A promising direction for improving the durability and transport and operational performance of road pavements is the use of modifiers, including those based on sulfur as a component of the asphalt concrete mixture. However, sulfur and its toxic gases are active substances that can enter into chemical interactions with fillers to form water-soluble calcium and magnesium sulfides CaS and MgS. This process leads to the destruction of the dispersed phase and a decrease in the water resistance of sulfur asphalt concrete. A promising direction that has received wide approbation in the manufacture of polymer composites is the finishing of the filler surface, which makes it possible to prevent the formation of water-soluble sulfides. The coupling agents form a shell impermeable to sulfur, which prevents its chemical interaction with the dispersed phase. The following components are offered as coupling agents: Polymethylsiloxane (PMS-100), SKDN-N rubber, silicic acid sol in a medium containing Fe(OH)3 nanoparticles, and iron (III) hydroxide sol.

Keywords: sulfur asphalt concrete, asphalt concrete, water resistance, strength, sulfur bitumen binders, nanoscale additive

It is known that the voids of the soil are able to absorb water at every opportunity, filling the voids of the skeleton with ground water. The article deals with the deformation of soils under compression, accompanied by the movement of water in the voids of the skeleton. The physical cause of fluid movement is the difference of hydrostatic pressures at different points in its volume. This movement is called the length of the filtration line and depends on the filtration rate. The process of filtering water from the voids of the skeleton under variable pressure will determine the course of compression of the soil skeleton in time. Taking into account that water filtration ceases at the end of deformation, it is possible, by comparing the equations, to obtain for these conditions the desired relationship between the time of complete deformation and the soil filtration coefficient.

Keywords: soil deformation, hydrostatic pressure, water-saturated state, water filtration, stresses of the soil skeleton

The article presents a description of the computational model and the results of modeling the stress-strain condition of cable-stayed structures. The calculations are performed in a geometrically nonlinear formulation.

Keywords: stress-strain condition, cable-stayed structure, geometric nonlinearity, flexible cable system, spatial framed system

The article deals with the mechanical and mathematical model of deformation and development of zones of plastic deformations in landslide slopes under static and dynamic influence taking into account physical and geometrical nonlinearity.

Keywords: landslide slope, plastic deformation zone, dynamic impact, physical nonlinearity, geometric nonlinearity, stress deviator, stress tensor, deformation of the soil medium

The article deals with creep in structural mechanics. Systems of non-linear resolving equations for different types of creep kernels are written. An algorithm for solving the problem of nonlinear heredity is considered.

Keywords: creep, nonlinear heredity, creep kernel approximations, finite elements method, exponential-type kernels, least-squares method, collocation nodes

In the article it describes the main disadvantages of modern methods of modeling of reinforced landslide slope behavior, proposed in our research approach and the results of calculation made in the developed software complex "Polus-W"

Keywords: reinforced landslide slope, limit state, finite element method, a stepper method, a continuous system, calculation

The article deals with the direct and alternative forms of nonlinear heredity hypothesis. A relation between the nuclei produce relaxation and direct and alternative formulations. The algorithm for solving the problem of small elastic-plastic deformations in view of the heredity material finite element method.

Keywords: nonlinear heredity, integral, function, creep kernel, theory of elasticity, strain, relaxation, creep, stress, finite element method