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.

Two methods are combined for description and assessment of slope stability. In the first step, elasto-plastic analysis of a slope is performed with suitable plasticity condition which results in determination of failure surface. The second step takes into account position of the failure surface and uses domain decomposition method for description of discontinuity along the failure surface due to landslide. Introduction of discontinuities into numerical methods causes difficulties but it can be done very efficiently within domain decomposition methods.

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.

The paper shows some conceptual and numerical aspects of two non-local spatial averaging formulations applied to scalar damage models for concrete. A short numerical study is performed on selected benchmark tests to identify similarities and differences in the numerical predictions of the formulations in different strain states. It has been illustrated in the paper that large differences in the load capacity and damage areas exist and may be predicted by the models based on the loading situation. It is the non-local averaging formulation in combination with the damage evolution in the structure that are crucial factors of the different model predictions.