New unloading criterion for enhancing multi-stage triaxial tests based on radial strain gradient

This paper presents a new criterion for determining the unloading points quantitatively and consistently in a multi-stage triaxial test. The radial strain gradient (RSG) is first introduced as an arc tangent function of the rate of change of radial strain to time. RSG is observed to correlate closely with the stress state of a compressed sample, and reaches a horizontal asymptote as approaching failure. For a given rock type, RSG value at peak stress is almost the same, irrespective of the porosity and permeability. These findings lead to the development of RSG criterion: Unloading points can be precisely determined at the time when RSG reaches a pre-determined value that is a little smaller than or equal to the RSG at peak stress. The RSG criterion is validated against other criteria and the single-stage triaxial test on various types of rocks. Failure envelopes from the RSG criterion match well with those from single-stage tests. A practical procedure is recommended to use the RSG criterion: an unconfined compression or single-stage test is first conducted to determine the RSG at peak stress for one sample, the unloading point is then selected to be a value close to the RSG at peak stress, and the multi-stage test is finally performed on another sample using the pre-selected RSG unloading criterion. Generally, the RSG criterion is applicable for any type of rocks, especially brittle rocks, where other criteria are not suitable. Further, it can be practically implemented on the most available rock mechanical testing instruments.