A revisit to the Lekhnitskii-Amadei solution for borehole stress calculation in tilted transversely isotropic media

Abstract

A wellbore drilled in pre-stressed formations concentrates the far-field stresses. These concentrations often lead to borehole instability producing breakouts, drilling-induced fractures, or complete failure. In isotropic rock masses this problem has been extensively studied. However, fewer studies attempt to understand borehole failure in more realistic rocks characterized by both elastic and strength anisotropy. A program to calculate the failure pattern in elastic and strength anisotropic rocks is developed. The program combines a recent algorithm for calculating stress concentrations around a borehole within an anisotropic rock mass with anisotropic rock strength as applied through differing failure criteria. Shear failure in the rock matrix and the weak plane are examined based on Jaeger’s single plane of weakness theory. Results from test models clearly indicate that failure in the weak plane complicates the failure pattern around the wellbore, resulting in that the breakout orientation cannot correctly represent the minimum horizontal stress orientation as commonly suggested for a vertical wellbore aligned with the principal stresses. The complexity of failure patterns due to formation anisotropy suggests that additional care must be taken when borehole image logs are interpreted for stress direction indication and stress magnitude constraint.