An Elastic-Perfect Plastic Constitutive Model Based on Mogi-Coulomb Yield Criterion

Summary : Wellbore instability can increase drilling time and sometimes leads to wells being side-tracked. Appropriate estimation of the weight of drilling mud can be mentioned as the key designing factor to ensure the mechanical stability of wellbores. Considering the elastoplastic behavior of the medium, yield criterion plays a key role in this analysis and estimation. Applying the Mohr-Coulomb criterion leads to underestimation of rock strength due to ignoring the effect of the intermediate principal stress. On the other hand, the Mogi-Coulomb yield criterion is able to consider the effect of the intermediate principal stress, while preserves the simplicity of the Mohr-Coulomb model. In this study, the elastic - perfectly plastic constitutive model is developed based on the Mogi-Coulomb criterion. Model predictions for some triaxial tests are compared with experimental data, and reasonable agreement is achieved. The proposed model is also applied for analyzing a wellbore stability problem and results are compared with two popular models, Mohr-Coulomb and Drucker-Prager, to investigate the effect of the intermediate principal stress.
The simplicity of the Mohr-Coulomb criterion makes it as one the most popular models in geomechanical analysis. However, ignoring the effect of the intermediate principal stress can be mentioned as the main shortcoming of this model. On the other hand, the effect of the intermediate principal stress has been widely studied in experimental and analytical investigations. The Mogi-Coulomb yield criterion, not only overcomes this shortcoming, but also conserves the simplicity of the Mohr-Coulomb model. Alajmi and Zimmerman (2005) analytically showed the ability of Mogi-Coulomb criterion in considering the effect of the intermediate principal stress. This investigation showed that this criterion can introduce a more realistic estimation of rocks strength.
Methodology and Approaches : An elastic-perfectly plastic constitutive model is developed based on the Mogi-Coulomb yield criterion. The proposed model is implemented to “FLAC”. Verification is done by simulating some triaxial test data. Numerical example is also conducted to investigate the efficiency of the model.
Results and Results of the numerical study shows that the Mohr-Coulomb criterion results in underestimation of rocks strength by ignoring the effect of the intermediate principal stress. On the other hand, the Drucker-Prager criterion leads to overestimation of the strength by considering identical effects for both intermediate and minimum principal stress. While the Mogi-Coulomb criterion introduces a more realistic estimation of the strength by moderating the effect of the intermediate principal stress.