PLASTIC FLOWS OF GRANULAR-MATERIALS OF SHEAR INDEX-N .1. YIELD FUNCTIONS

GRANULAR MATERIALS fail due to frictional slip between particles when the shear component of stress tau attains a critical value which depends on the normal component of stress sigma. A number of authors have investigated the so-called Warren Spring equation (tau/c)n = 1 - (sigma/t) where c, t and n are positive constants which are referred to as the cohesion, tensile strength and shear index respectively and known numerical values of the shear index indicate that for certain materials n lies between the values 1 and 2. Here, the yield function in terms of principal stresses corresponding to the Warren Spring equation is derived and bounding external and internal yield cones are deduced. Other than the Coulomb-Mohr yield function arising from n = 1, the yield function corresponding to the shear index n = 2 turns out to be the simplest for n lying in the range of physical interest and in Part II of the paper simple plane and axially symmetric flows are obtained for this special case. This means that the well known Coulomb-Mohr yield function (n = 1) and that for n = 2 provide idealized limiting behaviour for many real granular materials. Finally, some mathematical details which relate to the general yield function of the Warren Spring equation are noted in the Appendix.