Capturing the Turning Hook of Stress-Dilatancy Curve of Crushable Calcareous Sand

For crushable calcareous sand, the stress-dilatancy curve has a significant turning hook around the peak stress ratio, the hook contains the main features of the loading process, including the phase transformation point and the peak stress ratio point. However, more than half of this turning hook, i.e., the line after the peak stress ratio point, is usually ignored by known stress-dilatancy models. It is difficult to directly establish the stress-dilatancy model with such turning hook characteristics, since such turning hook demonstrates that the dilatancy is not a single-valued function of the stress ratio. Based on the first law of thermodynamic, we related dilatancy to breakage energy. Then, we mapped breakage energy from the stress-energy plane to the strain-energy plane to avoid the non-single-valued function problem. Then, the stress-dilatancy model was conveniently established. Compared with the other four existing stress-dilatancy models, the benefit of our modeling process is that it can easily capture the turning hook of the stress-dilatancy curve. Our model is also verified by simulating colloidal-silica-stabilized and MICP-stabilized calcareous sands, as well as three types of calcareous sands, respectively.