Wellbore stability analysis using strain hardening and/or softening plasticity models

In this paper, the general shear strain hardening and/or softening Drucker-Prager models based on the common triaxial compression test results have been introduced to model the mechanical behaviour of rock formations. These elastoplastic models are then adopted to develop rigorous analytical solutions for the drained wellbore drilling problem subjected to in-plane isotropic stress field, and to further predict the borehole collapse failure. The illustration numerical examples show the distributions of stress components and the progressive development of the plastic deviatoric strain, in addition to the effective stress trajectory for a rock point at the borehole surface due to the wellbore drilling. The advantage of the desired wellbore drilling curve presented lies in the fact that it can track the deformation responses of the borehole surface from elastic to elastoplastic states and down to the peak and ultimate/residual conditions, thus offering much more flexibility and more appropriate mud pressure design over the conventional elastic-brittle models. The critical (minimum) mud pressures, predicted by the current elastoplastic analysis based on different wellbore instability criteria, are compared with the value corresponding to the elastic theory. The solution procedure proposed can also be utilized for the tunnelling analysis and extended to the design of lining required to stabilize a tunnel.