New description of the mechanical creep response of rocks by fractional derivative theory

Abstract

Accurate estimation and modeling of rock behavior during creep is an essential step to ensure reliability safety in the engineering of underground structures. In this work we proposed a new way of adjusting the fractional order to obtain a new variable fractional order rheological model to describe the evolution of mechanical properties and to model the full- creep response. It is proved that the function law of our variable order fractional model is defined only by four parameters a,b,m,n. An analysis on the different parameters of the fractional model shows that the mechanical behavior of the rock softens faster when the temperature and the applied stress level are high and hardens in the opposite case. Moreover, through its derived version, the physical meaning of our fractional model is explored in more detail, as it allows to highlight the hardening/softening duality of the rock behavior. This fractional model allows us to model the full creep behavior of the rock with a reduced number of parameters, a simple form, a sufficiently guaranteed accuracy and a unified law. We believe that the results of this work will be able to help in the decision making during the realization of underground structures.