A graphical method for producing yield surfaces for soils

Abstract

A procedure is described by which three-dimensional yield criteria and flow rules can be derived graphically by drawing envelopes. Using computer graphics, this provides the modeller with a simple, clear, precise and flexible method with which to generate data that can be compared with results obtained analytically or experimentally. As illustrative examples, yield surfaces are constructed in the constant-pressure plane in principal stress space using the Drucker–Prager and Frossard's dissipation functions, and two modified forms of Houlsby's dissipation function. For constant-volume flow these produce the Drucker–Prager, Mohr–Coulomb and Matsuoka–Nakai yield surfaces. Each is paired with both an isotropic and an anisotropic dilatancy rule. The direction of plastic flow at yield, consistent with the choice of dissipation function and dilatancy rule, can be determined from these constructions. One of the yield surfaces produced is compared with the results from true triaxial tests where the rate of dilatancy has been determined. An example of Rowe's stress–dilatancy plots is also produced.