# Wellbore stability analysis based on a new true-triaxial failure criterion

Sammanfattning: A main aspect of wellbore stability analysis is the selection of an appropriate rock failure criterion. The most commonly used criterion for brittle failure of rocks is the Mohr-Coulomb criterion. This criterion involves only the maximum and minimum principal stresses, s1 and s3, and therefore assumes that the intermediate stress s2 has no influence on rock strength. When the Mohr-Coulomb criterion had been developed, it was justified by experimental evidence from conventional triaxial tests (s1>s2=s3). Based on triaxial failure mechanics, the Mohr-Coulomb criterion has been extensively used to represent rock failure under the polyaxial stress state (s1>s2>s3).In contrast to the predictions of Mohr-Coulomb criterion, much evidence has been accumulating to suggest that s2 does indeed have a strengthening effect. In this research, I have shown that Mohr-Coulomb failure criterion only represents the triaxial stress state (s2=s3 or s2=s1), which is a special case that will only occasionally be encountered in situ. Accordingly, I then developed a new true-triaxial failure criterion called the Mogi-Coulomb criterion. This failure criterion is a linear failure envelope in the Mogi domain (toct-sm,2 space) which can be directly related to the Coulomb strength parameters, cohesion and friction angle. This linear failure criterion has been justified by experimental evidence from triaxial tests as well as polyaxial tests. It is a natural extension of the classical Coulomb criterion into three dimensions.As the Mohr-Coulomb criterion only represents rock failure under triaxial stress states, it is expected to be too conservative in predicting wellbore instability. To overcome this problem, I have developed a new 3D analytical model to estimate the mud pressure required to avoid shear failure at the wall of vertical, horizontal and deviated boreholes. This has been achieved by using linear elasticity theory to calculate the stresses, and the fully-polyaxial Mogi-Coulomb criterion to predict failure. The solution is achieved in closed-form for vertical wellbores, for all stress regimes. For deviated or horizontal wellbores, Mathcad programs have been written to evaluate the solution. These solutions have been applied to several field cases available in the literature, and the new model in each case seems to be consistent with the field experience.

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