An Improved Nonlinear Creep Model for Rock Applied to Tunnel Displacement Prediction

Traditional creep models cannot describe the nonlinear creep characteristics of rock; thus, considerable efforts have been made to establish better rock creep models. However, many of the previously presented improved models are too complicated, leading to difficulties in mathematical derivation and engineering application. To address this problem, this study proposes a simple model that can comprehensively describe rock creep characteristics and that can be effectively applied in practical engineering. Based on the variable-order fractional derivatives and continuum damage mechanics, an improved Burgers creep model is established. The use of this proposed model can be divided into two stages based on whether the accumulated creep strain of the rock reaches the threshold of starting accelerated creep. Then, both the one-dimensional and three-dimensional constitutive equations of the improved model are provided. In addition, the compression creep test results of six groups of rock samples are used to verify the effectiveness and reliability of the improved Burgers model proposed in this study. Furthermore, an analytical solution for tunnel displacement is derived on the basis of the improved model. This analytical solution is applied to the time-dependent displacement prediction of an auxiliary tunnel in Jinping hydropower station, and a good agreement between the theoretical results and monitoring data is achieved. The outcome of this study can provide useful guidance for related engineering designs.