Non-stationary and nonlinear visco-elastic shear creep model for shale

Based on visco-elastic shear creep experimental results of shale with four various shear stress levels, a new non-stationary and nonlinear visco-elastic shear creep model is put forward. First, stationary (linear) visco-elastic shear creep model is used to identify the creep parameters by the discrimination criterion of the square of correlation coefficient (R2) and sum of least error square (Q). In stationary (linear) visco-elastic shear creep model, the visco-elastic shear modulus G2 of shale decreases but the visco-coefficient η1 increases with increasing time, which has distinct time scale effect. Then by constructing the relation between stationary creep parameters G2, η1 and time, a non-stationary visco-elastic shear creep model is put forward to describe visco-elastic shear creep deformation behavior of shale. The non-stationary shear creep model has a better agreement with the experimental data than does the stationary shear creep model, but fails in predicting long-term deformation characteristics. Therefore by introducing a time index, a nonlinear visco-elastic shear creep model is constructed, which can predict better for long-term deformation behavior of shale. In the end, based on the relation between nonlinear creep parameters and shear stress, the shear creep deformation with all kinds of shear stress levels is predicted approximately in the range of 0.45 MPa≤τ≤1.45 MPa.

► Stationary shear creep parameters of shale have a distinct time scale effect. ► A non-stationary visco-elastic shear creep model for shale is put forward. ► A nonlinear visco-elastic shear creep model for shale is constructed. ► Nonlinear shear creep model can predict better visco-elastic deformation behavior.