A constitutive relation for granular (frictional) soils that links the mobilized shear stress (or shear stress ratio) to the rate of volume change (dilatancy) during shear; it states that the shear resistance mobilized at a given state depends both on interparticle friction and on the instantaneous dilatant or contractive tendency of the fabric. Typically used within plasticity and critical‑state frameworks to explain peak strength and strain‑softening in dense granular materials. Assumptions: particulate granular material where volume change is mechanically coupled to shear (not a viscous continuum), sufficiently small strain increments to define incremental relations.

Principle

Mobilized shear strength is not solely a function of interparticle friction: dilatancy (the ratio between volumetric strain increment and shear strain increment) modifies the stress ratio required for continued shearing; positive dilatancy raises instantaneous shear resistance above the critical‑state value, while contraction reduces it.

Demonstration

Illustrative scenario: In a drained triaxial test on a dense sand, the specimen initially densifies under confinement, then during shearing shows positive volumetric expansion (dilatancy) concurrent with a peak in shear stress; applying Rowe’s relation, the observed peak stress exceeds the critical‑state shear stress because dilation increases the mobilized stress ratio.

Misapplication

Applying Rowe’s stress‑dilatancy relation to cohesive clays where interparticle bonding, rate‑dependent behaviour or viscous pore‑fluid effects control volume change misreads the theory’s domain; the semantic error is extending a granular, dilation‑controlled constitutive link to materials where dilation is not the governing mechanism.

Consequence

Rowe’s relation explains why dense granular soils can develop peak strengths above their critical‑state friction and why post‑peak softening occurs as dilatancy decreases toward zero; this causal insight guides interpretation of laboratory tests and selection of constitutive models for numerical analysis.

Reversal

At the critical state (steady large strains) dilatancy tends to zero and the stress ratio reduces to a unique critical value independent of initial density; conversely, at very small strains or when particle crushing, cementation, viscous effects or significant fabric anisotropy dominate, Rowe’s incremental relation may not hold.

Boundary

Clearly within: drained shear of dense, cohesionless or weakly cohesive granular soils where volume change during shear is measurable and controls strength. Boundary case: slightly plastic silty sands where both dilation and plastic compressibility matter—Rowe gives partial guidance. Clearly outside: viscous clays, cemented soils, or suspensions where volume change is controlled by pore‑fluid migration or chemical bonding rather than granular rearrangement.

Semantic Tension

The relation highlights tension between shear strength and volume change: designs that increase strength via densification also increase dilation and potentially alter stress paths; engineers must balance exploiting peak strength against post‑peak instability and serviceability.

Synthesis

Rowe’s stress‑dilatancy relation reframes shear strength as a coupled outcome of friction and kinematics: strength emerges from both interparticle resistance and the instantaneous tendency of the fabric to dilate or contract, explaining peak behaviour and guiding constitutive model choice in granular soil analysis.