VERTICAL STRESS DISTRIBUTION AT THE BASE OF SOIL DAMS WITH A TRAPEZOIDAL CROSS SECTION

Problem statement. The research materials outlined in this work make it possible to construct the design profile of dams from soil materials, taking into account the strong compressibility of the soil and check the strength of the foundation of soil dams in depth. In addition, the results obtained by us can be used to determine the lower boundary of the compressible thickness of the bases, to the upper boundary of which a distributed load of either a triangular or trapezoidal shape is applied. Methods. Theoretical studies of geomechanical processes using analytical and numerical mathematical methods. Analysis and generalization of the results of theoretical research. Results. In the course of writing this article, we obtained analytical dependences of stresses at the base of earth dams on the coordinates and applied to the upper boundary of the base of the trapezoidal external load and showed the methods of accounting. Scientific novelty. Analytical dependences of vertical normal at the base of a soil dam with a trapezoidal profile have been obtained. The profiles of the dam in the form of isosceles and non-isosceles trapezoids are considered. Practical significance. The research materials outlined in this work make it possible to construct the design profile of dams from soil materials, taking into account the strong compressibility of the soil and check the strength of the foundation of soil dams in depth. In addition, our results can be used to determine the lower boundary of the compressible strata of the bases, to the upper boundary of which a distributed load of either a triangular or trapezoidal shape is applied.

Investigation of Lateral Confinement, Roller Aspect Ratio and Wear Condition on HPGR Performance Using DEM-MBD-PRM Simulations

It has been known that the performance of high-pressure grinding rolls (HPGR) varies as a function of the method used to laterally confine the rolls, their diameter/length (aspect) ratio as well as their condition, if new or worn. However, quantifying these effects through direct experimentation in machines with reasonably large dimensions is not straightforward, given the challenge, among others, of guaranteeing that the feed material remains unchanged. The present work couples the discrete element method (DEM) to multibody dynamics (MBD) and a novel particle replacement model (PRM) to simulate the performance of a pilot-scale HPGR grinding pellet feed. It shows that rotating side plates, in particular when fitted with studs, will result in more uniform forces along the bed, which also translates in a more constant product size along the rolls as well as higher throughput. It also shows that the edge effect is not affected by roll length, leading to substantially larger proportional edge regions for high-aspect ratio rolls. On the other hand, the product from the center region of such rolls was found to be finer when pressed at identical specific forces. Finally, rolls were found to have higher throughput, but generate a coarser product when worn following the commonly observed trapezoidal profile. The approach often used in industry to compensate for roller wear is to increase the specific force and roll speed. It has been demonstrated to be effective in maintaining product fineness and throughput, as long as the minimum safety gap is not reached.

Roadbed Sedimentation on Folded Bases with Weak Soils

Purpose. The main purpose of the work is to construct accurate analytical dependences of the sedimentation of the roadbed base on its coordinates and the trapezoidal external load applied to the upper limit of the base. This will allow the foundation settlement profile to be calculated within and outside the embankment using the layer-by-layer stacking method. Methodology. Theoretical studies of geomechanical processes using analytical and numerical mathematical methods were applied to achieve the purpose, as well as analysis and generalization of the results of theoretical research. Findings. Analytical dependences of vertical and horizontal normal deformations on the half-plane coordinates to the upper limit of which the trapezoidal load is applied were obtained within the framework of the base model in the form of a linear elastic isotropic medium and the calculated scheme of planar deformation. On this basis, an algorithm for constructing a profile of a roadbed sedimentation made of soil materials has been developed. Originality. Analytical dependences of vertical normal deformations in the roadbed base with a trapezoidal profile on its coordinates are obtained. Practical value. The research materials presented in this work make it possible to construct the design profile of the roadbed of soil materials, taking into account the strong compressibility of the soil. In addition, the results obtained can be used to determine the lower limit of the compressible strata of the bases, to the upper limit of which a distributed load of either a triangular or a trapezoidal form is applied.

Analysis of the reclamation canal condition and cleaning methods

The operating quality of reclamation drainage and irrigation systems depends on the condition of their main elements. The main elements of reclamation systems are canals with various profiles, ranging from rectangular to parabolic. The most widespread in land reclamation are canals with a trapezoidal profile. At the same time, it is possible to note that the natural production characteristics of reclamation systems are quite diverse, this issue is especially relevant for geometric parameters of the canals. In this case, the stable slopes of canals, restoring their profile and cleaning from sediments and silting can only be provided by special complexes of machines. Knowledge of defect types and causes in reclamation canals allows them to be prevented and eliminated in a timely manner. One of the main tasks in this case is to ensure the stability of canal slopes.

Energy and exergy analyses of LiBr/H2O absorption cooling system having recto-trapezoidal profile absorber plate

This paper develops a theoretical model for energy and exergy analyses of a solar-powered Lithium-water absorption refrigeration system using a recto-trapezoidal flat plate solar collector. The effect of collector fluid inlet temperature is to examine the overall performance of the solar collector and the vapour absorption system for a wide range of design variables. The parameters computed are energy and exergy efficiencies of the solar collector plate, coefficient of performance, cooling efficiency, exergy destruction rates, thermal exergy loss rates, irreversibility, and exergetic efficiency of the absorption refrigeration cycle. The simulation results indicate that there exists an optimum inlet temperature of collector fluid for the maximum system coefficient of performance and exergetic efficiency. When the cooling system runs at this temperature, the absorber plate volume attains a minimum value. Furthermore, the performance results are significantly better when a higher absorber plate thickness parameter is for the recto-trapezoidal profile. Finally, a comparative study analyzes the collector performance parameters of an absorber plate having rectangular, triangular, or trapezoidal profile by selecting their respective parameters of geometries. When an additional constraint imposes on the plate volume, it found that using a recto-trapezoidal profile instead of a rectangular profile saves at least 30% or more collector material, and also it may have better performance than a triangular or trapezoidal profile.

Рhysical simulation of erosion of bottom pits

The present paper is devoted to research of the erosion of large-scale sand pits in the water flow. The investigations were performed in the hydrodynamic flume with sandy bottom. To provide suitable conditions for sediment transport in the flume, the analysis of the factors leading to the motion of sediments was carried out in accordance with the Shields diagram. It was shown that the flow regime created in the laboratory channel promotes the development of natural bed forms such as ripples. Estimations of the velocity of movement of the ripples were obtained. The experiments with large sand pits on the flume bottom demonstrated that those disturb the balance of sediments and cause the reformatting of the water flow. To assess the influence of the pit configuration on the erosion process, two-dimensional triangular and trapezoidal pits were considered. It was found that the longitudinal profile of the triangular pit changes due to sediment deposition on its upper slope and erosion of the lower slope. The pit upper slope levels out and shifts forward due to the continuous flow of sediment in this region. The depth of the unevenness also decreases owing to deposition of the sediment directly on its bottom. Due to the blow of water jet to the pit lower slope, the zone of maximum erosion of the bottom surface is observed here. The bottom reformatting leads to the displacement of the pit downstream. Studies of the erosion of the trapezoidal pit have shown that its upper slope is first shifted toward the lower slope until the trapezoidal profile turns into a triangular one. The pit erosion causes also the deformation of natural forms of the channel bed and destabilization of sediment discharge. The analysis of the obtained data demonstrated that the reformation of channel bed is a durable process depending of the ratio of pit scales to the volume of sediment. The present study is useful for development of engineering solutions directed to reduction of risks caused by the interaction of sand quarries with hydraulic structures in rivers.

Performance of a shallow-water model for simulating flow over trapezoidal broad-crested weirs

Shallow-water models are standard for simulating flow in river systems during floods, including in the near-field of sudden changes in the topography, where vertical flow contraction occurs such as in case of channel overbanking, side spillways or levee overtopping. In the case of stagnant inundation and for frontal flow, the flow configurations are close to the flow over a broad-crested weir with the trapezoidal profile in the flow direction (i.e. inclined upstream and downstream slopes). In this study, results of shallow-water numerical modelling were compared with seven sets of previous experimental observations of flow over a frontal broad-crested weir, to assess the effect of vertical contraction and surface roughness on the accuracy of the computational results. Three different upstream slopes of the broad-crested weir (V:H = 1:Z1 = 1:1, 1:2, 1:3) and three roughness scenarios were tested. The results indicate that, for smooth surface, numerical simulations overestimate by about 2 to 5% the weir discharge coefficient. In case of a rough surface, the difference between computations and observations reach up to 10%, for high relative roughness. When taking into account mentioned the differences, the shallow-water model may be applied for a range of engineering purposes.

A Trapezoidal Velocity Profile Generator for Position Control Using a Feedback Strategy

Position control is usually achieved using a position controller and a profile generator. The profile generator produces a desired position trajectory from a position reference and predefined profiles. The position controller forces the actual position to trace the generated position trajectory. A time-based profile generator is the most famous profile generator due to its capability of generating various profiles. However, time base difference in analysis and implementation causes a steady-state error. In order to remove the steady-state error, this paper proposes a novel profile generator for a trapezoidal velocity profile generation. The proposed generator is based on a cascaded P-PI position controller which is designed to trace the position reference. A dynamic range limiter is adopted to provide the acceleration and velocity restrictions which are basic functions for generating the trapezoidal profile. In spite of these restrictions, it cannot make a desired velocity profile only using the limiter because deceleration point is inaccurate. To adjust the deceleration point, a feedback compensator is designed which requires the velocity of the deceleration point. The velocity of the deceleration point is estimated from the initial position error. The compensator moves the deceleration point to the appropriate point which can generate the desired velocity profile. The proposed profile generator can remove the steady-state error, and the position response can be easily adjusted to be either overdamped or underdamped by selecting the two gains appropriately. Several experimental results are presented to verify the usefulness of the proposed generator.

TO THE QUESTION OF THE DETERMINATION OF GEOMETRIC CHARACTERISTICS OF THE SECTION OF CORRUGATED BEAMS WITH TRAPEZOIDAL WEBS BASED ON THE SIMULATION RESULTS

An algorithm for calculating the geometric characteristics of steel I-beams with plate corrugated webs of arbitrary type is proposed. The algorithm is implemented using the I-beam with plate trapezoid webs as an example. The determination of reduced area and moments of inertia in the axes of the cross section of the trapezoidal profile based on the finite element modeling of the beam with shell elements in calculations for bending and axial compression in the “ANSYS 14.5” software package is described. The verification procedure has been performed for a shell finite element model using the example of an I-beam with a standard flat web. A table has been compiled of geometric characteristics of rod corrugated elements of a trapezoidal profile in order to realize their finite element calculation using a rod diagram. An example of the calculation of a flat frame with a horizontal corrugated element, made in software package “LIRA-SAPR” using a flat rod diagram is given.