Construction of mathematical models of the stressed-strained state of a material with a porous water-saturated base under dynamic load

Materials of beams, plates, slabs, strips have been commonly applied in various fields of industry and agriculture as flat elements in the structures for machinery and construction. They are associated with the design of numerous engineering structures and facilities, such as the foundations of various buildings, airfield and road surfaces, floodgates, including underground structures. This paper reports a study into the interaction of the material (of beams, plates, slabs, strips) with the deformable base as a three-dimensional body and in the exact statement of a three-dimensional problem of mathematical physics under dynamic loads. The tasks of studying the interaction of a material (beams, plates, slabs, strips) with a deformable base have been set. A material lying on a porous water-saturated viscoelastic base is considered as a viscoelastic layer of the same geometry. It is assumed that the lower surface of the layer is flat while the upper surface, in a general case, is not flat and is given by some equation. Classical approximate theories of the interaction of a layer with a deformable base, based on the Kirchhoff hypothesis, have been considered. Using the well-known hypothesis by Timoshenko and others, the general three-dimensional problem is reduced to a two-dimensional one relative to the displacement of points of the median plane of the layer, which imposes restrictions on external efforts. In the examined problem, there is no median plane. Therefore, as the desired values, displacements and deformations of the points in the plane have been considered, which, under certain conditions, pass into the median plane of the layer. It is not possible to find a closed analytical solution for most problems while experimental studies often turn out to be time-consuming and dangerous processes

Load Bearing Capacity Calculation of the System “Reinforced Concrete Beam – Deformable Base” under Torsion with Bending

It is presented the formulation and solution of the load bearing capacity of statically indeterminable systems “reinforced concrete beam – deformable base” by spatial cross-sections under force and deformation effects. The solution of problem is currently practically absent in general form. It has been established the relationship between stresses and strains of compressed concrete and tensile reinforcement in the form of diagrams. The properties of the base model connections are described based on a variable rigidity coefficient. It is constructed a system of n equations in the form of the initial parameters method with using the modules of the force (strain) action vector. The equations of state are the dependences that establish the relationship between displacements which are acting on the beam with load. Constants of integration are determined by recurrent formulas. It makes possible to obtain the method of initial parameters in the expanded form and, consequently, the method of displacements for calculating statically indefinable systems. The values of the effort obtained could be used to determine the curvature and rigidity of the sections in this way. It is necessary not to set the vector modulusP, the deformation is set in any section (the module is considered as an unknown) during the problem is solving. This allows us to obtain an unambiguous solution even in the case when the dependence M–χ has a downward section, i.e one value of moment can correspond to two values of curvature.

EXPERIMENTAL RESEARCH TECHNIQUE OF RETAINING WALLS OF A SPECIAL TYPE

The article reviewed the issue of wide use of the retaining walls in construction. It is established the existing retaining walls are not designed for additional forces from horizontal soil displacement that consequently leads to the destruction of the structure. In this regard, there is a need for the development of new structural solutions for retaining walls. The purpose of the research is to develop the technique for conducting experimental studies of the contact interaction of retaining walls and a deformable base. The experiments were carried out on small-scale models in a specially designed tray. At modeling was applied the method of the expanded similarity in which geometrical, mechanical and power analogues with a real object are maintained. As base soil, the models used loamy structure. Models of retaining walls were made on a digital 3D model. A technique for conducting experimental studies of the contact interaction of retaining walls and a deformable base has been developed. The technique is universal and will allow carrying out model experiments under equal conditions, which will ensure reliable results.