The Rule of Equivalent States in Limit-State Analysis of Soils

Abstract

Soil is typically regarded as a frictional or cohesive-frictional material in limit-state considerations. Often the solution to a limit-state problem (for instance, the bearing capacity of footings) for a purely frictional soil is easier to obtain than the solution for a cohesive-frictional material. A theorem was presented that makes it possible to obtain a solution for cohesive-frictional soil through a transformation of a known solution for purely frictional soil. However, application of the transformation rule based on this theorem is shown to have limitations. This rule appears to be applicable for boundary-value problems where boundary stresses have only normal components and principal stress trajectories are not altered by the transformation. With modern computational tools the correspondence rule is bypassed. However, its applicability is a consequential issue in soil mechanics education, even if of a somewhat historical nature. An example of limit loads on a strip footing is presented, a solution to inclination coefficients is produced, and the consequences of the rule of corresponding states are discussed. Finally, the application of the rule of correspondence in the kinematic approach of limit analysis is investigated. A convenient method is developed for calculations of the energy dissipation rate, which does not require tedious calculations of dissipation on all velocity discontinuity surfaces or in continually deforming regions.