Developing the method of constructing mathematical models of soil condition under the action of a wedge

Abstract

Studies of the technique of construction of mathematical models on the condition of soil under the action of wedge are presented. Based on hypothesis about separation of the layer of soil by a wedge through its bending, we constructed a mathematical model of determining normal and tangential stresses in soil under the action of wedge. Using mathematical dependencies, we obtained patterns of the distribution of maximum tensile and compression stresses, dependent on the depth of motion of wedge at different angles of crushing the soil. It was found that crushing of soil, which is determined by the size of lumps and chunks, formed under the action of the soil­cultivating working bodies, has a direct dependence on the covered path to reaching limiting stresses in soil. The increase in the distance of the passage of working bodies until the start of the process of cleaving the soil layer contributes to formation of lumps and chunks of larger size. The studies revealed that the wedge, depending on the angle of crushing, strength indices of soil and depth of cultivation, may create in it stresses, necessary for the cleaving, at the initial moment of motion after covering the distance equal to 10 mm and longer. Stresses in soil grow with an increase in the angle of crushing and depth of cultivation. To substantiate parameters of a chisel blade, in particular geometric profile of the rack, we used the method of the calculus of variations. Substantiation of the point of a chisel blade was carried out in two stages. At the first stage we substantiated the profile of chisel of the point taking into account the provision of necessary deepening into soil at minimum energy consumption, at the second stage – the profile of the point with minimum energy consumption by the results of studies, connected with substantiation of the chisel. Analysis of traction resistance of chisel working bodies established that the improvement in the profile of the point ensures reduction in traction resistance of a chisel working body. The data analysis of experiment demonstrated that the coefficient of structuredness of soil after its treatment by standard and experimental points has practically identical value; the improvement of profiles of the points of chisel organs does not lead to worsening the quality of soil treatment. The data analysis on determining traction resistance of chisel working bodies showed that, compared to the standard one, the experimental working body has lower traction resistance. Thus, experimental studies confirm reliability of results of theoretical studies on the substantiation of the profile of the chisel of a chisel working body from the point of view of reduction in their energy consumption while providing for the quality of crushing the soil.