Critical State Line

The critical state line represents the ultimate shear strength of soil in both stress space (τ vs σ) and void ratio space (e vs ln σ). On it, τ = Mσ and e = Γ − λ ln σ. The normal compression line, e = N − λ ln σ, has the same slope λ and is drawn at τ = 0.

What you are seeing

• 3D view. The critical state line (solid blue) in σ–τ–e space, and the normal compression line (dashed black) in the τ = 0 plane. The translucent surface joins the critical state line to the τ = 0 plane at the same void ratio. Drag to rotate.
• τ–σ view. The critical state line in stress space: a straight line through the origin of slope M.
• e–σ view. The critical state line (solid blue) and the normal compression line (dashed black) in void ratio space. On a logarithmic σ axis both are straight and parallel.