Hyperbolic Stress-Strain Response: Cohesive Soils

TLDR

The hyperbolic stress‑strain relation reconciles stability analysis with load‑deformation approaches, embedding the soil’s ultimate shear strength as the asymptotic limit of stress at large strain. The relation incorporates preconsolidation pressure, rebound stress, lateral and vertical stresses, strain, strain rate, and overconsolidation ratio, and its consolidated‑undrained triaxial formulations are benchmarked against published drained and undrained data. These formulations were quantitatively validated on a remolded cohesive soil in consolidated‑undrained triaxial compression tests.

Abstract

The divergent concepts of a stability analysis, as compared with a load-deformation approach to soil mechanics, are shown to be compatible within the framework of a hyperbolic stress-strain relation. The two-constant hyperbolic form of the stress-strain response is such that the ultimate shear strength of the soil is contained within the general formulation and appears in the mathematical limit of the stress as the strain becomes excessive. This is quantiatively demonstrated for a remolded cohesive soil tested in consolidated-undrained triaxial compression. The variables contained in the hyperbolic stress-strain relation include the preconsolidation pressure, rebound stress, lateral pressure during the test, vertical normal stress, strain, and rate of strain. History effects are included in terms of the overconsolidation ratio. The general formulations obtained for the consolidated-undrained triaxial tests are compared with the results reported in the literature by other investigators for both drained and undrained consolidated triaxial tests under various conditions.