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In a large extent, durability and service life of reinforced concrete structures is influenced by penetration of deicing salts or seawater salts to the steel reinforcement. The steel corrosion is induced by a raising chloride concentration and possibly can lead to concrete cover spalling due to volumetric changes of oxides formed at the steel surface. Therefore, a critical concentration of chlorides is monitored and investigated by numerical simulations in service life assessments. This contribution is devoted to modeling and numerical solution of the diffusion–convection problem applied to chloride migration in concrete. The theoretical background is reviewed with some of the numerical consequences and strategies that need to be used for a successful problem solution. The solution is implemented into an in-house open-source FEM software accounting for non-constant electric field and chloride binding existing in a real reinforced concrete element. The three stage approach is applied and demonstrated on an example of a reinforced concrete beam. First, an increased concentration of chlorides in the cover layer of the beam is simulated with pure diffusion over a long time period (10 years). Second, the two-dimensional distribution of an externally applied electric field is calculated in the beam. Third, an electrochemical extraction process in which the migration of ions is accelerated by an application of the electric field is simulated. The short time (2 days) treatment leads to rapid decrease of chloride concentration in the concrete cover but leaves elevated concentrations in deeper areas of the beam cross section as a direct consequence of the real action of two-dimensional and non-constant electric field.

Prediction of effective elastic and strength parameters of both regular and irregular masonry walls from homogenization is presented. To that end, the widely accepted first order homogenization method is adopted to provide the homogenized elastic stiffnesses or compliances as well as macroscopic parameters of the selected nonlinear constitutive models. These include the tensile and compressive strength and fracture energies of a generally orthotropic material extracted from the computationally derived macroscopic stress strain curves. In this regard, two types of boundary/loading conditions resulting from the strain-based and mix type formulation of the homogenization problem are examined. The response provided by an orthotropic damage model, expected to describe the behavior of the homogenized structure on macroscale, is compared to that derived via a classical isotropic scalar damage model. It reveals that strong constraints of the orthotropic damage model offer results inapplicable for estimating the macroscopic fracture properties thus promoting the application of a simple isotropic damage model when solving the homogenization problem. The results also show that the mixed boundary conditions, allowing us to represent a pure tension/compression loading mode while being capable of tracking the softening branch of the stress–strain curve, deliver the response comparable to that of a purely strain-based formulation.

Numerical simulations of transport processes, e.g., heat and moisture transport, in heterogeneous masonry structures performed on single processor computers are very time consuming. The classical description by the finite element method leads to enormous numbers of degrees of freedom. It is caused by the fact that there are relatively thin layers of mortar in contrary to large bricks or stones. The mortar and stones have very different material parameters and the finite element mesh has to be able to describe the temperature and moisture fields in the thin layers of mortar and in their vicinity. An application of a multi-scale approach in connection with parallel computing can be successfully exploited. The whole structure is described by a reasonably coarse finite element mesh, called the macro-scale problem, and the material parameters are obtained from the lower-level problems, called the meso-scale problem, by a homogenization procedure. In this procedure, the macro-problem is assigned to the master processor and the meso-scale problems belong to the slave processors. This proposed approach is called hybrid parallel method.

The paper deals with the coupled hydro-mechanical model for clayey soils capable for the description of slope stability or bearing capacity of the footing problems in geotechnics. The model is composed from simplified model for saturated-unsaturated water flow in deforming porous medium and plasticity model based on the Cam-Clay yield criterion. The set of partial differential equations is discretized in space with the help of finite element method. The model was implemented to the SIFEL software package and some numerical example of the footing problem is presented.

This contribution presents a homogenization of the elastic properties of trabecular structures used in modern implantology. Trabecular structures can be characterized as spatial truss structures composed of beams. Their numerical modeling and precise three-dimensional discretization by finite elements usually lead to a huge number of degrees of freedom. One of the possible solutions of this problem can be a homogenization approach based on a two-level analysis, where the specimen, the implant, is discretized by a coarse mesh at the macro-level, and the elements of the trabecular structure are represented by effective (homogenized) material properties obtained from a representative volume element at the meso-level. The application of this multi-scale procedure is illustrated by a numerical simulation of laboratory compression tests of trabecular specimens.

Numerical modeling of implants and specimens made from trabecular structures can be difficult and time-consuming. Trabecular structures are characterized as spatial truss structures composed of beams. A detailed discretization using the finite element method usually leads to a large number of degrees of freedom. It is attributed to the effort of creating a very fine mesh to capture the geometry of beams of the structure as accurately as possible. This contribution presents a numerical homogenization as one of the possible methods of trabecular structures modeling. The proposed approach is based on a multi-scale analysis, where the whole specimen is assumed to be homogeneous at a macro-level with assigned effective properties derived from an independent homogenization problem at a meso-level. Therein, the trabecular structure is seen as a porous or two-component medium with the metal structure and voids filled with the air or bone tissue at the meso-level. This corresponds to a two-level finite element homogenization scheme. The specimen is discretized by a reasonable coarse mesh at the macro-level, called the macro-scale problem, while the actual microstructure represented by a periodic unit cell is discretized with sufficient accuracy, called the meso-scale problem. Such a procedure was already applied to modeling of composite materials or masonry structures. The application of this multi-scale analysis is illustrated by a numerical simulation of laboratory compression tests of trabecular specimens.

Freezing-thawing cycles affect strongly durability and service life of porous building materials. Two reference years, where one represents a mild climate and second represents severe climate, are taken into account. Freezing-thawing cycles are modelled with the help of porosimetry curve and the Gibbs-Thompson equation. Distribution of volumetric moisture content and temperature are obtained from coupled heat and moisture transfer. Finally, the volume of frozen water is used for determination of volumetric strain which is used in mechanical analysis.

Several nonlinear simulations of concrete and reinforced concrete slabs are performed using a layered model. Two Drucker-Prager criteria are employed to form a concrete plasticity model that is used for simulating the plastic yielding of layers. Moreover, an interaction with elastic Winkler-Pasternak subsoil model is considered for the case of a reinforced concrete foundation slab that is subjected to a concentrated loading force. All computations are done by the SIFEL solver using finite element method.

This paper is devoted to numerical analysis of plaster detachment and numerical experiments for determination of the appropriate material parameters. Interaction between the plaster and masonry is described with the help of interface finite elements which are equipped with traction-displacement relationship. Laboratory tests were introduced in order to determine the shear capacity of the masonry-plaster connection. Unfortunately, variability of measured behaviour was very large and additional tests are needed.

A layered model is used for nonlinear analysis of plates. Calculation is performed using DKT plate elements and considering plastic yielding of layers with the use of double Drucker-Prager yield criterion model for concrete and J2 plasticity model for reinforcement. Computation is done by the SIFEL solver using the Finite Element Method.

A layered model is used for nonlinear analysis of a foundation concrete slab. Calculation is performed using interaction with elastic Winkler-Pasternak subsoil model and considering plastic yielding of slab layers. Two Drucker-Prager yield criterions define a nonlinear material model for concrete. Computation is done by the SIFEL solver using the Finite Element Method.

This paper is devoted to the influence of mechanical damage on moisture transport in quasi-brittle materials, such as concrete. The mechanical analysis is based on the isotropic damage model with the equivalent strain suitable for concrete. The mechanical model is formulated in the rate form in order to connect it with the nonstationary moisture transport which is modeled by a simple diffusion model derived from convection approach. The moisture transport is based on the volumetric moisture content. Three different formulas are used for description of the change of permeability with respect to growing damage parameter. Numerical approach is tested on an example of four-point shear test.

This paper is devoted to analysis of shrinkage and damage of autoclaved aerated concrete. Coupled hydro-thermo-mechanical analysis is used for detailed description of drying which causes the shrinkage and damage consequently. The heat and moisture transfer are fully coupled while the staggered approach is used between transports and mechanics. Material parameters were obtained from laboratory experiments and the results of numerical simulations correspond with measured data.

This paper is devoted to a computer simulation of coupled-thermo-hydro mechanical analysis of concrete structures. The attention is concentrated to concrete structures at early stage, when hydration heat evolution and moisture content changes can influence significantly the reliability and service life of these structures. The results of computation are illustrated by the simulation of a foundation slab, which is situated in the basement of the administration building Prague-Tìšnov, Czech Republic. The Künzel and Kiessl approach is used to analyze heat and moisture fields and it is extended by a set of climatic conditions and by a model of hydration heat evolution in concrete. The problem is solved using the open source program SIFEL.

The paper describes several integration schemes suitable for the hydro-mechanical model for expansive clayey soils. The complex model is based on hypoplasticity with parameters influenced by suction and the model is formulated in the rate form which requires time integration not only of the stresses but also state variables. Several integration schemes based on Runge-Kutta-Fehlberg method have been tested and their performance is compared in the last section of the paper.

The paper contains a model of penetration and electrically accelerated extraction of chlorides from a reinforced concrete structure. A numerical framework is formulated based on the Fick’s law, Nernst-Planck equation and Gauss law of electrostatics. Finite element approximation and the Galerkin-Petrov approach is used to solve the task. A sample calculation of extraction of chlorides from a bridge deck taking into account several solution stages like developing of chloride profile by diffusion, calculation of the electric field and accelerated extraction chlorides is performed. The example clearly shows uneven distribution of the computed fields (electric potential, chloride concentration) and uneven efficiency of the method in a real reinforced concrete structure.

This paper outlines prediction of macroscopic effective properties of a regular masonry from homogenization. It focuses on the derivation of nonlinear macroscopic stress strain curves adopting either classical isotropic or more advanced orthotropic damage model. The response resulting from both tensile and compressive uniaxial loading is examined in the light of strain and stress loading regimes. A masonry structure typical of ”Placa” buildings (mixed masonry- reinforced concrete buildings) built in Portugal is selected as one particular example to illustrate the differences in the predictive capabilities of the two constitute models on the one hand and the formulation of the homogenization problem on the other hand. It is suggested that the mixed loading conditions are essentially required when estimating all macroscopic material parameters needed in the corresponding macroscopic constitutive model

This paper is devoted to efficient computer implementation of coupled salt and moisture transport processes. Three material models are summarized first and then a general form of coupled transport processes is formulated. The system of balance equations is solved numerically with the help of the Galerkin method (in space) and the generalized trapezoidal rule time integration. Implementation of the transport processes into the open source computer program SIFEL is briefly described.

The paper presents a numerical model of coupled hydro-mechanical behaviour of soils. The micro-mechanics model is based on the effective stress concept which covers the theory of deformation of soils (soil skeleton) and other porous materials. The final set of equations is simplified and derived for the water flow in a porous media and the spatial discretization is performed by the finite element method. The model was implemented to the SIFEL software package and some numerical examples are presented.

The paper deals with the hydro-mechanical model for expansive clayey soils. The complex model is based on the hypoplasticity, which parameters are influenced by suction, and additionally on Schrefler’s model for saturated-unsaturated water flow in deforming porous medium. The model has been implemented into the open source software SIFEL and selected results of a simple numerical example are presented in the last section of the paper.

Coupled analysis of heat and moisture transport in complicated structural elements or in whole structures deserves a special attention because after space discretization, large number of degrees of freedom are needed. This paper describes possible solution of such problems based on domain decomposition methods executed on parallel computers. The Schur complement method is used with respect to nonsymmetric systems of algebraic equations. The method described is an alternative to other methods, e.g. two or more scale homogenization.

This paper summarizes suitable material models for creep and damage of concrete which are coupled with heat and moisture transfer. The fully coupled approach or the staggered coupling is assumed. Governing equations are spatially dis-cretized by the finite element method and the temporal discretization is done by the generalized trapezoidal method. Systems of non-linear algebraic equations are solved by the Newton method. Development of an efficient and extensible computer code based on the C++ programming language is described. Finally, successful analyses of two real engineering problems are described.

Hydro-thermo-mechanical analysis of reactor vessels based on the finite element method is a very demanding task due to its complexity as well as the large number of unknowns. This contribution deals with efficient computer implementation of the coupled analysis and attention is also devoted to domain decomposition methods which enable utilisation of parallel computers. The parallel processing leads to very good speedup and it also enables to solve significantly large problems in acceptable time. The proposed strategy is demonstrated on a coupled analysis of an existing reactor vessel.

The paper describes damage-plasticity model for the modelling of the host rock environment of a nuclear waste repository. Radioactive Waste Repository Authority in Czech Republic assumes the repository to be in a granite rock mass which exhibit anisotropic behaviour where the strength in tension is lower than in compression. In order to describe this phenomenon, the damage-plasticity model is formulated with the help of the Drucker-Prager yield criterion which can be set to capture the compression behaviour while the tensile stress states is described with the help of scalar isotropic damage model. The concept of damage-plasticity model was implemented in the SIFEL finite element code and consequently, the code was used for the simulation of the Aspo Pillar Stability Experiment (APSE) which was performed in order to determine yielding strength under various conditions in similar granite rocks as in Czech Republic. The results from the performed analysis are presented and discussed in the paper.

Durability and life time of porous building materials depend significantly on distribution of moisture and salt concentration. Transport of moisture and salt is affected by damage evolution caused by mechanical loading. The permeability grows with evolution of microcracks and microvoids. This paper describes coupled thermo-hydro-mechanical model which connects the damage parameter and permeability.

The paper deals with numerical modeling of damage evolution in autoclaved aerated concrete (AAC) due to shrinkage. It represents coupled thermo-hydro-mechanical problem where the temperature and moisture transports are fully coupled. The mechanical problem is partially coupled with transport part because the AAC shrinkage is influenced by moisture evolution. These models were implemented to the SIFEL software package and they were used for numerical simulation of drying wall made from AAC blocks.

A mathematical model for the description of drying shrinkage of autoclaved aerated concrete (AAC) is presented, bringing together the hygrothermal and mechanical considerations. The verification of the model is done using an approximation of a real laboratory experiment. Then, the applicability of the model is demonstrated by a numerical simulation of drying shrinkage and wetting expansion of AAC under real weather data. The presented results showed that the model works precisely and the presumption was made to extend the model in subsequent research.

Determining the durability of a reactor vessel requires a hygro-thermo-mechanical analysis of the vessel throughout its service life. Damage, prestress losses, distribution of heat and moisture and some other quantities are needed for a durability assessment. A coupled analysis was performed on a two-level model because of the huge demands on computer hardware. This paper deals with a hygro-thermo-mechanical analysis of a reactor vessel made of prestressed concrete with a steel inner liner. The reactor vessel is located in Temelín, Czech Republic.