas, vapor, which can cause damaging corrosion of the rebars of various kind. The fibers serve also as defense from influence of relaxation due to change of temperature. Since the structures of this kind are of length span, the construction of them demands special treatment during the soil covering of the roof of such structures, which are here considered pelted. Moreover, very important phenomenon, creep, should be involved in the calculation as the time for building up such robust structures requires long period, during which the creep in particular parts of the structure can influence the stress state in the whole structure. The starting idea is based on creation of lathwork supporting the whole structure. On this lathwork all parts of the concrete structure will be positioned in stages, which are prescribed with respect to successive loading and optimal bearing capacity in overall structure involving successive influence of creep. In this paper, advantages of surface nuclear power stations, underground drilled power stations and pelted nuclear power stations are discussed and for the latter fiber reinforce concrete is discussed. Some results of tests of selected fibers aiming to application if structures of pelted power stations are presented. The influence of mechanical behavior, as well as the thermal and chemical effects is shown.
In several previous papers by the authors the problem of bumps occurrence has been solved by dist... more In several previous papers by the authors the problem of bumps occurrence has been solved by distinct element methods, namely by the free hexagon method. The latter method proved its significance in the description of the most probable nucleation of debonding of rock mass, when cracks or flaws occurred, which at the moment of bumps create the contact surface of the moving part of the coal seam. The movement of particles after bumps is described. In this paper another approach is used. Starting with the aim of describing whether the bumps occur or not, or under which condition they appear, the continuum of both the rock seam and the overburden (rock) is considered. The decision whether the bumps are triggered can then be derived from conditions at different points of the coal seam. For the solution, the boundary element method is used and elastic behavior (more precisely brittle behavior of the material of coal) is assumed.
This paper deals with damage localized on interfaces between the fibres and the matrix in composi... more This paper deals with damage localized on interfaces between the fibres and the matrix in composite materials, which are often regarded as macroscopically homogeneous solids with certain effective properties derived from information on phase properties and local geometry. This viewpoint is justified only for loading conditions that do not impair the integrity of the microstructure. In this contribution we start with a survey of models describing the transfer of elastic stresses from the matrix to the fiber. Then. the contact problems are formulated in a manner leading to a very fast Uzawa's algorithm (cf. [4]) for their solving. Debonding processes in the iriterfacial zone are illustrated by an example and discussed from the stability standpoint. A simple solution of the overall response of a damaged composite system is based on the TFA model. Finally, an approximative formula describes the size effect.
WIT transactions on modelling and simulation, Aug 22, 2000
complicated problem is to determine the properties of the springs. ties of the material. The part... more complicated problem is to determine the properties of the springs. ties of the material. The particles are considered to be rigid. The most normal and tangential directions. The springs express the elastic proper-particles are in mutual contact and the contact is realized by springs in both shape, particularly in geotechnics, is a ball in 3D, or a circle in 2D. The particles, which may be of different shape. One of the most prospective The distinct element method consists of discretization of a continuum into that the solution of the algebraic equations by iterative methods is natural. it is nonlinear in any case), the iteration process must be used anyway, so solving these equations. When formulating the problem as a nonlinear (and numerical treatment are nested, an iteration procedure can to be employed the systern of algebraic equations may be enormous. Since the matrices in tion of several types of contact conditions is also possible. On the other hand tic, viscoplastic, or other nonlinear behavior in the particles and introduc-hexagonal elements in 2D using the BEM. This enables one to involve plas-Our objective in this paper is to avoid this difficulty by solving the free elasticity, etc.). parameters of the medium (angle of internal friction, cohesion, modulus of balls. Also, the contact material values are compatible with the material the natural conditions is more probable and faithful in comparison with the ing medium, which is the case of, e.g., soil. In our case the description of In comparison with continuum our concept leads to possibly disconnectengineering and brittle material of strongly compressed rock (coal). excavation of longwall mines in great depths, i.e., particularly to mining The theory is applied to constructions of underground works, namely
WIT transactions on engineering sciences, Sep 25, 2002
The discrete element methods (DEM) are very often used in mechanics of granular media. They subst... more The discrete element methods (DEM) are very often used in mechanics of granular media. They substitute the methods solving continuum. The DEM enables researchers to find local discontinuities in displacements, propagation of cracks, etc., although the location of such disturbances is not known in advance. This is why the principal idea of the DEM is used in this paper, and 3D balls being in mutual contact in the undeformed state are used. The rigid balls are elastically connected in the beginning of deformation, then the interracial boundary conditions between adjacent particles are obeyed and are the reason for jumps in displacements.
WIT transactions on engineering sciences, Oct 14, 2005
Eigenstresses and eigenstrains act out a very important role in many branches of applied mechanic... more Eigenstresses and eigenstrains act out a very important role in many branches of applied mechanics. The eigenparameters may represent plastic strains, or relaxation stresses (or also prestresses, changes of temperature, etc.), and may also serve as free parameters for improving numerical models to get the computed quantities that should be as close as possible to the real state. A special variational formulation can be formulated, dealing with the minimum variance of differences between measured and computed values. When using a very useful treatment, the generalized transformation field analysis (GTFA), having recently been proposed by Dvorak and Procházka, and the Disturbed State Concept proposed by Desai, the primary problem leads to a linear system of algebraic equations. First, we briefly introduce an estimation of physically nonlinear behavior of the body by Desai. The eigenparameters will then be introduced in such a manner that the optimal variance of errors from measurement and numerical results are sought. It appears that the number of components of eigenparameters should not exceed the number of data points from measurements either on site or on a scale model, and hence, the number of free eigenparameters is restricted. The main problem remains: how to select the zones with, say, uniformly distributed eigenparameters in order to achieve the minimum deviation of computed and measured results in dependence of the minimum variation of errors from computation and of the topology of the eigenparameters zone. They basically influence the final results from the procedure to be described. The main goal of this paper consists in finding out both the phenomena. While the minimum of the error functional leads to linear algebraic equations, searching for optimal topology of eigenparameters zones brings about a nonlinear problem, which should be solved in some reasonable way. We first concentrate on the optimization of the error functional under the condition that the zones are known and then the zones will be sought.
WIT transactions on modelling and simulation, 1970
Homogenization and shape optimization of fibers in a composite structure has been solved by many ... more Homogenization and shape optimization of fibers in a composite structure has been solved by many authors mostly by means of the FEM. In this paper a new procedure for homogenization of composites is proposed. This is based on the BEM, which seems to be more efficient and more accurate in applications than the FEM solution. Special properties of the distribution of stresses (or concentration factors) on a unit cell are used. Averaging process including integration over the unit cell, particularly in the case of fiber reinforced concrete (when the fiber ratio is relatively small) follows the fact that the stresses "relax" on the matrix and their distribution converges to constant except for a zone being in the vicinity of the fiber-matrix interfacial surface. This is why boundary element method is more suitable than finite element method, particularly in problems concerning fiber reinforced concretes. A comparison medium is employed and the jump in material properties is involved in integral form, Prochazka, Sejnoha^. Hence, no Eshelby forces have to be applied along the interface fiber-matrix, Suquet^. Then, inverse variational principles, Prochazka^ (including variation of the domain of fiber under subsidiary condition that the volume of the fiber is fixed), may be used and the mechanical behavior on the interface fiber-matrix is more viewable during the iteration process solving this strictly nonlinear problem). From the point of view of numerical solution, two basic steps will be observed: 1 the homogenization (periodic medium),
WIT transactions on engineering sciences, May 8, 2007
Inverse variational principles proved their importance in shape optimization of structures. In th... more Inverse variational principles proved their importance in shape optimization of structures. In this paper they are applied to searching for the optimal shape of fibers in a composite structure. As the boundary element method seems to be more promising than other modern numerical methods applied to the search for optimal shape, in the submitting paper the boundary element method is redefined to enable one to use such an approach, which leads to possibility for the optimal interfacial energies and, hence, to the optimal bearing capacity of the composite structure. Necessary discretization of the domain, which occurs in the finite elements, is suppressed in our case. Standard procedure in the finite elements leads to dependence of the stiffness matrix on the shape of the fibers. In this case, following a basic idea for homogenization and localization, concentration factors have to be calculated in terms of the boundary element method instead. These terms are dependent on the shape of the fibers. It appears that the procedure is still not convergent (we solve a strongly nonlinear problem) and additional constraint has to be involved in the formulation. In order to formulate and solve this problem, the idea of Inverse variational principles is applied here for expressing necessary quantities. The paper concentrates on the calculation of quantities, which are necessary to formulate the optimization problem. The main attention is focused on calculation of concentration factors, which play the most important role in the approach proposed.
WIT Transactions on the Built Environment, Apr 18, 2006
Fibers in concrete should primarily restrain the material from cracks during the curing process a... more Fibers in concrete should primarily restrain the material from cracks during the curing process and dehydration. For standard evaluation of the influence of the fibers, the three or four point test is studied, both experimentally and numerically on a straight beam. In tunnel lining the situation is slightly different. While the three or four point test leads to the assessment of the structure being only bended, in tunnel reinforcement not only this but also bending with normal force has to be observed. Moreover, the curing is affected by the non-uniform distribution of moistening, as from the side of the surrounding rock the measure of wet is principally higher than on the face where ventilation speeds up the dehydration. These two assumptions are considered and treated experimentally and numerically. Because a real tunnel lining is too large, a scale model is used and, consequently, more samples can be studied. Similarity rules and an appropriate calibration have to be obeyed. This paper is principally focused on the theory of possible coupled modeling of behavior of the one-sided moistened tunnel lining.
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