Models for representing limit states in geomechanics

Abstract

Abstract A new paradigm of scientific knowledge enabling to display the ultimate stress-strain states in geomechanics is presented in the article. In this case, distortion serves as a natural science theory. The main results concerning the development of distortion theory in natural systems are presented. Geometrical models for representing limiting states and determining distortion invariance during the materials deformation are shown. The format for forming a “strength certificate” of organic mineral soils for solving power and energy problems in the design of executive working bodies of mining machines is given. The technique for representing deformation processes in a reduced square system is described. The proposed methodology and criteria for the stress-strain state are a further development of the E.I. Shemyakin’s synthetic theory of strength. Areas of mutual influence of the main parameters of the soils strength certificate are as follows: specific adhesion and angle of internal friction and their compliance with the experiments of Buisman. The universality of the models under consideration is shown. This enables to give a mathematical description of the limiting parameters and criteria of stress-strain states in an invariant form and a clear geometric mapping.