"Вестник МГСУ"

The article is a brief review of the research of stress-strain state of a structure that represents a hemispherical geodetic dome exposed to the dead load. Double-contour geodetic domes composed of plates and rods are the subject of the research. The process of their design has two stages: (a) design of geometric models of geodetic domes and (b) analysis of the domes.The author demonstrates that the first stage can be implemented through the employment of the library of ArchiCAD objects. Supplementary research is needed to have the second stage implemented. The objective of this research is to present the results of the research using computeraided methods of metal structures modeling.The article presents a study of the stress-strain state of a construction with a geodetic dome (shell) of the system “R” (classification of prof. G.N. Pavlov). The purpose of the paper is to present the results of numerical modeling in PATRAN/NASTRAN system in the form of approximate formulas. Approximate formulas are presented for calculation of global maximum of stress in second contour.

Introduction. At present the urgent problem in hydraulic construction is establishing the causes of crack formation in seepage-control reinforced concrete faces at a number of rockfill dams. For solving this problem the studies are conducted of stress-strain state (SSS) of concrete-faced rockfill dams which are fulfilled by different methods. Materials and methods. Gives a review and analysis of the results of studies of stress-strain state of concrete-faced rockfill dams (CFRD) fulfilled by different authors over the last 15 years. The results of analytical, experimental and numerical studies are considered. Descriptions are given of the models used for simulation of non-linear character of rockfill deformation at numerical modeling of dam SSS. Results. Analysis showed that solving the problem of CFRD SSS causes a number of methodological difficulties. At present the only method permitting study of CFRD SSS is numerical modeling. The rest methods do not permit considering the impact of important factors on SSS. Large complications are caused by scarce knowledge of rockfill deformation properties in real dams. Conclusions. It was revealed that at present SSS of reinforced concrete faces has been studied insufficiently. The results of conducted studies do not give full and adequate understanding about operation conditions of reinforced concrete faces. Impact of various factors on the face SSS has not been studied. Besides, there are contradictions in the results of studies obtained by different authors. Differences in the results are based on objective and subjective reasons. A considerable obstruction for numerical studies is complicated modeling of rigid thin-walled reinforced concrete face behavior at large deformations inherent to rockfill. The obtained results of studies often do not permit conducting full analysis of SSS of concrete-faced rockfill dams.

The authors consider a dynamic problem solving procedure based on the theory of elasticity in the Cartesian coordinate system. This method consists in the development of the pattern of numerical solutions to dynamic elastic problems within any coordinate system and, in particular, in the polar coordinate system. Numerical solutions of dynamic problems within the theory of elasticity are the most accurate ones, if the boundaries of the areas under consideration coincide with the coordinate lines of the selected coordinate system.The first order linear system of differential equations is converted into an implicit difference scheme. The implicit scheme is transformed into the explicit method of numerical solutions. Using the Galerkin method, the authors obtain formulas for the calculation of both the points of the computational domain and the boundary points.Difference ratios similar to those obtained for a discrete rectangular grid and derived in this paper are suitable to design any geometry, which fact significantly increases the value of the methods considered in this paper.As a test case, the problem of diffraction of a longitudinal wave in a circular cavity, where maximum stresses are obtained analytically, was considered by the authors. The proposed method demonstrated sufficient accuracy of calculations and convergence of numerical solutions, depending on the size of discrete steps. The problem of diffraction of longitudinal waves in a circular cavity was taken for example; however, the proposed method is applicable to any problems within any computational domain.The polar coordinate system is the best one for any research into the diffraction of plane longitudinal waves in a circular cavity, since the boundaries of the computational domain coincide with the coordinate lines of the selected system.

Numerical modeling of dynamic problems of the theory of elasticity remains a relevant task.
A complex network of waves that propagate within solid bodies, including longitudinal, transverse,
conical and surface Rayleigh waves, etc., prevents the separation of wave fronts for modeling purposes.
Therefore, it is required to apply the so-called "pass-through analysis".
The method applied to resolve dynamic problems of the two-dimensional theory of elasticity
employs finite elements to approximate computational domains of complex shapes, whereby the
software calculates the speed and voltage in the medium at each step. Preset boundary conditions
are satisfied precisely.
The resulting method is classified as explicit bilayer difference schemes that form special
relationships at the boundary points.
The method is based on an implicit bilayer time-difference scheme based on a system of
dynamic equations of the theory of elasticity of the first order, which is converted into an explicit
scheme with the help of a Taylor series in time, while basic relations are resolved with the help of
the Galerkin method. The author demonstrates that the speed and voltage are calculated with the
same accuracy as the one provided by the classical finite element method, whereby determination
of stresses has to act as a numerically differentiating displacement.
The author identifies the relations needed to calculate both the internal points of the computational
domain and the boundary points. The author has also analyzed the accuracy and convergence
of the resulting method having completed a numerical simulation of the well-known problem
of diffraction of a longitudinal wave speed in a circular aperture. The problem has an analytical
solution.

The authors considered the issues of reinforcement of embankments by high-strength geosynthetic materials. It is suggested to use flat geogrid with metal cores as a reinforcement material for constructing reinforced ground supporting walls on automobile and railway roads. The results of calculations of the volumes of horizontal displacements of the front parts of supporting walls are offered. They were obtained as a result of numerical modeling using finite element method.

Subject: the dam of compound design in which the water pressure is borne mutually by a concrete gravity dam and a higher rockfill dam with reinforced concrete facing. Research objectives: 1) study the stress-strain state (SSS) of a compound dam, identify the effect of three main factors on the dam SSS. The first factor is the height of the concrete structure. The second factor is the height of the contact zone (conjugation) between the earth fill and the concrete structure. The third factor is deformability of riprap; 2) based on these studies, give recommendations for selection of the compound dam design. Materials and methods: SSS studies were conducted by numerical analysis using the finite element method (FEM). Nonlinear character of soils deformability and contacts of concrete structure with soils, foundation and reinforced concrete facing was taken into consideration. Sequence of the dam erection and loading was taken into account. Riprap’s modulus of deformation varied from 70 to 270 МPа. Results: results of the analysis showed that the concrete structure as a part of the compound dam withstands hydrostatic load almost independently, practically without transferring it to the earth fill. We have found out that the most sensitive part of the compound dam design is conjugation of the earth fill with the concrete structure. This zone is characterized by failures of the soil strength. The consequence of these failures are considerable displacements in the joint between the facing and the concrete structure as well as bending deformations of the lower part of the facing. Bending of the facing causes considerable tensile stresses. Conclusions: the results of studies permitted us to formulate the following recommendations: 1) it is not desirable to select the height of contact zone between the earth fill and the concrete structure more than 60-75 % of the concrete structure height because it leads to increase of loads borne by the concrete structure and may result in failure of strength of its contact with foundation; 2) it is not recommended to choose the height of contact between the earth fill and the concrete structure less than 30 % of the height of the latter as it results in increase of bending deformations of reinforced concrete facing; 3) for reliability of the compound dam, it is necessary to choose riprap’s modulus of deformation not lower than 200 МPа.

In the article the authors analyze numerical modeling results of the stress-strain state of a combined dam created by construction of a higher rockfill dam with a reinforced concrete face behind the downstream face of the concrete dam. The analysis was conducted on the example of the design of 150 meter high New Exchequer dam (USA). Numerical modeling was conducted with consideration of non-linearity of soils deformation as well as non-linear behavior of the interaction “concrete - soil”, “concrete - concrete”. The analysis showed that though in a combined dam the concrete part gets additional displacements and settlements, its stress state remains favorable without appearance of tensile stresses and opening of the contact “concrete - rock”. This is explained by the fact that on the top the concrete dam is weightened by the reservoir hydrostatic pressure. The role of rockfill lateral pressure on the concrete dam stress state is small. There may be expected sliding of soil in relation to the concrete dam downstream face due to the loss of its shear strength. Besides, decompaction of the contact "soil - concrete" may occur, as earthfill will have considerable displacements in the direction from the concrete dam. Due to this fact the loads from the earthfill weight do not actually transfer to the concrete dam. The most critical zone in the combined dam is the interface of the reinforced concrete face with the concrete dam. Under the action of the hydrostatic pressure the earth-fill under the face will have considerable settlements and displacements, because soil slides in relation to the concrete dam downstream face. This results in considerable openings (10 cm) and shear displacements (50 сm) in the perimeter joint. The results of the numerical modeling are confirmed by the presence of seepage in New Exchequer dam, which led to the necessity of its repair. Large displacements do not allow using traditional sealing like copper water stops in the perimeter joint of combined dams. The sealing should be made of geo-membrane with placement of an asphalt pad under the face. Due to bending deformations in the lower part of the reinforced concrete face considerable tensile forces may occur. It is recommended to arrange a transverse joint in this part of the face.

Mathematical models of secondary settlers have been intensively developed in the past several years. The challenge is to develop CFD models capable of taking account of the geometrical shape of the settler, the most important physical processes, and to perform calculations in the timely manner. The task of the authors was to develop a 2D numerical model designated for the research into the transfer of waste waters inside vertical settlers, for the model to take account of the geometrical shape and structural features of the settler. The authors employed finite difference schemes as the basic methods of research. As a result, a new 2D CFD model was developed. The novel model may be used to perform CFD studies of vertical settlers. This model takes account of the geometrical shape of the settler, the central pipe inside it, and other peculiarities. The CFD model and code developed by the authors constitute a solution to multi-parametric problems of the vertical settler design. Computer time taken by this model is equal to the one of a 1D model.

The article is a brief review of the research of the stress-deformation state of a structure
that represents a hemispherical geodetic dome exposed to the dead load. Single-contour geodetic
domes composed of flat plates are the subject of the research. The process of their design has two
stages: (a) design of geometric models of geodetic domes and (b) analysis of domes.
The authors demonstrate that the first stage can be implemented through the employment of
the library of ArchiCAD objects. Supplementary research is needed to have the second stage implemented.
The objective of this research is to present the results of the research using computer-aided
methods of modeling of metal structures. The analysis of smooth hemispherical domes is performed
using analytical and finite-element methods within the Patran/Nastran environment. The authors
demonstrate that the results of the finite-element method analysis converge with the results of the
analytical method analysis.
Conversion of geometric models of geodetic domes into the format that satisfies Patran preprocessor
requires the employment of the Visual Basic software. Ultimately, comparison between
the results obtained in respect of the geodetic dome and the analytical results obtained in respect
of the smooth dome exposed to the dead load is performed. The conclusion is that the maximal
stress experienced by a single-contour geodetic dome, in the event of reduction of sizes of plates,
converges with the maximal stress of similar smooth domes.

In the article the problem of designing pile foundations on claystones is reviewed. The purpose of this paper is comparative analysis of the analytical and numerical methods for forecasting the settlement of piles on claystones. The following tasks were solved during the study: 1) The existing researches of pile settlement are analyzed; 2) The characteristics of experimental studies and the parameters for numerical modeling are presented, methods of field research of single piles’ operation are described; 3) Calculation of single pile settlement is performed using numerical methods in the software package Plaxis 2D and analytical method according to the requirements SP 24.13330.2011; 4) Experimental data is compared with the results of analytical and numerical calculations; 5) Basing on these results recommendations for forecasting pile settlement on claystone are presented. Much attention is paid to the calculation of pile settlement considering the impacted areas in ground space beside pile and the comparison with the results of field experiments. Basing on the obtained results, for the prediction of settlement of single pile on claystone the authors recommend using the analytical method considered in SP 24.13330.2011 with account for the impacted areas in ground space beside driven pile. In the case of forecasting the settlement of single pile on claystone by numerical methods in Plaxis 2D the authors recommend using the Hardening Soil model considering the impacted areas in ground space beside the driven pile. The analyses of the results and calculations are presented for examination and verification; therefore it is necessary to continue the research work of deep foundation at another experimental sites to improve the reliability of the calculation of pile foundation settlement. The work is of great interest for geotechnical engineers engaged in research, design and construction of pile foundations.

There was studied the stress-strain state of 215 m high rockfill dam where the seepage-control element is presented by a reinforced concrete face of soil-cement concrete placed on the under-face zone. Calculations were carried out for two possible variants of deformability of rock outline taking into account the non-linearity of its deformative properties. It was obtained that the reinforced concrete face and the soil-cement concrete under-face zone work jointly as a single construction - a double-layer face. As the face assembly resting on rock is made with a sliding joint the scheme of its static operation is similar to the that of the beam operation on the elastic foundation. At that, the upstream surface of the double-layer face is in the compressed zone and lower one is in the tensile zone. This protects the face against cracking on the upstream surface but threatens with structural failure of soil-cement concrete. In order to avoid appearance of cracks in soil-cement concrete part due to tension it is necessary to achieve proper compaction of rockfill and arrange transverse joints in the double-layer face.

The article focuses on the assessment of stress-strain state of soil mass of dock-type lock chamber. Numerical modeling of the soil mass of dock-type lock chamber with a continuous bottom is performed. The soil model was selected, and calculation of stress-strain state of the lock chamber soil mass was performed applying the PLAXIS 2D programming and computing suite. In the process of the structure stress-strain state analysis the assessment of its state in conditions of filling-emptying of the lock chamber was performed. To assess the possibility of reducing the load of the backfill soil and pore pressure on the lock chamber wall, the article discusses the simulation of excavation of upper part of the lock chamber backfill; also, the possibility of replacing of clay soil filling by sandy soil filling is considered. A numerical modeling results verification with field observations materials obtained during operation of the facility was performed according to the results of calculations of horizontal and vertical shifts of the facility. The study demonstrated a satisfactory convergence of the results of calculations performed in the Plaxis programming and computing suite with the field observations materials. Presented calculation results show that the replacement of upper part of backfill soil without combining with other structural measures can not duly change the load from the soil on the chamber wall, nor its stress state.