Frontiers of Architecture and Civil Engineering in China, 2010
Many problems are linked with the long term behaviour of dams, both earth-dams and concrete dams.... more Many problems are linked with the long term behaviour of dams, both earth-dams and concrete dams. They range from hydraulic fracturing to alkali-silica reaction and to repair work in concrete dams, from seismic behaviour to secondary consolidation in earth-dams. A common framework for simulation of such systems is shown, based on the mechanics of multiphase porous media. The general model is particularized to specific situations and several examples are shown.
ABSTRACT The paper presents a fully-coupled numerical model for the analysis of fracture initiati... more ABSTRACT The paper presents a fully-coupled numerical model for the analysis of fracture initiation and propagation in a two dimensional non-homogeneous elastic medium driven by mechanical loads and transient thermal fields. Cohesive crack behaviour is assumed for the solid. The solution of the coupled problem is obtained by using the finite element method without using special approximation techniques nor interface elements. Evolution of the process zone results in continuous changes of the domain topology. This is accounted for by updating the boundary geometry and successive remeshing of the domain. Optimality of the shape of the finite elements generated is controlled and the mesh density is adjusted adaptively on the basis of an error estimator. Two numerical applications are presented, which demonstrate the effectiveness of the proposed procedure. In the first, comparison is made with a laboratory experiment, whereas the second handles a problem with crack path completely unknown.
Traditional phenomenological constitutive relationships sometimes fail in the description of mech... more Traditional phenomenological constitutive relationships sometimes fail in the description of mechanical behaviour of plain concrete. In such circumstances more refined models are necessary, which takes into account the multiphase structure of the material. This paper presents a generalised finite element formulation, which incorporates solid and fluid phases together with a temperature field. The model is developed to obtain time-dependent solutions of 2-D cases, such as concrete gravity dams subjected to loading-unloading cycles, non-homogeneous specimens subjected to thermo-mechanical effects, etc. A fully coupled cohesive-fracture discrete model, which includes thermal and hydraulic loads, is adopted to describe crack nucleation and propagation. The evolution of fractures leads to continuous topological changes of the domain and these are handled by systematic local remeshing of the domain and by a continuous change of fluid and thermal boundary conditions. In the adopted approac...
Traditional phenomenological constitutive relationships sometimes fail in the description of mech... more Traditional phenomenological constitutive relationships sometimes fail in the description of mechanical behaviour of plain concrete. In such circumstances more refined models are necessary, which takes into account the multiphase structure of the material. This paper presents a generalised finite element formulation, which incorporates solid and fluid phases together with a temperature field. The model is developed to obtain time-dependent solutions of 2-D cases, such as concrete gravity dams subjected to loading-unloading cycles, non-homogeneous specimens subjected to thermo-mechanical effects, etc. A fully coupled cohesive-fracture discrete model, which includes thermal and hydraulic loads, is adopted to describe crack nucleation and propagation. The evolution of fractures leads to continuous topological changes of the domain and these are handled by systematic local remeshing of the domain and by a continuous change of fluid and thermal boundary conditions. In the adopted approach, cracks may nucleate everywhere depending only on the stress field and propagate along paths and with a velocity of the tip that is a priori unknown. The determination of the crack path and the velocity of the tip propagation represent an important part of the solution, as the temperature and stress fields and allows for correct updating of the domain. Governing equations are firstly presented together with their space discretization. The solution procedure is finally discussed in particular as far as the projection of the solution between two successive meshes is concerned.
A new numerical model for the simulation of ASR in cement-based materials considering both the ef... more A new numerical model for the simulation of ASR in cement-based materials considering both the effect of temperature and moisture content is presented. A mechanistic approach, based on the mechanics of porous media, was used to obtain the governing equations by means of a hybrid mixture theory. The model equations, mass (water species and dry air), energy and momentum balances are written in terms of the chosen primary variables: gas pressure, capillary pressure, temperature and displacement vector, while the ASR evolution is described by the reaction extent being the internal variable. The model takes into account full coupling between hygral, thermal and chemical phenomena, as well as changes of concrete properties caused by chemical reaction, i.e. porosity, density, permeability. Phase changes and chemical processes, as well as the related heat and mass sources are considered. Material chemical and mechanical degradation is considered with the isotropic damage theory. The model e...
It is now generally recognized that mode I fracturing in saturated geomaterials is a stepwise pro... more It is now generally recognized that mode I fracturing in saturated geomaterials is a stepwise process. This is true both for mechanical loading and for pressure induced fracturing. Evidence comes from geophysics, from unconventional hydrocarbon extraction, and from experiments. Despite the evidence only very few numerical models capture this behavior. From our numerical experiments, both with a model based on Standard Galerkin Finite Elements in conjunction with a cohesive fracture model, and with a truss lattice model in combination with Monte Carlo simulations, it appears that already in dry geomaterials under mechanical loading the fracturing process is time discontinuous. In a two-phase fracture context, in case of mechanical loading, the fluid not only follows the fate of the solid phase material and gives rise to pressure peaks at the fracturing event, but it also influences this event. In case of pressure induced fracture clearly pressure peaks appear too but are of opposite ...
A systematic approach to the estimation of errors of a staggered predictor-corrector solution sch... more A systematic approach to the estimation of errors of a staggered predictor-corrector solution scheme for consolidation of porous media problems is presented. The total error is split into the temporal discretization error, the error of iterations and the stability error. The errors are investigated for linear and nonlinear problems and comparisons with the direct method are made.
We address stepwise crack tip advancement and pressure fluctuations, which have been observed in ... more We address stepwise crack tip advancement and pressure fluctuations, which have been observed in the field and experimentally in fracturing saturated porous media. Both fracturing due to mechanical loading and pressure driven fracture are considered. After presenting the experimental evidence and the different explanations for the phenomena put forward and mentioning briefly what has been obtained so far by published numerical and analytical methods we propose our explanation based on Biot’s theory. A short presentation of three methods able to simulate the observed phenomena namely the Central Force Model, the Standard Galerkin Finite Element Method SGFEM and extended finite element method XFEM follows. With the Central Force Model it is evidenced that already dry geomaterials break in an intermittent fashion and that the presence of a fluid affects the behavior more or less depending on the loading and boundary conditions. Examples dealing both with hydraulic fracturing and mechanical loading are shown. The conditions needed to reproduce the observed phenomena with FE models at macroscopic level are evidenced. They appear to be the adoption of a crack tip advancement/time step algorithm which interferes the least possible with the three interacting velocities, namely the crack tip advancement velocity on one side, the seepage velocity of the fluid in the domain and from the crack (leak-off), and the fluid velocity within the crack on the other side. Further the crack tip advancement algorithm must allow for reproducing jumps observed in the experiments.
A generalized Biot formulation for the mechanics of saturated-unsaturated porous media is present... more A generalized Biot formulation for the mechanics of saturated-unsaturated porous media is presented. Particular emphasis is given to the derivation of a modified effective stress vector applicable in rock mechanics and concrete. An example relating to soil mechanics situation is presented.
A numerical model for the mechanics of partially saturated porous media is presented where the fl... more A numerical model for the mechanics of partially saturated porous media is presented where the flow of both fluid phases is taken into account. The attention is focused on the choice of the field variables so that the model may easily be extended to deal with the important case when the gaseous phase is at constant reference pressure and with the limiting case of a fully saturated situation. To solve the semidiscretized governing differential equation system in the time domain a staggered procedure is presented, which also allows for a straightforward solution of the two aforementioned cases. The stability and convergence analyses of the proposed solution scheme are presented for a 3 degree-of-freedom model system. In this way it is possible to assess the behaviour of the proposed solution scheme.
ABSTRACT This paper analyses the numerical difficulties commonly encountered in solving fully cou... more ABSTRACT This paper analyses the numerical difficulties commonly encountered in solving fully coupled numerical models and proposes a numerical strategy apt to overcome them. The proposed procedure is based on space refinement and time adaptivity. The latter, which in mainly studied here, is based on the use of a finite element approach in the space domain and a Discontinuous Galerkin approximation within each time span. Error measures are defined for the jump of the solution at each time station. These constitute the parameters allowing for the time adaptivity. Some care is however, needed for a useful definition of the jump measures. Numerical tests are presented firstly to demonstrate the advantages and shortcomings of the method over the more traditional use of finite differences in time, then to assess the efficiency of the proposed procedure for adapting the time step. The proposed method reveals its efficiency and simplicity to adapt the time step in the solution of coupled field problems.
ABSTRACT We present as areas of interest for multifield fracturing thermomechanical fracturing, f... more ABSTRACT We present as areas of interest for multifield fracturing thermomechanical fracturing, fluid pressure induced isothermal and nonisothermal fracturing, fracturing due to radiation, drying, hydrogen embrittlement, and fractures induced by chemical effects. We discuss the most appropriate constitutive models for their simulation and choose the cohesive fracture model for quasi-brittle materials. Successively we show governing equations for a thermo-hydro-mechanical problem, which is representative for multifield problems. Possible extensions to more fields are addressed. Then methods for numerical modeling of multifield fracturing are presented and the most representative ones, i.e., interface and embedded discontinuity elements, X-FEM, thick level set and phase field models, and discrete crack approach with adaptive remeshing are discussed in some detail. After incorporating this last method in the governing equations, their numerical solution is shown together with the necessary adaptivity in time and space. This solution is validated. Successively applications to thermomechanical fracture; hydraulic fracturing in case of a pumped well and of 2D and 3D dams; fracturing of drying concrete and of a massive concrete beam and finally mechanical effects of chemical processes in concrete are shown. In the case of the pumped well with constant pumping rate, a comparison between an Extended Finite Element solution and that of the discrete crack approach with adaptive remeshing is made which allows for interesting considerations about the nature of hydraulic fracturing. The examples permit to conclude that with increasing complexity of the multifield problems that of the employed fracture models decreases, i.e., advanced fracture models have to date only been applied to problems with a limited number of fields, mainly displacement, thermal and/or pressure fields. There is hence plenty of room for improvement.
Frontiers of Architecture and Civil Engineering in China, 2010
Many problems are linked with the long term behaviour of dams, both earth-dams and concrete dams.... more Many problems are linked with the long term behaviour of dams, both earth-dams and concrete dams. They range from hydraulic fracturing to alkali-silica reaction and to repair work in concrete dams, from seismic behaviour to secondary consolidation in earth-dams. A common framework for simulation of such systems is shown, based on the mechanics of multiphase porous media. The general model is particularized to specific situations and several examples are shown.
ABSTRACT The paper presents a fully-coupled numerical model for the analysis of fracture initiati... more ABSTRACT The paper presents a fully-coupled numerical model for the analysis of fracture initiation and propagation in a two dimensional non-homogeneous elastic medium driven by mechanical loads and transient thermal fields. Cohesive crack behaviour is assumed for the solid. The solution of the coupled problem is obtained by using the finite element method without using special approximation techniques nor interface elements. Evolution of the process zone results in continuous changes of the domain topology. This is accounted for by updating the boundary geometry and successive remeshing of the domain. Optimality of the shape of the finite elements generated is controlled and the mesh density is adjusted adaptively on the basis of an error estimator. Two numerical applications are presented, which demonstrate the effectiveness of the proposed procedure. In the first, comparison is made with a laboratory experiment, whereas the second handles a problem with crack path completely unknown.
Traditional phenomenological constitutive relationships sometimes fail in the description of mech... more Traditional phenomenological constitutive relationships sometimes fail in the description of mechanical behaviour of plain concrete. In such circumstances more refined models are necessary, which takes into account the multiphase structure of the material. This paper presents a generalised finite element formulation, which incorporates solid and fluid phases together with a temperature field. The model is developed to obtain time-dependent solutions of 2-D cases, such as concrete gravity dams subjected to loading-unloading cycles, non-homogeneous specimens subjected to thermo-mechanical effects, etc. A fully coupled cohesive-fracture discrete model, which includes thermal and hydraulic loads, is adopted to describe crack nucleation and propagation. The evolution of fractures leads to continuous topological changes of the domain and these are handled by systematic local remeshing of the domain and by a continuous change of fluid and thermal boundary conditions. In the adopted approac...
Traditional phenomenological constitutive relationships sometimes fail in the description of mech... more Traditional phenomenological constitutive relationships sometimes fail in the description of mechanical behaviour of plain concrete. In such circumstances more refined models are necessary, which takes into account the multiphase structure of the material. This paper presents a generalised finite element formulation, which incorporates solid and fluid phases together with a temperature field. The model is developed to obtain time-dependent solutions of 2-D cases, such as concrete gravity dams subjected to loading-unloading cycles, non-homogeneous specimens subjected to thermo-mechanical effects, etc. A fully coupled cohesive-fracture discrete model, which includes thermal and hydraulic loads, is adopted to describe crack nucleation and propagation. The evolution of fractures leads to continuous topological changes of the domain and these are handled by systematic local remeshing of the domain and by a continuous change of fluid and thermal boundary conditions. In the adopted approach, cracks may nucleate everywhere depending only on the stress field and propagate along paths and with a velocity of the tip that is a priori unknown. The determination of the crack path and the velocity of the tip propagation represent an important part of the solution, as the temperature and stress fields and allows for correct updating of the domain. Governing equations are firstly presented together with their space discretization. The solution procedure is finally discussed in particular as far as the projection of the solution between two successive meshes is concerned.
A new numerical model for the simulation of ASR in cement-based materials considering both the ef... more A new numerical model for the simulation of ASR in cement-based materials considering both the effect of temperature and moisture content is presented. A mechanistic approach, based on the mechanics of porous media, was used to obtain the governing equations by means of a hybrid mixture theory. The model equations, mass (water species and dry air), energy and momentum balances are written in terms of the chosen primary variables: gas pressure, capillary pressure, temperature and displacement vector, while the ASR evolution is described by the reaction extent being the internal variable. The model takes into account full coupling between hygral, thermal and chemical phenomena, as well as changes of concrete properties caused by chemical reaction, i.e. porosity, density, permeability. Phase changes and chemical processes, as well as the related heat and mass sources are considered. Material chemical and mechanical degradation is considered with the isotropic damage theory. The model e...
It is now generally recognized that mode I fracturing in saturated geomaterials is a stepwise pro... more It is now generally recognized that mode I fracturing in saturated geomaterials is a stepwise process. This is true both for mechanical loading and for pressure induced fracturing. Evidence comes from geophysics, from unconventional hydrocarbon extraction, and from experiments. Despite the evidence only very few numerical models capture this behavior. From our numerical experiments, both with a model based on Standard Galerkin Finite Elements in conjunction with a cohesive fracture model, and with a truss lattice model in combination with Monte Carlo simulations, it appears that already in dry geomaterials under mechanical loading the fracturing process is time discontinuous. In a two-phase fracture context, in case of mechanical loading, the fluid not only follows the fate of the solid phase material and gives rise to pressure peaks at the fracturing event, but it also influences this event. In case of pressure induced fracture clearly pressure peaks appear too but are of opposite ...
A systematic approach to the estimation of errors of a staggered predictor-corrector solution sch... more A systematic approach to the estimation of errors of a staggered predictor-corrector solution scheme for consolidation of porous media problems is presented. The total error is split into the temporal discretization error, the error of iterations and the stability error. The errors are investigated for linear and nonlinear problems and comparisons with the direct method are made.
We address stepwise crack tip advancement and pressure fluctuations, which have been observed in ... more We address stepwise crack tip advancement and pressure fluctuations, which have been observed in the field and experimentally in fracturing saturated porous media. Both fracturing due to mechanical loading and pressure driven fracture are considered. After presenting the experimental evidence and the different explanations for the phenomena put forward and mentioning briefly what has been obtained so far by published numerical and analytical methods we propose our explanation based on Biot’s theory. A short presentation of three methods able to simulate the observed phenomena namely the Central Force Model, the Standard Galerkin Finite Element Method SGFEM and extended finite element method XFEM follows. With the Central Force Model it is evidenced that already dry geomaterials break in an intermittent fashion and that the presence of a fluid affects the behavior more or less depending on the loading and boundary conditions. Examples dealing both with hydraulic fracturing and mechanical loading are shown. The conditions needed to reproduce the observed phenomena with FE models at macroscopic level are evidenced. They appear to be the adoption of a crack tip advancement/time step algorithm which interferes the least possible with the three interacting velocities, namely the crack tip advancement velocity on one side, the seepage velocity of the fluid in the domain and from the crack (leak-off), and the fluid velocity within the crack on the other side. Further the crack tip advancement algorithm must allow for reproducing jumps observed in the experiments.
A generalized Biot formulation for the mechanics of saturated-unsaturated porous media is present... more A generalized Biot formulation for the mechanics of saturated-unsaturated porous media is presented. Particular emphasis is given to the derivation of a modified effective stress vector applicable in rock mechanics and concrete. An example relating to soil mechanics situation is presented.
A numerical model for the mechanics of partially saturated porous media is presented where the fl... more A numerical model for the mechanics of partially saturated porous media is presented where the flow of both fluid phases is taken into account. The attention is focused on the choice of the field variables so that the model may easily be extended to deal with the important case when the gaseous phase is at constant reference pressure and with the limiting case of a fully saturated situation. To solve the semidiscretized governing differential equation system in the time domain a staggered procedure is presented, which also allows for a straightforward solution of the two aforementioned cases. The stability and convergence analyses of the proposed solution scheme are presented for a 3 degree-of-freedom model system. In this way it is possible to assess the behaviour of the proposed solution scheme.
ABSTRACT This paper analyses the numerical difficulties commonly encountered in solving fully cou... more ABSTRACT This paper analyses the numerical difficulties commonly encountered in solving fully coupled numerical models and proposes a numerical strategy apt to overcome them. The proposed procedure is based on space refinement and time adaptivity. The latter, which in mainly studied here, is based on the use of a finite element approach in the space domain and a Discontinuous Galerkin approximation within each time span. Error measures are defined for the jump of the solution at each time station. These constitute the parameters allowing for the time adaptivity. Some care is however, needed for a useful definition of the jump measures. Numerical tests are presented firstly to demonstrate the advantages and shortcomings of the method over the more traditional use of finite differences in time, then to assess the efficiency of the proposed procedure for adapting the time step. The proposed method reveals its efficiency and simplicity to adapt the time step in the solution of coupled field problems.
ABSTRACT We present as areas of interest for multifield fracturing thermomechanical fracturing, f... more ABSTRACT We present as areas of interest for multifield fracturing thermomechanical fracturing, fluid pressure induced isothermal and nonisothermal fracturing, fracturing due to radiation, drying, hydrogen embrittlement, and fractures induced by chemical effects. We discuss the most appropriate constitutive models for their simulation and choose the cohesive fracture model for quasi-brittle materials. Successively we show governing equations for a thermo-hydro-mechanical problem, which is representative for multifield problems. Possible extensions to more fields are addressed. Then methods for numerical modeling of multifield fracturing are presented and the most representative ones, i.e., interface and embedded discontinuity elements, X-FEM, thick level set and phase field models, and discrete crack approach with adaptive remeshing are discussed in some detail. After incorporating this last method in the governing equations, their numerical solution is shown together with the necessary adaptivity in time and space. This solution is validated. Successively applications to thermomechanical fracture; hydraulic fracturing in case of a pumped well and of 2D and 3D dams; fracturing of drying concrete and of a massive concrete beam and finally mechanical effects of chemical processes in concrete are shown. In the case of the pumped well with constant pumping rate, a comparison between an Extended Finite Element solution and that of the discrete crack approach with adaptive remeshing is made which allows for interesting considerations about the nature of hydraulic fracturing. The examples permit to conclude that with increasing complexity of the multifield problems that of the employed fracture models decreases, i.e., advanced fracture models have to date only been applied to problems with a limited number of fields, mainly displacement, thermal and/or pressure fields. There is hence plenty of room for improvement.
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