Failure, instability, and the second work increment in loose silty sand

Triaxial tests have been performed to demonstrate the conditions for stability and instability in loose silty sand. Drucker (1951) and Hill (1958) stability conditions in terms of the sign of the second work increment were employed in the design of the stress paths used in the triaxial compression and extension tests performed with quasi-constant shear stress while the mean normal stress was reduced until failure occurred. It is shown that the sand is completely stable under drained conditions for any stress path and irrespective of the sign of the second work increment. This is demonstrated by completely stopping the change in stresses and observing the stable behavior in the range of stresses where the sand contracts and where it dilates. Once the effective stress failure surface is passed, the sand becomes unstable, and the sign of the second work increment is always negative. Run-away instability can occur inside the failure surface for loose silty sand under undrained conditions for which the sand tends to contract, pore pressures continue to develop, and the second work increment is negative. Liquefaction may follow if the loose silty sand is sufficiently loose.