Critical transition of post-peak failure of sandstone under tri-axial cyclic loading and unloading stress

A design of cyclic loading and unloading stress path before or after strength in triaxial compression is often adopted to describe the accumulated damage in rock. Considering the sudden failure of sandstone，a design with the same stress increment as the gradient to load axial stress was adopted in pre-peak，another stress drop-based unloading path was suggested in post-peak stage. The experimental results show that there are obvious stress drop，energy density drop and accumulated damage surges in the cyclic process after the peak strength，which are all strongly correlated to the generation of macro fracture surfaces separating the intact sandstone into discrete parts. Then，according to the correlation of volumetric strain and axial strain，an accurate division of the post-peak stress drop into two parts is effectively made by defining the ductile soften behavior and the macro surfaces-fracturing behavior. Three correlation modes are summarized to characterize the variation of volumetric strain with deviator stress during the whole loading-unloading stage，which are compression at the full process，compression after expansion, and expansion at full process. A new definition of post-peak fracture strength is made as stress boundary of ductile soften behavior and macro fracturing behavior，which is determined based on recognizing the critical transition of post-peak volumetric-axial strain relationship or the maximum drop of energy density. In addition， the non-linear evolution of elastic energy density is effectively described in the pre- and post-peak stages of sand rock under tri-axial cyclic loading and unloading stress. A new damage variable considering the accumulation of energy lost in each cyclic is defined. The results show that there is a liner relationship between the new damage variable and fracture volumetric strain in the ductile softening stage after post-peak and a clear surge of accumulated damage occurs in the macro surface-fracturing stage，as well as the corresponding damage increment linearly decreases with the confining pressure. The research results indicate that the design of tri-axial cyclic loading and unloading tests provides a feasible way to gradually reveal the critical mechanics of sand rock.