Linear Representation of Steady-State Line for Sand

TLDR

The steady‑state line links effective confining pressure and void ratio in soils, is usually plotted as a straight line in the e–log p′ plane, but cohesionless soils generally exhibit curvature in that representation, so straight‑line treatment is only a simplification. The study proposes plotting cohesionless soil steady‑state lines in an e–(p′/pa)^α plane, using atmospheric pressure as a reference and a tunable exponent α ≈ 0.7. The authors introduce the e–(p′/pa)^α coordinate system and illustrate its straightening effect on cohesionless soil lines using illustrative examples. The analysis shows that sand steady‑state lines become nearly straight in the e–(p′/pa)^α plane, and this straightness is largely independent of the exponent α.

Abstract

The steady-state line relates the effective confining pressure (p′) with the void ratio (e) of a soil during steady-state deformation. The line is commonly plotted in an e–log p′ plane and is treated as a straight line in that plane. However, it has long been observed that the steady-state lines for cohesionless soils are in general curved in the e–log p′ plane, and treating them as straight lines is done only for simplicity. As an alternative, this note suggests the steady-state lines of cohesionless soils be plotted in the e–(p′/pa)α plane, where pa is the atmospheric pressure serving as a reference pressure for normalization, and α is a number around 0.7 that can be fine tuned for optimization. It is shown in the note that the steady-state lines of sand are nearly straight in the e–(p′/pa)α plane, and the straightness is insensitive to the parameter α. This note presents the consideration behind the choice of the plane and demonstrates the straightening effects by examples.