Dilatancy Equation and Yield Function for Granular Materials Based on Energy Accumulation

Abstract

Abstract The dilatancy equation and yield function are the two important components of the elastoplastic constitutive model for soils. Because the incremental energy equations of the Cam-Clay and Rowe models do not consider the particle breakage energy, the predicted dilatancy for the granular materials is not convincing. Accordingly, the total input energy during shearing, Es, is taken as the equivalent of the energy equation, and Es is found to be directly proportional to the shearing strain, εs. The slope, K, of the Es∼εs line is theoretically induced and experimentally demonstrated to be equal to the critical shear stress, qc. Thus, a new dilatancy equation and yield function are derived and preliminarily verified using different kinds of granular materials, e.g., calcareous sand, gravel, and rockfill. The shape of the proposed yield surface can be adjusted automatically from bullet-shaped to drop-shaped with an increasing Mc, which is better for expressing the yielding behavior of granular materials. Additionally, another significant advantage of the proposed dilatancy equation and yield function is that no additional fitting or nonphysical parameters except Mc (critical stress ratio) is included, whereas the predictions for the granular materials are still satisfactory.