An equilibrium condition of residual edge wedge-type nanotwin in a deformed solid body has been derived in the paper. The condition conclusion is based on the necessity to ensure an equilibrium of force balance acting on every twinning dislocation from the side of the rest twin dislocations. In this case dislocation structure and stress condition at nanotwin mouth have not been taken into account. Results of dislocation theory obtained in the framework of elasticity theory and continuum mechanics have been used in the paper. The paper has considered a component of the resultant force acting in a twinning plane under an assumption that there is no motion of twinning dislocations in the direction which is perpendicular to the twinning plane. The following condition has been made in the model: a discrete distribution of twinning dislocations at twin boundaries. In order to reduce cumbersome calculations a limited number of twinning dislocations has been considered in the paper and an assumption has been made about small value of a helical component in the Burgers vector, in other words the paper has considered an edge nanotwin. In order to decrease a number of equations in the system of equilibrium conditions a symmetric property of a shear component in a stress tensor has been used in the paper. The paper contains description how restrictions on the order of twinning dislocation arrangement on twin boundaries have been imposed. In this case it has been assumed that an arrangement of twinning dislocation pairs in different twin boundaries is in one plane which is perpendicular to the twinning plane. It is necessary to keep in mind that only one twinning dislocation can be located in one twinning plane. Calculations have shown that it is possible to ensure a stable and unstable equilibrium of an edge nanotwin in an ideal unloaded crystal. Sustainable balance is provided by alignment of twinning dislocations in a wall. This leads to a twin disappearance due to annihilation of twin boundary dislocations with its dislocations at the mouth. In order to ensure an unstable equilibrium of a wedge edge nanotwin it is necessary that the distance between twinning dislocations along the length of the twin is equal to interplanar distance.

Elementary approximate formulae for numerical integration of functions containing oscillating factors of a special form with a parameter have been proposed in the paper. In this case general quadrature formulae can be used only at sufficiently small values of the parameter. Therefore, it is necessary to consider in advance presence of strongly oscillating factors in order to obtain formulae for numerical integration which are suitable in the case when the parameter is changing within wide limits. This can be done by taking into account such factors as weighting functions. Moreover, since the parameter can take values which cannot always be predicted in advance, approximate formulae for calculation of such integrals should be constructed in such a way that they contain this parameter in a letter format and they are suitable for calculation at any and particularly large values of the parameter. Computational rules with such properties are generally obtained by dividing an interval of integration into elementary while making successive approximation of the integral density at each elementary interval with polynomials of the first, second and third degrees and taking the oscillating factors as weighting functions. The paper considers the variant when density of the integrals at each elementary interval is approximated by a polynomial of zero degree that is a constant which is equal to the value of density in the middle of the interval. At the same time one approximate formula for calculation of an improper integral with infinite interval of the function with oscillating factor of a special type has been constructed in the paper. In this case it has been assumed that density of the improper integral rather quickly goes to zero when an argument module is increasing indefinitely. In other words it is considered as small to negligible outside some finite interval. Uniforms in parameter used for evaluation of errors in approximate formulae have been obtained in the paper and they make it possible to calculate integrals with the required accuracy.

Methods for estimation of dynamic magnification pertaining to motion in biomechanics have been developed and approbаted in the paper. It has been ascertained that widely-used characteristics for evaluation of motion influence on mechanisms and machinery such as a dynamic coefficient and acceleration capacity factor become irrelevant while investigating human locomotion under elastic support conditions. The reason is an impossibility to compare human motion in case when there is a contact with elastic and rigid supports because while changing rigidity of the support exercise performing technique is also changing. In this case the technique still depends on a current state of a specific sportsman. Such situation is observed in sports gymnastics. Structure of kinematic and dynamic models for human motion has been investigated in the paper. It has been established that properties of an elastic support are reflected in models within two aspects: in an explicit form, when models have parameters of dynamic deformation for a gymnastic apparatus, and in an implicit form, when we have numerically changed parameters of human motion. The first part can be evaluated quantitatively while making comparison with calculations made in accordance with complete models. For this reason notions of selected and complete models have been introduced in the paper. It has been proposed to specify models for support and models of biomechanical system that represent models pertaining only to human locomotor system. It has been revealed that the selected models of support in kinematics and dynamics have structural difference. Kinematics specifies only parameters of elastic support deformation and dynamics specifies support parameters in an explicit form and additionally in models of human motion in an explicit form as well. Quantitative estimation of a dynamic motion magnification in kinematics and dynamics models has been given while using computing experiment for grand circle backward on a gymnastics horizontal bar as an example. It has been shown that an influence of a gymnastic apparatus on motion has numerically the same order as motion of a sportsman without taking into account elastic properties of the support.

The paper considers a problem on a rectilinear crack in hardening elastoplastic material with load which is applied at infinity under plane-strain deformation conditions. While distributing J-integral in this case it is necessary to take into account specific characteristics associated with strain potential for environments with nonholonomic state equations. While considering a problem on a crack in elastoplastic material a principal term of asymptotic expansion in crack tip vicinity has an unknown singularity index in addition to an indefinite multiplier. It has been shown for steel 12X18H9T that while having invariance of energy integral it is possible to trace a singularity index for a principal term of stresses. The paper presents dependences of crack length compared to permissible Griffith’s length in accordance with the applied load which is associated with yield strength. Conceptions of J-integrals have been described for solution of a quasi-static problem. The developed approach can be used to formulate a criterion for destruction of elastoplastic material containing a rectilinear crack. The obtained theoretical dependences pertaining to determination of structure limit state characteristics have permitted to make a motivated selection of geometric parameters with due account of material strength properties. Results of the investigations can be used while preparing recommendations for development of structures with prescribed properties. The given approach makes most sense to be applied for determination of critical forces and critical value of crack length for elastoplastic material.

The most challenging processes to be investigated further which are occurring in residential areas, suburbs in the largest Belarusian cities have been determined and systematized in the paper. The paper considers modern processes of transformation and development of residential areas on the studied territories; ongoing changes in the typology of dwellings and inhabitant composition of the suburban zones; problems pertaining to infrastructure development of suburban territories; preservation and improvement of recreational and ecological functions of the suburban zones in the largest cities. The paper presents a hypothesis on the possibility to modernize an urbanized region while using digital technologies and it also provides architectural and artistic characteristics of the residential environment. The main research methods are the following: field surveys; analysis of statistical data, project and regulatory documentation. So it has been revealed that it is necessary to carry out a detailed study of inhabitant composition in the settlements in order to determine their actual requirements in schools, kindergartens, and other facilities of public services. Development of town planning regulations taking into account actual typology of residential buildings and inhabitant composition is required for organization of suburban areas in the largest Belarusian cities. Current transformation processes of traditional settlement in the suburban zones of large cities are in need to have new requirements to their infrastructure development. It is necessary to improve a monitoring system and respond to population requirements and emerging problems. Nowadays there are conditions for formation of active population communities on the suburban territories. It is necessary to execute a coordinated development of all forms and types of suburban zones in the largest cities. The paper recommends to form, develop and preserve landscape and recreational areas in order to ensure an efficient recreational and ecological functions of the suburban zones.

While being operated auto-road pavements are subjected to intensive mechanical impacts, ultraviolet ray irradiation, freeze-thaw temperatures, freezing and thawing, drying and moistening. Due to these actions various types of pavement distresses appear on the road pavement. The most significant and dangerous type of distresses is micro-cracks on the road surface. One of the main reasons for their formation is an action of weather and climatic factors that initiate large changes in temperature of coating surface and occurrence of large temperature gradients in the upper layer. In this context while designing and operating auto-roads it is rather essential to investigate a stress state in road surface which is caused by temperature action. Purpose of the described investigations is to determine permissible temperature gradients for cement-concrete pavements that exclude formation of micro-cracks on their surface and thickness of damaged surface layer. Calculations of road pavement have been carried out at various laws for temperature distribution in its depth. A finite difference method realized in PARUS software has been used for studying a stress state of cement-concrete auto-roads. Regularities for distribution of stresses in cement-concrete pavement of auto-roads have been obtained at various surface temperatures. Permissible temperature gradients in the upper pavement layer have been determined and thickness of the layer where micro-cracks are formed has been assessed in the paper. Strength criterion based on the process of micro-crack formation and development in the concrete has been used for calculations. Risk of micro-crack formation on the auto-road pavement depends on material strength, conditions of plate fixing and temperature gradients.

The existing non-destructive testing system of structure concrete is actually orientated on the usage of longitudinal acoustical waves. This is due to simplicity of technical realization for measuring velocity (time) of acoustical pulse propagation in bulk concrete. But a reverse side of simple measuring procedure is a loss of additional information on concrete which is contained in the accepted acoustical signal. Therefore usage of an ultrasonic concrete testing method is limited by assessment of its strength. Joint usage of several wave types, so-called multi-wave testing, allows to refine metrology parameters of the ultrasonic method and to gain more information while determining physical and mechanical properties of concrete in laboratory and in situ conditions. The paper considers testing of elongated concrete elements and structures by an ultrasonic pulsing method on the basis of longitudinal subsurface and Rayleigh waves. It has been proposed to use methodology for time selection of wave components according to amplitude parameter and it has been applied for standard acoustical transformers with considerable reverberation time and not possessing spatial selectivity Basic principle of the proposed methodology is visual (according to oscillogram of the received signal) determination of characteristic time moments which are used for calculation of differential value of a propagation velocity in the Rayleigh wave impulse. The paper presents results pertaining to simulation of acoustical pulse propagation on the basis of 0.15 m and data of concrete ultrasonic in situ testing on measuring bases from 0.25 to 1.75 m. Advantage of large baseline for sonic test is a possibility for execution of a hundred percent inspection for surface of large-sized elements and structures, and so there is no need to make a selective inspection in some control areas as it is stipulated by provided by existing regulations. Responsivity of the Rayleigh wave parameters to near surface concrete defects permits quickly and efficiently to detect crack areas in a reinforced structure. Energy localization of a surface wave in a layer having width λ/2–λ provides a possibility to ignore reinforcement availability under appropriate selection of oscillation frequency. In addition to this, large measuring baseline makes it possible to lower effect of concrete structural inhomogeneity on statistical stability for pulse velocity assessment that ultimately reveals a possibility to register an appearance of concrete acoustical elasticity effect under in situ conditions.

Territory protection against flood water inundation and creation of polder systems are carried out with the help of protection dikes. One of the main requirements to the composition of polder systems in flood plains is a location of border dikes beyond meander belt in order to avoid their erosion when meander development occurs. Meander belt width can be determined on the basis of the analysis of multi-year land surveying pertaining top river-bed building and in the case when such data is not available this parameter is calculated in accordance with the Snishchenko formula. While banking-up a river bed a flooded area is decreasing and, consequently, water level in inter-dike space and rate of flood water are significantly increasing. For this reason it is necessary to locate dikes at a such distance from a river bed which will not cause rather high increase in water level and flow velocity in the inter-dike space. Methodology for hydraulic calculation of river regulation has been developed in order to substantiate design parameters for levee systems, creation of favourable hydraulic regime in these systems and provision of sustainability for dikes. Its main elements are calculations of pass-through capacity of the leveed channel and rise of water level in inter-dike space, and distance between dikes and their crest level. Peculiar feature of the proposed calculated formulae is an interaction consideration of channel and inundated flows. Their mass-exchanging process results in slowing-down of the channel flow and acceleration of the inundated flow. This occurrence is taken into account and coefficients of kinematic efficiency are introduced to the elements of water flow rate in the river channel and flood plain, respectively. The adduced dependencies for determination of a dike crest level (consequently their height) take into consideration a rise of water level in inter-dike space for two types of polder systems: non-inundable (winter) dikes with maximum spring flood rate and inundable (summer) dikes with summer-autumn flood rates. The proposed calculated formulae can be recommended for application at design organizations.

For the last one hundred years development of mathematical statistics has reached rather high level. A universal relative and non-dimensional factor which is known as a coefficient of variation is widely used for practical calculations, analysis and comparison of various stochastic processes. A variety of methodologies for evaluation of possible variations in definienda is used in case when a small amount of measurements (less that 30) is made in order to study the required parameter. While doing that a number of measurements executed with the help of these regularities can be significantly increased that permits reliably (correctly) to assess numerical characterristics of the investigated parameters. However according to GOST (All Union State Standard) 21153.2–84 some corrections in methodology for determination of minimum required number of measurements (less 30) have appeared to be insignificant for obtaining a reliable safety, for example, in the field of civil construction (catastrophic accidents: in Moscow – Transvaal Park and Basmanny Market; assembly and other constructions: in Poland, France and others). In 2007 it has been proposed to use chi-square criterion for determination of the required number of measurements when their number is less than 30 and appropriate patents of Eurasian Patent Organization and the Republic of Belarus have been obtained for the proposal. For this purpose Brownlie’s proposal has been used to assess confidence limits of dispersion values with the help of the chi-square criterion and the proposal has been supported by A.N. Kolmogorov who is an originator of exact mathematical probability calculus. The paper presents results of calculations for the required number of measurements in accordance with four methodologies and comparative analysis of the obtained results. It has appeared that in case when we are using chi-square criterion for the reliability level of 0.9 or even more it is necessary to make the largest number of measurements (determinations). While increasing variation coefficient and predicted reliability level the number of the required measurements is also increased. An effort has been made to apply a robust methodology, which does not depend on the form of a distribution law, for determination of minimum number of the required measurements. Having multi-year experience on practical usage of stochastic characteristics for various parameters classification of non-stability has been proposed on the basis of variation coefficient values.

The paper considers a possibility to use sand asphalt concrete as a material for protection of asphalt concrete and cement concrete road pavements against affection of external destructive factors. Advantages and disadvantages of sand asphalt concrete road pavements have been determined in the paper. The paper provides recommendations on improvement of sand asphalt concrete properties and contains an analysis of possible variants for usage of complex-modified sand asphalt concrete in the road construction. It has been noted that according to its potentially possible physical and mechanical properties activated quartz sand being micro-reinforced by dispersive industrial wastes is considered as an efficient component for creation of constructive layers in road asphalt concrete pavements. The paper reveals only specific aspects of the efficient application of quartz sand in road asphalt concrete. The subject of the paper loоks rather interesting for regions where there are no rock deposits for obtaining broken-stone ballast but there is rather significant spreading of local quarts sand. Its successful application is connected with the necessity to develop special equipment for physical and chemical activation of sand grain surface that permits strongly to increase an adhesive strength in the area of phase separation within the “bitumen–SiO2” system. The considered problem is a topical one and its solution will make it possible to local sand in a maximum way and partially to exclude application of broken stone in road construction.

Solar systems are actively applied for heat supply of buildings in Europe. Usage of solar energy for heat supply of residential buildings is considered as rather efficient for the Republic of Belarus because total amount of direct and scattered solar radiation entering horizontal surface is equivalent to an average European index for the climate of Belarus. The paper analyzes an existing dependence on determination of solar system efficiency and proposes an amended formula for calculations while designing solar consumption systems and its legitimacy has been experimentally proved. A scheme of an experimental unit with explanations and a brief description for execution of experiments and main results of the completed investigations have been presented in the paper. Experiments have been carried out for solar systems with natural and forced coolant circulation. Attention has been paid to obtaining maximum possible temperature potential of the coolant during operation of the solar system within periods of high and low solar radiation intensity. Recommendations on practical application of solar systems for multi-storey residential buildings houses and mansion-type houses have been given in the paper. The paper presents technological principles of constructing “passive” solar heating devices. A comparison of traditionally applied and proposed alternative solar systems has been made for operational conditions in Belarus. The paper proposes a solar system for hot water supply of multi-storey buildings. The proposed system has found its first realization in the Republic while designing and constructing an energy-efficient demonstration 10-storey residential building in Mogilev within the framework of the UN Development Program project and Global Environment Fund “Improvement of energy efficiency for residential buildings in the Republic of Belarus”