TWO APPROACHES FOR DETERMINING AREAS OF PLASTIC DEFORMATION IN A HOMOGENEOUS BASE FOUNDATION

Abstract

The paper presents comparison of results of calculations of position, sizes and shapes of plastic deformation areas carried out on the basis of use of Coulomb plasticity condition and solution of elastic-plastic problem and mixed problem of elasticity theory and ground plasticity theory which resulted, among other things, in graphs of dependence of depth of plastic zones development on value of intensity of external influence. Calculations have been executed at three values of coefficient of side pressure of ground about = 0.37; 0.54; 0.72 for uniform strip load (no die), and for absolutely rigid die under condition of full sticking and under condition of no friction on ground-stamp contact. As a result, it was found that the plastic regions corresponding to the "Coulomb" solution differ essentially from similar regions based on elastic-plastic (mixed) solutions. Their sizes, with the same intensity of loading, are larger, their rate of development into the deepening of the base is higher than that of the alternative ones, and when the load reaches the maximum permissible value, they merge under the punch and form a single sickle-shaped area. In the case of "Coulomb" plastic areas, their shape and rate of development into the foundation in the initial stages of loading are rather strongly dependent on the value of soil side pressure coefficient. In the case of "mixed" solution, the "velocity" of this process is practically independent of the value of coefficient o. If we use the condition of closing of plastic regions in the foundation under load as the criterion for determination of the maximum permissible value of intensity of external action, then in "Coulomb" regions this value will be substantially lower than in alternative ones for all considered values of the coefficient of lateral pressure of soil.